diff --git a/api/GL/glext.h b/api/GL/glext.h
index 39267fe..151dcf2 100644
--- a/api/GL/glext.h
+++ b/api/GL/glext.h
@@ -51,7 +51,7 @@
 #define GLAPI extern
 #endif
 
-#define GL_GLEXT_VERSION 20181130
+#define GL_GLEXT_VERSION 20190204
 
 #include <KHR/khrplatform.h>
 
diff --git a/api/GL/glxext.h b/api/GL/glxext.h
index 38f6c67..bb13702 100755
--- a/api/GL/glxext.h
+++ b/api/GL/glxext.h
@@ -34,7 +34,7 @@
 **   https://github.com/KhronosGroup/OpenGL-Registry
 */
 
-#define GLX_GLXEXT_VERSION 20181130
+#define GLX_GLXEXT_VERSION 20190204
 
 /* Generated C header for:
  * API: glx
diff --git a/api/GL/wgl.h b/api/GL/wgl.h
index 3391185..afeee84 100644
--- a/api/GL/wgl.h
+++ b/api/GL/wgl.h
@@ -39,7 +39,7 @@
 #include <windows.h>
 #endif
 
-/* Generated on date 20181130 */
+/* Generated on date 20190204 */
 
 /* Generated C header for:
  * API: wgl
@@ -409,7 +409,7 @@
 #define WGL_GPU_NUM_RB_AMD                0x21A7
 #define WGL_GPU_NUM_SPI_AMD               0x21A8
 typedef UINT (WINAPI * PFNWGLGETGPUIDSAMDPROC) (UINT maxCount, UINT *ids);
-typedef INT (WINAPI * PFNWGLGETGPUINFOAMDPROC) (UINT id, int property, GLenum dataType, UINT size, void *data);
+typedef INT (WINAPI * PFNWGLGETGPUINFOAMDPROC) (UINT id, INT property, GLenum dataType, UINT size, void *data);
 typedef UINT (WINAPI * PFNWGLGETCONTEXTGPUIDAMDPROC) (HGLRC hglrc);
 typedef HGLRC (WINAPI * PFNWGLCREATEASSOCIATEDCONTEXTAMDPROC) (UINT id);
 typedef HGLRC (WINAPI * PFNWGLCREATEASSOCIATEDCONTEXTATTRIBSAMDPROC) (UINT id, HGLRC hShareContext, const int *attribList);
@@ -419,7 +419,7 @@
 typedef VOID (WINAPI * PFNWGLBLITCONTEXTFRAMEBUFFERAMDPROC) (HGLRC dstCtx, GLint srcX0, GLint srcY0, GLint srcX1, GLint srcY1, GLint dstX0, GLint dstY0, GLint dstX1, GLint dstY1, GLbitfield mask, GLenum filter);
 #ifdef WGL_WGLEXT_PROTOTYPES
 UINT WINAPI wglGetGPUIDsAMD (UINT maxCount, UINT *ids);
-INT WINAPI wglGetGPUInfoAMD (UINT id, int property, GLenum dataType, UINT size, void *data);
+INT WINAPI wglGetGPUInfoAMD (UINT id, INT property, GLenum dataType, UINT size, void *data);
 UINT WINAPI wglGetContextGPUIDAMD (HGLRC hglrc);
 HGLRC WINAPI wglCreateAssociatedContextAMD (UINT id);
 HGLRC WINAPI wglCreateAssociatedContextAttribsAMD (UINT id, HGLRC hShareContext, const int *attribList);
@@ -816,12 +816,12 @@
 #define WGL_NV_present_video 1
 DECLARE_HANDLE(HVIDEOOUTPUTDEVICENV);
 #define WGL_NUM_VIDEO_SLOTS_NV            0x20F0
-typedef int (WINAPI * PFNWGLENUMERATEVIDEODEVICESNVPROC) (HDC hDC, HVIDEOOUTPUTDEVICENV *phDeviceList);
-typedef BOOL (WINAPI * PFNWGLBINDVIDEODEVICENVPROC) (HDC hDC, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
+typedef int (WINAPI * PFNWGLENUMERATEVIDEODEVICESNVPROC) (HDC hDc, HVIDEOOUTPUTDEVICENV *phDeviceList);
+typedef BOOL (WINAPI * PFNWGLBINDVIDEODEVICENVPROC) (HDC hDc, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
 typedef BOOL (WINAPI * PFNWGLQUERYCURRENTCONTEXTNVPROC) (int iAttribute, int *piValue);
 #ifdef WGL_WGLEXT_PROTOTYPES
-int WINAPI wglEnumerateVideoDevicesNV (HDC hDC, HVIDEOOUTPUTDEVICENV *phDeviceList);
-BOOL WINAPI wglBindVideoDeviceNV (HDC hDC, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
+int WINAPI wglEnumerateVideoDevicesNV (HDC hDc, HVIDEOOUTPUTDEVICENV *phDeviceList);
+BOOL WINAPI wglBindVideoDeviceNV (HDC hDc, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
 BOOL WINAPI wglQueryCurrentContextNV (int iAttribute, int *piValue);
 #endif
 #endif /* WGL_NV_present_video */
@@ -926,14 +926,14 @@
 typedef BOOL (WINAPI * PFNWGLGETSYNCVALUESOMLPROC) (HDC hdc, INT64 *ust, INT64 *msc, INT64 *sbc);
 typedef BOOL (WINAPI * PFNWGLGETMSCRATEOMLPROC) (HDC hdc, INT32 *numerator, INT32 *denominator);
 typedef INT64 (WINAPI * PFNWGLSWAPBUFFERSMSCOMLPROC) (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder);
-typedef INT64 (WINAPI * PFNWGLSWAPLAYERBUFFERSMSCOMLPROC) (HDC hdc, int fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
+typedef INT64 (WINAPI * PFNWGLSWAPLAYERBUFFERSMSCOMLPROC) (HDC hdc, INT fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
 typedef BOOL (WINAPI * PFNWGLWAITFORMSCOMLPROC) (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder, INT64 *ust, INT64 *msc, INT64 *sbc);
 typedef BOOL (WINAPI * PFNWGLWAITFORSBCOMLPROC) (HDC hdc, INT64 target_sbc, INT64 *ust, INT64 *msc, INT64 *sbc);
 #ifdef WGL_WGLEXT_PROTOTYPES
 BOOL WINAPI wglGetSyncValuesOML (HDC hdc, INT64 *ust, INT64 *msc, INT64 *sbc);
 BOOL WINAPI wglGetMscRateOML (HDC hdc, INT32 *numerator, INT32 *denominator);
 INT64 WINAPI wglSwapBuffersMscOML (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder);
-INT64 WINAPI wglSwapLayerBuffersMscOML (HDC hdc, int fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
+INT64 WINAPI wglSwapLayerBuffersMscOML (HDC hdc, INT fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
 BOOL WINAPI wglWaitForMscOML (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder, INT64 *ust, INT64 *msc, INT64 *sbc);
 BOOL WINAPI wglWaitForSbcOML (HDC hdc, INT64 target_sbc, INT64 *ust, INT64 *msc, INT64 *sbc);
 #endif
diff --git a/api/GL/wglext.h b/api/GL/wglext.h
index a9a5a5b..e36c02a 100755
--- a/api/GL/wglext.h
+++ b/api/GL/wglext.h
@@ -39,7 +39,7 @@
 #include <windows.h>
 #endif
 
-#define WGL_WGLEXT_VERSION 20181130
+#define WGL_WGLEXT_VERSION 20190204
 
 /* Generated C header for:
  * API: wgl
@@ -318,7 +318,7 @@
 #define WGL_GPU_NUM_RB_AMD                0x21A7
 #define WGL_GPU_NUM_SPI_AMD               0x21A8
 typedef UINT (WINAPI * PFNWGLGETGPUIDSAMDPROC) (UINT maxCount, UINT *ids);
-typedef INT (WINAPI * PFNWGLGETGPUINFOAMDPROC) (UINT id, int property, GLenum dataType, UINT size, void *data);
+typedef INT (WINAPI * PFNWGLGETGPUINFOAMDPROC) (UINT id, INT property, GLenum dataType, UINT size, void *data);
 typedef UINT (WINAPI * PFNWGLGETCONTEXTGPUIDAMDPROC) (HGLRC hglrc);
 typedef HGLRC (WINAPI * PFNWGLCREATEASSOCIATEDCONTEXTAMDPROC) (UINT id);
 typedef HGLRC (WINAPI * PFNWGLCREATEASSOCIATEDCONTEXTATTRIBSAMDPROC) (UINT id, HGLRC hShareContext, const int *attribList);
@@ -328,7 +328,7 @@
 typedef VOID (WINAPI * PFNWGLBLITCONTEXTFRAMEBUFFERAMDPROC) (HGLRC dstCtx, GLint srcX0, GLint srcY0, GLint srcX1, GLint srcY1, GLint dstX0, GLint dstY0, GLint dstX1, GLint dstY1, GLbitfield mask, GLenum filter);
 #ifdef WGL_WGLEXT_PROTOTYPES
 UINT WINAPI wglGetGPUIDsAMD (UINT maxCount, UINT *ids);
-INT WINAPI wglGetGPUInfoAMD (UINT id, int property, GLenum dataType, UINT size, void *data);
+INT WINAPI wglGetGPUInfoAMD (UINT id, INT property, GLenum dataType, UINT size, void *data);
 UINT WINAPI wglGetContextGPUIDAMD (HGLRC hglrc);
 HGLRC WINAPI wglCreateAssociatedContextAMD (UINT id);
 HGLRC WINAPI wglCreateAssociatedContextAttribsAMD (UINT id, HGLRC hShareContext, const int *attribList);
@@ -725,12 +725,12 @@
 #define WGL_NV_present_video 1
 DECLARE_HANDLE(HVIDEOOUTPUTDEVICENV);
 #define WGL_NUM_VIDEO_SLOTS_NV            0x20F0
-typedef int (WINAPI * PFNWGLENUMERATEVIDEODEVICESNVPROC) (HDC hDC, HVIDEOOUTPUTDEVICENV *phDeviceList);
-typedef BOOL (WINAPI * PFNWGLBINDVIDEODEVICENVPROC) (HDC hDC, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
+typedef int (WINAPI * PFNWGLENUMERATEVIDEODEVICESNVPROC) (HDC hDc, HVIDEOOUTPUTDEVICENV *phDeviceList);
+typedef BOOL (WINAPI * PFNWGLBINDVIDEODEVICENVPROC) (HDC hDc, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
 typedef BOOL (WINAPI * PFNWGLQUERYCURRENTCONTEXTNVPROC) (int iAttribute, int *piValue);
 #ifdef WGL_WGLEXT_PROTOTYPES
-int WINAPI wglEnumerateVideoDevicesNV (HDC hDC, HVIDEOOUTPUTDEVICENV *phDeviceList);
-BOOL WINAPI wglBindVideoDeviceNV (HDC hDC, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
+int WINAPI wglEnumerateVideoDevicesNV (HDC hDc, HVIDEOOUTPUTDEVICENV *phDeviceList);
+BOOL WINAPI wglBindVideoDeviceNV (HDC hDc, unsigned int uVideoSlot, HVIDEOOUTPUTDEVICENV hVideoDevice, const int *piAttribList);
 BOOL WINAPI wglQueryCurrentContextNV (int iAttribute, int *piValue);
 #endif
 #endif /* WGL_NV_present_video */
@@ -835,14 +835,14 @@
 typedef BOOL (WINAPI * PFNWGLGETSYNCVALUESOMLPROC) (HDC hdc, INT64 *ust, INT64 *msc, INT64 *sbc);
 typedef BOOL (WINAPI * PFNWGLGETMSCRATEOMLPROC) (HDC hdc, INT32 *numerator, INT32 *denominator);
 typedef INT64 (WINAPI * PFNWGLSWAPBUFFERSMSCOMLPROC) (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder);
-typedef INT64 (WINAPI * PFNWGLSWAPLAYERBUFFERSMSCOMLPROC) (HDC hdc, int fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
+typedef INT64 (WINAPI * PFNWGLSWAPLAYERBUFFERSMSCOMLPROC) (HDC hdc, INT fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
 typedef BOOL (WINAPI * PFNWGLWAITFORMSCOMLPROC) (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder, INT64 *ust, INT64 *msc, INT64 *sbc);
 typedef BOOL (WINAPI * PFNWGLWAITFORSBCOMLPROC) (HDC hdc, INT64 target_sbc, INT64 *ust, INT64 *msc, INT64 *sbc);
 #ifdef WGL_WGLEXT_PROTOTYPES
 BOOL WINAPI wglGetSyncValuesOML (HDC hdc, INT64 *ust, INT64 *msc, INT64 *sbc);
 BOOL WINAPI wglGetMscRateOML (HDC hdc, INT32 *numerator, INT32 *denominator);
 INT64 WINAPI wglSwapBuffersMscOML (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder);
-INT64 WINAPI wglSwapLayerBuffersMscOML (HDC hdc, int fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
+INT64 WINAPI wglSwapLayerBuffersMscOML (HDC hdc, INT fuPlanes, INT64 target_msc, INT64 divisor, INT64 remainder);
 BOOL WINAPI wglWaitForMscOML (HDC hdc, INT64 target_msc, INT64 divisor, INT64 remainder, INT64 *ust, INT64 *msc, INT64 *sbc);
 BOOL WINAPI wglWaitForSbcOML (HDC hdc, INT64 target_sbc, INT64 *ust, INT64 *msc, INT64 *sbc);
 #endif
diff --git a/api/GLES/gl.h b/api/GLES/gl.h
index 0d49769..681ecc9 100644
--- a/api/GLES/gl.h
+++ b/api/GLES/gl.h
@@ -36,7 +36,7 @@
 
 #include <GLES/glplatform.h>
 
-/* Generated on date 20181130 */
+/* Generated on date 20190204 */
 
 /* Generated C header for:
  * API: gles1
diff --git a/api/GLES/glext.h b/api/GLES/glext.h
index 41de807..f9d2852 100644
--- a/api/GLES/glext.h
+++ b/api/GLES/glext.h
@@ -38,7 +38,7 @@
 #define GL_APIENTRYP GL_APIENTRY*
 #endif
 
-/* Generated on date 20181130 */
+/* Generated on date 20190204 */
 
 /* Generated C header for:
  * API: gles1
diff --git a/api/GLES2/gl2.h b/api/GLES2/gl2.h
index cf3b7f3..d63eda1 100644
--- a/api/GLES2/gl2.h
+++ b/api/GLES2/gl2.h
@@ -44,7 +44,7 @@
 #define GL_GLES_PROTOTYPES 1
 #endif
 
-/* Generated on date 20181130 */
+/* Generated on date 20190204 */
 
 /* Generated C header for:
  * API: gles2
diff --git a/api/GLES2/gl2ext.h b/api/GLES2/gl2ext.h
index 81d712e..dccffce 100644
--- a/api/GLES2/gl2ext.h
+++ b/api/GLES2/gl2ext.h
@@ -38,7 +38,7 @@
 #define GL_APIENTRYP GL_APIENTRY*
 #endif
 
-/* Generated on date 20181130 */
+/* Generated on date 20190204 */
 
 /* Generated C header for:
  * API: gles2
diff --git a/api/GLES3/gl3.h b/api/GLES3/gl3.h
index 4570785..7c41bb4 100644
--- a/api/GLES3/gl3.h
+++ b/api/GLES3/gl3.h
@@ -44,7 +44,7 @@
 #define GL_GLES_PROTOTYPES 1
 #endif
 
-/* Generated on date 20181130 */
+/* Generated on date 20190204 */
 
 /* Generated C header for:
  * API: gles2
diff --git a/index_es.php b/index_es.php
index 0dada0f..3b2aeeb 100644
--- a/index_es.php
+++ b/index_es.php
@@ -56,11 +56,12 @@
      Documentation </h2>
 
 <ul>
-<li> OpenGL ES 3.2 Specification (May 14, 2018)
+<li> OpenGL ES 3.2 Specification (February 2, 2019)
      <a href="specs/es/3.2/es_spec_3.2.pdf"> without changes marked </a>
      and
      <a href="specs/es/3.2/es_spec_3.2.withchanges.pdf"> with changes marked </a>. </li>
-<li> OpenGL ES Shading Language 3.20 Specification (May 11, 2018)
+<li> OpenGL ES Shading Language 3.20 Specification (December 12, 2018)
+     <a href="specs/es/3.2/GLSL_ES_Specification_3.20.html"> (HTML) </a>
      <a href="specs/es/3.2/GLSL_ES_Specification_3.20.pdf"> (PDF) </a>
 <li> <a href="http://www.khronos.org/opengles/sdk/docs/man32/">
      OpenGL ES 3.2 Online Manual Pages.</a> </li>
diff --git a/index_gl.php b/index_gl.php
index d72b667..c96075b 100644
--- a/index_gl.php
+++ b/index_gl.php
@@ -48,7 +48,7 @@
 
 <ul>
 <li> <b> Current Specifications (OpenGL 4.6) </b>
-<li> OpenGL 4.6 API Specification (updated May 14, 2018)
+<li> OpenGL 4.6 API Specification (February 2, 2019)
     <ul>
     <li> <a href="specs/gl/glspec46.core.pdf"> Core Profile Specification
          </a> </li>
@@ -60,7 +60,8 @@
          Compatibility Profile Specification with changes marked </a>
          </li>
     </ul> </li>
-<li> OpenGL Shading Language 4.60 Specification (updated May 11, 2018)
+<li> OpenGL Shading Language 4.60 Specification (December 12, 2018)
+     <a href="specs/gl/GLSLangSpec.4.60.html"> (HTML) </a> </li>
      <a href="specs/gl/GLSLangSpec.4.60.pdf"> (PDF) </a> </li>
 
 <li> <a href="http://www.opengl.org/sdk/docs/man4/"> OpenGL 4.5 API and
diff --git a/specs/es/3.2/GLSL_ES_Specification_3.20.html b/specs/es/3.2/GLSL_ES_Specification_3.20.html
new file mode 100644
index 0000000..128d8d6
--- /dev/null
+++ b/specs/es/3.2/GLSL_ES_Specification_3.20.html
@@ -0,0 +1,15228 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8">
+<!--[if IE]><meta http-equiv="X-UA-Compatible" content="IE=edge"><![endif]-->
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="generator" content="Asciidoctor 1.5.7.1">
+<meta name="author" content="Robert J. Simpson, Qualcomm (Editor) ; John Kessenich, Dave Baldwin and Randi Rost (Version 1.1 Authors)">
+<title>The OpenGL ES&#174; Shading Language, Version 3.20.5</title>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700">
+<style>
+/* Asciidoctor default stylesheet | MIT License | http://asciidoctor.org */
+/* Uncomment @import statement below to use as custom stylesheet */
+/*@import "https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700";*/
+article,aside,details,figcaption,figure,footer,header,hgroup,main,nav,section,summary{display:block}
+audio,canvas,video{display:inline-block}
+audio:not([controls]){display:none;height:0}
+script{display:none!important}
+html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}
+a{background:transparent}
+a:focus{outline:thin dotted}
+a:active,a:hover{outline:0}
+h1{font-size:2em;margin:.67em 0}
+abbr[title]{border-bottom:1px dotted}
+b,strong{font-weight:bold}
+dfn{font-style:italic}
+hr{-moz-box-sizing:content-box;box-sizing:content-box;height:0}
+mark{background:#ff0;color:#000}
+code,kbd,pre,samp{font-family:monospace;font-size:1em}
+pre{white-space:pre-wrap}
+q{quotes:"\201C" "\201D" "\2018" "\2019"}
+small{font-size:80%}
+sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}
+sup{top:-.5em}
+sub{bottom:-.25em}
+img{border:0}
+svg:not(:root){overflow:hidden}
+figure{margin:0}
+fieldset{border:1px solid silver;margin:0 2px;padding:.35em .625em .75em}
+legend{border:0;padding:0}
+button,input,select,textarea{font-family:inherit;font-size:100%;margin:0}
+button,input{line-height:normal}
+button,select{text-transform:none}
+button,html input[type="button"],input[type="reset"],input[type="submit"]{-webkit-appearance:button;cursor:pointer}
+button[disabled],html input[disabled]{cursor:default}
+input[type="checkbox"],input[type="radio"]{box-sizing:border-box;padding:0}
+button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}
+textarea{overflow:auto;vertical-align:top}
+table{border-collapse:collapse;border-spacing:0}
+*,*::before,*::after{-moz-box-sizing:border-box;-webkit-box-sizing:border-box;box-sizing:border-box}
+html,body{font-size:100%}
+body{background:#fff;color:rgba(0,0,0,.8);padding:0;margin:0;font-family:"Noto Serif","DejaVu Serif",serif;font-weight:400;font-style:normal;line-height:1;position:relative;cursor:auto;tab-size:4;-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased}
+a:hover{cursor:pointer}
+img,object,embed{max-width:100%;height:auto}
+object,embed{height:100%}
+img{-ms-interpolation-mode:bicubic}
+.left{float:left!important}
+.right{float:right!important}
+.text-left{text-align:left!important}
+.text-right{text-align:right!important}
+.text-center{text-align:center!important}
+.text-justify{text-align:justify!important}
+.hide{display:none}
+img,object,svg{display:inline-block;vertical-align:middle}
+textarea{height:auto;min-height:50px}
+select{width:100%}
+.center{margin-left:auto;margin-right:auto}
+.stretch{width:100%}
+.subheader,.admonitionblock td.content>.title,.audioblock>.title,.exampleblock>.title,.imageblock>.title,.listingblock>.title,.literalblock>.title,.stemblock>.title,.openblock>.title,.paragraph>.title,.quoteblock>.title,table.tableblock>.title,.verseblock>.title,.videoblock>.title,.dlist>.title,.olist>.title,.ulist>.title,.qlist>.title,.hdlist>.title{line-height:1.45;color:#7a2518;font-weight:400;margin-top:0;margin-bottom:.25em}
+div,dl,dt,dd,ul,ol,li,h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6,pre,form,p,blockquote,th,td{margin:0;padding:0;direction:ltr}
+a{color:#2156a5;text-decoration:underline;line-height:inherit}
+a:hover,a:focus{color:#1d4b8f}
+a img{border:none}
+p{font-family:inherit;font-weight:400;font-size:1em;line-height:1.6;margin-bottom:1.25em;text-rendering:optimizeLegibility}
+p aside{font-size:.875em;line-height:1.35;font-style:italic}
+h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{font-family:"Open Sans","DejaVu Sans",sans-serif;font-weight:300;font-style:normal;color:#ba3925;text-rendering:optimizeLegibility;margin-top:1em;margin-bottom:.5em;line-height:1.0125em}
+h1 small,h2 small,h3 small,#toctitle small,.sidebarblock>.content>.title small,h4 small,h5 small,h6 small{font-size:60%;color:#e99b8f;line-height:0}
+h1{font-size:2.125em}
+h2{font-size:1.6875em}
+h3,#toctitle,.sidebarblock>.content>.title{font-size:1.375em}
+h4,h5{font-size:1.125em}
+h6{font-size:1em}
+hr{border:solid #ddddd8;border-width:1px 0 0;clear:both;margin:1.25em 0 1.1875em;height:0}
+em,i{font-style:italic;line-height:inherit}
+strong,b{font-weight:bold;line-height:inherit}
+small{font-size:60%;line-height:inherit}
+code{font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;font-weight:400;color:rgba(0,0,0,.9)}
+ul,ol,dl{font-size:1em;line-height:1.6;margin-bottom:1.25em;list-style-position:outside;font-family:inherit}
+ul,ol{margin-left:1.5em}
+ul li ul,ul li ol{margin-left:1.25em;margin-bottom:0;font-size:1em}
+ul.square li ul,ul.circle li ul,ul.disc li ul{list-style:inherit}
+ul.square{list-style-type:square}
+ul.circle{list-style-type:circle}
+ul.disc{list-style-type:disc}
+ol li ul,ol li ol{margin-left:1.25em;margin-bottom:0}
+dl dt{margin-bottom:.3125em;font-weight:bold}
+dl dd{margin-bottom:1.25em}
+abbr,acronym{text-transform:uppercase;font-size:90%;color:rgba(0,0,0,.8);border-bottom:1px dotted #ddd;cursor:help}
+abbr{text-transform:none}
+blockquote{margin:0 0 1.25em;padding:.5625em 1.25em 0 1.1875em;border-left:1px solid #ddd}
+blockquote cite{display:block;font-size:.9375em;color:rgba(0,0,0,.6)}
+blockquote cite::before{content:"\2014 \0020"}
+blockquote cite a,blockquote cite a:visited{color:rgba(0,0,0,.6)}
+blockquote,blockquote p{line-height:1.6;color:rgba(0,0,0,.85)}
+@media screen and (min-width:768px){h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{line-height:1.2}
+h1{font-size:2.75em}
+h2{font-size:2.3125em}
+h3,#toctitle,.sidebarblock>.content>.title{font-size:1.6875em}
+h4{font-size:1.4375em}}
+table{background:#fff;margin-bottom:1.25em;border:solid 1px #dedede}
+table thead,table tfoot{background:#f7f8f7}
+table thead tr th,table thead tr td,table tfoot tr th,table tfoot tr td{padding:.5em .625em .625em;font-size:inherit;color:rgba(0,0,0,.8);text-align:left}
+table tr th,table tr td{padding:.5625em .625em;font-size:inherit;color:rgba(0,0,0,.8)}
+table tr.even,table tr.alt,table tr:nth-of-type(even){background:#f8f8f7}
+table thead tr th,table tfoot tr th,table tbody tr td,table tr td,table tfoot tr td{display:table-cell;line-height:1.6}
+h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{line-height:1.2;word-spacing:-.05em}
+h1 strong,h2 strong,h3 strong,#toctitle strong,.sidebarblock>.content>.title strong,h4 strong,h5 strong,h6 strong{font-weight:400}
+.clearfix::before,.clearfix::after,.float-group::before,.float-group::after{content:" ";display:table}
+.clearfix::after,.float-group::after{clear:both}
+*:not(pre)>code{font-size:.9375em;font-style:normal!important;letter-spacing:0;padding:.1em .5ex;word-spacing:-.15em;background-color:#f7f7f8;-webkit-border-radius:4px;border-radius:4px;line-height:1.45;text-rendering:optimizeSpeed;word-wrap:break-word}
+*:not(pre)>code.nobreak{word-wrap:normal}
+*:not(pre)>code.nowrap{white-space:nowrap}
+pre,pre>code{line-height:1.45;color:rgba(0,0,0,.9);font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;font-weight:400;text-rendering:optimizeSpeed}
+em em{font-style:normal}
+strong strong{font-weight:400}
+.keyseq{color:rgba(51,51,51,.8)}
+kbd{font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;display:inline-block;color:rgba(0,0,0,.8);font-size:.65em;line-height:1.45;background-color:#f7f7f7;border:1px solid #ccc;-webkit-border-radius:3px;border-radius:3px;-webkit-box-shadow:0 1px 0 rgba(0,0,0,.2),0 0 0 .1em white inset;box-shadow:0 1px 0 rgba(0,0,0,.2),0 0 0 .1em #fff inset;margin:0 .15em;padding:.2em .5em;vertical-align:middle;position:relative;top:-.1em;white-space:nowrap}
+.keyseq kbd:first-child{margin-left:0}
+.keyseq kbd:last-child{margin-right:0}
+.menuseq,.menuref{color:#000}
+.menuseq b:not(.caret),.menuref{font-weight:inherit}
+.menuseq{word-spacing:-.02em}
+.menuseq b.caret{font-size:1.25em;line-height:.8}
+.menuseq i.caret{font-weight:bold;text-align:center;width:.45em}
+b.button::before,b.button::after{position:relative;top:-1px;font-weight:400}
+b.button::before{content:"[";padding:0 3px 0 2px}
+b.button::after{content:"]";padding:0 2px 0 3px}
+p a>code:hover{color:rgba(0,0,0,.9)}
+#header,#content,#footnotes,#footer{width:100%;margin-left:auto;margin-right:auto;margin-top:0;margin-bottom:0;max-width:62.5em;*zoom:1;position:relative;padding-left:.9375em;padding-right:.9375em}
+#header::before,#header::after,#content::before,#content::after,#footnotes::before,#footnotes::after,#footer::before,#footer::after{content:" ";display:table}
+#header::after,#content::after,#footnotes::after,#footer::after{clear:both}
+#content{margin-top:1.25em}
+#content::before{content:none}
+#header>h1:first-child{color:rgba(0,0,0,.85);margin-top:2.25rem;margin-bottom:0}
+#header>h1:first-child+#toc{margin-top:8px;border-top:1px solid #ddddd8}
+#header>h1:only-child,body.toc2 #header>h1:nth-last-child(2){border-bottom:1px solid #ddddd8;padding-bottom:8px}
+#header .details{border-bottom:1px solid #ddddd8;line-height:1.45;padding-top:.25em;padding-bottom:.25em;padding-left:.25em;color:rgba(0,0,0,.6);display:-ms-flexbox;display:-webkit-flex;display:flex;-ms-flex-flow:row wrap;-webkit-flex-flow:row wrap;flex-flow:row wrap}
+#header .details span:first-child{margin-left:-.125em}
+#header .details span.email a{color:rgba(0,0,0,.85)}
+#header .details br{display:none}
+#header .details br+span::before{content:"\00a0\2013\00a0"}
+#header .details br+span.author::before{content:"\00a0\22c5\00a0";color:rgba(0,0,0,.85)}
+#header .details br+span#revremark::before{content:"\00a0|\00a0"}
+#header #revnumber{text-transform:capitalize}
+#header #revnumber::after{content:"\00a0"}
+#content>h1:first-child:not([class]){color:rgba(0,0,0,.85);border-bottom:1px solid #ddddd8;padding-bottom:8px;margin-top:0;padding-top:1rem;margin-bottom:1.25rem}
+#toc{border-bottom:1px solid #efefed;padding-bottom:.5em}
+#toc>ul{margin-left:.125em}
+#toc ul.sectlevel0>li>a{font-style:italic}
+#toc ul.sectlevel0 ul.sectlevel1{margin:.5em 0}
+#toc ul{font-family:"Open Sans","DejaVu Sans",sans-serif;list-style-type:none}
+#toc li{line-height:1.3334;margin-top:.3334em}
+#toc a{text-decoration:none}
+#toc a:active{text-decoration:underline}
+#toctitle{color:#7a2518;font-size:1.2em}
+@media screen and (min-width:768px){#toctitle{font-size:1.375em}
+body.toc2{padding-left:15em;padding-right:0}
+#toc.toc2{margin-top:0!important;background-color:#f8f8f7;position:fixed;width:15em;left:0;top:0;border-right:1px solid #efefed;border-top-width:0!important;border-bottom-width:0!important;z-index:1000;padding:1.25em 1em;height:100%;overflow:auto}
+#toc.toc2 #toctitle{margin-top:0;margin-bottom:.8rem;font-size:1.2em}
+#toc.toc2>ul{font-size:.9em;margin-bottom:0}
+#toc.toc2 ul ul{margin-left:0;padding-left:1em}
+#toc.toc2 ul.sectlevel0 ul.sectlevel1{padding-left:0;margin-top:.5em;margin-bottom:.5em}
+body.toc2.toc-right{padding-left:0;padding-right:15em}
+body.toc2.toc-right #toc.toc2{border-right-width:0;border-left:1px solid #efefed;left:auto;right:0}}
+@media screen and (min-width:1280px){body.toc2{padding-left:20em;padding-right:0}
+#toc.toc2{width:20em}
+#toc.toc2 #toctitle{font-size:1.375em}
+#toc.toc2>ul{font-size:.95em}
+#toc.toc2 ul ul{padding-left:1.25em}
+body.toc2.toc-right{padding-left:0;padding-right:20em}}
+#content #toc{border-style:solid;border-width:1px;border-color:#e0e0dc;margin-bottom:1.25em;padding:1.25em;background:#f8f8f7;-webkit-border-radius:4px;border-radius:4px}
+#content #toc>:first-child{margin-top:0}
+#content #toc>:last-child{margin-bottom:0}
+#footer{max-width:100%;background-color:rgba(0,0,0,.8);padding:1.25em}
+#footer-text{color:rgba(255,255,255,.8);line-height:1.44}
+#content{margin-bottom:.625em}
+.sect1{padding-bottom:.625em}
+@media screen and (min-width:768px){#content{margin-bottom:1.25em}
+.sect1{padding-bottom:1.25em}}
+.sect1:last-child{padding-bottom:0}
+.sect1+.sect1{border-top:1px solid #efefed}
+#content h1>a.anchor,h2>a.anchor,h3>a.anchor,#toctitle>a.anchor,.sidebarblock>.content>.title>a.anchor,h4>a.anchor,h5>a.anchor,h6>a.anchor{position:absolute;z-index:1001;width:1.5ex;margin-left:-1.5ex;display:block;text-decoration:none!important;visibility:hidden;text-align:center;font-weight:400}
+#content h1>a.anchor::before,h2>a.anchor::before,h3>a.anchor::before,#toctitle>a.anchor::before,.sidebarblock>.content>.title>a.anchor::before,h4>a.anchor::before,h5>a.anchor::before,h6>a.anchor::before{content:"\00A7";font-size:.85em;display:block;padding-top:.1em}
+#content h1:hover>a.anchor,#content h1>a.anchor:hover,h2:hover>a.anchor,h2>a.anchor:hover,h3:hover>a.anchor,#toctitle:hover>a.anchor,.sidebarblock>.content>.title:hover>a.anchor,h3>a.anchor:hover,#toctitle>a.anchor:hover,.sidebarblock>.content>.title>a.anchor:hover,h4:hover>a.anchor,h4>a.anchor:hover,h5:hover>a.anchor,h5>a.anchor:hover,h6:hover>a.anchor,h6>a.anchor:hover{visibility:visible}
+#content h1>a.link,h2>a.link,h3>a.link,#toctitle>a.link,.sidebarblock>.content>.title>a.link,h4>a.link,h5>a.link,h6>a.link{color:#ba3925;text-decoration:none}
+#content h1>a.link:hover,h2>a.link:hover,h3>a.link:hover,#toctitle>a.link:hover,.sidebarblock>.content>.title>a.link:hover,h4>a.link:hover,h5>a.link:hover,h6>a.link:hover{color:#a53221}
+.audioblock,.imageblock,.literalblock,.listingblock,.stemblock,.videoblock{margin-bottom:1.25em}
+.admonitionblock td.content>.title,.audioblock>.title,.exampleblock>.title,.imageblock>.title,.listingblock>.title,.literalblock>.title,.stemblock>.title,.openblock>.title,.paragraph>.title,.quoteblock>.title,table.tableblock>.title,.verseblock>.title,.videoblock>.title,.dlist>.title,.olist>.title,.ulist>.title,.qlist>.title,.hdlist>.title{text-rendering:optimizeLegibility;text-align:left;font-family:"Noto Serif","DejaVu Serif",serif;font-size:1rem;font-style:italic}
+table.tableblock.fit-content>caption.title{white-space:nowrap;width:0}
+.paragraph.lead>p,#preamble>.sectionbody>[class="paragraph"]:first-of-type p{font-size:1.21875em;line-height:1.6;color:rgba(0,0,0,.85)}
+table.tableblock #preamble>.sectionbody>[class="paragraph"]:first-of-type p{font-size:inherit}
+.admonitionblock>table{border-collapse:separate;border:0;background:none;width:100%}
+.admonitionblock>table td.icon{text-align:center;width:80px}
+.admonitionblock>table td.icon img{max-width:none}
+.admonitionblock>table td.icon .title{font-weight:bold;font-family:"Open Sans","DejaVu Sans",sans-serif;text-transform:uppercase}
+.admonitionblock>table td.content{padding-left:1.125em;padding-right:1.25em;border-left:1px solid #ddddd8;color:rgba(0,0,0,.6)}
+.admonitionblock>table td.content>:last-child>:last-child{margin-bottom:0}
+.exampleblock>.content{border-style:solid;border-width:1px;border-color:#e6e6e6;margin-bottom:1.25em;padding:1.25em;background:#fff;-webkit-border-radius:4px;border-radius:4px}
+.exampleblock>.content>:first-child{margin-top:0}
+.exampleblock>.content>:last-child{margin-bottom:0}
+.sidebarblock{border-style:solid;border-width:1px;border-color:#e0e0dc;margin-bottom:1.25em;padding:1.25em;background:#f8f8f7;-webkit-border-radius:4px;border-radius:4px}
+.sidebarblock>:first-child{margin-top:0}
+.sidebarblock>:last-child{margin-bottom:0}
+.sidebarblock>.content>.title{color:#7a2518;margin-top:0;text-align:center}
+.exampleblock>.content>:last-child>:last-child,.exampleblock>.content .olist>ol>li:last-child>:last-child,.exampleblock>.content .ulist>ul>li:last-child>:last-child,.exampleblock>.content .qlist>ol>li:last-child>:last-child,.sidebarblock>.content>:last-child>:last-child,.sidebarblock>.content .olist>ol>li:last-child>:last-child,.sidebarblock>.content .ulist>ul>li:last-child>:last-child,.sidebarblock>.content .qlist>ol>li:last-child>:last-child{margin-bottom:0}
+.literalblock pre,.listingblock pre:not(.highlight),.listingblock pre[class="highlight"],.listingblock pre[class^="highlight "],.listingblock pre.CodeRay,.listingblock pre.prettyprint{background:#f7f7f8}
+.sidebarblock .literalblock pre,.sidebarblock .listingblock pre:not(.highlight),.sidebarblock .listingblock pre[class="highlight"],.sidebarblock .listingblock pre[class^="highlight "],.sidebarblock .listingblock pre.CodeRay,.sidebarblock .listingblock pre.prettyprint{background:#f2f1f1}
+.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{-webkit-border-radius:4px;border-radius:4px;word-wrap:break-word;padding:1em;font-size:.8125em}
+.literalblock pre.nowrap,.literalblock pre[class].nowrap,.listingblock pre.nowrap,.listingblock pre[class].nowrap{overflow-x:auto;white-space:pre;word-wrap:normal}
+@media screen and (min-width:768px){.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{font-size:.90625em}}
+@media screen and (min-width:1280px){.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{font-size:1em}}
+.literalblock.output pre{color:#f7f7f8;background-color:rgba(0,0,0,.9)}
+.listingblock pre.highlightjs{padding:0}
+.listingblock pre.highlightjs>code{padding:1em;-webkit-border-radius:4px;border-radius:4px}
+.listingblock pre.prettyprint{border-width:0}
+.listingblock>.content{position:relative}
+.listingblock code[data-lang]::before{display:none;content:attr(data-lang);position:absolute;font-size:.75em;top:.425rem;right:.5rem;line-height:1;text-transform:uppercase;color:#999}
+.listingblock:hover code[data-lang]::before{display:block}
+.listingblock.terminal pre .command::before{content:attr(data-prompt);padding-right:.5em;color:#999}
+.listingblock.terminal pre .command:not([data-prompt])::before{content:"$"}
+table.pyhltable{border-collapse:separate;border:0;margin-bottom:0;background:none}
+table.pyhltable td{vertical-align:top;padding-top:0;padding-bottom:0;line-height:1.45}
+table.pyhltable td.code{padding-left:.75em;padding-right:0}
+pre.pygments .lineno,table.pyhltable td:not(.code){color:#999;padding-left:0;padding-right:.5em;border-right:1px solid #ddddd8}
+pre.pygments .lineno{display:inline-block;margin-right:.25em}
+table.pyhltable .linenodiv{background:none!important;padding-right:0!important}
+.quoteblock{margin:0 1em 1.25em 1.5em;display:table}
+.quoteblock>.title{margin-left:-1.5em;margin-bottom:.75em}
+.quoteblock blockquote,.quoteblock blockquote p{color:rgba(0,0,0,.85);font-size:1.15rem;line-height:1.75;word-spacing:.1em;letter-spacing:0;font-style:italic;text-align:justify}
+.quoteblock blockquote{margin:0;padding:0;border:0}
+.quoteblock blockquote::before{content:"\201c";float:left;font-size:2.75em;font-weight:bold;line-height:.6em;margin-left:-.6em;color:#7a2518;text-shadow:0 1px 2px rgba(0,0,0,.1)}
+.quoteblock blockquote>.paragraph:last-child p{margin-bottom:0}
+.quoteblock .attribution{margin-top:.5em;margin-right:.5ex;text-align:right}
+.quoteblock .quoteblock{margin-left:0;margin-right:0;padding:.5em 0;border-left:3px solid rgba(0,0,0,.6)}
+.quoteblock .quoteblock blockquote{padding:0 0 0 .75em}
+.quoteblock .quoteblock blockquote::before{display:none}
+.verseblock{margin:0 1em 1.25em}
+.verseblock pre{font-family:"Open Sans","DejaVu Sans",sans;font-size:1.15rem;color:rgba(0,0,0,.85);font-weight:300;text-rendering:optimizeLegibility}
+.verseblock pre strong{font-weight:400}
+.verseblock .attribution{margin-top:1.25rem;margin-left:.5ex}
+.quoteblock .attribution,.verseblock .attribution{font-size:.9375em;line-height:1.45;font-style:italic}
+.quoteblock .attribution br,.verseblock .attribution br{display:none}
+.quoteblock .attribution cite,.verseblock .attribution cite{display:block;letter-spacing:-.025em;color:rgba(0,0,0,.6)}
+.quoteblock.abstract{margin:0 1em 1.25em;display:block}
+.quoteblock.abstract>.title{margin:0 0 .375em;font-size:1.15em;text-align:center}
+.quoteblock.abstract blockquote,.quoteblock.abstract blockquote p{word-spacing:0;line-height:1.6}
+.quoteblock.abstract blockquote::before,.quoteblock.abstract p::before{display:none}
+table.tableblock{max-width:100%;border-collapse:separate}
+p.tableblock:last-child{margin-bottom:0}
+td.tableblock>.content{margin-bottom:-1.25em}
+table.tableblock,th.tableblock,td.tableblock{border:0 solid #dedede}
+table.grid-all>thead>tr>.tableblock,table.grid-all>tbody>tr>.tableblock{border-width:0 1px 1px 0}
+table.grid-all>tfoot>tr>.tableblock{border-width:1px 1px 0 0}
+table.grid-cols>*>tr>.tableblock{border-width:0 1px 0 0}
+table.grid-rows>thead>tr>.tableblock,table.grid-rows>tbody>tr>.tableblock{border-width:0 0 1px}
+table.grid-rows>tfoot>tr>.tableblock{border-width:1px 0 0}
+table.grid-all>*>tr>.tableblock:last-child,table.grid-cols>*>tr>.tableblock:last-child{border-right-width:0}
+table.grid-all>tbody>tr:last-child>.tableblock,table.grid-all>thead:last-child>tr>.tableblock,table.grid-rows>tbody>tr:last-child>.tableblock,table.grid-rows>thead:last-child>tr>.tableblock{border-bottom-width:0}
+table.frame-all{border-width:1px}
+table.frame-sides{border-width:0 1px}
+table.frame-topbot,table.frame-ends{border-width:1px 0}
+table.stripes-all tr,table.stripes-odd tr:nth-of-type(odd){background:#f8f8f7}
+table.stripes-none tr,table.stripes-odd tr:nth-of-type(even){background:none}
+th.halign-left,td.halign-left{text-align:left}
+th.halign-right,td.halign-right{text-align:right}
+th.halign-center,td.halign-center{text-align:center}
+th.valign-top,td.valign-top{vertical-align:top}
+th.valign-bottom,td.valign-bottom{vertical-align:bottom}
+th.valign-middle,td.valign-middle{vertical-align:middle}
+table thead th,table tfoot th{font-weight:bold}
+tbody tr th{display:table-cell;line-height:1.6;background:#f7f8f7}
+tbody tr th,tbody tr th p,tfoot tr th,tfoot tr th p{color:rgba(0,0,0,.8);font-weight:bold}
+p.tableblock>code:only-child{background:none;padding:0}
+p.tableblock{font-size:1em}
+td>div.verse{white-space:pre}
+ol{margin-left:1.75em}
+ul li ol{margin-left:1.5em}
+dl dd{margin-left:1.125em}
+dl dd:last-child,dl dd:last-child>:last-child{margin-bottom:0}
+ol>li p,ul>li p,ul dd,ol dd,.olist .olist,.ulist .ulist,.ulist .olist,.olist .ulist{margin-bottom:.625em}
+ul.checklist,ul.none,ol.none,ul.no-bullet,ol.no-bullet,ol.unnumbered,ul.unstyled,ol.unstyled{list-style-type:none}
+ul.no-bullet,ol.no-bullet,ol.unnumbered{margin-left:.625em}
+ul.unstyled,ol.unstyled{margin-left:0}
+ul.checklist{margin-left:.625em}
+ul.checklist li>p:first-child>.fa-square-o:first-child,ul.checklist li>p:first-child>.fa-check-square-o:first-child{width:1.25em;font-size:.8em;position:relative;bottom:.125em}
+ul.checklist li>p:first-child>input[type="checkbox"]:first-child{margin-right:.25em}
+ul.inline{display:-ms-flexbox;display:-webkit-box;display:flex;-ms-flex-flow:row wrap;-webkit-flex-flow:row wrap;flex-flow:row wrap;list-style:none;margin:0 0 .625em -1.25em}
+ul.inline>li{margin-left:1.25em}
+.unstyled dl dt{font-weight:400;font-style:normal}
+ol.arabic{list-style-type:decimal}
+ol.decimal{list-style-type:decimal-leading-zero}
+ol.loweralpha{list-style-type:lower-alpha}
+ol.upperalpha{list-style-type:upper-alpha}
+ol.lowerroman{list-style-type:lower-roman}
+ol.upperroman{list-style-type:upper-roman}
+ol.lowergreek{list-style-type:lower-greek}
+.hdlist>table,.colist>table{border:0;background:none}
+.hdlist>table>tbody>tr,.colist>table>tbody>tr{background:none}
+td.hdlist1,td.hdlist2{vertical-align:top;padding:0 .625em}
+td.hdlist1{font-weight:bold;padding-bottom:1.25em}
+.literalblock+.colist,.listingblock+.colist{margin-top:-.5em}
+.colist td:not([class]):first-child{padding:.4em .75em 0;line-height:1;vertical-align:top}
+.colist td:not([class]):first-child img{max-width:none}
+.colist td:not([class]):last-child{padding:.25em 0}
+.thumb,.th{line-height:0;display:inline-block;border:solid 4px #fff;-webkit-box-shadow:0 0 0 1px #ddd;box-shadow:0 0 0 1px #ddd}
+.imageblock.left,.imageblock[style*="float: left"]{margin:.25em .625em 1.25em 0}
+.imageblock.right,.imageblock[style*="float: right"]{margin:.25em 0 1.25em .625em}
+.imageblock>.title{margin-bottom:0}
+.imageblock.thumb,.imageblock.th{border-width:6px}
+.imageblock.thumb>.title,.imageblock.th>.title{padding:0 .125em}
+.image.left,.image.right{margin-top:.25em;margin-bottom:.25em;display:inline-block;line-height:0}
+.image.left{margin-right:.625em}
+.image.right{margin-left:.625em}
+a.image{text-decoration:none;display:inline-block}
+a.image object{pointer-events:none}
+sup.footnote,sup.footnoteref{font-size:.875em;position:static;vertical-align:super}
+sup.footnote a,sup.footnoteref a{text-decoration:none}
+sup.footnote a:active,sup.footnoteref a:active{text-decoration:underline}
+#footnotes{padding-top:.75em;padding-bottom:.75em;margin-bottom:.625em}
+#footnotes hr{width:20%;min-width:6.25em;margin:-.25em 0 .75em;border-width:1px 0 0}
+#footnotes .footnote{padding:0 .375em 0 .225em;line-height:1.3334;font-size:.875em;margin-left:1.2em;margin-bottom:.2em}
+#footnotes .footnote a:first-of-type{font-weight:bold;text-decoration:none;margin-left:-1.05em}
+#footnotes .footnote:last-of-type{margin-bottom:0}
+#content #footnotes{margin-top:-.625em;margin-bottom:0;padding:.75em 0}
+.gist .file-data>table{border:0;background:#fff;width:100%;margin-bottom:0}
+.gist .file-data>table td.line-data{width:99%}
+div.unbreakable{page-break-inside:avoid}
+.big{font-size:larger}
+.small{font-size:smaller}
+.underline{text-decoration:underline}
+.overline{text-decoration:overline}
+.line-through{text-decoration:line-through}
+.aqua{color:#00bfbf}
+.aqua-background{background-color:#00fafa}
+.black{color:#000}
+.black-background{background-color:#000}
+.blue{color:#0000bf}
+.blue-background{background-color:#0000fa}
+.fuchsia{color:#bf00bf}
+.fuchsia-background{background-color:#fa00fa}
+.gray{color:#606060}
+.gray-background{background-color:#7d7d7d}
+.green{color:#006000}
+.green-background{background-color:#007d00}
+.lime{color:#00bf00}
+.lime-background{background-color:#00fa00}
+.maroon{color:#600000}
+.maroon-background{background-color:#7d0000}
+.navy{color:#000060}
+.navy-background{background-color:#00007d}
+.olive{color:#606000}
+.olive-background{background-color:#7d7d00}
+.purple{color:#600060}
+.purple-background{background-color:#7d007d}
+.red{color:#bf0000}
+.red-background{background-color:#fa0000}
+.silver{color:#909090}
+.silver-background{background-color:#bcbcbc}
+.teal{color:#006060}
+.teal-background{background-color:#007d7d}
+.white{color:#bfbfbf}
+.white-background{background-color:#fafafa}
+.yellow{color:#bfbf00}
+.yellow-background{background-color:#fafa00}
+span.icon>.fa{cursor:default}
+a span.icon>.fa{cursor:inherit}
+.admonitionblock td.icon [class^="fa icon-"]{font-size:2.5em;text-shadow:1px 1px 2px rgba(0,0,0,.5);cursor:default}
+.admonitionblock td.icon .icon-note::before{content:"\f05a";color:#19407c}
+.admonitionblock td.icon .icon-tip::before{content:"\f0eb";text-shadow:1px 1px 2px rgba(155,155,0,.8);color:#111}
+.admonitionblock td.icon .icon-warning::before{content:"\f071";color:#bf6900}
+.admonitionblock td.icon .icon-caution::before{content:"\f06d";color:#bf3400}
+.admonitionblock td.icon .icon-important::before{content:"\f06a";color:#bf0000}
+.conum[data-value]{display:inline-block;color:#fff!important;background-color:rgba(0,0,0,.8);-webkit-border-radius:100px;border-radius:100px;text-align:center;font-size:.75em;width:1.67em;height:1.67em;line-height:1.67em;font-family:"Open Sans","DejaVu Sans",sans-serif;font-style:normal;font-weight:bold}
+.conum[data-value] *{color:#fff!important}
+.conum[data-value]+b{display:none}
+.conum[data-value]::after{content:attr(data-value)}
+pre .conum[data-value]{position:relative;top:-.125em}
+b.conum *{color:inherit!important}
+.conum:not([data-value]):empty{display:none}
+dt,th.tableblock,td.content,div.footnote{text-rendering:optimizeLegibility}
+h1,h2,p,td.content,span.alt{letter-spacing:-.01em}
+p strong,td.content strong,div.footnote strong{letter-spacing:-.005em}
+p,blockquote,dt,td.content,span.alt{font-size:1.0625rem}
+p{margin-bottom:1.25rem}
+.sidebarblock p,.sidebarblock dt,.sidebarblock td.content,p.tableblock{font-size:1em}
+.exampleblock>.content{background-color:#fffef7;border-color:#e0e0dc;-webkit-box-shadow:0 1px 4px #e0e0dc;box-shadow:0 1px 4px #e0e0dc}
+.print-only{display:none!important}
+@page{margin:1.25cm .75cm}
+@media print{*{-webkit-box-shadow:none!important;box-shadow:none!important;text-shadow:none!important}
+html{font-size:80%}
+a{color:inherit!important;text-decoration:underline!important}
+a.bare,a[href^="#"],a[href^="mailto:"]{text-decoration:none!important}
+a[href^="http:"]:not(.bare)::after,a[href^="https:"]:not(.bare)::after{content:"(" attr(href) ")";display:inline-block;font-size:.875em;padding-left:.25em}
+abbr[title]::after{content:" (" attr(title) ")"}
+pre,blockquote,tr,img,object,svg{page-break-inside:avoid}
+thead{display:table-header-group}
+svg{max-width:100%}
+p,blockquote,dt,td.content{font-size:1em;orphans:3;widows:3}
+h2,h3,#toctitle,.sidebarblock>.content>.title{page-break-after:avoid}
+#toc,.sidebarblock,.exampleblock>.content{background:none!important}
+#toc{border-bottom:1px solid #ddddd8!important;padding-bottom:0!important}
+body.book #header{text-align:center}
+body.book #header>h1:first-child{border:0!important;margin:2.5em 0 1em}
+body.book #header .details{border:0!important;display:block;padding:0!important}
+body.book #header .details span:first-child{margin-left:0!important}
+body.book #header .details br{display:block}
+body.book #header .details br+span::before{content:none!important}
+body.book #toc{border:0!important;text-align:left!important;padding:0!important;margin:0!important}
+body.book #toc,body.book #preamble,body.book h1.sect0,body.book .sect1>h2{page-break-before:always}
+.listingblock code[data-lang]::before{display:block}
+#footer{padding:0 .9375em}
+.hide-on-print{display:none!important}
+.print-only{display:block!important}
+.hide-for-print{display:none!important}
+.show-for-print{display:inherit!important}}
+@media print,amzn-kf8{#header>h1:first-child{margin-top:1.25rem}
+.sect1{padding:0!important}
+.sect1+.sect1{border:0}
+#footer{background:none}
+#footer-text{color:rgba(0,0,0,.6);font-size:.9em}}
+@media amzn-kf8{#header,#content,#footnotes,#footer{padding:0}}
+</style>
+<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
+<style>
+/* Stylesheet for CodeRay to match GitHub theme | MIT License | http://foundation.zurb.com */
+/*pre.CodeRay {background-color:#f7f7f8;}*/
+.CodeRay .line-numbers{border-right:1px solid #d8d8d8;padding:0 0.5em 0 .25em}
+.CodeRay span.line-numbers{display:inline-block;margin-right:.5em;color:rgba(0,0,0,.3)}
+.CodeRay .line-numbers strong{color:rgba(0,0,0,.4)}
+table.CodeRay{border-collapse:separate;border-spacing:0;margin-bottom:0;border:0;background:none}
+table.CodeRay td{vertical-align: top;line-height:1.45}
+table.CodeRay td.line-numbers{text-align:right}
+table.CodeRay td.line-numbers>pre{padding:0;color:rgba(0,0,0,.3)}
+table.CodeRay td.code{padding:0 0 0 .5em}
+table.CodeRay td.code>pre{padding:0}
+.CodeRay .debug{color:#fff !important;background:#000080 !important}
+.CodeRay .annotation{color:#007}
+.CodeRay .attribute-name{color:#000080}
+.CodeRay .attribute-value{color:#700}
+.CodeRay .binary{color:#509}
+.CodeRay .comment{color:#998;font-style:italic}
+.CodeRay .char{color:#04d}
+.CodeRay .char .content{color:#04d}
+.CodeRay .char .delimiter{color:#039}
+.CodeRay .class{color:#458;font-weight:bold}
+.CodeRay .complex{color:#a08}
+.CodeRay .constant,.CodeRay .predefined-constant{color:#008080}
+.CodeRay .color{color:#099}
+.CodeRay .class-variable{color:#369}
+.CodeRay .decorator{color:#b0b}
+.CodeRay .definition{color:#099}
+.CodeRay .delimiter{color:#000}
+.CodeRay .doc{color:#970}
+.CodeRay .doctype{color:#34b}
+.CodeRay .doc-string{color:#d42}
+.CodeRay .escape{color:#666}
+.CodeRay .entity{color:#800}
+.CodeRay .error{color:#808}
+.CodeRay .exception{color:inherit}
+.CodeRay .filename{color:#099}
+.CodeRay .function{color:#900;font-weight:bold}
+.CodeRay .global-variable{color:#008080}
+.CodeRay .hex{color:#058}
+.CodeRay .integer,.CodeRay .float{color:#099}
+.CodeRay .include{color:#555}
+.CodeRay .inline{color:#000}
+.CodeRay .inline .inline{background:#ccc}
+.CodeRay .inline .inline .inline{background:#bbb}
+.CodeRay .inline .inline-delimiter{color:#d14}
+.CodeRay .inline-delimiter{color:#d14}
+.CodeRay .important{color:#555;font-weight:bold}
+.CodeRay .interpreted{color:#b2b}
+.CodeRay .instance-variable{color:#008080}
+.CodeRay .label{color:#970}
+.CodeRay .local-variable{color:#963}
+.CodeRay .octal{color:#40e}
+.CodeRay .predefined{color:#369}
+.CodeRay .preprocessor{color:#579}
+.CodeRay .pseudo-class{color:#555}
+.CodeRay .directive{font-weight:bold}
+.CodeRay .type{font-weight:bold}
+.CodeRay .predefined-type{color:inherit}
+.CodeRay .reserved,.CodeRay .keyword {color:#000;font-weight:bold}
+.CodeRay .key{color:#808}
+.CodeRay .key .delimiter{color:#606}
+.CodeRay .key .char{color:#80f}
+.CodeRay .value{color:#088}
+.CodeRay .regexp .delimiter{color:#808}
+.CodeRay .regexp .content{color:#808}
+.CodeRay .regexp .modifier{color:#808}
+.CodeRay .regexp .char{color:#d14}
+.CodeRay .regexp .function{color:#404;font-weight:bold}
+.CodeRay .string{color:#d20}
+.CodeRay .string .string .string{background:#ffd0d0}
+.CodeRay .string .content{color:#d14}
+.CodeRay .string .char{color:#d14}
+.CodeRay .string .delimiter{color:#d14}
+.CodeRay .shell{color:#d14}
+.CodeRay .shell .delimiter{color:#d14}
+.CodeRay .symbol{color:#990073}
+.CodeRay .symbol .content{color:#a60}
+.CodeRay .symbol .delimiter{color:#630}
+.CodeRay .tag{color:#008080}
+.CodeRay .tag-special{color:#d70}
+.CodeRay .variable{color:#036}
+.CodeRay .insert{background:#afa}
+.CodeRay .delete{background:#faa}
+.CodeRay .change{color:#aaf;background:#007}
+.CodeRay .head{color:#f8f;background:#505}
+.CodeRay .insert .insert{color:#080}
+.CodeRay .delete .delete{color:#800}
+.CodeRay .change .change{color:#66f}
+.CodeRay .head .head{color:#f4f}
+</style>
+<link rel="stylesheet" href="../katex/katex.min.css">
+<script src="../katex/katex.min.js"></script>
+<script src="../katex/contrib/auto-render.min.js"></script>
+    <!-- Use KaTeX to render math once document is loaded, see
+         https://github.com/Khan/KaTeX/tree/master/contrib/auto-render -->
+<script>
+    document.addEventListener("DOMContentLoaded", function () {
+        renderMathInElement(
+            document.body,
+            {
+                delimiters: [
+                    { left: "$$", right: "$$", display: true},
+                    { left: "\\[", right: "\\]", display: true},
+                    { left: "$", right: "$", display: false},
+                    { left: "\\(", right: "\\)", display: false}
+                ]
+            }
+        );
+    });
+</script></head>
+<body class="book toc2 toc-left" style="max-width: 100;">
+<div id="header">
+<h1>The OpenGL ES<sup>&#174;</sup> Shading Language, Version 3.20.5</h1>
+<div class="details">
+<span id="author" class="author">Robert J. Simpson, Qualcomm (Editor) ; John Kessenich, Dave Baldwin and Randi Rost (Version 1.1 Authors)</span><br>
+<span id="revnumber">version 3.20.5,</span>
+<span id="revdate">Wed, 12 Dec 2018 23:37:49 +0000</span>
+<br><span id="revremark">Git branch information not available</span>
+</div>
+<div id="toc" class="toc2">
+<div id="toctitle">Table of Contents</div>
+<ul class="sectlevel1">
+<li><a href="#introduction">1. Introduction</a>
+<ul class="sectlevel2">
+<li><a href="#changes">1.1. Changes</a></li>
+<li><a href="#overview">1.2. Overview</a></li>
+<li><a href="#error-handling">1.3. Error Handling</a></li>
+<li><a href="#typographical-conventions">1.4. Typographical Conventions</a></li>
+<li><a href="#compatibility">1.5. Compatibility</a></li>
+</ul>
+</li>
+<li><a href="#overview-of-opengl-shading">2. Overview of OpenGL ES Shading</a>
+<ul class="sectlevel2">
+<li><a href="#vertex-processor">2.1. Vertex Processor</a></li>
+<li><a href="#tessellation-control-processor">2.2. Tessellation Control Processor</a></li>
+<li><a href="#tessellation-evaluation-processor">2.3. Tessellation Evaluation Processor</a></li>
+<li><a href="#geometry-processor">2.4. Geometry Processor</a></li>
+<li><a href="#fragment-processor">2.5. Fragment Processor</a></li>
+<li><a href="#compute-processor">2.6. Compute Processor</a></li>
+</ul>
+</li>
+<li><a href="#basics">3. Basics</a>
+<ul class="sectlevel2">
+<li><a href="#character-set">3.1. Character Set</a></li>
+<li><a href="#source-strings">3.2. Source Strings</a></li>
+<li><a href="#version-declaration">3.3. Version Declaration</a></li>
+<li><a href="#preprocessor">3.4. Preprocessor</a></li>
+<li><a href="#comments">3.5. Comments</a></li>
+<li><a href="#tokens">3.6. Tokens</a></li>
+<li><a href="#keywords">3.7. Keywords</a></li>
+<li><a href="#identifiers">3.8. Identifiers</a></li>
+<li><a href="#definitions">3.9. Definitions</a></li>
+<li><a href="#logical-phases-of-compilation">3.10. Logical Phases of Compilation</a></li>
+</ul>
+</li>
+<li><a href="#variables-and-types">4. Variables and Types</a>
+<ul class="sectlevel2">
+<li><a href="#basic-types">4.1. Basic Types</a></li>
+<li><a href="#scoping">4.2. Scoping</a></li>
+<li><a href="#storage-qualifiers">4.3. Storage Qualifiers</a></li>
+<li><a href="#layout-qualifiers">4.4. Layout Qualifiers</a></li>
+<li><a href="#interpolation-qualifiers">4.5. Interpolation Qualifiers</a></li>
+<li><a href="#parameter-qualifiers">4.6. Parameter Qualifiers</a></li>
+<li><a href="#precision-and-precision-qualifiers">4.7. Precision and Precision Qualifiers</a></li>
+<li><a href="#variance-and-the-invariant-qualifier">4.8. Variance and the Invariant Qualifier</a></li>
+<li><a href="#the-precise-qualifier">4.9. The Precise Qualifier</a></li>
+<li><a href="#memory-qualifiers">4.10. Memory Qualifiers</a></li>
+<li><a href="#order-of-qualification">4.11. Order and Repetition of Qualification</a></li>
+<li><a href="#empty-declarations">4.12. Empty Declarations</a></li>
+</ul>
+</li>
+<li><a href="#operators-and-expressions">5. Operators and Expressions</a>
+<ul class="sectlevel2">
+<li><a href="#operators">5.1. Operators</a></li>
+<li><a href="#array-operations">5.2. Array Operations</a></li>
+<li><a href="#function-calls">5.3. Function Calls</a></li>
+<li><a href="#constructors">5.4. Constructors</a></li>
+<li><a href="#vector-components">5.5. Vector Components</a></li>
+<li><a href="#matrix-components">5.6. Matrix Components</a></li>
+<li><a href="#structure-and-array-operations">5.7. Structure and Array Operations</a></li>
+<li><a href="#assignments">5.8. Assignments</a></li>
+<li><a href="#expressions">5.9. Expressions</a></li>
+<li><a href="#vector-and-matrix-operations">5.10. Vector and Matrix Operations</a></li>
+<li><a href="#evaluation-of-expressions">5.11. Evaluation of Expressions</a></li>
+</ul>
+</li>
+<li><a href="#statements-and-structure">6. Statements and Structure</a>
+<ul class="sectlevel2">
+<li><a href="#function-definitions">6.1. Function Definitions</a></li>
+<li><a href="#selection">6.2. Selection</a></li>
+<li><a href="#iteration">6.3. Iteration</a></li>
+<li><a href="#jumps">6.4. Jumps</a></li>
+</ul>
+</li>
+<li><a href="#built-in-variables">7. Built-In Variables</a>
+<ul class="sectlevel2">
+<li><a href="#built-in-language-variables">7.1. Built-In Language Variables</a></li>
+<li><a href="#built-in-constants">7.2. Built-In Constants</a></li>
+<li><a href="#built-in-uniform-state">7.3. Built-In Uniform State</a></li>
+<li><a href="#redeclaring-built-in-blocks">7.4. Redeclaring Built-In Blocks</a></li>
+</ul>
+</li>
+<li><a href="#built-in-functions">8. Built-In Functions</a>
+<ul class="sectlevel2">
+<li><a href="#angle-and-trigonometry-functions">8.1. Angle and Trigonometry Functions</a></li>
+<li><a href="#exponential-functions">8.2. Exponential Functions</a></li>
+<li><a href="#common-functions">8.3. Common Functions</a></li>
+<li><a href="#floating-point-pack-and-unpack-functions">8.4. Floating-Point Pack and Unpack Functions</a></li>
+<li><a href="#geometric-functions">8.5. Geometric Functions</a></li>
+<li><a href="#matrix-functions">8.6. Matrix Functions</a></li>
+<li><a href="#vector-relational-functions">8.7. Vector Relational Functions</a></li>
+<li><a href="#integer-functions">8.8. Integer Functions</a></li>
+<li><a href="#texture-functions">8.9. Texture Functions</a></li>
+<li><a href="#atomic-counter-functions">8.10. Atomic Counter Functions</a></li>
+<li><a href="#atomic-memory-functions">8.11. Atomic Memory Functions</a></li>
+<li><a href="#image-functions">8.12. Image Functions</a></li>
+<li><a href="#geometry-shader-functions">8.13. Geometry Shader Functions</a></li>
+<li><a href="#fragment-processing-functions">8.14. Fragment Processing Functions</a></li>
+<li><a href="#shader-invocation-control-functions">8.15. Shader Invocation Control Functions</a></li>
+<li><a href="#shader-memory-control-functions">8.16. Shader Memory Control Functions</a></li>
+</ul>
+</li>
+<li><a href="#shader-interface-matching">9. Shader Interface Matching</a>
+<ul class="sectlevel2">
+<li><a href="#input-output-matching-by-name-in-linked-programs">9.1. Input Output Matching by Name in Linked Programs</a></li>
+<li><a href="#matching-of-qualifiers">9.2. Matching of Qualifiers</a></li>
+</ul>
+</li>
+<li><a href="#shading-language-grammar">10. Shading Language Grammar</a></li>
+<li><a href="#counting-of-inputs-and-outputs">11. Counting of Inputs and Outputs</a></li>
+<li><a href="#acknowledgments">12. Acknowledgments</a></li>
+<li><a href="#references">13. Normative References</a></li>
+</ul>
+</div>
+</div>
+<div id="content">
+<div id="preamble">
+<div class="sectionbody">
+<div style="page-break-after: always;"></div>
+<div class="paragraph">
+<p>Copyright &#169; 2008-2018 The Khronos Group Inc. All Rights Reserved.</p>
+</div>
+<div class="paragraph">
+<p>This specification is protected by copyright laws and contains material
+proprietary to the Khronos Group, Inc. It or any components may not be
+reproduced, republished, distributed, transmitted, displayed, broadcast,
+or otherwise exploited in any manner without the express prior written
+permission of Khronos Group. You may use this specification for
+implementing the functionality therein, without altering or removing any
+trademark, copyright or other notice from the specification, but the
+receipt or possession of this specification does not convey any rights
+to reproduce, disclose, or distribute its contents, or to manufacture,
+use, or sell anything that it may describe, in whole or in part.</p>
+</div>
+<div class="paragraph">
+<p>Khronos Group grants express permission to any current Promoter,
+Contributor or Adopter member of Khronos to copy and redistribute
+UNMODIFIED versions of this specification in any fashion, provided that
+NO CHARGE is made for the specification and the latest available update
+of the specification for any version of the API is used whenever
+possible. Such distributed specification may be reformatted AS LONG AS
+the contents of the specification are not changed in any way. The
+specification may be incorporated into a product that is sold as long as
+such product includes significant independent work developed by the
+seller. A link to the current version of this specification on the
+Khronos Group website should be included whenever possible with
+specification distributions.</p>
+</div>
+<div class="paragraph">
+<p>Khronos Group makes no, and expressly disclaims any, representations or
+warranties, express or implied, regarding this specification, including,
+without limitation, any implied warranties of merchantability or fitness
+for a particular purpose or noninfringement of any intellectual
+property. Khronos Group makes no, and expressly disclaims any,
+warranties, express or implied, regarding the correctness, accuracy,
+completeness, timeliness, and reliability of the specification. Under no
+circumstances will the Khronos Group, or any of its Promoters,
+Contributors or Members or their respective partners, officers,
+directors, employees, agents, or representatives be liable for any
+damages, whether direct, indirect, special or consequential damages for
+lost revenues, lost profits, or otherwise, arising from or in connection
+with these materials.</p>
+</div>
+<div class="paragraph">
+<p>Khronos, Vulkan, SYCL, SPIR, WebGL, EGL, COLLADA, StreamInput, OpenVX,
+OpenKCam, glTF, OpenKODE, OpenVG, OpenWF, OpenSL ES, OpenMAX, OpenMAX
+AL, OpenMAX IL and OpenMAX DL are trademarks and WebCL is a
+certification mark of the Khronos Group Inc. OpenCL is a trademark of
+Apple Inc. and OpenGL and OpenML are registered trademarks and the
+OpenGL ES and OpenGL SC logos are trademarks of Silicon Graphics
+International used under license by Khronos. All other product names,
+trademarks, and/or company names are used solely for identification and
+belong to their respective owners.</p>
+</div>
+<div style="page-break-after: always;"></div>
+<!-- toc disabled -->
+</div>
+</div>
+<div class="sect1">
+<h2 id="introduction">1. Introduction</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>This document specifies only version 3.20 of the OpenGL ES Shading Language.
+It requires __VERSION__ to substitute 320, and requires
+<strong>#version</strong> to accept only
+<code>320 es</code>.
+If <strong>#version</strong> is declared with a smaller number, the language accepted is a
+previous version of the shading language, which will be supported depending
+on the version and type of context in the OpenGL ES API.
+See the <a href="#references">OpenGL ES Specification</a> for details on what language versions are
+supported.</p>
+</div>
+<div class="paragraph">
+<p>All references in this specification to the <a href="#references">OpenGL ES Specification</a> are to
+version 3.2.</p>
+</div>
+<div class="sect2">
+<h3 id="changes">1.1. Changes</h3>
+<div class="sect3">
+<h4 id="changes-from-glsl-es-3.2-revision-4">1.1.1. Changes from GLSL ES 3.2 revision 4</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Clarified that this specification completely defines the OpenGL ES Shading Language.
+Normatively reference C++ only for the preprocessor.</p>
+</li>
+<li>
+<p>Private GLSL issues 7, 38: Corrected the values of some builtin constants.
+The values were given correctly in the OpenGL ES Specification.</p>
+</li>
+<li>
+<p>Private GLSL issue 30: Clarify that output packing rules apply to the last
+vertex pipeline stage, not necessarily the vertex stage.</p>
+</li>
+<li>
+<p>Private GLSL issue 15: Clarify the ordering of bindings for arrays of arrays.</p>
+</li>
+<li>
+<p>Private GLSL issue 14: Uniform variables need only match at link time if they
+are statically used.</p>
+</li>
+<li>
+<p>For <strong>precise</strong> computations, the controlling expressions for
+control flow and ternary operators (<strong>?:</strong>) are not included.</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="changes-from-glsl-es-3.2-revision-3">1.1.2. Changes from GLSL ES 3.2 revision 3</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Matching of default uniforms when shaders are linked.</p>
+</li>
+<li>
+<p><em>gl_DepthRange</em> is only guaranteed to be available in the fragment
+stage.</p>
+</li>
+<li>
+<p>Clarification of definition of static use.</p>
+</li>
+<li>
+<p>Sampling behavior in the absence of <strong>sample</strong> and <strong>centroid</strong>.</p>
+</li>
+<li>
+<p>Clarified the requirements when the specification uses the terms
+<em>should</em>/<em>should not</em> and <em>undefined behavior</em>.</p>
+</li>
+<li>
+<p>Arrayed blocks cannot have layout location qualifiers on members</p>
+</li>
+<li>
+<p><strong>barrier</strong>() defines a partial order which includes tessellation control
+shader outputs.</p>
+</li>
+<li>
+<p>Vertex shader integer output qualification.</p>
+</li>
+<li>
+<p>Incorrect use of predefined pragmas.</p>
+</li>
+<li>
+<p>Clarified use of <strong>readonly</strong> and <strong>writeonly</strong> qualifiers.</p>
+</li>
+<li>
+<p>USAMPLERBUFFER added to grammar.</p>
+</li>
+<li>
+<p>Clarified precision qualifiers can be used in interface blocks.</p>
+</li>
+<li>
+<p>Clarified <strong>memoryBarrierShared</strong> only applies to the current workgroup.</p>
+</li>
+<li>
+<p>The layout qualifier <em>invocations</em> must not be zero.</p>
+</li>
+<li>
+<p>The layout qualifier <em>local_size</em> must not be zero.</p>
+</li>
+<li>
+<p>Clarified the definition of static assignment.</p>
+</li>
+<li>
+<p>Removed list of types with no default precision.</p>
+</li>
+<li>
+<p>Removed scoping rules from the grammar. Refer instead to the <a href="#scoping">scoping</a> section.</p>
+</li>
+<li>
+<p>Require a statement after the final label of a switch.</p>
+</li>
+<li>
+<p>Define <strong>gl_BoundingBox</strong>.</p>
+</li>
+<li>
+<p><strong>length</strong>() expressions returning a constant-value may not include side effects.</p>
+</li>
+<li>
+<p>Clarified that variables may be declared <strong>readonly writeonly</strong>.</p>
+</li>
+<li>
+<p>Use of constant expressions within <strong>#line</strong> directives is undefined.</p>
+</li>
+<li>
+<p><strong>gl_in</strong> can be redeclared using unsized-array syntax.</p>
+</li>
+<li>
+<p>Clarified which sampler types may be used for depth and stencil textures.</p>
+</li>
+<li>
+<p>Added order-of-operation and other explanations to the
+<a href="#the-precise-qualifier">Precise Qualifier</a> section.</p>
+</li>
+<li>
+<p>The <strong>precise</strong> qualifier applied to a block/struct applies recursively to the members.</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="changes-from-glsl-es-3.2-revision-2">1.1.3. Changes from GLSL ES 3.2 revision 2</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Updated value for <em>gl_MaxTessControlTotalOutputComponents</em></p>
+</li>
+<li>
+<p>Clarified the allowed character set for pre-processing</p>
+</li>
+<li>
+<p>Integer division wrapping behavior</p>
+</li>
+<li>
+<p>Clarified pre-processor expressions (<em>pp-constant-expression</em>)</p>
+</li>
+<li>
+<p>UBO and SSBO precisions do not need to match for linked shaders
+(consistent with GLSL ES 3.1)</p>
+</li>
+<li>
+<p><strong>modf</strong> function</p>
+</li>
+<li>
+<p>Sequence and ternary operators with <strong>void</strong> type</p>
+</li>
+<li>
+<p>Sequence and ternary operators with array types</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="changes-from-glsl-es-3.2-revision-1">1.1.4. Changes from GLSL ES 3.2 revision 1</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Signed zeros must be supported</p>
+</li>
+<li>
+<p>Layout qualifier table</p>
+</li>
+<li>
+<p>Allowed optimizations when evaluating expressions</p>
+</li>
+<li>
+<p>Updated value for <em>gl_MaxTessControlInputComponents</em></p>
+</li>
+<li>
+<p>Updated value for <em>gl_MaxTessControlOutputComponents</em></p>
+</li>
+<li>
+<p>Updated value for <em>gl_MaxTessEvaluationInputComponents</em></p>
+</li>
+<li>
+<p>Updated value for <em>gl_MaxTessEvaluationOutputComponents</em></p>
+</li>
+<li>
+<p>Updated value for <em>gl_MaxGeometryOutputComponents</em></p>
+</li>
+<li>
+<p>Require precisions in blocks to match when linking</p>
+</li>
+<li>
+<p>Updated conclusions in issues section</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="changes-from-glsl-es-3.1-revision-4">1.1.5. Changes from GLSL ES 3.1 revision 4</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Added the following extensions:</p>
+<div class="ulist">
+<ul>
+<li>
+<p><a href="https://www.opengl.org/registry/specs/KHR/blend_equation_advanced.txt">KHR_blend_equation_advanced</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_sample_variables.txt">OES_sample_variables</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_shader_image_atomic.txt">OES_shader_image_atomic</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_shader_multisample_interpolation.txt">OES_shader_multisample_interpolation</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_texture_storage_multisample_2d_array.txt">OES_texture_storage_multisample_2d_array</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_geometry_shader.txt">OES_geometry_shader</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_gpu_shader5.txt">OES_gpu_shader5</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_primitive_bounding_box.txt">OES_primitive_bounding_box</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_shader_io_blocks.txt">OES_shader_io_blocks</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_tessellation_shader.txt">OES_tessellation_shader</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_texture_buffer.txt">OES_texture_buffer</a></p>
+</li>
+<li>
+<p><a href="https://www.khronos.org/registry/gles/extensions/OES/OES_texture_cube_map_array.txt">OES_texture_cube_map_array</a></p>
+</li>
+<li>
+<p><a href="https://www.opengl.org/registry/specs/KHR/robustness.txt">KHR_robustness</a></p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="overview">1.2. Overview</h3>
+<div class="paragraph">
+<p>This document describes <em>The OpenGL ES Shading Language, version 3.20</em>.</p>
+</div>
+<div class="paragraph">
+<p>Independent compilation units written in this language are called <em>shaders</em>.
+A <em>program</em> is a set of shaders that are compiled and linked
+together.
+The aim of this document is to thoroughly specify the programming language.
+The <a href="#references">OpenGL ES Specification</a> will specify the OpenGL ES entry points used to
+manipulate and communicate with programs and shaders.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="error-handling">1.3. Error Handling</h3>
+<div class="paragraph">
+<p>Compilers, in general, accept programs that are ill-formed, due to the
+impossibility of detecting all ill-formed programs.
+Portability is only ensured for well-formed programs, which this
+specification describes.
+Compilers are encouraged to detect ill-formed programs and issue diagnostic
+messages, but are not required to do so for all cases.</p>
+</div>
+<div class="paragraph">
+<p>The compilation process is implementation-dependent but is generally split
+into a number of stages, each of which occurs at one of the following times:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A call to <em>glCompileShader</em></p>
+</li>
+<li>
+<p>A call to <em>glLinkProgram</em></p>
+</li>
+<li>
+<p>A draw call or a call to <em>glValidateProgram</em></p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The implementation should report errors as early a possible but in any case
+must satisfy the following:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>All lexical, grammatical and semantic errors must have been detected
+following a call to <em>glLinkProgram</em></p>
+</li>
+<li>
+<p>Errors due to mismatch between the shaders (link-time errors) must have
+been detected following a call to <em>glLinkProgram</em></p>
+</li>
+<li>
+<p>Errors due to exceeding resource limits must have been detected
+following any draw call or a call to <em>glValidateProgram</em></p>
+</li>
+<li>
+<p>A call to <em>glValidateProgram</em> must report all errors associated with a
+program object given the current GL state.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Where the specification uses the terms <em>required</em>, <em>must</em>/<em>must</em> <em>not</em>,
+<em>does</em>/<em>does</em> <em>not</em>, <em>disallowed</em>, or <em>not</em> <em>supported</em>, the compiler or
+linker is required to detect and report any violations.
+Similarly when a condition or situation is an <strong>error</strong>, it must be reported.
+Use of any feature marked as <em>reserved</em> is an error.
+Where the specification uses the terms <em>should</em>/<em>should</em> <em>not</em>, <em>undefined</em>
+<em>behavior</em>, <em>undefined</em> <em>value</em> or <em>undefined</em> <em>*results*</em>, implementations
+will not produce a compile-time error but are encouraged to issue a warning
+for violations.
+The run-time behavior of the program in these cases is not constrained (and
+so may include termination or system instability).
+It is expected that systems will be designed to handle these cases
+gracefully but specification of this is outside the scope of OpenGL ES.</p>
+</div>
+<div class="paragraph">
+<p>Implementations may not in general support functionality beyond the mandated
+parts of the specification without use of the relevant extension.
+The only exceptions are:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>If a feature is marked as optional.</p>
+</li>
+<li>
+<p>Where a maximum value is stated (e.g. the maximum number of vertex
+outputs), the implementation may support a higher value than that
+specified.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Where the implementation supports more than the mandated specification,
+off-target compilers are encouraged to issue warnings if these features are
+used.</p>
+</div>
+<div class="paragraph">
+<p>The compilation process is split between the compiler and linker.
+The allocation of tasks between the compiler and linker is implementation
+dependent.
+Consequently there are many errors which may be detected either at compile
+or link time, depending on the implementation.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="typographical-conventions">1.4. Typographical Conventions</h3>
+<div class="paragraph">
+<p>Italic, bold, and font choices have been used in this specification
+primarily to improve readability.
+Code fragments use a fixed width font.
+Identifiers embedded in text are italicized.
+Keywords embedded in text are bold.
+Operators are called by their name, followed by their symbol in bold in
+parentheses.
+The clarifying grammar fragments in the text use bold for literals and
+italics for non-terminals.
+The official grammar in &#8220;<a href="#shading-language-grammar">Shading Language
+Grammar</a>&#8221; uses all capitals for terminals and lower case for
+non-terminals.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="compatibility">1.5. Compatibility</h3>
+<div class="paragraph">
+<p>The OpenGL ES 3.2 API is designed to work with GLSL ES v1.00, GLSL
+ES 3.00, GLSL ES 3.10 and GLSL ES 3.20.
+In general a shader written for versions prior to OpenGL ES 3.2
+should work without modification in OpenGL ES 3.2.</p>
+</div>
+<div class="paragraph">
+<p>When porting applications from an earlier to later version of the API, the
+following points should be noted:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Not all language constructs present in earlier versions of the language
+are available in later versions e.g. attribute and varying qualifiers
+are present in v1.00 but not v3.00.
+However, the functionality of GLSL ES 3.20 is a super-set of GLSL
+ES 3.10.</p>
+</li>
+<li>
+<p>Some features of later versions of the API require language features
+that are not present in earlier version of the language.</p>
+</li>
+<li>
+<p>It is an error to link shaders if they are written in different versions
+of the language.</p>
+</li>
+<li>
+<p>The OpenGL ES 2.0 and 3.0 APIs do not support shaders written in GLSL ES
+3.20.</p>
+</li>
+<li>
+<p>Using GLSL ES 1.00 shaders within OpenGL ES 3.x may extend the resources
+available beyond the minima specified in GLSL ES 1.0.
+Shaders which make use of this will not necessarily run on an OpenGL ES
+2.0 implementation: Similarly for GLSL ES 3.00 shaders running within
+OpenGL ES 3.2.</p>
+</li>
+<li>
+<p>Support of line continuation and support of UTF-8 characters within
+comments is optional in GLSL ES 1.00 when used with the OpenGL ES 2.0
+API.
+However, support is mandated for both of these when a GLSL ES 1.00
+shader is used with the OpenGL ES 3.x APIs.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="overview-of-opengl-shading">2. Overview of OpenGL ES Shading</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The OpenGL ES Shading Language is actually several closely related languages.
+These languages are used to create shaders for each of the programmable
+processors contained in the OpenGL ES processing pipeline.
+Currently, these processors are the vertex, tessellation control,
+tessellation evaluation, geometry, fragment, and compute processors.</p>
+</div>
+<div class="paragraph">
+<p>Compilation units for these processors are referred to as <em>shaders</em> and the
+processors themselves are also referred to as <em>shader stages</em>.
+Only one shader can be run on a processor at any one time; there is no
+support for linking multiple compilation units together for a single shader
+stage.
+One or more shaders are linked together to form a single program and each
+program contains shader <em>executables</em> for one or more consecutive shader
+stages.</p>
+</div>
+<div class="paragraph">
+<p>Unless otherwise noted in this paper, a language feature applies to all
+languages, and common usage will refer to these languages as a single
+language.
+The specific languages will be referred to by the name of the processor they
+target: vertex, tessellation control, tessellation evaluation, geometry,
+fragment, or compute.</p>
+</div>
+<div class="paragraph">
+<p>Most OpenGL ES state is not tracked or made available to shaders.
+Typically, user-defined variables will be used for communicating between
+different stages of the OpenGL ES pipeline.
+However, a small amount of state is still tracked and automatically made
+available to shaders, and there are a few built-in variables for interfaces
+between different stages of the OpenGL ES pipeline.</p>
+</div>
+<div class="sect2">
+<h3 id="vertex-processor">2.1. Vertex Processor</h3>
+<div class="paragraph">
+<p>The <em>vertex processor</em> is a programmable unit that operates on incoming
+vertices and their associated data.
+Compilation units written in the OpenGL ES Shading Language to run on this processor are called
+<em>vertex shaders</em>.</p>
+</div>
+<div class="paragraph">
+<p>The vertex processor operates on one vertex at a time.
+It does not replace graphics operations that require knowledge of several
+vertices at a time.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="tessellation-control-processor">2.2. Tessellation Control Processor</h3>
+<div class="paragraph">
+<p>The <em>tessellation control processor</em> is a programmable unit that operates on
+a patch of incoming vertices and their associated data, emitting a new
+output patch.
+Compilation units written in the OpenGL ES Shading Language to run on this processor are called
+tessellation control shaders.</p>
+</div>
+<div class="paragraph">
+<p>The tessellation control shader is invoked for each vertex of the output
+patch.
+Each invocation can read the attributes of any vertex in the input or output
+patches, but can only write per-vertex attributes for the corresponding
+output patch vertex.
+The shader invocations collectively produce a set of per-patch attributes
+for the output patch.</p>
+</div>
+<div class="paragraph">
+<p>After all tessellation control shader invocations have completed, the output
+vertices and per-patch attributes are assembled to form a patch to be used
+by subsequent pipeline stages.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control shader invocations run mostly independently, with
+undefined relative execution order.
+However, the built-in function <strong>barrier</strong>() can be used to control execution
+order by synchronizing invocations, effectively dividing tessellation
+control shader execution into a set of phases.
+Tessellation control shaders will get undefined results if one invocation
+reads from a per-vertex or per-patch attribute written by another invocation
+at any point during the same phase, or if two invocations attempt to write
+different values to the same per-patch output
+in a single phase.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="tessellation-evaluation-processor">2.3. Tessellation Evaluation Processor</h3>
+<div class="paragraph">
+<p>The <em>tessellation evaluation processor</em> is a programmable unit that
+evaluates the position and other attributes of a vertex generated by the
+tessellation primitive generator, using a patch of incoming vertices and
+their associated data.
+Compilation units written in the OpenGL ES Shading Language to run on this processor are called
+tessellation evaluation shaders.</p>
+</div>
+<div class="paragraph">
+<p>Each invocation of the tessellation evaluation executable computes the
+position and attributes of a single vertex generated by the tessellation
+primitive generator.
+The executable can read the attributes of any vertex in the input patch,
+plus the tessellation coordinate, which is the relative location of the
+vertex in the primitive being tessellated.
+The executable writes the position and other attributes of the vertex.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="geometry-processor">2.4. Geometry Processor</h3>
+<div class="paragraph">
+<p>The <em>geometry processor</em> is a programmable unit that operates on data for
+incoming vertices for a primitive assembled after vertex processing and
+outputs a sequence of vertices forming output primitives.
+Compilation units written in the OpenGL ES Shading Language to run on this processor are called
+<em>geometry shaders</em>.</p>
+</div>
+<div class="paragraph">
+<p>A single invocation of the geometry shader executable on the geometry
+processor will operate on a declared input primitive with a fixed number of
+vertices.
+This single invocation can emit a variable number of vertices that are
+assembled into primitives of a declared output primitive type and passed to
+subsequent pipeline stages.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="fragment-processor">2.5. Fragment Processor</h3>
+<div class="paragraph">
+<p>The <em>fragment processor</em> is a programmable unit that operates on fragment
+values and their associated data.
+Compilation units written in the OpenGL ES Shading Language to run on this processor are called
+<em>fragment shaders</em>.</p>
+</div>
+<div class="paragraph">
+<p>A fragment shader cannot change a fragment&#8217;s (<em>x</em>, <em>y</em>) position.
+Access to neighboring fragments is not allowed.
+The values computed by the fragment shader are ultimately used to update
+framebuffer memory or texture memory, depending on the current OpenGL ES
+state and the OpenGL ES command that caused the fragments to be generated.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="compute-processor">2.6. Compute Processor</h3>
+<div class="paragraph">
+<p>The <em>compute processor</em> is a programmable unit that operates independently
+from the other shader processors.
+Compilation units written in the OpenGL ES Shading Language to run on this processor are called
+<em>compute shaders</em>.</p>
+</div>
+<div class="paragraph">
+<p>A compute shader has access to many of the same resources as fragment and
+other shader processors, such as textures, buffers, image variables, and
+atomic counters.
+It does not have fixed-function outputs.
+It is not part of the graphics pipeline and its visible side effects are
+through changes to images, storage buffers, and atomic counters.</p>
+</div>
+<div class="paragraph">
+<p>A compute shader operates on a group of work items called a <em>workgroup</em>.
+A workgroup is a collection of shader invocations that execute the same
+code, potentially in parallel.
+An invocation within a workgroup may share data with other members of the
+same workgroup through shared variables and issue memory and control flow
+barriers to synchronize with other members of the same workgroup.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="basics">3. Basics</h2>
+<div class="sectionbody">
+<div class="sect2">
+<h3 id="character-set">3.1. Character Set</h3>
+<div class="paragraph">
+<p>The source character set used for the OpenGL ES Shading Language is Unicode in the UTF-8
+encoding scheme.
+Invalid UTF-8 characters are ignored.
+During pre-processing, the following applies:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A byte with the value zero is always interpreted as the end of the
+string</p>
+</li>
+<li>
+<p>Backslash ('\'), is used to indicate line continuation when immediately
+preceding a new-line.</p>
+</li>
+<li>
+<p>White space consists of one or more of the following characters: the
+space character, horizontal tab, vertical tab, form feed,
+carriage-return, line-feed.</p>
+</li>
+<li>
+<p>The number sign (<strong>#</strong>) is used for preprocessor directives</p>
+</li>
+<li>
+<p>Macro names are restricted to:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>The letters <strong>a-z</strong>, <strong>A-Z</strong>, and the underscore (<strong>_</strong>).</p>
+</li>
+<li>
+<p>The numbers <strong>0-9</strong>, except for the first character of a macro name.</p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>After preprocessing, only the following characters are allowed in the
+resulting stream of GLSL tokens:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The letters <strong>a-z</strong>, <strong>A-Z</strong>, and the underscore (<strong>_</strong>).</p>
+</li>
+<li>
+<p>The numbers <strong>0-9</strong>.</p>
+</li>
+<li>
+<p>The symbols period (<strong>.</strong>), plus (<strong>+</strong>), dash (<strong>-</strong>), slash (<strong>/</strong>), asterisk
+(<strong>*</strong>), percent (<strong>%</strong>), angled brackets (<strong>&lt;</strong> and <strong>&gt;</strong>), square brackets
+(<strong>[</strong> and <strong>]</strong>), parentheses (<strong>(</strong> and <strong>)</strong>), braces (<strong>{</strong> and <strong>}</strong>), caret
+(<strong>^</strong>), vertical bar (<strong>|</strong>), ampersand (<strong>&amp;</strong>), tilde (<strong>~</strong>), equals (<strong>=</strong>),
+exclamation point (<strong>!</strong>), colon (<strong>:</strong>), semicolon (<strong>;</strong>), comma (<strong>,</strong>), and
+question mark (<strong>?</strong>).</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>There are no digraphs or trigraphs.
+There are no escape sequences or other uses of the backslash beyond use as
+the line-continuation character.</p>
+</div>
+<div class="paragraph">
+<p>Lines are relevant for compiler diagnostic messages and the preprocessor.
+They are terminated by carriage-return or line-feed.
+If both are used together, it will count as only a single line termination.
+For the remainder of this document, any of these combinations is simply
+referred to as a new-line.
+Lines may be of arbitrary length.</p>
+</div>
+<div class="paragraph">
+<p>In general, the language&#8217;s use of this character set is case sensitive.</p>
+</div>
+<div class="paragraph">
+<p>There are no character or string data types, so no quoting characters are
+included.</p>
+</div>
+<div class="paragraph">
+<p>There is no end-of-file character.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="source-strings">3.2. Source Strings</h3>
+<div class="paragraph">
+<p>The source for a single shader is an array of strings of characters from the
+character set.
+A single shader is made from the concatenation of these strings.
+Each string can contain multiple lines, separated by new-lines.
+No new-lines need be present in a string; a single line can be formed from
+multiple strings.
+No new-lines or other characters are inserted by the implementation when it
+concatenates the strings to form a single shader.</p>
+</div>
+<div class="paragraph">
+<p>Diagnostic messages returned from compiling a shader must identify both the
+line number within a string and which source string the message applies to.
+Source strings are counted sequentially with the first string being string
+0.
+Line numbers are one more than the number of new-lines that have been
+processed, including counting the new-lines that will be removed by the
+line-continuation character (<strong>\</strong>).</p>
+</div>
+<div class="paragraph">
+<p>Lines separated by the line-continuation character preceding a new-line are
+concatenated together before either comment processing or preprocessing.
+This means that no white space is substituted for the line-continuation
+character.
+That is, a single token could be formed by the concatenation by taking the
+characters at the end of one line concatenating them with the characters at
+the beginning of the next line.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> f\
+oo;
+<span class="comment">// forms a single line equivalent to &quot;float foo;&quot;</span>
+<span class="comment">// (assuming '\' is the last character before the new-line and &quot;oo&quot; are</span>
+<span class="comment">// the first two characters of the next line)</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="version-declaration">3.3. Version Declaration</h3>
+<div class="paragraph">
+<p>Shaders must declare the version of the language they are written to.
+The version is specified in the first line of a shader by a character
+string:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#version</span> number es</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>number</em> must be a version of the language, following the same
+convention as __VERSION__ above.
+The directive &#8220;<strong>#version 320 es</strong>&#8221; is required in any shader that
+uses version 3.20 of the language.
+Any <em>number</em> representing a version of the language a compiler does not
+support will cause an error to be generated.
+Version 1.00 of the language does not require shaders to include this
+directive, and shaders that do not include a <strong>#version</strong> directive will be
+treated as targeting version 1.00.</p>
+</div>
+<div class="paragraph">
+<p>Shaders declaring version 3.20 of the shading language cannot be
+linked with shaders declaring a previous version.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>#version</strong> directive must be present in the first line of a shader and
+must be followed by a newline.
+It may contain optional white-space as specified below but no other
+characters are allowed.
+The directive is only permitted in the first line of a shader.</p>
+</div>
+<div class="paragraph">
+<p>Processing of the #version directive occurs before all other preprocessing,
+including line concatenation and comment processing.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>version-declaration</em> : </dt>
+<dd>
+<p><em>whitespace<sub>opt</sub></em> POUND <em>whitespace<sub>opt</sub></em> VERSION <em>whitespace</em> <em>number</em>
+<em>whitespace</em> ES <em>whitespace<sub>opt</sub></em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Tokens:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>POUND <strong>#</strong><br>
+VERSION <strong>version</strong><br>
+ES <strong>es</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+<div class="sect2">
+<h3 id="preprocessor">3.4. Preprocessor</h3>
+<div class="paragraph">
+<p>There is a preprocessor that processes the source strings as part of the
+compilation process.
+Except as noted below, it behaves as the C++ standard preprocessor (see
+&#8220;<a href="#references">Normative References</a>&#8221;).</p>
+</div>
+<div class="paragraph">
+<p>The complete list of preprocessor directives is as follows.</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#<br>
+#define<br>
+#undef<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#if<br>
+#ifdef<br>
+#ifndef<br>
+#else<br>
+#elif<br>
+#endif<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#error<br>
+#pragma<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#extension<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#line</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The following
+operator is
+also available:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>defined<br></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Note that the version directive is not considered to be a preprocessor
+directive and so is not listed here.</p>
+</div>
+<div class="paragraph">
+<p>Each number sign (<strong>#</strong>) can be preceded in its line only by spaces or
+horizontal tabs.
+It may also be followed by spaces and horizontal tabs, preceding the
+directive.
+Each directive is terminated by a new-line.
+Preprocessing does not change the number or relative location of new-lines
+in a source string.</p>
+</div>
+<div class="paragraph">
+<p>The number sign (<strong>#</strong>) on a line by itself is ignored.
+Any directive not listed above will cause an error.</p>
+</div>
+<div class="paragraph">
+<p><strong>#define</strong> and <strong>#undef</strong> functionality are defined as is standard for C++
+preprocessors for macro definitions both with and without macro parameters.</p>
+</div>
+<div class="paragraph">
+<p>The following predefined macros are available:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>__LINE__<br>
+__FILE__<br>
+__VERSION__<br>
+GL_ES</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>__LINE__ will substitute a decimal integer constant that is one more than
+the number of preceding new-lines in the current source string.</p>
+</div>
+<div class="paragraph">
+<p>__FILE__ will substitute a decimal integer constant that says which source
+string number is currently being processed.</p>
+</div>
+<div class="paragraph">
+<p>__VERSION__ will substitute a decimal integer reflecting the version
+number of the OpenGL ES Shading Language.
+The version of the shading language described in this document will have
+__VERSION__ substitute the decimal integer 320.</p>
+</div>
+<div class="paragraph">
+<p>GL_ES will be defined and set to 1.
+This is not true for the non-ES OpenGL Shading Language, so it can be used
+to do a compile time test to determine if a shader is running on an ES
+system.</p>
+</div>
+<div class="paragraph">
+<p>By convention, all macro names containing two consecutive underscores (__)
+are reserved for use by underlying software layers.
+Defining
+such a name in a shader does not itself result in an error, but may
+result in unintended behaviors that stem from having multiple definitions of
+the same name.
+All macro names prefixed with &#8220;GL_&#8221; (&#8220;GL&#8221; followed by a single
+underscore) are also reserved, and defining
+such a name results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>It is an error to undefine or to redefine a built-in (pre-defined) macro
+name.</p>
+</div>
+<div class="paragraph">
+<p>Implementations must support macro-name lengths of up to 1024 characters.
+It is an error to declare a name with a length greater than this.</p>
+</div>
+<div class="paragraph">
+<p><strong>#if</strong>, <strong>#ifdef</strong>, <strong>#ifndef</strong>, <strong>#else</strong>, <strong>#elif</strong>, and <strong>#endif</strong> are defined to
+operate as is standard for C++ preprocessors except for the following:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Expressions following <strong>#if</strong> and <strong>#elif</strong> are
+restricted to <em>pp-constant-expressions</em> as defined below.</p>
+</li>
+<li>
+<p>Undefined identifiers not consumed by the <strong>defined</strong> operator do not
+default to '0'.
+Use of such identifiers causes an error.</p>
+</li>
+<li>
+<p>Character constants are not supported.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>As in C++, a macro name defined with an empty replacement list does not
+default to '0' when used in a preprocessor expression.</p>
+</div>
+<div class="paragraph">
+<p>A <em>pp-constant-expression</em> is an integral expression, evaluated at
+compile-time during preprocessing and formed from literal integer constants
+and the following operators:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Precedence</th>
+<th class="tableblock halign-left valign-top">Operator class</th>
+<th class="tableblock halign-left valign-top">Operators</th>
+<th class="tableblock halign-left valign-top">Associativity</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1 (highest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">parenthetical grouping</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">( )</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">NA</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">unary</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">defined<br>
+                                         + - ~ !</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">multiplicative</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">* / %</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">additive</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">+ -</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise shift</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;&lt; &gt;&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">relational</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt; &gt; &lt;= &gt;=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">7</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">equality</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">== !=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">8</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">9</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise exclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">^</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">10</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">|</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">11</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">12 (lowest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">||</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The <strong>defined</strong> operator can be used in either of the following ways:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">defined identifier
+defined ( identifier )</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There are no number sign based operators (e.g. no <strong><mark></strong> or <strong></mark>@</strong>), no <strong>##</strong>
+operator, nor is there a <strong>sizeof</strong> operator.</p>
+</div>
+<div class="paragraph">
+<p>The semantics of applying operators in the preprocessor match those standard
+in the C++ preprocessor with the following exceptions:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The 2<sup>nd</sup> operand in a logical and ('&amp;&amp;') operation is evaluated if and
+only if the 1<sup>st</sup> operand evaluates to non-zero.</p>
+</li>
+<li>
+<p>The 2<sup>nd</sup> operand in a logical or ('||') operation is evaluated if and
+only if the 1<sup>st</sup> operand evaluates to zero.</p>
+</li>
+<li>
+<p>There is no boolean type and no boolean literals.
+A <em>true</em> or <em>false</em> result is returned as integer <em>one</em> or <em>zero</em>
+respectively.
+Wherever a boolean operand is expected, any non-zero integer is
+interpreted as <em>true</em> and a zero integer as <em>false</em>.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>If an operand is not evaluated, the presence of undefined identifiers in the
+operand will not cause an error.</p>
+</div>
+<div class="paragraph">
+<p><strong>#error</strong> will cause the implementation to put a compile-time diagnostic message
+into the shader object&#8217;s information log (see section 7.12 &#8220;Shader, Program
+and Program Pipeline Queries&#8221; of the <a href="#references">OpenGL ES Specification</a> for how to
+access a shader object&#8217;s information log).
+The message will be the tokens following the <strong>#error</strong> directive, up to the
+first new-line.
+The implementation must treat the presence of a <strong>#error</strong> directive as a
+compile-time error.</p>
+</div>
+<div class="paragraph">
+<p><strong>#pragma</strong> allows implementation-dependent compiler control.
+Tokens following <strong>#pragma</strong> are not subject to preprocessor macro expansion.
+If an implementation does not recognize the tokens following <strong>#pragma</strong>, then
+it will ignore that pragma.
+The following pragmas are defined as part of the language.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> STDGL</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>STDGL</strong> pragma is used to reserve pragmas for use by future revisions of
+this language.
+No implementation may use a pragma whose first token is <strong>STDGL</strong>.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> optimize(on)
+<span class="preprocessor">#pragma</span> optimize(off)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>can be used to turn off optimizations as an aid in developing and debugging
+shaders.
+It can only be used outside function definitions.
+By default, optimization is turned on for all shaders.
+The debug pragma</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> debug(on)
+<span class="preprocessor">#pragma</span> debug(off)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>can be used to enable compiling and annotating a shader with debug
+information, so that it can be used with a debugger.
+It can only be used outside function definitions.
+By default, debug is turned off.</p>
+</div>
+<div class="paragraph">
+<p>The scope as well as the effect of the optimize and debug pragmas is
+implementation-dependent except that their use must not generate an error.
+Incorrect use of predefined pragmas does not cause an error.</p>
+</div>
+<div class="paragraph">
+<p>By default, compilers of this language must issue compile-time
+syntactic, semantic,
+and
+grammatical errors for shaders that do not conform to this specification.
+Any extended behavior must first be enabled.
+Directives to control the behavior of the compiler with respect to
+extensions are declared with the <strong>#extension</strong> directive</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#extension</span> extension_name : behavior
+<span class="preprocessor">#extension</span> all : behavior</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>extension_name</em> is the name of an extension.
+Extension names are not documented in this specification.
+The token <strong>all</strong> means the behavior applies to all extensions supported by
+the compiler.
+The <em>behavior</em> can be one of the following:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Behavior</th>
+<th class="tableblock halign-left valign-top">Effect</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>require</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave as specified by the extension <em>extension_name</em>.<br>
+              Give a compile-time error on the <strong>#extension</strong> if the extension
+              <em>extension_name</em> is not supported, or if <strong>all</strong> is specified.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>enable</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave as specified by the extension <em>extension_name</em>.<br>
+              Warn on the <strong>#extension</strong> if the extension <em>extension_name</em> is
+              not supported.<br>
+              Give an error on the <strong>#extension</strong> if <strong>all</strong> is
+              specified.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>warn</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave as specified by the extension <em>extension_name</em>,
+              except issue warnings on any detectable use of that extension,
+              unless such use is supported by other enabled or required
+              extensions.<br>
+              If <strong>all</strong> is specified, then warn on all detectable uses of any
+              extension used.<br>
+              Warn on the <strong>#extension</strong> if the extension <em>extension_name</em> is
+              not supported.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>disable</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave (including issuing errors and warnings) as if the
+              extension <em>extension_name</em> is not part of the language
+              definition.<br>
+              If <strong>all</strong> is specified, then behavior must revert back to that
+              of the non-extended core version of the language being
+              compiled to.<br>
+              Warn on the <strong>#extension</strong> if the extension <em>extension_name</em> is
+              not supported.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The <strong>extension</strong> directive is a simple, low-level mechanism to set the
+behavior for each extension.
+It does not define policies such as which combinations are appropriate,
+those must be defined elsewhere.
+Order of directives matters in setting the behavior for each extension:
+Directives that occur later override those seen earlier.
+The <strong>all</strong> variant sets the behavior for all extensions, overriding all
+previously issued <strong>extension</strong> directives, but only for the <em>behaviors</em>
+<strong>warn</strong> and <strong>disable</strong>.</p>
+</div>
+<div class="paragraph">
+<p>The initial state of the compiler is as if the directive</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#extension</span> all : disable</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>was issued, telling the compiler that all error and warning reporting must
+be done according to this specification, ignoring any extensions.</p>
+</div>
+<div class="paragraph">
+<p>Each extension can define its allowed granularity of scope.
+If nothing is said, the granularity is a shader (that is, a single
+compilation unit), and the extension directives must occur before any
+non-preprocessor tokens.
+If necessary, the linker can enforce granularities larger than a single
+compilation unit, in which case each involved shader will have to contain
+the necessary extension directive.</p>
+</div>
+<div class="paragraph">
+<p>Macro expansion is not done on lines containing <strong>#extension</strong> and <strong>#version</strong>
+directives.</p>
+</div>
+<div class="paragraph">
+<p>For each extension there is an associated macro.
+The macro is always defined in an implementation that supports the
+extension.
+This allows the following construct to be used:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#ifdef</span> OES_extension_name
+    <span class="preprocessor">#extension</span> OES_extension_name : enable
+    <span class="comment">// code that requires the extension</span>
+<span class="preprocessor">#else</span>
+    <span class="comment">// alternative code</span>
+<span class="preprocessor">#endif</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p><strong>#line</strong> must have, after macro substitution, one of the following forms:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#line</span> line
+<span class="preprocessor">#line</span> line source-<span class="predefined-type">string</span>-number</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>line</em> and <em>source-string-number</em> are
+<em>pp-constant-expressions</em>.
+If these constant expressions are not integer literals then behavior is undefined.
+After processing this directive (including its new-line), the implementation
+will behave as if it is compiling at line number <em>line</em> and source string
+number <em>source-string-number</em>.
+Subsequent source strings will be numbered sequentially, until another
+<strong>#line</strong> directive overrides that numbering.</p>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="title">Note</div>
+<div class="paragraph">
+<p>Some implementations have allowed constant expressions in #line directives and
+some have not. Even where expressions are supported the grammar is ambiguous and so
+results are implementation dependent. For example,
++ #line +2 +2               // Line number set to 4, or file to 2 and line to 2</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="paragraph">
+<p>If during macro expansion a preprocessor directive is encountered, the
+results are undefined; the compiler may or may not report an error in such
+cases.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="comments">3.5. Comments</h3>
+<div class="paragraph">
+<p>Comments are delimited by <strong>/*</strong> and <strong>*/</strong>, or by <strong>//</strong> and a new-line.
+// style comments include the initial // marker and continue up to, but
+not including, the terminating newline.
+/*...*/ comments include both the start and end marker.
+The begin comment delimiters (/* or //) are not recognized as comment
+delimiters inside of a comment, hence comments cannot be nested.
+Comments are treated syntactically as a single space.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="tokens">3.6. Tokens</h3>
+<div class="paragraph">
+<p>The language, after preprocessing, is a sequence of tokens.
+A token can be</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>token</em> : </dt>
+<dd>
+<p><em>keyword</em><br>
+<em>identifier</em><br>
+<em>integer-constant</em><br>
+<em>floating-constant</em><br>
+<em>operator</em><br>
+<strong>;</strong> <strong>{</strong> <strong>}</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="keywords">3.7. Keywords</h3>
+<div class="paragraph">
+<p>The following are the keywords in the language and (after
+preprocessing) can only be used as described in this specification,
+or an error results:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>const</strong> <strong>uniform</strong> <strong>buffer</strong> <strong>shared</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>coherent</strong> <strong>volatile</strong> <strong>restrict</strong> <strong>readonly</strong> <strong>writeonly</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>atomic_uint</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>layout</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>centroid</strong> <strong>flat</strong> <strong>smooth</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>patch</strong> <strong>sample</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>invariant</strong> <strong>precise</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>break</strong> <strong>continue</strong> <strong>do</strong> <strong>for</strong> <strong>while</strong> <strong>switch</strong> <strong>case</strong> <strong>default</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>if</strong> <strong>else</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>in</strong> <strong>out</strong> <strong>inout</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>int</strong> <strong>void</strong> <strong>bool</strong> <strong>true</strong> <strong>false</strong> <strong>float</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>discard</strong> <strong>return</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>vec2</strong> <strong>vec3</strong> <strong>vec4</strong> <strong>ivec2</strong> <strong>ivec3</strong> <strong>ivec4</strong> <strong>bvec2</strong> <strong>bvec3</strong> <strong>bvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>uint</strong> <strong>uvec2</strong> <strong>uvec3</strong> <strong>uvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat2</strong> <strong>mat3</strong> <strong>mat4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat2x2</strong> <strong>mat2x3</strong> <strong>mat2x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat3x2</strong> <strong>mat3x3</strong> <strong>mat3x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat4x2</strong> <strong>mat4x3</strong> <strong>mat4x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>lowp</strong> <strong>mediump</strong> <strong>highp</strong> <strong>precision</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2D</strong> <strong>sampler2DShadow</strong> <strong>sampler2DArray</strong> <strong>sampler2DArrayShadow</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>isampler2D</strong> <strong>isampler2DArray</strong> <strong>usampler2D</strong> <strong>usampler2DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2DMS</strong> <strong>isampler2DMS</strong> <strong>usampler2DMS</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2DMSArray</strong> <strong>isampler2DMSArray</strong> <strong>usampler2DMSArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler3D</strong> <strong>isampler3D</strong> <strong>usampler3D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>samplerCube</strong> <strong>samplerCubeShadow</strong> <strong>isamplerCube</strong> <strong>usamplerCube</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>samplerCubeArray</strong> <strong>samplerCubeArrayShadow</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>isamplerCubeArray</strong> <strong>usamplerCubeArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>samplerBuffer</strong> <strong>isamplerBuffer</strong> <strong>usamplerBuffer</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2D</strong> <strong>iimage2D</strong> <strong>uimage2D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DArray</strong> <strong>iimage2DArray</strong> <strong>uimage2DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image3D</strong> <strong>iimage3D</strong> <strong>uimage3D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>imageCube</strong> <strong>iimageCube</strong> <strong>uimageCube</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>imageCubeArray</strong> <strong>iimageCubeArray</strong> <strong>uimageCubeArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>imageBuffer</strong> <strong>iimageBuffer</strong> <strong>uimageBuffer</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>struct</strong></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The following are the keywords reserved for future use.
+Using them will result in an error:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>attribute</strong> <strong>varying</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>noperspective</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>subroutine</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>common</strong> <strong>partition</strong> <strong>active</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>asm</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>class</strong> <strong>union</strong> <strong>enum</strong> <strong>typedef</strong> <strong>template</strong> <strong>this</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>resource</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>goto</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>inline</strong> <strong>noinline</strong> <strong>public</strong> <strong>static</strong> <strong>extern</strong> <strong>external</strong> <strong>interface</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>long</strong> <strong>short</strong> <strong>half</strong> <strong>fixed</strong> <strong>unsigned</strong> <strong>superp</strong>
+<strong>double</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>input</strong> <strong>output</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>hvec2</strong> <strong>hvec3</strong> <strong>hvec4</strong> <strong>fvec2</strong> <strong>fvec3</strong> <strong>fvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dvec2</strong> <strong>dvec3</strong> <strong>dvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat2</strong> <strong>dmat3</strong> <strong>dmat4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat2x2</strong> <strong>dmat2x3</strong> <strong>dmat2x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat3x2</strong> <strong>dmat3x3</strong> <strong>dmat3x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat4x2</strong> <strong>dmat4x3</strong> <strong>dmat4x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>filter</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sizeof</strong> <strong>cast</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>namespace</strong> <strong>using</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler1D</strong> <strong>sampler1DShadow</strong> <strong>sampler1DArray</strong> <strong>sampler1DArrayShadow</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>isampler1D</strong> <strong>isampler1DArray</strong> <strong>usampler1D</strong> <strong>usampler1DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2DRect</strong> <strong>sampler2DRectShadow</strong> <strong>isampler2DRect</strong> <strong>usampler2DRect</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler3DRect</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image1D</strong> <strong>iimage1D</strong> <strong>uimage1D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image1DArray</strong> <strong>iimage1DArray</strong> <strong>uimage1DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DRect</strong> <strong>iimage2DRect</strong> <strong>uimage2DRect</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DMS</strong> <strong>iimage2DMS</strong> <strong>uimage2DMS</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DMSArray</strong> <strong>iimage2DMSArray</strong> <strong>uimage2DMSArray</strong></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>In addition, all identifiers containing two consecutive underscores (__)
+are reserved for use by underlying software layers.
+Defining such a name in a shader does not itself result in an error, but may
+result in unintended behaviors that stem from having multiple definitions of
+the same name.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="identifiers">3.8. Identifiers</h3>
+<div class="paragraph">
+<p>Identifiers are used for variable names, function names, structure names,
+and field selectors (field selectors select components of
+<code><a href="#vector-components">vectors</a></code> and <code><a href="#matrix-components">matrices</a></code>,
+similarly to structure members).
+Identifiers have the form:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>identifier</em> : </dt>
+<dd>
+<p><em>nondigit</em><br>
+<em>identifier</em> <em>nondigit</em><br>
+<em>identifier</em> <em>digit</em></p>
+</dd>
+<dt class="hdlist1"><em>nondigit</em> : one of </dt>
+<dd>
+<p><strong>_</strong> <strong>a b c d e f g h i j k l m n o p q r s t u v w x y z</strong><br>
+<strong>A B C D E F G H I J K L M N O P Q R S T U V W X Y Z</strong></p>
+</dd>
+<dt class="hdlist1"><em>digit</em> : one of </dt>
+<dd>
+<p><strong>0 1 2 3 4 5 6 7 8 9</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Identifiers starting with &#8220;gl_&#8221; are reserved for use by OpenGL ES, and
+in general, may not be declared in a shader;
+this results in an error.
+However, as noted in the specification, there are some cases where
+previously declared variables can be redeclared, and predeclared &#8220;gl_&#8221;
+names are allowed to be redeclared in a shader only for these specific
+purposes.</p>
+</div>
+<div class="paragraph">
+<p>Implementations must support identifier lengths of up to 1024 characters.
+It is an error if the length exceeds this value.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="definitions">3.9. Definitions</h3>
+<div class="paragraph">
+<p>Some language rules described below depend on the following definitions.</p>
+</div>
+<div class="sect3">
+<h4 id="static-use">3.9.1. Static Use</h4>
+<div class="paragraph">
+<p>A shader contains a <em>static use</em> of a variable <em>x</em> if, after preprocessing,
+the shader contains a statement that would access any part of <em>x</em>,
+whether or not flow of control will cause that statement to be executed.
+Such a variable is referred to as being <em>statically used</em>. If the access is a
+write then <em>x</em> is further said to be <em>statically assigned</em>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-and-non-uniform-control-flow">3.9.2. Uniform and Non-Uniform Control Flow</h4>
+<div class="paragraph">
+<p>When executing statements in a fragment shader, control flow starts as
+<em>uniform control flow</em>; all fragments enter the same control path into
+<em>main()</em>.
+Control flow becomes <em>non-uniform</em> when different fragments take different
+paths through control-flow statements (selection, iteration, and jumps).
+Control flow subsequently returns to being uniform after such divergent
+sub-statements or skipped code completes, until the next time different
+control paths are taken.</p>
+</div>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">main()
+{
+    <span class="predefined-type">float</span> a = ...; <span class="comment">// this is uniform control flow</span>
+    <span class="keyword">if</span> (a &lt; b) {   <span class="comment">// this expression is true for some fragments, not all</span>
+        ...;       <span class="comment">// non-uniform control flow</span>
+    } <span class="keyword">else</span> {
+        ...;       <span class="comment">// non-uniform control flow</span>
+    }
+    ...;           <span class="comment">// uniform control flow again</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Other examples of non-uniform control flow can occur within switch
+statements and after conditional breaks, continues, early returns, and after
+fragment discards, when the condition is true for some fragments but not
+others.
+Loop iterations that only some fragments execute are also non-uniform
+control flow.</p>
+</div>
+<div class="paragraph">
+<p>This is similarly defined for other shader stages, based on the per-instance
+data items they process.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="dynamically-uniform-expressions">3.9.3. Dynamically Uniform Expressions</h4>
+<div class="paragraph">
+<p>A fragment-shader expression is <em>dynamically uniform</em> if all fragments
+evaluating it get the same resulting value.
+When loops are involved, this refers to the expression&#8217;s value for the same
+loop iteration.
+When functions are involved, this refers to calls from the same call point.</p>
+</div>
+<div class="paragraph">
+<p>This is similarly defined for other shader stages, based on the per-instance
+data they process.</p>
+</div>
+<div class="paragraph">
+<p>Note that constant expressions are trivially dynamically uniform.
+It follows that typical loop counters based on these are also dynamically
+uniform.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="logical-phases-of-compilation">3.10. Logical Phases of Compilation</h3>
+<div class="paragraph">
+<p>The compilation units for the shader processors are processed separately
+before optionally being linked together in the final stage of compilation.
+The logical phases of compilation are:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>Source strings are input as byte sequences.
+The value 'zero' is interpreted as a terminator.</p>
+</li>
+<li>
+<p>Source strings are concatenated to form a single input.
+Zero bytes are discarded but all other values are retained.</p>
+</li>
+<li>
+<p>Each string is interpreted according to the UTF-8 standard, with the
+exception that all invalid byte sequences are retained in their original
+form for subsequent processing.</p>
+</li>
+<li>
+<p>Each {carriage-return, line-feed} and {line-feed, carriage return}
+sequence is replaced by a single newline.
+All remaining carriage-return and line-feed characters are then each
+replaced by a newline.</p>
+</li>
+<li>
+<p>Line numbering for each character, which is equal to the number of
+preceding newlines plus one, is noted.
+Note this can only be subsequently changed by the #line directive and is
+not affected by the removal of newlines in phase 6 of compilation.</p>
+</li>
+<li>
+<p>Wherever a backslash ('\') occurs immediately before a newline, both are
+deleted.
+Note that no whitespace is substituted, thereby allowing a single
+preprocessing token to span a newline.
+This operation is not recursive; any new {backslash newline} sequences
+generated are not removed.</p>
+</li>
+<li>
+<p>All comments are replaced with a single space.
+All (non-zero) characters and invalid UTF-8 byte sequences are allowed
+within comments.
+'//' style comments include the initial '//' marker and continue up to,
+but not including, the terminating newline.
+'/<strong>&#8230;&#8203;</strong>/' comments include both the start and end marker.</p>
+</li>
+<li>
+<p>The source string is converted into a sequence of preprocessing tokens.
+These tokens include preprocessing numbers, identifiers and
+preprocessing operations.
+The line number associated with each token is copied from the line
+number of the first character of the token.</p>
+</li>
+<li>
+<p>The preprocessor is run.
+Directives are executed and macro expansion is performed.</p>
+</li>
+<li>
+<p>White space and newlines are discarded.</p>
+</li>
+<li>
+<p>Preprocessing tokens are converted into tokens.</p>
+</li>
+<li>
+<p>The syntax is analyzed according to the GLSL ES grammar.</p>
+</li>
+<li>
+<p>The result is checked according to the semantic rules of the language.</p>
+</li>
+<li>
+<p>Optionally, the shaders are linked together to form one or more programs
+or separable programs.
+When a pair of shaders from consecutive stages are linked into the same
+program, any outputs and corresponding inputs not used in both shaders
+may be discarded.</p>
+</li>
+<li>
+<p>The binary is generated.</p>
+</li>
+</ol>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="variables-and-types">4. Variables and Types</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>All variables and functions must be declared before being used.
+Variable and function names are identifiers.</p>
+</div>
+<div class="paragraph">
+<p>There are no default types.
+All variable and function declarations must have a declared type, and
+optionally qualifiers.
+A variable is declared by specifying its type followed by one or more names
+separated by commas.
+In many cases, a variable can be initialized as part of its declaration by
+using the assignment operator (<strong>=</strong>).</p>
+</div>
+<div class="paragraph">
+<p>User-defined types may be defined using <strong>struct</strong> to aggregate a list of
+existing types into a single name.</p>
+</div>
+<div class="paragraph">
+<p>The OpenGL ES Shading Language is type safe.
+There are no implicit conversions between types.</p>
+</div>
+<div class="sect2">
+<h3 id="basic-types">4.1. Basic Types</h3>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>A <em>basic type</em> is a type defined by a keyword in the language.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The OpenGL ES Shading Language supports the following basic data types, grouped as follows.</p>
+</div>
+<div class="sect3">
+<h4 id="_transparent_types">4.1.1. Transparent Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>void</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for functions that do not return a value</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bool</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a conditional type, taking on values of true or false</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>int</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a signed integer</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uint</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">an unsigned integer</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>float</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point scalar</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component single-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component single-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component single-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bvec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component Boolean vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bvec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component Boolean vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bvec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component Boolean vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component signed integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component signed integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component signed integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component unsigned integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component unsigned integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component unsigned integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 2 × 2 single-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 3 × 3 single-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 4 × 4 single-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>mat2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 2 columns and 3 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 2 columns and 4 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 3 columns and 2 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>mat3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 3 columns and 4 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 4 columns and 2 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 4 columns and 3 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>mat4</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Note that where the following tables say &#8220;accessing a texture&#8221;, the
+<strong>sampler*</strong> opaque types access textures, and the <strong>image*</strong> opaque types
+access images, of a specified type.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="_floating_point_opaque_types">4.1.2. Floating-Point Opaque Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2D</strong><br>
+  <strong>image2D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DArray</strong><br>
+  <strong>image2DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DArrayShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D array depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DMS</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D multisample texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DMSArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D multisample array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler3D</strong><br>
+  <strong>image3D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 3D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCube</strong><br>
+  <strong>imageCube</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube mapped texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCubeShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube map depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCubeArray</strong><br>
+  <strong>imageCubeArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube map array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCubeArrayShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube map array depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerBuffer</strong><br>
+  <strong>imageBuffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a buffer texture</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="_signed_integer_opaque_types">4.1.3. Signed Integer Opaque Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2D</strong><br>
+  <strong>iimage2D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DArray</strong><br>
+  <strong>iimage2DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DMS</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D multisample texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DMSArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D multisample array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler3D</strong><br>
+  <strong>iimage3D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 3D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isamplerCube</strong><br>
+  <strong>iimageCube</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer cube mapped texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isamplerCubeArray</strong><br>
+  <strong>iimageCubeArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer cube map array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isamplerBuffer</strong><br>
+  <strong>iimageBuffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer buffer texture</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="_unsigned_integer_opaque_types">4.1.4. Unsigned Integer Opaque Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2D</strong><br>
+  <strong>uimage2D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DArray</strong><br>
+  <strong>uimage2DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DMS</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D multisample texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DMSArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D multisample array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler3D</strong><br>
+  <strong>uimage3D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 3D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usamplerCube</strong><br>
+  <strong>uimageCube</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer cube mapped texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usamplerCubeArray</strong><br>
+  <strong>uimageCubeArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer cube map array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usamplerBuffer</strong><br>
+  <strong>uimageBuffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer buffer texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>atomic_uint</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer atomic counter</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>In addition, a shader can aggregate these basic types using arrays and
+structures to build more complex types.</p>
+</div>
+<div class="paragraph">
+<p>There are no pointer types.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="void">4.1.5. Void</h4>
+<div class="paragraph">
+<p>Functions that do not return a value must be declared as <strong>void</strong>.
+There is no default function return type.
+The keyword <strong>void</strong> cannot be used in any other declarations (except for
+empty formal or actual parameter lists), or an error results.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="booleans">4.1.6. Booleans</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>A <em>boolean type</em> is any boolean scalar or vector type (<strong>bool</strong>, <strong>bvec2</strong>,
+<strong>bvec3</strong>, <strong>bvec4</strong>)</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>To make conditional execution of code easier to express, the type <strong>bool</strong> is
+supported.
+There is no expectation that hardware directly supports variables of this
+type.
+It is a genuine Boolean type, holding only one of two values meaning either
+true or false.
+Two keywords <strong>true</strong> and <strong>false</strong> can be used as literal Boolean constants.
+Booleans are declared and optionally initialized as in the follow example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">bool</span> success;      <span class="comment">// declare &quot;success&quot; to be a Boolean</span>
+<span class="predefined-type">bool</span> done = <span class="predefined-constant">false</span>; <span class="comment">// declare and initialize &quot;done&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Expressions used for conditional jumps (<strong>if</strong>, <strong>for</strong>, <strong>?:</strong>, <strong>while</strong>,
+<strong>do</strong>-<strong>while</strong>) must evaluate to the type <strong>bool</strong>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="integers">4.1.7. Integers</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definitions</dt>
+<dd>
+<p>An <em>integral type</em> is any signed or unsigned, scalar or vector integer type.
+It excludes arrays and structures.</p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>A <em>scalar integral type</em> is a scalar signed or unsigned integer type:</p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>A <em>vector integral type</em> is a vector of signed or unsigned integers:</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Signed and unsigned integer variables are fully supported.
+In this document, the term <em>integer</em> is meant to generally include both
+signed and unsigned integers.
+<strong>highp</strong> unsigned
+integers have exactly 32 bits of precision.
+<strong>highp</strong> signed
+integers use 32 bits, including a sign bit, in two&#8217;s complement form.</p>
+</div>
+<div class="paragraph">
+<p><strong>mediump</strong> and <strong>lowp</strong> integers have implementation-defined numbers of bits.
+See &#8220;<a href="#range-and-precision">Range and Precision</a>&#8221; for details.
+For all precisions,
+operations resulting in overflow or
+underflow will not cause any exception, nor will they saturate, rather they
+will &#8220;wrap&#8221; to yield the low-order
+n bits of the result where n is the size in bits of the integer.
+However, for the case where the minimum representable value is divided by
+-1, it is allowed to return either the minimum representable value or the
+maximum representable value.</p>
+</div>
+<div class="paragraph">
+<p>Integers are declared and optionally initialized with integer expressions,
+as in the following example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> i, j = <span class="integer">42</span>; <span class="comment">// default integer literal type is int</span>
+uint k = <span class="integer">3</span>u;   <span class="comment">// &quot;u&quot; establishes the type as uint</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Literal integer constants can be expressed in decimal (base 10), octal (base
+8), or hexadecimal (base 16) as follows.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>integer-constant</em> : </dt>
+<dd>
+<p><em>decimal-constant</em> <em>integer-suffix<sub>opt</sub></em><br>
+<em>octal-constant</em> <em>integer-suffix<sub>opt</sub></em><br>
+<em>hexadecimal-constant</em> <em>integer-suffix<sub>opt</sub></em></p>
+</dd>
+<dt class="hdlist1"><em>integer-suffix</em> : one of </dt>
+<dd>
+<p><strong>u</strong> <strong>U</strong></p>
+</dd>
+<dt class="hdlist1"><em>decimal-constant</em> : </dt>
+<dd>
+<p><em>nonzero-digit</em><br>
+<em>decimal-constant</em> <em>digit</em></p>
+</dd>
+<dt class="hdlist1"><em>octal-constant</em> : </dt>
+<dd>
+<p><strong>0</strong><br>
+<em>octal-constant</em> <em>octal-digit</em></p>
+</dd>
+<dt class="hdlist1"><em>hexadecimal-constant</em> : </dt>
+<dd>
+<p><strong>0x</strong> <em>hexadecimal-digit</em><br>
+<strong>0X</strong> <em>hexadecimal-digit</em><br>
+<em>hexadecimal-constant</em> <em>hexadecimal-digit</em></p>
+</dd>
+<dt class="hdlist1"><em>digit</em> : </dt>
+<dd>
+<p><strong>0</strong><br>
+<em>nonzero-digit</em></p>
+</dd>
+<dt class="hdlist1"><em>nonzero-digit</em> : one of </dt>
+<dd>
+<p><strong>1 2 3 4 5 6 7 8 9</strong></p>
+</dd>
+<dt class="hdlist1"><em>octal-digit</em> : one of </dt>
+<dd>
+<p><strong>0 1 2 3 4 5 6 7</strong></p>
+</dd>
+<dt class="hdlist1"><em>hexadecimal-digit</em> : one of </dt>
+<dd>
+<p><strong>0 1 2 3 4 5 6 7 8 9<br>
+a b c d e f<br>
+A B C D E F</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>No white space is allowed between the digits of an integer constant,
+including after the leading <strong>0</strong> or after the leading <strong>0x</strong> or <strong>0X</strong> of a
+constant, or before the suffix <strong>u</strong> or <strong>U</strong>.
+When the suffix <strong>u</strong> or <strong>U</strong> is present, the literal has type <strong>uint</strong>,
+otherwise the type is <strong>int</strong>.
+A leading unary minus sign (-) is interpreted as an arithmetic unary
+negation, not as part of the constant.
+Hence, literals themselves are always expressed with non-negative syntax,
+though they could result in a negative value.</p>
+</div>
+<div class="paragraph">
+<p>It is an error to provide a literal integer whose bit pattern
+cannot fit in 32 bits.
+The bit pattern of the literal is always used unmodified.
+So a signed literal whose bit pattern includes a set sign bit creates a
+negative value.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="integer">1</span>             <span class="comment">// OK. Signed integer, value 1</span>
+<span class="integer">1</span>u            <span class="comment">// OK. Unsigned integer, value 1</span>
+-<span class="integer">1</span>            <span class="comment">// OK. Unary minus applied to signed integer.</span>
+              <span class="comment">// result is a signed integer, value -1</span>
+-<span class="integer">1</span>u           <span class="comment">// OK. Unary minus applies to unsigned integer.</span>
+              <span class="comment">// Result is an unsigned integer, value 0xffffffff</span>
+<span class="hex">0xA0000000</span>    <span class="comment">// OK. 32-bit signed hexadecimal</span>
+<span class="hex">0xABcdEF00</span>u   <span class="comment">// OK. 32-bit unsigned hexadecimal</span>
+<span class="hex">0xffffffff</span>    <span class="comment">// OK. Signed integer, value -1</span>
+<span class="hex">0x80000000</span>    <span class="comment">// OK. Evaluates to -2147483648</span>
+<span class="hex">0xffffffff</span>u   <span class="comment">// OK. Unsigned integer, value 0xffffffff</span>
+<span class="hex">0xfffffffff</span>   <span class="comment">// Error: needs more than 32 bits</span>
+<span class="integer">3000000000</span>    <span class="comment">// OK. A signed decimal literal taking 32 bits.</span>
+              <span class="comment">// It evaluates to -1294967296</span>
+<span class="integer">2147483648</span>    <span class="comment">// OK. Evaluates to -2147483648 (the literal set the sign bit)</span>
+<span class="integer">5000000000</span>    <span class="comment">// Error: needs more than 32 bits</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="floats">4.1.8. Floats</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>A <em>floating-point type</em> is any floating-point scalar, vector or matrix type.
+It excludes arrays and structures.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Floats are available for use in a variety of scalar calculations.
+Floating-point variables are defined as in the following example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a, b = <span class="float">1</span><span class="float">.5</span>;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>As an input value to one of the processing units, a floating-point variable
+is expected to match the IEEE 754 single precision floating-point definition
+for precision and dynamic range.
+<strong>highp</strong> floating-point variables within a shader are encoded according to
+the IEEE 754 specification for single-precision floating-point values
+(logically, not necessarily physically).
+While encodings are logically IEEE 754, operations (addition,
+multiplication, etc.) are not necessarily performed as required by IEEE 754.
+See &#8220;<a href="#range-and-precision">Range and Precision</a>&#8221; for more details on
+precision and usage of NaNs (Not a Number) and Infs (positive or negative
+infinities).</p>
+</div>
+<div class="paragraph">
+<p>Floating-point constants are defined as follows.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>floating-constant</em> : </dt>
+<dd>
+<p><em>fractional-constant</em> <em>exponent-part<sub>opt</sub></em> <em>floating-suffix<sub>opt</sub></em><br>
+<em>digit-sequence</em> <em>exponent-part</em> <em>floating-suffix<sub>opt</sub></em></p>
+</dd>
+<dt class="hdlist1"><em>fractional-constant</em> : </dt>
+<dd>
+<p><em>digit-sequence</em> <strong>.</strong> <em>digit-sequence</em><br>
+<em>digit-sequence</em> <strong>.</strong><br>
+<strong>.</strong> <em>digit-sequence</em></p>
+</dd>
+<dt class="hdlist1"><em>exponent-part</em> : </dt>
+<dd>
+<p><strong>e</strong> <em>sign<sub>opt</sub></em> <em>digit-sequence</em><br>
+<strong>E</strong> <em>sign<sub>opt</sub></em> <em>digit-sequence</em></p>
+</dd>
+<dt class="hdlist1"><em>sign</em> : one of </dt>
+<dd>
+<p><strong>+</strong> <strong>-</strong></p>
+</dd>
+<dt class="hdlist1"><em>digit-sequence</em> : </dt>
+<dd>
+<p><em>digit</em><br>
+<em>digit-sequence</em> <em>digit</em></p>
+</dd>
+<dt class="hdlist1"><em>floating-suffix</em> : one of </dt>
+<dd>
+<p><strong>f</strong> <strong>F</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>A decimal point (<strong>.</strong>) is not needed if the exponent part is present.
+No white space may appear anywhere within a floating-point constant,
+including before a suffix.
+A leading unary minus sign (<strong>-</strong>) is interpreted as a unary operator and is
+not part of the floating-point constant.</p>
+</div>
+<div class="paragraph">
+<p>There is no limit on the number of digits in any <em>digit-sequence</em>.
+If the value of the floating-point number is too large (small) to be stored
+as a single precision value, it is converted to positive (negative)
+infinity.
+A value with a magnitude too small to be represented as a mantissa and
+exponent is converted to zero.
+Implementations may also convert subnormal (denormalized) numbers to zero.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="vectors">4.1.9. Vectors</h4>
+<div class="paragraph">
+<p>The OpenGL ES Shading Language includes data types for generic 2-, 3-, and 4-component vectors
+of floating-point values, integers, and Booleans.
+Floating-point vector variables can be used to store colors, normals,
+positions, texture coordinates, texture lookup results and the like.
+Boolean vectors can be used for component-wise comparisons of numeric
+vectors.
+Some examples of vector declarations are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec2 texcoord1, texcoord2;
+vec3 position;
+vec4 myRGBA;
+ivec2 textureLookup;
+bvec3 less;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Initialization of vectors can be done with constructors.
+See &#8220;<a href="#vector-and-matrix-constructors">Vector and Matrix Constructors</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="matrices">4.1.10. Matrices</h4>
+<div class="paragraph">
+<p>The OpenGL ES Shading Language has built-in types for 2 × 2, 2 × 3, 2 × 4, 3
+× 2, 3 × 3, 3 × 4, 4 × 2, 4 × 3, and 4 ×
+4 matrices of floating-point numbers.
+The first number in the type is the number of columns, the second is the
+number of rows.
+If there is only one number, the matrix is square.
+Example matrix declarations:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2 mat2D;
+mat3 optMatrix;
+mat4 view, projection;
+mat4x4 view; <span class="comment">// an alternate way of declaring a mat4</span>
+mat3x2 m;    <span class="comment">// a matrix with 3 columns and 2 rows</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Initialization of matrix values is done with constructors (described in
+&#8220;<a href="#vector-and-matrix-constructors">Vector and Matrix Constructors</a>&#8221;) in
+column-major order.</p>
+</div>
+<div class="paragraph">
+<p><strong>mat2</strong> is an alias for <strong>mat2x2</strong>, not a distinct type.
+Similarly for <strong>mat3</strong> and <strong>mat4.</strong> The following is legal:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2 a;
+mat2x2 b = a;</code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="opaque-types">4.1.11. Opaque Types</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>An <em>opaque type</em> is a type where the internal structure of the type is
+hidden from the language.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The opaque types, as listed in the following sections, declare variables
+that are effectively opaque handles to other objects.
+These objects are accessed through built-in functions, not through direct
+reading or writing of the declared variable.
+They can only be declared as function parameters or in <strong>uniform</strong>-qualified
+variables (see &#8220;<a href="#uniform-variables">Uniform Variables</a>&#8221;).
+The only opaque types that take memory qualifiers are the image types.
+Except for array indexing, structure member selection, and parentheses,
+opaque variables are not allowed to be operands in expressions; such use
+results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>When aggregated into arrays within a shader, opaque types can only be
+indexed with a dynamically uniform integral expression (see &#8220;Dynamically
+Uniform Expressions&#8221;) unless otherwise noted; otherwise, results are
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>Opaque variables cannot be treated as l-values; hence cannot be used as
+<strong>out</strong> or <strong>inout</strong> function parameters, nor can they be assigned into.
+Any such use results in a compile-time error.
+However, they can be passed as <strong>in</strong> parameters with matching types and
+memory qualifiers.
+They cannot be declared with an initializer.</p>
+</div>
+<div class="paragraph">
+<p>Because a single opaque type declaration effectively declares two objects,
+the opaque handle itself and the object it is a handle to, there is room for
+both a storage qualifier and a memory qualifier.
+The storage qualifier will qualify the opaque handle, while the memory
+qualifier will qualify the object it is a handle to.</p>
+</div>
+<div class="sect4">
+<h5 id="samplers">Samplers</h5>
+<div class="paragraph">
+<p>Sampler types (e.g. <strong>sampler2D</strong>) are opaque types, declared and behaving as
+described above for opaque types.</p>
+</div>
+<div class="paragraph">
+<p>Sampler variables are handles to
+two-, and three- dimensional textures, cube maps, depth textures (shadowing),
+etc., as enumerated in the basic types tables.
+There are distinct sampler types for each texture target, and for each of
+float, integer, and unsigned integer data types.
+Texture accesses are done through built-in texture functions (described in
+&#8220;<a href="#texture-functions">Texture Functions</a>&#8221;) and samplers are used to
+specify which texture to access and how it is to be filtered.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="images">Images</h5>
+<div class="paragraph">
+<p>Image types are opaque types, declared and behaving as described above for
+opaque types.
+They can be further qualified with memory qualifiers.
+When aggregated into arrays within a shader, images can only be indexed with
+a constant integral expression.</p>
+</div>
+<div class="paragraph">
+<p>Image variables are handles to
+two-, or three-dimensional images
+corresponding to all or a portion of a single level of a texture image bound
+to an image unit.
+There are distinct image variable types for each texture target, and for
+each of float, integer, and unsigned integer data types.
+Image accesses should use an image type that matches the target of the
+texture whose level is bound to the image unit, or for non-layered bindings
+of 3D or array images should use the image type that matches the
+dimensionality of the layer of the image (i.e., a layer of 3D, 2DArray,
+Cube, or CubeArray should use
+<strong>image2D</strong>).
+If the image target type does not match the bound image in this manner, if
+the data type does not match the bound image, or if the format layout
+qualifier does not match the image unit format as described in section
+8.22
+&#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL ES Specification</a>, the
+results of image accesses are undefined but cannot include program
+termination.</p>
+</div>
+<div class="paragraph">
+<p>Image variables are used in the image load, store, and atomic functions
+described in &#8220;<a href="#image-functions">Image Functions</a>&#8221; to specify an image to
+access.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="atomic-counters">Atomic Counters</h5>
+<div class="paragraph">
+<p>Atomic counter types (e.g. <strong>atomic_uint</strong>) are opaque handles to counters,
+declared and behaving as described above for opaque types.
+The variables they declare specify which counter to access when using the
+built-in atomic counter functions as described in
+&#8220;<a href="#atomic-counter-functions">Atomic Counter Functions</a>&#8221;.
+They are bound to buffers as described in
+&#8220;<a href="#atomic-counter-layout-qualifiers">Atomic Counter Layout Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Atomic counters aggregated into arrays within a shader can only be indexed
+with dynamically uniform integral expressions, otherwise results are
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>Members of structures cannot be declared as atomic counter types.</p>
+</div>
+<div class="paragraph">
+<p>The default precision of all atomic types is <strong>highp</strong>.
+It is an error to declare an atomic type with a different precision or to
+specify the default precision for an atomic type to be <strong>lowp</strong> or <strong>mediump</strong>.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="structures">4.1.12. Structures</h4>
+<div class="paragraph">
+<p>User-defined types can be created by aggregating other already defined types
+into a structure using the <strong>struct</strong> keyword.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> light {
+    <span class="predefined-type">float</span> intensity;
+    vec3 position;
+} lightVar;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>In this example, <em>light</em> becomes the name of the new type, and <em>lightVar</em>
+becomes a variable of type <em>light</em>.
+To declare variables of the new type, use its name (without the keyword
+<strong>struct</strong>).</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">light lightVar2;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>More formally, structures are declared as follows.
+However, the definitive grammar is as given in
+&#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221;.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>struct-definition</em> : </dt>
+<dd>
+<p><em>qualifier<sub>opt</sub></em> <strong>struct</strong> name<sub>opt</sub>_ <strong>{</strong> <em>member-list</em> <strong>}</strong>
+<em>declarators<sub>opt</sub></em> <strong>;</strong></p>
+</dd>
+<dt class="hdlist1"><em>member-list</em> : </dt>
+<dd>
+<p><em>member-declaration</em> <strong>;</strong><br>
+<em>member-declaration</em> <em>member-list</em> <strong>;</strong></p>
+</dd>
+<dt class="hdlist1"><em>member-declaration</em> : </dt>
+<dd>
+<p><em>basic-type</em> <em>declarators</em> <strong>;</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>name</em> becomes the user-defined type, and can be used to declare
+variables to be of this new type.
+The <em>name</em> shares the same name space as other variables, types, and
+functions.
+All previously visible variables, types, constructors, or functions with
+that name are hidden.
+The optional <em>qualifier</em> only applies to any <em>declarators</em>, and is not part
+of the type being defined for <em>name</em>.</p>
+</div>
+<div class="paragraph">
+<p>Structures must have at least one member declaration.
+Member declarators may contain precision qualifiers, but use of any other
+qualifier results in an error.
+Bit fields are not supported.
+Member types must be already defined (there are no forward references).
+Member declarations cannot contain initializers.
+Member declarators can contain arrays.
+Such arrays must have a size specified, and the size must be a constant
+integral expression that&#8217;s greater than zero (see
+&#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;).
+Each level of structure has its own name space for names given in member
+declarators; such names need only be unique within that name space.</p>
+</div>
+<div class="paragraph">
+<p>Anonymous structures are not supported.
+Embedded structure definitions are not supported.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> S { <span class="predefined-type">float</span> f; }; <span class="comment">// Allowed: S is defined as a structure.</span>
+
+<span class="keyword">struct</span> T {
+    S;              <span class="comment">// Error: anonymous structures disallowed</span>
+    <span class="keyword">struct</span> { ... }; <span class="comment">// Error: embedded structures disallowed</span>
+    S s;            <span class="comment">// Allowed: nested structure with a name.</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Structures can be initialized at declaration time using constructors, as
+discussed in &#8220;<a href="#structure-constructors">Structure Constructors</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Any restrictions on the usage of a type or qualifier also apply to any
+structure that contains a member of that type or qualifier.
+This also applies to structure members that are structures, recursively.</p>
+</div>
+<div class="paragraph">
+<p>Structures can contain variables of any type except:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>atomic_uint</strong> (since there is no mechanism to specify the binding)</p>
+</li>
+<li>
+<p>image types (since there is no mechanism to specify the format
+qualifier)</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="arrays">4.1.13. Arrays</h4>
+<div class="paragraph">
+<p>Variables of the same type can be aggregated into arrays by declaring a name
+followed by brackets (<strong>[ ]</strong>) enclosing an optional size.</p>
+</div>
+<div class="paragraph">
+<p>When present, the array size must be a constant integral expression (see
+&#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;) greater than zero.
+The type of the size parameter can be a signed or unsigned integer and the
+choice of type does not affect the type of the resulting array.
+Arrays only have a single dimension (a single number within &#8220;[ ]&#8221;),
+however, arrays of arrays can be declared.
+Any type can be formed into an array.</p>
+</div>
+<div class="paragraph">
+<p>Arrays are sized either at compile-time or at run-time.
+To size an array at compile-time, either the size must be specified within
+the brackets as above or must be inferred from the type of the initializer.</p>
+</div>
+<div class="paragraph">
+<p>If an array is declared as the last member of a shader storage block and the
+size is not specified at compile-time, it is sized at run-time.
+In all other cases, arrays are sized only at compile-time.
+An array declaration sized at compile-time which leaves the size of the
+array unspecified is an error.</p>
+</div>
+<div class="paragraph">
+<p>For compile-time sized arrays, it is illegal to index an array with a
+constant integral expression greater than or equal to the declared size or
+with a negative constant expression.
+Arrays declared as formal parameters in a function declaration must also
+specify a size.
+Undefined behavior results from indexing an array with a non-constant
+expression that&#8217;s greater than or equal to the array&#8217;s size or less than 0.
+If robust buffer access is enabled (see section 10.3.5 &#8220;Robust Buffer
+Access&#8221; of the <a href="#references">OpenGL ES Specification</a>), such indexing must not result in
+abnormal program termination.
+The results are still undefined, but implementations are encouraged to
+produce zero values for such accesses.</p>
+</div>
+<div class="paragraph">
+<p>Some examples are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> frequencies[<span class="integer">3</span>];
+uniform vec4 lightPosition[<span class="integer">4</span>u];
+<span class="directive">const</span> <span class="predefined-type">int</span> numLights = <span class="integer">2</span>;
+light lights[numLights];
+vec4 a[<span class="integer">3</span>][<span class="integer">2</span>];
+a.length() <span class="comment">// this is 3</span>
+a[x].length() <span class="comment">// this is 2</span>
+<span class="comment">// a shader storage block, introduced in section 4.3.7 &quot;Buffer Variables&quot;</span>
+buffer b {
+    <span class="predefined-type">float</span> u[]; <span class="comment">// an error</span>
+    vec4 v[];  <span class="comment">// okay, v will be sized at run-time</span>
+} name[<span class="integer">3</span>];     <span class="comment">// when the block is arrayed, all u will be the same size,</span>
+               <span class="comment">// but not necessarily all v, if sized dynamically</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When the <strong>length</strong>() method will return a compile-time constant, the
+expression in brackets (x above) will be evaluated and subject to the rules
+required for array indices, but the array will not be dereferenced.
+Thus, behavior is well defined even if the run-time value of the expression
+is out of bounds.</p>
+</div>
+<div class="paragraph">
+<p>An array type can be formed by specifying a non-array type
+(<a href="#type_specifier_nonarray">[type_specifier_nonarray]</a>) followed by an <a href="#array_specifier">[array_specifier]</a>.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>]</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Note that the construct <em>type [size]</em> does not always result in an array of
+length <em>size</em> of type <em>type</em>:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">2</span>][<span class="integer">3</span>] <span class="comment">// an array of size [2] of array of size [3] of float,</span>
+            <span class="comment">// not size [3] of float[2]</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This type can be used anywhere any other type can be used, including as the
+return value from a function</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>] foo() { }</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>as a constructor of an array:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>as an unnamed parameter:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> foo(<span class="predefined-type">float</span>[<span class="integer">5</span>])</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and as an alternate way of declaring a variable or function parameter:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>] a;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>An array type can also be formed without specifying a size if the definition
+includes an initializer:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> x[] = <span class="predefined-type">float</span>[<span class="integer">2</span>] (<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>); <span class="comment">// declares an array of size 2</span>
+<span class="predefined-type">float</span> y[] = <span class="predefined-type">float</span>[] (<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>); <span class="comment">// declares an array of size 3</span>
+<span class="predefined-type">float</span> a[<span class="integer">5</span>];
+<span class="predefined-type">float</span> b[] = a;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Note that the initializer itself does not need to be a constant expression
+but the length of the initializer will be a constant expression.</p>
+</div>
+<div class="paragraph">
+<p>Arrays can have initializers formed from array constructors:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[<span class="integer">5</span>] = <span class="predefined-type">float</span>[<span class="integer">5</span>](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+<span class="predefined-type">float</span> a[<span class="integer">5</span>] = <span class="predefined-type">float</span>[](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);  <span class="comment">// same thing</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>An array of arrays can be declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 a[<span class="integer">3</span>][<span class="integer">2</span>]; <span class="comment">// size-3 array of size-2 array of vec4</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>which declares a one-dimensional array of size 3 of one-dimensional arrays
+of size 2 of <strong>vec4</strong>.
+The following declarations do the same thing:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4[<span class="integer">2</span>] a[<span class="integer">3</span>]; <span class="comment">// size-3 array of size-2 array of vec4</span>
+vec4[<span class="integer">3</span>][<span class="integer">2</span>] a; <span class="comment">// size-3 array of size-2 array of vec4</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When in transparent memory (like in a uniform block), the layout is that the
+inner-most (right-most in declaration) dimensions iterate faster than the
+outer dimensions.
+That is, for the above, the order in memory would be:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>Low address : a[0][0] : a[0][1] : a[1][0] : a[1][1] : a[2][0] : a[2][1]
+: High address</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The last member of a shader storage block (see &#8220;<a href="#buffer-variables">Buffer
+Variables</a>&#8221;), may be declared without specifying a size.
+For such arrays, the effective array size is inferred at run-time from the
+size of the data store backing the shader storage block.
+Such runtime-sized arrays may be indexed with general integer expressions,
+but may not be passed as an argument to a function or indexed with a
+negative constant expression.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> S { <span class="predefined-type">float</span> f; };
+buffer ShaderStorageBlock1
+{
+    vec4 a[]; <span class="comment">// illegal</span>
+    vec4 b[]; <span class="comment">// legal, runtime-sized arrays are last member</span>
+};
+buffer ShaderStorageBlock2
+{
+    vec4 a[<span class="integer">4</span>]; <span class="comment">// legal, size declared</span>
+    S b[]; <span class="comment">// legal, runtime-sized arrays are allowed,</span>
+    <span class="comment">// including arrays of structures</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>However, it is a compile-time error to assign to a runtime-sized array.
+Assignments to individual elements of the array is allowed.</p>
+</div>
+<div class="paragraph">
+<p>Arrays have a fixed number of elements.
+This can be obtained by using the <strong>length</strong>() method:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[<span class="integer">5</span>];
+a.length(); <span class="comment">// returns 5</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The return value is a signed integral expression.
+For compile-time sized arrays, the value returned by the length method is a
+constant expression.
+For run-time sized arrays , the value returned will not be constant
+expression and will be determined at run time based on the size of the
+buffer object providing storage for the block.</p>
+</div>
+<div class="paragraph">
+<p>The precision is determined using the same rules as for other cases where
+there is no intrinsic precision.
+See &#8220;<a href="#precision-qualifiers">Precision Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Any restrictions on the usage of a type also apply to arrays of that type.
+This applies recursively.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="scoping">4.2. Scoping</h3>
+<div class="paragraph">
+<p>The scope of a declaration determines where the declaration is visible.
+GLSL ES uses a system of statically nested scopes.
+This allows names to be redefined within a shader.</p>
+</div>
+<div class="sect3">
+<h4 id="definition-of-terms">4.2.1. Definition of Terms</h4>
+<div class="paragraph">
+<p>The term <em>scope</em> refers to a specified region of the program where names are
+guaranteed to be visible.
+For example, a <em>compound_statement_with_scope</em> ('{' <em>statement</em> <em>statement</em>
+&#8230;&#8203;
+'}') defines a scope.</p>
+</div>
+<div class="paragraph">
+<p>A <em>nested scope</em> is a scope defined within an outer scope.</p>
+</div>
+<div class="paragraph">
+<p>The terms '<em>same scope'</em> and '<em>current scope</em>' are equivalent to the term
+'<em>scope</em>' but used to emphasize that nested scopes are excluded.</p>
+</div>
+<div class="paragraph">
+<p>The <em>scope of a declaration</em> is the region or regions of the program where
+that declaration is visible.</p>
+</div>
+<div class="paragraph">
+<p>A <em>name space</em> defines where names may be defined.
+Within a single name space, a name has at most one entry, specifying it to
+be one of: structure, variable, or function.</p>
+</div>
+<div class="paragraph">
+<p>In general, each scope has an associated name space.
+However, in certain cases e.g. for uniforms, multiple scopes share the same
+name space.
+In these cases, conflicting declarations are an error, even though the name
+is only visible in the scopes where it is declared.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="types-of-scope">4.2.2. Types of Scope</h4>
+<div class="paragraph">
+<p>The scope of a variable is determined by where it is declared.
+If it is declared outside all function definitions, it has global scope,
+which starts from where it is declared and persists to the end of the shader
+it is declared in.
+If it is declared in a <strong>while</strong> test or a <strong>for</strong> statement, then it is scoped
+to the end of the following sub-statement (specified as
+<em>statement-no-new-scope</em> in the grammar).
+Otherwise, if it is declared as a statement within a compound statement, it
+is scoped to the end of that compound statement.
+If it is declared as a parameter in a function definition, it is scoped
+until the end of that function definition.
+A function&#8217;s parameter declarations and body together form a single scope.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> f( <span class="comment">/* nested scope begins here */</span> <span class="predefined-type">int</span> k)
+{
+    <span class="predefined-type">int</span> k = k + <span class="integer">3</span>; <span class="comment">// redeclaration error of the name k</span>
+    ...
+}
+<span class="predefined-type">int</span> f(<span class="predefined-type">int</span> k)
+{
+    {
+       <span class="predefined-type">int</span> k = k + <span class="integer">3</span>; <span class="comment">// 2nd k is parameter, initializing nested first k</span>
+       <span class="predefined-type">int</span> m = k <span class="comment">// use of new k, which is hiding the parameter</span>
+    }
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For both for and while loops, the sub-statement itself does not introduce a
+new scope for variable names, so the following has a redeclaration
+compile-time error:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">for</span> ( <span class="comment">/* nested scope begins here */</span> <span class="predefined-type">int</span> i = <span class="integer">0</span>; i &lt; <span class="integer">10</span>; i++)
+{
+    <span class="predefined-type">int</span> i; <span class="comment">// redeclaration error</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The body of a <strong>do</strong>-<strong>while</strong> loop introduces a new scope lasting only between
+the do and while (not including the while test expression), whether or not
+the body is simple or compound:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> _i_ = <span class="integer">17</span>;
+<span class="keyword">do</span>
+    <span class="predefined-type">int</span> i = <span class="integer">4</span>; <span class="comment">// okay, in nested scope</span>
+<span class="keyword">while</span> (i == <span class="integer">0</span>); <span class="comment">// i is 17, scoped outside the do-while body</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The statement following a <strong>switch</strong> (&#8230;&#8203;) forms a nested scope.</p>
+</div>
+<div class="paragraph">
+<p>Representing the if construct as:</p>
+</div>
+<div class="paragraph">
+<p><strong>if</strong> if-expression <strong>then</strong> if-statement <strong>else</strong> else-statement,</p>
+</div>
+<div class="paragraph">
+<p>a variable declared in the if-statement is scoped to the end of the
+if-statement.
+A variable declared in the else-statement is scoped to the end of the
+else-statement.
+This applies both when these statements are simple statements and when they
+are compound statements.
+The if-expression does not allow new variables to be declared, hence does
+not form a new scope.</p>
+</div>
+<div class="paragraph">
+<p>Within a declaration, the scope of a name starts immediately after the
+initializer if present or immediately after the name being declared if not.
+Several examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> x = <span class="integer">1</span>;
+{
+    <span class="predefined-type">int</span> x = <span class="integer">2</span>,<span class="comment">/* 2nd x visible here */</span> y = x; <span class="comment">// y is initialized to 2</span>
+    <span class="predefined-type">int</span> z = z; <span class="comment">// error if z not previously defined.</span>
+}
+{
+<span class="predefined-type">int</span> x = x; <span class="comment">// x is initialized to '1'</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A structure name declaration is visible at the end of the <em>struct_specifier</em>
+in which it was declared:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> S
+{
+    <span class="predefined-type">int</span> x;
+};
+{
+    S S = S(<span class="integer">0</span>); <span class="comment">// 'S' is only visible as a struct and constructor</span>
+    S; <span class="comment">// 'S' is now visible as a variable</span>
+}
+<span class="predefined-type">int</span> x = x; <span class="comment">// Error if x has not been previously defined.</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="redeclaring-names">4.2.3. Redeclaring Names</h4>
+<div class="paragraph">
+<p>All variable names, structure type names, and function names in a given
+scope share the same name space.
+Function names can be redeclared in the same scope, with the same or
+different parameters, without error.
+Otherwise, within a shader, a declared name cannot be redeclared in the same
+scope; doing so results in a redeclaration error.
+If a nested scope redeclares a name used in an outer scope, it hides all
+existing uses of that name.
+There is no way to access the hidden name or make it unhidden, without
+exiting the scope that hid it.</p>
+</div>
+<div class="paragraph">
+<p>Names of built-in functions cannot be redeclared as functions.
+Therefore overloading or redefining built-in functions is an error.</p>
+</div>
+<div class="paragraph">
+<p>A <em>declaration</em> is considered to be a statement that adds a name or
+signature to the symbol table.
+A <em>definition</em> is a statement that fully defines that name or signature.
+E.g.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> f();<span class="comment">// declaration;</span>
+<span class="predefined-type">int</span> f() {<span class="keyword">return</span> <span class="integer">0</span>;}<span class="comment">// declaration and definition</span>
+<span class="predefined-type">int</span> x; <span class="comment">// declaration and definition</span>
+<span class="predefined-type">int</span> a[<span class="integer">4</span>];<span class="comment">// array declaration and definition</span>
+<span class="keyword">struct</span> S {<span class="predefined-type">int</span> x;};<span class="comment">// structure declaration and definition</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The determination of equivalence of two declarations depends on the type of
+declaration.
+For functions, the whole function signature must be considered (see
+&#8220;Function Definitions&#8221;).
+For variables (including arrays) and structures only the names must match.</p>
+</div>
+<div class="paragraph">
+<p>Within each scope, a name may be declared either as a variable declaration
+<em>or</em> as function declarations <em>or</em> as a structure.</p>
+</div>
+<div class="paragraph">
+<p>Examples of combinations that are allowed:</p>
+</div>
+<div class="paragraph">
+<p>1.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> f(<span class="predefined-type">int</span>) {...}
+<span class="directive">void</span> f(<span class="predefined-type">float</span>) {...}<span class="comment">// function overloading allowed</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>2.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> f(<span class="predefined-type">int</span>);<span class="comment">// 1^st^ declaration (allowed)</span>
+<span class="directive">void</span> f(<span class="predefined-type">int</span>);<span class="comment">// repeated declaration (allowed)</span>
+<span class="directive">void</span> f(<span class="predefined-type">int</span>) {...}<span class="comment">// single definition (allowed)</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Examples of combinations that are disallowed:</p>
+</div>
+<div class="paragraph">
+<p>1.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> f(<span class="predefined-type">int</span>) {...}
+<span class="directive">void</span> f(<span class="predefined-type">int</span>) {...}<span class="comment">// Error: repeated definition</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>2.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> f(<span class="predefined-type">int</span>);
+<span class="keyword">struct</span> f {<span class="predefined-type">int</span> x;};<span class="comment">// Error: type 'f' conflicts with function 'f'</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>3.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> f {<span class="predefined-type">int</span> x;};
+<span class="predefined-type">int</span> f;<span class="comment">// Error: conflicts with the type 'f'</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>4.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> a[<span class="integer">3</span>];
+<span class="predefined-type">int</span> a[<span class="integer">3</span>];<span class="comment">// Error: repeated array definition</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>5.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> x;
+<span class="predefined-type">int</span> x;<span class="comment">// Error: repeated variable definition</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="global-scope">4.2.4. Global Scope</h4>
+<div class="paragraph">
+<p>The built-in functions are scoped in the global scope users declare global
+variables in.
+That is, a shader&#8217;s global scope, available for user-defined functions and
+global variables, is the same as the scope containing the built-in
+functions.
+Function declarations (prototypes) cannot occur inside of functions; they
+must be at global scope.
+Hence it is not possible to hide a name with a function.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="shared-globals">4.2.5. Shared Globals</h4>
+<div class="paragraph">
+<p>Shared globals are variables that can be accessed by multiple compilation
+units.
+In GLSL ES the only shared globals are uniforms.
+Vertex shader outputs are not considered to be shared globals since they
+must pass through the rasterization stage before they are used as input by
+the fragment shader.</p>
+</div>
+<div class="paragraph">
+<p>Shared globals share the same name space, and must be declared with the same
+type and precision.
+They will share the same storage.
+Shared global arrays must have the same base type and the same explicit
+size.
+Scalars must have exactly the same precision, type name and type definition.
+Structures must have the same name, sequence of type names, and type
+definitions, and member names to be considered the same type.
+This rule applies recursively for nested or embedded types.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="storage-qualifiers">4.3. Storage Qualifiers</h3>
+<div class="paragraph">
+<p>Variable declarations may have at most one storage qualifier specified in
+front of the type.
+These are summarized as</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Storage Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;none: default&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">local read/write memory, or an input parameter to a
+                      function</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>const</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a compile-time constant</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>in</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">linkage into a shader from a previous stage, variable
+                      is copied in</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>out</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">linkage out of a shader to a subsequent stage,
+                      variable is copied out</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uniform</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">value does not change across the primitive being
+                      processed, uniforms form the linkage between a shader,
+                      OpenGL ES, and the application</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>buffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">value is stored in a buffer object, and can be read or
+                      written both by shader invocations and the OpenGL ES
+                      API</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>shared</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compute shader only; variable storage is shared across
+                      all work items in a workgroup</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Some input and output qualified variables can be qualified with at most one
+additional auxiliary storage qualifier:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Auxiliary Storage Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>centroid</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">centroid-based interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sample</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">per-sample interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>patch</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">per-tessellation-patch attributes</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Local variables can only use the <strong>const</strong> storage qualifier (or use no
+storage qualifier).</p>
+</div>
+<div class="paragraph">
+<p>Note that function parameters can use <strong>const</strong>, <strong>in</strong>, and <strong>out</strong> qualifiers,
+but as <em>parameter qualifiers</em>.
+Parameter qualifiers are discussed in
+&#8220;<a href="#function-calling-conventions">Function Calling Conventions</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Function return types and structure members do not use storage qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Data types for communication from one run of a shader executable to its next
+run (to communicate between fragments or between vertices) do not exist.
+This would prevent parallel execution of the same shader executable on
+multiple vertices or fragments.</p>
+</div>
+<div class="paragraph">
+<p>In declarations of global variables with no storage qualifier or with a
+const qualifier, any initializer must be a constant expression.
+Declarations of global variables with other storage qualifiers may not
+contain initializers.
+Global variables without storage qualifiers that are not initialized in
+their declaration or by the application will not be initialized by
+OpenGL ES, but rather will enter <em>main()</em> with undefined values.</p>
+</div>
+<div class="sect3">
+<h4 id="default-storage-qualifier">4.3.1. Default Storage Qualifier</h4>
+<div class="paragraph">
+<p>If no qualifier is present on a global variable, then the variable has no
+linkage to the application or shaders running on other pipeline stages.
+For either global or local unqualified variables, the declaration will
+appear to allocate memory associated with the processor it targets.
+This variable will provide read/write access to this allocated memory.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="constant-qualifier">4.3.2. Constant Qualifier</h4>
+<div class="paragraph">
+<p>Named compile-time constants
+can be declared using
+the <strong>const</strong> qualifier.
+Any variables qualified as constant are read-only variables for that shader.
+Declaring variables as constant allows more descriptive shaders than using
+hard-wired numerical constants.
+The <strong>const</strong> qualifier can be used with any of the non-void transparent basic
+data types, as well as with structures and arrays of these.
+It is an error to write to a <strong>const</strong> variable outside of its
+declaration, so they must be initialized when declared.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> vec3 zAxis = vec3 (<span class="float">0</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span>);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Structure members may not be qualified with <strong>const</strong>.
+Structure variables can be declared as <strong>const</strong>, and initialized with a
+structure
+constructor.</p>
+</div>
+<div class="paragraph">
+<p>Initializers for <strong>const</strong> declarations
+must be constant expressions, as defined in
+&#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="constant-expressions">4.3.3. Constant Expressions</h4>
+<div class="paragraph">
+<p>A <em>constant expression</em> is one of</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A literal value (e.g. <strong>5</strong> or <strong>true</strong>).</p>
+</li>
+<li>
+<p>A global or local variable qualified as <strong>const</strong> (i.e., not including
+function parameters).</p>
+</li>
+<li>
+<p>An expression formed by an operator on operands that are all constant
+expressions, including getting an element of a constant array, or a
+member of a constant structure, or components of a constant vector.
+However, the lowest precedence operators of the sequence operator (<strong>,</strong>)
+and the assignment operators (<strong>=</strong>, <strong>+=</strong>, <strong>&#8230;&#8203;</strong>) are not included in the
+operators that can create a constant expression.</p>
+</li>
+<li>
+<p>The <strong>length</strong>() method on a compile-time sized array, whether or not the
+object itself is constant.</p>
+</li>
+<li>
+<p>A constructor whose arguments are all constant expressions.</p>
+</li>
+<li>
+<p>A built-in function call whose arguments are all constant expressions,
+with the exception of the texture lookup functions.
+This rule excludes functions with a <strong>void</strong> return or functions that have
+an <strong>out</strong> parameter.
+The built-in functions <strong>dFdx</strong>, <strong>dFdy</strong>, and <strong>fwidth</strong> must return 0 when
+evaluated inside an initializer with an argument that is a constant
+expression.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Function calls to user-defined functions (non-built-in functions) cannot be
+used to form constant expressions.</p>
+</div>
+<div class="paragraph">
+<p>Scalar, vector, matrix, array and structure variables are constant
+expressions if qualified as <strong>const</strong>.
+Opaque types cannot be constant expressions.</p>
+</div>
+<div class="paragraph">
+<p>A <em>constant integral expression</em> is a constant expression that evaluates to
+a scalar signed or unsigned integer.</p>
+</div>
+<div class="paragraph">
+<p>Constant expressions will be evaluated in an invariant way so as to create
+the same value in multiple shaders when the same constant expressions appear
+in those shaders.
+See &#8220;<a href="#the-invariant-qualifier">The Invariant Qualifier</a>&#8221; for more details
+on how to create invariant expressions and
+&#8220;<a href="#precision-qualifiers">Precision Qualifiers</a>&#8221; for detail on how
+expressions are evaluated.</p>
+</div>
+<div class="paragraph">
+<p>Constant expressions respect the <strong>precise</strong> and <strong>invariant</strong> qualifiers but
+will be always be evaluated in an invariant way, independent of the use of
+such qualification, so as to create the same value in multiple shaders when
+the same constant expressions appear in those shaders.
+See &#8220;<a href="#the-invariant-qualifier">The Invariant Qualifier</a>&#8221; and
+&#8220;<a href="#the-precise-qualifier">The Precise Qualifier</a>&#8221; for more details on how
+to create invariant expressions.</p>
+</div>
+<div class="paragraph">
+<p>Constant
+expressions may be evaluated by the compiler&#8217;s
+host platform, and are therefore not required to compute the same value that
+the same expression would evaluate to on the shader execution target.
+However, the host must use the same or greater precision than the target
+would use.
+When the precision qualification cannot be determined, the expression is
+evaluated at <strong>highp</strong>.
+See &#8220;<a href="#default-precision-qualifiers">Default Precision Qualifiers</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="input-variables">4.3.4. Input Variables</h4>
+<div class="paragraph">
+<p>Shader input variables are declared with the <strong>in</strong> storage qualifier.
+They form the input interface between previous stages of the OpenGL ES
+pipeline and the declaring shader.
+Input variables must be declared at global scope.
+Values from the previous pipeline stage are copied into input variables at
+the beginning of shader execution.
+It is an error to write to a variable declared as an input.</p>
+</div>
+<div class="paragraph">
+<p>Only the input variables that are
+actually
+read need to be written by the
+previous stage; it is allowed to have superfluous declarations of input
+variables.</p>
+</div>
+<div class="paragraph">
+<p>See &#8220;<a href="#built-in-variables">Built-In Variables</a>&#8221; for a list of the built-in
+input names.</p>
+</div>
+<div class="paragraph">
+<p>Vertex shader input variables (or attributes) receive per-vertex data.
+It is an error to use auxiliary storage or interpolation qualifiers
+on a vertex shader input.
+The values copied in are established by the OpenGL ES API or through the use
+of the layout identifier <strong>location</strong>.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a vertex shader input with, or that
+contains, any of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>An array</p>
+</li>
+<li>
+<p>A structure</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Example declarations in a vertex shader:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 position;
+in vec3 normal;
+in vec2 texCoord[<span class="integer">4</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is expected that graphics hardware will have a small number of fixed
+vector locations for passing vertex inputs.
+Therefore, the OpenGL ES Shading Language defines each non-matrix input variable as taking up
+one such vector location.
+There is an implementation-dependent limit on the number of locations that
+can be used, and if this is exceeded it will cause a link-time error.
+(Declared input variables that are not statically used do not count against
+this limit.) A scalar input counts the same amount against this limit as a
+<strong>vec4</strong>, so applications may want to consider packing groups of four
+unrelated float inputs together into a vector to better utilize the
+capabilities of the underlying hardware.
+A matrix input will use up multiple locations.
+The number of locations used will equal the number of columns in the matrix.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control, evaluation, and geometry shader input variables get
+the per-vertex values written out by output variables of the same names in
+the previous active shader stage.
+For these inputs, <strong>centroid</strong> and interpolation qualifiers are allowed, but
+have no effect.
+Since tessellation control, tessellation evaluation, and geometry shaders
+operate on a set of vertices, each input variable (or input block, see
+interface blocks below) needs to be declared as an array.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in <span class="predefined-type">float</span> foo[]; <span class="comment">// geometry shader input for vertex &quot;out float foo&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Each element of such an array corresponds to one vertex of the primitive
+being processed.
+Each array can optionally have a size declared.
+For geometry shaders, the array size will be set by, (or if provided must be
+consistent with) the input <strong>layout</strong> declaration(s) establishing the type of
+input primitive, as described later in &#8220;<a href="#input-layout-qualifiers">Input
+Layout Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Some inputs and outputs are <em>arrayed</em>, meaning that for an interface between
+two shader stages either the input or output declaration requires an extra
+level of array indexing for the declarations to match.
+For example, with the interface between a vertex shader and a geometry
+shader, vertex shader output variables and geometry shader input variables
+of the same name must have matching types, except that the geometry shader
+will have one more array dimension than the vertex shader, to allow for
+vertex indexing.
+If such an arrayed interface variable is not declared with the necessary
+additional input or output array dimension, a link-time error will result.
+Geometry shader inputs, tessellation control shader inputs and outputs, and
+tessellation evaluation inputs all have an additional level of arrayness
+relative to other shader inputs and outputs.
+These inputs and outputs are known as <em>per-vertex-arrayed</em> inputs and
+outputs.
+Component limits for arrayed interfaces (e.g.
+<em>gl_MaxTessControlInputComponents</em>) are limits per vertex, not limits for
+the entire interface.</p>
+</div>
+<div class="paragraph">
+<p>For non-arrayed interfaces (meaning array dimensionally stays the same
+between stages), it is a link-time error if the input variable is not
+declared with the same type, including array dimensionality, as the matching
+output variable.</p>
+</div>
+<div class="paragraph">
+<p>The link-time type-matching rules apply to all declared input and output
+variables, whether or not they are used.</p>
+</div>
+<div class="paragraph">
+<p>Additionally, tessellation evaluation shaders support per-patch input
+variables declared with the <strong>patch</strong> and <strong>in</strong> qualifiers.
+Per-patch input variables are filled with the values of per-patch output
+variables written by the tessellation control shader.
+Per-patch inputs may be declared as one-dimensional arrays, but are not
+indexed by vertex number.
+Applying the <strong>patch</strong> qualifier to inputs can only be done in tessellation
+evaluation shaders.
+As with other input variables, per-patch inputs must be declared using the
+same type and qualification as per-patch outputs from the previous
+(tessellation control) shader stage.
+It is a compile-time error to use <strong>patch</strong> with inputs in any other stage.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a tessellation control, tessellation
+evaluation or geometry shader input with, or that contains, any of the
+following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>A structure containing an array</p>
+</li>
+<li>
+<p>A structure containing a structure</p>
+</li>
+<li>
+<p>For per-vertex-arrayed variables:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>Per-vertex-arrayed arrays of arrays</p>
+</li>
+<li>
+<p>Per-vertex-arrayed arrays of structures</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>For non-per-vertex-arrayed variables:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>An array of arrays</p>
+</li>
+<li>
+<p>An array of structures</p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Fragment shader inputs get per-fragment values, typically interpolated from
+a previous stage&#8217;s outputs.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a fragment shader input with, or that
+contains, any of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>An array of arrays</p>
+</li>
+<li>
+<p>An array of structures</p>
+</li>
+<li>
+<p>A structure containing an array</p>
+</li>
+<li>
+<p>A structure containing a structure</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Fragment shader inputs that are, or contain, integral
+types must be
+qualified with the interpolation qualifier <strong>flat</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Fragment inputs are declared as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec3 normal;
+centroid in vec2 TexCoord;
+flat in vec3 myColor;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The fragment shader inputs form an interface with the last active shader in
+the vertex processing pipeline.
+For this interface, the last active shader stage output variables and
+fragment shader input variables of the same name must match in type and
+qualification, with a few exceptions: The storage qualifiers must, of
+course, differ (one is <strong>in</strong> and one is <strong>out</strong>).
+Also,
+auxiliary qualification (e.g. <strong>centroid</strong>) may differ.
+When
+auxiliary qualifiers do not match, those provided in
+the fragment shader supersede those provided in previous stages.
+If any such qualifiers are completely missing in the fragment shaders, then
+the default is used, rather than any qualifiers that may have been declared
+in previous stages.
+That is, what matters is what is declared in the fragment shaders, not what
+is declared in shaders in previous stages.</p>
+</div>
+<div class="paragraph">
+<p>When an interface between shader stages is formed using shaders from two
+separate program objects, it is not possible to detect mismatches between
+inputs and outputs when the programs are linked.
+When there are mismatches between inputs and outputs on such interfaces,
+attempting to use the two programs in the same program pipeline will result
+in program pipeline validation failures, as described in section 7.4.1
+&#8220;Shader Interface Matching&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>Shaders can ensure matches across such interfaces either by using input and
+output layout qualifiers (sections &#8220;<a href="#input-layout-qualifiers">Input Layout
+Qualifiers</a>&#8221; and &#8220;<a href="#output-layout-qualifiers">Output Layout
+Qualifiers</a>&#8221;) or by using identical input and output declarations of
+blocks or variables.
+Complete rules for interface matching are found in section 7.4.1 &#8220;Shader
+Interface Matching&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>Compute shaders do not permit user-defined input variables and do not form a
+formal interface with any other shader stage.
+See &#8220;<a href="#compute-shader-special-variables">Compute Shader Special
+Variables</a>&#8221; for a description of built-in compute shader input variables.
+All other input to a compute shader is retrieved explicitly through image
+loads, texture fetches, loads from uniforms or uniform buffers, or other
+user supplied code.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-variables">4.3.5. Uniform Variables</h4>
+<div class="paragraph">
+<p>The <strong>uniform</strong> qualifier is used to declare global variables whose values are
+the same across the entire primitive being processed.
+All <strong>uniform</strong> variables are read-only.
+Except for variables declared within a uniform block, all uniform variables
+are initialized to 0 at link time and may be updated through the API.</p>
+</div>
+<div class="paragraph">
+<p>Example declarations are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform vec4 lightPosition;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>uniform</strong> qualifier can be used with any of the basic data types, or
+when declaring a variable whose type is a structure, or an array of any of
+these.</p>
+</div>
+<div class="paragraph">
+<p>There is an implementation-dependent limit on the amount of storage for
+uniforms that can be used for each type of shader and if this is exceeded it
+will cause a compile-time or link-time error.
+Uniform variables that are declared but not
+statically
+used do not count against this limit.
+The number of user-defined uniform variables and the number of built-in
+uniform variables that are used within a shader are added together to
+determine whether available uniform storage has been exceeded.</p>
+</div>
+<div class="paragraph">
+<p>Uniforms in shaders all share a single global name space when linked into a
+program or separable program.
+Hence, the types,
+precisions,
+and any location specifiers of all statically used uniform variables with the
+same name must match across all shaders that are linked into a single program.
+However it is not required to repeat the
+location specifier in all the linked shaders.
+While this single uniform name space is cross stage, a uniform variable
+name&#8217;s scope is per stage: If a uniform variable name is declared in one
+stage (e.g. a vertex shader) but not in another (e.g. a fragment shader),
+then that name is still available in the other stage for a different use.</p>
+</div>
+<div class="paragraph">
+<p>A compile or link-time error is generated if any of the explicitly given or
+compiler generated uniform locations is greater than the
+implementation-defined maximum number of uniform locations minus one.</p>
+</div>
+<div class="paragraph">
+<p>Unlike locations for inputs and outputs, uniform locations are logical
+values, not register locations, and there is no concept of overlap.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">2</span>) uniform mat4 x;
+layout(location = <span class="integer">3</span>) uniform mat4 y; <span class="comment">// No overlap with x</span>
+layout(location = <span class="integer">2</span>) in mat4 x;
+layout(location = <span class="integer">3</span>) in mat4 y; <span class="comment">// Error, locations conflict with x</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="output-variables">4.3.6. Output Variables</h4>
+<div class="paragraph">
+<p>Shader output variables are declared with the <strong>out</strong> storage qualifier.
+They form the output interface between the declaring shader and the
+subsequent stages of the OpenGL ES pipeline.
+Output variables must be declared at global scope.
+During shader execution they will behave as normal unqualified global
+variables.
+Their values are copied out to the subsequent pipeline stage on shader exit.
+Only output variables that are read by the subsequent pipeline stage need to
+be written; it is allowed to have superfluous declarations of output
+variables.</p>
+</div>
+<div class="paragraph">
+<p>There is <em>not</em> an <strong>inout</strong> storage qualifier for declaring a single variable
+name as both input and output to a shader.
+Also, a variable cannot be declared with both the <strong>in</strong> and the <strong>out</strong>
+qualifiers, this will result in a compile-time or link-time error.
+Output variables must be declared with different names than input variables.
+However, nesting an input or output inside an interface block with an
+instance name allows the same names with one referenced through a block
+instance name.</p>
+</div>
+<div class="paragraph">
+<p>Vertex, tessellation evaluation, and geometry output variables output
+per-vertex data and are declared using the <strong>out</strong> storage qualifier.
+Applying <strong>patch</strong> to an output can only be done in a tessellation control
+shader.
+It is a compile-time error to use <strong>patch</strong> on outputs in any other stage.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a vertex, tessellation evaluation,
+tessellation control, or geometry shader output with, or that contains, any
+of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>A structure containing an array</p>
+</li>
+<li>
+<p>A structure containing a structure</p>
+</li>
+<li>
+<p>For per-vertex-arrayed variables (applies to tessellation control,
+tessellation evaluation and geometry shaders):</p>
+<div class="ulist">
+<ul>
+<li>
+<p>Per-vertex-arrayed arrays of arrays</p>
+</li>
+<li>
+<p>Per-vertex-arrayed arrays of structures</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>For non-per-vertex-arrayed variables:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>An array of arrays</p>
+</li>
+<li>
+<p>An array of structures</p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Vertex shader outputs may be qualified with the interpolation qualifier
+<strong>flat</strong><sup>1</sup>.</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">1</dt>
+<dd>
+<p>Unlike previous versions of the OpenGL ES Shading Language, there is no requirement for
+outputs containing integers to be qualified as <strong>flat</strong>, since the vertex
+shader may interface with the tessellation control shader.
+However, in all cases, the qualifier must match across interfaces.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Individual outputs are declared as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec3 normal;
+centroid out vec2 TexCoord;
+invariant centroid out vec4 Color;
+flat out vec3 myColor;
+sample out vec4 perSampleColor;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>These can also appear in interface blocks, as described in
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221;.
+Interface blocks allow simpler addition of arrays to the interface from
+vertex to geometry shader.
+They also allow a fragment shader to have the same input interface as a
+geometry shader for a given vertex shader.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control shader output variables are used to output
+per-vertex and per-patch data.
+Per-vertex output variables are arrayed (see <em>arrayed</em> under
+&#8220;<a href="#input-variables">Input Variables</a>&#8221;) and declared using the <strong>out</strong>
+qualifier without the <strong>patch</strong> qualifier.
+Per-patch output variables are declared using the <strong>patch</strong> and <strong>out</strong>
+qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Since tessellation control shaders produce an arrayed primitive comprising
+multiple vertices, each per-vertex output variable (or output block, see
+interface blocks below) needs to be declared as an array.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out <span class="predefined-type">float</span> foo[]; <span class="comment">// feeds next stage input &quot;in float foo[]&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Each element of such an array corresponds to one vertex of the primitive
+being produced.
+Each array can optionally have a size declared.
+The array size will be set by (or if provided must be consistent with) the
+output layout declaration(s) establishing the number of vertices in the
+output patch, as described later in
+&#8220;<a href="#tessellation-control-outputs">Tessellation Control Outputs</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Each tessellation control shader invocation has a corresponding output patch
+vertex, and may assign values to per-vertex outputs only if they belong to
+that corresponding vertex.
+If a per-vertex output variable is used as an l-value, it is a compile-time
+or link-time error if the expression indicating the vertex index is not the
+identifier <em>gl_InvocationID</em>.</p>
+</div>
+<div class="paragraph">
+<p>The order of execution of a tessellation control shader invocation relative
+to the other invocations for the same input patch is undefined unless the
+built-in function <strong>barrier</strong>() is used.
+This provides some control over relative execution order.
+When a shader invocation calls <strong>barrier</strong>(), its execution pauses until all
+other invocations have reached the same point of execution.
+Output variable assignments performed by any invocation executed prior to
+calling <strong>barrier</strong>() will be visible to any other invocation after the call
+to <strong>barrier</strong>() returns.</p>
+</div>
+<div class="paragraph">
+<p>Because tessellation control shader invocations execute in undefined order
+between barriers, the values of per-vertex or per-patch output variables
+will sometimes be undefined.
+Consider the beginning and end of shader execution and each call to
+<strong>barrier</strong>() as synchronization points.
+The value of an output variable will be undefined in any of the three
+following cases:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>At the beginning of execution.</p>
+</li>
+<li>
+<p>At each synchronization point, unless</p>
+<div class="openblock">
+<div class="content">
+<div class="ulist">
+<ul>
+<li>
+<p>the value was well-defined after the previous synchronization point and
+was not written by any invocation since, or</p>
+</li>
+<li>
+<p>the value was written by exactly one shader invocation since the previous
+synchronization point, or</p>
+</li>
+<li>
+<p>the value was written by multiple shader invocations since the previous
+synchronization point, and the last write performed by all such
+invocations wrote the same value.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</li>
+<li>
+<p>When read by a shader invocation, if</p>
+<div class="openblock">
+<div class="content">
+<div class="ulist">
+<ul>
+<li>
+<p>the value was undefined at the previous synchronization point and has not
+been written by the same shader invocation since, or</p>
+</li>
+<li>
+<p>the output variable is written to by any other shader invocation between
+the previous and next synchronization points, even if that assignment
+occurs in code following the read.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Fragment outputs output per-fragment data and are declared using the <strong>out</strong>
+storage qualifier.
+It is an error to use auxiliary storage qualifiers or
+interpolation qualifiers in a fragment shader output declaration.
+It is a compile-time error to declare a fragment shader output with, or that
+contains, any of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>A matrix type</p>
+</li>
+<li>
+<p>A structure</p>
+</li>
+<li>
+<p>An array of arrays</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Fragment shader outputs declared as arrays may only be indexed by a constant
+integral expression.</p>
+</div>
+<div class="paragraph">
+<p>Fragment outputs are declared as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec4 FragmentColor;
+out uint Luminosity;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Compute shaders have no built-in output variables, do not support
+user-defined output variables and do not form a formal interface with any
+other shader stage.
+All outputs from a compute shader take the form of the side effects such as
+image stores and operations on atomic counters.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="buffer-variables">4.3.7. Buffer Variables</h4>
+<div class="paragraph">
+<p>The <strong>buffer</strong> qualifier is used to declare global variables whose values are
+stored in the data store of a buffer object bound through the OpenGL ES API.
+Buffer variables can be read and written, with the underlying storage shared
+among all active shader invocations.
+Buffer variable memory reads and writes within a single shader invocation
+are processed in order.
+However, the order of reads and writes performed in one invocation relative
+to those performed by another invocation is largely undefined.
+Buffer variables may be qualified with memory qualifiers affecting how the
+underlying memory is accessed, as described in &#8220;<a href="#memory-qualifiers">Memory
+Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>buffer</strong> qualifier can be used to declare interface blocks (see
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221;), which are then referred to as
+shader storage blocks.
+It is a compile-time error to declare buffer variables outside a block.
+Buffer variables cannot have initializers.</p>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="title">Note</div>
+<div class="paragraph">
+<p>The terms <em>shader storage buffer (object)</em>, and <em>shader storage block</em> are
+often used interchangeably.
+The former generally refers to the underlying storage whereas the latter
+refers only to the interface definition in the shader.
+Similarly for <em>uniform buffer objects</em> and _uniform blocks.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// use buffer to create a buffer block (shader storage block)</span>
+buffer BufferName { <span class="comment">// externally visible name of buffer</span>
+    <span class="predefined-type">int</span> count;      <span class="comment">// typed, shared memory...</span>
+    ...             <span class="comment">// ...</span>
+    vec4 v[];       <span class="comment">// last member may be an array that is not sized</span>
+                    <span class="comment">// until after link time (dynamically sized)</span>
+} Name;             <span class="comment">// name of block within the shader</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There are implementation-dependent limits on the number of shader storage
+blocks used for each type of shader, the combined number of shader storage
+blocks used for a program, and the amount of storage required by each
+individual shader storage block.
+If any of these limits are exceeded, it will cause a compile-time or
+link-time error.</p>
+</div>
+<div class="paragraph">
+<p>If multiple shaders are linked together, then they will share a single
+global buffer variable name space.
+Hence, the types of all declared buffer variables with the same name must
+match across all shaders that are linked into a single program.</p>
+</div>
+<div class="paragraph">
+<p>Precision qualifiers for such variables need not match.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="shared-variables">4.3.8. Shared Variables</h4>
+<div class="paragraph">
+<p>The <strong>shared</strong> qualifier is used to declare global variables that have storage
+shared between all work items in a compute shader workgroup.
+Variables declared as <strong>shared</strong> may only be used in compute shaders (see
+&#8220;<a href="#compute-processor">Compute Processor</a>&#8221;).
+Any other declaration of a <strong>shared</strong> variable is an error.
+Shared variables are implicitly coherent (see
+&#8220;<a href="#memory-qualifiers">Memory Qualifiers</a>&#8221;).</p>
+</div>
+<div class="paragraph">
+<p>Variables declared as <strong>shared</strong> may not have initializers and their contents
+are undefined at the beginning of shader execution.
+Any data written to <strong>shared</strong> variables will be visible to other work items
+(executing the same shader) within the same workgroup.</p>
+</div>
+<div class="paragraph">
+<p>In the absence of synchronization, the order of reads and writes to the same
+<strong>shared</strong> variable by different invocations of a shader is not defined.</p>
+</div>
+<div class="paragraph">
+<p>In order to achieve ordering with respect to reads and writes to <strong>shared</strong>
+variables, control flow barriers must be employed using the <strong>barrier</strong>() function
+(see &#8220;<a href="#shader-invocation-control-functions">Shader Invocation Control
+Functions</a>&#8221;).</p>
+</div>
+<div class="paragraph">
+<p>There is a limit to the total size of all variables declared as <strong>shared</strong> in a
+single program.
+This limit, expressed in units of basic machine units may be determined by
+using the OpenGL ES API to query the value of
+MAX_COMPUTE_SHARED_MEMORY_SIZE.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="interface-blocks">4.3.9. Interface Blocks</h4>
+<div class="paragraph">
+<p>Input, output, uniform, and buffer variable declarations can be grouped into
+named interface blocks to provide coarser granularity backing than is
+achievable with individual declarations.
+They can have an optional instance name, used in the shader to reference
+their members.
+An output block of one programmable stage is backed by a corresponding input
+block in the subsequent programmable stage.
+A <em>uniform block</em> is backed by the application with a buffer object.
+A block of buffer variables, called a <em>shader storage block</em>, is also backed
+by the application with a buffer object.
+It is a compile-time error to have an input block in a vertex shader or an
+output block in a fragment shader.
+These uses are reserved for future use.</p>
+</div>
+<div class="paragraph">
+<p>An interface block is started by an <strong>in</strong>, <strong>out</strong>, <strong>uniform</strong>, or <strong>buffer</strong>
+keyword, followed by a block name, followed by an open curly brace (<strong>{</strong>) as
+follows:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>interface-block</em> : </dt>
+<dd>
+<p><em>layout-qualifier<sub>opt</sub></em> <em>interface-qualifier</em> <em>block-name</em> <strong>{</strong>
+<em>member-list</em> <strong>}</strong> <em>instance-name<sub>opt</sub></em> <strong>;</strong></p>
+</dd>
+</dl>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>interface-qualifier</em> : </dt>
+<dd>
+<p><strong>in</strong><br>
+<strong>out</strong><br>
+<strong>patch</strong> <strong>in</strong> // Note: Qualifiers can be in any order.<br>
+<strong>patch</strong> <strong>out</strong><br>
+<strong>uniform</strong><br>
+<strong>buffer</strong></p>
+</dd>
+</dl>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>member-list</em> : </dt>
+<dd>
+<p><em>member-declaration</em><br>
+<em>member-declaration</em> <em>member-list</em></p>
+</dd>
+<dt class="hdlist1"><em>member-declaration</em> : </dt>
+<dd>
+<p><em>layout-qualifier<sub>opt</sub></em> <em>qualifiers<sub>opt</sub></em> <em>type</em> <em>declarators</em> <strong>;</strong></p>
+</dd>
+</dl>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>instance-name</em> : </dt>
+<dd>
+<p><em>identifier</em><br>
+<em>identifier</em> <strong>[</strong> <strong>]</strong><br>
+<em>identifier</em> <strong>[</strong> <em>constant-integral-expression</em> <strong>]</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Each of the above elements is discussed below, with the exception of layout
+qualifiers (<em>layout-qualifier</em>), which are defined in the next section.</p>
+</div>
+<div class="paragraph">
+<p>First, an example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform Transform {
+    mat4 ModelViewMatrix;
+    mat4 ModelViewProjectionMatrix;
+    uniform mat3 NormalMatrix;      <span class="comment">// allowed restatement of qualifier</span>
+    <span class="predefined-type">float</span> Deformation;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The above establishes a uniform block named &#8220;Transform&#8221; with four uniforms
+grouped inside it.</p>
+</div>
+<div class="paragraph">
+<p>Types and declarators are the same as for other input, output, uniform, and
+buffer variable declarations outside blocks, with these exceptions:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Opaque types are not allowed</p>
+</li>
+<li>
+<p>Structure definitions cannot be nested inside a block</p>
+</li>
+<li>
+<p>Arrays of arrays of blocks are not allowed, except for the case in the
+tessellation pipe where the declaration is a per-vertex-array of arrays
+of blocks.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>If no optional qualifier is used in a member-declaration, the qualification
+of the member includes all <strong>in</strong>, <strong>out</strong>, <strong>patch</strong>, <strong>uniform</strong>, or <strong>buffer</strong> as
+determined by <em>interface-qualifier</em>.
+If optional qualifiers are used, they can include interpolation qualifiers,
+auxiliary storage qualifiers,
+precision qualifiers,
+and storage qualifiers and they must declare
+an input, output, or uniform member consistent with the interface qualifier
+of the block: Input variables, output variables, uniform variables, and
+<strong>buffer</strong> members can only be in <strong>in</strong> blocks, <strong>out</strong> blocks, <strong>uniform</strong> blocks,
+and shader storage blocks, respectively.</p>
+</div>
+<div class="paragraph">
+<p>Repeating the <strong>in</strong>, <strong>out</strong>, <strong>patch</strong>, <strong>uniform</strong>, or <strong>buffer</strong> interface
+qualifier for a member&#8217;s storage qualifier is optional.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in Material {
+    smooth in vec4 Color1; <span class="comment">// legal, input inside in block</span>
+    smooth vec4 Color2;    <span class="comment">// legal, 'in' inherited from 'in Material'</span>
+    vec2 TexCoord;         <span class="comment">// legal, TexCoord is an input</span>
+    uniform <span class="predefined-type">float</span> Atten;   <span class="comment">// illegal, mismatched storage qualifier</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A <em>shader interface</em> is defined to be one of these:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>All the uniform variables and uniform blocks declared in a program.
+This spans all compilation units linked together within one program.</p>
+</li>
+<li>
+<p>All the <strong>buffer</strong> blocks declared in a program.</p>
+</li>
+<li>
+<p>The boundary between adjacent programmable pipeline stages: This spans
+all the outputs declared in all compilation units of the first stage and
+all the inputs declared in all compilation units of the second stage.
+Note that for the purposes of this definition, the fragment shader and
+the preceding shader are considered to have a shared boundary even
+though in practice, all values passed to the fragment shader first pass
+through the rasterizer and interpolator.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The block name (<em>block-name</em>) is used to match within shader interfaces: an
+output block of one pipeline stage will be matched to an input block with
+the same name in the subsequent pipeline stage.
+For uniform or shader storage blocks, the application uses the block name to
+identify the block.
+Block names have no other use within a shader beyond interface matching; it
+is an error
+to use a block name at global scope for anything other than as a
+block name (e.g. use of a block name for a global variable name or function
+name is currently reserved).
+It is a compile-time error to use the same block name for more than one
+block declaration in the same shader interface (as defined above) within one
+shader, even if the block contents are identical.</p>
+</div>
+<div class="paragraph">
+<p>Matched block names within a shader interface (as defined above) must match
+in terms of having the same number of declarations with the same sequence of
+types and the same sequence of member names, as well as having matching
+member-wise layout qualification
+as defined in &#8220;<a href="#matching-of-qualifiers">Matching of Qualifiers</a>&#8221;.
+Matched uniform or shader storage block names (but not input or output block
+names) must also either all be lacking an instance name or all having an
+instance name, putting their members at the same scoping level.
+When instance names are present on matched block names, it is allowed for
+the instance names to differ; they need not match for the blocks to match.
+Furthermore, if a matching block is declared as an array, then the array
+sizes must also match (or follow array matching rules for the shader
+interface between consecutive shader stages).
+Any mismatch will generate a link-time error.
+A block name is allowed to have different definitions in different shader
+interfaces within the same shader, allowing, for example, an input block and
+output block to have the same name.</p>
+</div>
+<div class="paragraph">
+<p>If an instance name (<em>instance-name</em>) is not used, the names declared inside
+the block are scoped at the global level and accessed as if they were
+declared outside the block.
+If an instance name (<em>instance-name</em>) is used, then it puts all the members
+inside a scope within its own name space, accessed with the field selector
+(<strong>.</strong>) operator (analogously to structures).
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in Light {
+    vec4 LightPos;
+    vec3 LightColor;
+};
+in ColoredTexture {
+    vec4 Color;
+    vec2 TexCoord;
+} Material;           <span class="comment">// instance name</span>
+vec3 Color;           <span class="comment">// different Color than Material.Color</span>
+vec4 LightPos;        <span class="comment">// illegal, already defined</span>
+...
+... = LightPos;       <span class="comment">// accessing LightPos</span>
+... = Material.Color; <span class="comment">// accessing Color in ColoredTexture block</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Outside the shading language (i.e., in the API), members are similarly
+identified except the block name is always used in place of the instance
+name (API accesses are to shader interfaces, not to shaders).
+If there is no instance name, then the API does not use the block name to
+access a member, just the member name.</p>
+</div>
+<div class="paragraph">
+<p>Within a shader interface, all declarations of the same global name must be
+for the same object and must match in type and in whether they declare a
+variable or member of a block with no instance name.
+The API also needs this name to uniquely identify an object in the shader
+interface.
+It is a link-time error if any particular shader interface contains</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>two different blocks, each having no instance name, and each having a
+member of the same name, or</p>
+</li>
+<li>
+<p>a variable outside a block, and a block with no instance name, where the
+variable has the same name as a member in the block.</p>
+</li>
+</ul>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out Vertex {
+    vec4 Position;  <span class="comment">// API transform/feedback will use &quot;Vertex.Position&quot;</span>
+    vec2 Texture;
+} Coords;           <span class="comment">// shader will use &quot;Coords.Position&quot;</span>
+out Vertex2 {
+    vec4 Color;     <span class="comment">// API will use &quot;Color&quot;</span>
+    <span class="predefined-type">float</span> Color2;
+};
+
+<span class="comment">// in same program as Vertex2 above:</span>
+out Vertex3 {
+    <span class="predefined-type">float</span> Intensity;
+    vec4 Color;     <span class="comment">// ERROR, name collision with Color in Vertex2</span>
+};
+<span class="predefined-type">float</span> Color2;       <span class="comment">// ERROR, collides with Color2 in Vertex2</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For blocks declared as arrays, the array index must also be included when
+accessing members, as in this example</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform Transform { <span class="comment">// API uses &quot;Transform[2]&quot; to refer to instance 2</span>
+    mat4 ModelViewMatrix;
+    mat4 ModelViewProjectionMatrix;
+    <span class="predefined-type">float</span> Deformation;
+} transforms[<span class="integer">4</span>];
+...
+... = transforms[<span class="integer">2</span>].ModelViewMatrix; <span class="comment">// shader access of instance 2</span>
+<span class="comment">// API uses &quot;Transform.ModelViewMatrix&quot; to query an offset or other query</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For uniform or shader storage blocks declared as an array, each individual
+array element corresponds to a separate buffer object bind range, backing
+one instance of the block.
+As the array size indicates the number of buffer objects needed, uniform and
+shader storage block array declarations must specify an array size.
+All indices used to index a shader storage block array must be constant
+integral expressions.
+A uniform block array can only be indexed with a dynamically uniform
+integral expression, otherwise results are undefined.</p>
+</div>
+<div class="paragraph">
+<p>When using OpenGL ES API entry points to identify the name of an individual
+block in an array of blocks, the name string may include an array index
+(e.g. <em>Transform[2]</em>).
+When using OpenGL ES API entry points to refer to offsets or other
+characteristics of a block member, an array index must not be specified
+(e.g. <em>Transform.ModelViewMatrix</em>).
+See section 7.3.1 &#8220;Program Interfaces&#8221; of the <a href="#references">OpenGL ES Specification</a> for
+details.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control, tessellation evaluation and geometry shader input
+blocks must be declared as arrays and follow the array declaration and
+linking rules for all shader inputs for the respective stages.
+All other input and output block arrays must specify an array size.</p>
+</div>
+<div class="paragraph">
+<p>There are implementation-dependent limits on the number of uniform blocks
+and the number of shader storage blocks that can be used per stage.
+If either limit is exceeded, it will cause a link-time error.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="layout-qualifiers">4.4. Layout Qualifiers</h3>
+<div class="paragraph">
+<p>Layout qualifiers can appear in several forms of declaration.
+They can appear as part of an interface block definition or block member, as
+shown in the grammar in the previous section.
+They can also appear with just an <em>interface-qualifier</em> to establish layouts
+of other declarations made with that qualifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="paragraph">
+<p><em>layout-qualifier</em> <em>interface-qualifier</em> <strong>;</strong></p>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Or, they can appear with an individual variable declared with an interface
+qualifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="paragraph">
+<p><em>layout-qualifier</em> <em>interface-qualifier</em> <em>declaration</em> <strong>;</strong></p>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Declarations of layouts can only be made at global scope or block members,
+and only where indicated in the following subsections; their details are
+specific to what the interface qualifier is, and are discussed individually.</p>
+</div>
+<div class="paragraph">
+<p>The <em>layout-qualifier</em> expands to:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier</em> : </dt>
+<dd>
+<p><strong>layout</strong> <strong>(</strong> <em>layout-qualifier-id-list</em> <strong>)</strong></p>
+</dd>
+<dt class="hdlist1"><em>layout-qualifier-id-list</em> : </dt>
+<dd>
+<p><em>layout-qualifier-id</em><br>
+<em>layout-qualifier-id</em> <strong>,</strong> <em>layout-qualifier-id-list</em></p>
+</dd>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><em>layout-qualifier-name</em><br>
+<em>layout-qualifier-name</em> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>shared</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-value</em> : </dt>
+<dd>
+<p><em>integer-constant</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The tokens used for <em>layout-qualifier-name</em> are identifiers, not keywords,
+however, the <strong>shared</strong> keyword is allowed as a <em>layout-qualifier-id</em>.
+Generally, they can be listed in any order.
+Order-dependent meanings exist only if explicitly called out below.
+As for other identifiers, they are case sensitive.</p>
+</div>
+<div class="paragraph">
+<p>The set of allowed layout qualifiers depends on the shader, the interface
+and the variable type as specified in the following sections.
+For example, a sampler in the default uniform block in a fragment shader can
+have <strong>location</strong> and <strong>binding</strong> layout qualifiers but no others.
+Invalid use of layout qualifiers is an error.</p>
+</div>
+<div class="paragraph">
+<p>The following table summarizes the use of layout qualifiers.
+It shows for each one what kinds of declarations it may be applied to.
+These are all discussed in detail in the following sections.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.667%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Layout Qualifier</th>
+<th class="tableblock halign-left valign-top">Qualifier Only</th>
+<th class="tableblock halign-left valign-top">Individual Variable</th>
+<th class="tableblock halign-left valign-top">Block</th>
+<th class="tableblock halign-left valign-top">Block Member</th>
+<th class="tableblock halign-left valign-top">Allowed Interfaces</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>shared</strong><br>
+  <strong>packed</strong><br>
+  <strong>std140</strong><br>
+  <strong>std430</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top" rowspan="4"><p class="tableblock"><strong>uniform</strong> / <strong>buffer</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>row_major</strong><br>
+  <strong>column_major</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>binding</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">opaque types only</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>offset</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">atomic counters only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>location</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uniform</strong> / <strong>buffer</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>location</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X<sup>1</sup></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">all <strong>in</strong> / <strong>out</strong>, except for compute</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>triangles</strong><br>
+  <strong>quads</strong><br>
+  <strong>isolines</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>equal_spacing</strong><br>
+  <strong>fractional_even_spacing</strong><br>
+  <strong>fractional_odd_spacing</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cw</strong><br>
+  <strong>ccw</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>point_mode</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>points</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>in</strong>/<strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">[ <strong>points</strong> ]<br>
+  <strong>lines</strong><br>
+  <strong>lines_adjacency</strong><br>
+  <strong>triangles</strong><br>
+  <strong>triangles_adjacency</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>invocations</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>early_fragment_tests</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">fragment <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>local_size_x</strong> =<br>
+  <strong>local_size_y</strong> =<br>
+  <strong>local_size_z</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compute <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vertices</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation control <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">[ <strong>points</strong> ]<br>
+  <strong>line_strip</strong><br>
+  <strong>triangle_strip</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>max_vertices</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>rgba32f</strong><br>
+  <strong>rgba16f</strong><br>
+  <strong>r32f</strong><br>
+  <strong>rgba8</strong><br>
+  <strong>rgba8_snorm</strong><br>
+  <strong>rgba32i</strong><br>
+  <strong>rgba16i</strong><br>
+  <strong>rgba8i</strong><br>
+  <strong>r32i</strong><br>
+  <strong>rgba32ui</strong><br>
+  <strong>rgba16ui</strong><br>
+  <strong>rgba8ui</strong><br>
+  <strong>r32ui</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">image types only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uniform</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_multiply</strong><br>
+  <strong>blend_support_screen</strong><br>
+  <strong>blend_support_overlay</strong><br>
+  <strong>blend_support_darken</strong><br>
+  <strong>blend_support_lighten</strong><br>
+  <strong>blend_support_colordodge blend_support_colorburn</strong><br>
+  <strong>blend_support_hardlight</strong><br>
+  <strong>blend_support_softlight</strong><br>
+  <strong>blend_support_difference</strong><br>
+  <strong>blend_support_exclusion</strong><br>
+  <strong>blend_support_hsl_hue</strong><br>
+  <strong>blend_support_hsl_saturation</strong><br>
+  <strong>blend_support_hsl_color blend_support_hsl_luminosity</strong><br>
+  <strong>blend_support_all_equations</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">fragment <strong>out</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">1</dt>
+<dd>
+<p>Location qualifiers are not allowed for members of an arrayed block,
+except for per-vertex-arrays (see &#8220;<a href="#interface-blocks">Interface
+Blocks</a>&#8221;).</p>
+</dd>
+</dl>
+</div>
+<div class="sect3">
+<h4 id="input-layout-qualifiers">4.4.1. Input Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Layout qualifiers specific to a particular shader language are discussed in
+separate sections below.</p>
+</div>
+<div class="paragraph">
+<p>All shaders except compute shaders allow <strong>location</strong> layout qualifiers on
+input variable declarations, input block declarations, and input block
+member declarations.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>location</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>) in vec4 normal;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the shader input <em>normal</em> is assigned to vector location
+number
+3.
+For vertex shader inputs, the location specifies the number of the
+vertex attribute from which input values are taken.
+For inputs of all other shader types, the location specifies a vector number
+that can be used to match against outputs from a previous shader stage, even
+if that shader is in a different program object.</p>
+</div>
+<div class="paragraph">
+<p>The following language describes how many locations are consumed by a given
+type.
+However, geometry shader inputs, tessellation control shader inputs and
+outputs, and tessellation evaluation inputs all have an additional level of
+arrayness relative to other shader inputs and outputs.
+This outer array level is removed from the type before considering how many
+locations the type consumes.</p>
+</div>
+<div class="paragraph">
+<p>If a shader input is any scalar or vector type, it will consume a single
+location.</p>
+</div>
+<div class="paragraph">
+<p>If the declared input (after potentially removing an outer array level as
+just described above) is an array of size <em>n</em> and each of the elements takes
+<em>m</em> locations, it will be assigned <em>m</em> * <em>n</em> consecutive locations starting
+with the location specified.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">6</span>) in vec4 colors[<span class="integer">3</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the shader input <em>colors</em> is assigned to vector location
+numbers 6, 7, and 8.</p>
+</div>
+<div class="paragraph">
+<p>If the declared input is an <em>n</em> × <em>m</em>
+matrix, it will be assigned multiple locations starting with the location
+specified.
+The number of locations assigned for each matrix will be the same as for an
+<em>n</em>-element array of <em>m</em>-component vectors.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">9</span>) in mat4 transforms[<span class="integer">2</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that shader input <em>transforms</em> is assigned to vector
+locations 9-16, with <em>transforms[0]</em> being assigned to locations 9-12, and
+<em>transforms[1]</em> being assigned to locations 13-16.</p>
+</div>
+<div class="paragraph">
+<p>If the declared input is a structure or block, its members will be assigned
+consecutive locations in their order of declaration, with the first member
+assigned the location provided in the layout qualifier.
+For a structure, this process applies to the entire structure.
+It is a compile-time error to use a <strong>location</strong> qualifier on a member of a
+structure.
+For a block, this process applies to the entire block, or until the first
+member is reached that has a <strong>location</strong> layout qualifier.</p>
+</div>
+<div class="paragraph">
+<p>When a block member is declared with a <strong>location</strong> qualifier, its location
+comes from that qualifier; the member&#8217;s <strong>location</strong> qualifier overrides the
+block-level declaration.
+Subsequent members are again assigned consecutive locations, based on the
+newest location, until the next member declared with a <strong>location</strong> qualifier.
+The values used for locations do not have to be declared in increasing
+order.</p>
+</div>
+<div class="paragraph">
+<p>If a block has no block-level <strong>location</strong> layout qualifier, it is required
+that either all or none of its members have a <strong>location</strong> layout qualifier,
+or a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>If an input is declared as an array of blocks, excluding per-vertex-arrays
+as required for tessellation, it is an error to declare a member of the
+block with a <strong>location</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>The locations consumed by block and structure members are determined by
+applying the rules above recursively as though the structure member were
+declared as an input variable of the same type.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>) in <span class="keyword">struct</span> S
+{
+    vec3 a;                      <span class="comment">// gets location 3</span>
+    mat2 b;                      <span class="comment">// gets locations 4 and 5</span>
+    vec4 c[<span class="integer">2</span>];                   <span class="comment">// gets locations 6 and 7</span>
+    layout(location = <span class="integer">8</span>) vec2 A; <span class="comment">// ERROR, can't use on struct member</span>
+} s;
+layout(location = <span class="integer">4</span>) in block
+{
+    vec4 d;                      <span class="comment">// gets location 4</span>
+    vec4 e;                      <span class="comment">// gets location 5</span>
+    layout(location = <span class="integer">7</span>) vec4 f; <span class="comment">// gets location 7</span>
+    vec4 g;                      <span class="comment">// gets location 8</span>
+    layout(location = <span class="integer">1</span>) vec4 h; <span class="comment">// gets location 1</span>
+    vec4 i;                      <span class="comment">// gets location 2</span>
+    vec4 j;                      <span class="comment">// gets location 3</span>
+    vec4 k;                      <span class="comment">// ERROR, location 4 already used</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The number of input locations available to a shader is limited.
+For vertex shaders, the limit is the advertised number of vertex attributes.
+For all other shaders, the limit is implementation-dependent and must be no
+less than one fourth of the advertised maximum input component count.</p>
+</div>
+<div class="paragraph">
+<p>A program will fail to link if any attached shader uses a location greater
+than or equal to the number of supported locations, unless device-dependent
+optimizations are able to make the program fit within available hardware
+resources.</p>
+</div>
+<div class="paragraph">
+<p>A program will fail to link if explicit location assignments leave the
+linker unable to find space for other variables without explicit
+assignments.</p>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if a non-vertex input matches an output from
+a previous shader stage, the <strong>location</strong> layout qualifier (if any) must
+match.</p>
+</div>
+<div class="paragraph">
+<p>If a vertex shader input variable with no location assigned in the shader
+text has a location specified through the OpenGL ES API, the API-assigned
+location will be used.
+Otherwise, such variables will be assigned a location by the linker.
+See section 11.1.1 &#8220;Vertex Attributes&#8221; of the <a href="#references">OpenGL ES Specification</a> for
+more details.</p>
+</div>
+<div class="paragraph">
+<p>It is an error if more than one input or element of a matrix input is bound
+to the same location.</p>
+</div>
+<div class="sect4">
+<h5 id="tessellation-evaluation-inputs">Tessellation Evaluation Inputs</h5>
+<div class="paragraph">
+<p>Additional input layout qualifier identifiers allowed for tessellation
+evaluation shaders are described below.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><em>primitive_mode</em><br>
+<em>vertex_spacing</em><br>
+<em>ordering</em><br>
+<em>point_mode</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>primitive-mode</strong> is used to specify a tessellation primitive mode to be
+used by the tessellation primitive generator.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>primitive-mode</em>: </dt>
+<dd>
+<p><strong>triangles</strong><br>
+<strong>quads</strong><br>
+<strong>isolines</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>If present, the <em>primitive-mode</em> specifies that the tessellation primitive
+generator should subdivide a triangle into smaller triangles, a quad into
+triangles, or a quad into a collection of lines, respectively.</p>
+</div>
+<div class="paragraph">
+<p>A second group of layout identifiers, <em>vertex spacing</em>, is used to specify
+the spacing used by the tessellation primitive generator when subdividing an
+edge.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>vertex-spacing</em>: </dt>
+<dd>
+<p><strong>equal_spacing</strong><br>
+<strong>fractional_even_spacing</strong><br>
+<strong>fractional_odd_spacing</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p><strong>equal_spacing</strong> specifies that edges should be divided into a collection of
+equal-sized segments;</p>
+</div>
+<div class="paragraph">
+<p><strong>fractional_even_spacing</strong> specifies that edges should be divided into an
+even number of equal-length segments plus two additional shorter
+&#8220;fractional&#8221; segments; or</p>
+</div>
+<div class="paragraph">
+<p><strong>fractional_odd_spacing</strong> specifies that edges should be divided into an odd
+number of equal-length segments plus two additional shorter &#8220;fractional&#8221;
+segments.</p>
+</div>
+<div class="paragraph">
+<p>A third group of layout identifiers, <em>ordering</em>, specifies whether the
+tessellation primitive generator produces triangles in clockwise or
+counter-clockwise order, according to the coordinate system depicted in the
+<a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>ordering</em>: </dt>
+<dd>
+<p><strong>cw</strong><br>
+<strong>ccw</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifiers <strong>cw</strong> and <strong>ccw</strong> indicate clockwise and counter-clockwise
+triangles, respectively.
+If the tessellation primitive generator does not produce triangles, the
+order is ignored.</p>
+</div>
+<div class="paragraph">
+<p>Finally, <em>point mode</em> indicates that the tessellation primitive generator
+should produce one point for each distinct vertex in the subdivided
+primitive, rather than generating lines or triangles.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>point-mode</em>: </dt>
+<dd>
+<p><strong>point_mode</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Any or all of these identifiers may be specified one or more times in a
+single input layout declaration.</p>
+</div>
+<div class="paragraph">
+<p>The tessellation evaluation shader object in a program must declare a
+primitive mode in its input layout.
+Declaring vertex spacing, ordering, or point mode identifiers is optional.
+If spacing or vertex ordering declarations are omitted, the tessellation
+primitive generator will use equal spacing or counter-clockwise vertex
+ordering, respectively.
+If a point mode declaration is omitted, the tessellation primitive generator
+will produce lines or triangles according to the primitive mode.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-shader-inputs">Geometry Shader Inputs</h5>
+<div class="paragraph">
+<p>Additional layout qualifier identifiers for geometry shader inputs include
+<em>primitive</em> identifiers and an <em>invocation count</em> identifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>points</strong><br>
+<strong>lines</strong><br>
+<strong>lines_adjacency</strong><br>
+<strong>triangles</strong><br>
+<strong>triangles_adjacency</strong><br>
+<strong>invocations</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifiers <strong>points</strong>, <strong>lines</strong>, <strong>lines_adjacency</strong>, <strong>triangles</strong>, and
+<strong>triangles_adjacency</strong> are used to specify the type of input primitive
+accepted by the geometry shader, and only one of these is accepted.
+The geometry shader must declare this input primitive layout.</p>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>invocations</strong> is used to specify the number of times the
+geometry shader executable is invoked for each input primitive received.
+Invocation count declarations are optional.
+If no invocation count is declared in the geometry shader, it will be run
+once for each input primitive.
+If an invocation count is declared, all such declarations must specify the
+same count.
+If a shader specifies an invocation count greater than the
+implementation-dependent maximum, or less than or equal to zero,
+a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(triangles, invocations = <span class="integer">6</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that all inputs to the geometry shader are triangles and that
+the geometry shader executable is run six times for each triangle processed.</p>
+</div>
+<div class="paragraph">
+<p>All geometry shader input unsized array declarations will be sized by an
+earlier input primitive layout qualifier, when present, as per the following
+table.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Layout</th>
+<th class="tableblock halign-left valign-top">Size of Input Arrays</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>points</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lines</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lines_adjacency</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>triangles</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>triangles_adjacency</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The intrinsically declared input array <em>gl_in[]</em> will also be sized by any
+input primitive-layout declaration.
+Hence, the expression</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_in.length()</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will return the value from the table above.</p>
+</div>
+<div class="paragraph">
+<p>An input can be declared without an array size if there is a previous layout
+which specifies the size.
+For built-in inputs (e.g. <em>gl_in[]</em>), a layout must be declared before any
+use.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error if a layout declaration&#8217;s array size (from the
+table above) does not match all the explicit array sizes specified in
+declarations of an input variables in the same shader.
+The following includes examples of compile-time errors:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// code sequence within one shader...</span>
+in vec4 Color2[<span class="integer">2</span>];    <span class="comment">// legal, size is 2</span>
+in vec4 Color3[<span class="integer">3</span>];    <span class="comment">// illegal, input sizes are inconsistent</span>
+layout(lines) in;     <span class="comment">// legal for Color2, input size is 2, matching Color2</span>
+in vec4 Color4[<span class="integer">3</span>];    <span class="comment">// illegal, contradicts layout of lines</span>
+layout(lines) in;     <span class="comment">// legal, matches other layout() declaration</span>
+layout(triangles) in; <span class="comment">// illegal, does not match earlier layout() declaration</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is a link-time error if not all provided sizes (sized input arrays and
+layout size) match in the geometry shader of a program.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="fragment-shader-inputs">Fragment Shader Inputs</h5>
+<div class="paragraph">
+<p>Fragment shaders allow the following layout qualifier on <strong>in</strong> only (not with
+variable declarations):</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>early_fragment_tests</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>to request that fragment tests be performed before fragment shader
+execution, as described in section 13.8.4 &#8220;Early Fragment Tests&#8221; of the
+<a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(early_fragment_tests) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Specifying this will make per-fragment tests be performed before fragment
+shader execution.
+In addition it is an error to statically write to <em>gl_FragDepth</em> in the
+fragment shader.
+If this is not declared, per-fragment tests will be performed after fragment
+shader execution.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="compute-shader-inputs">Compute Shader Inputs</h5>
+<div class="paragraph">
+<p>There are no layout location qualifiers for compute shader inputs.</p>
+</div>
+<div class="paragraph">
+<p>Layout qualifier identifiers for compute shader inputs are the workgroup
+size qualifiers:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>local_size_x</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>local_size_y</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>local_size_z</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>local_size_x</strong>, <strong>local_size_y</strong>, and <strong>local_size_z</strong> qualifiers are used
+to declare a fixed workgroup size by the compute shader in the first,
+second, and third dimension, respectively.
+If a shader does not specify a size for one of the dimensions, that
+dimension will have a size of 1.</p>
+</div>
+<div class="paragraph">
+<p>For example, the following declaration in a compute shader</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(local_size_x = <span class="integer">32</span>, local_size_y = <span class="integer">32</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is used to declare a two-dimensional compute shader with a workgroup size of 32
+X 32 elements, which is equivalent to a three-dimensional compute shader
+where the third dimension has size one.</p>
+</div>
+<div class="paragraph">
+<p>As another example, the declaration</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(local_size_x = <span class="integer">8</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>effectively specifies that a one-dimensional compute shader is being
+compiled, and its size is 8 elements.</p>
+</div>
+<div class="paragraph">
+<p>If the fixed workgroup size of the shader in any dimension is less than
+or equal to zero or greater than the maximum size supported by the
+implementation for that dimension, a compile-time error results.
+Also, if such a layout qualifier is declared more than once in the same
+shader, all those declarations must set the same set of workgroup
+sizes and set them to the same values; otherwise a compile-time error
+results.</p>
+</div>
+<div class="paragraph">
+<p>Furthermore, if a program object contains a compute shader, that shader must
+contain an input layout qualifier specifying a fixed workgroup size for
+the program, or a link-time error will occur.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="output-layout-qualifiers">4.4.2. Output Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Some output layout qualifiers apply to all shader stages and some apply only
+to specific stages.
+The latter are discussed in separate sections below.</p>
+</div>
+<div class="paragraph">
+<p>As with input layout qualifiers, all shaders except compute shaders allow
+<strong>location</strong> layout qualifiers on output variable declarations, output block
+declarations, and output block member declarations.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>location</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The usage and rules for applying the <strong>location</strong> qualifier
+to blocks and structures are exactly as described in
+&#8220;<a href="#input-layout-qualifiers">Input Layout Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>The qualifier may appear at most once within a declaration.
+For example, in a fragment shader,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>) out vec4 color;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the fragment shader output <em>color</em> is assigned to</p>
+</div>
+<div class="paragraph">
+<p>fragment color 3.</p>
+</div>
+<div class="paragraph">
+<p>For fragment shader outputs, the location
+specifies
+the color output number
+receiving the values of the output.
+For outputs of all other shader stages, the location specifies a vector
+number that can be used to match against inputs in a subsequent shader
+stage, even if that shader is in a different program object.</p>
+</div>
+<div class="paragraph">
+<p>Declared outputs of scalar or vector type consume a single location.</p>
+</div>
+<div class="paragraph">
+<p>If the declared output is an array, it will be assigned consecutive
+locations starting with the location specified.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">2</span>) out vec4 colors[<span class="integer">3</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that <em>colors</em> is assigned to vector location numbers 2, 3,
+and 4.</p>
+</div>
+<div class="paragraph">
+<p>If the declared output is an <em>n</em> × <em>m</em>
+matrix, it will be assigned multiple locations starting with the location
+specified.
+The number of locations assigned will be the same as for an <em>n</em>-element
+array of <em>m</em>-component vectors.</p>
+</div>
+<div class="paragraph">
+<p>If the declared output is a structure, its members will be assigned
+consecutive locations in the order of declaration, with the first member
+assigned the location specified for the structure.
+The number of locations consumed by a structure member is determined by
+applying the rules above recursively as though the structure member were
+declared as an output variable of the same type.</p>
+</div>
+<div class="paragraph">
+<p><strong>location</strong> layout qualifiers may be used on output variables declared as
+structures.
+However, it is a compile-time error to use a <strong>location</strong> qualifier on a
+structure member.
+Location layout qualifiers may be used on output blocks and output block
+members.</p>
+</div>
+<div class="paragraph">
+<p>If an output is declared as an array of blocks, excluding per-vertex-arrays
+as required for tessellation, it is an error to declare a member of the
+block with a <strong>location</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>The number of output locations available to a shader is limited.
+For fragment shaders, the limit is the advertised number of draw buffers.</p>
+</div>
+<div class="paragraph">
+<p>For all other shaders, the limit is implementation-dependent and must be no
+less than one fourth of the advertised maximum output component count
+(compute shaders have no outputs).
+A program will fail to link if any attached shader uses a location greater
+than or equal to the number of supported locations, unless device-dependent
+optimizations are able to make the program fit within available hardware
+resources.</p>
+</div>
+<div class="paragraph">
+<p>Compile-time errors may also be given if at compile time it is known the
+link will fail.
+A negative output location will result in an error.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time or link-time error if any of the following occur:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>any two fragment shader output variables are assigned to the same
+location.</p>
+</li>
+<li>
+<p>if any two output variables from the same vertex, tessellation or
+geometry shader stage are assigned to the same location.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>For all shader types, a program will fail to link if explicit location
+assignments leave the linker unable to find space for other variables
+without explicit assignments.</p>
+</div>
+<div class="paragraph">
+<p>If an output variable has no location assigned in the shader text, it will
+be assigned a location by the linker.
+See section 11.1.3 &#8220;Shader Execution&#8221; of the <a href="#references">OpenGL ES Specification</a> for
+more details.</p>
+</div>
+<div class="paragraph">
+<p>If there is only a single output, the location does not need to be
+specified, in which case it defaults to zero.
+This applies for all output types, including arrays.
+If there is more than one fragment output, the location must be specified
+for all outputs.</p>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if a non-fragment output matches an input
+from a subsequent shader stage, the <strong>location</strong> layout qualifier (if any)
+must match.</p>
+</div>
+<div class="sect4">
+<h5 id="tessellation-control-outputs">Tessellation Control Outputs</h5>
+<div class="paragraph">
+<p>Tessellation control shaders allow output layout qualifiers only on the
+interface
+qualifier <strong>out</strong>, not on an output block, block member, or variable
+declaration.
+The output layout qualifier identifiers allowed for tessellation control
+shaders are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>vertices</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>vertices</strong> specifies the number of vertices in the output
+patch produced by the tessellation control shader, which also specifies the
+number of times the tessellation control shader is invoked.
+It is a compile- or link-time error for the output vertex count to be less
+than or equal to zero, or greater than the implementation-dependent maximum
+patch size.</p>
+</div>
+<div class="paragraph">
+<p>The intrinsically declared tessellation control output array <em>gl_out[]</em> will
+also be sized by any output layout declaration.
+Hence, the expression</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_out.length()</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will return the output patch vertex count specified in a previous output
+layout qualifier.
+For outputs declared without an array size, including intrinsically declared
+outputs (i.e., <em>gl_out</em>), a layout must be declared before any use of the
+method <strong>length</strong>() or other array use that requires its size to be known.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error if the output patch vertex count specified in an
+output layout qualifier does not match the array size specified in any
+output variable declaration in the same shader.</p>
+</div>
+<div class="paragraph">
+<p>All tessellation control shader layout declarations in a program must
+specify the same output patch vertex count.
+There must be at least one layout qualifier specifying an output patch
+vertex count in any program containing a tessellation control shader.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-outputs">Geometry Outputs</h5>
+<div class="paragraph">
+<p>Geometry shaders can have two additional types of output layout identifiers:
+an output primitive type and a maximum output vertex count.
+The primitive type and vertex count identifiers are allowed only on the
+interface qualifier <strong>out</strong>, not on an output block, block member, or variable
+declaration.</p>
+</div>
+<div class="paragraph">
+<p>The layout qualifier identifiers for geometry shader outputs are</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>points</strong><br>
+<strong>line_strip</strong><br>
+<strong>triangle_strip</strong><br>
+<strong>max_vertices</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The primitive type identifiers <strong>points</strong>, <strong>line_strip</strong>, and <strong>triangle_strip</strong>
+are used to specify the type of output primitive produced by the geometry
+shader, and only one of these is accepted.
+The geometry shader object in a program must declare an output primitive
+type, and all geometry shader output primitive type declarations in a
+program must declare the same primitive type.</p>
+</div>
+<div class="paragraph">
+<p>The vertex count identifier <strong>max_vertices</strong> is used to specify the maximum
+number of vertices the shader will ever emit in a single invocation.
+The geometry shader object in a program must declare a maximum output vertex
+count, and all geometry shader output vertex count declarations in a program
+must declare the same count.</p>
+</div>
+<div class="paragraph">
+<p>In this example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(triangle_strip, max_vertices = <span class="integer">60</span>) out; <span class="comment">// order does not matter</span>
+layout(max_vertices = <span class="integer">60</span>) out;  <span class="comment">// redeclaration okay</span>
+layout(triangle_strip) out;     <span class="comment">// redeclaration okay</span>
+layout(points) out;             <span class="comment">// error, contradicts triangle_strip</span>
+layout(max_vertices = <span class="integer">30</span>) out;  <span class="comment">// error, contradicts 60</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>all outputs from the geometry shader are triangles and at most 60 vertices
+will be emitted by the shader.
+It is an error for the maximum number of vertices to be greater than
+<em>gl_MaxGeometryOutputVertices</em>.</p>
+</div>
+<div class="paragraph">
+<p>All geometry shader output layout declarations in a program must declare the
+same layout and same value for <strong>max_vertices</strong>.
+If geometry shaders are in a program, there must be at least one geometry
+output layout declaration somewhere in that
+program.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="fragment-outputs">Fragment Outputs</h5>
+<div class="paragraph">
+<p>Fragment shaders can have an output layout for redeclaring the built-in
+variable <em>gl_FragDepth</em>:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// redeclaration that changes nothing is allowed +</span>
+out <span class="predefined-type">float</span> gl_FragDepth;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The built-in <em>gl_FragDepth</em> is only predeclared in fragment shaders, so
+redeclaring it in any other shader language results in an error.</p>
+</div>
+<div class="paragraph">
+<p>Fragment shaders additionally support layout qualifiers specifying a set of
+advanced blend equations supported when the fragment shader is used.
+These layout qualifiers are only permitted on the interface qualifier <strong>out</strong>,
+and use the identifiers specified in the &#8220;Layout Qualifier&#8221; column of the
+table below.</p>
+</div>
+<div class="paragraph">
+<p>If a layout qualifier in the table below is specified in the fragment
+shader, the fragment shader may be used with the corresponding advanced
+blend equation in the &#8220;Blend Equation(s) Supported&#8221; column.
+Additionally, the special qualifier <strong>blend_support_all_equations</strong> indicates
+that the shader may be used with any advanced blending equation supported by
+the <a href="#references">OpenGL ES Specification</a>.
+It is not an error to specify more than one of these identifiers in any
+fragment shader.
+Specifying more than one qualifier or <strong>blend_support_all_equations</strong> means
+that the fragment shader may be used with multiple advanced blend equations.
+Additionally, it is not an error to specify any single one of these layout
+qualifiers more than once.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Layout Qualifier</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Blend Equations(s) Supported</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_multiply</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">MULTIPLY</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_screen</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">SCREEN</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_overlay</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">OVERLAY</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_darken</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">DARKEN</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_lighten</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">LIGHTEN</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_colordodge</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">COLORDODGE</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_colorburn</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">COLORBURN</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_hardlight</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">HARDLIGHT</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_softlight</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">SOFTLIGHT</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_difference</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">DIFFERENCE</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_exclusion</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">EXCLUSION</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_hsl_hue</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">HSL_HUE</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_hsl_saturation</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">HSL_SATURATION</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_hsl_color</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">HSL_COLOR</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_hsl_luminosity</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">HSL_LUMINOSITY</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>blend_support_all_equations</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">all blend equations</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-variable-layout-qualifiers">4.4.3. Uniform Variable Layout Qualifiers</h4>
+<div class="paragraph">
+<p>The following layout qualifier can be used for all default-block uniform
+variables but not for variables in uniform or shader storage blocks.
+The layout qualifier identifier for uniform variables is:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>location</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The location specifies the location by which the OpenGL ES API can reference
+the uniform and update its value.
+Individual elements of a uniform array are assigned consecutive locations
+with the first element taking location <strong>location</strong>.
+No two default-block uniform variables in the program can have the same
+location, even if they are unused, otherwise a compile-time or link-time
+error will be generated.
+Valid locations for default-block uniform variable locations are in the
+range of 0 to the implementation-defined maximum number of uniform locations
+minus one.</p>
+</div>
+<div class="paragraph">
+<p>Locations can be assigned to default-block uniform arrays and structures.
+The first inner-most scalar, vector or matrix member or element takes the
+specified <strong>location</strong> and the compiler assigns the next inner-most member or
+element the next incremental location value.
+Each subsequent inner-most member or element gets incremental locations for
+the entire structure or array.
+This rule applies to nested structures and arrays and gives each inner-most
+scalar, vector, or matrix member a unique location.
+When the linker generates locations for uniforms without an explicit
+location, it assumes for all uniforms with an explicit location all their
+array elements and structure members are used and the linker will not
+generate a conflicting location, even if that element or member is deemed
+unused.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-and-shader-storage-block-layout-qualifiers">4.4.4. Uniform and Shader Storage Block Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Layout qualifiers can be used for uniform and shader storage blocks, but not
+for non-block uniform declarations.
+The layout qualifier identifiers (and <strong>shared</strong> keyword) for uniform and
+shader storage blocks are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>shared</strong><br>
+<strong>packed</strong><br>
+<strong>std140</strong><br>
+<strong>std430</strong><br>
+<strong>row_major</strong><br>
+<strong>column_major</strong><br>
+<strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>None of these have any semantic effect at all on the usage of the variables
+being declared; they only describe how data is laid out in memory.
+For example, matrix semantics are always column-based, as described in the
+rest of this specification, no matter what layout qualifiers are being used.</p>
+</div>
+<div class="paragraph">
+<p>Uniform and shader storage block layout qualifiers can be declared for
+global scope, on a single uniform or shader storage block, or on a single
+block member declaration.</p>
+</div>
+<div class="paragraph">
+<p>Default layouts are established at global scope for uniform blocks as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(layout-qualifier-id-list) uniform;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and for shader storage blocks as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(layout-qualifier-id-list) buffer;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When this is done, the previous default qualification is first inherited and
+then overridden as per the override rules listed below for each qualifier
+listed in the declaration.
+The result becomes the new default qualification scoped to subsequent
+uniform or shader storage block definitions.</p>
+</div>
+<div class="paragraph">
+<p>The initial state of compilation
+is as if the following were declared:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(shared, column_major) uniform;
+layout(shared, column_major) buffer;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Uniform and shader storage blocks can be declared with optional layout
+qualifiers, and so can their individual member declarations.
+Such block layout qualification is scoped only to the content of the block.
+As with global layout declarations, block layout qualification first
+inherits from the current default qualification and then overrides it.
+Similarly, individual member layout qualification is scoped just to the
+member declaration, and inherits from and overrides the block&#8217;s
+qualification.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>shared</strong> qualifier overrides only the <strong>std140</strong>, <strong>std430</strong>, and <strong>packed</strong>
+qualifiers; other qualifiers are inherited.
+The compiler/linker will ensure that multiple programs and programmable
+stages containing this definition will share the same memory layout for this
+block, as long as they also matched in their <strong>row_major</strong> and/or
+<strong>column_major</strong> qualifications.
+This allows use of the same buffer to back the same block definition across
+different programs.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>packed</strong> qualifier overrides only <strong>std140</strong>, <strong>std430</strong>, and <strong>shared</strong>;
+other qualifiers are inherited.
+When <strong>packed</strong> is used, no shareable layout is guaranteed.
+The compiler and linker can optimize memory use based on what variables
+actively get used and on other criteria.
+Offsets must be queried, as there is no other way of guaranteeing where (and
+which) variables reside within the block.</p>
+</div>
+<div class="paragraph">
+<p>It is a link-time error to access the same packed uniform or shader storage
+block in multiple stages within a program.
+Attempts to access the same packed uniform or shader storage block across
+programs can result in conflicting member offsets and in undefined values
+being read.
+However, implementations may aid application management of packed blocks by
+using canonical layouts for packed blocks.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>std140</strong> and <strong>std430</strong> qualifiers override only the <strong>packed</strong>, <strong>shared</strong>,
+<strong>std140</strong>, and <strong>std430</strong> qualifiers; other qualifiers are inherited.
+The <strong>std430</strong> qualifier is supported only for shader storage blocks; a shader
+using the <strong>std430</strong> qualifier on a uniform block will fail to compile.</p>
+</div>
+<div class="paragraph">
+<p>The layout is explicitly determined by this, as described in section 7.6.2.2
+&#8220;Standard Uniform Block Layout&#8221; of the <a href="#references">OpenGL ES Specification</a>.
+Hence, as in <strong>shared</strong> above, the resulting layout is shareable across
+programs.</p>
+</div>
+<div class="paragraph">
+<p>Layout qualifiers on member declarations cannot use the <strong>shared</strong>, <strong>packed</strong>,
+<strong>std140</strong>, or <strong>std430</strong> qualifiers.
+These can only be used at global scope (without an object) or on a block
+declaration, or an error results.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>row_major</strong> and <strong>column_major</strong> qualifiers only affect the layout of
+matrices, including all matrices contained in structures and arrays they are
+applied to, to all depths of nesting.
+These qualifiers can be applied to other types, but will have no effect.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>row_major</strong> qualifier overrides only the <strong>column_major</strong> qualifier; other
+qualifiers are inherited.
+Elements within a matrix row will be contiguous in memory.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>column_major</strong> qualifier overrides only the <strong>row_major</strong> qualifier; other
+qualifiers are inherited.
+Elements within a matrix column will be contiguous in memory.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>binding</strong> qualifier specifies the uniform buffer binding point
+corresponding to the uniform or shader storage block, which will be used to
+obtain the values of the member variables of the block.
+It is a compile-time error to specify the <strong>binding</strong> qualifier for the global
+scope or for block member declarations.
+Any uniform or shader storage block declared without a <strong>binding</strong> qualifier
+is initially assigned to block binding point zero.
+After a program is linked, the binding points used for uniform
+(but not shader storage) blocks
+declared with or without a <strong>binding</strong> qualifier can be updated
+by the OpenGL ES API.</p>
+</div>
+<div class="paragraph">
+<p>If the <strong>binding</strong> qualifier is used with a uniform block or shader storage
+block instanced as an array, the first element of the array takes the
+specified block binding and each subsequent element takes the next
+consecutive binding point.
+For an array of arrays, each element (e.g. 6 elements for a[2][3]) gets a
+binding point, and they are ordered per the array of array ordering
+described in &#8220;<a href="#arrays.">Arrays.</a>&#8221;</p>
+</div>
+<div class="paragraph">
+<p>If the binding point for any uniform or shader storage block instance is
+less than zero, or greater than or equal to the corresponding
+implementation-dependent maximum number of buffer bindings, a compile-time
+error will occur.
+When the <strong>binding</strong> qualifier is used with a uniform or shader storage block
+instanced as an array of size <em>N</em>, all elements of the array from <strong>binding</strong>
+through <em>binding + N - 1</em> must be within this range.</p>
+</div>
+<div class="paragraph">
+<p>When multiple arguments are listed in a <strong>layout</strong> declaration, the effect
+will be the same as if they were declared one at a time, in order from left
+to right, each in turn inheriting from and overriding the result from the
+previous qualification.</p>
+</div>
+<div class="paragraph">
+<p>For example</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(row_major, column_major)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>results in the qualification being <strong>column_major</strong>.
+Other examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(shared, row_major) uniform; <span class="comment">// default is now shared and row_major</span>
+
+layout(std140) uniform Transform { <span class="comment">// layout of this block is std140</span>
+    mat4 M1;                       <span class="comment">// row major</span>
+    layout(column_major) mat4 M2;  <span class="comment">// column major</span>
+    mat3 N1;                       <span class="comment">// row major</span>
+};
+
+uniform T2 {                       <span class="comment">// layout of this block is shared</span>
+    ...
+};
+
+layout(column_major) uniform T3 {  <span class="comment">// shared and column major</span>
+    mat4 M3;                       <span class="comment">// column major</span>
+    layout(row_major) mat4 m4;     <span class="comment">// row major</span>
+    mat3 N2;                       <span class="comment">// column major</span>
+};</code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="opaque-uniform-layout-qualifiers">4.4.5. Opaque Uniform Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Uniform layout qualifiers can be used to bind opaque uniform variables to
+specific buffers or units.
+Samplers can be bound to texture image units, images can be bound to image
+units, and atomic counters can be bound to buffers.</p>
+</div>
+<div class="paragraph">
+<p>Sampler, image and atomic counter types take the uniform layout qualifier
+identifier for binding:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>binding</strong> specifies which unit will be bound.
+Any uniform sampler, image or atomic counter
+variable declared without a binding qualifier
+is initially bound to unit zero.
+After a program is linked, the unit referenced by a sampler
+uniform variable declared with or without a <strong>binding</strong> qualifier can be
+updated by the OpenGL ES API.</p>
+</div>
+<div class="paragraph">
+<p>If the <strong>binding</strong> qualifier is used with an array, the first element of the
+array takes the specified unit and each subsequent element takes the next
+consecutive unit.
+For an array of arrays, each element (e.g. 6 elements for a[2][3]) gets a
+binding point, and they are ordered per the array of array ordering
+described in &#8220;<a href="#arrays.">Arrays.</a>&#8221;</p>
+</div>
+<div class="paragraph">
+<p>If the <strong>binding</strong> is less than zero, or greater than or equal to the
+implementation-dependent maximum supported number of units, a compile-time
+error will occur.
+When the <strong>binding</strong> qualifier is used with an array of size <em>N</em>, all elements
+of the array from <strong>binding</strong> through <em>binding + N - 1</em> must be within this
+range.</p>
+</div>
+<div class="paragraph">
+<p>A link-time error will result if two shaders in a program specify different
+<em>layout-qualifier-value</em> bindings for the same opaque-uniform name.
+However, it is not an error to specify a binding on some but not all
+declarations for the same name, as shown in the examples below.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// in one shader...</span>
+layout(binding=<span class="integer">3</span>) uniform sampler2D s; <span class="comment">// s bound to unit 3</span>
+
+<span class="comment">// in another shader...</span>
+uniform sampler2D s;                   <span class="comment">// okay, s still bound at 3</span>
+
+<span class="comment">// in another shader...</span>
+layout(binding=<span class="integer">4</span>) uniform sampler2D s; <span class="comment">// ERROR: contradictory bindings</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="atomic-counter-layout-qualifiers">4.4.6. Atomic Counter Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Atomic counter layout qualifiers can be used on atomic counter declarations.
+The atomic counter qualifiers are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>offset</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>, offset = <span class="integer">4</span>) uniform atomic_uint a;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the opaque handle to the atomic counter <em>a</em> will be
+bound to atomic counter buffer binding point 2 at an offset of 4 basic
+machine units into that buffer.
+The default <em>offset</em> for binding point 2 will be post incremented by 4 (the
+size of an atomic counter).</p>
+</div>
+<div class="paragraph">
+<p>A subsequent atomic counter declaration will inherit the previous (post
+incremented) offset.
+For example, a subsequent declaration of</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>) uniform atomic_uint bar;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the atomic counter <em>bar</em> has a binding to buffer binding
+point 2 at an offset of 8 basic machine units into that buffer.
+The offset for binding point 2 will again be post-incremented by 4 (the size
+of an atomic counter).</p>
+</div>
+<div class="paragraph">
+<p>When multiple variables are listed in a layout declaration, the effect will
+be the same as if they were declared one at a time, in order from left to
+right.</p>
+</div>
+<div class="paragraph">
+<p>Binding points are not inherited, only offsets.
+Each binding point tracks its own current default <em>offset</em> for inheritance
+of subsequent variables using the same <strong>binding</strong>.
+The initial state of compilation is that all <strong>binding</strong> points have an
+<em>offset</em> of 0.
+The <em>offset</em> can be set per binding point at global scope (without declaring
+a variable).
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>, offset = <span class="integer">4</span>) uniform atomic_uint;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Establishes that the next <strong>atomic_uint</strong> declaration for binding point 2 will
+inherit <em>offset</em> 4 (but does not establish a default <strong>binding</strong>):</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>) uniform atomic_uint bar; <span class="comment">// offset is 4</span>
+layout(offset = <span class="integer">8</span>) uniform atomic_uint bar;  <span class="comment">// error, no default binding</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Atomic counters may share the same binding point, but if a binding is
+shared, their offsets must be either explicitly or implicitly (from
+inheritance) unique and non overlapping.</p>
+</div>
+<div class="paragraph">
+<p>Example valid uniform declarations, assuming top of shader:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding=<span class="integer">3</span>, offset=<span class="integer">4</span>) uniform atomic_uint a; <span class="comment">// offset = 4</span>
+layout(binding=<span class="integer">2</span>) uniform atomic_uint b;           <span class="comment">// offset = 0</span>
+layout(binding=<span class="integer">3</span>) uniform atomic_uint c;           <span class="comment">// offset = 8</span>
+layout(binding=<span class="integer">2</span>) uniform atomic_uint d;           <span class="comment">// offset = 4</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Example of an invalid uniform declaration:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(offset=<span class="integer">4</span>) ...               <span class="comment">// error, must include binding</span>
+layout(binding=<span class="integer">1</span>, offset=<span class="integer">0</span>) ... a; <span class="comment">// okay</span>
+layout(binding=<span class="integer">2</span>, offset=<span class="integer">0</span>) ... b; <span class="comment">// okay</span>
+layout(binding=<span class="integer">1</span>, offset=<span class="integer">0</span>) ... c; <span class="comment">// error, offsets must not be shared</span>
+                                   <span class="comment">// between a and c</span>
+layout(binding=<span class="integer">1</span>, offset=<span class="integer">2</span>) ... d; <span class="comment">// error, overlaps offset 0 of a</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to bind an atomic counter with a binding value
+greater than or equal to <em>gl_MaxAtomicCounterBindings</em>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="format-layout-qualifiers">4.4.7. Format Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Format layout qualifiers can be used on image variable declarations (those
+declared with a basic type having &#8220;<strong>image</strong>&#8221; in its keyword).
+The format layout qualifier identifiers for image variable declarations are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><em>float-image-format-qualifier</em><br>
+<em>int-image-format-qualifier</em><br>
+<em>uint-image-format-qualifier</em><br>
+<strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>float-image-format-qualifier</em> : </dt>
+<dd>
+<p><strong>rgba32f</strong><br>
+<strong>rgba16f</strong><br>
+<strong>r32f</strong><br>
+<strong>rgba8</strong><br>
+<strong>rgba8_snorm</strong></p>
+</dd>
+<dt class="hdlist1"><em>int-image-format-qualifier</em> : </dt>
+<dd>
+<p><strong>rgba32i</strong><br>
+<strong>rgba16i</strong><br>
+<strong>rgba8i</strong><br>
+<strong>r32i</strong></p>
+</dd>
+<dt class="hdlist1"><em>uint-image-format-qualifier</em> : </dt>
+<dd>
+<p><strong>rgba32ui</strong><br>
+<strong>rgba16ui</strong><br>
+<strong>rgba8ui</strong><br>
+<strong>r32ui</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>A format layout qualifier specifies the image format associated with a
+declared image variable.
+Only one format qualifier may be specified for any image variable
+declaration.
+For image variables with floating-point component types (keywords starting
+with &#8220;<strong>image</strong>&#8221;), signed integer component types (keywords starting with
+&#8220;<strong>iimage</strong>&#8221;), or unsigned integer component types (keywords starting with
+&#8220;<strong>uimage</strong>&#8221;), the format qualifier used must match the
+<em>float-image-format-qualifier</em>, <em>int-image-format-qualifier</em>, or
+<em>uint-image-format-qualifier</em> grammar rules, respectively.
+It is an error to declare an image variable where the format
+qualifier does not match the image variable type.</p>
+</div>
+<div class="paragraph">
+<p>Any image variable must specify a format layout qualifier.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>binding</strong> qualifier was described in
+&#8220;<a href="#opaque-uniform-layout-qualifiers">Opaque Uniform Layout Qualifiers</a>&#8221;.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="interpolation-qualifiers">4.5. Interpolation Qualifiers</h3>
+<div class="paragraph">
+<p>Inputs and outputs that could be interpolated can be further qualified by at
+most one of the following interpolation qualifiers:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>smooth</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">perspective correct interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>flat</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">no interpolation</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The presence of and type of interpolation is controlled by the above
+interpolation qualifiers as well as the auxiliary storage qualifiers
+<strong>centroid</strong> and <strong>sample</strong>.
+When no interpolation qualifier is present, smooth interpolation is used.
+It is a compile-time error to use more than one interpolation qualifier.
+The auxiliary storage qualifier <strong>patch</strong> is not used for interpolation; it is
+a compile-time error to use interpolation qualifiers with <strong>patch</strong>.</p>
+</div>
+<div class="paragraph">
+<p>A variable qualified as <strong>flat</strong> will not be interpolated.
+Instead, it will have the same value for every fragment within a primitive.
+This value will come from a single provoking vertex, as described by the
+<a href="#references">OpenGL ES Specification</a>.
+A variable qualified as <strong>flat</strong> may also be qualified as <strong>centroid</strong> or
+<strong>sample</strong>, which will mean the same thing as qualifying it only as <strong>flat</strong>.</p>
+</div>
+<div class="paragraph">
+<p>A variable qualified as <strong>smooth</strong> will be interpolated in a
+perspective-correct manner over the primitive being rendered.</p>
+</div>
+<div class="paragraph">
+<p>Interpolation in a perspective correct manner is specified in equations 13.4
+of the <a href="#references">OpenGL ES Specification</a>, section 13.4.1 &#8220;Line Segments&#8221; and
+equation 13.7, section 13.5.1 &#8220;Polygon Interpolation&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>When multisample rasterization is disabled, or for fragment shader input
+variables qualified with neither <strong>centroid</strong> nor <strong>sample</strong>, the value of the
+assigned variable may be interpolated anywhere within the pixel and a single
+value may be assigned to each sample within the pixel, to the extent
+permitted by the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>When multisample rasterization is enabled, <strong>centroid</strong> and <strong>sample</strong> may be
+used to control the location and frequency of the sampling of the qualified
+fragment shader input.
+If a fragment shader input is qualified with <strong>centroid</strong>, a single value may
+be assigned to that variable for all samples in the pixel, but that value
+must be interpolated at a location that lies in both the pixel and in the
+primitive being rendered, including any of the pixel&#8217;s samples covered by
+the primitive.
+Because the location at which the variable is interpolated may be different
+in neighboring pixels, and derivatives may be computed by computing
+differences between neighboring pixels, derivatives of centroid-sampled
+inputs may be less accurate than those for non-centroid interpolated
+variables.
+If a fragment shader input is qualified with <strong>sample</strong>, a separate value must
+be assigned to that variable for each covered sample in the pixel, and that
+value must be sampled at the location of the individual sample.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="parameter-qualifiers">4.6. Parameter Qualifiers</h3>
+<div class="paragraph">
+<p>In addition to precision qualifiers and memory qualifiers, parameters can
+have these parameter qualifiers.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;none: default&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>in</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters passed into a function</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>out</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters passed back out of a function,
+                   but not initialized for use when passed in</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>inout</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters passed both into and out of a
+                   function</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Parameter qualifiers are discussed in more detail in
+&#8220;<a href="#function-calling-conventions">Function Calling Conventions</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="precision-and-precision-qualifiers">4.7. Precision and Precision Qualifiers</h3>
+<div class="sect3">
+<h4 id="range-and-precision">4.7.1. Range and Precision</h4>
+<div class="paragraph">
+<p>The precision of <strong>highp</strong> floating-point variables is defined by the IEEE 754
+standard for 32-bit floating-point numbers.
+This includes support for NaNs (Not a Number) and Infs (positive or negative
+infinities) and positive and negative zeros.</p>
+</div>
+<div class="paragraph">
+<p>The following rules apply to
+<strong>highp</strong>
+operations:
+Signed infinities and zeros are generated as dictated by IEEE, but subject
+to the precisions allowed in the following table.
+Any subnormal (denormalized) value input into a shader or potentially
+generated by any operation in a shader can be flushed to 0.
+The rounding mode cannot be set and is undefined but must not affect the
+result by more than 1 ULP.
+NaNs are not required to be generated.
+Support for signaling NaNs is not required and exceptions are never raised.
+Operations including built-in functions that operate on a NaN are not
+required to return a NaN as the result.
+However if NaNs are generated, <strong>isnan</strong>() must return the correct value.</p>
+</div>
+<div class="paragraph">
+<p>Precisions are expressed in terms of maximum relative error in units of ULP
+(units in the last place), unless otherwise noted.</p>
+</div>
+<div class="paragraph">
+<p>For single precision operations, precisions are required as follows:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Operation</th>
+<th class="tableblock halign-left valign-top">Precision</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>a</em> + <em>b</em>, <em>a</em> - <em>b</em>, <em>a</em> * <em>b</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correctly rounded.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;, &lt;=, ==, &gt;, &gt;=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correct result.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>a</em> / <em>b</em>, 1.0 / <em>b</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2.5 ULP for <span class="eq">|b|</span> in the range <span class="eq">[2<sup>-126</sup>, 2<sup>126</sup>]</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>a</em> * <em>b</em> + <em>c</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correctly rounded single operation or
+                                    sequence of two correctly rounded operations.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>fma</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inherited from <em>a</em> * <em>b</em> + <em>c</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>pow</strong>(<em>x</em>, <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inherited from <strong>exp2</strong>(<em>y</em> * <strong>log2</strong>(<em>x</em>)).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>exp</strong>(<em>x</em>), <strong>exp2</strong>(<em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">(3 + 2 · |x|)</span> ULP.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>log</strong>(), <strong>log2</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3 ULP outside the range <span class="eq">[0.5,2.0]</span>.<br>
+                                    Absolute error &lt; 2<sup>-21</sup> inside the range
+                                    <span class="eq">[0.5,2.0]</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sqrt</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inherited from 1.0 / <strong>inversesqrt</strong>().</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>inversesqrt</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2 ULP.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">implicit and explicit
+  conversions between types</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correctly rounded.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Built-in functions defined in the specification with an equation built from
+the above operations inherit the above errors.
+These include, for example, the geometric functions, the common functions,
+and many of the matrix functions.
+Built-in functions not listed above and not defined as equations of the
+above have undefined precision.
+These include, for example, the trigonometric functions and determinant.</p>
+</div>
+<div class="paragraph">
+<p>Storage requirements are declared through use of <em>precision qualifiers</em>.
+The precision of operations must preserve the storage precisions of the
+variables involved.</p>
+</div>
+<div class="paragraph">
+<p><strong>highp</strong> floating-point values are stored in IEEE 754 single precision
+floating-point format.
+<strong>mediump</strong> and <strong>lowp</strong> floating-point values have minimum range and precision
+requirements as detailed below and have maximum range and precision as
+defined by IEEE 754.</p>
+</div>
+<div class="paragraph">
+<p>All integral types are assumed to be implemented as integers and so may not
+be emulated by floating-point values.
+<strong>highp</strong> signed integers are represented as twos-complement 32-bit signed
+integers.
+<strong>highp</strong> unsigned integers are represented as unsigned 32-bit integers.
+<strong>mediump</strong> integers (signed and unsigned) must be represented as an integer
+with between 16 and 32 bits inclusive.
+<strong>lowp</strong> integers (signed and unsigned) must be represented as an integer with
+between 9 and 32 bits inclusive.</p>
+</div>
+<div class="paragraph">
+<p>The required ranges and precisions for precision qualifiers are:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.667%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Floating-Point Range</th>
+<th class="tableblock halign-left valign-top">Floating-Point Magnitude Range</th>
+<th class="tableblock halign-left valign-top">Floating-Point Precision</th>
+<th class="tableblock halign-left valign-top">Signed Integer Range</th>
+<th class="tableblock halign-left valign-top">Unsigned Integer Range</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>highp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Subset of IEEE-754<br>
+      <span class="eq">(-2<sup>128</sup>,2<sup>128</sup>)</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Subset of IEEE-754<br>
+      0.0, <span class="eq">[2<sup>-126</sup>,2<sup>128</sup>)</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Subset of IEEE-754 relative:<br>
+      <span class="eq">2<sup>-24</sup></span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">[-2<sup>31</sup>,2<sup>31</sup>-1]</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">[0,2<sup>32</sup>-1]</span></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mediump</strong> (minimum requirements)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">(-2<sup>14</sup>,2<sup>14</sup>)</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">(2<sup>14</sup>,2<sup>14</sup>)</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Relative:<br>
+      <span class="eq">2<sup>-10</sup></span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">[-2<sup>15</sup>,2<sup>15</sup>-1]</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">[0,2<sup>16</sup>-1]</span></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lowp</strong> (minimum requirements)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">(-2,2)</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">(2<sup>-8</sup>,2)</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Absolute:<br>
+      <span class="eq">2<sup>-8</sup></span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">[-2<sup>8</sup>,2<sup>8</sup>-1]</span></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">[0,2<sup>9</sup>-1]</span></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p><em>Relative precision</em> is defined as the worst case (i.e. largest) ratio of
+the smallest step in relation to the value for all non-zero values:</p>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\begin{aligned}
+    \mathit{Precision}_{relative} = {
+        \left| {
+            { \left| v_1 - v_2 \right| }_{min} } \over { v_1 }
+        \right|
+    }_{max}, &amp;
+    v_1,v_2 \neq 0, v_1 \neq v_2
+\end{aligned}\]
+</div>
+</div>
+<div class="paragraph">
+<p>It is therefore twice the maximum rounding error when converting from a real
+number.</p>
+</div>
+<div class="paragraph">
+<p>In addition, the range and precision of a <strong>mediump</strong> floating-point value
+must be the same as or greater than the range and precision of a <strong>lowp</strong>
+floating-point value.
+The range and precision of a <strong>highp</strong> floating-point value must be the same
+as or greater than the range and precision of a <strong>mediump</strong> floating-point
+value.</p>
+</div>
+<div class="paragraph">
+<p>The range of a <strong>mediump</strong> integer value must be the same as or greater than
+the range of a <strong>lowp</strong> integer value.
+The range of a <strong>highp</strong> integer value must be the same as or greater than the
+range of a <strong>mediump</strong> integer value.</p>
+</div>
+<div class="paragraph">
+<p>Within the above specification, an implementation is allowed to vary the
+representation of numeric values, both within a shader and between different
+shaders.
+If necessary, this variance can be controlled using the invariance
+qualifier.</p>
+</div>
+<div class="paragraph">
+<p>The actual ranges and precisions provided by an implementation can be
+queried through the API.
+See the <a href="#references">OpenGL ES Specification</a> specification for details on how to do
+this.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="conversion-between-precisions">4.7.2. Conversion between precisions</h4>
+<div class="paragraph">
+<p>Within the same type, conversion from a lower to a higher precision must be
+exact.
+When converting from a higher precision to a lower precision, if the value
+is representable by the implementation of the target precision, the
+conversion must also be exact.
+If the value is not representable, the behavior is dependent on the type:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>For signed and unsigned integers, the value is truncated; bits in
+positions not present in the target precision are set to zero.
+(Positions start at zero and the least significant bit is considered to
+be position zero for this purpose.)</p>
+</li>
+<li>
+<p>For floating-point values, the value should either clamp to +Inf or
+-Inf, or to the maximum or minimum value that the implementation
+supports.
+While this behavior is implementation-dependent, it should be consistent
+for a given implementation.</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="precision-qualifiers">4.7.3. Precision Qualifiers</h4>
+<div class="paragraph">
+<p>Any
+floating-point, integer, or opaque-type declaration can have the type
+preceded by one of these precision qualifiers:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Qualifier</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Meaning</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>highp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The variable satisfies the minimum requirements for <strong>highp</strong>
+              described above. <strong>highp</strong> variables have the maximum range and
+              precision available but may cause operations to run more
+              slowly on some implementations.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mediump</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The variable satisfies the minimum requirements for <strong>mediump</strong>
+              described above. <strong>mediump</strong> variables may typically be used to
+              store high dynamic range colors and low precision geometry.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lowp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The variable satisfies the minimum requirements for <strong>lowp</strong>
+              described above. <strong>lowp</strong> variables may typically be used to
+              store 8-bit color values.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">lowp <span class="predefined-type">float</span> color;
+out mediump vec2 P;
+lowp ivec2 foo(lowp mat3);
+highp mat4 m;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Literal constants do not have precision qualifiers.
+Neither do Boolean variables.
+Neither do constructors.</p>
+</div>
+<div class="paragraph">
+<p>For this paragraph, &#8220;operation&#8221; includes operators, built-in functions,
+and constructors, and &#8220;operand&#8221; includes function arguments and
+constructor arguments.
+The precision used to internally evaluate an operation, and the precision
+qualification subsequently associated with any resulting intermediate
+values, must be at least as high as the highest precision qualification of
+the operands consumed by the operation.</p>
+</div>
+<div class="paragraph">
+<p>In cases where operands do not have a precision qualifier, the precision
+qualification will come from the other operands.
+If no operands have a precision qualifier, then the precision qualifications
+of the operands of the next consuming operation in the expression will be
+used.
+This rule can be applied recursively until a precision qualified operand is
+found.
+If necessary, it will also include the precision qualification of l-values
+for assignments, of the declared variable for initializers, of formal
+parameters for function call arguments, or of function return types for
+function return values.
+If the precision cannot be determined by this method e.g. if an entire
+expression is composed only of operands with no precision qualifier, and the
+result is not assigned or passed as an argument, then it is evaluated at the
+default precision of the type or greater.
+When this occurs in the fragment shader, the default precision must be
+defined.</p>
+</div>
+<div class="paragraph">
+<p>For example, consider the statements:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform highp <span class="predefined-type">float</span> h1;
+highp <span class="predefined-type">float</span> h2 = <span class="float">2</span><span class="float">.3</span> * <span class="float">4</span><span class="float">.7</span>; <span class="comment">// operation and result are highp</span>
+precision
+mediump <span class="predefined-type">float</span> m;
+m = <span class="float">3</span><span class="float">.7</span> * h1 * h2; <span class="comment">// all operations are highp precision</span>
+h2 = m * h1; <span class="comment">// operation is highp precision</span>
+m = h2 - h1; <span class="comment">// operation is highp precision</span>
+h2 = m + m; <span class="comment">// addition and result at mediump precision</span>
+<span class="directive">void</span> f(highp <span class="predefined-type">float</span> p);
+f(<span class="float">3</span><span class="float">.3</span>); <span class="comment">// 3.3 will be passed in at highp precision</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Precision qualifiers, as with other qualifiers, do not affect the basic type
+of the variable.
+In particular, there are no constructors for precision conversions;
+constructors only convert types.
+Similarly, precision qualifiers, as with other qualifiers, do not contribute
+to function overloading based on parameter types.
+As discussed in &#8220;<a href="#function-calling-conventions">Function Calling
+Conventions</a>&#8221;, function input and output is done through copies, and
+therefore qualifiers do not have to match.</p>
+</div>
+<div class="paragraph">
+<p>Precision qualifiers for outputs in one shader matched to inputs in another
+shader need not match when both shaders are linked into the same program.
+When both shaders are in separate programs, mismatched precision qualifiers
+will result in a program interface mismatch that will result in program
+pipeline validation failures, as described in section 7.4.1 &#8220;Shader
+Interface Matching&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>The precision of a variable is determined when the variable is declared and
+cannot be subsequently changed.</p>
+</div>
+<div class="paragraph">
+<p>Where the precision of a constant integral or constant floating-point
+expression is not specified, evaluation is performed at <strong>highp</strong>.
+This rule does not affect the precision qualification of the expression.</p>
+</div>
+<div class="paragraph">
+<p>The evaluation of constant expressions must be invariant and will usually be
+performed at compile time.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="default-precision-qualifiers">4.7.4. Default Precision Qualifiers</h4>
+<div class="paragraph">
+<p>The precision statement</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision precision-qualifier type;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>can be used to establish a default precision qualifier.
+The <em>type</em> field can be either <strong>int</strong>, <strong>float</strong>, or any of the opaque types,
+and the <em>precision-qualifier</em> can be <strong>lowp</strong>, <strong>mediump</strong>, or <strong>highp</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Any other types or qualifiers will result in an error.
+If <em>type</em> is <strong>float</strong>, the directive applies to non-precision-qualified
+floating-point type (scalar, vector, and matrix) declarations.
+If <em>type</em> is <strong>int</strong>, the directive applies to all non-precision-qualified
+integer type (scalar, vector, signed, and unsigned) declarations.
+This includes global variable declarations, function return declarations,
+function parameter declarations, and local variable declarations.</p>
+</div>
+<div class="paragraph">
+<p>Non-precision qualified declarations will use the precision qualifier
+specified in the most recent <strong>precision</strong> statement that is still in scope.
+The <strong>precision</strong> statement has the same scoping rules as variable
+declarations.
+If it is declared inside a compound statement, its effect stops at the end
+of the inner-most statement it was declared in.
+Precision statements in nested scopes override precision statements in outer
+scopes.
+Multiple precision statements for the same basic type can appear inside the
+same scope, with later statements overriding earlier statements within that
+scope.</p>
+</div>
+<div class="paragraph">
+<p>All languages except for the fragment language have the following
+predeclared globally scoped default precision statements:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision highp <span class="predefined-type">float</span>;
+precision highp <span class="predefined-type">int</span>;
+precision lowp sampler2D;
+precision lowp samplerCube;
+precision highp atomic_uint;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The fragment language has the following predeclared globally scoped default
+precision statements:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision mediump <span class="predefined-type">int</span>;
+precision lowp sampler2D;
+precision lowp samplerCube;
+precision highp atomic_uint;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The fragment language has no default precision qualifier for floating-point
+types.
+Hence for <strong>float</strong>, floating-point vector and matrix variable declarations,
+either the declaration must include a precision qualifier or the default
+float precision must have been previously declared.
+Similarly, there is no default precision qualifier in any of the languages
+for any type not listed above.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="available-precision-qualifiers">4.7.5. Available Precision Qualifiers</h4>
+<div class="paragraph">
+<p>The built-in macro GL_FRAGMENT_PRECISION_HIGH is defined to one:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#define</span> GL_FRAGMENT_PRECISION_HIGH <span class="integer">1</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This macro is available in all languages except compute.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="variance-and-the-invariant-qualifier">4.8. Variance and the Invariant Qualifier</h3>
+<div class="paragraph">
+<p>In this section, <em>variance</em> refers to the possibility of getting different
+values from the same expression in different programs.
+For example, consider the situation where two vertex shaders, in different
+programs, each set <em>gl_Position</em> with the same expression, and the input
+values into that expression are the same when both shaders run.
+It is possible, due to independent compilation of the two shaders, that the
+values assigned to <em>gl_Position</em> are not exactly the same when the two
+shaders run.
+In this example, this can cause problems with alignment of geometry in a
+multi-pass algorithm.</p>
+</div>
+<div class="paragraph">
+<p>In general, such variance between shaders is allowed.
+When such variance does not exist for a particular output variable, that
+variable is said to be <em>invariant</em>.</p>
+</div>
+<div class="sect3">
+<h4 id="the-invariant-qualifier">4.8.1. The Invariant Qualifier</h4>
+<div class="paragraph">
+<p>To ensure that a particular output variable is invariant, it is necessary to
+use the <strong>invariant</strong> qualifier.
+It can either be used to qualify a previously declared variable as being
+invariant:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">invariant gl_Position; <span class="comment">// make existing gl_Position be invariant</span>
+out vec3 Color;
+invariant Color;       <span class="comment">// make existing Color be invariant</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>or as part of a declaration when a variable is declared:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">invariant centroid out vec3 Color;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Only variables output from a shader can be candidates for invariance.
+This includes user-defined output variables and the built-in output
+variables.
+As only outputs can be declared as invariant, an output from one shader
+stage will still match an input of a subsequent stage without the input
+being declared as invariant.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>invariant</strong> keyword can be followed by a comma separated list of
+previously declared identifiers.
+All uses of <strong>invariant</strong> must be at global scope or on block
+members, and before any use of the variables being declared as invariant.</p>
+</div>
+<div class="paragraph">
+<p>To guarantee invariance of a particular output variable across two programs,
+the following must also be true:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The output variable is declared as invariant in both programs.</p>
+</li>
+<li>
+<p>The same values must be input to all shader input variables consumed by
+expressions and control flow contributing to the value assigned to the
+output variable.</p>
+</li>
+<li>
+<p>The texture formats, texel values, and texture filtering are set the
+same way for any texture function calls contributing to the value of the
+output variable.</p>
+</li>
+<li>
+<p>All input values are all operated on in the same way.
+    All operations in the consuming expressions and any intermediate
+    expressions must be the same, with the same order of operands and same
+    associativity, to give the same order of evaluation.
+    Intermediate variables and functions must be declared as the same type
+    with the same explicit or implicit precision
+qualifiers and the same constant qualifiers.
+    Any control flow affecting the output value must be the same, and any
+    expressions consumed to determine this control flow must also follow
+    these invariance rules.</p>
+</li>
+<li>
+<p>All the data flow and control flow leading to setting the invariant
+output variable reside in a single compilation unit.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Essentially, all the data flow and control flow leading to an invariant
+output must match.</p>
+</div>
+<div class="paragraph">
+<p>Initially, by default, all output variables are allowed to be variant.
+To force all output variables to be invariant, use the pragma</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> STDGL invariant(all)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>before all declarations in a shader.
+If this pragma is used after the declaration of any variables or functions,
+then the set of outputs that behave as invariant is undefined.</p>
+</div>
+<div class="paragraph">
+<p>Generally, invariance is ensured at the cost of flexibility in optimization,
+so performance can be degraded by use of invariance.
+Hence, use of this pragma is intended as a debug aid, to avoid individually
+declaring all output variables as invariant.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="invariance-within-a-shader">4.8.2. Invariance Within a Shader</h4>
+<div class="paragraph">
+<p>When a value is stored in a variable, it is usually assumed it will remain
+constant unless explicitly changed.
+However, during the process of optimization, it is possible that the
+compiler may choose to recompute a value rather than store it in a register.
+Since the precision of operations is not completely specified (e.g. a low
+precision operation may be done at medium or high precision), it would be
+possible for the recomputed value to be different from the original value.</p>
+</div>
+<div class="paragraph">
+<p>Values are allowed to be variant within a shader.
+To prevent this, the invariant qualifier or invariant pragma must be used.</p>
+</div>
+<div class="paragraph">
+<p>Within a shader, there is no invariance for values generated by different
+non-constant expressions, even if those expressions are identical.</p>
+</div>
+<div class="paragraph">
+<p>Example 1:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision mediump;
+vec4 col;
+vec2 a = ...
+...
+col = texture(tex, a);<span class="comment">// a has a value _a1 _</span>
+...
+col = texture(tex, a); <span class="comment">// a has a value a2 where possibly a1 != a2</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>To enforce invariance in this example use:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> STDGL invariant(all)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Example 2:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec2 m = ...;
+vec2 n = ...;
+vec2 a = m + n;
+vec2 b = m + n; <span class="comment">// a and b are not guaranteed to be exactly equal</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There is no mechanism to enforce invariance between a and b.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="invariance-of-constant-expressions">4.8.3. Invariance of Constant Expressions</h4>
+<div class="paragraph">
+<p>Invariance must be guaranteed for constant expressions.
+A particular constant expression must evaluate to the same result if it
+appears again in the same shader or a different shader.
+This includes the same expression appearing in two shaders of the same
+language or shaders of two different languages.</p>
+</div>
+<div class="paragraph">
+<p>Constant expressions must evaluate to the same result when operated on as
+already described above for invariant variables.
+Constant expressions are not invariant with respect to equivalent
+non-constant expressions, even when the <strong>invariant</strong> qualifier or pragma is
+used.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="invariance-of-undefined-values">4.8.4. Invariance of Undefined Values</h4>
+<div class="paragraph">
+<p>Undefined values are not invariant nor can they be made invariant by use of
+the invariant qualifier or pragma.
+In some implementations, undefined values may cause unexpected behavior if
+they are used in control-flow expressions e.g. in the following case, one,
+both or neither functions may be executed and this may not be consistent
+over multiple invocations of the shader:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> x; <span class="comment">// undefined value</span>
+<span class="keyword">if</span> (x == <span class="integer">1</span>)
+{
+    f(); <span class="comment">// Undefined whether f() is executed</span>
+}
+<span class="keyword">if</span> (x == <span class="integer">2</span>)
+{
+    g(); <span class="comment">// Undefined whether g() is executed.</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Note that an undefined value is a value that has not been specified.
+A value that has been specified but has a potentially large error due to,
+for example, lack of precision in an expression, is not undefined and so can
+be made invariant.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="the-precise-qualifier">4.9. The Precise Qualifier</h3>
+<div class="paragraph">
+<p>Some algorithms require floating-point computations to exactly follow the
+order of operations specified in the source code and to treat all operations
+consistently, even if the implementation supports optimizations that could
+produce nearly equivalent results with higher performance.
+For example, many GL implementations support a &#8220;multiply-add&#8221; instruction
+that can compute a floating-point expression such as</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">result = (a * b) + (c * d);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>in two operations instead of three operations; one multiply and one
+multiply-add instead of two multiplies and one add.
+The result of a floating-point multiply-add might not always be identical to
+first doing a multiply yielding a floating-point result and then doing a
+floating-point add.
+Hence, in this example, the two multiply operations would not be treated
+consistently; the two multiplies could effectively appear to have differing
+precisions.</p>
+</div>
+<div class="paragraph">
+<p>The key computation that needs to be made consistent appears when
+tessellating, where intermediate points for subdivision are synthesized in
+different directions, yet need to yield the same result, as shown in the
+diagram below.</p>
+</div>
+<div id="img-precise" class="imageblock">
+<div class="content">
+<img src="data:image/svg+xml;base64,<?xml version="1.0" encoding="UTF-8"?>

<svg version="1.2" baseProfile="tiny" width="210mm" height="297mm" viewBox="0 0 21000 29700" preserveAspectRatio="xMidYMid" fill-rule="evenodd" clip-path="url(#presentation_clip_path)" stroke-width="28.222" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" xmlns:ooo="http://xml.openoffice.org/svg/export" xmlns:xlink="http://www.w3.org/1999/xlink" xml:space="preserve">
 <defs class="ClipPathGroup">
  <clipPath id="presentation_clip_path" clipPathUnits="userSpaceOnUse">
   <rect x="0" y="0" width="21000" height="29700"/>
  </clipPath>
 </defs>
 <defs>
  <font id="EmbeddedFont_1" horiz-adv-x="2048">
   <font-face font-family="Liberation Sans embedded" units-per-em="2048" font-weight="normal" font-style="normal" ascent="1852" descent="423"/>
   <missing-glyph horiz-adv-x="2048" d="M 0,0 L 2047,0 2047,2047 0,2047 0,0 Z"/>
   <glyph unicode="w" horiz-adv-x="1509" d="M 1174,0 L 965,0 792,698 C 787,716 781,738 776,765 770,792 764,818 759,843 752,872 746,903 740,934 734,904 728,874 721,845 716,820 710,793 704,766 697,739 691,715 686,694 L 508,0 300,0 -3,1082 175,1082 358,347 C 363,332 367,313 372,291 377,268 381,246 386,225 391,200 396,175 401,149 406,174 412,199 418,223 423,244 429,265 434,286 439,307 444,325 448,339 L 644,1082 837,1082 1026,339 C 1031,322 1036,302 1041,280 1046,258 1051,237 1056,218 1061,195 1067,172 1072,149 1077,174 1083,199 1088,223 1093,244 1098,265 1103,288 1108,310 1112,330 1117,347 L 1308,1082 1484,1082 1174,0 Z"/>
   <glyph unicode="v" horiz-adv-x="1033" d="M 613,0 L 400,0 7,1082 199,1082 437,378 C 442,363 447,346 454,325 460,304 466,282 473,259 480,236 486,215 492,194 497,173 502,155 506,141 510,155 515,173 522,194 528,215 534,236 541,258 548,280 555,302 562,323 569,344 575,361 580,376 L 826,1082 1017,1082 613,0 Z"/>
   <glyph unicode="u" horiz-adv-x="874" d="M 314,1082 L 314,396 C 314,343 318,299 326,264 333,229 346,200 363,179 380,157 403,142 432,133 460,124 495,119 537,119 580,119 618,127 653,142 687,157 716,178 741,207 765,235 784,270 797,312 810,353 817,401 817,455 L 817,1082 997,1082 997,231 C 997,208 997,185 998,160 998,135 998,111 999,89 1000,66 1000,47 1001,31 1002,15 1002,5 1003,0 L 833,0 C 832,3 832,12 831,27 830,42 830,59 829,78 828,97 827,116 826,136 825,155 825,172 825,185 L 822,185 C 805,154 786,125 765,100 744,75 720,53 693,36 666,18 634,4 599,-6 564,-15 523,-20 476,-20 416,-20 364,-13 321,2 278,17 242,39 214,70 186,101 166,140 153,188 140,236 133,294 133,361 L 133,1082 314,1082 Z"/>
   <glyph unicode="t" horiz-adv-x="531" d="M 554,8 C 527,1 499,-5 471,-10 442,-14 409,-16 372,-16 228,-16 156,66 156,229 L 156,951 31,951 31,1082 163,1082 216,1324 336,1324 336,1082 536,1082 536,951 336,951 336,268 C 336,216 345,180 362,159 379,138 408,127 450,127 467,127 484,128 501,131 517,134 535,137 554,141 L 554,8 Z"/>
   <glyph unicode="s" horiz-adv-x="901" d="M 950,299 C 950,248 940,203 921,164 901,124 872,91 835,64 798,37 752,16 698,2 643,-13 581,-20 511,-20 448,-20 392,-15 342,-6 291,4 247,20 209,41 171,62 139,91 114,126 88,161 69,203 57,254 L 216,285 C 231,227 263,185 311,158 359,131 426,117 511,117 550,117 585,120 618,125 650,130 678,140 701,153 724,166 743,183 756,205 769,226 775,253 775,285 775,318 767,345 752,366 737,387 715,404 688,418 661,432 628,444 589,455 550,465 507,476 460,489 417,500 374,513 331,527 288,541 250,560 216,583 181,606 153,634 132,668 111,702 100,745 100,796 100,895 135,970 206,1022 276,1073 378,1099 513,1099 632,1099 727,1078 798,1036 868,994 912,927 931,834 L 769,814 C 763,842 752,866 736,885 720,904 701,919 678,931 655,942 630,951 602,956 573,961 544,963 513,963 432,963 372,951 333,926 294,901 275,864 275,814 275,785 282,761 297,742 311,723 331,707 357,694 382,681 413,669 449,660 485,650 525,640 568,629 597,622 626,614 656,606 686,597 715,587 744,576 772,564 799,550 824,535 849,519 870,500 889,478 908,456 923,430 934,401 945,372 950,338 950,299 Z"/>
   <glyph unicode="r" horiz-adv-x="530" d="M 142,0 L 142,830 C 142,853 142,876 142,900 141,923 141,946 140,968 139,990 139,1011 138,1030 137,1049 137,1067 136,1082 L 306,1082 C 307,1067 308,1049 309,1030 310,1010 311,990 312,969 313,948 313,929 314,910 314,891 314,874 314,861 L 318,861 C 331,902 344,938 359,969 373,999 390,1024 409,1044 428,1063 451,1078 478,1088 505,1097 537,1102 575,1102 590,1102 604,1101 617,1099 630,1096 641,1094 648,1092 L 648,927 C 636,930 622,933 606,935 590,936 572,937 552,937 511,937 476,928 447,909 418,890 394,865 376,832 357,799 344,759 335,714 326,668 322,618 322,564 L 322,0 142,0 Z"/>
   <glyph unicode="p" horiz-adv-x="953" d="M 1053,546 C 1053,464 1046,388 1033,319 1020,250 998,190 967,140 936,90 895,51 844,23 793,-6 730,-20 655,-20 578,-20 510,-5 452,24 394,53 350,101 319,168 L 314,168 C 315,167 315,161 316,150 316,139 316,126 317,110 317,94 317,76 318,57 318,37 318,17 318,-2 L 318,-425 138,-425 138,861 C 138,887 138,912 138,936 137,960 137,982 136,1002 135,1021 135,1038 134,1052 133,1066 133,1076 132,1082 L 306,1082 C 307,1080 308,1073 309,1061 310,1049 311,1035 312,1018 313,1001 314,982 315,963 316,944 316,925 316,908 L 320,908 C 337,943 356,972 377,997 398,1021 423,1041 450,1057 477,1072 508,1084 542,1091 575,1098 613,1101 655,1101 730,1101 793,1088 844,1061 895,1034 936,997 967,949 998,900 1020,842 1033,774 1046,705 1053,629 1053,546 Z M 864,542 C 864,609 860,668 852,720 844,772 830,816 811,852 791,888 765,915 732,934 699,953 658,962 609,962 569,962 531,956 496,945 461,934 430,912 404,880 377,848 356,804 341,748 326,691 318,618 318,528 318,451 324,387 337,334 350,281 368,238 393,205 417,172 447,149 483,135 519,120 560,113 607,113 657,113 699,123 732,142 765,161 791,189 811,226 830,263 844,308 852,361 860,414 864,474 864,542 Z"/>
   <glyph unicode="o" horiz-adv-x="980" d="M 1053,542 C 1053,353 1011,212 928,119 845,26 724,-20 565,-20 490,-20 422,-9 363,14 304,37 254,71 213,118 172,165 140,223 119,294 97,364 86,447 86,542 86,915 248,1102 571,1102 655,1102 728,1090 789,1067 850,1044 900,1009 939,962 978,915 1006,857 1025,787 1044,717 1053,635 1053,542 Z M 864,542 C 864,626 858,695 845,750 832,805 813,848 788,881 763,914 732,937 696,950 660,963 619,969 574,969 528,969 487,962 450,949 413,935 381,912 355,879 329,846 309,802 296,747 282,692 275,624 275,542 275,458 282,389 297,334 312,279 332,235 358,202 383,169 414,146 449,133 484,120 522,113 563,113 609,113 651,120 688,133 725,146 757,168 783,201 809,234 829,278 843,333 857,388 864,458 864,542 Z"/>
   <glyph unicode="n" horiz-adv-x="874" d="M 825,0 L 825,686 C 825,739 821,783 814,818 806,853 793,882 776,904 759,925 736,941 708,950 679,959 644,963 602,963 559,963 521,956 487,941 452,926 423,904 399,876 374,847 355,812 342,771 329,729 322,681 322,627 L 322,0 142,0 142,851 C 142,874 142,898 142,923 141,948 141,971 140,994 139,1016 139,1035 138,1051 137,1067 137,1077 136,1082 L 306,1082 C 307,1079 307,1070 308,1055 309,1040 310,1024 311,1005 312,986 312,966 313,947 314,927 314,910 314,897 L 317,897 C 334,928 353,957 374,982 395,1007 419,1029 446,1047 473,1064 505,1078 540,1088 575,1097 616,1102 663,1102 723,1102 775,1095 818,1080 861,1065 897,1043 925,1012 953,981 974,942 987,894 1000,845 1006,788 1006,721 L 1006,0 825,0 Z"/>
   <glyph unicode="m" horiz-adv-x="1457" d="M 768,0 L 768,686 C 768,739 765,783 758,818 751,853 740,882 725,904 709,925 688,941 663,950 638,959 607,963 570,963 532,963 498,956 467,941 436,926 410,904 389,876 367,847 350,812 339,771 327,729 321,681 321,627 L 321,0 142,0 142,851 C 142,874 142,898 142,923 141,948 141,971 140,994 139,1016 139,1035 138,1051 137,1067 137,1077 136,1082 L 306,1082 C 307,1079 307,1070 308,1055 309,1040 310,1024 311,1005 312,986 312,966 313,947 314,927 314,910 314,897 L 317,897 C 333,928 350,957 369,982 388,1007 410,1029 435,1047 460,1064 488,1078 521,1088 553,1097 590,1102 633,1102 715,1102 780,1086 828,1053 875,1020 908,968 927,897 L 930,897 C 946,928 964,957 984,982 1004,1007 1027,1029 1054,1047 1081,1064 1111,1078 1144,1088 1177,1097 1215,1102 1258,1102 1313,1102 1360,1095 1400,1080 1439,1065 1472,1043 1497,1012 1522,981 1541,942 1553,894 1565,845 1571,788 1571,721 L 1571,0 1393,0 1393,686 C 1393,739 1390,783 1383,818 1376,853 1365,882 1350,904 1334,925 1313,941 1288,950 1263,959 1232,963 1195,963 1157,963 1123,956 1092,942 1061,927 1035,906 1014,878 992,850 975,815 964,773 952,731 946,682 946,627 L 946,0 768,0 Z"/>
   <glyph unicode="l" horiz-adv-x="187" d="M 138,0 L 138,1484 318,1484 318,0 138,0 Z"/>
   <glyph unicode="k" horiz-adv-x="901" d="M 816,0 L 450,494 318,385 318,0 138,0 138,1484 318,1484 318,557 793,1082 1004,1082 565,617 1027,0 816,0 Z"/>
   <glyph unicode="i" horiz-adv-x="187" d="M 137,1312 L 137,1484 317,1484 317,1312 137,1312 Z M 137,0 L 137,1082 317,1082 317,0 137,0 Z"/>
   <glyph unicode="h" horiz-adv-x="874" d="M 317,897 C 337,934 359,965 382,991 405,1016 431,1037 459,1054 487,1071 518,1083 551,1091 584,1098 622,1102 663,1102 732,1102 789,1093 834,1074 878,1055 913,1029 939,996 964,962 982,922 992,875 1001,828 1006,777 1006,721 L 1006,0 825,0 825,686 C 825,732 822,772 817,807 811,842 800,871 784,894 768,917 745,934 716,946 687,957 649,963 602,963 559,963 521,955 487,940 452,925 423,903 399,875 374,847 355,813 342,773 329,733 322,688 322,638 L 322,0 142,0 142,1484 322,1484 322,1098 C 322,1076 322,1054 321,1032 320,1010 320,990 319,971 318,952 317,937 316,924 315,911 315,902 314,897 L 317,897 Z"/>
   <glyph unicode="g" horiz-adv-x="927" d="M 548,-425 C 486,-425 431,-419 383,-406 335,-393 294,-375 260,-352 226,-328 198,-300 177,-267 156,-234 140,-198 131,-158 L 312,-132 C 324,-182 351,-220 392,-248 433,-274 486,-288 553,-288 594,-288 631,-282 664,-271 697,-260 726,-241 749,-217 772,-191 790,-159 803,-119 816,-79 822,-30 822,27 L 822,201 820,201 C 807,174 790,148 771,123 751,98 727,75 699,56 670,37 637,21 600,10 563,-2 520,-8 472,-8 403,-8 345,4 296,27 247,50 207,84 176,130 145,176 122,233 108,302 93,370 86,449 86,539 86,626 93,704 108,773 122,842 145,901 178,950 210,998 252,1035 304,1061 355,1086 418,1099 492,1099 569,1099 635,1082 692,1047 748,1012 791,962 822,897 L 824,897 C 824,914 825,932 826,953 827,974 828,993 829,1012 830,1030 831,1046 832,1059 833,1072 835,1080 836,1082 L 1007,1082 C 1006,1076 1006,1066 1005,1052 1004,1037 1004,1020 1003,1000 1002,980 1002,958 1002,934 1001,909 1001,884 1001,858 L 1001,31 C 1001,-120 964,-234 890,-311 815,-387 701,-425 548,-425 Z M 822,541 C 822,616 814,681 798,735 781,788 760,832 733,866 706,900 676,925 642,941 607,957 572,965 536,965 490,965 451,957 418,941 385,925 357,900 336,866 314,831 298,787 288,734 277,680 272,616 272,541 272,463 277,398 288,345 298,292 314,249 335,216 356,183 383,160 416,146 449,132 488,125 533,125 569,125 604,133 639,148 673,163 704,188 731,221 758,254 780,297 797,350 814,403 822,466 822,541 Z"/>
   <glyph unicode="f" horiz-adv-x="557" d="M 361,951 L 361,0 181,0 181,951 29,951 29,1082 181,1082 181,1204 C 181,1243 185,1280 192,1314 199,1347 213,1377 233,1402 252,1427 279,1446 313,1461 347,1475 391,1482 445,1482 466,1482 489,1481 512,1479 535,1477 555,1474 572,1470 L 572,1333 C 561,1335 548,1337 533,1339 518,1340 504,1341 492,1341 465,1341 444,1337 427,1330 410,1323 396,1312 387,1299 377,1285 370,1268 367,1248 363,1228 361,1205 361,1179 L 361,1082 572,1082 572,951 361,951 Z"/>
   <glyph unicode="e" horiz-adv-x="980" d="M 276,503 C 276,446 282,394 294,347 305,299 323,258 348,224 372,189 403,163 441,144 479,125 525,115 578,115 656,115 719,131 766,162 813,193 844,233 861,281 L 1019,236 C 1008,206 992,176 972,146 951,115 924,88 890,64 856,39 814,19 763,4 712,-12 650,-20 578,-20 418,-20 296,28 213,123 129,218 87,360 87,548 87,649 100,735 125,806 150,876 185,933 229,977 273,1021 324,1053 383,1073 442,1092 504,1102 571,1102 662,1102 738,1087 799,1058 860,1029 909,988 946,937 983,885 1009,824 1025,754 1040,684 1048,608 1048,527 L 1048,503 276,503 Z M 862,641 C 852,755 823,838 775,891 727,943 658,969 568,969 538,969 507,964 474,955 441,945 410,928 382,903 354,878 330,845 311,803 292,760 281,706 278,641 L 862,641 Z"/>
   <glyph unicode="d" horiz-adv-x="927" d="M 821,174 C 788,105 744,55 689,25 634,-5 565,-20 484,-20 347,-20 247,26 183,118 118,210 86,349 86,536 86,913 219,1102 484,1102 566,1102 634,1087 689,1057 744,1027 788,979 821,914 L 823,914 C 823,921 823,931 823,946 822,960 822,975 822,991 821,1006 821,1021 821,1035 821,1049 821,1059 821,1065 L 821,1484 1001,1484 1001,223 C 1001,197 1001,172 1002,148 1002,124 1002,102 1003,82 1004,62 1004,45 1005,31 1006,16 1006,6 1007,0 L 835,0 C 834,7 833,16 832,29 831,41 830,55 829,71 828,87 827,104 826,122 825,139 825,157 825,174 L 821,174 Z M 275,542 C 275,467 280,403 289,350 298,297 313,253 334,219 355,184 381,159 413,143 445,127 484,119 530,119 577,119 619,127 656,142 692,157 722,182 747,217 771,251 789,296 802,351 815,406 821,474 821,554 821,631 815,696 802,749 789,802 771,844 746,877 721,910 691,933 656,948 620,962 579,969 532,969 488,969 450,961 418,946 386,931 359,906 338,872 317,838 301,794 291,740 280,685 275,619 275,542 Z"/>
   <glyph unicode="c" horiz-adv-x="901" d="M 275,546 C 275,484 280,427 289,375 298,323 313,278 334,241 355,203 384,174 419,153 454,132 497,122 548,122 612,122 666,139 709,173 752,206 778,258 788,328 L 970,328 C 964,283 951,239 931,197 911,155 884,118 850,86 815,54 773,28 724,9 675,-10 618,-20 553,-20 468,-20 396,-6 337,23 278,52 230,91 193,142 156,192 129,251 112,320 95,388 87,462 87,542 87,615 93,679 105,735 117,790 134,839 156,881 177,922 203,957 232,986 261,1014 293,1037 328,1054 362,1071 398,1083 436,1091 474,1098 512,1102 551,1102 612,1102 666,1094 713,1077 760,1060 801,1038 836,1009 870,980 898,945 919,906 940,867 955,824 964,779 L 779,765 C 770,825 746,873 708,908 670,943 616,961 546,961 495,961 452,953 418,936 383,919 355,893 334,859 313,824 298,781 289,729 280,677 275,616 275,546 Z"/>
   <glyph unicode="b" horiz-adv-x="953" d="M 1053,546 C 1053,169 920,-20 655,-20 573,-20 505,-5 451,25 396,54 352,102 318,168 L 316,168 C 316,151 316,133 315,114 314,95 313,78 312,62 311,46 310,32 309,21 308,10 307,3 306,0 L 132,0 C 133,6 133,16 134,31 135,45 135,62 136,82 137,102 137,124 138,148 138,172 138,197 138,223 L 138,1484 318,1484 318,1061 C 318,1041 318,1022 318,1004 317,985 317,969 316,955 315,938 315,923 314,908 L 318,908 C 351,977 396,1027 451,1057 506,1087 574,1102 655,1102 792,1102 892,1056 957,964 1021,872 1053,733 1053,546 Z M 864,540 C 864,615 859,679 850,732 841,785 826,829 805,864 784,898 758,923 726,939 694,955 655,963 609,963 562,963 520,955 484,940 447,925 417,900 393,866 368,832 350,787 337,732 324,677 318,609 318,529 318,452 324,387 337,334 350,281 368,239 393,206 417,173 447,149 483,135 519,120 560,113 607,113 651,113 689,121 721,136 753,151 780,176 801,210 822,244 838,288 849,343 859,397 864,463 864,540 Z"/>
   <glyph unicode="a" horiz-adv-x="1060" d="M 414,-20 C 305,-20 224,9 169,66 114,124 87,203 87,303 87,375 101,434 128,480 155,526 190,562 234,588 277,614 327,632 383,642 439,652 496,657 554,657 L 797,657 797,717 C 797,762 792,800 783,832 774,863 759,889 740,908 721,928 697,942 668,951 639,960 604,965 565,965 530,965 499,963 471,958 443,953 419,944 398,931 377,918 361,900 348,878 335,855 327,827 323,793 L 135,810 C 142,853 154,892 173,928 192,963 218,994 253,1020 287,1046 330,1066 382,1081 433,1095 496,1102 569,1102 705,1102 807,1071 876,1009 945,946 979,856 979,738 L 979,272 C 979,219 986,179 1000,152 1014,125 1041,111 1080,111 1090,111 1100,112 1110,113 1120,114 1130,116 1139,118 L 1139,6 C 1116,1 1094,-3 1072,-6 1049,-9 1025,-10 1000,-10 966,-10 937,-5 913,4 888,13 868,26 853,45 838,63 826,86 818,113 810,140 805,171 803,207 L 797,207 C 778,172 757,141 734,113 711,85 684,61 653,42 622,22 588,7 549,-4 510,-15 465,-20 414,-20 Z M 455,115 C 512,115 563,125 606,146 649,167 684,194 713,226 741,259 762,294 776,332 790,371 797,408 797,443 L 797,531 600,531 C 556,531 514,528 475,522 435,517 400,506 370,489 340,472 316,449 299,418 281,388 272,349 272,300 272,241 288,195 320,163 351,131 396,115 455,115 Z"/>
   <glyph unicode="S" horiz-adv-x="1192" d="M 1272,389 C 1272,330 1261,275 1238,225 1215,175 1179,132 1131,96 1083,59 1023,31 950,11 877,-10 790,-20 690,-20 515,-20 378,11 280,72 182,133 120,222 93,338 L 278,375 C 287,338 302,305 321,275 340,245 367,219 400,198 433,176 473,159 522,147 571,135 629,129 697,129 754,129 806,134 853,144 900,153 941,168 975,188 1009,208 1036,234 1055,266 1074,297 1083,335 1083,379 1083,425 1073,462 1052,491 1031,520 1001,543 963,562 925,581 880,596 827,609 774,622 716,635 652,650 613,659 573,668 534,679 494,689 456,701 420,716 383,730 349,747 317,766 285,785 257,809 234,836 211,863 192,894 179,930 166,965 159,1006 159,1053 159,1120 173,1177 200,1225 227,1272 264,1311 312,1342 360,1373 417,1395 482,1409 547,1423 618,1430 694,1430 781,1430 856,1423 918,1410 980,1396 1032,1375 1075,1348 1118,1321 1152,1287 1178,1247 1203,1206 1224,1159 1239,1106 L 1051,1073 C 1042,1107 1028,1137 1011,1164 993,1191 970,1213 941,1231 912,1249 878,1263 837,1272 796,1281 747,1286 692,1286 627,1286 572,1280 528,1269 483,1257 448,1241 421,1221 394,1201 374,1178 363,1151 351,1124 345,1094 345,1063 345,1021 356,987 377,960 398,933 426,910 462,892 498,874 540,859 587,847 634,835 685,823 738,811 781,801 825,791 868,781 911,770 952,758 991,744 1030,729 1067,712 1102,693 1136,674 1166,650 1191,622 1216,594 1236,561 1251,523 1265,485 1272,440 1272,389 Z"/>
   <glyph unicode="O" horiz-adv-x="1430" d="M 1495,711 C 1495,601 1479,501 1448,411 1416,321 1370,244 1310,180 1250,116 1177,67 1090,32 1003,-3 905,-20 795,-20 679,-20 577,-2 490,35 403,71 330,122 272,187 214,252 170,329 141,418 112,507 97,605 97,711 97,821 112,920 143,1009 174,1098 219,1173 278,1236 337,1298 411,1346 498,1380 585,1413 684,1430 797,1430 909,1430 1009,1413 1096,1379 1183,1345 1256,1297 1315,1234 1374,1171 1418,1096 1449,1007 1480,918 1495,820 1495,711 Z M 1300,711 C 1300,796 1289,873 1268,942 1246,1011 1214,1071 1172,1120 1129,1169 1077,1207 1014,1234 951,1261 879,1274 797,1274 713,1274 639,1261 576,1234 513,1207 460,1169 418,1120 375,1071 344,1011 323,942 302,873 291,796 291,711 291,626 302,549 324,479 345,408 377,348 420,297 462,246 515,206 578,178 641,149 713,135 795,135 883,135 959,149 1023,178 1086,207 1139,247 1180,298 1221,349 1251,409 1271,480 1290,551 1300,628 1300,711 Z"/>
   <glyph unicode="C" horiz-adv-x="1324" d="M 792,1274 C 712,1274 641,1261 580,1234 518,1207 466,1169 425,1120 383,1071 351,1011 330,942 309,873 298,796 298,711 298,626 310,549 333,479 356,408 389,348 432,297 475,246 527,207 590,179 652,151 722,137 800,137 855,137 905,144 950,159 995,173 1035,193 1072,219 1108,245 1140,276 1169,312 1198,347 1223,387 1245,430 L 1401,352 C 1376,299 1344,250 1307,205 1270,160 1226,120 1176,87 1125,54 1068,28 1005,9 941,-10 870,-20 791,-20 677,-20 577,-2 492,35 406,71 334,122 277,187 219,252 176,329 147,418 118,507 104,605 104,711 104,821 119,920 150,1009 180,1098 224,1173 283,1236 341,1298 413,1346 498,1380 583,1413 681,1430 790,1430 940,1430 1065,1401 1166,1342 1267,1283 1341,1196 1388,1081 L 1207,1021 C 1194,1054 1176,1086 1153,1117 1130,1147 1102,1174 1068,1197 1034,1220 994,1239 949,1253 903,1267 851,1274 792,1274 Z"/>
   <glyph unicode=" " horiz-adv-x="556"/>
  </font>
 </defs>
 <defs class="TextShapeIndex">
  <g ooo:slide="id1" ooo:id-list="id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"/>
 </defs>
 <defs class="EmbeddedBulletChars">
  <g id="bullet-char-template(57356)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 580,1141 L 1163,571 580,0 -4,571 580,1141 Z"/>
  </g>
  <g id="bullet-char-template(57354)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 8,1128 L 1137,1128 1137,0 8,0 8,1128 Z"/>
  </g>
  <g id="bullet-char-template(10146)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 174,0 L 602,739 174,1481 1456,739 174,0 Z M 1358,739 L 309,1346 659,739 1358,739 Z"/>
  </g>
  <g id="bullet-char-template(10132)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 2015,739 L 1276,0 717,0 1260,543 174,543 174,936 1260,936 717,1481 1274,1481 2015,739 Z"/>
  </g>
  <g id="bullet-char-template(10007)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 0,-2 C -7,14 -16,27 -25,37 L 356,567 C 262,823 215,952 215,954 215,979 228,992 255,992 264,992 276,990 289,987 310,991 331,999 354,1012 L 381,999 492,748 772,1049 836,1024 860,1049 C 881,1039 901,1025 922,1006 886,937 835,863 770,784 769,783 710,716 594,584 L 774,223 C 774,196 753,168 711,139 L 727,119 C 717,90 699,76 672,76 641,76 570,178 457,381 L 164,-76 C 142,-110 111,-127 72,-127 30,-127 9,-110 8,-76 1,-67 -2,-52 -2,-32 -2,-23 -1,-13 0,-2 Z"/>
  </g>
  <g id="bullet-char-template(10004)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 285,-33 C 182,-33 111,30 74,156 52,228 41,333 41,471 41,549 55,616 82,672 116,743 169,778 240,778 293,778 328,747 346,684 L 369,508 C 377,444 397,411 428,410 L 1163,1116 C 1174,1127 1196,1133 1229,1133 1271,1133 1292,1118 1292,1087 L 1292,965 C 1292,929 1282,901 1262,881 L 442,47 C 390,-6 338,-33 285,-33 Z"/>
  </g>
  <g id="bullet-char-template(9679)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 813,0 C 632,0 489,54 383,161 276,268 223,411 223,592 223,773 276,916 383,1023 489,1130 632,1184 813,1184 992,1184 1136,1130 1245,1023 1353,916 1407,772 1407,592 1407,412 1353,268 1245,161 1136,54 992,0 813,0 Z"/>
  </g>
  <g id="bullet-char-template(8226)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 346,457 C 273,457 209,483 155,535 101,586 74,649 74,723 74,796 101,859 155,911 209,963 273,989 346,989 419,989 480,963 531,910 582,859 608,796 608,723 608,648 583,586 532,535 482,483 420,457 346,457 Z"/>
  </g>
  <g id="bullet-char-template(8211)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M -4,459 L 1135,459 1135,606 -4,606 -4,459 Z"/>
  </g>
 </defs>
 <defs class="TextEmbeddedBitmaps"/>
 <g>
  <g id="id2" class="Master_Slide">
   <g id="bg-id2" class="Background"/>
   <g id="bo-id2" class="BackgroundObjects"/>
  </g>
 </g>
 <g class="SlideGroup">
  <g>
   <g id="id1" class="Slide" clip-path="url(#presentation_clip_path)">
    <g class="Page">
     <g class="com.sun.star.drawing.RectangleShape">
      <g id="id3">
       <path fill="none" stroke="rgb(0,0,0)" d="M 8450,7000 L 7000,7000 7000,3000 9900,3000 9900,7000 8450,7000 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.RectangleShape">
      <g id="id4">
       <path fill="none" stroke="rgb(0,0,0)" d="M 12050,7000 L 10100,7000 10100,3000 14000,3000 14000,7000 12050,7000 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.EllipseShape">
      <g id="id5">
       <path fill="none" stroke="rgb(0,0,0)" d="M 8999,3300 C 9105,3312 9195,3383 9288,3531 9387,3690 9459,3889 9516,4165 9574,4441 9600,4712 9600,5031 9600,5350 9574,5621 9516,5897 9459,6173 9402,6328 9319,6478"/>
       <path fill="rgb(0,0,0)" stroke="none" d="M 9141,6701 L 9405,6526 9248,6403 9141,6701 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.EllipseShape">
      <g id="id6">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10794,6710 C 10748,6669 10710,6618 10668,6540 10583,6380 10521,6181 10472,5905 10422,5628 10400,5356 10400,5036 10400,4716 10422,4444 10472,4168 10521,3891 10583,3692 10668,3532 10748,3383 10690,3492 10701,3474"/>
       <path fill="rgb(0,0,0)" stroke="none" d="M 10916,3300 L 10622,3416 10750,3569 10916,3300 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id7">
       <path fill="none" stroke="rgb(0,0,0)" d="M 9899,6900 C 9955,6900 9999,6943 9999,6999 9999,7055 9955,7099 9899,7099 9843,7099 9800,7055 9800,6999 9800,6943 9843,6900 9899,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9800,6900 L 9800,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10001,7101 L 10001,7101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id8">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10099,2900 C 10155,2900 10199,2943 10199,2999 10199,3055 10155,3099 10099,3099 10043,3099 10000,3055 10000,2999 10000,2943 10043,2900 10099,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10000,2900 L 10000,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10201,3101 L 10201,3101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id9">
       <path fill="none" stroke="rgb(0,0,0)" d="M 9899,2900 C 9955,2900 9999,2943 9999,2999 9999,3055 9955,3099 9899,3099 9843,3099 9800,3055 9800,2999 9800,2943 9843,2900 9899,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9800,2900 L 9800,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10001,3101 L 10001,3101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id10">
       <path fill="none" stroke="rgb(0,0,0)" d="M 9899,4900 C 9955,4900 9999,4943 9999,4999 9999,5055 9955,5099 9899,5099 9843,5099 9800,5055 9800,4999 9800,4943 9843,4900 9899,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9800,4900 L 9800,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10001,5101 L 10001,5101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id11">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10099,4900 C 10155,4900 10199,4943 10199,4999 10199,5055 10155,5099 10099,5099 10043,5099 10000,5055 10000,4999 10000,4943 10043,4900 10099,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10000,4900 L 10000,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10201,5101 L 10201,5101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id12">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10099,6900 C 10155,6900 10199,6943 10199,6999 10199,7055 10155,7099 10099,7099 10043,7099 10000,7055 10000,6999 10000,6943 10043,6900 10099,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10000,6900 L 10000,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10201,7101 L 10201,7101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id13">
       <path fill="rgb(255,255,255)" stroke="none" d="M 5100,5200 L 3500,5200 3500,3000 6700,3000 6700,5200 5100,5200 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="3750" y="3433"><tspan fill="rgb(0,0,0)" stroke="none">Subdivision </tspan></tspan><tspan class="TextPosition" x="3750" y="3827"><tspan fill="rgb(0,0,0)" stroke="none">points need to </tspan></tspan><tspan class="TextPosition" x="3750" y="4221"><tspan fill="rgb(0,0,0)" stroke="none">land on the same </tspan></tspan><tspan class="TextPosition" x="3750" y="4615"><tspan fill="rgb(0,0,0)" stroke="none">location to </tspan></tspan><tspan class="TextPosition" x="3750" y="5009"><tspan fill="rgb(0,0,0)" stroke="none">prevent cracking</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.LineShape">
      <g id="id14">
       <path fill="none" stroke="rgb(0,0,0)" d="M 6600,4200 L 6651,4213"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 6703,4227 L 6754,4240"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 6806,4253 L 6857,4266"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 6908,4280 L 6960,4293"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7011,4306 L 7063,4319"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7114,4333 L 7165,4346"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7217,4359 L 7268,4372"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7320,4386 L 7371,4399"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7423,4412 L 7474,4426"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7525,4439 L 7577,4452"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7628,4465 L 7680,4479"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7731,4492 L 7782,4505"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7834,4518 L 7885,4532"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7937,4545 L 7988,4558"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8039,4571 L 8091,4585"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8142,4598 L 8194,4611"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8245,4625 L 8296,4638"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8348,4651 L 8399,4664"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8451,4678 L 8502,4691"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8553,4704 L 8605,4717"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8656,4731 L 8708,4744"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8759,4757 L 8811,4770"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8862,4784 L 8913,4797"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8965,4810 L 9016,4824"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9068,4837 L 9119,4850"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9170,4863 L 9222,4877"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9273,4890 L 9325,4903"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9376,4916 L 9427,4930"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9479,4943 L 9530,4956"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9582,4969 L 9633,4983"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9684,4996 L 9700,5000"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id15">
       <path fill="rgb(255,255,255)" stroke="none" d="M 12650,2700 L 10700,2700 10700,1500 14600,1500 14600,2700 12650,2700 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="10950" y="2024"><tspan fill="rgb(0,0,0)" stroke="none">Corner points start </tspan></tspan><tspan class="TextPosition" x="10950" y="2418"><tspan fill="rgb(0,0,0)" stroke="none">with the same values</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id16">
       <path fill="rgb(255,255,255)" stroke="none" d="M 12850,8500 L 10900,8500 10900,7300 14800,7300 14800,8500 12850,8500 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="11150" y="7824"><tspan fill="rgb(0,0,0)" stroke="none">Corner points start </tspan></tspan><tspan class="TextPosition" x="11150" y="8218"><tspan fill="rgb(0,0,0)" stroke="none">with the same values</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id17">
       <path fill="rgb(255,255,255)" stroke="none" d="M 12400,5200 L 10900,5200 10900,3300 13900,3300 13900,5200 12400,5200 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="11150" y="3780"><tspan fill="rgb(0,0,0)" stroke="none">Opposing </tspan></tspan><tspan class="TextPosition" x="11150" y="4174"><tspan fill="rgb(0,0,0)" stroke="none">directions of </tspan></tspan><tspan class="TextPosition" x="11150" y="4568"><tspan fill="rgb(0,0,0)" stroke="none">edge walking </tspan></tspan><tspan class="TextPosition" x="11150" y="4962"><tspan fill="rgb(0,0,0)" stroke="none">for subdivision</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.LineShape">
      <g id="id18">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10300,2900 L 10341,2867"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10383,2834 L 10424,2801"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10466,2767 L 10507,2734"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10549,2701 L 10590,2668"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10632,2635 L 10673,2602"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10715,2568 L 10756,2535"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10797,2502 L 10800,2500"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.LineShape">
      <g id="id19">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10200,7100 L 10243,7131"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10286,7162 L 10330,7193"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10373,7223 L 10416,7254"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10459,7285 L 10502,7316"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10546,7347 L 10589,7378"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10632,7409 L 10675,7439"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10718,7470 L 10762,7501"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10805,7532 L 10848,7563"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10891,7594 L 10900,7600"/>
      </g>
     </g>
    </g>
   </g>
  </g>
 </g>
</svg>" alt="precise">
+</div>
+</div>
+<div class="paragraph">
+<p>As stated in &#8220;<a href="#evaluation-of-expressions">Evaluation of Expressions</a>&#8221;,
+the compiler may transform expressions even if this changes the resulting
+value.
+Without any qualifiers, implementations are permitted to perform
+optimizations that effectively modify the order or number of operations used
+to evaluate an expression, even if those optimizations may produce slightly
+different results relative to unoptimized code.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>precise</strong> qualifier ensures that operations contributing to a
+variable&#8217;s value are done in their stated order and with operator consistency.
+The order is determined by operator precedence and parenthesis, as described in
+&#8220;<a href="#operators">Operators</a>&#8221;.
+Operator consistency means for each particular operator, for example the
+multiply operator (<strong>*</strong>), its operation is always computed with the same
+precision.
+Specifically, values computed by compiler-generated code must adhere to the
+following identities:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>a + b = b + a</p>
+</li>
+<li>
+<p>a * b = b * a</p>
+</li>
+<li>
+<p>a * b + c * d = b * a + c* d = d * c + b * a = &lt;any other mathematically
+valid combination&gt;</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>While the following are prevented:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>a + (b + c) is not allowed to become (a + b) + c</p>
+</li>
+<li>
+<p>a * (b * c) is not allowed to become (a * b) * c</p>
+</li>
+<li>
+<p>a * b + c is not allowed to become a single operation <strong>fma</strong>(a, b, c)</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Where <em>a</em>, <em>b</em>, <em>c</em>, and <em>d</em>, are scalars or vectors, not matrices.
+(Matrix multiplication generally does not commute.) It is the shader
+writer&#8217;s responsibility to express the computation in terms of these rules
+and the compiler&#8217;s responsibility to follow these rules.
+See the description of <em>gl_TessCoord</em> for the rules the tessellation stages
+are responsible for following, which in conjunction with the above allow
+avoiding cracking when subdividing.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precise out vec4 position;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>declares that operations used to produce the value of <em>position</em> must be
+performed in exactly the order specified in the source code and with all
+operators being treated consistently.
+As with the <strong>invariant</strong> qualifier (see &#8220;<a href="#the-invariant-qualifier">The
+Invariant Qualifier</a>&#8221;), the <strong>precise</strong> qualifier may be used to qualify a
+built-in or previously declared user-defined variable as being precise:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec3 Color;
+precise Color; <span class="comment">// make existing Color be precise</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When applied to a block, a structure type, or a variable of structure type,
+<strong>precise</strong> applies to each contained member, recursively.</p>
+</div>
+<div class="paragraph">
+<p>This qualifier will affect the evaluation of an r-value in a particular
+function if and only if the result is eventually consumed in the same
+function by an l-value qualified as <strong>precise</strong>.
+Any other expressions within a function are not affected, including return
+values and output parameters not declared as <strong>precise</strong> but that are
+eventually consumed outside the function by a variable qualified as
+<strong>precise</strong>. Unaffected expressions also include the controlling expressions
+in selection and iteration statements and the condition in ternary
+operators (<strong>?:</strong>).</p>
+</div>
+<div class="paragraph">
+<p>Some examples of the use of <strong>precise</strong>:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 a, b, c, d;
+precise out vec4 v;
+
+<span class="predefined-type">float</span> func(<span class="predefined-type">float</span> e, <span class="predefined-type">float</span> f, <span class="predefined-type">float</span> g, <span class="predefined-type">float</span> h)
+{
+    <span class="keyword">return</span> (e*f) + (g*h); <span class="comment">// no constraint on order or operator consistency</span>
+}
+
+<span class="predefined-type">float</span> func2(<span class="predefined-type">float</span> e, <span class="predefined-type">float</span> f, <span class="predefined-type">float</span> g, <span class="predefined-type">float</span> h)
+{
+    precise <span class="predefined-type">float</span> result = (e*f) + (g*h); <span class="comment">// ensures same precision for the two multiplies</span>
+    <span class="keyword">return</span> result;
+}
+
+<span class="predefined-type">float</span> func3(<span class="predefined-type">float</span> i, <span class="predefined-type">float</span> j, precise out <span class="predefined-type">float</span> k)
+{
+    k = i * i + j;        <span class="comment">// precise, due to &lt;k&gt; declaration</span>
+}
+
+<span class="directive">void</span> main()
+{
+    vec3 r = vec3(a * b);             <span class="comment">// precise, used to compute v.xyz</span>
+    vec3 s = vec3(c * d);             <span class="comment">// precise, used to compute v.xyz</span>
+    v.xyz = r + s;                    <span class="comment">// precise</span>
+    v.w = (a.w * b.w) + (c.w * d.w);  <span class="comment">// precise</span>
+    v.x = func(a.x, b.x, c.x, d.x);   <span class="comment">// values computed in func() are NOT precise</span>
+    v.x = func2(a.x, b.x, c.x, d.x);  <span class="comment">// precise!</span>
+    func3(a.x * b.x, c.x * d.x, v.x); <span class="comment">// precise!</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if an output from one shader stage matches
+an input of the next stage, the <strong>precise</strong> qualifier need not match between
+the input and the output.</p>
+</div>
+<div class="paragraph">
+<p>All constant expressions are evaluated as if <strong>precise</strong> was present, whether
+or not it is present.
+However, as described in &#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;,
+there is no requirement that a compile-time constant expression evaluates to
+the same value as a corresponding non-constant expression.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="memory-qualifiers">4.10. Memory Qualifiers</h3>
+<div class="paragraph">
+<p>Shader storage blocks, variables declared within shader storage blocks and
+variables declared as image types (the basic opaque types with &#8220;<strong>image</strong>&#8221;
+in their keyword), can be further qualified with one or more of the
+following memory qualifiers:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>coherent</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable where reads and writes are coherent with
+                reads and writes from other shader invocations</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>volatile</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable whose underlying value may be changed at any
+                point during shader execution by some source other than the
+                current shader invocation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>restrict</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable where use of that variable is the only way
+                to read and write the underlying memory in the relevant
+                shader stage</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>readonly</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable that can be used to read the underlying
+                memory, but cannot be used to write the underlying memory</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>writeonly</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable that can be used to write the underlying
+                memory, but cannot be used to read the underlying memory</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>coherent</strong> qualifier
+are performed coherently with accesses to the same location from other
+shader invocations.</p>
+</div>
+<div class="paragraph">
+<p>As described in section
+7.11
+&#8220;Shader Memory Access&#8221; of the
+<a href="#references">OpenGL ES Specification</a>, shader memory reads and writes complete in a
+largely undefined order.
+The built-in function <strong>memoryBarrier</strong>() can be used if needed to guarantee
+the completion and relative ordering of memory accesses performed by a
+single shader invocation.</p>
+</div>
+<div class="paragraph">
+<p>When accessing memory using variables not declared as <strong>coherent</strong>, the memory
+accessed by a shader may be cached by the implementation to service future
+accesses to the same address.
+Memory stores may be cached in such a way that the values written may not be
+visible to other shader invocations accessing the same memory.
+The implementation may cache the values fetched by memory reads and return
+the same values to any shader invocation accessing the same memory, even if
+the underlying memory has been modified since the first memory read.
+While variables not declared as <strong>coherent</strong> may not be useful for
+communicating between shader invocations, using non-coherent accesses may
+result in higher performance.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>volatile</strong> qualifier
+must treat the underlying memory as though it could be read or written at
+any point during shader execution by some source other than the executing
+shader invocation.
+When a volatile variable is read, its value must be re-fetched from the
+underlying memory, even if the shader invocation performing the read had
+previously fetched its value from the same memory.
+When a volatile variable is written, its value must be written to the
+underlying memory, even if the compiler can conclusively determine that its
+value will be overwritten by a subsequent write.
+Since the external source reading or writing a <strong>volatile</strong> variable may be
+another shader invocation, variables declared as <strong>volatile</strong> are
+automatically treated as coherent.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>restrict</strong> qualifier
+may be compiled assuming that the variable used to perform the memory access
+is the only way to access the underlying memory using the shader stage in
+question.
+This allows the compiler to coalesce or reorder loads and stores using
+<strong>restrict</strong>-qualified image variables in ways that wouldn&#8217;t be permitted
+for image variables not so qualified, because the compiler can assume that
+the underlying image won&#8217;t be read or written by other code.
+Applications are responsible for ensuring that image memory referenced by
+variables qualified with <strong>restrict</strong> will not be referenced using other
+variables in the same scope; otherwise, accesses to <strong>restrict</strong>-qualified
+variables will have undefined results.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>readonly</strong> qualifier
+may only read the underlying memory, which is treated as read-only memory
+and cannot be written to.
+It is an error to pass an image variable qualified with
+<strong>readonly</strong> to <strong>imageStore</strong>() or other built-in functions that modify image
+memory.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>writeonly</strong> qualifier
+may only write the underlying memory; the underlying memory cannot be read.
+It is an error to pass an image variable qualified with
+<strong>writeonly</strong> to <strong>imageLoad</strong>() or other built-in functions that read image
+memory.</p>
+</div>
+<div class="paragraph">
+<p>A variable could be qualified as both <strong>readonly</strong> and <strong>writeonly</strong>, disallowing
+both read and write. Such variables can still be used with some queries, for
+example <strong>imageSize</strong>() and <strong>.length</strong>().</p>
+</div>
+<div class="paragraph">
+<p>Except for image variables qualified with the format qualifiers <strong>r32f</strong>,
+<strong>r32i</strong>, and <strong>r32ui</strong>, image variables must specify a memory qualifier
+(<strong>readonly</strong>, <strong>writeonly</strong>, or both).</p>
+</div>
+<div class="paragraph">
+<p>The memory qualifiers <strong>coherent</strong>, <strong>volatile</strong>, <strong>restrict</strong>, <strong>readonly</strong>, and
+<strong>writeonly</strong> may be used in the declaration of buffer variables (i.e.,
+members of shader storage blocks).
+When a buffer variable is declared with a memory qualifier, the behavior
+specified for memory accesses involving image variables described above
+applies identically to memory accesses involving that buffer variable.
+It is a compile-time error to assign to a buffer variable qualified with
+<strong>readonly</strong> or to read from a buffer variable qualified with <strong>writeonly</strong>.
+The combination <strong>readonly</strong> <strong>writeonly</strong> is allowed.</p>
+</div>
+<div class="paragraph">
+<p>Additionally, memory qualifiers may be used at the block-level declaration
+of a shader storage block, including the combination <strong>readonly</strong> <strong>writeonly</strong>.
+When a block declaration is qualified with a memory qualifier, it is as if
+all of its members were declared with the same memory qualifier.
+For example, the block declaration</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">coherent buffer Block {
+    readonly vec4 member1;
+    vec4 member2;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">buffer Block {
+    coherent readonly vec4 member1;
+    coherent vec4 member2;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Memory qualifiers are only supported in the declarations of image variables,
+buffer variables, and shader storage blocks; it is an error to use such
+qualifiers in any other declarations.</p>
+</div>
+<div class="paragraph">
+<p>When calling user-defined functions, variables qualified with <strong>coherent</strong>,
+<strong>volatile</strong>, <strong>readonly</strong>, or <strong>writeonly</strong> may not be passed to functions whose
+formal parameters lack such qualifiers.
+(See &#8220;<a href="#function-definitions">Function Definitions</a>&#8221; for more detail on
+function calling.) It is legal to have any additional memory qualifiers on a
+formal parameter, but only <strong>restrict</strong> can be taken away from a calling
+argument, by a formal parameter that lacks the <strong>restrict</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>When a built-in function is called, the code generated is to be based on the
+actual qualification of the calling argument, not on the list of memory
+qualifiers specified on the formal parameter in the prototype.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 funcA(restrict image2D a) { ... }
+vec4 funcB(image2D a) { ... }
+layout(rgba32f) uniform image2D img1;
+layout(rgba32f) coherent uniform image2D img2;
+
+funcA(img1);        <span class="comment">// OK, adding &quot;restrict&quot; is allowed</span>
+funcB(img2);        <span class="comment">// illegal, stripping &quot;coherent&quot; is not</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Layout qualifiers cannot be used on formal function parameters, and layout
+qualification is not included in parameter matching.</p>
+</div>
+<div class="paragraph">
+<p>Note that the use of <strong>const</strong> in an image variable declaration is qualifying
+the const-ness of the variable being declared, not the image it refers to.
+The qualifier <strong>readonly</strong> qualifies the image memory (as accessed through
+that variable) while <strong>const</strong> qualifies the variable itself.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="order-of-qualification">4.11. Order and Repetition of Qualification</h3>
+<div class="paragraph">
+<p>When multiple qualifiers are present in a declaration, they may appear in
+any order, but they must all appear before the type.
+The <strong>layout</strong> qualifier is the only qualifier that can appear more than once.
+Further, a declaration can have at most one storage qualifier, at most one
+auxiliary storage qualifier, and at most one interpolation qualifier.
+Multiple memory qualifiers can be used.
+Any violation of these rules will cause a compile-time error.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="empty-declarations">4.12. Empty Declarations</h3>
+<div class="paragraph">
+<p><em>Empty declarations</em> are declarations without a variable name, meaning no
+object is instantiated by the declaration.
+Generally, empty declarations are allowed.
+Some are useful when declaring structures, while many others have no effect.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span>;               <span class="comment">// No effect</span>
+<span class="keyword">struct</span> S {<span class="predefined-type">int</span> x;}; <span class="comment">// Defines a struct S</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The combinations of qualifiers that cause compile-time or link-time errors
+are the same whether or not the declaration is empty, for example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">invariant in <span class="predefined-type">float</span> x; <span class="comment">// Error. An input cannot be invariant.</span>
+invariant in <span class="predefined-type">float</span>;   <span class="comment">// Error even though no variable is declared.</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="operators-and-expressions">5. Operators and Expressions</h2>
+<div class="sectionbody">
+<div class="sect2">
+<h3 id="operators">5.1. Operators</h3>
+<div class="paragraph">
+<p>The OpenGL ES Shading Language has the following operators.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Precedence</th>
+<th class="tableblock halign-left valign-top">Operator Class</th>
+<th class="tableblock halign-left valign-top">Operators</th>
+<th class="tableblock halign-left valign-top">Associativity</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1 (highest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">parenthetical grouping</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">( )</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">NA</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">array subscript<br>
+                 function call and constructor structure<br>
+                 field or method selector, swizzle<br>
+                 post fix increment and decrement</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">[ ]<br>
+                                                  ( )<br>
+                                                  .<br>
+                                                  ++ --</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">prefix increment and decrement<br>
+                 unary</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">++ --<br>
+                                                  + - ~ !</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">multiplicative</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">* / %</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">additive</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">+ -</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise shift</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;&lt; &gt;&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">7</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">relational</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt; &gt; &lt;= &gt;=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">8</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">equality</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">== !=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">9</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">10</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise exclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">^</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">11</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">|</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">12</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">13</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical exclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">^^</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">14</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">||</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">15</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">selection</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">? :</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">16</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Assignment<br>
+                 arithmetic assignments</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">=<br>
+                                                  += -=<br>
+                                                  *= /=<br>
+                                                  %= &lt;&lt;= &gt;&gt;=<br>
+                                                  &amp;= ^= |=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">17 (lowest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">sequence</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">,</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>There is no address-of operator nor a dereference operator.
+There is no typecast operator; constructors are used instead.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="array-operations">5.2. Array Operations</h3>
+<div class="paragraph">
+<p>These are now described in &#8220;<a href="#structure-and-array-operations">Structure and
+Array Operations</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="function-calls">5.3. Function Calls</h3>
+<div class="paragraph">
+<p>If a function returns a value, then a call to that function may be used as
+an expression, whose type will be the type that was used to declare or
+define the function.</p>
+</div>
+<div class="paragraph">
+<p>Function definitions and calling conventions are discussed in
+&#8220;<a href="#function-definitions">Function Definitions</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="constructors">5.4. Constructors</h3>
+<div class="paragraph">
+<p>Constructors use the function call syntax, where the function name is a
+type, and the call makes an object of that type.
+Constructors are used the same way in both initializers and expressions.
+(See &#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; for details.)
+The parameters are used to initialize the constructed value.
+Constructors can be used to request a data type conversion to change from
+one scalar type to another scalar type, or to build larger types out of
+smaller types, or to reduce a larger type to a smaller type.</p>
+</div>
+<div class="paragraph">
+<p>In general, constructors are not built-in functions with predetermined
+prototypes.
+For arrays and structures, there must be exactly one argument in the
+constructor for each element or member.
+For the other types, the arguments must provide a sufficient number of
+components to perform the initialization, and it is an error to
+include so many arguments that they cannot all be used.
+Detailed rules follow.
+The prototypes actually listed below are merely a subset of examples.</p>
+</div>
+<div class="sect3">
+<h4 id="conversion-and-scalar-constructors">5.4.1. Conversion and Scalar Constructors</h4>
+<div class="paragraph">
+<p>Converting between scalar types is done as the following prototypes
+indicate:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span>(uint)     <span class="comment">// converts an unsigned integer to a signed integer</span>
+<span class="predefined-type">int</span>(<span class="predefined-type">bool</span>)     <span class="comment">// converts a Boolean value to an int</span>
+<span class="predefined-type">int</span>(<span class="predefined-type">float</span>)    <span class="comment">// converts a float value to an int</span>
+uint(<span class="predefined-type">int</span>)     <span class="comment">// converts a signed integer value to an unsigned integer</span>
+uint(<span class="predefined-type">bool</span>)    <span class="comment">// converts a Boolean value to an unsigned integer</span>
+uint(<span class="predefined-type">float</span>)   <span class="comment">// converts a float value to an unsigned integer</span>
+<span class="predefined-type">bool</span>(<span class="predefined-type">int</span>)     <span class="comment">// converts a signed integer value to a Boolean</span>
+<span class="predefined-type">bool</span>(uint)    <span class="comment">// converts an unsigned integer value to a Boolean value</span>
+<span class="predefined-type">bool</span>(<span class="predefined-type">float</span>)   <span class="comment">// converts a float value to a Boolean</span>
+<span class="predefined-type">float</span>(<span class="predefined-type">int</span>)    <span class="comment">// converts a signed integer value to a float</span>
+<span class="predefined-type">float</span>(uint)   <span class="comment">// converts an unsigned integer value to a float value</span>
+<span class="predefined-type">float</span>(<span class="predefined-type">bool</span>)   <span class="comment">// converts a Boolean value to a float</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When constructors are used to convert a floating-point type to an integer
+type, the fractional part of the floating-point value is dropped.
+It is undefined to convert a negative floating-point value to an <strong>uint</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Integer values having more bits of precision than a single-precision
+floating-point mantissa will lose precision when converted to <strong>float</strong>.</p>
+</div>
+<div class="paragraph">
+<p>When a constructor is used to convert any integer or floating-point type to
+a <strong>bool</strong>, 0 and 0.0 are converted to <strong>false</strong>, and non-zero values are
+converted to <strong>true</strong>.
+When a constructor is used to convert a <strong>bool</strong> to any integer or
+floating-point type, <strong>false</strong> is converted to 0 or 0.0, and <strong>true</strong> is
+converted to 1 or 1.0.</p>
+</div>
+<div class="paragraph">
+<p>The constructor <strong>int</strong>(<strong>uint</strong>) preserves the bit pattern in the argument,
+which will change the argument&#8217;s value if its sign bit is set.
+The constructor <strong>uint</strong>(<strong>int</strong>) preserves the bit pattern in the argument,
+which will change its value if it is negative.</p>
+</div>
+<div class="paragraph">
+<p>Identity constructors, like <strong>float</strong>(<strong>float</strong>) are also legal, but of little
+use.</p>
+</div>
+<div class="paragraph">
+<p>Scalar constructors with non-scalar parameters can be used to take the first
+element from a non-scalar.
+For example, the constructor <strong>float</strong>(<strong>vec3</strong>) will select the first component
+of the <strong>vec3</strong> parameter.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="vector-and-matrix-constructors">5.4.2. Vector and Matrix Constructors</h4>
+<div class="paragraph">
+<p>Constructors can be used to create vectors or matrices from a set of
+scalars, vectors, or matrices.
+This includes the ability to shorten vectors.</p>
+</div>
+<div class="paragraph">
+<p>If there is a single scalar parameter to a vector constructor, it is used to
+initialize all components of the constructed vector to that scalar&#8217;s value.
+If there is a single scalar parameter to a matrix constructor, it is used to
+initialize all the components on the matrix&#8217;s diagonal, with the remaining
+components initialized to 0.0.</p>
+</div>
+<div class="paragraph">
+<p>If a vector is constructed from multiple scalars, one or more vectors, or
+one or more matrices, or a mixture of these, the vector&#8217;s components will be
+constructed in order from the components of the arguments.
+The arguments will be consumed left to right, and each argument will have
+all its components consumed, in order, before any components from the next
+argument are consumed.
+Similarly for constructing a matrix from multiple scalars or vectors, or a
+mixture of these.
+Matrix components will be constructed and consumed in column major order.
+In these cases, there must be enough components provided in the arguments to
+provide an initializer for every component in the constructed value.
+It is an error to provide extra arguments beyond this last used
+argument.</p>
+</div>
+<div class="paragraph">
+<p>If a matrix is constructed from a matrix, then each component (column <em>i</em>,
+row <em>j</em>) in the result that has a corresponding component (column <em>i</em>, row
+<em>j</em>) in the argument will be initialized from there.
+All other components will be initialized to the identity matrix.
+If a matrix argument is given to a matrix constructor, it is
+an error to have any other arguments.</p>
+</div>
+<div class="paragraph">
+<p>If the basic type (<strong>bool</strong>, <strong>int</strong>,
+or <strong>float</strong>)
+of a parameter to a
+constructor does not match the basic type of the object being constructed,
+the scalar construction rules (above) are used to convert the parameters.</p>
+</div>
+<div class="paragraph">
+<p>Some useful vector constructors are as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3(<span class="predefined-type">float</span>)          <span class="comment">// initializes each component of the vec3 with the float</span>
+vec4(ivec4)          <span class="comment">// makes a vec4 with component-wise conversion</span>
+vec4(mat2)           <span class="comment">// the vec4 is column 0 followed by column 1</span>
+vec2(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>)   <span class="comment">// initializes a vec2 with 2 floats</span>
+ivec3(<span class="predefined-type">int</span>, <span class="predefined-type">int</span>, <span class="predefined-type">int</span>) <span class="comment">// initializes an ivec3 with 3 ints</span>
+bvec4(<span class="predefined-type">int</span>, <span class="predefined-type">int</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>) <span class="comment">// uses 4 Boolean conversions</span>
+vec2(vec3)           <span class="comment">// drops the third component of a vec3</span>
+vec3(vec4)           <span class="comment">// drops the fourth component of a vec4</span>
+vec3(vec2, <span class="predefined-type">float</span>)    <span class="comment">// vec3.x = vec2.x, vec3.y = vec2.y, vec3.z = float</span>
+vec3(<span class="predefined-type">float</span>, vec2)    <span class="comment">// vec3.x = float, vec3.y = vec2.x, vec3.z = vec2.y</span>
+vec4(vec3, <span class="predefined-type">float</span>)
+vec4(<span class="predefined-type">float</span>, vec3)
+vec4(vec2, vec2)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Some examples of these are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 color = vec4(<span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span>);
+vec4 rgba = vec4(<span class="float">1</span><span class="float">.0</span>);      <span class="comment">// sets each component to 1.0</span>
+vec3 rgb = vec3(color);     <span class="comment">// drop the 4th component</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>To initialize the diagonal of a matrix with all other elements set to zero:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2(<span class="predefined-type">float</span>)
+mat3(<span class="predefined-type">float</span>)
+mat4(<span class="predefined-type">float</span>)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>That is, <em>result[i][j]</em> is set to the <em>float</em> argument for all \(i
+= j\) and set to 0 for all \(i \neq j\).</p>
+</div>
+<div class="paragraph">
+<p>To initialize a matrix by specifying vectors or scalars, the components are
+assigned to the matrix elements in column-major order.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2(vec2, vec2);                 <span class="comment">// one column per argument</span>
+mat3(vec3, vec3, vec3);           <span class="comment">// one column per argument</span>
+mat4(vec4, vec4, vec4, vec4);     <span class="comment">// one column per argument</span>
+mat3x2(vec2, vec2, vec2);         <span class="comment">// one column per argument</span>
+mat2(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>,                <span class="comment">// first column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>);               <span class="comment">// second column</span>
+mat3(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,         <span class="comment">// first column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,         <span class="comment">// second column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>);        <span class="comment">// third column</span>
+mat4(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,  <span class="comment">// first column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,  <span class="comment">// second column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,  <span class="comment">// third column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>); <span class="comment">// fourth column</span>
+mat2x3(vec2, <span class="predefined-type">float</span>,               <span class="comment">// first column</span>
+       vec2, <span class="predefined-type">float</span>);              <span class="comment">// second column</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A wide range of other possibilities exist, to construct a matrix from
+vectors and scalars, as long as enough components are present to initialize
+the matrix.
+To construct a matrix from a matrix:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat3x3(mat4x4); <span class="comment">// takes the upper-left 3x3 of the mat4x4</span>
+mat2x3(mat4x2); <span class="comment">// takes the upper-left 2x2 of the mat4x4, last row is 0,0</span>
+mat4x4(mat3x3); <span class="comment">// puts the mat3x3 in the upper-left, sets the lower right</span>
+                <span class="comment">// component to 1, and the rest to 0</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="structure-constructors">5.4.3. Structure Constructors</h4>
+<div class="paragraph">
+<p>Once a structure is defined, and its type is given a name, a constructor is
+available with the same name to construct instances of that structure.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> light {
+    <span class="predefined-type">float</span> intensity;
+    vec3 position;
+};
+
+light lightVar = light(<span class="float">3</span><span class="float">.0</span>, vec3(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>));</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The arguments to the constructor will be used to set the structure&#8217;s
+members, in order, using one argument per member.
+Each argument must be the same type as the member it
+sets.</p>
+</div>
+<div class="paragraph">
+<p>Structure constructors can be used as initializers or in expressions.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="array-constructors">5.4.4. Array Constructors</h4>
+<div class="paragraph">
+<p>Array types can also be used as constructor names, which can then be used in
+expressions or initializers.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> <span class="predefined-type">float</span> c[<span class="integer">3</span>] = <span class="predefined-type">float</span>[<span class="integer">3</span>](<span class="float">5</span><span class="float">.0</span>, <span class="float">7</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+<span class="directive">const</span> <span class="predefined-type">float</span> d[<span class="integer">3</span>] = <span class="predefined-type">float</span>[](<span class="float">5</span><span class="float">.0</span>, <span class="float">7</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+
+<span class="predefined-type">float</span> g;
+...
+<span class="predefined-type">float</span> a[<span class="integer">5</span>] = <span class="predefined-type">float</span>[<span class="integer">5</span>](g, <span class="integer">1</span>, g, <span class="float">2</span><span class="float">.3</span>, g);
+<span class="predefined-type">float</span> b[<span class="integer">3</span>];
+
+b = <span class="predefined-type">float</span>[<span class="integer">3</span>](g, g + <span class="float">1</span><span class="float">.0</span>, g + <span class="float">2</span><span class="float">.0</span>);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There must be exactly the same number of arguments as the size of the array
+being constructed.
+If no size is present in the constructor, then the array is explicitly sized
+to the number of arguments provided.
+The arguments are assigned in order, starting at element 0, to the elements
+of the constructed array.
+Each argument must be the same type as the element type of the
+array.</p>
+</div>
+<div class="paragraph">
+<p>Arrays of arrays are similarly constructed, and the size for any dimension
+is <strong class="purple">optional</strong></p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 b[<span class="integer">2</span>] = ...;
+vec4[<span class="integer">3</span>][<span class="integer">2</span>](b, b, b);    <span class="comment">// constructor</span>
+vec4[][<span class="integer">2</span>](b, b, b);     <span class="comment">// constructor, valid, size deduced</span>
+vec4[<span class="integer">3</span>][](b, b, b);     <span class="comment">// constructor, valid, size deduced</span>
+vec4[][](b, b, b);      <span class="comment">// constructor, valid, both sizes deduced</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="vector-components">5.5. Vector Components</h3>
+<div class="paragraph">
+<p>The names of the components of a vector
+are denoted by a single letter.
+As a notational convenience, several letters are associated with each
+component based on common usage of position, color or texture coordinate
+vectors.
+The individual components can be selected by following the variable name
+with period (<strong>.</strong>) and then the component name.</p>
+</div>
+<div class="paragraph">
+<p>The component names supported are:</p>
+</div>
+<table class="tableblock frame-all grid-all fit-content">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>{ x, y, z, w }</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Useful when accessing vectors that represent points or normals</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>{ r, g, b, a }</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Useful when accessing vectors that represent colors</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>{ s, t, p, q }</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Useful when accessing vectors that represent texture coordinates</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The component names <em>x</em>, <em>r</em>, and <em>s</em> are, for example, synonyms for the
+same (first) component in a vector.</p>
+</div>
+<div class="paragraph">
+<p>Note that the third component of the texture coordinate set, <em>r</em> in
+OpenGL ES, has been renamed <em>p</em> so as to avoid the confusion with <em>r</em> (for
+red) in a color.</p>
+</div>
+<div class="paragraph">
+<p>Accessing components beyond those declared for the type is
+an error so, for example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec2 pos;
+pos.x       <span class="comment">// is legal</span>
+pos.z       <span class="comment">// is illegal</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The component selection syntax allows multiple components to be selected by
+appending their names (from the same name set) after the period (<strong>.</strong>).</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 v4;
+v4.rgba;    <span class="comment">// is a vec4 and the same as just using v4,</span>
+v4.rgb;     <span class="comment">// is a vec3,</span>
+v4.b;       <span class="comment">// is a float,</span>
+v4.xy;      <span class="comment">// is a vec2,</span>
+v4.xgba;    <span class="comment">// is illegal - the component names do not come from the same set</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>No more than 4 components can be selected.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 v4;
+v4.xyzwxy;      <span class="comment">// is illegal since it has 6 components</span>
+(v4.xyzwxy).xy; <span class="comment">// is illegal since the intermediate value has 6</span>
+components</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The order of the components can be different to swizzle them, or replicated:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 pos = vec4(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>, <span class="float">4</span><span class="float">.0</span>);
+vec4 swiz = pos.wzyx;   <span class="comment">// swiz = (4.0, 3.0, 2.0, 1.0)</span>
+vec4 dup = pos.xxyy;    <span class="comment">// dup = (1.0, 1.0, 2.0, 2.0)</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This notation is more concise than the constructor syntax.
+To form an r-value, it can be applied to any expression that results in a
+vector r-value.</p>
+</div>
+<div class="paragraph">
+<p>The component group notation can occur on the left hand side of an
+expression.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 pos = vec4(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>, <span class="float">4</span><span class="float">.0</span>);
+pos.xw = vec2(<span class="float">5</span><span class="float">.0</span>, <span class="float">6</span><span class="float">.0</span>);        <span class="comment">// pos = (5.0, 2.0, 3.0, 6.0)</span>
+pos.wx = vec2(<span class="float">7</span><span class="float">.0</span>, <span class="float">8</span><span class="float">.0</span>);        <span class="comment">// pos = (8.0, 2.0, 3.0, 7.0)</span>
+pos.xx = vec2(<span class="float">3</span><span class="float">.0</span>, <span class="float">4</span><span class="float">.0</span>);        <span class="comment">// illegal - 'x' used twice</span>
+pos.xy = vec3(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>);   <span class="comment">// illegal - mismatch between vec2 and vec3</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>To form an l-value, swizzling must further be applied to an l-value and
+contain no duplicate components. It results in an l-value of scalar or
+vector type, depending on number of components specified.</p>
+</div>
+<div class="paragraph">
+<p>Array subscripting syntax can also be applied to vectors (but not to
+scalars) to provide numeric indexing.
+So in</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 pos;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p><em>pos[2]</em> refers to the third element of <em>pos</em> and is equivalent to <em>pos.z</em>.
+This allows variable indexing into a vector, as well as a generic way of
+accessing components.
+Any integer expression can be used as the subscript.
+The first component is at index zero.
+Reading from or writing to a vector using a constant integral expression
+with a value that is negative or greater than or equal to the size of the
+vector results in an error.
+When indexing with non-constant expressions, behavior is undefined if the
+index is negative, or greater than or equal to the size of the vector.</p>
+</div>
+<div class="paragraph">
+<p>Note that scalars are not considered to be single-component vectors and
+therefore the use of component selection operators on scalars is illegal.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="matrix-components">5.6. Matrix Components</h3>
+<div class="paragraph">
+<p>The components of a matrix can be accessed using array subscripting syntax.
+Applying a single subscript to a matrix treats the matrix as an array of
+column vectors, and selects a single column, whose type is a vector of the
+same size as the (column size of the) matrix.
+The leftmost column is column 0.
+A second subscript would then operate on the resulting vector, as defined
+earlier for vectors.
+Hence, two subscripts select a column and then a row.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat4 m;
+m[<span class="integer">1</span>] = vec4(<span class="float">2</span><span class="float">.0</span>);   <span class="comment">// sets the second column to all 2.0</span>
+m[<span class="integer">0</span>][<span class="integer">0</span>] = <span class="float">1</span><span class="float">.0</span>;      <span class="comment">// sets the upper left element to 1.0</span>
+m[<span class="integer">2</span>][<span class="integer">3</span>] = <span class="float">2</span><span class="float">.0</span>;      <span class="comment">// sets the 4th element of the third column to 2.0</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Behavior is undefined when accessing a component outside the bounds of a
+matrix with a non-constant expression.
+It is an error to access a matrix with a constant expression
+that is outside the bounds of the matrix.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="structure-and-array-operations">5.7. Structure and Array Operations</h3>
+<div class="paragraph">
+<p>The members of a structure and the <strong>length</strong>() method of an array are
+selected using the period (<strong>.</strong>).</p>
+</div>
+<div class="paragraph">
+<p>In total, only the following operators are allowed to operate on arrays and
+structures as whole entities:</p>
+</div>
+<table class="tableblock frame-all grid-all fit-content">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">field selector</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>.</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">equality</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>==</strong> <strong>!=</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">assignment</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>=</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Ternary operator</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>?:</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Sequence operator</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>,</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">indexing (arrays only)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>[</strong> <strong>]</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The equality operators and assignment operator are only allowed if the two
+operands are same size and type.
+The operands cannot contain any opaque types.
+Structure types must be of the same declared structure.
+Both array operands must be
+compile-time
+sized.
+When using the equality operators, two structures are equal if and only if
+all the members are component-wise equal, and two arrays are equal if and
+only if all the elements are element-wise equal.</p>
+</div>
+<div class="paragraph">
+<p>Array elements are accessed using the array subscript operator (<strong>[ ]</strong>).
+An example of accessing an array element is</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">diffuseColor += lightIntensity[<span class="integer">3</span>] * NdotL;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Array indices start at zero.
+Array elements are accessed using an expression whose type is <strong>int</strong> or
+<strong>uint</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Behavior is undefined if a shader subscripts an array with an index less
+than 0 or greater than or equal to the size the array was declared with.</p>
+</div>
+<div class="paragraph">
+<p>Arrays can also be accessed with the method operator (<strong>.</strong>) and the <strong>length</strong>
+method to query the size of the array:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">lightIntensity.length() <span class="comment">// return the size of the array</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="assignments">5.8. Assignments</h3>
+<div class="paragraph">
+<p>Assignments of values to variable names are done with the assignment
+operator (<strong>=</strong>):</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>lvalue-expression</em> = <em>rvalue-expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The <em>lvalue-expression</em> evaluates to an l-value.
+The assignment operator stores the value of <em>rvalue-expression</em> into the
+l-value and returns an r-value with the type and precision of
+<em>lvalue-expression</em>.
+The <em>lvalue-expression</em> and <em>rvalue-expression</em> must have the same
+type.
+Any type-conversions must be specified explicitly via constructors.
+It is an error if the l-value is not writable.
+Variables that are built-in types, entire structures or arrays, structure
+members, l-values with the field selector (<strong>.</strong>) applied to select components
+or swizzles without repeated fields, l-values within parentheses, and
+l-values dereferenced with the array subscript operator (<strong>[ ]</strong>) are all
+l-values.
+Other binary or unary expressions, function names, swizzles with repeated
+fields, and constants cannot be l-values.
+The ternary operator (<strong>?:</strong>) is also not allowed as an l-value.
+Using an incorrect expression as an l-value results in an error.</p>
+</div>
+<div class="paragraph">
+<p>Expressions on the left of an assignment are evaluated before expressions on
+the right of the assignment.</p>
+</div>
+<div class="paragraph">
+<p>The other assignment operators are</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>add into (<strong>+=</strong>)</p>
+</li>
+<li>
+<p>subtract from (<strong>-=</strong>)</p>
+</li>
+<li>
+<p>multiply into (<strong>*=</strong>)</p>
+</li>
+<li>
+<p>divide into (<strong>/=</strong>)</p>
+</li>
+<li>
+<p>modulus into (<strong>%=</strong>)</p>
+</li>
+<li>
+<p>left shift by (<strong>&lt;&lt;=</strong>)</p>
+</li>
+<li>
+<p>right shift by (<strong>&gt;&gt;=</strong>)</p>
+</li>
+<li>
+<p>and into (<strong>&amp;=</strong>)</p>
+</li>
+<li>
+<p>inclusive-or into (<strong>|=</strong>)</p>
+</li>
+<li>
+<p>exclusive-or into (<strong>^=</strong>)</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>where the general expression</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>lvalue</em> <em>op</em>= <em>expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>lvalue</em> = <em>lvalue</em> <em>op</em> <em>expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>where <em>lvalue</em> is the value returned by <em>lvalue-expression</em>, <em>op</em> is as
+described below, and the <em>lvalue-expression</em> and <em>expression</em> must satisfy
+the semantic requirements of both <em>op</em> and equals (<strong>=</strong>).</p>
+</div>
+<div class="paragraph">
+<p>Reading a variable before writing (or initializing) it is legal, however the
+value is undefined.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="expressions">5.9. Expressions</h3>
+<div class="paragraph">
+<p>Expressions in the shading language are built from the following:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Constants of type <strong>bool</strong>, all integral types, all floating-point types,
+all vector types, and all matrix types.</p>
+</li>
+<li>
+<p>Constructors of all types.</p>
+</li>
+<li>
+<p>Variable names of all types.</p>
+</li>
+<li>
+<p>Arrays with the length method applied.</p>
+</li>
+<li>
+<p>Subscripted arrays.</p>
+</li>
+<li>
+<p>Function calls that return values.
+In some cases, function calls returning <strong>void</strong> are also allowed in
+expressions as specified below.</p>
+</li>
+<li>
+<p>Component field selectors and array subscript results.</p>
+</li>
+<li>
+<p>Parenthesized expressions.
+Any expression, including expressions with void type can be
+parenthesized.
+Parentheses can be used to group operations.
+Operations within parentheses are done before operations across
+parentheses.</p>
+</li>
+<li>
+<p>The arithmetic binary operators add (<strong>+</strong>), subtract (<strong>-</strong>), multiply
+(<strong>*</strong>), and divide (<strong>/</strong>) operate on integer and floating-point scalars,
+vectors, and matrices.
+If the operands are integral types, they must both be signed or both be
+unsigned.
+All arithmetic binary operators result in the same fundamental type
+(signed integer, unsigned integer, or floating-point) as the operands
+they operate on.
+The following cases are valid</p>
+<div class="ulist">
+<ul>
+<li>
+<p>The two operands are scalars.
+In this case the operation is applied, resulting in a scalar.</p>
+</li>
+<li>
+<p>One operand is a scalar, and the other is a vector or matrix.
+In this case, the scalar operation is applied independently to each
+component of the vector or matrix, resulting in the same size vector or
+matrix.</p>
+</li>
+<li>
+<p>The two operands are vectors of the same size.
+In this case, the operation is done component-wise resulting in the
+same size vector.</p>
+</li>
+<li>
+<p>The operator is add (<strong>+</strong>), subtract (<strong>-</strong>), or divide (<strong>/</strong>), and the
+operands are matrices with the same number of rows and the same number
+of columns.
+In this case, the operation is done component-wise resulting in the
+same size matrix.</p>
+</li>
+<li>
+<p>The operator is multiply (<strong>*</strong>), where both operands are matrices or one
+operand is a vector and the other a matrix.
+A right vector operand is treated as a column vector and a left vector
+operand as a row vector.
+In all these cases, it is required that the number of columns of the
+left operand is equal to the number of rows of the right operand.
+Then, the multiply (<strong>*</strong>) operation does a linear algebraic multiply,
+yielding an object that has the same number of rows as the left operand
+and the same number of columns as the right operand.
+&#8220;<a href="#vector-and-matrix-operations">Vector and Matrix Operations</a>&#8221;
+explains in more detail how vectors and matrices are operated on.</p>
+<div class="openblock">
+<div class="content">
+<div class="paragraph">
+<p>All other cases result in an error.</p>
+</div>
+<div class="paragraph">
+<p>Use the built-in functions <strong>dot</strong>, <strong>cross</strong>, <strong>matrixCompMult</strong>, and
+<strong>outerProduct</strong>, to get, respectively, vector dot product, vector cross
+product, matrix component-wise multiplication, and the matrix product of a
+column vector times a row vector.</p>
+</div>
+</div>
+</div>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>The operator modulus (<strong>%</strong>) operates on signed or unsigned integers or
+integer vectors.
+The operand types must both be signed or both be unsigned.
+The operands cannot be vectors of differing size; this is
+an error.
+If one operand is a scalar and the other vector, then the scalar is
+applied component-wise to the vector, resulting in the same type as the
+vector.
+If both are vectors of the same size, the result is computed
+component-wise.
+The resulting value is undefined for any component computed with a
+second operand that is zero, while results for other components with
+non-zero second operands remain defined.
+If both operands are non-negative, then the remainder is non-negative.
+Results are undefined if one or both operands are negative.
+The operator modulus (<strong>%</strong>) is not defined for any other data types
+(non-integer types).</p>
+</li>
+<li>
+<p>The arithmetic unary operators negate (<strong>-</strong>), post- and pre-increment and
+decrement (<strong>--</strong> and <strong>++</strong>) operate on integer or floating-point values
+(including vectors and matrices).
+All unary operators work component-wise on their operands.
+These result with the same type they operated on.
+For post- and pre-increment and decrement, the expression must be a writable
+l-value.
+Pre-increment and pre-decrement add or subtract 1 or 1.0 to the contents
+of the expression they operate on, and the value of the pre-increment or
+pre-decrement expression is the resulting value of that modification.
+Post-increment and post-decrement expressions add or subtract 1 or 1.0
+to the contents of the expression they operate on, but the resulting
+expression has the expression&#8217;s value before the post-increment or
+post-decrement was executed.</p>
+</li>
+<li>
+<p>The relational operators greater than (<strong>&gt;</strong>), less than (<strong>&lt;</strong>), greater
+than or equal (<strong>&gt;=</strong>), and less than or equal (<strong>&lt;=</strong>) operate only on
+scalar integer and scalar floating-point expressions.
+The result is scalar Boolean.
+The types of the operands must match.
+To do component-wise relational comparisons on vectors, use the built-in
+functions <strong>lessThan</strong>, <strong>lessThanEqual</strong>, <strong>greaterThan</strong>, and
+<strong>greaterThanEqual.</strong></p>
+</li>
+<li>
+<p>The equality operators <strong>equal</strong> (<strong>==</strong>), and not equal (<strong>!=</strong>) operate on
+all types except opaque types.
+They result in a scalar Boolean.
+The types of the operands must match.
+For vectors, matrices, structures, and arrays, all components, members,
+or elements of one operand must equal the corresponding components,
+members, or elements in the other operand for the operands to be
+considered equal.
+To get a vector of component-wise equality results for vectors, use the
+built-in functions <strong>equal</strong> and <strong>notEqual</strong>.</p>
+</li>
+<li>
+<p>The logical binary operators and (<strong>&amp;&amp;</strong>), or (<strong>||</strong>), and exclusive or
+(<strong>^^</strong>) operate only on two Boolean expressions and result in a Boolean
+expression.
+And (<strong>&amp;&amp;</strong>) will only evaluate the right hand operand if the left hand
+operand evaluated to <strong>true</strong>.
+Or (<strong>||</strong>) will only evaluate the right hand operand if the left hand
+operand evaluated to <strong>false</strong>.
+Exclusive or (<strong>^^</strong>) will always evaluate both operands.</p>
+</li>
+<li>
+<p>The logical unary operator not (<strong>!</strong>).
+It operates only on a Boolean expression and results in a Boolean
+expression.
+To operate on a vector, use the built-in function <strong>not</strong>.</p>
+</li>
+<li>
+<p>The sequence (<strong>,</strong>) operator that operates on expressions by returning
+the type and value of the right-most expression in a comma separated
+list of expressions.
+All expressions are evaluated, in order, from left to right.
+The operands to the sequence operator may have <strong>void</strong> type.</p>
+</li>
+<li>
+<p>The ternary selection operator (<strong>?:</strong>).
+It operates on three expressions (<em>exp1</em> <strong>?</strong> <em>exp2</em> <strong>:</strong> <em>exp3</em>).
+This operator evaluates the first expression, which must result in a
+scalar Boolean.
+If the result is true, it selects to evaluate the second expression,
+otherwise it selects to evaluate the third expression.
+Only one of the second and third expressions is evaluated.
+The second and third expressions can be any type, including <strong>void</strong>, as
+long their types match.
+This resulting matching type is the type of the entire expression.</p>
+</li>
+<li>
+<p>The one&#8217;s complement operator (<strong>~</strong>).
+The operand must be of type signed or unsigned integer or integer
+vector, and the result is the one&#8217;s complement of its operand; each bit
+of each component is complemented, including any sign bits.</p>
+</li>
+<li>
+<p>The shift operators (<strong>&lt;&lt;</strong>) and (<strong>&gt;&gt;</strong>).
+For both operators, the operands must be signed or unsigned integers or
+integer vectors.
+One operand can be signed while the other is unsigned.
+In all cases, the resulting type will be the same type as the left
+operand.
+If the first operand is a scalar, the second operand has to be a scalar
+as well.
+If the first operand is a vector, the second operand must be a scalar or
+a vector with the same size as the first operand, and the result is
+computed component-wise.
+The result is undefined if the right operand is negative, or greater
+than or equal to the number of bits in the left expression&#8217;s base type.
+The value of E1 &lt;&lt; E2 is E1 (interpreted as a bit pattern) left-shifted
+by E2 bits.
+The value of E1 &gt;&gt; E2 is E1 right-shifted by E2 bit positions.
+If E1 is a signed integer, the right-shift will extend the sign bit.
+If E1 is an unsigned integer, the right-shift will zero-extend.</p>
+</li>
+<li>
+<p>The bitwise operators and (<strong>&amp;</strong>), exclusive-or (<strong>^</strong>), and inclusive-or
+(<strong>|</strong>).
+The operands must be of type signed or unsigned integers or integer
+vectors.
+The operands cannot be vectors of differing size; this is an error.
+If one operand is a scalar and the other a vector, the scalar is applied
+component-wise to the vector, resulting in the same type as the vector.
+The fundamental types of the operands (signed or unsigned) must match,
+and will be the resulting fundamental type.
+For and (<strong>&amp;</strong>), the result is the bitwise-and function of the operands.
+For exclusive-or (<strong>^</strong>), the result is the bitwise exclusive-or function
+of the operands.
+For inclusive-or (<strong>|</strong>), the result is the bitwise inclusive-or function
+of the operands.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>For a complete specification of the syntax of expressions, see
+&#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="vector-and-matrix-operations">5.10. Vector and Matrix Operations</h3>
+<div class="paragraph">
+<p>With a few exceptions, operations are component-wise.
+Usually, when an operator operates on a vector or matrix, it is operating
+independently on each component of the vector or matrix, in a component-wise
+fashion.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v, u;
+<span class="predefined-type">float</span> f;
+v = u + f;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will be equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">v.x = u.x + f;
+v.y = u.y + f;
+v.z = u.z + f;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>And</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v, u, w;
+w = v + u;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will be equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">w.x = v.x + u.x;
+w.y = v.y + u.y;
+w.z = v.z + u.z;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and likewise for most operators and all integer and floating-point vector
+and matrix types.
+The exceptions are matrix multiplied by vector, vector multiplied by matrix,
+and matrix multiplied by matrix.
+These do not operate component-wise, but rather perform the correct linear
+algebraic multiply.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v, u;
+mat3 m;
+u = v * m;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">u.x = dot(v, m[<span class="integer">0</span>]); <span class="comment">// m[0] is the left column of m</span>
+u.y = dot(v, m[<span class="integer">1</span>]); <span class="comment">// dot(a,b) is the inner (dot) product of a and b</span>
+u.z = dot(v, m[<span class="integer">2</span>]);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>And</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">u = m * v;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">u.x = m[<span class="integer">0</span>].x * v.x + m[<span class="integer">1</span>].x * v.y + m[<span class="integer">2</span>].x * v.z;
+u.y = m[<span class="integer">0</span>].y * v.x + m[<span class="integer">1</span>].y * v.y + m[<span class="integer">2</span>].y * v.z;
+u.z = m[<span class="integer">0</span>].z * v.x + m[<span class="integer">1</span>].z * v.y + m[<span class="integer">2</span>].z * v.z;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>And</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat3 m, n, r;
+r = m * n;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">r[<span class="integer">0</span>].x = m[<span class="integer">0</span>].x * n[<span class="integer">0</span>].x + m[<span class="integer">1</span>].x * n[<span class="integer">0</span>].y + m[<span class="integer">2</span>].x * n[<span class="integer">0</span>].z;
+r[<span class="integer">1</span>].x = m[<span class="integer">0</span>].x * n[<span class="integer">1</span>].x + m[<span class="integer">1</span>].x * n[<span class="integer">1</span>].y + m[<span class="integer">2</span>].x * n[<span class="integer">1</span>].z;
+r[<span class="integer">2</span>].x = m[<span class="integer">0</span>].x * n[<span class="integer">2</span>].x + m[<span class="integer">1</span>].x * n[<span class="integer">2</span>].y + m[<span class="integer">2</span>].x * n[<span class="integer">2</span>].z;
+r[<span class="integer">0</span>].y = m[<span class="integer">0</span>].y * n[<span class="integer">0</span>].x + m[<span class="integer">1</span>].y * n[<span class="integer">0</span>].y + m[<span class="integer">2</span>].y * n[<span class="integer">0</span>].z;
+r[<span class="integer">1</span>].y = m[<span class="integer">0</span>].y * n[<span class="integer">1</span>].x + m[<span class="integer">1</span>].y * n[<span class="integer">1</span>].y + m[<span class="integer">2</span>].y * n[<span class="integer">1</span>].z;
+r[<span class="integer">2</span>].y = m[<span class="integer">0</span>].y * n[<span class="integer">2</span>].x + m[<span class="integer">1</span>].y * n[<span class="integer">2</span>].y + m[<span class="integer">2</span>].y * n[<span class="integer">2</span>].z;
+r[<span class="integer">0</span>].z = m[<span class="integer">0</span>].z * n[<span class="integer">0</span>].x + m[<span class="integer">1</span>].z * n[<span class="integer">0</span>].y + m[<span class="integer">2</span>].z * n[<span class="integer">0</span>].z;
+r[<span class="integer">1</span>].z = m[<span class="integer">0</span>].z * n[<span class="integer">1</span>].x + m[<span class="integer">1</span>].z * n[<span class="integer">1</span>].y + m[<span class="integer">2</span>].z * n[<span class="integer">1</span>].z;
+r[<span class="integer">2</span>].z = m[<span class="integer">0</span>].z * n[<span class="integer">2</span>].x + m[<span class="integer">1</span>].z * n[<span class="integer">2</span>].y + m[<span class="integer">2</span>].z * n[<span class="integer">2</span>].z;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and similarly for other sizes of vectors and matrices.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="evaluation-of-expressions">5.11. Evaluation of Expressions</h3>
+<div class="paragraph">
+<p>In general expressions must be evaluated in the order specified by the
+precedence of operations and may only be regrouped if the result is the same or
+where the result is undefined.
+No other transforms may be applied that affect the result of an operation.
+GLSL ES relaxes these requirements for scalar operations in the following
+ways:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Addition and multiplication are assumed to be associative.</p>
+</li>
+<li>
+<p>Multiplication is assumed to be distributive over addition.
+Therefore expressions may be expanded and re-factored.</p>
+</li>
+<li>
+<p>Floating-point division may be replaced by reciprocal and
+multiplication.</p>
+</li>
+<li>
+<p>Multiplication may be replaced by repeated addition.</p>
+</li>
+<li>
+<p>Within the constraints of invariance (where applicable), the precision
+used may vary.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>These rules also apply to the built-in functions.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="statements-and-structure">6. Statements and Structure</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The fundamental building blocks of the OpenGL ES Shading Language are:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>statements and declarations</p>
+</li>
+<li>
+<p>function definitions</p>
+</li>
+<li>
+<p>selection (<strong>if</strong>-<strong>else</strong> and <strong>switch</strong>-<strong>case</strong>-<strong>default</strong>)</p>
+</li>
+<li>
+<p>iteration (<strong>for</strong>, <strong>while</strong>, and <strong>do</strong>-<strong>while</strong>)</p>
+</li>
+<li>
+<p>jumps (<strong>discard</strong>, <strong>return</strong>, <strong>break</strong>, and <strong>continue</strong>)</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The overall structure of a shader is as follows</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>translation-unit</em> : </dt>
+<dd>
+<p><em>global-declaration</em><br>
+<em>translation-unit</em> <em>global-declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>global-declaration</em> : </dt>
+<dd>
+<p><em>function-definition</em><br>
+<em>declaration</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>That is, a shader is a sequence of declarations and function bodies.
+Function bodies are defined as</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>function-definition</em> : </dt>
+<dd>
+<p><em>function-prototype</em> <strong>{</strong> <em>statement-list</em> <strong>}</strong></p>
+</dd>
+<dt class="hdlist1"><em>statement-list</em> : </dt>
+<dd>
+<p><em>statement</em><br>
+<em>statement-list</em> <em>statement</em></p>
+</dd>
+<dt class="hdlist1"><em>statement</em> : </dt>
+<dd>
+<p><em>compound-statement</em><br>
+<em>simple-statement</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Curly braces are used to group sequences of statements into compound
+statements.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>compound-statement</em> : </dt>
+<dd>
+<p><strong>{</strong> <em>statement-list</em> <strong>}</strong></p>
+</dd>
+<dt class="hdlist1"><em>simple-statement</em> : </dt>
+<dd>
+<p><em>declaration-statement</em><br>
+<em>expression-statement</em><br>
+<em>selection-statement</em><br>
+<em>iteration-statement</em><br>
+<em>jump-statement</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Simple declaration, expression, and jump statements end in a semi-colon.</p>
+</div>
+<div class="paragraph">
+<p>This above is slightly simplified, and the complete grammar specified in
+&#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; should be used as
+the definitive specification.</p>
+</div>
+<div class="paragraph">
+<p>Declarations and expressions have already been discussed.</p>
+</div>
+<div class="sect2">
+<h3 id="function-definitions">6.1. Function Definitions</h3>
+<div class="paragraph">
+<p>As indicated by the grammar above, a valid shader is a sequence of global
+declarations and function definitions.
+A function is declared as the following example shows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// prototype</span>
+returnType functionName (type0 arg0, type1 arg1, ..., typen argn);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and a function is defined like</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// definition</span>
+returnType functionName (type0 arg0, type1 arg1, ..., typen argn)
+{
+    <span class="comment">// do some computation</span>
+    <span class="keyword">return</span> returnValue;
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>returnType</em> must be present and cannot be void, or:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> functionName (type0 arg0, type1 arg1, ..., typen argn)
+{
+    <span class="comment">// do some computation</span>
+    <span class="keyword">return</span>; <span class="comment">// optional</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Each of the <em>typeN</em> must include a type and can optionally include a
+parameter qualifier and/or <strong>const</strong>.</p>
+</div>
+<div class="paragraph">
+<p>A function is called by using its name followed by a list of arguments in
+parentheses.</p>
+</div>
+<div class="paragraph">
+<p>Arrays are allowed as arguments and as the return type.
+In both cases, the array must be
+compile-time
+sized.
+An array is passed or returned by using just its name, without brackets, and
+the size of the array must match the size specified in the function&#8217;s
+declaration.</p>
+</div>
+<div class="paragraph">
+<p>Structures are also allowed as argument types.
+The return type can also be a structure.</p>
+</div>
+<div class="paragraph">
+<p>See &#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; for the
+definitive reference on the syntax to declare and define functions.</p>
+</div>
+<div class="paragraph">
+<p>All functions must be either declared with a prototype or defined with a
+body before they are called.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> myfunc (<span class="predefined-type">float</span> f,      <span class="comment">// f is an input parameter</span>
+              out <span class="predefined-type">float</span> g); <span class="comment">// g is an output parameter</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Functions that return no value must be declared as <strong>void</strong>.
+A <strong>void</strong> function can only use <strong>return</strong> without a return argument, even if
+the return argument has <strong>void</strong> type.
+Return statements only accept values:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> func1() { }
+<span class="directive">void</span> func2() { <span class="keyword">return</span> func1(); } <span class="comment">// illegal return statement</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Only a precision qualifier is allowed on the return type of a function.
+Formal parameters can have parameter, precision, and memory qualifiers, but
+no other qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Functions that accept no input arguments need not use <strong>void</strong> in the argument
+list because prototypes (or definitions) are required and therefore there is
+no ambiguity when an empty argument list &#8220;( )&#8221; is declared.
+The idiom &#8220;(<strong>void</strong>)&#8221; as a parameter list is provided for convenience.</p>
+</div>
+<div class="paragraph">
+<p>Function names can be overloaded.
+The same function name can be used for multiple functions, as long as the
+parameter types differ.
+If a function name is declared twice with the same parameter types, then the
+return types and all qualifiers must also match, and it is the same function
+being declared.
+When function calls are resolved, an exact type match for all the arguments
+is required.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 f(in vec4 x, out vec4 y);
+vec4 f(in vec4 x, out uvec4 y);      <span class="comment">// allowed, different argument type</span>
+<span class="predefined-type">int</span> f(in vec4 x, out vec4 y);        <span class="comment">// error, only return type differs</span>
+vec4 f(in vec4 x, in vec4 y);        <span class="comment">// error, only qualifier differs</span>
+vec4 f(<span class="directive">const</span> in vec4 x, out vec4 y); <span class="comment">// error, only qualifier differs</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Calling the first two functions above with the following argument types
+yields</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">f(vec4, vec4)   <span class="comment">// exact match of vec4 f(in vec4 x, out vec4 y)</span>
+f(vec4, uvec4)  <span class="comment">// exact match of vec4 f(in vec4 x, out uvec4 y)</span>
+f(ivec4, vec4)  <span class="comment">// error, no exact match.</span>
+f(ivec4, uvec4) <span class="comment">// error, no exact match.</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>User-defined functions can have multiple declarations, but only one
+definition.</p>
+</div>
+<div class="paragraph">
+<p>A shader cannot redefine or overload built-in functions.</p>
+</div>
+<div class="paragraph">
+<p>The function <em>main</em> is used as the entry point to a shader executable.
+All shaders must define a function named <em>main</em>.
+This function takes no arguments, returns no value, and must be declared as
+type <strong>void</strong>:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> main()
+{
+    ...
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The function <em>main</em> can contain uses of <strong>return</strong>.
+See &#8220;<a href="#jumps">Jumps</a>&#8221; for more details.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time or link-time error to declare or define a function
+<strong>main</strong> with any other parameters or return type.</p>
+</div>
+<div class="sect3">
+<h4 id="function-calling-conventions">6.1.1. Function Calling Conventions</h4>
+<div class="paragraph">
+<p>Functions are called by value-return.
+This means input arguments are copied into the function at call time, and
+output arguments are copied back to the caller before function exit.
+Because the function works with local copies of parameters, there are no
+issues regarding aliasing of variables within a function.
+To control what parameters are copied in and/or out through a function
+definition or declaration:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The keyword <strong>in</strong> is used as a qualifier to denote a parameter is to be
+copied in, but not copied out.</p>
+</li>
+<li>
+<p>The keyword <strong>out</strong> is used as a qualifier to denote a parameter is to be
+copied out, but not copied in.
+This should be used whenever possible to avoid unnecessarily copying
+parameters in.</p>
+</li>
+<li>
+<p>The keyword <strong>inout</strong> is used as a qualifier to denote the parameter is to
+be both copied in and copied out.
+It means the same thing as specifying both <strong>in</strong> and <strong>out</strong>.</p>
+</li>
+<li>
+<p>A function parameter declared with no such qualifier means the same
+thing as specifying <strong>in</strong>.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>All arguments are evaluated at call time, exactly once, in order, from left
+to right.
+Evaluation of an <strong>in</strong> parameter results in a value that is copied to the
+formal parameter.
+Evaluation of an <strong>out</strong> parameter results in an l-value that is used to copy
+out a value when the function returns.
+Evaluation of an <strong>inout</strong> parameter results in both a value and an l-value;
+the value is copied to the formal parameter at call time and the l-value is
+used to copy out a value when the function returns.</p>
+</div>
+<div class="paragraph">
+<p>The order in which output parameters are copied back to the caller is
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>In a function, writing to an input-only parameter is allowed.
+Only the function&#8217;s copy is modified.
+This can be prevented by declaring a parameter with the <strong>const</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>When calling a function, expressions that do not evaluate to l-values cannot
+be passed to parameters declared as <strong>out</strong> or <strong>inout</strong>, or an error
+results.</p>
+</div>
+<div class="paragraph">
+<p>Only precision qualifiers are allowed on the return type of a function.</p>
+</div>
+<div class="paragraph">
+<p>The syntax for function prototypes can be informally expressed as:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>function_prototype</em> : </dt>
+<dd>
+<p>[ <em>type_qualifier</em> ] <em>type_specifier</em> <em>IDENTIFIER</em> <em>LEFT_PAREN</em>
+<em>parameter_declaration</em> , <em>parameter_declaration</em> , &#8230;&#8203;
+, <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_declaration</em> : </dt>
+<dd>
+<p>[ <em>type_qualifier</em> ] <em>type_specifier</em> [ <em>IDENTIFIER</em> [ <em>array_specifier</em>
+] ]</p>
+</dd>
+<dt class="hdlist1"><em>type_qualifier</em> : </dt>
+<dd>
+<p><em>single_type_qualifier</em> , <em>single_type_qualifier</em> , &#8230;&#8203;</p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The qualifiers allowed on formal parameters are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>empty</em><br>
+<strong>const</strong><br>
+<strong>in</strong><br>
+<strong>out</strong><br>
+<strong>inout</strong><br>
+<strong>precise</strong><br>
+<em>memory-qualifier</em><br>
+<em>precision-qualifier</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>const</strong> qualifier cannot be used with <strong>out</strong> or <strong>inout</strong>, or
+an error results.
+The above is used both for function declarations (i.e., prototypes) and for
+function definitions.
+Hence, function definitions can have unnamed arguments.</p>
+</div>
+<div class="paragraph">
+<p>Static, and hence dynamic recursion, are not allowed.
+Static recursion is present if the static function-call graph of a program
+contains cycles.
+Dynamic recursion occurs if at any time control flow has entered but not
+exited a single function more than once.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="selection">6.2. Selection</h3>
+<div class="paragraph">
+<p>Conditional control flow in the shading language is done by either <strong>if</strong>,
+<strong>if</strong>-<strong>else</strong>, or <strong>switch</strong> statements:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>selection-statement</em> : </dt>
+<dd>
+<p><strong>if</strong> <strong>(</strong> <em>bool-expression</em> <strong>)</strong> <em>statement</em><br>
+<strong>if</strong> <strong>(</strong> <em>bool-expression</em> <strong>)</strong> <em>statement</em> <strong>else</strong> <em>statement</em><br>
+<strong>switch</strong> <strong>(</strong> <em>init-expression</em> <strong>)</strong> <strong>{</strong> <em>switch-statement-list<sub>opt</sub></em> <strong>}</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Where <em>switch-statement-list</em> is a nested scope containing a list of zero or
+more <em>switch-statement</em> and other statements defined by the language, where
+<em>switch-statement</em> adds some forms of labels.
+That is</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>switch-statement-list</em> : </dt>
+<dd>
+<p><em>switch-statement</em><br>
+<em>switch-statement-list</em> <em>switch-statement</em></p>
+</dd>
+<dt class="hdlist1"><em>switch-statement</em> : </dt>
+<dd>
+<p><strong>case</strong> <em>constant-expression</em> <strong>:</strong><br>
+<strong>default</strong> <strong>:</strong> <em>statement</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Note the above grammar&#8217;s purpose is to aid discussion in this section; the
+normative grammar is in &#8220;<a href="#shading-language-grammar">Shading Language
+Grammar</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>If an <strong>if</strong>-expression evaluates to <strong>true</strong>, then the first <em>statement</em> is
+executed.
+If it evaluates to <strong>false</strong> and there is an <strong>else</strong> part then the second
+<em>statement</em> is executed.</p>
+</div>
+<div class="paragraph">
+<p>Any expression whose type evaluates to a Boolean can be used as the
+conditional expression <em>bool-expression</em>.
+Vector types are not accepted as the expression to <strong>if</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Conditionals can be nested.</p>
+</div>
+<div class="paragraph">
+<p>The type of <em>init-expression</em> in a <strong>switch</strong> statement must be a scalar
+integer.
+The type of <em>init-expression</em> must match the type of the <strong>case</strong> labels
+within each <strong>switch</strong> statement.
+Either signed integers or unsigned integers are allowed but there is no
+implicit type conversion between the two.
+If a <strong>case</strong> label has a <em>constant-expression</em> of equal value to
+<em>init-expression</em>, execution will continue after that label.
+Otherwise, if there is a <strong>default</strong> label, execution will continue after that
+label.
+Otherwise, execution skips the rest of the switch statement.
+It is an error to have more than one <strong>default</strong> or a replicated
+<em>constant-expression</em>.
+A <strong>break</strong> statement not nested in a loop or other switch statement (either
+not nested or nested only in <strong>if</strong> or <strong>if</strong>-<strong>else</strong> statements) will also skip
+the rest of the switch statement.
+Fall through labels are allowed, but it is an error to have no
+statement between a label and the end of the switch statement.
+No statements are allowed in a switch statement before the first <strong>case</strong>
+statement.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>case</strong> and <strong>default</strong> labels can only appear within a <strong>switch</strong> statement.
+No <strong>case</strong> or <strong>default</strong> labels can be nested inside other statements or
+compound statements within their corresponding <strong>switch</strong>.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="iteration">6.3. Iteration</h3>
+<div class="paragraph">
+<p>For, while, and do loops are allowed as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">for</span> (init-expression; condition-expression; loop-expression)
+    sub-statement
+<span class="keyword">while</span> (condition-expression)
+    sub-statement
+<span class="keyword">do</span>
+    statement
+<span class="keyword">while</span> (condition-expression)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>See &#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; for the
+definitive specification of loops.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>for</strong> loop first evaluates the <em>init-expression</em>, then the
+<em>condition-expression</em>.
+If the <em>condition-expression</em> evaluates to <strong>true</strong>, then the body of the loop
+is executed.
+After the body is executed, a <strong>for</strong> loop will then evaluate the
+<em>loop-expression</em>, and then loop back to evaluate the
+<em>condition-expression</em>, repeating until the <em>condition-expression</em> evaluates
+to <strong>false</strong>.
+The loop is then exited, skipping its body and skipping its
+<em>loop-expression</em>.
+Variables modified by the <em>loop-expression</em> maintain their value after the
+loop is exited, provided they are still in scope.
+Variables declared in <em>init-expression</em> or <em>condition-expression</em> are only
+in scope until the end of the sub-statement of the <strong>for</strong> loop.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>while</strong> loop first evaluates the <em>condition-expression</em>.
+If <strong>true</strong>, then the body is executed.
+This is then repeated, until the <em>condition-expression</em> evaluates to
+<strong>false</strong>, exiting the loop and skipping its body.
+Variables declared in the <em>condition-expression</em> are only in scope until the
+end of the sub-statement of the <strong>while</strong> loop.</p>
+</div>
+<div class="paragraph">
+<p>For both <strong>for</strong> and <strong>while</strong> loops, the sub-statement does not introduce a new
+scope for variable names, so the following has a redeclaration error:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">for</span> (<span class="predefined-type">int</span> i = <span class="integer">0</span>; i &lt; <span class="integer">10</span>; i++) +
+{
+    <span class="predefined-type">int</span> i; <span class="comment">// redeclaration error +</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>do</strong>-<strong>while</strong> loop first executes the body, then executes the
+<em>condition-expression</em>.
+This is repeated until <em>condition-expression</em> evaluates to <strong>false</strong>, and then
+the loop is exited.</p>
+</div>
+<div class="paragraph">
+<p>Expressions for <em>condition-expression</em> must evaluate to a Boolean.</p>
+</div>
+<div class="paragraph">
+<p>Both the <em>condition-expression</em> and the <em>init-expression</em> can declare and
+initialize a variable, except in the <strong>do</strong>-<strong>while</strong> loop, which cannot declare
+a variable in its <em>condition-expression</em>.
+The variable&#8217;s scope lasts only until the end of the sub-statement that
+forms the body of the loop.</p>
+</div>
+<div class="paragraph">
+<p>Loops can be nested.</p>
+</div>
+<div class="paragraph">
+<p>Non-terminating loops are allowed.
+The consequences of very long or non-terminating loops are platform
+dependent.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="jumps">6.4. Jumps</h3>
+<div class="paragraph">
+<p>These are the jumps:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>jump_statement</em> : </dt>
+<dd>
+<p><strong>continue</strong> <strong>;</strong><br>
+<strong>break</strong> <strong>;</strong><br>
+<strong>return</strong> <strong>;</strong><br>
+<strong>return</strong> <em>expression</em> <strong>;</strong><br>
+<strong>discard</strong> <strong>;</strong> // in the fragment shader language only</p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>There is no &#8220;goto&#8221; or other non-structured flow of control.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>continue</strong> jump is used only in loops.
+It skips the remainder of the body of the inner-most loop of which it is
+inside.
+For <strong>while</strong> and <strong>do</strong>-<strong>while</strong> loops, this jump is to the next evaluation of
+the loop <em>condition-expression</em> from which the loop continues as previously
+defined.
+For <strong>for</strong> loops, the jump is to the <em>loop-expression</em>, followed by the
+<em>condition-expression</em>.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>break</strong> jump can also be used only in loops and <strong>switch</strong> statements.
+It is simply an immediate exit of the inner-most loop or <strong>switch</strong> statements
+containing the <strong>break</strong>.
+No further execution of <em>condition-expression</em>, <em>loop-expression</em>, or
+<em>switch-statement</em> is done.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>discard</strong> keyword is only allowed within fragment shaders.
+It can be used within a fragment shader to abandon the operation on the
+current fragment.
+This keyword causes the fragment to be discarded and no updates to any
+buffers will occur.
+Any prior writes to other buffers such as shader storage buffers are
+unaffected.
+Control flow exits the shader, and subsequent implicit or explicit
+derivatives are undefined when this control flow is non-uniform (meaning
+different fragments within the primitive take different control paths).
+It would typically be used within a conditional statement, for example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">if</span> (intensity &lt; <span class="float">0</span><span class="float">.0</span>)
+    discard;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A fragment shader may test a fragment&#8217;s alpha value and discard the fragment
+based on that test.
+However, it should be noted that coverage testing occurs after the fragment
+shader runs, and the coverage test can change the alpha value.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>return</strong> jump causes immediate exit of the current function.
+If it has <em>expression</em> then that is the return value for the function.</p>
+</div>
+<div class="paragraph">
+<p>The function <em>main</em> can use <strong>return</strong>.
+This simply causes <em>main</em> to exit in the same way as when the end of the
+function had been reached.
+It does not imply a use of <strong>discard</strong> in a fragment shader.
+Using <strong>return</strong> in <em>main</em> before defining outputs will have the same behavior
+as reaching the end of <em>main</em> before defining outputs.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="built-in-variables">7. Built-In Variables</h2>
+<div class="sectionbody">
+<div class="sect2">
+<h3 id="built-in-language-variables">7.1. Built-In Language Variables</h3>
+<div class="paragraph">
+<p>Some OpenGL ES operations occur in fixed functionality and need to provide
+values to or receive values from shader executables.
+Shaders communicate with fixed-function OpenGL ES pipeline stages, and
+optionally with other shader executables, through the use of built-in input
+and output variables.</p>
+</div>
+<div class="sect3">
+<h4 id="vertex-shader-special-variables">7.1.1. Vertex Shader Special Variables</h4>
+<div class="paragraph">
+<p>The built-in vertex shader variables are intrinsically declared as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in highp <span class="predefined-type">int</span> gl_VertexID;
+in highp <span class="predefined-type">int</span> gl_InstanceID;
+
+out gl_PerVertex {
+    out highp vec4 gl_Position;
+    out highp <span class="predefined-type">float</span> gl_PointSize;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_Position</em> is intended for writing the homogeneous vertex
+position.
+It can be written at any time during shader execution.
+This value will be used by primitive assembly, clipping, culling, and other
+fixed functionality operations, if present, that operate on primitives after
+vertex processing has occurred.
+Its value is undefined after the vertex processing stage if the vertex
+shader executable does not write <em>gl_Position</em>.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_PointSize</em> is intended for a shader to write the size of
+the point to be rasterized.
+It is measured in pixels.
+If <em>gl_PointSize</em> is not written to, its value is undefined in subsequent
+pipe stages.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_VertexID</em> is a vertex shader input variable that holds an
+integer index for the vertex, as defined under &#8220;Shader Inputs&#8221; in section
+11.1.3.9 &#8220;Shader Inputs&#8221; of the <a href="#references">OpenGL ES Specification</a>.
+While the variable <em>gl_VertexID</em> is always present, its value is not always
+defined.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_InstanceID</em> is a vertex shader input variable that holds
+the instance number of the current primitive in an instanced draw call (see
+&#8220;Shader Inputs&#8221; in section 11.1.3.9 &#8220;Shader Inputs&#8221; of the
+<a href="#references">OpenGL ES Specification</a>).
+If the current primitive does not come from an instanced draw call, the
+value of <em>gl_InstanceID</em> is zero.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="tessellation-control-shader-special-variables">7.1.2. Tessellation Control Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the tessellation control shader, built-in variables are intrinsically
+declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    highp vec4 gl_Position;
+} gl_in[gl_MaxPatchVertices];
+
+in highp <span class="predefined-type">int</span> gl_PatchVerticesIn;
+in highp <span class="predefined-type">int</span> gl_PrimitiveID;
+in highp <span class="predefined-type">int</span> gl_InvocationID;
+
+out gl_PerVertex {
+    highp vec4 gl_Position;
+} gl_out[];
+
+patch out highp <span class="predefined-type">float</span> gl_TessLevelOuter[<span class="integer">4</span>];
+patch out highp <span class="predefined-type">float</span> gl_TessLevelInner[<span class="integer">2</span>];
+patch out highp vec4 gl_BoundingBox[<span class="integer">2</span>];</code></pre>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-control-input-variables">Tessellation Control Input Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em> contains the output written in the previous shader stage to
+<em>gl_Position</em>.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PatchVerticesIn</em> contains the number of vertices in the input patch
+being processed by the shader.
+A single shader can read patches of differing sizes, so the value of
+<em>gl_PatchVerticesIn</em> may differ between patches.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PrimitiveID</em> contains the number of primitives processed by the shader
+since the current set of rendering primitives was started.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_InvocationID</em> contains the number of the output patch vertex assigned to
+the tessellation control shader invocation.
+It is assigned integer values in the range [0, N-1], where N is the number
+of output patch vertices per primitive.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-control-output-variables">Tessellation Control Output Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em> is used in the same fashion as the corresponding output
+variable in the vertex shader.</p>
+</div>
+<div class="paragraph">
+<p>The values written to <em>gl_TessLevelOuter</em> and <em>gl_TessLevelInner</em> are
+assigned to the corresponding outer and inner tessellation levels of the
+output patch.
+They are used by the tessellation primitive generator to control primitive
+tessellation and may be read by tessellation evaluation shaders.</p>
+</div>
+<div class="paragraph">
+<p>The values written to <em>gl_BoundingBox</em> specify the minimum and maximum
+clip-space extents of a bounding box containing all primitives generated
+from the patch by the primitive generator, geometry shader, and clipping.
+Fragments may or may not be generated for portions of these primitives
+that extend outside the window-coordinate projection of this bounding
+box.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="tessellation-evaluation-shader-special-variables">7.1.3. Tessellation Evaluation Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the tessellation evaluation shader, built-in variables are intrinsically
+declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    highp vec4 gl_Position;
+} gl_in[gl_MaxPatchVertices];
+
+in highp <span class="predefined-type">int</span> gl_PatchVerticesIn;
+in highp <span class="predefined-type">int</span> gl_PrimitiveID;
+in highp vec3 gl_TessCoord;
+patch in highp <span class="predefined-type">float</span> gl_TessLevelOuter[<span class="integer">4</span>];
+patch in highp <span class="predefined-type">float</span> gl_TessLevelInner[<span class="integer">2</span>];
+
+out gl_PerVertex {
+    highp vec4 gl_Position;
+};</code></pre>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-evaluation-input-variables">Tessellation Evaluation Input Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em> contains the output written in the previous shader stage to
+<em>gl_Position</em>.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PatchVerticesIn</em> and <em>gl_PrimitiveID</em> are defined in the same fashion as
+the corresponding input variables in the tessellation control shader.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_TessCoord</em> specifies a three-component <em>(u,v,w)</em> vector identifying the
+position of the vertex being processed by the shader relative to the
+primitive being tessellated.
+Its values will obey the properties</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_TessCoord.x == <span class="float">1</span><span class="float">.0</span> - (<span class="float">1</span><span class="float">.0</span> - gl_TessCoord.x) <span class="comment">// two operations performed</span>
+gl_TessCoord.y == <span class="float">1</span><span class="float">.0</span> - (<span class="float">1</span><span class="float">.0</span> - gl_TessCoord.y) <span class="comment">// two operations performed</span>
+gl_TessCoord.z == <span class="float">1</span><span class="float">.0</span> - (<span class="float">1</span><span class="float">.0</span> - gl_TessCoord.z) <span class="comment">// two operations performed</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>to aid in replicating subdivision computations.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_TessLevelOuter</em> and <em>gl_TessLevelInner</em> are filled with the
+corresponding outputs written by the active tessellation control shader.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-evaluation-output-variables">Tessellation Evaluation Output Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em> is used in the same fashion as the corresponding output
+variable in the vertex shader.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="geometry-shader-special-variables">7.1.4. Geometry Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the geometry shader, built-in variables are intrinsically declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    highp vec4 gl_Position;
+} gl_in[];
+
+in highp <span class="predefined-type">int</span> gl_PrimitiveIDIn;
+in highp <span class="predefined-type">int</span> gl_InvocationID;
+
+out gl_PerVertex {
+    highp vec4 gl_Position;
+};
+
+out highp <span class="predefined-type">int</span> gl_PrimitiveID;
+out highp <span class="predefined-type">int</span> gl_Layer;</code></pre>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-shader-input-variables">Geometry Shader Input Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em> contains the output written in the previous shader stage to
+<em>gl_Position</em>.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PrimitiveIDIn</em> contains the number of primitives processed by the shader
+since the current set of rendering primitives was started.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_InvocationID</em> contains the invocation number assigned to the geometry
+shader invocation.
+It is assigned integer values in the range [0, N-1], where N is the number
+of geometry shader invocations per primitive.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-shader-output-variables">Geometry Shader Output Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em> is used in the same fashion as the corresponding output
+variable in the vertex shader.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PrimitiveID</em> is filled with a single integer that serves as a primitive
+identifier to the fragment shader.
+This is then available to fragment shaders, which will select the written
+primitive ID from the provoking vertex of the primitive being shaded.
+If a fragment shader using <em>gl_PrimitiveID</em> is active and a geometry shader
+is also active, the geometry shader must write to <em>gl_PrimitiveID</em> or the
+fragment shader input <em>gl_PrimitiveID</em> is undefined.
+See section 11.3.4.4 &#8220;Geometry Shader Outputs&#8221; of the
+<a href="#references">OpenGL ES Specification</a> for more information.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_Layer</em> is used to select a specific layer (or face and layer of a cube
+map) of a multi-layer framebuffer attachment.
+The actual layer used will come from one of the vertices in the primitive
+being shaded.
+Which vertex the layer comes from is determined as discussed in section
+11.3.4.4 of the <a href="#references">OpenGL ES Specification</a>
+but may be undefined, so it is best to write the same layer value for all
+vertices of a primitive.
+If a shader statically assigns a value to <em>gl_Layer</em>, layered rendering mode
+is enabled.
+See section 11.3.4.4 &#8220;Geometry Shader Outputs&#8221; and section 9.8 &#8220;Layered
+Framebuffers&#8221; of the <a href="#references">OpenGL ES Specification</a> for more information.
+If a shader statically assigns a value to <em>gl_Layer</em>, and there is an
+execution path through the shader that does not set <em>gl_Layer</em>, then the
+value of <em>gl_Layer</em> is undefined for executions of the shader that take that
+path.</p>
+</div>
+<div class="paragraph">
+<p>The output variable <em>gl_Layer</em> takes on a special value when used with an
+array of cube map textures.
+Instead of only referring to the layer, it is used to select a cube map face
+and a layer.
+Setting <em>gl_Layer</em> to the value <em>layer*6+face</em> will render to face <em>face</em> of
+the cube defined in layer <em>layer</em>.
+The face values are defined in table 8.25 of the <a href="#references">OpenGL ES Specification</a>,
+but repeated below for clarity.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Face Value</th>
+<th class="tableblock halign-left valign-top">Resulting Target</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">0</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_POSITIVE_X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_NEGATIVE_X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_POSITIVE_Y</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_NEGATIVE_Y</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_POSITIVE_Z</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_NEGATIVE_Z</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>For example, to render to the positive <em>y</em> cube map face located in the 5th
+layer of the cube map array, <em>gl_Layer</em> should be set to <em>5 * 6 + 2</em>.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="fragment-shader-special-variables">7.1.5. Fragment Shader Special Variables</h4>
+<div class="paragraph">
+<p>The built-in special variables that are accessible from a fragment shader
+are intrinsically declared as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in highp vec4 gl_FragCoord;
+in <span class="predefined-type">bool</span> gl_FrontFacing;
+out highp <span class="predefined-type">float</span> gl_FragDepth;
+in mediump vec2 gl_PointCoord;
+in <span class="predefined-type">bool</span> gl_HelperInvocation;
+in highp <span class="predefined-type">int</span> gl_PrimitiveID;
+in highp <span class="predefined-type">int</span> gl_Layer;
+in lowp <span class="predefined-type">int</span> gl_SampleID;
+in mediump vec2 gl_SamplePosition;
+in highp <span class="predefined-type">int</span> gl_SampleMaskIn[(gl_MaxSamples+<span class="integer">31</span>)/<span class="integer">32</span>];
+out highp <span class="predefined-type">int</span> gl_SampleMask[(gl_MaxSamples+<span class="integer">31</span>)/<span class="integer">32</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The output of the fragment shader executable is processed by the fixed
+function operations at the back end of the OpenGL ES pipeline.</p>
+</div>
+<div class="paragraph">
+<p>The fixed functionality computed depth for a fragment may be obtained by
+reading <em>gl_FragCoord.z</em>, described below.</p>
+</div>
+<div class="paragraph">
+<p>Writing to <em>gl_FragDepth</em> will establish the depth value for the fragment
+being processed.
+If depth buffering is enabled, and no shader writes <em>gl_FragDepth</em>, then the
+fixed function value for depth will be used as the fragment&#8217;s depth value.
+If a shader statically assigns a value to <em>gl_FragDepth</em>, and there is an
+execution path through the shader that does not set <em>gl_FragDepth</em>, then the
+value of the fragment&#8217;s depth may be undefined for executions of the shader
+that take that path.
+That is, if the set of linked fragment shaders statically contain a write to
+<em>gl_FragDepth</em>, then it is responsible for always writing it.</p>
+</div>
+<div class="paragraph">
+<p>If a shader executes the <strong>discard</strong> keyword, the fragment is discarded, and
+the values of any user-defined fragment outputs, <em>gl_FragDepth</em>, and
+<em>gl_SampleMask</em> become irrelevant.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_FragCoord</em> is available as an input variable from within
+fragment shaders and it holds the window relative coordinates (<em>x</em>, <em>y</em>,
+<em>z</em>, <em>1/w</em>) values for the fragment.
+If multi-sampling, this value can be for any location within the pixel, or
+one of the fragment samples.
+The use of <strong>centroid</strong> does not further restrict this value to be inside the
+current primitive.
+This value is the result of the fixed functionality that interpolates
+primitives after vertex processing to generate fragments.
+The <em>z</em> component is the depth value that would be used for the fragment&#8217;s
+depth if no shader contained any writes to <em>gl_FragDepth</em>.
+This is useful for invariance if a shader conditionally computes
+<em>gl_FragDepth</em> but otherwise wants the fixed functionality fragment depth.</p>
+</div>
+<div class="paragraph">
+<p>Fragment shaders have access to the input built-in variable
+<em>gl_FrontFacing</em>, whose value is <strong>true</strong> if the fragment belongs to a
+front-facing primitive.
+One use of this is to emulate two-sided lighting by selecting one of two
+colors calculated by a vertex or geometry shader.</p>
+</div>
+<div class="paragraph">
+<p>The values in <em>gl_PointCoord</em> are two-dimensional coordinates indicating
+where within a point primitive the current fragment is located, when point
+sprites are enabled.
+They range from 0.0 to 1.0 across the point.
+If the current primitive is not a point, or if point sprites are not
+enabled, then the values read from <em>gl_PointCoord</em> are undefined.</p>
+</div>
+<div class="paragraph">
+<p>For both the input array <em>gl_SampleMaskIn[]</em> and the output array
+<em>gl_SampleMask[]</em>, bit <em>B</em> of mask <em>M</em> (<em>gl_SampleMaskIn[M]</em> or
+<em>gl_SampleMask[M]</em>) corresponds to sample <em>32*M+B</em>.
+These arrays have <strong>ceil</strong>(<em>s</em>/32) elements, where <em>s</em> is the maximum number
+of color samples supported by the implementation.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_SampleMaskIn</em> indicates the set of samples covered by
+the primitive generating the fragment during multisample rasterization.
+It has a sample bit set if and only if the sample is considered covered for
+this fragment shader invocation.</p>
+</div>
+<div class="paragraph">
+<p>The output array <em>gl_SampleMask[]</em> sets the sample mask for the fragment
+being processed.
+Coverage for the current fragment will become the logical AND of the
+coverage mask and the output <em>gl_SampleMask</em>.
+This array must be sized in the fragment shader either implicitly or
+explicitly, to be no larger than the implementation-dependent maximum
+sample-mask (as an array of 32bit elements), determined by the maximum
+number of samples..
+If the fragment shader statically assigns a value to <em>gl_SampleMask</em>, the
+sample mask will be undefined for any array elements of any fragment shader
+invocations that fail to assign a value.
+If a shader does not statically assign a value to <em>gl_SampleMask</em>, the
+sample mask has no effect on the processing of a fragment.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_SampleID</em> is filled with the sample number of the
+sample currently being processed.
+This variable is in the range <em>0</em> to <em>gl_NumSamples-1</em>, where
+<em>gl_NumSamples</em> is the total number of samples in the framebuffer, or 1 if
+rendering to a non-multisample framebuffer.
+Any static use of this variable in a fragment shader causes the entire
+shader to be evaluated per-sample.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_SamplePosition</em> contains the position of the current
+sample within the multisample draw buffer.
+The <em>x</em> and <em>y</em> components of <em>gl_SamplePosition</em> contain the sub-pixel
+coordinate of the current sample and will have values in the range 0.0 to
+1.0.
+Any static use of this variable in a fragment shader causes the entire
+shader to be evaluated per sample.</p>
+</div>
+<div class="paragraph">
+<p>The value <em>gl_HelperInvocation</em> is <strong>true</strong> if the fragment shader invocation
+is considered a <em>helper invocation</em> and is <strong>false</strong> otherwise.
+A helper invocation is a fragment shader invocation that is created solely
+for the purposes of evaluating derivatives for use in non-helper fragment
+shader invocations.
+Such derivatives are computed implicitly in the built-in function
+<strong>texture</strong>() (see &#8220;<a href="#texture-functions">Texture Functions</a>&#8221;), and
+explicitly in the derivative functions in
+&#8220;<a href="#derivative-functions">Derivative Functions</a>&#8221;, for example <strong>dFdx</strong>() and
+<strong>dFdy</strong>().</p>
+</div>
+<div class="paragraph">
+<p>Fragment shader helper invocations execute the same shader code as
+non-helper invocations, but will not have side effects that modify the
+framebuffer or other shader-accessible memory.
+In particular:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Fragments corresponding to helper invocations are discarded when shader
+execution is complete, without updating the framebuffer.</p>
+</li>
+<li>
+<p>Stores to image and buffer variables performed by helper invocations
+have no effect on the underlying image or buffer memory.</p>
+</li>
+<li>
+<p>Atomic operations to image, buffer, or atomic counter variables
+performed by helper invocations have no effect on the underlying image
+or buffer memory.
+The values returned by such atomic operations are undefined.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Helper invocations may be generated for pixels not covered by a primitive
+being rendered.
+While fragment shader inputs qualified with <strong>centroid</strong> are normally required
+to be sampled in the intersection of the pixel and the primitive, the
+requirement is ignored for such pixels since there is no intersection
+between the pixel and primitive.</p>
+</div>
+<div class="paragraph">
+<p>Helper invocations may also be generated for fragments that are covered by a
+primitive being rendered when the fragment is killed by early fragment tests
+(using the <strong>early_fragment_tests</strong> qualifier) or where the implementation is
+able to determine that executing the fragment shader would have no effect
+other than assisting in computing derivatives for other fragment shader
+invocations.</p>
+</div>
+<div class="paragraph">
+<p>The set of helper invocations generated when processing any set of
+primitives is implementation-dependent.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_PrimitiveID</em> is filled with the value written to the
+<em>gl_PrimitiveID</em> geometry shader output, if a geometry shader is present.
+Otherwise, it is filled with the number of primitives processed by the
+shader since the current set of rendering primitives was started.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_Layer</em> is filled with the value written to the
+<em>gl_Layer</em> geometry shader output, if a geometry shader is present.
+If the geometry stage does not dynamically assign a value to <em>gl_Layer</em>, the
+value of <em>gl_Layer</em> in the fragment stage will be undefined.
+If the geometry stage makes no static assignment to <em>gl_Layer</em>, the input
+value in the fragment stage will be zero.
+Otherwise, the fragment stage will read the same value written by the
+geometry stage, even if that value is out of range.
+If a fragment shader contains a static access to <em>gl_Layer</em>, it will count
+against the implementation defined limit for the maximum number of inputs to
+the fragment stage.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="compute-shader-special-variables">7.1.6. Compute Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the compute shader, built-in variables are declared as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// workgroup dimensions</span>
+in uvec3 gl_NumWorkGroups;
+<span class="directive">const</span> uvec3 gl_WorkGroupSize;
+
+<span class="comment">// workgroup and invocation IDs</span>
+in uvec3 gl_WorkGroupID;
+in uvec3 gl_LocalInvocationID;
+
+<span class="comment">// derived variables</span>
+in uvec3 gl_GlobalInvocationID;
+in uint gl_LocalInvocationIndex;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_NumWorkGroups</em> is a compute-shader input variable
+containing the number of workgroups in each dimension of the dispatch that
+will execute the compute shader.
+Its content is equal to the values specified in the <em>num_groups_x</em>,
+<em>num_groups_y</em>, and <em>num_groups_z</em> parameters passed to the
+<em>DispatchCompute</em> API entry point.</p>
+</div>
+<div class="paragraph">
+<p>The built-in constant <em>gl_WorkGroupSize</em> is a compute-shader constant
+containing the workgroup size of the shader.
+The size of the workgroup in the <em>X</em>, <em>Y</em>, and <em>Z</em> dimensions is stored in
+the <em>x</em>, <em>y</em>, and <em>z</em> components.
+The constants values in <em>gl_WorkGroupSize</em> will match those specified in the
+required <strong>local_size_x</strong>, <strong>local_size_y</strong>, and <strong>local_size_z</strong> layout
+qualifiers for the current shader.
+This is a constant so that it can be used to size arrays of memory that can
+be shared within the workgroup.
+It is a compile-time error to use <em>gl_WorkGroupSize</em> in a shader that does
+not declare a fixed workgroup size, or before that shader has declared a
+fixed workgroup size, using <strong>local_size_x</strong>, <strong>local_size_y</strong>, and
+<strong>local_size_z</strong>.</p>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_WorkGroupID</em> is a compute-shader input variable
+containing the three-dimensional index of the workgroup that the
+current invocation is executing in.
+The possible values range across the parameters passed into
+<em>DispatchCompute</em>, i.e., from (0, 0, 0) to (<em>gl_NumWorkGroups.x</em> - 1,
+<em>gl_NumWorkGroups.y</em> - 1, <em>gl_NumWorkGroups.z</em> -1).</p>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_LocalInvocationID</em> is a compute-shader input
+variable containing the three-dimensional index of the current work item
+within the workgroup.
+The possible values for this variable range across the workgroup
+size, i.e., (0,0,0) to (<em>gl_WorkGroupSize.x</em> - 1, <em>gl_WorkGroupSize.y</em> - 1,
+<em>gl_WorkGroupSize.z</em> - 1).</p>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_GlobalInvocationID</em> is a compute shader input
+variable containing the global index of the current work item.
+This value uniquely identifies this invocation from all other invocations
+across all workgroups initiated by the current <em>DispatchCompute</em> call.
+This is computed as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_GlobalInvocationID =
+    gl_WorkGroupID * gl_WorkGroupSize + gl_LocalInvocationID;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_LocalInvocationIndex</em> is a compute shader input
+variable that contains the one-dimensional representation of the
+<em>gl_LocalInvocationID</em>.
+This is computed as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_LocalInvocationIndex =
+    gl_LocalInvocationID.z * gl_WorkGroupSize.x * gl_WorkGroupSize.y +
+    gl_LocalInvocationID.y * gl_WorkGroupSize.x +
+    gl_LocalInvocationID.x;</code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="built-in-constants">7.2. Built-In Constants</h3>
+<div class="paragraph">
+<p>The following built-in constants are provided to all shaders.
+The actual values used are implementation-dependent, but must be at least
+the value shown.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">//</span>
+<span class="comment">// Implementation-dependent constants. The example values below</span>
+<span class="comment">// are the minimum values allowed for these maximums.</span>
+<span class="comment">//</span></code></pre>
+</div>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexAttribs = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexUniformVectors = <span class="integer">256</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexOutputVectors = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxVertexAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlInputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlOutputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlTotalOutputComponents = <span class="integer">2048</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessControlAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessPatchComponents = <span class="integer">120</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxPatchVertices = <span class="integer">32</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessGenLevel = <span class="integer">64</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationInputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationOutputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTessEvaluationAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryInputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryOutputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryOutputVertices = <span class="integer">256</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryTotalOutputComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxGeometryAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxFragmentInputVectors = <span class="integer">15</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxFragmentImageUniforms = <span class="integer">4</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxFragmentUniformVectors = <span class="integer">256</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxFragmentAtomicCounters = <span class="integer">8</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxFragmentAtomicCounterBuffers = <span class="integer">1</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxDrawBuffers = <span class="integer">4</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MinProgramTexelOffset = -<span class="integer">8</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxProgramTexelOffset = <span class="integer">7</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxImageUnits = <span class="integer">4</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxSamples = <span class="integer">4</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxComputeImageUniforms = <span class="integer">4</span>;
+<span class="directive">const</span> highp ivec3 gl_MaxComputeWorkGroupCount = ivec3(<span class="integer">65535</span>, <span class="integer">65535</span>, <span class="integer">65535</span>);
+<span class="directive">const</span> highp ivec3 gl_MaxComputeWorkGroupSize = ivec3(<span class="integer">128</span>, <span class="integer">128</span>, <span class="integer">64</span>);
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxComputeUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxComputeTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxComputeAtomicCounters = <span class="integer">8</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxComputeAtomicCounterBuffers = <span class="integer">1</span>;
+
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxCombinedTextureImageUnits = <span class="integer">96</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxCombinedImageUniforms = <span class="integer">4</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxCombinedShaderOutputResources = <span class="integer">4</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxCombinedAtomicCounters = <span class="integer">8</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxCombinedAtomicCounterBuffers = <span class="integer">1</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxAtomicCounterBindings = <span class="integer">1</span>;
+<span class="directive">const</span> mediump <span class="predefined-type">int</span> gl_MaxAtomicCounterBufferSize = <span class="integer">32</span>;</code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="built-in-uniform-state">7.3. Built-In Uniform State</h3>
+<div class="paragraph">
+<p>As an aid to accessing OpenGL ES processing state, the following uniform
+variables are built into the OpenGL ES Shading Language.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">//</span>
+<span class="comment">// Depth range in window coordinates,</span>
+<span class="comment">// section 12.5.1 &quot;Controlling the Viewport&quot; in the</span>
+<span class="comment">// OpenGL ES Specification.</span>
+<span class="comment">//</span>
+<span class="keyword">struct</span> gl_DepthRangeParameters {
+    highp <span class="predefined-type">float</span> near; <span class="comment">// n</span>
+    highp <span class="predefined-type">float</span> far;  <span class="comment">// f</span>
+    highp <span class="predefined-type">float</span> diff; <span class="comment">// f - n</span>
+};
+uniform gl_DepthRangeParameters gl_DepthRange;
+uniform lowp <span class="predefined-type">int</span> gl_NumSamples;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>These variables are only guaranteed to be available in the fragment stage.
+In other stages, their presence and function is implementation-defined.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="redeclaring-built-in-blocks">7.4. Redeclaring Built-In Blocks</h3>
+<div class="paragraph">
+<p>The <em>gl_PerVertex</em> block can be redeclared in a shader to explicitly
+indicate what subset of the fixed pipeline interface will be used.
+This is necessary to establish the interface between multiple programs.</p>
+</div>
+<div class="paragraph">
+<p>If the <em>gl_PerVertex</em> block is not redefined in a given program, the
+intrinsically declared definition of that block is used for the program
+interface.</p>
+</div>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out gl_PerVertex {
+    highp vec4 gl_Position; <span class="comment">// will use gl_Position</span>
+    highp vec4 t;           <span class="comment">// error, only gl_PerVertex members allowed</span>
+}; <span class="comment">// no other members of gl_PerVertex will be used</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This establishes the output interface the shader will use with the
+subsequent pipeline stage.
+It must be a subset of the built-in members of <em>gl_PerVertex</em>.
+Such a redeclaration can also add the <strong>invariant</strong> qualifier and
+interpolation qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Other layout qualifiers, like <strong>location</strong>, cannot be added to such a
+redeclaration, unless specifically stated.</p>
+</div>
+<div class="paragraph">
+<p>If a built-in interface block is redeclared, it must appear in the shader
+before any use of any member included in the built-in declaration, or a
+compile-time error will result.
+It is also a compile-time error to redeclare the block more than once or to
+redeclare a built-in block and then use a member from that built-in block
+that was not included in the redeclaration.
+Also, if a built-in interface block is redeclared, no member of the built-in
+declaration can be redeclared outside the block redeclaration.
+If multiple shaders using members of a built-in block belonging to the same
+interface are linked together in the same program, they must all redeclare
+the built-in block in the same way, as described in
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221; for interface block matching, or a
+link-time error will result.
+It will also be a link-time error if some shaders in a program redeclare a
+specific built-in interface block while another shader in that program does
+not redeclare that interface block yet still uses a member of that interface
+block.
+If a built-in block interface is formed across shaders in different
+programs, the shaders must all redeclare the built-in block in the same way
+(as described for a single program), or the values passed along the
+interface are undefined.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="built-in-functions">8. Built-In Functions</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The OpenGL ES Shading Language defines an assortment of built-in convenience functions for
+scalar and vector operations.
+Many of these built-in functions can be used in more than one type of
+shader, but some are intended to provide a direct mapping to hardware and so
+are available only for a specific type of shader.</p>
+</div>
+<div class="paragraph">
+<p>The built-in functions basically fall into three categories:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>They expose some necessary hardware functionality in a convenient way
+such as accessing a texture map.
+There is no way in the language for these functions to be emulated by a
+shader.</p>
+</li>
+<li>
+<p>They represent a trivial operation (clamp, mix, etc.) that is very
+simple for the user to write, but they are very common and may have
+direct hardware support.
+It is a very hard problem for the compiler to map expressions to complex
+assembler instructions.</p>
+</li>
+<li>
+<p>They represent an operation graphics hardware is likely to accelerate at
+some point.
+The trigonometry functions fall into this category.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Many of the functions are similar to the same named ones in common C
+libraries, but they support vector input as well as the more traditional
+scalar input.</p>
+</div>
+<div class="paragraph">
+<p>Applications should be encouraged to use the built-in functions rather than
+do the equivalent computations in their own shader code since the built-in
+functions are assumed to be optimal (e.g. perhaps supported directly in
+hardware).</p>
+</div>
+<div class="paragraph">
+<p>When the built-in functions are specified below, where the input arguments
+(and corresponding output) can be <strong>float</strong>, <strong>vec2</strong>, <strong>vec3</strong>, or <strong>vec4</strong>,
+<em>genFType</em> is used as the argument.
+Where the input arguments (and corresponding output) can be <strong>int</strong>, <strong>ivec2</strong>,
+<strong>ivec3</strong>, or <strong>ivec4</strong>, <em>genIType</em> is used as the argument.
+Where the input arguments (and corresponding output) can be <strong>uint</strong>, <strong>uvec2</strong>,
+<strong>uvec3</strong>, or <strong>uvec4</strong>, <em>genUType</em> is used as the argument.
+Where the input arguments (or corresponding output) can be <strong>bool</strong>, <strong>bvec2</strong>,
+<strong>bvec3</strong>, or <strong>bvec4</strong>, <em>genBType</em> is used as the argument.
+For any specific use of a function, the actual types substituted for
+<em>genFType</em>, <em>genIType</em>, <em>genUType</em>, or <em>genBType</em> have to have the same
+number of components for all arguments and for the return type.
+Similarly, <em>mat</em> is used for any matrix basic
+type.</p>
+</div>
+<div class="paragraph">
+<p>Built-in functions have an effective precision qualification.
+This qualification cannot be set explicitly and may be different from the
+precision qualification of the result.</p>
+</div>
+<div class="paragraph">
+<p>The precision qualification of the operation of a built-in function is based
+on the precision qualification of its formal parameters and actual
+parameters (input arguments): When a formal parameter specifies a precision
+qualifier, that is used, otherwise, the precision qualification of the
+actual (calling) argument is used.
+The highest precision of these will be the precision of the operation of the
+built-in function.
+Generally, this is applied across all arguments to a built-in function, with
+the exceptions being:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>bitfieldExtract</strong> and <strong>bitfieldInsert</strong> ignore the <em>offset</em> and <em>bits</em>
+arguments.</p>
+</li>
+<li>
+<p><strong>interpolateAt</strong> functions only look at the <em>interpolant</em> argument.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The precision qualification of the result of a built-in function is
+determined in one of the following ways:</p>
+</div>
+<div class="paragraph">
+<p>For the texture sampling, image load and image store functions, the
+precision of the return type matches the precision of the sampler type:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform lowp sampler2D sampler;
+highp vec2 coord;
+...
+lowp vec4 col = texture (sampler, coord); <span class="comment">// texture() returns lowp</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Otherwise:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>For prototypes that do not specify a resulting precision qualifier, the
+precision will be the same as the precision of the operation (as defined
+earlier).</p>
+</li>
+<li>
+<p>For prototypes that do specify a resulting precision qualifier, the
+specified precision qualifier is the precision qualification of the
+result.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Where the built-in functions in the following sections specify an equation,
+the entire equation will be evaluated at the operation&#8217;s precision.
+This may lead to underflow or overflow in the result, even when the correct
+result could be represented in the operation precision.</p>
+</div>
+<div class="sect2">
+<h3 id="angle-and-trigonometry-functions">8.1. Angle and Trigonometry Functions</h3>
+<div class="paragraph">
+<p>Function parameters specified as <em>angle</em> are assumed to be in units of
+radians.
+In no case will any of these functions result in a divide by zero error.
+If the divisor of a ratio is 0, then results will be undefined.</p>
+</div>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>radians</strong>(genFType <em>degrees</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Converts <em>degrees</em> to radians, i.e.,
+      <span class="eq">(π / 180) · degrees</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>degrees</strong>(genFType <em>radians</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Converts <em>radians</em> to degrees, i.e.,
+      <span class="eq">(180 / π) · radians</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sin</strong>(genFType <em>angle</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The standard trigonometric sine function.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>cos</strong>(genFType <em>angle</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The standard trigonometric cosine function.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>tan</strong>(genFType <em>angle</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The standard trigonometric tangent.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>asin</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc sine.
+      Returns an angle whose sine is <em>x</em>.
+      The range of values returned by this function is
+      <span class="eq">[-π / 2, π / 2]</span>.
+      Results are undefined if <span class="eq">|x| &gt; 1</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>acos</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc cosine.
+      Returns an angle whose cosine is <em>x</em>.
+      The range of values returned by this function is <span class="eq">[0,π]</span>.
+      Results are undefined if <span class="eq">|x| &gt; 1</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>atan</strong>(genFType <em>y</em>, genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc tangent.
+      Returns an angle whose tangent is <span class="eq">y / x</span>.
+      The signs of <em>x</em> and <em>y</em> are used to determine what quadrant the angle
+      is in.
+      The range of values returned by this function is <span class="eq">[-π, π</span>.
+      Results are undefined if <em>x</em> and <em>y</em> are both 0.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>atan</strong>(genFType <em>y_over_x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc tangent.
+      Returns an angle whose tangent is <em>y_over_x</em>.
+      The range of values returned by this function is
+      <span class="eq">[-π / 2, π / 2]</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sinh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the hyperbolic sine function <span class="eq">(e<sup>x</sup> - e<sup>-x</sup>) / 2</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>cosh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the hyperbolic cosine function <span class="eq">(e<sup>x</sup> + e<sup>-x</sup>) / 2</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>tanh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the hyperbolic tangent function <span class="eq">sinh(x) / cosh(x)</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>asinh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc hyperbolic sine; returns the inverse of <strong>sinh</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>acosh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc hyperbolic cosine; returns the non-negative inverse of <strong>cosh</strong>.
+      Results are undefined if <span class="eq">x &lt; 1</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>atanh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc hyperbolic tangent; returns the inverse of <strong>tanh</strong>.
+      Results are undefined if <span class="eq">x ≥ 1</span>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="exponential-functions">8.2. Exponential Functions</h3>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>pow</strong>(genFType <em>x</em>, genFType <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> raised to the <em>y</em> power, i.e., <span class="eq">x<sup>y</sup></span>.
+      Results are undefined if <span class="eq">x &lt; 0</span>.
+      Results are undefined if <span class="eq">x = 0</span> and <span class="eq">y ≤ 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>exp</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the natural exponentiation of <em>x</em>, i.e., <span class="eq">e<sup>x</sup></span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>log</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the natural logarithm of <em>x</em>, i.e., returns the value <em>y</em>
+      which satisfies the equation <span class="eq">x = e<sup>y</sup></span>.
+      Results are undefined if <span class="eq">x ≤ 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>exp2</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 2 raised to the <em>x</em> power, i.e., <span class="eq">2<sup>x</sup></span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>log2</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the base 2 logarithm of <em>x</em>, i.e., returns the value <em>y</em> which
+      satisfies the equation <span class="eq">x = 2<sup>y</sup></span>.
+      Results are undefined if <span class="eq">x ≤ 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sqrt</strong>(genFType <em>x</em>)<br>
+  genDType <strong>sqrt</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <span class="eq">sqrt(x)</span>.
+      Results are undefined if <span class="eq">x &lt; 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>inversesqrt</strong>(genFType <em>x</em>)<br>
+  genDType <strong>inversesqrt</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <span class="eq">1 / sqrt(x)</span>.
+      Results are undefined if <span class="eq">x ≤ 0</span>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="common-functions">8.3. Common Functions</h3>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>abs</strong>(genFType <em>x</em>)<br>
+  genIType <strong>abs</strong>(genIType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> if <span class="eq">x ≥ 0</span>; otherwise it returns -<em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sign</strong>(genFType <em>x</em>)<br>
+  genIType <strong>sign</strong>(genIType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 1.0 if <em>x</em> &gt; 0, 0.0 if <em>x</em> = 0, or -1.0 if <em>x</em> &lt; 0.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>floor</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer that is less than or
+      equal to <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>trunc</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer to <em>x</em> whose absolute
+      value is not larger than the absolute value of <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>round</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer to <em>x</em>.
+      The fraction 0.5 will round in a direction chosen by the
+      implementation, presumably the direction that is fastest.
+      This includes the possibility that <strong>round</strong>(<em>x</em>) returns the same value
+      as <strong>roundEven</strong>(<em>x</em>) for all values of <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>roundEven</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer to <em>x</em>.
+      A fractional part of 0.5 will round toward the nearest even integer.
+      (Both 3.5 and 4.5 for x will return 4.0.)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>ceil</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer that is greater than or
+      equal to <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fract</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> - <strong>floor</strong>(<em>x</em>).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>mod</strong>(genFType <em>x</em>, float <em>y</em>)<br>
+  genFType <strong>mod</strong>(genFType <em>x</em>, genFType <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Modulus.
+      Returns <span class="eq">x - y · <strong>floor</strong>(x / y)</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>modf</strong>(genFType <em>x</em>, out genFType <em>i</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the fractional part of <em>x</em> and sets <em>i</em> to the integer part (as
+      a whole number floating-point value).
+      Both the return value and the output parameter will have the same sign
+      as <em>x</em>.
+      If <em>x</em> has the value +/- Inf, the return value should be NaN and must
+      be either NaN or 0.0.
+      For <strong>highp</strong> non-constant expressions, the value returned must be
+      consistent.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>min</strong>(genFType <em>x</em>, genFType <em>y</em>)<br>
+  genFType <strong>min</strong>(genFType <em>x</em>, float <em>y</em>)<br>
+  genIType <strong>min</strong>(genIType <em>x</em>, genIType <em>y</em>)<br>
+  genIType <strong>min</strong>(genIType <em>x</em>, int <em>y</em>)<br>
+  genUType <strong>min</strong>(genUType <em>x</em>, genUType <em>y</em>)<br>
+  genUType <strong>min</strong>(genUType <em>x</em>, uint <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>y</em> if <em>y</em> &lt; <em>x;</em> otherwise it returns <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>max</strong>(genFType <em>x</em>, genFType <em>y</em>)<br>
+  genFType <strong>max</strong>(genFType <em>x</em>, float <em>y</em>)<br>
+  genIType <strong>max</strong>(genIType <em>x</em>, genIType <em>y</em>)<br>
+  genIType <strong>max</strong>(genIType <em>x</em>, int <em>y</em>)<br>
+  genUType <strong>max</strong>(genUType <em>x</em>, genUType <em>y</em>)<br>
+  genUType <strong>max</strong>(genUType <em>x</em>, uint <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>y</em> if <em>x</em> &lt; <em>y;</em> otherwise it returns <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>clamp</strong>(genFType <em>x</em>, genFType <em>minVal</em>, genFType <em>maxVal</em>)<br>
+  genFType <strong>clamp</strong>(genFType <em>x</em>, float <em>minVal</em>, float <em>maxVal</em>)<br>
+  genIType <strong>clamp</strong>(genIType <em>x</em>, genIType <em>minVal</em>, genIType <em>maxVal</em>)<br>
+  genIType <strong>clamp</strong>(genIType <em>x</em>, int <em>minVal</em>, int <em>maxVal</em>)<br>
+  genUType <strong>clamp</strong>(genUType <em>x</em>, genUType <em>minVal</em>, genUType <em>maxVal</em>)<br>
+  genUType <strong>clamp</strong>(genUType <em>x</em>, uint <em>minVal</em>, uint <em>maxVal</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>min</strong>(<strong>max</strong>(<em>x</em>, <em>minVal</em>), <em>maxVal</em>).
+      Results are undefined if <em>minVal</em> &gt; <em>maxVal</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>, genFType <em>a</em>)<br>
+  genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>, float <em>a</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the linear blend of <em>x</em> and <em>y</em>, i.e.,
+      <span class="eq">x · (1 - a) + y · a</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>,  genBType <em>a</em>)<br>
+  genIType <strong>mix</strong>(genIType <em>x</em>, genIType <em>y</em>, genBType <em>a</em>)<br>
+  genUType <strong>mix</strong>(genUType <em>x</em>, genUType <em>y</em>, genBType <em>a</em>)<br>
+  genBType <strong>mix</strong>(genBType <em>x</em>, genBType <em>y</em>, genBType <em>a</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Selects which vector each returned component comes from.
+      For a component of <em>a</em> that is <strong>false</strong>, the corresponding component of
+      <em>x</em> is returned.
+      For a component of <em>a</em> that is <strong>true</strong>, the corresponding component of
+      <em>y</em> is returned.
+      Components of <em>x</em> and <em>y</em> that are not selected are allowed to be
+      invalid floating-point values and will have no effect on the results.
+      Thus, this provides different functionality than, for example,<br>
+      genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>, genFType(<em>a</em>))<br>
+      where <em>a</em> is a Boolean vector.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>step</strong>(genFType <em>edge</em>, genFType <em>x</em>)<br>
+  genFType <strong>step</strong>(float <em>edge</em>, genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 0.0 if <em>x</em> &lt; <em>edge;</em> otherwise it returns 1.0.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>smoothstep</strong>(genFType <em>edge0</em>, genFType <em>edge1</em>, genFType <em>x</em>)<br>
+  genFType <strong>smoothstep</strong>(float <em>edge0</em>, float <em>edge1</em>, genFType <em>x</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns 0.0 if <span class="eq">x ≤ edge0</span> and 1.0 if <span class="eq">x ≥ edge1</span>, and
+      performs smooth Hermite interpolation between 0 and 1 when <span class="eq">edge0
+      &lt; x &lt; edge1</span>.
+      This is useful in cases where you would want a threshold function with
+      a smooth transition.
+      This is equivalent to:</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">genFType t;
+t = clamp ((x - edge0) / (edge1 - edge0), <span class="integer">0</span>, <span class="integer">1</span>);
+<span class="keyword">return</span> t * t * (<span class="integer">3</span> - <span class="integer">2</span> * t);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>(And similarly for doubles.) Results are undefined if <span class="eq">edge0 ≥
+edge1</span>.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genBType <strong>isnan</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if <em>x</em> holds a NaN.
+      Returns <strong>false</strong> otherwise.
+      Always returns <strong>false</strong> if NaNs are not implemented.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genBType <strong>isinf</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if <em>x</em> holds a positive infinity or negative infinity.
+      Returns <strong>false</strong> otherwise.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>floatBitsToInt</strong>(highp genFType <em>value</em>)<br>
+  genUType <strong>floatBitsToUint</strong>(highp genFType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a signed or unsigned integer value representing the encoding
+      of a floating-point value.
+      The <strong>float</strong> value&#8217;s bit-level representation is preserved.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>intBitsToFloat</strong>(highp genIType <em>value</em>)<br>
+  genFType <strong>uintBitsToFloat</strong>(highp genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a floating-point value corresponding to a signed or unsigned
+      integer encoding of a floating-point value.
+      If an Inf or NaN is passed in, it will not signal, and the resulting
+      floating-point value is unspecified.
+      Otherwise, the bit-level representation is preserved.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fma</strong>(genFType <em>a</em>, genFType <em>b</em>, genFType <em>c</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Computes and returns <span class="eq">a * b + c</span>.
+      In uses where the return value is eventually consumed by a variable
+      declared as <strong>precise</strong>:</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="ulist">
+<ul>
+<li>
+<p><strong>fma</strong>() is considered a single operation, whereas the expression &#8220;a * b
++ c&#8221; consumed by a variable declared <strong>precise</strong> is considered two
+operations.</p>
+</li>
+<li>
+<p>The precision of <strong>fma</strong>() can differ from the precision of the expression
+&#8220;a * b + c&#8221;.</p>
+</li>
+<li>
+<p><strong>fma</strong>() will be computed with the same precision as any other <strong>fma</strong>()
+consumed by a precise variable, giving invariant results for the same
+input values of <em>a</em>, <em>b</em>, and <em>c</em>.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Otherwise, in the absence of <strong>precise</strong> consumption, there are no special
+constraints on the number of operations or difference in precision between
+<strong>fma</strong>() and the expression &#8220;_a_ * <em>b</em> + <em>c</em>&#8221;.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>frexp</strong>(highp genFType <em>x</em>, out highp genIType <em>exp</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Splits <em>x</em> into a floating-point significand in the range
+      <span class="eq">[0.5,1.0]</span>, and an integral exponent of two, such that</p>
+<p class="tableblock">      <span class="eq">x = significant · 2<sup>exponent</sup></span></p>
+<p class="tableblock">      The significand is returned by the function and the exponent is
+      returned in the parameter <em>exp</em>.
+      For a floating-point value of zero, the significand and exponent are
+      both zero.</p>
+<p class="tableblock">      If an implementation supports signed zero, an input value of minus
+      zero should return a significand of minus zero.
+      For a floating-point value that is an infinity or is not a number, the
+      results are undefined.</p>
+<p class="tableblock">      If the input <em>x</em> is a vector, this operation is performed in a
+      component-wise manner; the value returned by the function and the
+      value written to <em>exp</em> are vectors with the same number of components
+      as <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>ldexp</strong>(highp genFType <em>x</em>, highp genIType <em>exp</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Builds a floating-point number from <em>x</em> and the corresponding integral
+      exponent of two in <em>exp</em>, returning:</p>
+<p class="tableblock">      <span class="eq">significand · 2<sup>exponent</sup></span></p>
+<p class="tableblock">      If this product is too large to be represented in the floating-point
+      type, the result is undefined.</p>
+<p class="tableblock">      If <em>exp</em> is greater than +128, the value returned is undefined.
+      If <em>exp</em> is less than -126, the value returned may be flushed to zero.
+      Additionally, splitting the value into a significand and exponent
+      using <strong>frexp</strong>() and then reconstructing a floating-point value using
+      <strong>ldexp</strong>() should yield the original input for zero and all finite
+      non-denormalized values.<br>
+      If the input <em>x</em> is a vector, this operation is performed in a
+      component-wise manner; the value passed in <em>exp</em> and returned by the
+      function are vectors with the same number of components as <em>x</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="floating-point-pack-and-unpack-functions">8.4. Floating-Point Pack and Unpack Functions</h3>
+<div class="paragraph">
+<p>These functions do not operate component-wise, rather, as described in each
+case.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>packUnorm2x16</strong>(vec2 <em>v</em>)<br>
+  highp uint <strong>packSnorm2x16</strong>(vec2 <em>v</em>)<br>
+  highp uint <strong>packUnorm4x8</strong>(vec4 <em>v</em>)<br>
+  highp uint <strong>packSnorm4x8</strong>(vec4 <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">First, converts each component of the normalized floating-point value
+      <em>v</em> into 16-bit (<strong>2x16</strong>) or 8-bit (<strong>4x8</strong>) integer values.
+      Then, the results are packed into the returned 32-bit unsigned
+      integer.</p>
+<p class="tableblock">      The conversion for component <em>c</em> of <em>v</em> to fixed point is done as
+      follows:</p>
+<p class="tableblock">      <strong>packUnorm2x16</strong>: <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, 0, +1) * 65535.0)<br>
+      <strong>packSnorm2x16:</strong> <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, -1, +1) * 32767.0)<br>
+      <strong>packUnorm4x8</strong>: <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, 0, +1) * 255.0)<br>
+      <strong>packSnorm4x8</strong>: <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, -1, +1) * 127.0)</p>
+<p class="tableblock">      The first component of the vector will be written to the least
+      significant bits of the output; the last component will be written to
+      the most significant bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp vec2 <strong>unpackUnorm2x16</strong>(highp uint <em>p</em>)<br>
+  highp vec2 <strong>unpackSnorm2x16</strong>(highp uint <em>p</em>)<br>
+  mediump vec4 <strong>unpackUnorm4x8</strong>(highp uint <em>p</em>)<br>
+  mediump vec4 <strong>unpackSnorm4x8</strong>(highp uint <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">First, unpacks a single 32-bit unsigned integer <em>p</em> into a pair of
+      16-bit unsigned integers, a pair of 16-bit signed integers, four 8-bit
+      unsigned integers, or four 8-bit signed integers, respectively.
+      Then, each component is converted to a normalized floating-point value
+      to generate the returned two- or four-component vector.</p>
+<p class="tableblock">      The conversion for unpacked fixed-point value <em>f</em> to floating-point is
+      done as follows:</p>
+<p class="tableblock">      <strong>unpackUnorm2x16</strong>: <em>f</em> / 65535.0<br>
+      <strong>unpackSnorm2x16</strong>: <strong>clamp</strong>(<em>f</em> / 32767.0, -1, +1)<br>
+      <strong>unpackUnorm4x8</strong>: <em>f</em> / 255.0<br>
+      <strong>unpackSnorm4x8</strong>: <strong>clamp</strong>(<em>f</em> / 127.0, -1, +1)</p>
+<p class="tableblock">      The first component of the returned vector will be extracted from the
+      least significant bits of the input; the last component will be
+      extracted from the most significant bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>packHalf2x16</strong>(vec2 <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns an unsigned integer obtained by converting the components of a
+      two-component floating-point vector to the 16-bit floating-point
+      representation found in the <a href="#references">OpenGL ES Specification</a>, and
+      then packing these two 16-bit integers into a 32-bit unsigned integer.</p>
+<p class="tableblock">      The first vector component specifies the 16 least-significant bits of
+      the result; the second component specifies the 16 most-significant
+      bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mediump vec2 <strong>unpackHalf2x16</strong>(highp uint <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a two-component floating-point vector with components obtained
+      by unpacking a 32-bit unsigned integer into a pair of 16-bit values,
+      interpreting those values as 16-bit floating-point numbers according
+      to the <a href="#references">OpenGL ES Specification</a>, and converting them to
+      32-bit floating-point values.</p>
+<p class="tableblock">      The first component of the vector is obtained from the 16
+      least-significant bits of <em>v</em>; the second component is obtained from
+      the 16 most-significant bits of <em>v</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="geometric-functions">8.5. Geometric Functions</h3>
+<div class="paragraph">
+<p>These operate on vectors as vectors, not component-wise.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>length</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns the length of vector <em>x</em>, i.e.,
+      <span class="eq">sqrt( x<sub>0</sub><sup>2</sup> + x<sub>1</sub><sup>2</sup> + &#8230;&#8203; )</span>.</p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>distance</strong>(genFType <em>p0</em>, genFType <em>p1</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the distance between <em>p0</em> and <em>p1</em>, i.e.,
+      <strong>length</strong>(<em>p0</em> - <em>p1</em>)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>dot</strong>(genFType <em>x</em>, genFType <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the dot product of <em>x</em> and <em>y</em>, i.e.,
+      <span class="eq">x<sub>0</sub> · y<sub>0</sub> + x<sub>1</sub> · y<sub>1</sub> + &#8230;&#8203;</span></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec3 <strong>cross</strong>(vec3 <em>x</em>, vec3 <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns the cross product of <em>x</em> and <em>y</em>, i.e.,
+      <span class="eq">(x<sub>1</sub> · y<sub>2</sub> - y<sub>1</sub> · x<sub>2</sub>,
+            x<sub>2</sub> · y<sub>0</sub> - y<sub>2</sub> · x<sub>0</sub>,
+            x<sub>0</sub> · y<sub>1</sub> - y<sub>0</sub> · x<sub>1</sub>)</span>.</p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>normalize</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a vector in the same direction as <em>x</em> but with a length of 1,
+      i.e. <em>x</em> / <strong>length</strong>(x).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>faceforward</strong>(genFType <em>N</em>, genFType <em>I</em>, genFType <em>Nref</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">If <strong>dot</strong>(<em>Nref</em>, <em>I</em>) &lt; 0 return <em>N</em>, otherwise return -<em>N</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>reflect</strong>(genFType <em>I</em>, genFType <em>N</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">For the incident vector <em>I</em> and surface orientation <em>N</em>, returns the
+      reflection direction: <span class="eq">I - 2 · <strong>dot</strong>(N, I) · N</span>.
+      <em>N</em> must already be normalized in order to achieve the desired result.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>refract</strong>(genFType <em>I</em>, genFType <em>N</em>, float <em>eta</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>For the incident vector <em>I</em> and surface normal <em>N</em>, and the ratio of
+      indices of refraction <em>eta</em>, return the refraction vector.
+      The result is computed by the <a href="#refraction-equation">refraction
+      equation</a> shown below.</p>
+</div>
+<div class="literalblock">
+<div class="content">
+<pre>The input parameters for the incident vector _I_ and the surface
+normal _N_ must already be normalized to get the desired results.</pre>
+</div>
+</div></div></td>
+</tr>
+</tbody>
+</table>
+<div class="sect3">
+<h4 id="refraction-equation">8.5.1. Refraction Equation</h4>
+<div class="stemblock">
+<div class="content">
+\[k = 1.0 - eta * eta * (1.0 - \textbf{dot}(N,I) \cdot \textbf{dot}(N,I))\]
+</div>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\begin{aligned}
+result &amp;=
+  \begin{cases}
+    genFType(0.0), &amp; k &lt; 0.0 \\
+    eta * I - (eta * \textbf{dot}(N,I) + \sqrt { k }) * N, &amp; \textbf{otherwise}
+  \end{cases}
+\end{aligned}\]
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="matrix-functions">8.6. Matrix Functions</h3>
+<div class="paragraph">
+<p>For each of the following built-in matrix functions, there is both a
+single-precision floating-point version, where all arguments and return
+values are single precision, and a double-precision floating-point version,
+where all arguments and return values are double precision.
+Only the single-precision floating-point version is shown.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat <strong>matrixCompMult</strong>(mat <em>x</em>, mat <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Multiply matrix <em>x</em> by matrix <em>y</em> component-wise, i.e., result[i][j]
+      is the scalar product of <em>x</em>[i][j] and <em>y</em>[i][j].<br></p>
+<p class="tableblock">      Note: to get linear algebraic matrix multiplication, use the multiply
+      operator (<strong>*</strong>).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat2 <strong>outerProduct</strong>(vec2 <em>c</em>, vec2 <em>r</em>)<br>
+  mat3 <strong>outerProduct</strong>(vec3 <em>c</em>, vec3 <em>r</em>)<br>
+  mat4 <strong>outerProduct</strong>(vec4 <em>c</em>, vec4 <em>r</em>)<br>
+  mat2x3 <strong>outerProduct</strong>(vec3 <em>c</em>, vec2 <em>r</em>)<br>
+  mat3x2 <strong>outerProduct</strong>(vec2 <em>c</em>, vec3 <em>r</em>)<br>
+  mat2x4 <strong>outerProduct</strong>(vec4 <em>c</em>, vec2 <em>r</em>)<br>
+  mat4x2 <strong>outerProduct</strong>(vec2 <em>c</em>, vec4 <em>r</em>)<br>
+  mat3x4 <strong>outerProduct</strong>(vec4 <em>c</em>, vec3 <em>r</em>)<br>
+  mat4x3 <strong>outerProduct</strong>(vec3 <em>c</em>, vec4 <em>r</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Treats the first parameter <em>c</em> as a column vector (matrix with one
+      column) and the second parameter <em>r</em> as a row vector (matrix with one
+      row) and does a linear algebraic matrix multiply <em>c</em> * <em>r</em>, yielding a
+      matrix whose number of rows is the number of components in <em>c</em> and
+      whose number of columns is the number of components in <em>r</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat2 <strong>transpose</strong>(mat2 <em>m</em>)<br>
+  mat3 <strong>transpose</strong>(mat3 <em>m</em>)<br>
+  mat4 <strong>transpose</strong>(mat4 <em>m</em>)<br>
+  mat2x3 <strong>transpose</strong>(mat3x2 <em>m</em>)<br>
+  mat3x2 <strong>transpose</strong>(mat2x3 <em>m</em>)<br>
+  mat2x4 <strong>transpose</strong>(mat4x2 <em>m</em>)<br>
+  mat4x2 <strong>transpose</strong>(mat2x4 <em>m</em>)<br>
+  mat3x4 <strong>transpose</strong>(mat4x3 <em>m</em>)<br>
+  mat4x3 <strong>transpose</strong>(mat3x4 <em>m</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a matrix that is the transpose of <em>m</em>.
+      The input matrix <em>m</em> is not modified.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>determinant</strong>(mat2 <em>m</em>)<br>
+  float <strong>determinant</strong>(mat3 <em>m</em>)<br>
+  float <strong>determinant</strong>(mat4 <em>m</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the determinant of <em>m</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat2 <strong>inverse</strong>(mat2 <em>m</em>)<br>
+  mat3 <strong>inverse</strong>(mat3 <em>m</em>)<br>
+  mat4 <strong>inverse</strong>(mat4 <em>m</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a matrix that is the inverse of <em>m</em>.
+      The input matrix <em>m</em> is not modified.
+      The values in the returned matrix are undefined if <em>m</em> is singular or
+      poorly-conditioned (nearly singular).</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="vector-relational-functions">8.7. Vector Relational Functions</h3>
+<div class="paragraph">
+<p>Relational and equality operators (<strong>&lt;</strong>, <strong>&lt;=</strong>, <strong>&gt;</strong>, <strong>&gt;=</strong>, <strong>==</strong>, <strong>!=</strong>) are
+defined to operate on scalars and produce scalar Boolean results.
+For vector results, use the following built-in functions.
+Below, the following placeholders are used for the listed specific types:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Placeholder</th>
+<th class="tableblock halign-left valign-top">Specific Types Allowed</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec2, bvec3, bvec4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">ivec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">ivec2, ivec3, ivec4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uvec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uvec2, uvec3, uvec4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec2, vec3, vec4</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>In all cases, the sizes of all the input and return vectors for any
+particular call must match.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>lessThan</strong>(vec x, vec y)<br>
+  bvec <strong>lessThan</strong>(ivec x, ivec y)<br>
+  bvec <strong>lessThan</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x &lt; y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>lessThanEqual</strong>(vec x, vec y)<br>
+  bvec <strong>lessThanEqual</strong>(ivec x, ivec y)<br>
+  bvec <strong>lessThanEqual</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x ≤ y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>greaterThan</strong>(vec x, vec y)<br>
+  bvec <strong>greaterThan</strong>(ivec x, ivec y)<br>
+  bvec <strong>greaterThan</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x &gt; y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>greaterThanEqual</strong>(vec x, vec y)<br>
+  bvec <strong>greaterThanEqual</strong>(ivec x, ivec y)<br>
+  bvec <strong>greaterThanEqual</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x ≥ y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>equal</strong>(vec x, vec y)<br>
+  bvec <strong>equal</strong>(ivec x, ivec y)<br>
+  bvec <strong>equal</strong>(uvec x, uvec y)<br>
+  bvec <strong>equal</strong>(bvec x, bvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x == y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>notEqual</strong>(vec x, vec y)<br>
+  bvec <strong>notEqual</strong>(ivec x, ivec y)<br>
+  bvec <strong>notEqual</strong>(uvec x, uvec y)<br>
+  bvec <strong>notEqual</strong>(bvec x, bvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x ≠ y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>any</strong>(bvec x)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if any component of <em>x</em> is <strong>true</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>all</strong>(bvec x)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> only if all components of <em>x</em> are <strong>true</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>not</strong>(bvec x)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise logical complement of <em>x</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="integer-functions">8.8. Integer Functions</h3>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.
+The notation [<em>a</em>, <em>b</em>] means the set of bits from bit-number <em>a</em> through
+bit-number <em>b</em>, inclusive.
+The lowest-order bit is bit 0.
+&#8220;Bit number&#8221; will always refer to counting up from the lowest-order bit as
+bit 0.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genUType <strong>uaddCarry</strong>(highp genUType <em>x</em>, highp genUType <em>y</em>, out lowp genUType <em>carry</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Adds 32-bit unsigned integers <em>x</em> and <em>y</em>, returning the sum modulo
+      2<sup>32</sup>.
+      The value <em>carry</em> is set to zero if the sum was less than 2<sup>32</sup>, or
+      one otherwise.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genUType <strong>usubBorrow</strong>(highp genUType <em>x</em>, highp genUType <em>y</em>, out lowp genUType <em>borrow</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Subtracts the 32-bit unsigned integer <em>y</em> from <em>x</em>, returning the
+      difference if non-negative, or 2<sup>32</sup> plus the difference otherwise.
+      The value <em>borrow</em> is set to zero if <span class="eq">x ≥ y</span>, or one
+      otherwise.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>umulExtended</strong>(highp genUType <em>x</em>, highp genUType <em>y</em>, out highp genUType <em>msb</em>, out highp genUType <em>lsb</em>)<br>
+  void <strong>imulExtended</strong>(highp genIType <em>x</em>, highp genIType <em>y</em>, out highp genIType <em>msb</em>, out highp genIType <em>lsb</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Multiplies 32-bit unsigned or signed integers <em>x</em> and <em>y</em>, producing a
+      64-bit result.
+      The 32 least-significant bits are returned in <em>lsb</em>.
+      The 32 most-significant bits are returned in <em>msb</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>bitfieldExtract</strong>(genIType <em>value</em>, int <em>offset</em>, int <em>bits</em>)<br>
+  genUType <strong>bitfieldExtract</strong>(genUType <em>value</em>, int <em>offset</em>, int <em>bits</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Extracts bits <span class="eq">[offset, offset + bits - 1]</span> from <em>value</em>,
+      returning them in the least significant bits of the result.<br></p>
+<p class="tableblock">      For unsigned data types, the most significant bits of the result will
+      be set to zero.
+      For signed data types, the most significant bits will be set to the
+      value of bit <span class="eq">offset + bits - 1</span>.<br></p>
+<p class="tableblock">      If <em>bits</em> is zero, the result will be zero.
+      The result will be undefined if <em>offset</em> or <em>bits</em> is negative, or if
+      the sum of <em>offset</em> and <em>bits</em> is greater than the number of bits used
+      to store the operand.
+      Note that for vector versions of <strong>bitfieldExtract</strong>(), a single pair of
+      <em>offset</em> and <em>bits</em> values is shared for all components.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>bitfieldInsert</strong>(genIType <em>base</em>, genIType <em>insert</em>, int <em>offset</em>, int <em>bits</em>)<br>
+  genUType <strong>bitfieldInsert</strong>(genUType <em>base</em>, genUType <em>insert</em>, int <em>offset</em>, int <em>bits</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inserts the <em>bits</em> least significant bits of <em>insert</em> into <em>base</em>.</p>
+<p class="tableblock">      The result will have bits <span class="eq">[offset, offset + bits - 1]</span> taken from
+      bits <span class="eq">[0, bits - 1]</span> of <em>insert</em>, and all other bits taken
+      directly from the corresponding bits of <em>base</em>.
+      If <em>bits</em> is zero, the result will simply be <em>base</em>.
+      The result will be undefined if <em>offset</em> or <em>bits</em> is negative, or if
+      the sum of <em>offset</em> and <em>bits</em> is greater than the number of bits used
+      to store the operand.<br>
+      Note that for vector versions of <strong>bitfieldInsert</strong>(), a single pair of
+      <em>offset</em> and <em>bits</em> values is shared for all components.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>bitfieldReverse</strong>(highp genIType <em>value</em>)<br>
+  genUType <strong>bitfieldReverse</strong>(highp genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Reverses the bits of <em>value</em>.
+      The bit numbered <em>n</em> of the result will be taken from bit <span class="eq">(bits -
+      1) - n</span> of <em>value</em>, where <em>bits</em> is the total number of bits used to
+      represent <em>value</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">lowp genIType <strong>bitCount</strong>(genIType <em>value</em>)<br>
+  lowp genIType <strong>bitCount</strong>(genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the number of one bits in the binary representation of
+      <em>value</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">lowp genIType <strong>findLSB</strong>(genIType <em>value</em>)<br>
+  lowp genIType <strong>findLSB</strong>(genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the bit number of the least significant one bit in the binary
+      representation of <em>value</em>.
+      If <em>value</em> is zero, -1 will be returned.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">lowp genIType <strong>findMSB</strong>(highp genIType <em>value</em>)<br>
+  lowp genIType <strong>findMSB</strong>(highp genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the bit number of the most significant bit in the binary
+      representation of <em>value</em>.</p>
+<p class="tableblock">      For positive integers, the result will be the bit number of the most
+      significant one bit.
+      For negative integers, the result will be the bit number of the most
+      significant zero bit.
+      For a <em>value</em> of zero or negative one, -1 will be returned.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="texture-functions">8.9. Texture Functions</h3>
+<div class="paragraph">
+<p>Texture lookup functions are available in all shading stages.
+However, level-of-detail is implicitly computed only for fragment shaders.
+Other shaders operate as though the base level-of-detail were computed as
+zero.
+The functions in the table below provide access to textures through
+samplers, as set up through the OpenGL ES API.
+Texture properties such as size, pixel format, number of dimensions,
+filtering method, number of mipmap levels, depth comparison, and so on are
+also defined by OpenGL ES API calls.
+Such properties are taken into account as the texture is accessed via the
+built-in functions defined below.</p>
+</div>
+<div class="paragraph">
+<p>Texture data can be stored by the GL as single-precision floating-point,
+unsigned normalized integer, unsigned integer or signed integer data.
+This is determined by the type of the internal format of the texture.</p>
+</div>
+<div class="paragraph">
+<p>Texture lookup functions are provided that can return their result as
+floating-point, unsigned integer or signed integer, depending on the sampler
+type passed to the lookup function.
+Care must be taken to use the right sampler type for texture access.
+The following table lists the supported combinations of sampler types and
+texture internal formats.
+Blank entries are unsupported.
+Doing a texture lookup will return undefined values for unsupported
+combinations.</p>
+</div>
+<div class="paragraph">
+<p>For depth/stencil textures, the internal texture format is determined by the
+component being accessed as set through the OpenGL ES API.
+When the depth/stencil texture mode is set to DEPTH_COMPONENT, the internal
+format of the depth component should be used.
+When the depth/stencil texture mode is set to STENCIL_INDEX, the internal format
+of the stencil component should be used.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Internal Texture Format</th>
+<th class="tableblock halign-left valign-top">Floating-Point Sampler Types</th>
+<th class="tableblock halign-left valign-top">Signed Integer Sampler Types</th>
+<th class="tableblock halign-left valign-top">Unsigned Integer Sampler Types</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Floating-point</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Normalized Integer</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Signed Integer</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Unsigned Integer</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>If an integer sampler type is used, the result of a texture lookup is an
+<strong>ivec4</strong>.
+If an unsigned integer sampler type is used, the result of a texture lookup
+is a <strong>uvec4</strong>.
+If a floating-point sampler type is used, the result of a texture lookup is
+a <strong>vec4</strong>.</p>
+</div>
+<div class="paragraph">
+<p>In the prototypes below, the &#8220;_g_&#8221; in the return type &#8220;_gvec4_&#8221; is used
+as a placeholder for nothing, &#8220;_i_&#8221;, or &#8220;_u_&#8221; making a return type of
+<strong>vec4</strong>, <strong>ivec4</strong>, or <strong>uvec4</strong>.
+In these cases, the sampler argument type also starts with &#8220;_g_&#8221;,
+indicating the same substitution done on the return type; it is either a
+floating-point, signed integer, or unsigned integer sampler, matching the
+basic type of the return type, as described above.</p>
+</div>
+<div class="paragraph">
+<p>For shadow forms (the sampler parameter is a shadow-type), a depth
+comparison lookup on the depth texture bound to <em>sampler</em> is done as
+described in section
+8.20
+&#8220;Texture Comparison Modes&#8221; of the
+<a href="#references">OpenGL ES Specification</a>.
+See the table below for which component specifies <em>D<sub>ref</sub></em>.
+The texture bound to <em>sampler</em> must be a depth texture, or results are
+undefined.
+If a non-shadow texture call is made to a sampler that represents a depth
+texture with depth comparisons turned on, then results are undefined.
+If a shadow texture call is made to a sampler that represents a depth
+texture with depth comparisons turned off, then results are undefined.
+If a shadow texture call is made to a sampler that does not represent a
+depth texture, then results are undefined.</p>
+</div>
+<div class="paragraph">
+<p>In all functions below, the <em>bias</em> parameter is optional for fragment
+shaders.
+The <em>bias</em> parameter is not accepted in any other shader stage.
+For a fragment shader, if <em>bias</em> is present, it is added to the implicit
+level-of-detail prior to performing the texture access operation.
+No <em>bias</em> or <em>lod</em> parameters for
+multisample textures, or texture buffers
+are supported because mipmaps are not allowed for these types of textures.</p>
+</div>
+<div class="paragraph">
+<p>The implicit level-of-detail is selected as follows: For a texture that is
+not mipmapped, the texture is used directly.
+If it is mipmapped and running in a fragment shader, the level-of-detail
+computed by the implementation is used to do the texture lookup.
+If it is mipmapped and running in a non-fragment shader, then the base
+texture is used.</p>
+</div>
+<div class="paragraph">
+<p>Some texture functions (non-&#8220;<strong>Lod</strong>&#8221; and non-&#8220;<strong>Grad</strong>&#8221; versions) may
+require implicit derivatives.
+Implicit derivatives are undefined within non-uniform control flow and for
+non-fragment shader texture fetches.</p>
+</div>
+<div class="paragraph">
+<p>For <strong>Cube</strong> forms, the direction of <em>P</em> is used to select which face to do a
+2-dimensional texture lookup in, as described in section 8.13 &#8220;Cube Map
+Texture Selection&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>For <strong>Array</strong> forms, the array layer used will be</p>
+</div>
+<div class="paragraph">
+<p>\(\max(0,\min(d-1,\left\lfloor layer + 0.5\right\rfloor))\)</p>
+</div>
+<div class="paragraph">
+<p>where <em>d</em> is the depth of the texture array and <em>layer</em> comes from the
+component indicated in the tables below.</p>
+</div>
+<div class="sect3">
+<h4 id="texture-query-functions">8.9.1. Texture Query Functions</h4>
+<div class="paragraph">
+<p>The <strong>textureSize</strong> functions query the dimensions of a specific texture level
+for a sampler.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp ivec2 <strong>textureSize</strong>(gsampler2D <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec3 <strong>textureSize</strong>(gsampler3D <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec2 <strong>textureSize</strong>(gsamplerCube <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec2 <strong>textureSize</strong>(sampler2DShadow <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec2 <strong>textureSize</strong>(samplerCubeShadow <em>sampler</em>, int <em>lod</em>)
+  highp ivec3 <strong>textureSize</strong>(gsamplerCubeArray <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec3 <strong>textureSize</strong>(samplerCubeArrayShadow <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec3 <strong>textureSize</strong>(gsampler2DArray <em>sampler</em>, int <em>lod</em>)<br>
+  highp ivec3 <strong>textureSize</strong>(sampler2DArrayShadow <em>sampler</em>, int <em>lod</em>)<br>
+  highp int <strong>textureSize</strong>(gsamplerBuffer <em>sampler</em>)<br>
+  highp ivec2 <strong>textureSize</strong>(gsampler2DMS <em>sampler</em>)<br>
+  highp ivec3 <strong>textureSize</strong>(gsampler2DMSArray <em>sampler</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the dimensions of level <em>lod</em> (if present) for the texture
+      bound to <em>sampler</em>, as described in section
+      8.11 &#8220;Texture Queries&#8221; of the <a href="#references">OpenGL ES Specification</a>.<br>
+      The components in the return value are filled in, in order, with the
+      width, height, and depth of the texture.</p>
+<p class="tableblock">      For the array forms, the last component of the return value is the
+      number of layers in the texture array, or the number of cubes in the
+      texture cube map array.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="texel-lookup-functions">8.9.2. Texel Lookup Functions</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>texture</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>[, float <em>bias</em>] )<br>
+  float <strong>texture</strong>(sampler2DShadow <em>sampler</em>, <em>vec3 _P</em> [, float <em>bias</em>])<br>
+  float <strong>texture</strong>(samplerCubeShadow <em>sampler</em>, <em>vec4 _P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  float <strong>texture</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 <em>P</em>)<br>
+  float <strong>texture</strong>(samplerCubeArrayShadow <em>sampler</em>, vec4 <em>P</em>, float <em>compare</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Use the texture coordinate <em>P</em> to do a texture lookup in the texture
+      currently bound to <em>sampler</em>.</p>
+<p class="tableblock">      For shadow forms: When <em>compare</em> is present, it is used as <em>D<sub>ref</sub></em>
+      and the array layer comes from the last component of <em>P</em>.
+      When <em>compare</em> is not present, the last component of <em>P</em> is used as
+      <em>D<sub>ref</sub></em> and the array layer comes from the second to last component
+      of <em>P</em>.</p>
+<p class="tableblock">      For non-shadow forms: the array layer comes from the last component of
+      <em>P</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProj</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  float <strong>textureProj</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup with projection.
+      The texture coordinates consumed from <em>P</em>, not including the last
+      component of <em>P</em>, are divided by the last component of <em>P</em> to
+      form projected coordinates <em>P'</em>.
+      The resulting third component of <em>P</em> in the shadow forms is used as
+      <em>D<sub>ref</sub></em>.
+      The third component of <em>P</em> is ignored when <em>sampler</em> has type
+      <strong>gsampler2D</strong> and <em>P</em> has type <strong>vec4</strong>.
+      After these values are computed, texture lookup proceeds as in
+      <strong>texture</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureLod</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureLod</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Do a texture lookup as in <strong>texture</strong> but with explicit level-of-detail;
+      <em>lod</em> specifies <span class="eq">λ<sub>base</sub>]</span> and sets the partial derivatives
+      as follows:<br>
+      (See section 8.14 &#8220;Texture Minification&#8221; and equations 8.4-8.6 of
+      the <a href="#references">OpenGL ES Specification</a>.)<br>
+     <br>
+      <span class="eq">∂u / ∂x =
+           ∂v / ∂x =
+           ∂w / ∂x = 0</span>
+     <br>
+      <span class="eq">∂u / ∂y =
+           ∂v / ∂y =
+           ∂w / ∂y = 0</span></p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, ivec3 <em>offset</em> [, float <em>bias</em>] )<br>
+  float <strong>textureOffset</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup as in <strong>texture</strong> but with <em>offset</em> added to the
+      <span class="eq">(u,v,w)</span> texel coordinates before looking up each texel.
+      The offset value must be a constant expression.
+      A limited range of offset values are supported; the minimum and
+      maximum offset values are implementation-dependent and given by
+      <em>gl_MinProgramTexelOffset</em> and <em>gl_MaxProgramTexelOffset</em>,
+      respectively.</p>
+<p class="tableblock">      Note that <em>offset</em> does not apply to the layer coordinate for texture
+      arrays.
+      This is explained in detail in section 8.14.2 &#8220;Coordinate Wrapping
+      and Texel Selection&#8221; of the <a href="#references">OpenGL ES Specification</a>, where <em>offset</em>
+      is <span class="eq">(δ<sub>u</sub>, δ<sub>v</sub>, δ<sub>w</sub>)</span>.<br>
+      Note that texel offsets are also not supported for cube maps.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>texelFetch</strong>(gsampler2D <em>sampler</em>, ivec2 <em>P</em>, int <em>lod</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler3D <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>)
+  gvec4 <strong>texelFetch</strong>(gsampler2DArray <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsamplerBuffer <em>sampler</em>, int <em>P</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler2DMS <em>sampler</em>, ivec2 <em>P</em>, int <em>sample</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler2DMSArray <em>sampler</em>, ivec3 <em>P</em>, int <em>sample</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Use integer texture coordinate <em>P</em> to lookup a single texel from
+      <em>sampler</em>.
+      The array layer comes from the last component of <em>P</em> for the array
+      forms.
+      The level-of-detail <em>lod</em> (if present) is as described in sections
+      11.1.3.2 &#8220;Texel Fetches&#8221; and 8.14.1 &#8220;Scale Factor and Level of
+      Detail&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>texelFetchOffset</strong>(gsampler2D <em>sampler</em>, ivec2 <em>P</em>, int <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler3D <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>, ivec3 <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler2DArray <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Fetch a single texel as in <strong>texelFetch</strong>, offset by <em>offset</em> as
+      described in <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjOffset</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, ivec3 <em>offset</em> [, float <em>bias</em>] )<br>
+  float <strong>textureProjOffset</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a projective texture lookup as described in <strong>textureProj</strong>, offset
+      by <em>offset</em> as described in <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureLodOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureLodOffset</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>, ivec3 <em>offset</em>)<br>
+  float <strong>textureLodOffset</strong>(sampler2DShadow <em>sampler</em>,  <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureLodOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do an offset texture lookup with explicit level-of-detail.
+      See <strong>textureLod</strong> and <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjLod</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureProjLod</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureProjLod</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureProjLod</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a projective texture lookup with explicit level-of-detail.
+      See <strong>textureProj</strong> and <strong>textureLod</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjLodOffset</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjLodOffset</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjLodOffset</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, ivec3 <em>offset</em>)<br>
+  float <strong>textureProjLodOffset</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do an offset projective texture lookup with explicit level-of-detail.
+      See <strong>textureProj</strong>, <strong>textureLod</strong>, and <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGrad</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsampler3D <em>sampler</em>,  <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(samplerCubeShadow <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Do a texture lookup as in <strong>texture</strong> but with <a href="#explicit-gradients">explicit gradients</a> as shown below.
+      The partial derivatives of <em>P</em> are with respect to window <em>x</em> and
+      window <em>y</em>.
+      For the cube version, the partial derivatives of <em>P</em> are assumed to be
+      in the coordinate system used before texture coordinates are projected
+      onto the appropriate cube face.</p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGradOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>, ivec3 <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup with both explicit gradient and offset, as
+      described in <strong>textureGrad</strong> and <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjGrad</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  float <strong>textureProjGrad</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup both projectively, as described in <strong>textureProj</strong>,
+      and with explicit gradient as described in <strong>textureGrad</strong>.
+      The partial derivatives <em>dPdx</em> and <em>dPdy</em> are assumed to be already
+      projected.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjGradOffset</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>, ivec3 <em>offset</em>)<br>
+  float <strong>textureProjGradOffset</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup projectively and with explicit gradient as
+      described in <strong>textureProjGrad</strong>, as well as with offset, as described in
+      <strong>textureOffset</strong>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="explicit-gradients">8.9.3. Explicit Gradients</h4>
+<div class="paragraph">
+<p>In the <strong>textureGrad</strong> functions described above, explicit gradients control
+texture lookups as follows:</p>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\begin{aligned}
+  \frac{\partial{s}}{\partial{x}} &amp; = \frac{\partial{P.s}}{\partial{x}} \\[0.8em]
+  \frac{\partial{s}}{\partial{y}} &amp; = \frac{\partial{P.s}}{\partial{y}} \\[0.8em]
+  \frac{\partial{t}}{\partial{x}} &amp; = \frac{\partial{P.t}}{\partial{x}} \\[0.8em]
+  \frac{\partial{t}}{\partial{y}} &amp; = \frac{\partial{P.t}}{\partial{y}} \\[0.8em]
+  \frac{\partial{r}}{\partial{x}} &amp; =
+    \begin{cases}
+      0.0,                               &amp; \text{for 2D} \\[0.8em]
+      \frac{\partial{P.p}}{\partial{x}}, &amp; \text{cube, other}
+    \end{cases} \\[2.5em]
+  \frac{\partial{r}}{\partial{y}} &amp; =
+    \begin{cases}
+      0.0,                               &amp; \text{for 2D} \\[0.8em]
+      \frac{\partial{P.p}}{\partial{y}}, &amp; \text{cube, other}
+    \end{cases}
+\end{aligned}\]
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="texture-gather-functions">8.9.4. Texture Gather Functions</h4>
+<div class="paragraph">
+<p>The texture gather functions take components of a single floating-point
+vector operand as a texture coordinate, determine a set of four texels to
+sample from the base level-of-detail of the specified texture image, and
+return one component from each texel in a four-component result vector.</p>
+</div>
+<div class="paragraph">
+<p>When performing a texture gather operation, the minification and
+magnification filters are ignored, and the rules for LINEAR filtering in the
+<a href="#references">OpenGL ES Specification</a> are applied to the base level of the texture image
+to identify the four texels <em>i<sub>0</sub> j<sub>1</sub></em>, <em>i<sub>1</sub> j<sub>1</sub></em>, <em>i<sub>1</sub> j<sub>0</sub></em>, and <em>i<sub>0</sub>
+j<sub>0</sub></em>.
+The texels are then converted to texture base colors (<em>R<sub>s</sub></em>, <em>G<sub>s</sub></em>,
+<em>B<sub>s</sub></em>, <em>A<sub>s</sub></em>) according to table 15.1, followed by application of the
+texture swizzle as described in section 15.2.1 &#8220;Texture Access&#8221; of the
+<a href="#references">OpenGL ES Specification</a>.
+A four-component vector is assembled by taking the selected component from
+each of the post-swizzled texture source colors in the order (<em>i<sub>0</sub> j<sub>1</sub></em>,
+<em>i<sub>1</sub> j<sub>1</sub></em>, <em>i<sub>1</sub> j<sub>0</sub></em>, <em>i<sub>0</sub> j<sub>0</sub></em>).</p>
+</div>
+<div class="paragraph">
+<p>The selected component is identified by the optional <em>comp</em> argument, where
+the values zero, one, two, and three identify the <em>R<sub>s</sub></em>, <em>G<sub>s</sub></em>, <em>B<sub>s</sub></em>, or
+<em>A<sub>s</sub></em> component, respectively.
+If <em>comp</em> is omitted, it is treated as identifying the <em>R<sub>s</sub></em> component.</p>
+</div>
+<div class="paragraph">
+<p>Incomplete textures (see section 8.16 &#8220;Texture Completeness&#8221; of the
+<a href="#references">OpenGL ES Specification</a>) return a texture source color of (0,0,0,1) for all
+four source texels.</p>
+</div>
+<div class="paragraph">
+<p>For texture gather functions using a shadow sampler type, each of the four
+texel lookups perform a depth comparison against the depth reference value
+passed in (<em>refZ</em>), and returns the result of that comparison in the
+appropriate component of the result vector.</p>
+</div>
+<div class="paragraph">
+<p>As with other texture lookup functions, the results of a texture gather are
+undefined for shadow samplers if the texture referenced is not a depth
+texture or has depth comparisons disabled; or for non-shadow samplers if the
+texture referenced is a depth texture with depth comparisons enabled.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>textureGatherOffset</strong> built-in functions from the OpenGL ES Shading Language return a vector
+derived from sampling four texels in the image array of level <em>level<sub>base</sub></em>.
+For each of the four texel offsets specified by the <em>offsets</em> argument, the
+rules for the LINEAR minification filter are applied to identify a 2 ×
+2 texel footprint, from which the single texel T<sub>i0j0</sub> is selected.
+A four-component vector is then assembled by taking a single component from
+each of the four T<sub>i0j0</sub> texels in the same manner as for the
+<strong>textureGather</strong> function.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGather</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em> [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em> [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em> [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em>[, int <em>comp</em>])<br>
+  vec4 <strong>textureGather</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(sampler2DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(samplerCubeShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(samplerCubeArrayShadow <em>sampler</em>, vec4 <em>P</em>, float <em>refZ</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns the value<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4(Sample_i0_j1(P, base).comp,
+     Sample_i1_j1(P, base).comp,
+     Sample_i1_j0(P, base).comp,
+     Sample_i0_j0(P, base).comp)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If specified, the value of <em>comp</em> must be a constant integer expression with
+a value of 0, 1, 2, or 3, identifying the <em>x</em>, <em>y</em>, <em>z</em>, or <em>w</em>
+post-swizzled component of the four-component vector lookup result for each
+texel, respectively.
+If <em>comp</em> is not specified, it is treated as 0, selecting the <em>x</em> component
+of each texel to generate the result.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGatherOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offset</em>, [ int <em>comp</em>])<br>
+  gvec4 <strong>textureGatherOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [ int <em>comp</em>])<br>
+  vec4 <strong>textureGatherOffset</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>, ivec2 <em>offset</em>)<br>
+  vec4 <strong>textureGatherOffset</strong>(sampler2DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>, ivec2 <em>offset</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Perform a texture gather operation as in <strong>textureGather</strong> by <em>offset</em>
+      as described in <strong>textureOffset</strong> except that the <em>offset</em> can be
+      variable (non constant) and the implementation-dependent minimum and
+      maximum offset values are given by MIN_PROGRAM_TEXTURE_GATHER_OFFSET
+      and MAX_PROGRAM_TEXTURE_GATHER_OFFSET, respectively.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGatherOffsets</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offsets</em>[4] [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGatherOffsets</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offsets</em>[4]   [, int <em>comp</em>])<br>
+  vec4 <strong>textureGatherOffsets</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>, ivec2 <em>offsets</em>[4])<br>
+  vec4 <strong>textureGatherOffsets</strong>(sampler2DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>, ivec2 <em>offsets</em>[4])<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Operate identically to <strong>textureGatherOffset</strong> except that <em>offsets</em> is
+      used to determine the location of the four texels to sample.
+      Each of the four texels is obtained by applying the corresponding
+      offset in <em>offsets</em> as a (<em>u</em>, <em>v</em>) coordinate offset to <em>P</em>,
+      identifying the four-texel LINEAR footprint, and then selecting the
+      texel <em>i<sub>0</sub> j<sub>0</sub></em> of that footprint.
+      The specified values in <em>offsets</em> must be constant integral
+      expressions.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect2">
+<h3 id="atomic-counter-functions">8.10. Atomic Counter Functions</h3>
+<div class="paragraph">
+<p>The atomic-counter operations in this section operate atomically with
+respect to each other.
+They are atomic for any single counter, meaning any of these operations on a
+specific counter in one shader instantiation will be indivisible by any of
+these operations on the same counter from another shader instantiation.
+There is no guarantee that these operations are atomic with respect to other
+forms of access to the counter or that they are serialized when applied to
+separate counters.
+Such cases would require additional use of fences, barriers, or other forms
+of synchronization, if atomicity or serialization is desired.</p>
+</div>
+<div class="paragraph">
+<p>The underlying counter is a 32-bit unsigned integer.
+The result of operations will wrap to [0, 2<sup>32</sup>-1].</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterIncrement</strong>(atomic_uint <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>increments the counter for <em>c</em>, and</p>
+</li>
+<li>
+<p>returns its value prior to the increment operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterDecrement</strong>(atomic_uint <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>decrements the counter for <em>c</em>, and</p>
+</li>
+<li>
+<p>returns the value resulting from the decrement operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounter</strong>(atomic_uint <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the counter value for <em>c</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="atomic-memory-functions">8.11. Atomic Memory Functions</h3>
+<div class="paragraph">
+<p>Atomic memory functions perform atomic operations on an individual signed or
+unsigned integer stored in buffer object or shared variable storage.
+All of the atomic memory operations read a value from memory, compute a new
+value using one of the operations described below, write the new value to
+memory, and return the original value read.
+The contents of the memory being updated by the atomic operation are
+guaranteed not to be modified by any other assignment or atomic memory
+function in any shader invocation between the time the original value is
+read and the time the new value is written.</p>
+</div>
+<div class="paragraph">
+<p>Atomic memory functions are supported only for a limited set of variables.
+A shader will fail to compile if the value passed to the <em>mem</em> argument of
+an atomic memory function does not correspond to a buffer or shared
+variable.
+It is acceptable to pass an element of an array or a single component of a
+vector to the <em>mem</em> argument of an atomic memory function, as long as the
+underlying array or vector is a buffer or shared variable.</p>
+</div>
+<div class="paragraph">
+<p>All the built-in functions in this section accept arguments with
+combinations of <strong>restrict</strong>, <strong>coherent</strong>, and <strong>volatile</strong> memory qualification,
+despite not having them listed in the prototypes.
+The atomic operation will operate as required by the calling argument&#8217;s
+memory qualification, not by the built-in function&#8217;s formal parameter memory
+qualification.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicAdd</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicAdd</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by adding the value of <em>data</em> to the contents
+      <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicMin</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicMin</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the minimum of the value of <em>data</em> and
+      the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicMax</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicMax</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the maximum of the value of <em>data</em> and
+      the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicAnd</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicAnd</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise AND of the value of
+      <em>data</em> and the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicOr</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicOr</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise OR of the value of
+      <em>data</em> and the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicXor</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicXor</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise EXCLUSIVE OR of the
+      value of <em>data</em> and the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicExchange</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicExchange</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by simply copying the value of <em>data</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCompSwap</strong>(inout uint <em>mem</em>, uint <em>compare</em>, uint <em>data</em>)<br>
+  int <strong>atomicCompSwap</strong>(inout int <em>mem</em>, int <em>compare</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Compares the value of <em>compare</em> and the contents of <em>mem</em>.
+      If the values are equal, the new value is given by <em>data</em>; otherwise,
+      it is taken from the original contents of <em>mem</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="image-functions">8.12. Image Functions</h3>
+<div class="paragraph">
+<p>Variables using one of the image basic types may be used by the built-in
+shader image memory functions defined in this section to read and write
+individual texels of a texture.
+Each image variable references an image unit, which has a texture image
+attached.</p>
+</div>
+<div class="paragraph">
+<p>When image memory functions below access memory, an individual texel in the
+image is identified using an (<em>i</em>), (<em>i, j</em>), or (<em>i, j, k</em>) coordinate
+corresponding to the values of <em>P</em>.
+The coordinates
+are used to select an individual texel in the manner described in section
+8.22
+&#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>Loads and stores support float, integer, and unsigned integer types.
+The data types below starting &#8220;_gimage_&#8221; serve as placeholders meaning
+types starting either &#8220;<strong>image</strong>&#8221;, &#8220;<strong>iimage</strong>&#8221;, or &#8220;<strong>uimage</strong>&#8221; in the same
+way as <em>gvec</em> or <em>gsampler</em> in earlier sections.</p>
+</div>
+<div class="paragraph">
+<p>The <em>IMAGE_PARAMS</em> in the prototypes below is a placeholder representing
+18
+separate functions, each for a different type of image variable.
+The <em>IMAGE_PARAMS</em> placeholder is replaced by one of the following parameter
+lists:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2D <em>image</em>, ivec2 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage3D <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimageCube <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimageBuffer <em>image</em>, int <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2DArray <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimageCubeArray <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>where each of the lines represents one of three different image variable
+types, and <em>image</em>,
+<em>P</em>
+specify the individual texel to operate on.
+The method for identifying the individual texel operated on from <em>image</em>,
+<em>P</em>,
+and the method for reading and writing the texel are specified in section
+8.22
+&#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL ES Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>The atomic functions perform operations on individual texels or samples of
+an image variable.
+Atomic memory operations read a value from the selected texel, compute a new
+value using one of the operations described below, write the new value to
+the selected texel, and return the original value read.
+The contents of the texel being updated by the atomic operation are
+guaranteed not to be modified by any other image store or atomic function
+between the time the original value is read and the time the new value is
+written.</p>
+</div>
+<div class="paragraph">
+<p>Atomic memory operations are supported on only a subset of all image
+variable types; <em>image</em> must be either:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>a signed integer image variable (type starts &#8220;<strong>iimage</strong>&#8221;) and a format
+qualifier of <strong>r32i</strong>, used with a <em>data</em> argument of type <strong>int</strong>, or</p>
+</li>
+<li>
+<p>an unsigned integer image variable (type starts &#8220;<strong>uimage</strong>&#8221;) and a
+format qualifier of <strong>r32ui</strong>, used with a <em>data</em> argument of type <strong>uint</strong>,
+or</p>
+</li>
+<li>
+<p>a float image variable (type starts &#8220;<strong>image</strong>&#8221;) and a format qualifier
+of <strong>r32f</strong>, used with a <em>data</em> argument of type <strong>float</strong>
+(<strong>imageAtomicExchange</strong> only).</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>All the built-in functions in this section accept arguments with
+combinations of <strong>restrict</strong>, <strong>coherent</strong>, and <strong>volatile</strong> memory qualification,
+despite not having them listed in the prototypes.
+The image operation will operate as required by the calling argument&#8217;s
+memory qualification, not by the built-in function&#8217;s formal parameter memory
+qualification.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp ivec2 <strong>imageSize</strong>(readonly writeonly gimage2D <em>image</em>)<br>
+  highp ivec3 <strong>imageSize</strong>(readonly writeonly gimage3D <em>image</em>)<br>
+  highp ivec2 <strong>imageSize</strong>(readonly writeonly gimageCube <em>image</em>)<br>
+  highp ivec3 <strong>imageSize</strong>(readonly writeonly gimageCubeArray <em>image</em>)<br>
+  highp ivec3 <strong>imageSize</strong>(readonly writeonly gimage2DArray <em>image</em>)<br>
+  highp   int <strong>imageSize</strong>(readonly writeonly gimageBuffer <em>image</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the dimensions of the image or images bound to <em>image</em>.
+      For arrayed images, the last component of the return value will hold
+      the size of the array.
+      Cube images only return the dimensions of one face, and the number of
+      cubes in the cube map array, if arrayed.<br>
+      Note: The qualification <strong>readonly writeonly</strong> accepts a variable
+      qualified with <strong>readonly</strong>, <strong>writeonly</strong>, both, or neither.
+      It means the formal argument will be used for neither reading nor
+      writing to the underlying memory.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp gvec4 <strong>imageLoad</strong>(readonly <em>IMAGE_PARAMS</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Loads the texel at the coordinate <em>P</em> from the image unit <em>image</em> (in
+      <em>IMAGE_PARAMS</em>).
+      When <em>image</em> and <em>P</em>
+      identify a valid texel, the bits used to represent the selected texel in
+      memory are converted to a <strong>vec4</strong>, <strong>ivec4</strong>, or <strong>uvec4</strong> in the manner
+      described in section
+8.23
+      &#8220;Texture Image Loads and Stores&#8221; of the
+      <a href="#references">OpenGL ES Specification</a> and returned.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>imageStore</strong>(writeonly <em>IMAGE_PARAMS</em>, gvec4 <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Stores <em>data</em> into the texel at the coordinate <em>P</em> from the image
+      specified by <em>image</em>.
+      When <em>image</em> and <em>P</em>
+      identify a valid texel, the bits used to represent <em>data</em> are converted
+      to the format of the image unit in the manner described in section
+8.23
+      &#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL ES Specification</a>
+      and stored to the specified texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicAdd</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicAdd</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by adding the value of <em>data</em> to the contents of
+      the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicMin</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicMin</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the minimum of the value of <em>data</em> and
+      the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicMax</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicMax</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the maximum of the value <em>data</em> and the
+      contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicAnd</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicAnd</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise AND of the value of
+      <em>data</em> and the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicOr</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicOr</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise OR of the value of
+      <em>data</em> and the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicXor</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicXor</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise EXCLUSIVE OR of the
+      value of <em>data</em> and the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicExchange</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicExchange</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)<br>
+  highp float <strong>imageAtomicExchange</strong>(<em>IMAGE_PARAMS</em>, float <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by simply copying the value of <em>data</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">highp uint <strong>imageAtomicCompSwap</strong>(<em>IMAGE_PARAMS</em>, uint <em>compare</em>, uint <em>data</em>)<br>
+  highp int <strong>imageAtomicCompSwap</strong>(<em>IMAGE_PARAMS</em>, int <em>compare</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Compares the value of <em>compare</em> and the contents of the selected
+      texel.
+      If the values are equal, the new value is given by <em>data</em>; otherwise,
+      it is taken from the original value loaded from the texel.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="geometry-shader-functions">8.13. Geometry Shader Functions</h3>
+<div class="paragraph">
+<p>These functions are only available in geometry shaders.
+They are described in more depth following the table.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>EmitVertex</strong>()<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Emits the current values of output variables to the current output
+      primitive.
+      On return from this call, the values of output variables are
+      undefined.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>EndPrimitive</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Completes the current output primitive and starts a new one.
+      No vertex is emitted.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The function <strong>EmitVertex</strong>() specifies that a vertex is completed.
+A vertex is added to the current output primitive using the current values
+of all built-in and user-defined output variables.
+The values of all output variables are undefined after a call to
+<strong>EmitVertex</strong>().
+If a geometry shader invocation has emitted more vertices than permitted by
+the output layout qualifier <strong>max_vertices</strong>, the results of calling
+<strong>EmitVertex</strong>() are undefined.</p>
+</div>
+<div class="paragraph">
+<p>The function <strong>EndPrimitive</strong>() specifies that the current output primitive is
+completed and a new output primitive (of the same type) will be started by
+any subsequent <strong>EmitVertex</strong>().
+This function does not emit a vertex.
+If the output layout is declared to be <strong>points</strong>, calling <strong>EndPrimitive</strong>() is
+optional.</p>
+</div>
+<div class="paragraph">
+<p>A geometry shader starts with an output primitive containing no vertices.
+When a geometry shader terminates, the current output primitive is
+automatically completed.
+It is not necessary to call <strong>EndPrimitive</strong>() if the geometry shader writes
+only a single primitive.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="fragment-processing-functions">8.14. Fragment Processing Functions</h3>
+<div class="paragraph">
+<p>Fragment processing functions are only available in fragment shaders.</p>
+</div>
+<div class="sect3">
+<h4 id="derivative-functions">8.14.1. Derivative Functions</h4>
+<div class="paragraph">
+<p>Derivatives may be computationally expensive and/or numerically unstable.
+Therefore, an OpenGL ES implementation may approximate the true derivatives
+by using a fast but not entirely accurate derivative computation.
+Derivatives are undefined within non-uniform control flow.</p>
+</div>
+<div class="paragraph">
+<p>The expected behavior of a derivative is specified using forward/backward
+differencing.</p>
+</div>
+<div class="paragraph">
+<p>Forward differencing:</p>
+</div>
+<div class="paragraph">
+<p>\(F(x+dx) - F(x) \sim dFdx(x) \cdot dx (1a)\)</p>
+</div>
+<div class="paragraph">
+<p>\(dFdx(x) \sim \frac{F(x+dx) - F(x)}{dx} (1b)\)</p>
+</div>
+<div class="paragraph">
+<p>Backward differencing:</p>
+</div>
+<div class="paragraph">
+<p>\(F(x-dx) - F(x) \sim -dFdx(x) \cdot dx (2a)\)</p>
+</div>
+<div class="paragraph">
+<p>\(dFdx(x) \sim \frac{F(x) - F(x-dx)}{dx} (2b)\)</p>
+</div>
+<div class="paragraph">
+<p>With single-sample rasterization, \(dx \leq 1.0\) in equations 1b
+and 2b.
+For multisample rasterization, \(dx &lt; 2.0\) in equations 1b and 2b.</p>
+</div>
+<div class="paragraph">
+<p>\(dFdy\) is approximated similarly, with <em>y</em> replacing <em>x</em>.</p>
+</div>
+<div class="paragraph">
+<p>An OpenGL ES implementation may use the above or other methods to perform
+the calculation, subject to the following conditions:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>The method may use piecewise linear approximations.
+Such linear approximations imply that higher order derivatives,
+<strong>dFdx</strong>(<strong>dFdx</strong>(<em>x</em>)) and above, are undefined.</p>
+</li>
+<li>
+<p>The method may assume that the function evaluated is continuous.
+Therefore derivatives within the body of a non-uniform conditional are
+undefined.</p>
+</li>
+<li>
+<p>The method may differ per fragment, subject to the constraint that the
+method may vary by window coordinates, not screen coordinates.
+The invariance requirement described in section 13.2 &#8220;Invariance&#8221; of
+the <a href="#references">OpenGL ES Specification</a>, is relaxed for derivative calculations,
+because the method may be a function of fragment location.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Other properties that are desirable, but not required, are:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>Functions should be evaluated within the interior of a primitive
+(interpolated, not extrapolated).</p>
+</li>
+<li>
+<p>Functions for <strong>dFdx</strong> should be evaluated while holding <em>y</em> constant.
+Functions for <strong>dFdy</strong> should be evaluated while holding <em>x</em> constant.
+However, mixed higher order derivatives, like <strong>dFdx</strong>(<strong>dFdy</strong>(<em>y</em>)) and
+<strong>dFdy</strong>(<strong>dFdx</strong>(<em>x</em>)) are undefined.</p>
+</li>
+<li>
+<p>Derivatives of constant arguments should be 0.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>In some implementations, varying degrees of derivative accuracy may be
+obtained by providing GL hints (see section 19.1 &#8220;Hints&#8221; of the
+<a href="#references">OpenGL ES Specification</a>), allowing a user to make an image quality versus
+speed trade off.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdx</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the derivative in x using local differencing for the input
+      argument <em>p</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdy</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the derivative in y using local differencing for the input
+      argument <em>p</em>.<br>
+      <br>
+      These two functions are commonly used to estimate the filter width used
+      to anti-alias procedural textures. We are assuming that the expression
+      is being evaluated in parallel on a SIMD array so that at any given
+      point in time the value of the function is known at the grid points
+      represented by the SIMD array. Local differencing between SIMD array
+      elements can therefore be used to derive <strong>dFdx</strong>, <strong>dFdy</strong>, etc.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fwidth</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the sum of the absolute derivative in x and y using local
+      differencing for the input argument <em>p</em>, i.e., <strong>abs</strong>(<strong>dFdx</strong>(<em>p</em>))
+      + <strong>abs</strong>(<strong>dFdy</strong>(<em>p</em>));</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="interpolation-functions">8.14.2. Interpolation Functions</h4>
+<div class="paragraph">
+<p>Built-in interpolation functions are available to compute an interpolated
+value of a fragment shader input variable at a shader-specified (<em>x</em>, <em>y</em>)
+location.
+A separate (<em>x</em>, <em>y</em>) location may be used for each invocation of the
+built-in function, and those locations may differ from the default (<em>x</em>,
+<em>y</em>) location used to produce the default value of the input.
+For the <strong>interpolateAt*</strong> functions, the call will return a precision
+qualification matching the precision of the <em>interpolant</em> argument to the
+function call.</p>
+</div>
+<div class="paragraph">
+<p>For all of the interpolation functions, <em>interpolant</em> must be an l-value
+from an <strong>in</strong> declaration;
+this can be either a variable, or an array element.
+Component selection operators (e.g. <strong>.xy</strong>) may not be used when specifying <em>interpolant</em>.</p>
+</div>
+<div class="paragraph">
+<p>If <em>interpolant</em> is declared with the <strong>flat</strong> qualifier, the interpolated
+value will have the same value everywhere for a single primitive, so the
+location used for interpolation has no effect and the functions just return
+that same value.
+If <em>interpolant</em> is declared with the <strong>centroid</strong> qualifier, the value
+returned by <strong>interpolateAtSample</strong>() and <strong>interpolateAtOffset</strong>() will be
+evaluated at the specified location, ignoring the location normally used
+with the <strong>centroid</strong> qualifier.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>interpolateAtCentroid</strong>(float <em>interpolant</em>)<br>
+  vec2 <strong>interpolateAtCentroid</strong>(vec2 <em>interpolant</em>)<br>
+  vec3 <strong>interpolateAtCentroid</strong>(vec3 <em>interpolant</em>)<br>
+  vec4 <strong>interpolateAtCentroid</strong>(vec4 <em>interpolant</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the value of the input <em>interpolant</em> sampled at a location
+      inside both the pixel and the primitive being processed.
+      The value obtained would be the same value assigned to the input
+      variable if declared with the <strong>centroid</strong> qualifier.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>interpolateAtSample</strong>(float <em>interpolant</em>, int <em>sample</em>)<br>
+  vec2 <strong>interpolateAtSample</strong>(vec2 <em>interpolant</em>, int <em>sample</em>)<br>
+  vec3 <strong>interpolateAtSample</strong>(vec3 <em>interpolant</em>, int <em>sample</em>)<br>
+  vec4 <strong>interpolateAtSample</strong>(vec4 <em>interpolant</em>, int <em>sample</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the value of the input <em>interpolant</em> variable at the location
+      of sample number <em>sample</em>.
+      If multisample buffers are not available, the input variable will be
+      evaluated at the center of the pixel.
+      If sample <em>sample</em> does not exist, the position used to interpolate
+      the input variable is undefined.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>interpolateAtOffset</strong>(float <em>interpolant</em>, vec2 offset)<br>
+  vec2 <strong>interpolateAtOffset</strong>(vec2 <em>interpolant</em>, vec2 offset)<br>
+  vec3 <strong>interpolateAtOffset</strong>(vec3 <em>interpolant</em>, vec2 offset)<br>
+  vec4 <strong>interpolateAtOffset</strong>(vec4 <em>interpolant</em>, vec2 offset)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the value of the input <em>interpolant</em> variable sampled at an
+      offset from the center of the pixel specified by <em>offset</em>.
+      The two floating-point components of <em>offset</em>, give the offset in
+      pixels in the <em>x</em> and <em>y</em> directions, respectively.<br>
+      An offset of (0, 0) identifies the center of the pixel.
+      The range and granularity of offsets supported by this function is
+      implementation-dependent.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect2">
+<h3 id="shader-invocation-control-functions">8.15. Shader Invocation Control Functions</h3>
+<div class="paragraph">
+<p>The shader invocation control function is only available in tessellation
+control and compute shaders.
+It is used to control the relative execution order of multiple shader
+invocations used to process a patch (in the case of tessellation control
+shaders) or a workgroup (in the case of compute shaders), which are
+otherwise executed with an undefined relative order.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>barrier</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">For any given static instance of <strong>barrier</strong>(), all tessellation control
+      shader invocations for a single input patch must enter it before any
+      will be allowed to continue beyond it, or all compute shader
+      invocations for a single workgroup must enter it before any will
+      continue beyond it.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The function <strong>barrier</strong>() provides a partially defined order of execution
+between shader invocations.
+The ensures that, for some types of memory accesses, values written by one
+invocation prior to a given static instance of <strong>barrier</strong>() can be safely read
+by other invocations after their call to the same static instance <strong>barrier</strong>().
+Because invocations may execute in an undefined order between these barrier
+calls, the values of a per-vertex or per-patch output variable for tessellation
+control shaders, or the values of <strong>shared</strong> variables for compute shaders will be
+undefined in a number of cases enumerated in
+&#8220;<a href="#output-variables">Output Variables</a>&#8221; (for tessellation control shaders)
+and &#8220;<a href="#shared-variables">Shared Variables</a>&#8221; (for compute shaders).</p>
+</div>
+<div class="paragraph">
+<p>For tessellation control shaders, the <strong>barrier</strong>() function may only be
+placed inside the function <strong>main</strong>() of the shader and may not be called
+within any control flow.
+Barriers are also disallowed after a return statement in the function
+<strong>main</strong>().
+Any such misplaced barriers result in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>A <strong>barrier</strong>() affects control flow but only synchronizes memory accesses
+to <strong>shared</strong> variables and tessellation control output variables.
+For other memory accesses, it does not ensure that values written by one invocation
+prior to a given static instance of <strong>barrier</strong>() can be safely read by other
+invocations after their call to the same static instance of <strong>barrier</strong>().
+To achieve this requires the use of both <strong>barrier</strong>() and a memory barrier.</p>
+</div>
+<div class="paragraph">
+<p>For compute shaders, the <strong>barrier</strong>() function may be placed within control
+flow, but that control flow must be uniform control flow.
+That is, all the controlling expressions that lead to execution of the
+barrier must be dynamically uniform expressions.
+This ensures that if any shader invocation enters a conditional statement,
+then all invocations will enter it.
+While compilers are encouraged to give warnings if they can detect this
+might not happen, compilers cannot completely determine this.
+Hence, it is the author&#8217;s responsibility to ensure <strong>barrier</strong>() only exists
+inside uniform control flow.
+Otherwise, some shader invocations will stall indefinitely, waiting for a
+barrier that is never reached by other invocations.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="shader-memory-control-functions">8.16. Shader Memory Control Functions</h3>
+<div class="paragraph">
+<p>Within a single shader invocation, the visibility and order of writes made
+by that invocation are well-defined.
+However, the relative order of reads and writes to a single shared memory
+address from multiple separate shader invocations is largely undefined.
+Additionally, the order of accesses to multiple memory addresses performed
+by a single shader invocation, as observed by other shader invocations, is
+also undefined.</p>
+</div>
+<div class="paragraph">
+<p>The following built-in functions can be used to control the ordering of
+reads and writes:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrier</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions issued by a single shader
+      invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierAtomicCounter</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of accesses to atomic-counter variables issued by
+      a single shader invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierBuffer</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions to buffer variables issued
+      within a single shader invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierShared</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions to shared variables issued
+      within a single shader invocation, as viewed by other invocations in
+      the same workgroup.<br>
+      Only available in compute shaders.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierImage</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions to images issued within a
+      single shader invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>groupMemoryBarrier</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of all memory transactions issued within a single
+      shader invocation, as viewed by other invocations in the same workgroup.<br>
+      Only available in compute shaders.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The memory barrier built-in functions can be used to order reads and writes
+to variables stored in memory accessible to other shader invocations.
+When called, these functions will wait for the completion of all reads and
+writes previously performed by the caller that access selected variable
+types, and then return with no other effect.
+The built-in functions <strong>memoryBarrierAtomicCounter</strong>(),
+<strong>memoryBarrierBuffer</strong>(), <strong>memoryBarrierImage</strong>(), and <strong>memoryBarrierShared</strong>()
+wait for the completion of accesses to atomic counter, buffer, image, and
+shared variables, respectively.
+The built-in functions <strong>memoryBarrier</strong>() and <strong>groupMemoryBarrier</strong>() wait for
+the completion of accesses to all of the above variable types.
+The functions <strong>memoryBarrierShared</strong>() and <strong>groupMemoryBarrier</strong>() are
+available only in compute shaders; the other functions are available in all
+shader types.</p>
+</div>
+<div class="paragraph">
+<p>When these functions return, the effects of any memory stores performed
+using coherent variables prior to the call will be visible to any
+future<sup>1</sup> coherent access to the same memory performed by any other shader
+invocation.
+In particular, the values written this way in one shader stage are
+guaranteed to be visible to coherent memory accesses performed by shader
+invocations in subsequent stages when those invocations were triggered by
+the execution of the original shader invocation (e.g. fragment shader
+invocations for a primitive resulting from a particular geometry
+shader invocation).</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">1</dt>
+<dd>
+<p>An access is only a <em>future</em> access if a <em>happens-before</em> relation can
+be established between the store and the load.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Additionally, memory barrier functions order stores performed by the calling
+invocation, as observed by other shader invocations.
+Without memory barriers, if one shader invocation performs two stores to
+coherent variables, a second shader invocation might see the values written
+by the second store prior to seeing those written by the first.
+However, if the first shader invocation calls a memory barrier function
+between the two stores, selected other shader invocations will never see the
+results of the second store before seeing those of the first.
+When using the functions <strong>groupMemoryBarrier</strong>() or <strong>memoryBarrierShared</strong>(),
+this ordering guarantee applies only to other shader invocations in the same
+compute shader workgroup; all other memory barrier functions provide the
+guarantee to all other shader invocations.
+No memory barrier is required to guarantee the order of memory stores as
+observed by the invocation performing the stores; an invocation reading from
+a variable that it previously wrote will always see the most recently
+written value unless another shader invocation also wrote to the same
+memory.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="shader-interface-matching">9. Shader Interface Matching</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>As described in chapter 7 of the <a href="#references">OpenGL ES Specification</a>, shaders may be
+linked together to form a <em>program object</em> before being bound to the
+pipeline or may be linked and bound individually as <em>separable program
+objects</em>.</p>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="title">Note</div>
+<div class="paragraph">
+<p>These were previously known as separate shader objects (SSOs) but the
+mechanism has been extended to support future versions of the specification
+that have more than two shader stages.
+It allows a subset of the shaders to be linked together.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="paragraph">
+<p>Within a <em>program object</em> or a <em>separable program object</em>, qualifiers for
+matching variables must themselves match according to the rules specified in
+this section.
+There are also matching rules for qualifiers of matching variables between
+separable program objects but only for variables across an input/output
+boundary between shader stages.
+For other shader interface variables such as uniforms, each program object
+or separable program object has its own name space and so the same name can
+refer to multiple independent variables.
+Consequently, there are no matching rules for qualifiers in these cases.</p>
+</div>
+<div class="sect2">
+<h3 id="input-output-matching-by-name-in-linked-programs">9.1. Input Output Matching by Name in Linked Programs</h3>
+<div class="paragraph">
+<p>When linking shaders, the type of declared vertex outputs and fragment
+inputs with the same name must match, otherwise the link command will fail.
+Only those fragment inputs statically used (i.e. read) in the fragment
+shader must be declared as outputs in the vertex shader; declaring
+superfluous vertex shader outputs is permissible.</p>
+</div>
+<div class="paragraph">
+<p>The following table summarizes the rules for matching shader outputs to
+shader inputs in consecutive stages when shaders are linked together.</p>
+</div>
+<table class="tableblock frame-all grid-all fit-content">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top" colspan="2" rowspan="2"><p class="tableblock">Treatment of Mismatched Input Variables</p></td>
+<td class="tableblock halign-left valign-top" colspan="3"><p class="tableblock">Consuming Shader (input variables)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No Declaration</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declared but no Static Use</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declared and Static Use</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top" rowspan="3"><p class="tableblock">Generating Shader (output variables)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No Declaration</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">error</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declares; no static Use</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed (values are undefined)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declares and static Use</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed (values are potentially undefined)</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>See &#8220;<a href="#static-use">Static Use</a>&#8221; for the definition of <em>static use</em>.</p>
+</div>
+<div class="paragraph">
+<p>The precision of a vertex output does not need to match the precision of the
+corresponding fragment input.
+The minimum precision at which vertex outputs are interpolated is the
+minimum of the vertex output precision and the fragment input precision,
+with the exception that for <strong>highp</strong>, implementations do not have to support
+full IEEE 754 precision.</p>
+</div>
+<div class="paragraph">
+<p>The precision of values exported to a transform feedback buffer is the
+precision of the outputs of the vertex shader.
+However, they are converted to <strong>highp</strong> format before being written.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="matching-of-qualifiers">9.2. Matching of Qualifiers</h3>
+<div class="paragraph">
+<p>The following tables summarize the requirements for matching of qualifiers.
+It applies whenever there are two or more matching variables in a shader
+interface.</p>
+</div>
+<div class="paragraph">
+<p>Notes:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p><em>Yes</em> means the qualifiers must match.</p>
+</li>
+<li>
+<p><em>No</em> means the qualifiers do not need to match.</p>
+</li>
+<li>
+<p><em>Consistent</em> means qualifiers may be missing from a subset of
+declarations but they cannot conflict</p>
+</li>
+<li>
+<p>If there are conflicting qualifiers, only the last of these is
+significant.</p>
+</li>
+<li>
+<p>Matching is based only on the resulting qualification, not on the
+presence or otherwise of qualifiers.</p>
+</li>
+<li>
+<p>The rules apply to all declared variables, irrespective of whether they
+are statically used, with the exception of inputs and outputs when
+shaders are linked (see
+&#8220;<a href="#input-output-matching-by-name-in-linked-programs">Input Output
+Matching by Name in Linked Programs</a>&#8221;).</p>
+</li>
+<li>
+<p>Errors are generated for any conflicts.</p>
+</li>
+</ol>
+</div>
+<div class="sect3">
+<h4 id="linked-shaders">9.2.1. Linked Shaders</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.667%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier Class</th>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top"><strong>in</strong>/<strong>out</strong></th>
+<th class="tableblock halign-left valign-top">Default Uniforms</th>
+<th class="tableblock halign-left valign-top"><strong>uniform</strong> Block</th>
+<th class="tableblock halign-left valign-top"><strong>buffer</strong> Block</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Storage<sup>1</sup></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>in</strong><br>
+                    <strong>out</strong><br>
+                    <strong>uniform</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top" rowspan="2"><p class="tableblock">Auxiliary</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>centroid</strong><br>
+                    <strong>sample</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>patch</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top" rowspan="5"><p class="tableblock">Layout</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>location</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes<sup>2</sup></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Consistent</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Block layout<sup>3,4</sup></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>binding</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Consistent</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>offset</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">format</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Interpolation</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>smooth</strong><br>
+                    <strong>flat</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Precision</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lowp</strong><br>
+                    <strong>mediump</strong><br>
+                    <strong>highp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Variance</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>invariant</strong><br>
+                    <strong>precise</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Memory</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">all</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+</tbody>
+</table>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">1</dt>
+<dd>
+<p>Storage qualifiers determine <em>when</em> variables match rather than being
+<em>required</em> to match for matching variables.
+Note also that each shader interface has a separate name space so for
+example, it is possible to use the same name for a vertex output and
+fragment uniform.</p>
+</dd>
+<dt class="hdlist1">2</dt>
+<dd>
+<p>If present, the <strong>location</strong> qualifier determines the matching of inputs
+and outputs.
+See section 7.4.1 &#8220;Shader interface Matching&#8221; of the
+<a href="#references">OpenGL ES Specification</a> for details.]</p>
+</dd>
+<dt class="hdlist1">3</dt>
+<dd>
+<p>The <strong>row_major</strong> and <strong>column_major</strong> layout qualifiers do not need to
+match when applied to non-matrix types.</p>
+</dd>
+<dt class="hdlist1">4</dt>
+<dd>
+<p>In cases where a layout qualifier overrides a previous layout qualifier
+or a default, only the resulting qualification must match.</p>
+</dd>
+</dl>
+</div>
+</div>
+<div class="sect3">
+<h4 id="separable-programs">9.2.2. Separable Programs</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 33.3333%;">
+<col style="width: 33.3333%;">
+<col style="width: 33.3334%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier Class</th>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top"><strong>in</strong>/<strong>out</strong></th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Storage</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>in</strong><br>
+                    <strong>out</strong><br>
+                    <strong>uniform</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top" rowspan="2"><p class="tableblock">Auxiliary</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>centroid</strong><br>
+                    <strong>sample</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>patch</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top" rowspan="5"><p class="tableblock">Layout</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>location</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Block layout</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>binding</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>offset</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">format</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Interpolation</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>smooth</strong><br>
+                    <strong>flat</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Precision</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lowp</strong><br>
+                    <strong>mediump</strong><br>
+                    <strong>highp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Yes</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Variance</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>invariant</strong><br>
+                    <strong>precise</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Memory</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">all</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">N/A</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="shading-language-grammar">10. Shading Language Grammar</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The grammar is fed from the output of lexical analysis.
+The tokens returned from lexical analysis are</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">CONST BOOL FLOAT INT UINT
+
+BVEC2 BVEC3 BVEC4 IVEC2 IVEC3 IVEC4 UVEC2 UVEC3 UVEC4 VEC2 VEC3 VEC4
+
+MAT2 MAT3 MAT4 CENTROID IN OUT INOUT
+
+UNIFORM PATCH SAMPLE BUFFER SHARED
+
+COHERENT VOLATILE RESTRICT READONLY WRITEONLY
+
+FLAT SMOOTH LAYOUT
+
+MAT2X2 MAT2X3 MAT2X4
+
+MAT3X2 MAT3X3 MAT3X4
+
+MAT4X2 MAT4X3 MAT4X4
+
+
+
+
+
+ATOMIC_UINT
+
+SAMPLER2D SAMPLER3D SAMPLERCUBE SAMPLER2DSHADOW
+
+SAMPLERCUBESHADOW SAMPLER2DARRAY SAMPLER2DARRAYSHADOW
+
+ISAMPLER2D ISAMPLER3D ISAMPLERCUBE ISAMPLER2DARRAY
+
+USAMPLER2D USAMPLER3D USAMPLERCUBE USAMPLER2DARRAY
+
+
+
+
+
+
+SAMPLERBUFFER ISAMPLERBUFFER USAMPLERBUFFER
+
+SAMPLERCUBEARRAY SAMPLERCUBEARRAYSHADOW
+
+ISAMPLERCUBEARRAY USAMPLERCUBEARRAY
+
+SAMPLER2DMS ISAMPLER2DMS USAMPLER2DMS
+
+SAMPLER2DMSARRAY ISAMPLER2DMSARRAY USAMPLER2DMSARRAY
+
+IMAGE2D IIMAGE2D UIMAGE2D
+
+IMAGE3D IIMAGE3D UIMAGE3D
+
+IMAGECUBE IIMAGECUBE UIMAGECUBE
+
+IMAGEBUFFER IIMAGEBUFFER UIMAGEBUFFER
+
+IMAGE2DARRAY IIMAGE2DARRAY UIMAGE2DARRAY
+
+IMAGECUBEARRAY IIMAGECUBEARRAY UIMAGECUBEARRAY
+
+
+
+
+
+
+STRUCT VOID
+
+WHILE BREAK CONTINUE DO ELSE FOR IF DISCARD RETURN SWITCH CASE DEFAULT
+
+IDENTIFIER TYPE_NAME
+
+FLOATCONSTANT INTCONSTANT UINTCONSTANT BOOLCONSTANT
+
+FIELD_SELECTION
+
+LEFT_OP RIGHT_OP
+
+INC_OP DEC_OP LE_OP GE_OP EQ_OP NE_OP
+
+AND_OP OR_OP XOR_OP MUL_ASSIGN DIV_ASSIGN ADD_ASSIGN
+
+MOD_ASSIGN LEFT_ASSIGN RIGHT_ASSIGN AND_ASSIGN XOR_ASSIGN OR_ASSIGN
+
+SUB_ASSIGN
+
+LEFT_PAREN RIGHT_PAREN LEFT_BRACKET RIGHT_BRACKET LEFT_BRACE RIGHT_BRACE DOT
+
+COMMA COLON EQUAL SEMICOLON BANG DASH TILDE PLUS STAR SLASH PERCENT
+
+LEFT_ANGLE RIGHT_ANGLE VERTICAL_BAR CARET AMPERSAND QUESTION
+
+INVARIANT PRECISE
+
+HIGH_PRECISION MEDIUM_PRECISION LOW_PRECISION PRECISION</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The following describes the grammar for the OpenGL ES Shading Language in terms of the above
+tokens.
+The starting rule is <em>translation_unit</em>.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>variable_identifier</em> : </dt>
+<dd>
+<p><em>IDENTIFIER</em></p>
+</dd>
+<dt class="hdlist1"><em>primary_expression</em> : </dt>
+<dd>
+<p><em>variable_identifier</em><br>
+<em>INTCONSTANT</em><br>
+<em>UINTCONSTANT</em><br>
+<em>FLOATCONSTANT</em><br>
+<em>BOOLCONSTANT</em><br>
+<em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>postfix_expression</em> : </dt>
+<dd>
+<p><em>primary_expression</em><br>
+<em>postfix_expression</em> <em>LEFT_BRACKET</em> <em>integer_expression</em> <em>RIGHT_BRACKET</em><br>
+<em>function_call</em><br>
+<em>postfix_expression</em> <em>DOT</em> <em>FIELD_SELECTION</em><br>
+<em>postfix_expression</em> <em>INC_OP</em><br>
+<em>postfix_expression</em> <em>DEC_OP</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>FIELD_SELECTION includes members in structures, component selection for
+vectors and the 'length' identifier for the length() method</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>integer_expression</em> : </dt>
+<dd>
+<p><em>expression</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call</em> : </dt>
+<dd>
+<p><em>function_call_or_method</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_or_method</em> : </dt>
+<dd>
+<p><em>function_call_generic</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_generic</em> : </dt>
+<dd>
+<p><em>function_call_header_with_parameters</em> <em>RIGHT_PAREN</em><br>
+<em>function_call_header_no_parameters</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_header_no_parameters</em> : </dt>
+<dd>
+<p><em>function_call_header</em> <em>VOID</em><br>
+<em>function_call_header</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_header_with_parameters</em> : </dt>
+<dd>
+<p><em>function_call_header</em> <em>assignment_expression</em><br>
+<em>function_call_header_with_parameters</em> <em>COMMA</em> <em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_header</em> : </dt>
+<dd>
+<p><em>function_identifier</em> <em>LEFT_PAREN</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: Constructors look like functions, but lexical analysis
+recognized most of them as keywords.
+They are now recognized through <em>type_specifier</em>.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Methods (<strong>.length</strong>) and identifiers are recognized through
+<em>postfix_expression</em>.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>function_identifier</em> : </dt>
+<dd>
+<p><em>type_specifier</em><br>
+<em>postfix_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>unary_expression</em> : </dt>
+<dd>
+<p><em>postfix_expression</em><br>
+<em>INC_OP</em> <em>unary_expression</em><br>
+<em>DEC_OP</em> <em>unary_expression</em><br>
+<em>unary_operator</em> <em>unary_expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No traditional style type casts.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>unary_operator</em> : </dt>
+<dd>
+<p><em>PLUS</em><br>
+<em>DASH</em><br>
+<em>BANG</em><br>
+<em>TILDE</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No '*' or '&amp;' unary ops.
+Pointers are not supported.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>multiplicative_expression</em> : </dt>
+<dd>
+<p><em>unary_expression</em><br>
+<em>multiplicative_expression</em> <em>STAR</em> <em>unary_expression</em><br>
+<em>multiplicative_expression</em> <em>SLASH</em> <em>unary_expression</em><br>
+<em>multiplicative_expression</em> <em>PERCENT</em> <em>unary_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>additive_expression</em> : </dt>
+<dd>
+<p><em>multiplicative_expression</em><br>
+<em>additive_expression</em> <em>PLUS</em> <em>multiplicative_expression</em><br>
+<em>additive_expression</em> <em>DASH</em> <em>multiplicative_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>shift_expression</em> : </dt>
+<dd>
+<p><em>additive_expression</em><br>
+<em>shift_expression</em> <em>LEFT_OP</em> <em>additive_expression</em><br>
+<em>shift_expression</em> <em>RIGHT_OP</em> <em>additive_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>relational_expression</em> : </dt>
+<dd>
+<p><em>shift_expression</em><br>
+<em>relational_expression</em> <em>LEFT_ANGLE</em> <em>shift_expression</em><br>
+<em>relational_expression</em> <em>RIGHT_ANGLE</em> <em>shift_expression</em><br>
+<em>relational_expression</em> <em>LE_OP</em> <em>shift_expression</em><br>
+<em>relational_expression</em> <em>GE_OP</em> <em>shift_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>equality_expression</em> : </dt>
+<dd>
+<p><em>relational_expression</em><br>
+<em>equality_expression</em> <em>EQ_OP</em> <em>relational_expression</em><br>
+<em>equality_expression</em> <em>NE_OP</em> <em>relational_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>and_expression</em> : </dt>
+<dd>
+<p><em>equality_expression</em><br>
+<em>and_expression</em> <em>AMPERSAND</em> <em>equality_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>exclusive_or_expression</em> : </dt>
+<dd>
+<p><em>and_expression</em><br>
+<em>exclusive_or_expression</em> <em>CARET</em> <em>and_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>inclusive_or_expression</em> : </dt>
+<dd>
+<p><em>exclusive_or_expression</em><br>
+<em>inclusive_or_expression</em> <em>VERTICAL_BAR</em> <em>exclusive_or_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>logical_and_expression</em> : </dt>
+<dd>
+<p><em>inclusive_or_expression</em><br>
+<em>logical_and_expression</em> <em>AND_OP</em> <em>inclusive_or_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>logical_xor_expression</em> : </dt>
+<dd>
+<p><em>logical_and_expression</em><br>
+<em>logical_xor_expression</em> <em>XOR_OP</em> <em>logical_and_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>logical_or_expression</em> : </dt>
+<dd>
+<p><em>logical_xor_expression</em><br>
+<em>logical_or_expression</em> <em>OR_OP</em> <em>logical_xor_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>conditional_expression</em> : </dt>
+<dd>
+<p><em>logical_or_expression</em><br>
+<em>logical_or_expression</em> <em>QUESTION</em> <em>expression</em> <em>COLON</em>
+<em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>assignment_expression</em> : </dt>
+<dd>
+<p><em>conditional_expression</em><br>
+<em>unary_expression</em> <em>assignment_operator</em> <em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>assignment_operator</em> : </dt>
+<dd>
+<p><em>EQUAL</em><br>
+<em>MUL_ASSIGN</em><br>
+<em>DIV_ASSIGN</em><br>
+<em>MOD_ASSIGN</em><br>
+<em>ADD_ASSIGN</em><br>
+<em>SUB_ASSIGN</em><br>
+<em>LEFT_ASSIGN</em><br>
+<em>RIGHT_ASSIGN</em><br>
+<em>AND_ASSIGN</em><br>
+<em>XOR_ASSIGN</em><br>
+<em>OR_ASSIGN</em></p>
+</dd>
+<dt class="hdlist1"><em>expression</em> : </dt>
+<dd>
+<p><em>assignment_expression</em><br>
+<em>expression</em> <em>COMMA</em> <em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>constant_expression</em> : </dt>
+<dd>
+<p><em>conditional_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>declaration</em> : </dt>
+<dd>
+<p><em>function_prototype</em> <em>SEMICOLON</em><br>
+<em>init_declarator_list</em> <em>SEMICOLON</em><br>
+<em>PRECISION</em> <em>precision_qualifier</em> <em>type_specifier</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em> <em>IDENTIFIER</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em> <em>IDENTIFIER</em> <em>array_specifier</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>identifier_list</em> <em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>identifier_list</em> : </dt>
+<dd>
+<p><em>COMMA</em> <em>IDENTIFIER</em><br>
+<em>identifier_list</em> <em>COMMA</em> <em>IDENTIFIER</em></p>
+</dd>
+<dt class="hdlist1"><em>function_prototype</em> : </dt>
+<dd>
+<p><em>function_declarator</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>function_declarator</em> : </dt>
+<dd>
+<p><em>function_header</em><br>
+<em>function_header_with_parameters</em></p>
+</dd>
+<dt class="hdlist1"><em>function_header_with_parameters</em> : </dt>
+<dd>
+<p><em>function_header</em> <em>parameter_declaration</em><br>
+<em>function_header_with_parameters</em> <em>COMMA</em> <em>parameter_declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>function_header</em> : </dt>
+<dd>
+<p><em>fully_specified_type</em> <em>IDENTIFIER</em> <em>LEFT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_declarator</em> : </dt>
+<dd>
+<p><em>type_specifier</em> <em>IDENTIFIER</em><br>
+<em>type_specifier</em> <em>IDENTIFIER</em> <em>array_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_declaration</em> : </dt>
+<dd>
+<p><em>type_qualifier</em> <em>parameter_declarator</em><br>
+<em>parameter_declarator</em><br>
+<em>type_qualifier</em> <em>parameter_type_specifier</em><br>
+<em>parameter_type_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_type_specifier</em> : </dt>
+<dd>
+<p><em>type_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>init_declarator_list</em> : </dt>
+<dd>
+<p><em>single_declaration</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em> <em>array_specifier</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em> <em>array_specifier</em> <em>EQUAL</em>
+<em>initializer</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em> <em>EQUAL</em> <em>initializer</em></p>
+</dd>
+<dt class="hdlist1"><em>single_declaration</em> : </dt>
+<dd>
+<p><em>fully_specified_type</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>array_specifier</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>array_specifier</em> <em>EQUAL</em>
+<em>initializer</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>EQUAL</em> <em>initializer</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No 'enum', or 'typedef'.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>fully_specified_type</em> : </dt>
+<dd>
+<p><em>type_specifier</em><br>
+<em>type_qualifier</em> <em>type_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>invariant_qualifier</em> : </dt>
+<dd>
+<p><em>INVARIANT</em></p>
+</dd>
+<dt class="hdlist1"><em>interpolation_qualifier</em> : </dt>
+<dd>
+<p><em>SMOOTH</em><br>
+<em>FLAT</em></p>
+</dd>
+<dt class="hdlist1"><em>layout_qualifier</em> : </dt>
+<dd>
+<p><em>LAYOUT</em> <em>LEFT_PAREN</em> <em>layout_qualifier_id_list</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>layout_qualifier_id_list</em> : </dt>
+<dd>
+<p><em>layout_qualifier_id</em><br>
+<em>layout_qualifier_id_list</em> <em>COMMA</em> <em>layout_qualifier_id</em></p>
+</dd>
+<dt class="hdlist1"><em>layout_qualifier_id</em> : </dt>
+<dd>
+<p><em>IDENTIFIER</em><br>
+<em>IDENTIFIER</em> <em>EQUAL</em> <em>INTCONSTANT</em><br>
+<em>IDENTIFIER</em> <em>EQUAL</em> <em>UINTCONSTANT</em><br>
+<em>SHARED</em></p>
+</dd>
+<dt class="hdlist1"><em>precise_qualifier</em> : </dt>
+<dd>
+<p><em>PRECISE</em></p>
+</dd>
+<dt class="hdlist1"><em>type_qualifier</em> : </dt>
+<dd>
+<p><em>single_type_qualifier</em><br>
+<em>type_qualifier</em> <em>single_type_qualifier</em></p>
+</dd>
+<dt class="hdlist1"><em>single_type_qualifier</em> : </dt>
+<dd>
+<p><em>storage_qualifier</em><br>
+<em>layout_qualifier</em><br>
+<em>precision_qualifier</em><br>
+<em>interpolation_qualifier</em><br>
+<em>invariant_qualifier</em><br>
+<em>precise_qualifier</em></p>
+</dd>
+<dt class="hdlist1"><em>storage_qualifier</em> : </dt>
+<dd>
+<p><em>CONST</em><br>
+<em>IN</em><br>
+<em>OUT</em><br>
+<em>INOUT</em><br>
+<em>CENTROID</em><br>
+<em>PATCH</em><br>
+<em>SAMPLE</em><br>
+<em>UNIFORM</em><br>
+<em>BUFFER</em><br>
+<em>SHARED</em><br>
+<em>COHERENT</em><br>
+<em>VOLATILE</em><br>
+<em>RESTRICT</em><br>
+<em>READONLY</em><br>
+<em>WRITEONLY</em></p>
+</dd>
+<dt class="hdlist1"><em>type_specifier</em> : </dt>
+<dd>
+<p><em>type_specifier_nonarray</em><br>
+<em>type_specifier_nonarray</em> <em>array_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>array_specifier</em> : </dt>
+<dd>
+<p><em>LEFT_BRACKET</em> <em>RIGHT_BRACKET</em><br>
+<em>LEFT_BRACKET</em> <em>constant_expression</em> <em>RIGHT_BRACKET</em><br>
+<em>array_specifier</em> <em>LEFT_BRACKET</em> <em>RIGHT_BRACKET</em><br>
+<em>array_specifier</em> <em>LEFT_BRACKET</em> <em>constant_expression</em> <em>RIGHT_BRACKET</em></p>
+</dd>
+<dt class="hdlist1"><em>type_specifier_nonarray</em> : </dt>
+<dd>
+<p><em>VOID</em><br>
+<em>FLOAT</em><br>
+<em>INT</em><br>
+<em>UINT</em><br>
+<em>BOOL</em><br>
+<em>VEC2</em><br>
+<em>VEC3</em><br>
+<em>VEC4</em><br>
+<em>BVEC2</em><br>
+<em>BVEC3</em><br>
+<em>BVEC4</em><br>
+<em>IVEC2</em><br>
+<em>IVEC3</em><br>
+<em>IVEC4</em><br>
+<em>UVEC2</em><br>
+<em>UVEC3</em><br>
+<em>UVEC4</em><br>
+<em>MAT2</em><br>
+<em>MAT3</em><br>
+<em>MAT4</em><br>
+<em>MAT2X2</em><br>
+<em>MAT2X3</em><br>
+<em>MAT2X4</em><br>
+<em>MAT3X2</em><br>
+<em>MAT3X3</em><br>
+<em>MAT3X4</em><br>
+<em>MAT4X2</em><br>
+<em>MAT4X3</em><br>
+<em>MAT4X4</em><br>
+<em>ATOMIC_UINT</em><br>
+<em>SAMPLER2D</em><br>
+<em>SAMPLER3D</em><br>
+<em>SAMPLERCUBE</em><br>
+<em>SAMPLER2DSHADOW</em><br>
+<em>SAMPLERCUBESHADOW</em><br>
+<em>SAMPLER2DARRAY</em><br>
+<em>SAMPLER2DARRAYSHADOW</em><br>
+<em>SAMPLERCUBEARRAY</em><br>
+<em>SAMPLERCUBEARRAYSHADOW</em><br>
+<em>ISAMPLER2D</em><br>
+<em>ISAMPLER3D</em><br>
+<em>ISAMPLERCUBE</em><br>
+<em>ISAMPLER2DARRAY</em><br>
+<em>ISAMPLERCUBEARRAY</em><br>
+<em>USAMPLER2D</em><br>
+<em>USAMPLER3D</em><br>
+<em>USAMPLERCUBE</em><br>
+<em>USAMPLER2DARRAY</em><br>
+<em>USAMPLERCUBEARRAY</em><br>
+<em>SAMPLERBUFFER</em><br>
+<em>ISAMPLERBUFFER</em><br>
+<em>USAMPLERBUFFER</em><br>
+<em>SAMPLER2DMS</em><br>
+<em>ISAMPLER2DMS</em><br>
+<em>USAMPLER2DMS</em><br>
+<em>SAMPLER2DMSARRAY</em><br>
+<em>ISAMPLER2DMSARRAY</em><br>
+<em>USAMPLER2DMSARRAY</em><br>
+<em>IMAGE2D</em><br>
+<em>IIMAGE2D</em><br>
+<em>UIMAGE2D</em><br>
+<em>IMAGE3D</em><br>
+<em>IIMAGE3D</em><br>
+<em>UIMAGE3D</em><br>
+<em>IMAGECUBE</em><br>
+<em>IIMAGECUBE</em><br>
+<em>UIMAGECUBE</em><br>
+<em>IMAGEBUFFER</em><br>
+<em>IIMAGEBUFFER</em><br>
+<em>UIMAGEBUFFER</em><br>
+<em>IMAGE2DARRAY</em><br>
+<em>IIMAGE2DARRAY</em><br>
+<em>UIMAGE2DARRAY</em><br>
+<em>IMAGECUBEARRAY</em><br>
+<em>IIMAGECUBEARRAY</em><br>
+<em>UIMAGECUBEARRAY</em><br>
+<em>struct_specifier</em><br>
+<em>TYPE_NAME</em></p>
+</dd>
+<dt class="hdlist1"><em>precision_qualifier</em> : </dt>
+<dd>
+<p><em>HIGH_PRECISION</em><br>
+<em>MEDIUM_PRECISION</em><br>
+<em>LOW_PRECISION</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_specifier</em> : </dt>
+<dd>
+<p><em>STRUCT</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em><br>
+<em>STRUCT</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declaration_list</em> : </dt>
+<dd>
+<p><em>struct_declaration</em><br>
+<em>struct_declaration_list</em> <em>struct_declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declaration</em> : </dt>
+<dd>
+<p><em>type_specifier</em> <em>struct_declarator_list</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>type_specifier</em> <em>struct_declarator_list</em> <em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declarator_list</em> : </dt>
+<dd>
+<p><em>struct_declarator</em><br>
+<em>struct_declarator_list</em> <em>COMMA</em> <em>struct_declarator</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declarator</em> : </dt>
+<dd>
+<p><em>IDENTIFIER</em><br>
+<em>IDENTIFIER</em> <em>array_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>initializer</em> : </dt>
+<dd>
+<p><em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>declaration_statement</em> : </dt>
+<dd>
+<p><em>declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>statement</em> : </dt>
+<dd>
+<p><em>compound_statement</em><br>
+<em>simple_statement</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: labeled statements for SWITCH only; 'goto' is not supported.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>simple_statement</em> : </dt>
+<dd>
+<p><em>declaration_statement</em><br>
+<em>expression_statement</em><br>
+<em>selection_statement</em><br>
+<em>switch_statement</em><br>
+<em>case_label</em><br>
+<em>iteration_statement</em><br>
+<em>jump_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>compound_statement</em> : </dt>
+<dd>
+<p><em>LEFT_BRACE</em> <em>RIGHT_BRACE</em><br>
+<em>LEFT_BRACE</em> <em>statement_list</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>statement_no_new_scope</em> : </dt>
+<dd>
+<p><em>compound_statement_no_new_scope</em><br>
+<em>simple_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>compound_statement_no_new_scope</em> : </dt>
+<dd>
+<p><em>LEFT_BRACE</em> <em>RIGHT_BRACE</em><br>
+<em>LEFT_BRACE</em> <em>statement_list</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>statement_list</em> : </dt>
+<dd>
+<p><em>statement</em><br>
+<em>statement_list</em> <em>statement</em></p>
+</dd>
+<dt class="hdlist1"><em>expression_statement</em> : </dt>
+<dd>
+<p><em>SEMICOLON</em><br>
+<em>expression</em> <em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>selection_statement</em> : </dt>
+<dd>
+<p><em>IF</em> <em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em> <em>selection_rest_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>selection_rest_statement</em> : </dt>
+<dd>
+<p><em>statement</em> <em>ELSE</em> <em>statement</em><br>
+<em>statement</em></p>
+</dd>
+<dt class="hdlist1"><em>condition</em> : </dt>
+<dd>
+<p><em>expression</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>EQUAL</em> <em>initializer</em></p>
+</dd>
+<dt class="hdlist1"><em>switch_statement</em> : </dt>
+<dd>
+<p><em>SWITCH</em> <em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em> <em>LEFT_BRACE</em>
+<em>switch_statement_list</em><br>
+<em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>switch_statement_list</em> : </dt>
+<dd>
+<p>/* <em>nothing</em> */<br>
+<em>statement_list</em></p>
+</dd>
+<dt class="hdlist1"><em>case_label</em> : </dt>
+<dd>
+<p><em>CASE</em> <em>expression</em> <em>COLON</em><br>
+<em>DEFAULT</em> <em>COLON</em></p>
+</dd>
+<dt class="hdlist1"><em>iteration_statement</em> : </dt>
+<dd>
+<p><em>WHILE</em> <em>LEFT_PAREN</em> <em>condition</em> <em>RIGHT_PAREN</em> <em>statement_no_new_scope</em><br>
+<em>DO</em> <em>statement</em> <em>WHILE</em> <em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em>
+<em>SEMICOLON</em><br>
+<em>FOR</em> <em>LEFT_PAREN</em> <em>for_init_statement</em> <em>for_rest_statement</em>
+<em>RIGHT_PAREN</em> <em>statement_no_new_scope</em></p>
+</dd>
+<dt class="hdlist1"><em>for_init_statement</em> : </dt>
+<dd>
+<p><em>expression_statement</em><br>
+<em>declaration_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>conditionopt</em> : </dt>
+<dd>
+<p><em>condition</em><br>
+/* <em>empty</em> */</p>
+</dd>
+<dt class="hdlist1"><em>for_rest_statement</em> : </dt>
+<dd>
+<p><em>conditionopt</em> <em>SEMICOLON</em><br>
+<em>conditionopt</em> <em>SEMICOLON</em> <em>expression</em></p>
+</dd>
+<dt class="hdlist1"><em>jump_statement</em> : </dt>
+<dd>
+<p><em>CONTINUE</em> <em>SEMICOLON</em><br>
+<em>BREAK</em> <em>SEMICOLON</em><br>
+<em>RETURN</em> <em>SEMICOLON</em><br>
+<em>RETURN</em> <em>expression</em> <em>SEMICOLON</em><br>
+<em>DISCARD</em> <em>SEMICOLON</em> // Fragment shader only.</p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No 'goto'.
+Gotos are not supported.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>translation_unit</em> : </dt>
+<dd>
+<p><em>external_declaration</em><br>
+<em>translation_unit</em> <em>external_declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>external_declaration</em> : </dt>
+<dd>
+<p><em>function_definition</em><br>
+<em>declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>function_definition</em> : </dt>
+<dd>
+<p><em>function_prototype</em> <em>compound_statement_no_new_scope</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>In general the above grammar describes a super set of the OpenGL ES Shading Language.
+Certain constructs that are valid purely in terms of the grammar are
+disallowed by statements elsewhere in this specification.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="counting-of-inputs-and-outputs">11. Counting of Inputs and Outputs</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>This section applies to outputs from the last active vertex processing stage
+and inputs to the fragment stage.
+GLSL ES 3.20 specifies the storage available for such variables in terms of
+an array of 4-vectors.
+The assumption is that variables will be packed into these arrays without
+wasting space.
+This places significant burden on implementations since optimal packing is
+computationally intensive.
+Implementations may have more internal resources than exposed to the
+application and so avoid the need to perform packing but this is also
+considered an expensive solution.</p>
+</div>
+<div class="paragraph">
+<p>GLSL ES 3.20 therefore relaxes the requirements for packing by
+specifying a simpler algorithm that may be used.
+This algorithm specifies a minimum requirement for when a set of variables
+must be supported by an implementation.
+The implementation is allowed to support more than the minimum and so may
+use a more efficient algorithm and/or may support more registers than the
+virtual target machine.</p>
+</div>
+<div class="paragraph">
+<p>Outputs from the last active vertex stage and inputs to the fragment stage are
+counted separately.
+If statically used in the fragment shader, the built-in special variables
+(<em>gl_FragCoord</em>, <em>gl_FrontFacing</em> and <em>gl_PointCoord</em>) are included when
+calculating the storage requirements of fragment inputs.</p>
+</div>
+<div class="paragraph">
+<p>If the last active vertex-pipeline shader and fragment shader are linked
+together, inputs and outputs are only counted if they are statically used
+within the shader.
+If the shaders are each compiled into a separable program, all declared inputs
+and outputs are counted.</p>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="title">Note</div>
+<div class="paragraph">
+<p>GLSL ES 3.20 does not require the implementation to remove
+outputs which are not statically used in the fragment shader.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="paragraph">
+<p>For the algorithm used, failing resource allocation for a variable must
+result in an error.</p>
+</div>
+<div class="paragraph">
+<p>The resource allocation of variables must succeed for all cases where the
+following packing algorithm succeeds:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The target architecture consists of a grid of registers, 16 rows by 4
+columns.
+Each register can contain a scalar value, i.e. a float, int or uint.</p>
+</li>
+<li>
+<p>Variables with an explicit location are allocated first.
+When attempting to allocate a location for other variables, if there is
+a conflict, the search moves to the next available free location.</p>
+</li>
+<li>
+<p>Structures are assumed to be flattened.
+Each data member is treated as if it were at global scope.</p>
+</li>
+<li>
+<p>Variables are packed into the registers one at a time so that they each
+occupy a contiguous sub-rectangle.
+No splitting of variables is permitted.</p>
+</li>
+<li>
+<p>The orientation of variables is fixed.
+Vectors always occupy registers in a single row.
+Elements of an array must be in different rows.
+E.g. <strong>vec4</strong> will always occupy one row; float[16] will occupy one
+column.
+Since it is not permitted to split a variable, large arrays e.g.
+float[32] will always fail with this algorithm.</p>
+</li>
+<li>
+<p>Non-square matrices of type <strong>matCxR</strong> consume the same space as a square
+matrix of type <strong>matN</strong> where N is the greater of C and R.
+Variables of type <strong>mat2</strong> occupies 2 complete rows.
+These rules allow implementations more flexibility in how variables are
+stored.
++ Other variables consume only the minimum space required.</p>
+</li>
+<li>
+<p>Arrays of size N are assumed to take N times the size of the base type.</p>
+</li>
+<li>
+<p>Variables are packed in the following order:</p>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p><strong>mat4</strong> and arrays of <strong>mat4</strong>.</p>
+</li>
+<li>
+<p><strong>mat2</strong> and arrays of <strong>mat2</strong> (since they occupy full rows)</p>
+</li>
+<li>
+<p><strong>vec4</strong> and arrays of <strong>vec4</strong></p>
+</li>
+<li>
+<p><strong>mat3</strong> and arrays of <strong>mat3</strong></p>
+</li>
+<li>
+<p><strong>vec3</strong> and arrays of <strong>vec3</strong></p>
+</li>
+<li>
+<p><strong>vec2</strong> and arrays of <strong>vec2</strong></p>
+</li>
+<li>
+<p>Scalar types and arrays of scalar types</p>
+</li>
+</ol>
+</div>
+</li>
+<li>
+<p>For each of the above types, the arrays are processed in order of size,
+largest first.
+Arrays of size 1 and the base type are considered equivalent.
+The first type to be packed will be mat4[4], mat4[3], mat[2] followed by
+mat4, mat2[4]&#8230;&#8203;mat2[2], mat2, vec4[8], vec4[7],&#8230;&#8203;vec4[1], vec4,
+mat3[2], mat3 and so on.
+The last variables to be packed will be float (and float[1]).</p>
+</li>
+<li>
+<p>For 2,3 and 4 component variables packing is started using the 1<sup>st</sup>
+column of the 1<sup>st</sup> row.
+Variables are then allocated to successive rows, aligning them to the
+1<sup>st</sup> column.</p>
+</li>
+<li>
+<p>For 2 component variables, when there are no spare rows, the strategy is
+switched to using the highest numbered row and the lowest numbered
+column where the variable will fit.
+(In practice, this means they will be aligned to the x or z component.)
+Packing of any further 3 or 4 component variables will fail at this
+point.</p>
+</li>
+<li>
+<p>1 component variables (e.g. floats and arrays of floats) have their own
+packing rule.
+They are packed in order of size, largest first.
+Each variable is placed in the column that leaves the least amount of
+space in the column and aligned to the lowest available rows within that
+column.
+During this phase of packing, space will be available in up to 4
+columns.
+The space within each column is always contiguous in the case where no
+variables have explicit locations.</p>
+</li>
+<li>
+<p>For each type, variables with the 'smooth' property are packed first,
+followed by variables with the 'flat' property.</p>
+</li>
+<li>
+<p>Each row can contain either values with the 'smooth' property or the
+'flat' property but not both.
+If this situation is encountered during allocation, the algorithm skips
+the component location and continues with the next available location.
+These skipped locations may be used for other values later in the
+allocation process.</p>
+</li>
+<li>
+<p>There is no backtracking.
+Once a value is assigned a location, it cannot be changed, even if such
+a change is required for a successful allocation.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Example: pack the following types:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec4 a;     <span class="comment">// top left</span>
+out mat3 b;     <span class="comment">// align to left, lowest numbered rows</span>
+out mat2x3 c;   <span class="comment">// same size as mat3, align to left</span>
+out vec2 d[<span class="integer">6</span>];  <span class="comment">// align to left, lowest numbered rows</span>
+out vec2 e[<span class="integer">4</span>];  <span class="comment">// Cannot align to left so align to z column, highest</span>
+                <span class="comment">// numbered rows</span>
+out vec2 f;     <span class="comment">// Align to left, lowest numbered rows.</span>
+out <span class="predefined-type">float</span> g[<span class="integer">3</span>]  <span class="comment">// Column with minimum space</span>
+out <span class="predefined-type">float</span> h[<span class="integer">2</span>]; <span class="comment">// Column with minimum space (choice of 3, any</span>
+                <span class="comment">// can be used)</span>
+out <span class="predefined-type">float</span> i;    <span class="comment">// Column with minimum space</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>In this example, the variables happen to be listed in the order in which
+they are packed.
+Packing is independent of the order of declaration.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 20%;">
+<col style="width: 20%;">
+<col style="width: 20%;">
+<col style="width: 20%;">
+<col style="width: 20%;">
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>x</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>y</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>z</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>w</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">0</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>a</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>a</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>a</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>a</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>b</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>c</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">7</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>g</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">8</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>g</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">9</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>g</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">10</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">11</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">12</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>d</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">13</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>f</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>f</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">14</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>h</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>i</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">15</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>h</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>e</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Some types e.g. mat4[8] will be too large to fit.
+These always fail with this algorithm.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="acknowledgments">12. Acknowledgments</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>This specification is based on the work of those who contributed to past
+versions of the Open GL and Open GL ES Language Specifications and the
+following contributors to this version:</p>
+</div>
+<div class="paragraph">
+<p>Acorn Pooley, NVIDIA<br>
+Alberto Moreira, Qualcomm<br>
+Aleksandra Krstic, Qualcomm<br>
+Alon Or-bach, Nokia &amp; Samsung<br>
+Andrzej Kacprowski, Intel<br>
+Arzhange Safdarzadeh, Intel<br>
+Aske Simon Christensen, ARM<br>
+Avi Shapira, Graphic Remedy<br>
+Barthold Lichtenbelt, NVIDIA<br>
+Ben Bowman, Imagination Technologies<br>
+Ben Brierton, Broadcom<br>
+Benj Lipchak, Apple<br>
+Benson Tao, Vivante<br>
+Bill Licea-Kane, Qualcomm<br>
+Brent Insko, Intel<br>
+Brian Murray, Freescale<br>
+Bruce Merry, ARM<br>
+Carlos Santa, TI<br>
+Cass Everitt, Epic Games &amp; NVIDIA<br>
+Cemil Azizoglu, TI<br>
+Chang-Hyo Yu, Samsung<br>
+Chris Dodd, NVIDIA<br>
+Chris Knox, NVIDIA<br>
+Chris Tserng, TI<br>
+Clay Montgomery, TI<br>
+Daniel Kartch, NVIDIA<br>
+Daniel Koch, Transgaming&amp; NVIDIA<br>
+Daoxiang Gong, Imagination Technologies<br>
+Dave Shreiner, ARM<br>
+David Garcia, AMD<br>
+David Jarmon, Vivante<br>
+Derek Cornish, Epic Games<br>
+Dominick Witczak, Mobica<br>
+Eben Upton, Broadcom<br>
+Ed Plowman, ARM<br>
+Eisaku Ohbuchi, DMP<br>
+Elan Lennard, ARM<br>
+Erik Faye-Lund, ARM<br>
+Graham Connor, Imagination Technologies<br>
+Graham Sellers, AMD<br>
+Greg Roth, NVIDIA<br>
+Guillaume Portier, Hi Corporation<br>
+Guofang Jiao, Qualcomm<br>
+Hans-Martin Will, Vincent<br>
+Hwanyong Lee, Huone<br>
+I-Gene Leong, NVIDIA<br>
+Ian Romanick, Intel<br>
+Ian South-Dickinson, NVIDIA<br>
+Ilan Aelion-Exch, Samsung<br>
+Inkyun Lee, Huone<br>
+Jacob Strm, Ericsson<br>
+James Adams, Broadcom<br>
+James Jones, Imagination Technologies<br>
+James McCombe, Imagination Technologies<br>
+Jamie Gennis, Google<br>
+Jan-Harald Fredriksen, ARM<br>
+Jani Vaisanen, Nokia<br>
+Jarkko Kemppainen, Symbio<br>
+Jeff Bolz, NVIDIA<br>
+Jeff Leger, Qualcomm<br>
+Jeff Vigil, Qualcomm<br>
+Jeremy Sandmel, Apple<br>
+Jeremy Thorne, Broadcom<br>
+Jim Hauxwell, Broadcom<br>
+Jinsung Kim, Huone<br>
+Jiyoung Yoon, Huone<br>
+John Kessenich, Google<br>
+Jon Kennedy, 3DLabs<br>
+Jon Leech, Khronos<br>
+Jonathan Putsman, Imagination Technologies<br>
+Joohoon Lee, Samsung<br>
+JoukoKylmäoja, Symbio<br>
+Jrn Nystad, ARM<br>
+Jussi Rasanen, NVIDIA<br>
+Kalle Raita, drawElements<br>
+Kari Pulli, Nokia<br>
+Keith Whitwell, VMware<br>
+Kent Miller, Netlogic Microsystems<br>
+Kimmo Nikkanen, Nokia<br>
+Konsta Karsisto, Nokia<br>
+Krzysztof Kaminski, Intel<br>
+Larry Seiler, Intel<br>
+Lars Remes, Symbio<br>
+Lee Thomason, Adobe<br>
+Lefan Zhong, Vivante<br>
+Marcus Lorentzon, Ericsson<br>
+Mark Butler, Imagination Technologies<br>
+Mark Callow, Hi Corporation<br>
+Mark Cresswell, Broadcom<br>
+Mark Snyder, Alt Software<br>
+Mark Young, AMD<br>
+Mathieu Robart, STM<br>
+Matt Netsch, Qualcomm<br>
+Matt Russo, Matrox<br>
+Maurice Ribble, Qualcomm<br>
+Max Kazakov, DMP<br>
+Mika Pesonen, Nokia<br>
+Mike Cai, Vivante<br>
+Mike Weiblen, Zebra Imaging &amp; Qualcomm<br>
+Mila Smith, AMD<br>
+Nakhoon Baek, Kyungpook Univeristy<br>
+Nate Huang, NVIDIA<br>
+Neil Trevett, NVIDIA<br>
+Nelson Kidd, Intel<br>
+Nick Haemel, NVIDIA<br>
+Nick Penwarden, Epic Games<br>
+Niklas Smedberg, Epic Games<br>
+Nizar Romdan, ARM<br>
+Oliver Wohlmuth , Fujitsu<br>
+Pat Brown, NVIDIA<br>
+Paul Ruggieri, Qualcomm<br>
+Per Wennersten, Ericsson<br>
+Petri Talala, Symbio<br>
+Phil Huxley, ZiiLabs<br>
+Philip Hatcher, Freescale &amp; Intel<br>
+Piers Daniell, NVIDIA<br>
+Pyry Haulos, drawElements<br>
+Piotr Tomaszewski, Ericsson<br>
+Piotr Uminski, Intel<br>
+Rami Mayer, Samsung<br>
+Rauli Laatikainen, RightWare<br>
+Rob Barris, NVIDIA<br>
+Rob Simpson, Qualcomm<br>
+Roj Langhi, Vivante<br>
+Rune Holm, ARM<br>
+Sami Kyostila, Nokia<br>
+Sean Ellis, ARM<br>
+Shereef Shehata, TI<br>
+Sila Kayo, Nokia<br>
+Slawomir Cygan, Intel<br>
+Slawomir Grajewski, Intel<br>
+Steve Hill, STM &amp; Broadcom<br>
+Steven Olney, DMP<br>
+Suman Sharma, Intel<br>
+Tapani Palli, Nokia<br>
+Teemu Laakso, Symbio<br>
+Tero Karras, NVIDIA<br>
+Timo Suoranta, Imagination Technologies &amp; Broadcom<br>
+Tom Cooksey, ARM<br>
+Tom McReynolds, NVIDIA<br>
+Tom Olson, TI &amp; ARM<br>
+Tomi Aarnio, Nokia<br>
+Tommy Asano, Takumi<br>
+Wes Bang, Nokia<br>
+Yanjun Zhang, Vivante</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="references">13. Normative References</h2>
+<div class="sectionbody">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>International Standard ISO/IEC 14882:1998(E).
+Programming Languages - C++. Referenced for preprocessor only</p>
+</li>
+<li>
+<p>&#8220;OpenGL<sup>R</sup> ES, Version 3.2&#8221;,
+<a href="https://www.khronos.org/registry/OpenGL/index_es.php" class="bare">https://www.khronos.org/registry/OpenGL/index_es.php</a>, November 3, 2016.</p>
+</li>
+<li>
+<p>&#8220;The OpenGL<sup>R</sup> Graphics System: A Specification, Version 4.6 (Core
+Profile)&#8221;, <a href="https://www.khronos.org/registry/OpenGL/index_gl.php" class="bare">https://www.khronos.org/registry/OpenGL/index_gl.php</a>, June
+1, 2016.</p>
+</li>
+<li>
+<p>International Standard ISO/IEC 646:1991.
+Information technology - ISO 7-bit coded character set for information
+interchange</p>
+</li>
+<li>
+<p>The Unicode Standard Version 6.0 - Core Specification.</p>
+</li>
+<li>
+<p>IEEE 754-2008.
+<em>IEEE Standard for Floating-Point Arithmetic</em></p>
+</li>
+</ol>
+</div>
+</div>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Version 3.20.5<br>
+Last updated 2018-12-12 16:37:44 MST
+</div>
+</div>
+
+<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_HTMLorMML"></script>
+</body>
+</html>
\ No newline at end of file
diff --git a/specs/es/3.2/GLSL_ES_Specification_3.20.pdf b/specs/es/3.2/GLSL_ES_Specification_3.20.pdf
index 70434ce..c436090 100644
--- a/specs/es/3.2/GLSL_ES_Specification_3.20.pdf
+++ b/specs/es/3.2/GLSL_ES_Specification_3.20.pdf
Binary files differ
diff --git a/specs/es/3.2/es_spec_3.2.pdf b/specs/es/3.2/es_spec_3.2.pdf
index 93624e7..6c2b506 100644
--- a/specs/es/3.2/es_spec_3.2.pdf
+++ b/specs/es/3.2/es_spec_3.2.pdf
Binary files differ
diff --git a/specs/es/3.2/es_spec_3.2.withchanges.pdf b/specs/es/3.2/es_spec_3.2.withchanges.pdf
index 2d0ead6..04d5acc 100644
--- a/specs/es/3.2/es_spec_3.2.withchanges.pdf
+++ b/specs/es/3.2/es_spec_3.2.withchanges.pdf
Binary files differ
diff --git a/specs/es/3.2/katex/README.md b/specs/es/3.2/katex/README.md
new file mode 100644
index 0000000..5f8caa8
--- /dev/null
+++ b/specs/es/3.2/katex/README.md
@@ -0,0 +1,68 @@
+# [<img src="https://khan.github.io/KaTeX/katex-logo.svg" width="130" alt="KaTeX">](https://khan.github.io/KaTeX/) [![Build Status](https://travis-ci.org/Khan/KaTeX.svg?branch=master)](https://travis-ci.org/Khan/KaTeX)
+
+[![Join the chat at https://gitter.im/Khan/KaTeX](https://badges.gitter.im/Join%20Chat.svg)](https://gitter.im/Khan/KaTeX?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
+
+KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web.
+
+ * **Fast:** KaTeX renders its math synchronously and doesn't need to reflow the page. See how it compares to a competitor in [this speed test](http://jsperf.com/katex-vs-mathjax/).
+ * **Print quality:** KaTeX’s layout is based on Donald Knuth’s TeX, the gold standard for math typesetting.
+ * **Self contained:** KaTeX has no dependencies and can easily be bundled with your website resources.
+ * **Server side rendering:** KaTeX produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML.
+
+KaTeX supports all major browsers, including Chrome, Safari, Firefox, Opera, and IE 8 - IE 11.  A list of supported  commands can be on the [wiki](https://github.com/Khan/KaTeX/wiki/Function-Support-in-KaTeX).
+
+## Usage
+
+You can [download KaTeX](https://github.com/khan/katex/releases) and host it on your server or include the `katex.min.js` and `katex.min.css` files on your page directly from a CDN:
+
+```html
+<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.6.0/katex.min.css">
+<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.6.0/katex.min.js"></script>
+```
+
+#### In-browser rendering
+
+Call `katex.render` with a TeX expression and a DOM element to render into:
+
+```js
+katex.render("c = \\pm\\sqrt{a^2 + b^2}", element);
+```
+
+If KaTeX can't parse the expression, it throws a `katex.ParseError` error.
+
+#### Server side rendering or rendering to a string
+
+To generate HTML on the server or to generate an HTML string of the rendered math, you can use `katex.renderToString`:
+
+```js
+var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}");
+// '<span class="katex">...</span>'
+```
+
+Make sure to include the CSS and font files, but there is no need to include the JavaScript. Like `render`, `renderToString` throws if it can't parse the expression.
+
+#### Rendering options
+
+You can provide an object of options as the last argument to `katex.render` and `katex.renderToString`. Available options are:
+
+- `displayMode`: `boolean`. If `true` the math will be rendered in display mode, which will put the math in display style (so `\int` and `\sum` are large, for example), and will center the math on the page on its own line. If `false` the math will be rendered in inline mode. (default: `false`)
+- `throwOnError`: `boolean`. If `true`, KaTeX will throw a `ParseError` when it encounters an unsupported command. If `false`, KaTeX will render the unsupported command as text in the color given by `errorColor`. (default: `true`)
+- `errorColor`: `string`. A color string given in the format `"#XXX"` or `"#XXXXXX"`. This option determines the color which unsupported commands are rendered in. (default: `#cc0000`)
+
+For example:
+
+```js
+katex.render("c = \\pm\\sqrt{a^2 + b^2}", element, { displayMode: true });
+```
+
+#### Automatic rendering of math on a page
+
+Math on the page can be automatically rendered using the auto-render extension. See [the Auto-render README](contrib/auto-render/README.md) for more information.
+
+## Contributing
+
+See [CONTRIBUTING.md](CONTRIBUTING.md)
+
+## License
+
+KaTeX is licensed under the [MIT License](http://opensource.org/licenses/MIT).
diff --git a/specs/es/3.2/katex/contrib/auto-render.min.js b/specs/es/3.2/katex/contrib/auto-render.min.js
new file mode 100644
index 0000000..30cc312
--- /dev/null
+++ b/specs/es/3.2/katex/contrib/auto-render.min.js
@@ -0,0 +1 @@
+(function(e){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=e()}else if(typeof define==="function"&&define.amd){define([],e)}else{var t;if(typeof window!=="undefined"){t=window}else if(typeof global!=="undefined"){t=global}else if(typeof self!=="undefined"){t=self}else{t=this}t.renderMathInElement=e()}})(function(){var e,t,r;return function n(e,t,r){function a(o,l){if(!t[o]){if(!e[o]){var f=typeof require=="function"&&require;if(!l&&f)return f(o,!0);if(i)return i(o,!0);var d=new Error("Cannot find module '"+o+"'");throw d.code="MODULE_NOT_FOUND",d}var s=t[o]={exports:{}};e[o][0].call(s.exports,function(t){var r=e[o][1][t];return a(r?r:t)},s,s.exports,n,e,t,r)}return t[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)a(r[o]);return a}({1:[function(e,t,r){var n=e("./splitAtDelimiters");var a=function(e,t){var r=[{type:"text",data:e}];for(var a=0;a<t.length;a++){var i=t[a];r=n(r,i.left,i.right,i.display||false)}return r};var i=function(e,t){var r=a(e,t);var n=document.createDocumentFragment();for(var i=0;i<r.length;i++){if(r[i].type==="text"){n.appendChild(document.createTextNode(r[i].data))}else{var o=document.createElement("span");var l=r[i].data;try{katex.render(l,o,{displayMode:r[i].display})}catch(f){if(!(f instanceof katex.ParseError)){throw f}console.error("KaTeX auto-render: Failed to parse `"+r[i].data+"` with ",f);n.appendChild(document.createTextNode(r[i].rawData));continue}n.appendChild(o)}}return n};var o=function(e,t,r){for(var n=0;n<e.childNodes.length;n++){var a=e.childNodes[n];if(a.nodeType===3){var l=i(a.textContent,t);n+=l.childNodes.length-1;e.replaceChild(l,a)}else if(a.nodeType===1){var f=r.indexOf(a.nodeName.toLowerCase())===-1;if(f){o(a,t,r)}}}};var l={delimiters:[{left:"$$",right:"$$",display:true},{left:"\\[",right:"\\]",display:true},{left:"\\(",right:"\\)",display:false}],ignoredTags:["script","noscript","style","textarea","pre","code"]};var f=function(e){var t;var r;for(var n=1,a=arguments.length;n<a;n++){t=arguments[n];for(r in t){if(Object.prototype.hasOwnProperty.call(t,r)){e[r]=t[r]}}}return e};var d=function(e,t){if(!e){throw new Error("No element provided to render")}t=f({},l,t);o(e,t.delimiters,t.ignoredTags)};t.exports=d},{"./splitAtDelimiters":2}],2:[function(e,t,r){var n=function(e,t,r){var n=r;var a=0;var i=e.length;while(n<t.length){var o=t[n];if(a<=0&&t.slice(n,n+i)===e){return n}else if(o==="\\"){n++}else if(o==="{"){a++}else if(o==="}"){a--}n++}return-1};var a=function(e,t,r,a){var i=[];for(var o=0;o<e.length;o++){if(e[o].type==="text"){var l=e[o].data;var f=true;var d=0;var s;s=l.indexOf(t);if(s!==-1){d=s;i.push({type:"text",data:l.slice(0,d)});f=false}while(true){if(f){s=l.indexOf(t,d);if(s===-1){break}i.push({type:"text",data:l.slice(d,s)});d=s}else{s=n(r,l,d+t.length);if(s===-1){break}i.push({type:"math",data:l.slice(d+t.length,s),rawData:l.slice(d,s+r.length),display:a});d=s+r.length}f=!f}i.push({type:"text",data:l.slice(d)})}else{i.push(e[o])}}return i};t.exports=a},{}]},{},[1])(1)});
diff --git a/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.eot
new file mode 100644
index 0000000..784276a
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.ttf
new file mode 100644
index 0000000..6f1e0be
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.woff
new file mode 100644
index 0000000..4dded47
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.woff2
new file mode 100644
index 0000000..ea81079
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_AMS-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.eot b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.eot
new file mode 100644
index 0000000..1a0db0c
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.ttf b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.ttf
new file mode 100644
index 0000000..b94907d
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.woff b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.woff
new file mode 100644
index 0000000..799fa81
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.woff2
new file mode 100644
index 0000000..73bb542
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Bold.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.eot
new file mode 100644
index 0000000..6cc83d0
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.ttf
new file mode 100644
index 0000000..cf51e20
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.woff
new file mode 100644
index 0000000..f5e5c62
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.woff2
new file mode 100644
index 0000000..dd76d34
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Caligraphic-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.eot b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.eot
new file mode 100644
index 0000000..1960b10
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.ttf b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.ttf
new file mode 100644
index 0000000..7b0790f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.woff b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.woff
new file mode 100644
index 0000000..dc32571
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.woff2
new file mode 100644
index 0000000..fdc4292
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Bold.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.eot
new file mode 100644
index 0000000..e4e7379
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.ttf
new file mode 100644
index 0000000..063bc02
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.woff
new file mode 100644
index 0000000..c4b18d8
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.woff2
new file mode 100644
index 0000000..4318d93
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Fraktur-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.eot b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.eot
new file mode 100644
index 0000000..80fbd02
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.ttf b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.ttf
new file mode 100644
index 0000000..8e10722
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.woff b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.woff
new file mode 100644
index 0000000..43b361a
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.woff2
new file mode 100644
index 0000000..af57a96
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Bold.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.eot b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.eot
new file mode 100644
index 0000000..fc77016
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.ttf b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.ttf
new file mode 100644
index 0000000..d124495
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.woff b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.woff
new file mode 100644
index 0000000..e623236
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.woff2
new file mode 100644
index 0000000..944e974
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Italic.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.eot
new file mode 100644
index 0000000..dc60c09
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.ttf
new file mode 100644
index 0000000..da5797f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.woff
new file mode 100644
index 0000000..37db672
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.woff2
new file mode 100644
index 0000000..4882042
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Main-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.eot b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.eot
new file mode 100644
index 0000000..52c8b8c
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.ttf b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.ttf
new file mode 100644
index 0000000..a8b527c
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.woff b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.woff
new file mode 100644
index 0000000..8940e0b
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.woff2
new file mode 100644
index 0000000..15cf56d
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-BoldItalic.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.eot b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.eot
new file mode 100644
index 0000000..64c8992
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.ttf b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.ttf
new file mode 100644
index 0000000..06f39d3
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.woff b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.woff
new file mode 100644
index 0000000..cf3b4b7
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.woff2
new file mode 100644
index 0000000..5f8c4bf
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Italic.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.eot
new file mode 100644
index 0000000..5521e6a
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.ttf
new file mode 100644
index 0000000..7312708
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.woff
new file mode 100644
index 0000000..0e2ebdf
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.woff2
new file mode 100644
index 0000000..ebe3d02
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Math-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.eot b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.eot
new file mode 100644
index 0000000..1660e76
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.ttf b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.ttf
new file mode 100644
index 0000000..dbeb7b9
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.woff b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.woff
new file mode 100644
index 0000000..8f144a8
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.woff2 b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.woff2
new file mode 100644
index 0000000..329e855
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Bold.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.eot b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.eot
new file mode 100644
index 0000000..289ae3f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.ttf b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.ttf
new file mode 100644
index 0000000..b3a2f38
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.woff b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.woff
new file mode 100644
index 0000000..bddf7ea
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.woff2 b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.woff2
new file mode 100644
index 0000000..5fa767b
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Italic.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.eot
new file mode 100644
index 0000000..1b38b98
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.ttf
new file mode 100644
index 0000000..e4712f8
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.woff
new file mode 100644
index 0000000..33be368
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.woff2
new file mode 100644
index 0000000..4fcb2e2
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_SansSerif-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.eot
new file mode 100644
index 0000000..7870d7f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.ttf
new file mode 100644
index 0000000..da4d113
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.woff
new file mode 100644
index 0000000..d6ae79f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.woff2
new file mode 100644
index 0000000..1b43deb
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Script-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.eot
new file mode 100644
index 0000000..29950f9
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.ttf
new file mode 100644
index 0000000..194466a
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.woff
new file mode 100644
index 0000000..237f271
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.woff2
new file mode 100644
index 0000000..39b6f8f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size1-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.eot
new file mode 100644
index 0000000..b8b0536
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.ttf
new file mode 100644
index 0000000..b41b66a
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.woff
new file mode 100644
index 0000000..4a30558
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.woff2
new file mode 100644
index 0000000..3facec1
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size2-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.eot
new file mode 100644
index 0000000..576b864
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.ttf
new file mode 100644
index 0000000..790ddbb
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.woff
new file mode 100644
index 0000000..3a6d062
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.woff2
new file mode 100644
index 0000000..2cffafe
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size3-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.eot
new file mode 100644
index 0000000..c2b045f
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.ttf
new file mode 100644
index 0000000..ce660aa
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.woff
new file mode 100644
index 0000000..7826c6c
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.woff2
new file mode 100644
index 0000000..c921898
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Size4-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.eot b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.eot
new file mode 100644
index 0000000..4c178f4
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.eot
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.ttf b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.ttf
new file mode 100644
index 0000000..b0427ad
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.ttf
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.woff b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.woff
new file mode 100644
index 0000000..78e9904
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.woff
Binary files differ
diff --git a/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.woff2 b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.woff2
new file mode 100644
index 0000000..618de99
--- /dev/null
+++ b/specs/es/3.2/katex/fonts/KaTeX_Typewriter-Regular.woff2
Binary files differ
diff --git a/specs/es/3.2/katex/katex.css b/specs/es/3.2/katex/katex.css
new file mode 100644
index 0000000..ef0aa62
--- /dev/null
+++ b/specs/es/3.2/katex/katex.css
@@ -0,0 +1,976 @@
+@font-face {
+  font-family: 'KaTeX_AMS';
+  src: url('fonts/KaTeX_AMS-Regular.eot');
+  src: url('fonts/KaTeX_AMS-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_AMS-Regular.woff2') format('woff2'), url('fonts/KaTeX_AMS-Regular.woff') format('woff'), url('fonts/KaTeX_AMS-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Caligraphic';
+  src: url('fonts/KaTeX_Caligraphic-Bold.eot');
+  src: url('fonts/KaTeX_Caligraphic-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Caligraphic-Bold.woff2') format('woff2'), url('fonts/KaTeX_Caligraphic-Bold.woff') format('woff'), url('fonts/KaTeX_Caligraphic-Bold.ttf') format('truetype');
+  font-weight: bold;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Caligraphic';
+  src: url('fonts/KaTeX_Caligraphic-Regular.eot');
+  src: url('fonts/KaTeX_Caligraphic-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Caligraphic-Regular.woff2') format('woff2'), url('fonts/KaTeX_Caligraphic-Regular.woff') format('woff'), url('fonts/KaTeX_Caligraphic-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Fraktur';
+  src: url('fonts/KaTeX_Fraktur-Bold.eot');
+  src: url('fonts/KaTeX_Fraktur-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Fraktur-Bold.woff2') format('woff2'), url('fonts/KaTeX_Fraktur-Bold.woff') format('woff'), url('fonts/KaTeX_Fraktur-Bold.ttf') format('truetype');
+  font-weight: bold;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Fraktur';
+  src: url('fonts/KaTeX_Fraktur-Regular.eot');
+  src: url('fonts/KaTeX_Fraktur-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Fraktur-Regular.woff2') format('woff2'), url('fonts/KaTeX_Fraktur-Regular.woff') format('woff'), url('fonts/KaTeX_Fraktur-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Main';
+  src: url('fonts/KaTeX_Main-Bold.eot');
+  src: url('fonts/KaTeX_Main-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Bold.woff2') format('woff2'), url('fonts/KaTeX_Main-Bold.woff') format('woff'), url('fonts/KaTeX_Main-Bold.ttf') format('truetype');
+  font-weight: bold;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Main';
+  src: url('fonts/KaTeX_Main-Italic.eot');
+  src: url('fonts/KaTeX_Main-Italic.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Italic.woff2') format('woff2'), url('fonts/KaTeX_Main-Italic.woff') format('woff'), url('fonts/KaTeX_Main-Italic.ttf') format('truetype');
+  font-weight: normal;
+  font-style: italic;
+}
+@font-face {
+  font-family: 'KaTeX_Main';
+  src: url('fonts/KaTeX_Main-Regular.eot');
+  src: url('fonts/KaTeX_Main-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Regular.woff2') format('woff2'), url('fonts/KaTeX_Main-Regular.woff') format('woff'), url('fonts/KaTeX_Main-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Math';
+  src: url('fonts/KaTeX_Math-Italic.eot');
+  src: url('fonts/KaTeX_Math-Italic.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Math-Italic.woff2') format('woff2'), url('fonts/KaTeX_Math-Italic.woff') format('woff'), url('fonts/KaTeX_Math-Italic.ttf') format('truetype');
+  font-weight: normal;
+  font-style: italic;
+}
+@font-face {
+  font-family: 'KaTeX_SansSerif';
+  src: url('fonts/KaTeX_SansSerif-Regular.eot');
+  src: url('fonts/KaTeX_SansSerif-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_SansSerif-Regular.woff2') format('woff2'), url('fonts/KaTeX_SansSerif-Regular.woff') format('woff'), url('fonts/KaTeX_SansSerif-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Script';
+  src: url('fonts/KaTeX_Script-Regular.eot');
+  src: url('fonts/KaTeX_Script-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Script-Regular.woff2') format('woff2'), url('fonts/KaTeX_Script-Regular.woff') format('woff'), url('fonts/KaTeX_Script-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size1';
+  src: url('fonts/KaTeX_Size1-Regular.eot');
+  src: url('fonts/KaTeX_Size1-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size1-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size1-Regular.woff') format('woff'), url('fonts/KaTeX_Size1-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size2';
+  src: url('fonts/KaTeX_Size2-Regular.eot');
+  src: url('fonts/KaTeX_Size2-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size2-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size2-Regular.woff') format('woff'), url('fonts/KaTeX_Size2-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size3';
+  src: url('fonts/KaTeX_Size3-Regular.eot');
+  src: url('fonts/KaTeX_Size3-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size3-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size3-Regular.woff') format('woff'), url('fonts/KaTeX_Size3-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size4';
+  src: url('fonts/KaTeX_Size4-Regular.eot');
+  src: url('fonts/KaTeX_Size4-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size4-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size4-Regular.woff') format('woff'), url('fonts/KaTeX_Size4-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Typewriter';
+  src: url('fonts/KaTeX_Typewriter-Regular.eot');
+  src: url('fonts/KaTeX_Typewriter-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Typewriter-Regular.woff2') format('woff2'), url('fonts/KaTeX_Typewriter-Regular.woff') format('woff'), url('fonts/KaTeX_Typewriter-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+.katex-display {
+  display: block;
+  margin: 1em 0;
+  text-align: center;
+}
+.katex-display > .katex {
+  display: inline-block;
+  text-align: initial;
+}
+.katex {
+  font: normal 1.21em KaTeX_Main, Times New Roman, serif;
+  line-height: 1.2;
+  white-space: nowrap;
+  text-indent: 0;
+}
+.katex .katex-html {
+  display: inline-block;
+}
+.katex .katex-mathml {
+  position: absolute;
+  clip: rect(1px, 1px, 1px, 1px);
+  padding: 0;
+  border: 0;
+  height: 1px;
+  width: 1px;
+  overflow: hidden;
+}
+.katex .base {
+  display: inline-block;
+}
+.katex .strut {
+  display: inline-block;
+}
+.katex .mathrm {
+  font-style: normal;
+}
+.katex .textit {
+  font-style: italic;
+}
+.katex .mathit {
+  font-family: KaTeX_Math;
+  font-style: italic;
+}
+.katex .mathbf {
+  font-family: KaTeX_Main;
+  font-weight: bold;
+}
+.katex .amsrm {
+  font-family: KaTeX_AMS;
+}
+.katex .mathbb {
+  font-family: KaTeX_AMS;
+}
+.katex .mathcal {
+  font-family: KaTeX_Caligraphic;
+}
+.katex .mathfrak {
+  font-family: KaTeX_Fraktur;
+}
+.katex .mathtt {
+  font-family: KaTeX_Typewriter;
+}
+.katex .mathscr {
+  font-family: KaTeX_Script;
+}
+.katex .mathsf {
+  font-family: KaTeX_SansSerif;
+}
+.katex .mainit {
+  font-family: KaTeX_Main;
+  font-style: italic;
+}
+.katex .mord + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mord + .mbin {
+  margin-left: 0.22222em;
+}
+.katex .mord + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .mord + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mord {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .mop + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mbin + .mord {
+  margin-left: 0.22222em;
+}
+.katex .mbin + .mop {
+  margin-left: 0.22222em;
+}
+.katex .mbin + .mopen {
+  margin-left: 0.22222em;
+}
+.katex .mbin + .minner {
+  margin-left: 0.22222em;
+}
+.katex .mrel + .mord {
+  margin-left: 0.27778em;
+}
+.katex .mrel + .mop {
+  margin-left: 0.27778em;
+}
+.katex .mrel + .mopen {
+  margin-left: 0.27778em;
+}
+.katex .mrel + .minner {
+  margin-left: 0.27778em;
+}
+.katex .mclose + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mclose + .mbin {
+  margin-left: 0.22222em;
+}
+.katex .mclose + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .mclose + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mord {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mrel {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mopen {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mclose {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mpunct {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .minner {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mord {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mop {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mbin {
+  margin-left: 0.22222em;
+}
+.katex .minner + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .minner + .mopen {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mpunct {
+  margin-left: 0.16667em;
+}
+.katex .minner + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mord.mtight {
+  margin-left: 0;
+}
+.katex .mop.mtight {
+  margin-left: 0;
+}
+.katex .mbin.mtight {
+  margin-left: 0;
+}
+.katex .mrel.mtight {
+  margin-left: 0;
+}
+.katex .mopen.mtight {
+  margin-left: 0;
+}
+.katex .mclose.mtight {
+  margin-left: 0;
+}
+.katex .mpunct.mtight {
+  margin-left: 0;
+}
+.katex .minner.mtight {
+  margin-left: 0;
+}
+.katex .mord + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mord.mtight {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .mclose + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .reset-textstyle.textstyle {
+  font-size: 1em;
+}
+.katex .reset-textstyle.scriptstyle {
+  font-size: 0.7em;
+}
+.katex .reset-textstyle.scriptscriptstyle {
+  font-size: 0.5em;
+}
+.katex .reset-scriptstyle.textstyle {
+  font-size: 1.42857em;
+}
+.katex .reset-scriptstyle.scriptstyle {
+  font-size: 1em;
+}
+.katex .reset-scriptstyle.scriptscriptstyle {
+  font-size: 0.71429em;
+}
+.katex .reset-scriptscriptstyle.textstyle {
+  font-size: 2em;
+}
+.katex .reset-scriptscriptstyle.scriptstyle {
+  font-size: 1.4em;
+}
+.katex .reset-scriptscriptstyle.scriptscriptstyle {
+  font-size: 1em;
+}
+.katex .style-wrap {
+  position: relative;
+}
+.katex .vlist {
+  display: inline-block;
+}
+.katex .vlist > span {
+  display: block;
+  height: 0;
+  position: relative;
+}
+.katex .vlist > span > span {
+  display: inline-block;
+}
+.katex .vlist .baseline-fix {
+  display: inline-table;
+  table-layout: fixed;
+}
+.katex .msupsub {
+  text-align: left;
+}
+.katex .mfrac > span > span {
+  text-align: center;
+}
+.katex .mfrac .frac-line {
+  width: 100%;
+}
+.katex .mfrac .frac-line:before {
+  border-bottom-style: solid;
+  border-bottom-width: 1px;
+  content: "";
+  display: block;
+}
+.katex .mfrac .frac-line:after {
+  border-bottom-style: solid;
+  border-bottom-width: 0.04em;
+  content: "";
+  display: block;
+  margin-top: -1px;
+}
+.katex .mspace {
+  display: inline-block;
+}
+.katex .mspace.negativethinspace {
+  margin-left: -0.16667em;
+}
+.katex .mspace.thinspace {
+  width: 0.16667em;
+}
+.katex .mspace.negativemediumspace {
+  margin-left: -0.22222em;
+}
+.katex .mspace.mediumspace {
+  width: 0.22222em;
+}
+.katex .mspace.thickspace {
+  width: 0.27778em;
+}
+.katex .mspace.sixmuspace {
+  width: 0.333333em;
+}
+.katex .mspace.eightmuspace {
+  width: 0.444444em;
+}
+.katex .mspace.enspace {
+  width: 0.5em;
+}
+.katex .mspace.twelvemuspace {
+  width: 0.666667em;
+}
+.katex .mspace.quad {
+  width: 1em;
+}
+.katex .mspace.qquad {
+  width: 2em;
+}
+.katex .llap,
+.katex .rlap {
+  width: 0;
+  position: relative;
+}
+.katex .llap > .inner,
+.katex .rlap > .inner {
+  position: absolute;
+}
+.katex .llap > .fix,
+.katex .rlap > .fix {
+  display: inline-block;
+}
+.katex .llap > .inner {
+  right: 0;
+}
+.katex .rlap > .inner {
+  left: 0;
+}
+.katex .katex-logo .a {
+  font-size: 0.75em;
+  margin-left: -0.32em;
+  position: relative;
+  top: -0.2em;
+}
+.katex .katex-logo .t {
+  margin-left: -0.23em;
+}
+.katex .katex-logo .e {
+  margin-left: -0.1667em;
+  position: relative;
+  top: 0.2155em;
+}
+.katex .katex-logo .x {
+  margin-left: -0.125em;
+}
+.katex .rule {
+  display: inline-block;
+  border: solid 0;
+  position: relative;
+}
+.katex .overline .overline-line,
+.katex .underline .underline-line {
+  width: 100%;
+}
+.katex .overline .overline-line:before,
+.katex .underline .underline-line:before {
+  border-bottom-style: solid;
+  border-bottom-width: 1px;
+  content: "";
+  display: block;
+}
+.katex .overline .overline-line:after,
+.katex .underline .underline-line:after {
+  border-bottom-style: solid;
+  border-bottom-width: 0.04em;
+  content: "";
+  display: block;
+  margin-top: -1px;
+}
+.katex .sqrt > .sqrt-sign {
+  position: relative;
+}
+.katex .sqrt .sqrt-line {
+  width: 100%;
+}
+.katex .sqrt .sqrt-line:before {
+  border-bottom-style: solid;
+  border-bottom-width: 1px;
+  content: "";
+  display: block;
+}
+.katex .sqrt .sqrt-line:after {
+  border-bottom-style: solid;
+  border-bottom-width: 0.04em;
+  content: "";
+  display: block;
+  margin-top: -1px;
+}
+.katex .sqrt > .root {
+  margin-left: 0.27777778em;
+  margin-right: -0.55555556em;
+}
+.katex .sizing,
+.katex .fontsize-ensurer {
+  display: inline-block;
+}
+.katex .sizing.reset-size1.size1,
+.katex .fontsize-ensurer.reset-size1.size1 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size1.size2,
+.katex .fontsize-ensurer.reset-size1.size2 {
+  font-size: 1.4em;
+}
+.katex .sizing.reset-size1.size3,
+.katex .fontsize-ensurer.reset-size1.size3 {
+  font-size: 1.6em;
+}
+.katex .sizing.reset-size1.size4,
+.katex .fontsize-ensurer.reset-size1.size4 {
+  font-size: 1.8em;
+}
+.katex .sizing.reset-size1.size5,
+.katex .fontsize-ensurer.reset-size1.size5 {
+  font-size: 2em;
+}
+.katex .sizing.reset-size1.size6,
+.katex .fontsize-ensurer.reset-size1.size6 {
+  font-size: 2.4em;
+}
+.katex .sizing.reset-size1.size7,
+.katex .fontsize-ensurer.reset-size1.size7 {
+  font-size: 2.88em;
+}
+.katex .sizing.reset-size1.size8,
+.katex .fontsize-ensurer.reset-size1.size8 {
+  font-size: 3.46em;
+}
+.katex .sizing.reset-size1.size9,
+.katex .fontsize-ensurer.reset-size1.size9 {
+  font-size: 4.14em;
+}
+.katex .sizing.reset-size1.size10,
+.katex .fontsize-ensurer.reset-size1.size10 {
+  font-size: 4.98em;
+}
+.katex .sizing.reset-size2.size1,
+.katex .fontsize-ensurer.reset-size2.size1 {
+  font-size: 0.71428571em;
+}
+.katex .sizing.reset-size2.size2,
+.katex .fontsize-ensurer.reset-size2.size2 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size2.size3,
+.katex .fontsize-ensurer.reset-size2.size3 {
+  font-size: 1.14285714em;
+}
+.katex .sizing.reset-size2.size4,
+.katex .fontsize-ensurer.reset-size2.size4 {
+  font-size: 1.28571429em;
+}
+.katex .sizing.reset-size2.size5,
+.katex .fontsize-ensurer.reset-size2.size5 {
+  font-size: 1.42857143em;
+}
+.katex .sizing.reset-size2.size6,
+.katex .fontsize-ensurer.reset-size2.size6 {
+  font-size: 1.71428571em;
+}
+.katex .sizing.reset-size2.size7,
+.katex .fontsize-ensurer.reset-size2.size7 {
+  font-size: 2.05714286em;
+}
+.katex .sizing.reset-size2.size8,
+.katex .fontsize-ensurer.reset-size2.size8 {
+  font-size: 2.47142857em;
+}
+.katex .sizing.reset-size2.size9,
+.katex .fontsize-ensurer.reset-size2.size9 {
+  font-size: 2.95714286em;
+}
+.katex .sizing.reset-size2.size10,
+.katex .fontsize-ensurer.reset-size2.size10 {
+  font-size: 3.55714286em;
+}
+.katex .sizing.reset-size3.size1,
+.katex .fontsize-ensurer.reset-size3.size1 {
+  font-size: 0.625em;
+}
+.katex .sizing.reset-size3.size2,
+.katex .fontsize-ensurer.reset-size3.size2 {
+  font-size: 0.875em;
+}
+.katex .sizing.reset-size3.size3,
+.katex .fontsize-ensurer.reset-size3.size3 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size3.size4,
+.katex .fontsize-ensurer.reset-size3.size4 {
+  font-size: 1.125em;
+}
+.katex .sizing.reset-size3.size5,
+.katex .fontsize-ensurer.reset-size3.size5 {
+  font-size: 1.25em;
+}
+.katex .sizing.reset-size3.size6,
+.katex .fontsize-ensurer.reset-size3.size6 {
+  font-size: 1.5em;
+}
+.katex .sizing.reset-size3.size7,
+.katex .fontsize-ensurer.reset-size3.size7 {
+  font-size: 1.8em;
+}
+.katex .sizing.reset-size3.size8,
+.katex .fontsize-ensurer.reset-size3.size8 {
+  font-size: 2.1625em;
+}
+.katex .sizing.reset-size3.size9,
+.katex .fontsize-ensurer.reset-size3.size9 {
+  font-size: 2.5875em;
+}
+.katex .sizing.reset-size3.size10,
+.katex .fontsize-ensurer.reset-size3.size10 {
+  font-size: 3.1125em;
+}
+.katex .sizing.reset-size4.size1,
+.katex .fontsize-ensurer.reset-size4.size1 {
+  font-size: 0.55555556em;
+}
+.katex .sizing.reset-size4.size2,
+.katex .fontsize-ensurer.reset-size4.size2 {
+  font-size: 0.77777778em;
+}
+.katex .sizing.reset-size4.size3,
+.katex .fontsize-ensurer.reset-size4.size3 {
+  font-size: 0.88888889em;
+}
+.katex .sizing.reset-size4.size4,
+.katex .fontsize-ensurer.reset-size4.size4 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size4.size5,
+.katex .fontsize-ensurer.reset-size4.size5 {
+  font-size: 1.11111111em;
+}
+.katex .sizing.reset-size4.size6,
+.katex .fontsize-ensurer.reset-size4.size6 {
+  font-size: 1.33333333em;
+}
+.katex .sizing.reset-size4.size7,
+.katex .fontsize-ensurer.reset-size4.size7 {
+  font-size: 1.6em;
+}
+.katex .sizing.reset-size4.size8,
+.katex .fontsize-ensurer.reset-size4.size8 {
+  font-size: 1.92222222em;
+}
+.katex .sizing.reset-size4.size9,
+.katex .fontsize-ensurer.reset-size4.size9 {
+  font-size: 2.3em;
+}
+.katex .sizing.reset-size4.size10,
+.katex .fontsize-ensurer.reset-size4.size10 {
+  font-size: 2.76666667em;
+}
+.katex .sizing.reset-size5.size1,
+.katex .fontsize-ensurer.reset-size5.size1 {
+  font-size: 0.5em;
+}
+.katex .sizing.reset-size5.size2,
+.katex .fontsize-ensurer.reset-size5.size2 {
+  font-size: 0.7em;
+}
+.katex .sizing.reset-size5.size3,
+.katex .fontsize-ensurer.reset-size5.size3 {
+  font-size: 0.8em;
+}
+.katex .sizing.reset-size5.size4,
+.katex .fontsize-ensurer.reset-size5.size4 {
+  font-size: 0.9em;
+}
+.katex .sizing.reset-size5.size5,
+.katex .fontsize-ensurer.reset-size5.size5 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size5.size6,
+.katex .fontsize-ensurer.reset-size5.size6 {
+  font-size: 1.2em;
+}
+.katex .sizing.reset-size5.size7,
+.katex .fontsize-ensurer.reset-size5.size7 {
+  font-size: 1.44em;
+}
+.katex .sizing.reset-size5.size8,
+.katex .fontsize-ensurer.reset-size5.size8 {
+  font-size: 1.73em;
+}
+.katex .sizing.reset-size5.size9,
+.katex .fontsize-ensurer.reset-size5.size9 {
+  font-size: 2.07em;
+}
+.katex .sizing.reset-size5.size10,
+.katex .fontsize-ensurer.reset-size5.size10 {
+  font-size: 2.49em;
+}
+.katex .sizing.reset-size6.size1,
+.katex .fontsize-ensurer.reset-size6.size1 {
+  font-size: 0.41666667em;
+}
+.katex .sizing.reset-size6.size2,
+.katex .fontsize-ensurer.reset-size6.size2 {
+  font-size: 0.58333333em;
+}
+.katex .sizing.reset-size6.size3,
+.katex .fontsize-ensurer.reset-size6.size3 {
+  font-size: 0.66666667em;
+}
+.katex .sizing.reset-size6.size4,
+.katex .fontsize-ensurer.reset-size6.size4 {
+  font-size: 0.75em;
+}
+.katex .sizing.reset-size6.size5,
+.katex .fontsize-ensurer.reset-size6.size5 {
+  font-size: 0.83333333em;
+}
+.katex .sizing.reset-size6.size6,
+.katex .fontsize-ensurer.reset-size6.size6 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size6.size7,
+.katex .fontsize-ensurer.reset-size6.size7 {
+  font-size: 1.2em;
+}
+.katex .sizing.reset-size6.size8,
+.katex .fontsize-ensurer.reset-size6.size8 {
+  font-size: 1.44166667em;
+}
+.katex .sizing.reset-size6.size9,
+.katex .fontsize-ensurer.reset-size6.size9 {
+  font-size: 1.725em;
+}
+.katex .sizing.reset-size6.size10,
+.katex .fontsize-ensurer.reset-size6.size10 {
+  font-size: 2.075em;
+}
+.katex .sizing.reset-size7.size1,
+.katex .fontsize-ensurer.reset-size7.size1 {
+  font-size: 0.34722222em;
+}
+.katex .sizing.reset-size7.size2,
+.katex .fontsize-ensurer.reset-size7.size2 {
+  font-size: 0.48611111em;
+}
+.katex .sizing.reset-size7.size3,
+.katex .fontsize-ensurer.reset-size7.size3 {
+  font-size: 0.55555556em;
+}
+.katex .sizing.reset-size7.size4,
+.katex .fontsize-ensurer.reset-size7.size4 {
+  font-size: 0.625em;
+}
+.katex .sizing.reset-size7.size5,
+.katex .fontsize-ensurer.reset-size7.size5 {
+  font-size: 0.69444444em;
+}
+.katex .sizing.reset-size7.size6,
+.katex .fontsize-ensurer.reset-size7.size6 {
+  font-size: 0.83333333em;
+}
+.katex .sizing.reset-size7.size7,
+.katex .fontsize-ensurer.reset-size7.size7 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size7.size8,
+.katex .fontsize-ensurer.reset-size7.size8 {
+  font-size: 1.20138889em;
+}
+.katex .sizing.reset-size7.size9,
+.katex .fontsize-ensurer.reset-size7.size9 {
+  font-size: 1.4375em;
+}
+.katex .sizing.reset-size7.size10,
+.katex .fontsize-ensurer.reset-size7.size10 {
+  font-size: 1.72916667em;
+}
+.katex .sizing.reset-size8.size1,
+.katex .fontsize-ensurer.reset-size8.size1 {
+  font-size: 0.28901734em;
+}
+.katex .sizing.reset-size8.size2,
+.katex .fontsize-ensurer.reset-size8.size2 {
+  font-size: 0.40462428em;
+}
+.katex .sizing.reset-size8.size3,
+.katex .fontsize-ensurer.reset-size8.size3 {
+  font-size: 0.46242775em;
+}
+.katex .sizing.reset-size8.size4,
+.katex .fontsize-ensurer.reset-size8.size4 {
+  font-size: 0.52023121em;
+}
+.katex .sizing.reset-size8.size5,
+.katex .fontsize-ensurer.reset-size8.size5 {
+  font-size: 0.57803468em;
+}
+.katex .sizing.reset-size8.size6,
+.katex .fontsize-ensurer.reset-size8.size6 {
+  font-size: 0.69364162em;
+}
+.katex .sizing.reset-size8.size7,
+.katex .fontsize-ensurer.reset-size8.size7 {
+  font-size: 0.83236994em;
+}
+.katex .sizing.reset-size8.size8,
+.katex .fontsize-ensurer.reset-size8.size8 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size8.size9,
+.katex .fontsize-ensurer.reset-size8.size9 {
+  font-size: 1.19653179em;
+}
+.katex .sizing.reset-size8.size10,
+.katex .fontsize-ensurer.reset-size8.size10 {
+  font-size: 1.43930636em;
+}
+.katex .sizing.reset-size9.size1,
+.katex .fontsize-ensurer.reset-size9.size1 {
+  font-size: 0.24154589em;
+}
+.katex .sizing.reset-size9.size2,
+.katex .fontsize-ensurer.reset-size9.size2 {
+  font-size: 0.33816425em;
+}
+.katex .sizing.reset-size9.size3,
+.katex .fontsize-ensurer.reset-size9.size3 {
+  font-size: 0.38647343em;
+}
+.katex .sizing.reset-size9.size4,
+.katex .fontsize-ensurer.reset-size9.size4 {
+  font-size: 0.43478261em;
+}
+.katex .sizing.reset-size9.size5,
+.katex .fontsize-ensurer.reset-size9.size5 {
+  font-size: 0.48309179em;
+}
+.katex .sizing.reset-size9.size6,
+.katex .fontsize-ensurer.reset-size9.size6 {
+  font-size: 0.57971014em;
+}
+.katex .sizing.reset-size9.size7,
+.katex .fontsize-ensurer.reset-size9.size7 {
+  font-size: 0.69565217em;
+}
+.katex .sizing.reset-size9.size8,
+.katex .fontsize-ensurer.reset-size9.size8 {
+  font-size: 0.83574879em;
+}
+.katex .sizing.reset-size9.size9,
+.katex .fontsize-ensurer.reset-size9.size9 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size9.size10,
+.katex .fontsize-ensurer.reset-size9.size10 {
+  font-size: 1.20289855em;
+}
+.katex .sizing.reset-size10.size1,
+.katex .fontsize-ensurer.reset-size10.size1 {
+  font-size: 0.20080321em;
+}
+.katex .sizing.reset-size10.size2,
+.katex .fontsize-ensurer.reset-size10.size2 {
+  font-size: 0.2811245em;
+}
+.katex .sizing.reset-size10.size3,
+.katex .fontsize-ensurer.reset-size10.size3 {
+  font-size: 0.32128514em;
+}
+.katex .sizing.reset-size10.size4,
+.katex .fontsize-ensurer.reset-size10.size4 {
+  font-size: 0.36144578em;
+}
+.katex .sizing.reset-size10.size5,
+.katex .fontsize-ensurer.reset-size10.size5 {
+  font-size: 0.40160643em;
+}
+.katex .sizing.reset-size10.size6,
+.katex .fontsize-ensurer.reset-size10.size6 {
+  font-size: 0.48192771em;
+}
+.katex .sizing.reset-size10.size7,
+.katex .fontsize-ensurer.reset-size10.size7 {
+  font-size: 0.57831325em;
+}
+.katex .sizing.reset-size10.size8,
+.katex .fontsize-ensurer.reset-size10.size8 {
+  font-size: 0.69477912em;
+}
+.katex .sizing.reset-size10.size9,
+.katex .fontsize-ensurer.reset-size10.size9 {
+  font-size: 0.8313253em;
+}
+.katex .sizing.reset-size10.size10,
+.katex .fontsize-ensurer.reset-size10.size10 {
+  font-size: 1em;
+}
+.katex .delimsizing.size1 {
+  font-family: KaTeX_Size1;
+}
+.katex .delimsizing.size2 {
+  font-family: KaTeX_Size2;
+}
+.katex .delimsizing.size3 {
+  font-family: KaTeX_Size3;
+}
+.katex .delimsizing.size4 {
+  font-family: KaTeX_Size4;
+}
+.katex .delimsizing.mult .delim-size1 > span {
+  font-family: KaTeX_Size1;
+}
+.katex .delimsizing.mult .delim-size4 > span {
+  font-family: KaTeX_Size4;
+}
+.katex .nulldelimiter {
+  display: inline-block;
+  width: 0.12em;
+}
+.katex .op-symbol {
+  position: relative;
+}
+.katex .op-symbol.small-op {
+  font-family: KaTeX_Size1;
+}
+.katex .op-symbol.large-op {
+  font-family: KaTeX_Size2;
+}
+.katex .op-limits > .vlist > span {
+  text-align: center;
+}
+.katex .accent > .vlist > span {
+  text-align: center;
+}
+.katex .accent .accent-body > span {
+  width: 0;
+}
+.katex .accent .accent-body.accent-vec > span {
+  position: relative;
+  left: 0.326em;
+}
+.katex .mtable .vertical-separator {
+  display: inline-block;
+  margin: 0 -0.025em;
+  border-right: 0.05em solid black;
+}
+.katex .mtable .arraycolsep {
+  display: inline-block;
+}
+.katex .mtable .col-align-c > .vlist {
+  text-align: center;
+}
+.katex .mtable .col-align-l > .vlist {
+  text-align: left;
+}
+.katex .mtable .col-align-r > .vlist {
+  text-align: right;
+}
diff --git a/specs/es/3.2/katex/katex.js b/specs/es/3.2/katex/katex.js
new file mode 100644
index 0000000..e104be9
--- /dev/null
+++ b/specs/es/3.2/katex/katex.js
@@ -0,0 +1,9075 @@
+(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.katex = f()}})(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
+/* eslint no-console:0 */
+/**
+ * This is the main entry point for KaTeX. Here, we expose functions for
+ * rendering expressions either to DOM nodes or to markup strings.
+ *
+ * We also expose the ParseError class to check if errors thrown from KaTeX are
+ * errors in the expression, or errors in javascript handling.
+ */
+
+var ParseError = require("./src/ParseError");
+var Settings = require("./src/Settings");
+
+var buildTree = require("./src/buildTree");
+var parseTree = require("./src/parseTree");
+var utils = require("./src/utils");
+
+/**
+ * Parse and build an expression, and place that expression in the DOM node
+ * given.
+ */
+var render = function(expression, baseNode, options) {
+    utils.clearNode(baseNode);
+
+    var settings = new Settings(options);
+
+    var tree = parseTree(expression, settings);
+    var node = buildTree(tree, expression, settings).toNode();
+
+    baseNode.appendChild(node);
+};
+
+// KaTeX's styles don't work properly in quirks mode. Print out an error, and
+// disable rendering.
+if (typeof document !== "undefined") {
+    if (document.compatMode !== "CSS1Compat") {
+        typeof console !== "undefined" && console.warn(
+            "Warning: KaTeX doesn't work in quirks mode. Make sure your " +
+                "website has a suitable doctype.");
+
+        render = function() {
+            throw new ParseError("KaTeX doesn't work in quirks mode.");
+        };
+    }
+}
+
+/**
+ * Parse and build an expression, and return the markup for that.
+ */
+var renderToString = function(expression, options) {
+    var settings = new Settings(options);
+
+    var tree = parseTree(expression, settings);
+    return buildTree(tree, expression, settings).toMarkup();
+};
+
+/**
+ * Parse an expression and return the parse tree.
+ */
+var generateParseTree = function(expression, options) {
+    var settings = new Settings(options);
+    return parseTree(expression, settings);
+};
+
+module.exports = {
+    render: render,
+    renderToString: renderToString,
+    /**
+     * NOTE: This method is not currently recommended for public use.
+     * The internal tree representation is unstable and is very likely
+     * to change. Use at your own risk.
+     */
+    __parse: generateParseTree,
+    ParseError: ParseError
+};
+
+},{"./src/ParseError":6,"./src/Settings":8,"./src/buildTree":13,"./src/parseTree":22,"./src/utils":25}],2:[function(require,module,exports){
+/** @flow */
+
+"use strict";
+
+function getRelocatable(re) {
+  // In the future, this could use a WeakMap instead of an expando.
+  if (!re.__matchAtRelocatable) {
+    // Disjunctions are the lowest-precedence operator, so we can make any
+    // pattern match the empty string by appending `|()` to it:
+    // https://people.mozilla.org/~jorendorff/es6-draft.html#sec-patterns
+    var source = re.source + "|()";
+
+    // We always make the new regex global.
+    var flags = "g" + (re.ignoreCase ? "i" : "") + (re.multiline ? "m" : "") + (re.unicode ? "u" : "")
+    // sticky (/.../y) doesn't make sense in conjunction with our relocation
+    // logic, so we ignore it here.
+    ;
+
+    re.__matchAtRelocatable = new RegExp(source, flags);
+  }
+  return re.__matchAtRelocatable;
+}
+
+function matchAt(re, str, pos) {
+  if (re.global || re.sticky) {
+    throw new Error("matchAt(...): Only non-global regexes are supported");
+  }
+  var reloc = getRelocatable(re);
+  reloc.lastIndex = pos;
+  var match = reloc.exec(str);
+  // Last capturing group is our sentinel that indicates whether the regex
+  // matched at the given location.
+  if (match[match.length - 1] == null) {
+    // Original regex matched.
+    match.length = match.length - 1;
+    return match;
+  } else {
+    return null;
+  }
+}
+
+module.exports = matchAt;
+},{}],3:[function(require,module,exports){
+/**
+ * The Lexer class handles tokenizing the input in various ways. Since our
+ * parser expects us to be able to backtrack, the lexer allows lexing from any
+ * given starting point.
+ *
+ * Its main exposed function is the `lex` function, which takes a position to
+ * lex from and a type of token to lex. It defers to the appropriate `_innerLex`
+ * function.
+ *
+ * The various `_innerLex` functions perform the actual lexing of different
+ * kinds.
+ */
+
+var matchAt = require("match-at");
+
+var ParseError = require("./ParseError");
+
+// The main lexer class
+function Lexer(input) {
+    this.input = input;
+    this.pos = 0;
+}
+
+/**
+ * The resulting token returned from `lex`.
+ *
+ * It consists of the token text plus some position information.
+ * The position information is essentially a range in an input string,
+ * but instead of referencing the bare input string, we refer to the lexer.
+ * That way it is possible to attach extra metadata to the input string,
+ * like for example a file name or similar.
+ *
+ * The position information (all three parameters) is optional,
+ * so it is OK to construct synthetic tokens if appropriate.
+ * Not providing available position information may lead to
+ * degraded error reporting, though.
+ *
+ * @param {string}  text   the text of this token
+ * @param {number=} start  the start offset, zero-based inclusive
+ * @param {number=} end    the end offset, zero-based exclusive
+ * @param {Lexer=}  lexer  the lexer which in turn holds the input string
+ */
+function Token(text, start, end, lexer) {
+    this.text = text;
+    this.start = start;
+    this.end = end;
+    this.lexer = lexer;
+}
+
+/**
+ * Given a pair of tokens (this and endToken), compute a “Token” encompassing
+ * the whole input range enclosed by these two.
+ *
+ * @param {Token}  endToken  last token of the range, inclusive
+ * @param {string} text      the text of the newly constructed token
+ */
+Token.prototype.range = function(endToken, text) {
+    if (endToken.lexer !== this.lexer) {
+        return new Token(text); // sorry, no position information available
+    }
+    return new Token(text, this.start, endToken.end, this.lexer);
+};
+
+/* The following tokenRegex
+ * - matches typical whitespace (but not NBSP etc.) using its first group
+ * - does not match any control character \x00-\x1f except whitespace
+ * - does not match a bare backslash
+ * - matches any ASCII character except those just mentioned
+ * - does not match the BMP private use area \uE000-\uF8FF
+ * - does not match bare surrogate code units
+ * - matches any BMP character except for those just described
+ * - matches any valid Unicode surrogate pair
+ * - matches a backslash followed by one or more letters
+ * - matches a backslash followed by any BMP character, including newline
+ * Just because the Lexer matches something doesn't mean it's valid input:
+ * If there is no matching function or symbol definition, the Parser will
+ * still reject the input.
+ */
+var tokenRegex = new RegExp(
+    "([ \r\n\t]+)|" +                                 // whitespace
+    "([!-\\[\\]-\u2027\u202A-\uD7FF\uF900-\uFFFF]" +  // single codepoint
+    "|[\uD800-\uDBFF][\uDC00-\uDFFF]" +               // surrogate pair
+    "|\\\\(?:[a-zA-Z]+|[^\uD800-\uDFFF])" +           // function name
+    ")"
+);
+
+/**
+ * This function lexes a single token.
+ */
+Lexer.prototype.lex = function() {
+    var input = this.input;
+    var pos = this.pos;
+    if (pos === input.length) {
+        return new Token("EOF", pos, pos, this);
+    }
+    var match = matchAt(tokenRegex, input, pos);
+    if (match === null) {
+        throw new ParseError(
+            "Unexpected character: '" + input[pos] + "'",
+            new Token(input[pos], pos, pos + 1, this));
+    }
+    var text = match[2] || " ";
+    var start = this.pos;
+    this.pos += match[0].length;
+    var end = this.pos;
+    return new Token(text, start, end, this);
+};
+
+module.exports = Lexer;
+
+},{"./ParseError":6,"match-at":2}],4:[function(require,module,exports){
+/**
+ * This file contains the “gullet” where macros are expanded
+ * until only non-macro tokens remain.
+ */
+
+var Lexer = require("./Lexer");
+
+function MacroExpander(input, macros) {
+    this.lexer = new Lexer(input);
+    this.macros = macros;
+    this.stack = []; // contains tokens in REVERSE order
+    this.discardedWhiteSpace = [];
+}
+
+/**
+ * Recursively expand first token, then return first non-expandable token.
+ */
+MacroExpander.prototype.nextToken = function() {
+    for (;;) {
+        if (this.stack.length === 0) {
+            this.stack.push(this.lexer.lex());
+        }
+        var topToken = this.stack.pop();
+        var name = topToken.text;
+        if (!(name.charAt(0) === "\\" && this.macros.hasOwnProperty(name))) {
+            return topToken;
+        }
+        var expansion = this.macros[name];
+        if (typeof expansion === "string") {
+            var bodyLexer = new Lexer(expansion);
+            expansion = [];
+            var tok = bodyLexer.lex();
+            while (tok.text !== "EOF") {
+                expansion.push(tok);
+                tok = bodyLexer.lex();
+            }
+            expansion.reverse(); // to fit in with stack using push and pop
+            this.macros[name] = expansion;
+        }
+        this.stack = this.stack.concat(expansion);
+    }
+};
+
+MacroExpander.prototype.get = function(ignoreSpace) {
+    this.discardedWhiteSpace = [];
+    var token = this.nextToken();
+    if (ignoreSpace) {
+        while (token.text === " ") {
+            this.discardedWhiteSpace.push(token);
+            token = this.nextToken();
+        }
+    }
+    return token;
+};
+
+/**
+ * Undo the effect of the preceding call to the get method.
+ * A call to this method MUST be immediately preceded and immediately followed
+ * by a call to get.  Only used during mode switching, i.e. after one token
+ * was got in the old mode but should get got again in a new mode
+ * with possibly different whitespace handling.
+ */
+MacroExpander.prototype.unget = function(token) {
+    this.stack.push(token);
+    while (this.discardedWhiteSpace.length !== 0) {
+        this.stack.push(this.discardedWhiteSpace.pop());
+    }
+};
+
+module.exports = MacroExpander;
+
+},{"./Lexer":3}],5:[function(require,module,exports){
+/**
+ * This file contains information about the options that the Parser carries
+ * around with it while parsing. Data is held in an `Options` object, and when
+ * recursing, a new `Options` object can be created with the `.with*` and
+ * `.reset` functions.
+ */
+
+/**
+ * This is the main options class. It contains the style, size, color, and font
+ * of the current parse level. It also contains the style and size of the parent
+ * parse level, so size changes can be handled efficiently.
+ *
+ * Each of the `.with*` and `.reset` functions passes its current style and size
+ * as the parentStyle and parentSize of the new options class, so parent
+ * handling is taken care of automatically.
+ */
+function Options(data) {
+    this.style = data.style;
+    this.color = data.color;
+    this.size = data.size;
+    this.phantom = data.phantom;
+    this.font = data.font;
+
+    if (data.parentStyle === undefined) {
+        this.parentStyle = data.style;
+    } else {
+        this.parentStyle = data.parentStyle;
+    }
+
+    if (data.parentSize === undefined) {
+        this.parentSize = data.size;
+    } else {
+        this.parentSize = data.parentSize;
+    }
+}
+
+/**
+ * Returns a new options object with the same properties as "this".  Properties
+ * from "extension" will be copied to the new options object.
+ */
+Options.prototype.extend = function(extension) {
+    var data = {
+        style: this.style,
+        size: this.size,
+        color: this.color,
+        parentStyle: this.style,
+        parentSize: this.size,
+        phantom: this.phantom,
+        font: this.font
+    };
+
+    for (var key in extension) {
+        if (extension.hasOwnProperty(key)) {
+            data[key] = extension[key];
+        }
+    }
+
+    return new Options(data);
+};
+
+/**
+ * Create a new options object with the given style.
+ */
+Options.prototype.withStyle = function(style) {
+    return this.extend({
+        style: style
+    });
+};
+
+/**
+ * Create a new options object with the given size.
+ */
+Options.prototype.withSize = function(size) {
+    return this.extend({
+        size: size
+    });
+};
+
+/**
+ * Create a new options object with the given color.
+ */
+Options.prototype.withColor = function(color) {
+    return this.extend({
+        color: color
+    });
+};
+
+/**
+ * Create a new options object with "phantom" set to true.
+ */
+Options.prototype.withPhantom = function() {
+    return this.extend({
+        phantom: true
+    });
+};
+
+/**
+ * Create a new options objects with the give font.
+ */
+Options.prototype.withFont = function(font) {
+    return this.extend({
+        font: font || this.font
+    });
+};
+
+/**
+ * Create a new options object with the same style, size, and color. This is
+ * used so that parent style and size changes are handled correctly.
+ */
+Options.prototype.reset = function() {
+    return this.extend({});
+};
+
+/**
+ * A map of color names to CSS colors.
+ * TODO(emily): Remove this when we have real macros
+ */
+var colorMap = {
+    "katex-blue": "#6495ed",
+    "katex-orange": "#ffa500",
+    "katex-pink": "#ff00af",
+    "katex-red": "#df0030",
+    "katex-green": "#28ae7b",
+    "katex-gray": "gray",
+    "katex-purple": "#9d38bd",
+    "katex-blueA": "#ccfaff",
+    "katex-blueB": "#80f6ff",
+    "katex-blueC": "#63d9ea",
+    "katex-blueD": "#11accd",
+    "katex-blueE": "#0c7f99",
+    "katex-tealA": "#94fff5",
+    "katex-tealB": "#26edd5",
+    "katex-tealC": "#01d1c1",
+    "katex-tealD": "#01a995",
+    "katex-tealE": "#208170",
+    "katex-greenA": "#b6ffb0",
+    "katex-greenB": "#8af281",
+    "katex-greenC": "#74cf70",
+    "katex-greenD": "#1fab54",
+    "katex-greenE": "#0d923f",
+    "katex-goldA": "#ffd0a9",
+    "katex-goldB": "#ffbb71",
+    "katex-goldC": "#ff9c39",
+    "katex-goldD": "#e07d10",
+    "katex-goldE": "#a75a05",
+    "katex-redA": "#fca9a9",
+    "katex-redB": "#ff8482",
+    "katex-redC": "#f9685d",
+    "katex-redD": "#e84d39",
+    "katex-redE": "#bc2612",
+    "katex-maroonA": "#ffbde0",
+    "katex-maroonB": "#ff92c6",
+    "katex-maroonC": "#ed5fa6",
+    "katex-maroonD": "#ca337c",
+    "katex-maroonE": "#9e034e",
+    "katex-purpleA": "#ddd7ff",
+    "katex-purpleB": "#c6b9fc",
+    "katex-purpleC": "#aa87ff",
+    "katex-purpleD": "#7854ab",
+    "katex-purpleE": "#543b78",
+    "katex-mintA": "#f5f9e8",
+    "katex-mintB": "#edf2df",
+    "katex-mintC": "#e0e5cc",
+    "katex-grayA": "#f6f7f7",
+    "katex-grayB": "#f0f1f2",
+    "katex-grayC": "#e3e5e6",
+    "katex-grayD": "#d6d8da",
+    "katex-grayE": "#babec2",
+    "katex-grayF": "#888d93",
+    "katex-grayG": "#626569",
+    "katex-grayH": "#3b3e40",
+    "katex-grayI": "#21242c",
+    "katex-kaBlue": "#314453",
+    "katex-kaGreen": "#71B307"
+};
+
+/**
+ * Gets the CSS color of the current options object, accounting for the
+ * `colorMap`.
+ */
+Options.prototype.getColor = function() {
+    if (this.phantom) {
+        return "transparent";
+    } else {
+        return colorMap[this.color] || this.color;
+    }
+};
+
+module.exports = Options;
+
+},{}],6:[function(require,module,exports){
+/**
+ * This is the ParseError class, which is the main error thrown by KaTeX
+ * functions when something has gone wrong. This is used to distinguish internal
+ * errors from errors in the expression that the user provided.
+ *
+ * If possible, a caller should provide a Token or ParseNode with information
+ * about where in the source string the problem occurred.
+ *
+ * @param {string} message  The error message
+ * @param {(Token|ParseNode)=} token  An object providing position information
+ */
+function ParseError(message, token) {
+    var error = "KaTeX parse error: " + message;
+    var start;
+    var end;
+
+    if (token && token.lexer && token.start <= token.end) {
+        // If we have the input and a position, make the error a bit fancier
+
+        // Get the input
+        var input = token.lexer.input;
+
+        // Prepend some information
+        start = token.start;
+        end = token.end;
+        if (start === input.length) {
+            error += " at end of input: ";
+        } else {
+            error += " at position " + (start + 1) + ": ";
+        }
+
+        // Underline token in question using combining underscores
+        var underlined = input.slice(start, end).replace(/[^]/g, "$&\u0332");
+
+        // Extract some context from the input and add it to the error
+        var left;
+        if (start > 15) {
+            left = "…" + input.slice(start - 15, start);
+        } else {
+            left = input.slice(0, start);
+        }
+        var right;
+        if (end + 15 < input.length) {
+            right = input.slice(end, end + 15) + "…";
+        } else {
+            right = input.slice(end);
+        }
+        error += left + underlined + right;
+    }
+
+    // Some hackery to make ParseError a prototype of Error
+    // See http://stackoverflow.com/a/8460753
+    var self = new Error(error);
+    self.name = "ParseError";
+    self.__proto__ = ParseError.prototype;
+
+    self.position = start;
+    return self;
+}
+
+// More hackery
+ParseError.prototype.__proto__ = Error.prototype;
+
+module.exports = ParseError;
+
+},{}],7:[function(require,module,exports){
+/* eslint no-constant-condition:0 */
+var functions = require("./functions");
+var environments = require("./environments");
+var MacroExpander = require("./MacroExpander");
+var symbols = require("./symbols");
+var utils = require("./utils");
+var cjkRegex = require("./unicodeRegexes").cjkRegex;
+
+var parseData = require("./parseData");
+var ParseError = require("./ParseError");
+
+/**
+ * This file contains the parser used to parse out a TeX expression from the
+ * input. Since TeX isn't context-free, standard parsers don't work particularly
+ * well.
+ *
+ * The strategy of this parser is as such:
+ *
+ * The main functions (the `.parse...` ones) take a position in the current
+ * parse string to parse tokens from. The lexer (found in Lexer.js, stored at
+ * this.lexer) also supports pulling out tokens at arbitrary places. When
+ * individual tokens are needed at a position, the lexer is called to pull out a
+ * token, which is then used.
+ *
+ * The parser has a property called "mode" indicating the mode that
+ * the parser is currently in. Currently it has to be one of "math" or
+ * "text", which denotes whether the current environment is a math-y
+ * one or a text-y one (e.g. inside \text). Currently, this serves to
+ * limit the functions which can be used in text mode.
+ *
+ * The main functions then return an object which contains the useful data that
+ * was parsed at its given point, and a new position at the end of the parsed
+ * data. The main functions can call each other and continue the parsing by
+ * using the returned position as a new starting point.
+ *
+ * There are also extra `.handle...` functions, which pull out some reused
+ * functionality into self-contained functions.
+ *
+ * The earlier functions return ParseNodes.
+ * The later functions (which are called deeper in the parse) sometimes return
+ * ParseFuncOrArgument, which contain a ParseNode as well as some data about
+ * whether the parsed object is a function which is missing some arguments, or a
+ * standalone object which can be used as an argument to another function.
+ */
+
+/**
+ * Main Parser class
+ */
+function Parser(input, settings) {
+    // Create a new macro expander (gullet) and (indirectly via that) also a
+    // new lexer (mouth) for this parser (stomach, in the language of TeX)
+    this.gullet = new MacroExpander(input, settings.macros);
+    // Store the settings for use in parsing
+    this.settings = settings;
+    // Count leftright depth (for \middle errors)
+    this.leftrightDepth = 0;
+}
+
+var ParseNode = parseData.ParseNode;
+
+/**
+ * An initial function (without its arguments), or an argument to a function.
+ * The `result` argument should be a ParseNode.
+ */
+function ParseFuncOrArgument(result, isFunction, token) {
+    this.result = result;
+    // Is this a function (i.e. is it something defined in functions.js)?
+    this.isFunction = isFunction;
+    this.token = token;
+}
+
+/**
+ * Checks a result to make sure it has the right type, and throws an
+ * appropriate error otherwise.
+ *
+ * @param {boolean=} consume whether to consume the expected token,
+ *                           defaults to true
+ */
+Parser.prototype.expect = function(text, consume) {
+    if (this.nextToken.text !== text) {
+        throw new ParseError(
+            "Expected '" + text + "', got '" + this.nextToken.text + "'",
+            this.nextToken
+        );
+    }
+    if (consume !== false) {
+        this.consume();
+    }
+};
+
+/**
+ * Considers the current look ahead token as consumed,
+ * and fetches the one after that as the new look ahead.
+ */
+Parser.prototype.consume = function() {
+    this.nextToken = this.gullet.get(this.mode === "math");
+};
+
+Parser.prototype.switchMode = function(newMode) {
+    this.gullet.unget(this.nextToken);
+    this.mode = newMode;
+    this.consume();
+};
+
+/**
+ * Main parsing function, which parses an entire input.
+ *
+ * @return {?Array.<ParseNode>}
+ */
+Parser.prototype.parse = function() {
+    // Try to parse the input
+    this.mode = "math";
+    this.consume();
+    var parse = this.parseInput();
+    return parse;
+};
+
+/**
+ * Parses an entire input tree.
+ */
+Parser.prototype.parseInput = function() {
+    // Parse an expression
+    var expression = this.parseExpression(false);
+    // If we succeeded, make sure there's an EOF at the end
+    this.expect("EOF", false);
+    return expression;
+};
+
+var endOfExpression = ["}", "\\end", "\\right", "&", "\\\\", "\\cr"];
+
+/**
+ * Parses an "expression", which is a list of atoms.
+ *
+ * @param {boolean} breakOnInfix  Should the parsing stop when we hit infix
+ *                  nodes? This happens when functions have higher precendence
+ *                  than infix nodes in implicit parses.
+ *
+ * @param {?string} breakOnTokenText  The text of the token that the expression
+ *                  should end with, or `null` if something else should end the
+ *                  expression.
+ *
+ * @return {ParseNode}
+ */
+Parser.prototype.parseExpression = function(breakOnInfix, breakOnTokenText) {
+    var body = [];
+    // Keep adding atoms to the body until we can't parse any more atoms (either
+    // we reached the end, a }, or a \right)
+    while (true) {
+        var lex = this.nextToken;
+        if (endOfExpression.indexOf(lex.text) !== -1) {
+            break;
+        }
+        if (breakOnTokenText && lex.text === breakOnTokenText) {
+            break;
+        }
+        if (breakOnInfix && functions[lex.text] && functions[lex.text].infix) {
+            break;
+        }
+        var atom = this.parseAtom();
+        if (!atom) {
+            if (!this.settings.throwOnError && lex.text[0] === "\\") {
+                var errorNode = this.handleUnsupportedCmd();
+                body.push(errorNode);
+                continue;
+            }
+
+            break;
+        }
+        body.push(atom);
+    }
+    return this.handleInfixNodes(body);
+};
+
+/**
+ * Rewrites infix operators such as \over with corresponding commands such
+ * as \frac.
+ *
+ * There can only be one infix operator per group.  If there's more than one
+ * then the expression is ambiguous.  This can be resolved by adding {}.
+ *
+ * @returns {Array}
+ */
+Parser.prototype.handleInfixNodes = function(body) {
+    var overIndex = -1;
+    var funcName;
+
+    for (var i = 0; i < body.length; i++) {
+        var node = body[i];
+        if (node.type === "infix") {
+            if (overIndex !== -1) {
+                throw new ParseError(
+                    "only one infix operator per group",
+                    node.value.token);
+            }
+            overIndex = i;
+            funcName = node.value.replaceWith;
+        }
+    }
+
+    if (overIndex !== -1) {
+        var numerNode;
+        var denomNode;
+
+        var numerBody = body.slice(0, overIndex);
+        var denomBody = body.slice(overIndex + 1);
+
+        if (numerBody.length === 1 && numerBody[0].type === "ordgroup") {
+            numerNode = numerBody[0];
+        } else {
+            numerNode = new ParseNode("ordgroup", numerBody, this.mode);
+        }
+
+        if (denomBody.length === 1 && denomBody[0].type === "ordgroup") {
+            denomNode = denomBody[0];
+        } else {
+            denomNode = new ParseNode("ordgroup", denomBody, this.mode);
+        }
+
+        var value = this.callFunction(
+            funcName, [numerNode, denomNode], null);
+        return [new ParseNode(value.type, value, this.mode)];
+    } else {
+        return body;
+    }
+};
+
+// The greediness of a superscript or subscript
+var SUPSUB_GREEDINESS = 1;
+
+/**
+ * Handle a subscript or superscript with nice errors.
+ */
+Parser.prototype.handleSupSubscript = function(name) {
+    var symbolToken = this.nextToken;
+    var symbol = symbolToken.text;
+    this.consume();
+    var group = this.parseGroup();
+
+    if (!group) {
+        if (!this.settings.throwOnError && this.nextToken.text[0] === "\\") {
+            return this.handleUnsupportedCmd();
+        } else {
+            throw new ParseError(
+                "Expected group after '" + symbol + "'",
+                symbolToken
+            );
+        }
+    } else if (group.isFunction) {
+        // ^ and _ have a greediness, so handle interactions with functions'
+        // greediness
+        var funcGreediness = functions[group.result].greediness;
+        if (funcGreediness > SUPSUB_GREEDINESS) {
+            return this.parseFunction(group);
+        } else {
+            throw new ParseError(
+                "Got function '" + group.result + "' with no arguments " +
+                    "as " + name, symbolToken);
+        }
+    } else {
+        return group.result;
+    }
+};
+
+/**
+ * Converts the textual input of an unsupported command into a text node
+ * contained within a color node whose color is determined by errorColor
+ */
+Parser.prototype.handleUnsupportedCmd = function() {
+    var text = this.nextToken.text;
+    var textordArray = [];
+
+    for (var i = 0; i < text.length; i++) {
+        textordArray.push(new ParseNode("textord", text[i], "text"));
+    }
+
+    var textNode = new ParseNode(
+        "text",
+        {
+            body: textordArray,
+            type: "text"
+        },
+        this.mode);
+
+    var colorNode = new ParseNode(
+        "color",
+        {
+            color: this.settings.errorColor,
+            value: [textNode],
+            type: "color"
+        },
+        this.mode);
+
+    this.consume();
+    return colorNode;
+};
+
+/**
+ * Parses a group with optional super/subscripts.
+ *
+ * @return {?ParseNode}
+ */
+Parser.prototype.parseAtom = function() {
+    // The body of an atom is an implicit group, so that things like
+    // \left(x\right)^2 work correctly.
+    var base = this.parseImplicitGroup();
+
+    // In text mode, we don't have superscripts or subscripts
+    if (this.mode === "text") {
+        return base;
+    }
+
+    // Note that base may be empty (i.e. null) at this point.
+
+    var superscript;
+    var subscript;
+    while (true) {
+        // Lex the first token
+        var lex = this.nextToken;
+
+        if (lex.text === "\\limits" || lex.text === "\\nolimits") {
+            // We got a limit control
+            if (!base || base.type !== "op") {
+                throw new ParseError(
+                    "Limit controls must follow a math operator",
+                    lex);
+            } else {
+                var limits = lex.text === "\\limits";
+                base.value.limits = limits;
+                base.value.alwaysHandleSupSub = true;
+            }
+            this.consume();
+        } else if (lex.text === "^") {
+            // We got a superscript start
+            if (superscript) {
+                throw new ParseError("Double superscript", lex);
+            }
+            superscript = this.handleSupSubscript("superscript");
+        } else if (lex.text === "_") {
+            // We got a subscript start
+            if (subscript) {
+                throw new ParseError("Double subscript", lex);
+            }
+            subscript = this.handleSupSubscript("subscript");
+        } else if (lex.text === "'") {
+            // We got a prime
+            var prime = new ParseNode("textord", "\\prime", this.mode);
+
+            // Many primes can be grouped together, so we handle this here
+            var primes = [prime];
+            this.consume();
+            // Keep lexing tokens until we get something that's not a prime
+            while (this.nextToken.text === "'") {
+                // For each one, add another prime to the list
+                primes.push(prime);
+                this.consume();
+            }
+            // Put them into an ordgroup as the superscript
+            superscript = new ParseNode("ordgroup", primes, this.mode);
+        } else {
+            // If it wasn't ^, _, or ', stop parsing super/subscripts
+            break;
+        }
+    }
+
+    if (superscript || subscript) {
+        // If we got either a superscript or subscript, create a supsub
+        return new ParseNode("supsub", {
+            base: base,
+            sup: superscript,
+            sub: subscript
+        }, this.mode);
+    } else {
+        // Otherwise return the original body
+        return base;
+    }
+};
+
+// A list of the size-changing functions, for use in parseImplicitGroup
+var sizeFuncs = [
+    "\\tiny", "\\scriptsize", "\\footnotesize", "\\small", "\\normalsize",
+    "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"
+];
+
+// A list of the style-changing functions, for use in parseImplicitGroup
+var styleFuncs = [
+    "\\displaystyle", "\\textstyle", "\\scriptstyle", "\\scriptscriptstyle"
+];
+
+/**
+ * Parses an implicit group, which is a group that starts at the end of a
+ * specified, and ends right before a higher explicit group ends, or at EOL. It
+ * is used for functions that appear to affect the current style, like \Large or
+ * \textrm, where instead of keeping a style we just pretend that there is an
+ * implicit grouping after it until the end of the group. E.g.
+ *   small text {\Large large text} small text again
+ * It is also used for \left and \right to get the correct grouping.
+ *
+ * @return {?ParseNode}
+ */
+Parser.prototype.parseImplicitGroup = function() {
+    var start = this.parseSymbol();
+
+    if (start == null) {
+        // If we didn't get anything we handle, fall back to parseFunction
+        return this.parseFunction();
+    }
+
+    var func = start.result;
+    var body;
+
+    if (func === "\\left") {
+        // If we see a left:
+        // Parse the entire left function (including the delimiter)
+        var left = this.parseFunction(start);
+        // Parse out the implicit body
+        ++this.leftrightDepth;
+        body = this.parseExpression(false);
+        --this.leftrightDepth;
+        // Check the next token
+        this.expect("\\right", false);
+        var right = this.parseFunction();
+        return new ParseNode("leftright", {
+            body: body,
+            left: left.value.value,
+            right: right.value.value
+        }, this.mode);
+    } else if (func === "\\begin") {
+        // begin...end is similar to left...right
+        var begin = this.parseFunction(start);
+        var envName = begin.value.name;
+        if (!environments.hasOwnProperty(envName)) {
+            throw new ParseError(
+                "No such environment: " + envName, begin.value.nameGroup);
+        }
+        // Build the environment object. Arguments and other information will
+        // be made available to the begin and end methods using properties.
+        var env = environments[envName];
+        var args = this.parseArguments("\\begin{" + envName + "}", env);
+        var context = {
+            mode: this.mode,
+            envName: envName,
+            parser: this,
+            positions: args.pop()
+        };
+        var result = env.handler(context, args);
+        this.expect("\\end", false);
+        var endNameToken = this.nextToken;
+        var end = this.parseFunction();
+        if (end.value.name !== envName) {
+            throw new ParseError(
+                "Mismatch: \\begin{" + envName + "} matched " +
+                "by \\end{" + end.value.name + "}",
+                endNameToken);
+        }
+        result.position = end.position;
+        return result;
+    } else if (utils.contains(sizeFuncs, func)) {
+        // If we see a sizing function, parse out the implict body
+        body = this.parseExpression(false);
+        return new ParseNode("sizing", {
+            // Figure out what size to use based on the list of functions above
+            size: "size" + (utils.indexOf(sizeFuncs, func) + 1),
+            value: body
+        }, this.mode);
+    } else if (utils.contains(styleFuncs, func)) {
+        // If we see a styling function, parse out the implict body
+        body = this.parseExpression(true);
+        return new ParseNode("styling", {
+            // Figure out what style to use by pulling out the style from
+            // the function name
+            style: func.slice(1, func.length - 5),
+            value: body
+        }, this.mode);
+    } else {
+        // Defer to parseFunction if it's not a function we handle
+        return this.parseFunction(start);
+    }
+};
+
+/**
+ * Parses an entire function, including its base and all of its arguments.
+ * The base might either have been parsed already, in which case
+ * it is provided as an argument, or it's the next group in the input.
+ *
+ * @param {ParseFuncOrArgument=} baseGroup optional as described above
+ * @return {?ParseNode}
+ */
+Parser.prototype.parseFunction = function(baseGroup) {
+    if (!baseGroup) {
+        baseGroup = this.parseGroup();
+    }
+
+    if (baseGroup) {
+        if (baseGroup.isFunction) {
+            var func = baseGroup.result;
+            var funcData = functions[func];
+            if (this.mode === "text" && !funcData.allowedInText) {
+                throw new ParseError(
+                    "Can't use function '" + func + "' in text mode",
+                    baseGroup.token);
+            }
+
+            var args = this.parseArguments(func, funcData);
+            var token = baseGroup.token;
+            var result = this.callFunction(func, args, args.pop(), token);
+            return new ParseNode(result.type, result, this.mode);
+        } else {
+            return baseGroup.result;
+        }
+    } else {
+        return null;
+    }
+};
+
+/**
+ * Call a function handler with a suitable context and arguments.
+ */
+Parser.prototype.callFunction = function(name, args, positions, token) {
+    var context = {
+        funcName: name,
+        parser: this,
+        positions: positions,
+        token: token
+    };
+    return functions[name].handler(context, args);
+};
+
+/**
+ * Parses the arguments of a function or environment
+ *
+ * @param {string} func  "\name" or "\begin{name}"
+ * @param {{numArgs:number,numOptionalArgs:number|undefined}} funcData
+ * @return the array of arguments, with the list of positions as last element
+ */
+Parser.prototype.parseArguments = function(func, funcData) {
+    var totalArgs = funcData.numArgs + funcData.numOptionalArgs;
+    if (totalArgs === 0) {
+        return [[this.pos]];
+    }
+
+    var baseGreediness = funcData.greediness;
+    var positions = [this.pos];
+    var args = [];
+
+    for (var i = 0; i < totalArgs; i++) {
+        var nextToken = this.nextToken;
+        var argType = funcData.argTypes && funcData.argTypes[i];
+        var arg;
+        if (i < funcData.numOptionalArgs) {
+            if (argType) {
+                arg = this.parseGroupOfType(argType, true);
+            } else {
+                arg = this.parseGroup(true);
+            }
+            if (!arg) {
+                args.push(null);
+                positions.push(this.pos);
+                continue;
+            }
+        } else {
+            if (argType) {
+                arg = this.parseGroupOfType(argType);
+            } else {
+                arg = this.parseGroup();
+            }
+            if (!arg) {
+                if (!this.settings.throwOnError &&
+                    this.nextToken.text[0] === "\\") {
+                    arg = new ParseFuncOrArgument(
+                        this.handleUnsupportedCmd(this.nextToken.text),
+                        false);
+                } else {
+                    throw new ParseError(
+                        "Expected group after '" + func + "'", nextToken);
+                }
+            }
+        }
+        var argNode;
+        if (arg.isFunction) {
+            var argGreediness =
+                functions[arg.result].greediness;
+            if (argGreediness > baseGreediness) {
+                argNode = this.parseFunction(arg);
+            } else {
+                throw new ParseError(
+                    "Got function '" + arg.result + "' as " +
+                    "argument to '" + func + "'", nextToken);
+            }
+        } else {
+            argNode = arg.result;
+        }
+        args.push(argNode);
+        positions.push(this.pos);
+    }
+
+    args.push(positions);
+
+    return args;
+};
+
+
+/**
+ * Parses a group when the mode is changing.
+ *
+ * @return {?ParseFuncOrArgument}
+ */
+Parser.prototype.parseGroupOfType = function(innerMode, optional) {
+    var outerMode = this.mode;
+    // Handle `original` argTypes
+    if (innerMode === "original") {
+        innerMode = outerMode;
+    }
+
+    if (innerMode === "color") {
+        return this.parseColorGroup(optional);
+    }
+    if (innerMode === "size") {
+        return this.parseSizeGroup(optional);
+    }
+
+    this.switchMode(innerMode);
+    if (innerMode === "text") {
+        // text mode is special because it should ignore the whitespace before
+        // it
+        while (this.nextToken.text === " ") {
+            this.consume();
+        }
+    }
+    // By the time we get here, innerMode is one of "text" or "math".
+    // We switch the mode of the parser, recurse, then restore the old mode.
+    var res = this.parseGroup(optional);
+    this.switchMode(outerMode);
+    return res;
+};
+
+/**
+ * Parses a group, essentially returning the string formed by the
+ * brace-enclosed tokens plus some position information.
+ *
+ * @param {string} modeName  Used to describe the mode in error messages
+ * @param {boolean=} optional  Whether the group is optional or required
+ */
+Parser.prototype.parseStringGroup = function(modeName, optional) {
+    if (optional && this.nextToken.text !== "[") {
+        return null;
+    }
+    var outerMode = this.mode;
+    this.mode = "text";
+    this.expect(optional ? "[" : "{");
+    var str = "";
+    var firstToken = this.nextToken;
+    var lastToken = firstToken;
+    while (this.nextToken.text !== (optional ? "]" : "}")) {
+        if (this.nextToken.text === "EOF") {
+            throw new ParseError(
+                "Unexpected end of input in " + modeName,
+                firstToken.range(this.nextToken, str));
+        }
+        lastToken = this.nextToken;
+        str += lastToken.text;
+        this.consume();
+    }
+    this.mode = outerMode;
+    this.expect(optional ? "]" : "}");
+    return firstToken.range(lastToken, str);
+};
+
+/**
+ * Parses a regex-delimited group: the largest sequence of tokens
+ * whose concatenated strings match `regex`. Returns the string
+ * formed by the tokens plus some position information.
+ *
+ * @param {RegExp} regex
+ * @param {string} modeName  Used to describe the mode in error messages
+ */
+Parser.prototype.parseRegexGroup = function(regex, modeName) {
+    var outerMode = this.mode;
+    this.mode = "text";
+    var firstToken = this.nextToken;
+    var lastToken = firstToken;
+    var str = "";
+    while (this.nextToken.text !== "EOF"
+           && regex.test(str + this.nextToken.text)) {
+        lastToken = this.nextToken;
+        str += lastToken.text;
+        this.consume();
+    }
+    if (str === "") {
+        throw new ParseError(
+            "Invalid " + modeName + ": '" + firstToken.text + "'",
+            firstToken);
+    }
+    this.mode = outerMode;
+    return firstToken.range(lastToken, str);
+};
+
+/**
+ * Parses a color description.
+ */
+Parser.prototype.parseColorGroup = function(optional) {
+    var res = this.parseStringGroup("color", optional);
+    if (!res) {
+        return null;
+    }
+    var match = (/^(#[a-z0-9]+|[a-z]+)$/i).exec(res.text);
+    if (!match) {
+        throw new ParseError("Invalid color: '" + res.text + "'", res);
+    }
+    return new ParseFuncOrArgument(
+        new ParseNode("color", match[0], this.mode),
+        false);
+};
+
+/**
+ * Parses a size specification, consisting of magnitude and unit.
+ */
+Parser.prototype.parseSizeGroup = function(optional) {
+    var res;
+    if (!optional && this.nextToken.text !== "{") {
+        res = this.parseRegexGroup(
+            /^[-+]? *(?:$|\d+|\d+\.\d*|\.\d*) *[a-z]{0,2}$/, "size");
+    } else {
+        res = this.parseStringGroup("size", optional);
+    }
+    if (!res) {
+        return null;
+    }
+    var match = (/([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/).exec(res.text);
+    if (!match) {
+        throw new ParseError("Invalid size: '" + res.text + "'", res);
+    }
+    var data = {
+        number: +(match[1] + match[2]), // sign + magnitude, cast to number
+        unit: match[3]
+    };
+    if (data.unit !== "em" && data.unit !== "ex" && data.unit !== "mu") {
+        throw new ParseError("Invalid unit: '" + data.unit + "'", res);
+    }
+    return new ParseFuncOrArgument(
+        new ParseNode("color", data, this.mode),
+        false);
+};
+
+/**
+ * If the argument is false or absent, this parses an ordinary group,
+ * which is either a single nucleus (like "x") or an expression
+ * in braces (like "{x+y}").
+ * If the argument is true, it parses either a bracket-delimited expression
+ * (like "[x+y]") or returns null to indicate the absence of a
+ * bracket-enclosed group.
+ *
+ * @param {boolean=} optional  Whether the group is optional or required
+ * @return {?ParseFuncOrArgument}
+ */
+Parser.prototype.parseGroup = function(optional) {
+    var firstToken = this.nextToken;
+    // Try to parse an open brace
+    if (this.nextToken.text === (optional ? "[" : "{")) {
+        // If we get a brace, parse an expression
+        this.consume();
+        var expression = this.parseExpression(false, optional ? "]" : null);
+        var lastToken = this.nextToken;
+        // Make sure we get a close brace
+        this.expect(optional ? "]" : "}");
+        if (this.mode === "text") {
+            this.formLigatures(expression);
+        }
+        return new ParseFuncOrArgument(
+            new ParseNode("ordgroup", expression, this.mode,
+                          firstToken, lastToken),
+            false);
+    } else {
+        // Otherwise, just return a nucleus, or nothing for an optional group
+        return optional ? null : this.parseSymbol();
+    }
+};
+
+/**
+ * Form ligature-like combinations of characters for text mode.
+ * This includes inputs like "--", "---", "``" and "''".
+ * The result will simply replace multiple textord nodes with a single
+ * character in each value by a single textord node having multiple
+ * characters in its value.  The representation is still ASCII source.
+ *
+ * @param {Array.<ParseNode>} group  the nodes of this group,
+ *                                   list will be moified in place
+ */
+Parser.prototype.formLigatures = function(group) {
+    var i;
+    var n = group.length - 1;
+    for (i = 0; i < n; ++i) {
+        var a = group[i];
+        var v = a.value;
+        if (v === "-" && group[i + 1].value === "-") {
+            if (i + 1 < n && group[i + 2].value === "-") {
+                group.splice(i, 3, new ParseNode(
+                    "textord", "---", "text", a, group[i + 2]));
+                n -= 2;
+            } else {
+                group.splice(i, 2, new ParseNode(
+                    "textord", "--", "text", a, group[i + 1]));
+                n -= 1;
+            }
+        }
+        if ((v === "'" || v === "`") && group[i + 1].value === v) {
+            group.splice(i, 2, new ParseNode(
+                "textord", v + v, "text", a, group[i + 1]));
+            n -= 1;
+        }
+    }
+};
+
+/**
+ * Parse a single symbol out of the string. Here, we handle both the functions
+ * we have defined, as well as the single character symbols
+ *
+ * @return {?ParseFuncOrArgument}
+ */
+Parser.prototype.parseSymbol = function() {
+    var nucleus = this.nextToken;
+
+    if (functions[nucleus.text]) {
+        this.consume();
+        // If there exists a function with this name, we return the function and
+        // say that it is a function.
+        return new ParseFuncOrArgument(
+            nucleus.text,
+            true, nucleus);
+    } else if (symbols[this.mode][nucleus.text]) {
+        this.consume();
+        // Otherwise if this is a no-argument function, find the type it
+        // corresponds to in the symbols map
+        return new ParseFuncOrArgument(
+            new ParseNode(symbols[this.mode][nucleus.text].group,
+                          nucleus.text, this.mode, nucleus),
+            false, nucleus);
+    } else if (this.mode === "text" && cjkRegex.test(nucleus.text)) {
+        this.consume();
+        return new ParseFuncOrArgument(
+            new ParseNode("textord", nucleus.text, this.mode, nucleus),
+            false, nucleus);
+    } else {
+        return null;
+    }
+};
+
+Parser.prototype.ParseNode = ParseNode;
+
+module.exports = Parser;
+
+},{"./MacroExpander":4,"./ParseError":6,"./environments":16,"./functions":19,"./parseData":21,"./symbols":23,"./unicodeRegexes":24,"./utils":25}],8:[function(require,module,exports){
+/**
+ * This is a module for storing settings passed into KaTeX. It correctly handles
+ * default settings.
+ */
+
+/**
+ * Helper function for getting a default value if the value is undefined
+ */
+function get(option, defaultValue) {
+    return option === undefined ? defaultValue : option;
+}
+
+/**
+ * The main Settings object
+ *
+ * The current options stored are:
+ *  - displayMode: Whether the expression should be typeset by default in
+ *                 textstyle or displaystyle (default false)
+ */
+function Settings(options) {
+    // allow null options
+    options = options || {};
+    this.displayMode = get(options.displayMode, false);
+    this.throwOnError = get(options.throwOnError, true);
+    this.errorColor = get(options.errorColor, "#cc0000");
+    this.macros = options.macros || {};
+}
+
+module.exports = Settings;
+
+},{}],9:[function(require,module,exports){
+/**
+ * This file contains information and classes for the various kinds of styles
+ * used in TeX. It provides a generic `Style` class, which holds information
+ * about a specific style. It then provides instances of all the different kinds
+ * of styles possible, and provides functions to move between them and get
+ * information about them.
+ */
+
+var sigmas = require("./fontMetrics.js").sigmas;
+
+var metrics = [{}, {}, {}];
+var i;
+for (var key in sigmas) {
+    if (sigmas.hasOwnProperty(key)) {
+        for (i = 0; i < 3; i++) {
+            metrics[i][key] = sigmas[key][i];
+        }
+    }
+}
+for (i = 0; i < 3; i++) {
+    metrics[i].emPerEx = sigmas.xHeight[i] / sigmas.quad[i];
+}
+
+/**
+ * The main style class. Contains a unique id for the style, a size (which is
+ * the same for cramped and uncramped version of a style), a cramped flag, and a
+ * size multiplier, which gives the size difference between a style and
+ * textstyle.
+ */
+function Style(id, size, multiplier, cramped) {
+    this.id = id;
+    this.size = size;
+    this.cramped = cramped;
+    this.sizeMultiplier = multiplier;
+    this.metrics = metrics[size > 0 ? size - 1 : 0];
+}
+
+/**
+ * Get the style of a superscript given a base in the current style.
+ */
+Style.prototype.sup = function() {
+    return styles[sup[this.id]];
+};
+
+/**
+ * Get the style of a subscript given a base in the current style.
+ */
+Style.prototype.sub = function() {
+    return styles[sub[this.id]];
+};
+
+/**
+ * Get the style of a fraction numerator given the fraction in the current
+ * style.
+ */
+Style.prototype.fracNum = function() {
+    return styles[fracNum[this.id]];
+};
+
+/**
+ * Get the style of a fraction denominator given the fraction in the current
+ * style.
+ */
+Style.prototype.fracDen = function() {
+    return styles[fracDen[this.id]];
+};
+
+/**
+ * Get the cramped version of a style (in particular, cramping a cramped style
+ * doesn't change the style).
+ */
+Style.prototype.cramp = function() {
+    return styles[cramp[this.id]];
+};
+
+/**
+ * HTML class name, like "displaystyle cramped"
+ */
+Style.prototype.cls = function() {
+    return sizeNames[this.size] + (this.cramped ? " cramped" : " uncramped");
+};
+
+/**
+ * HTML Reset class name, like "reset-textstyle"
+ */
+Style.prototype.reset = function() {
+    return resetNames[this.size];
+};
+
+/**
+ * Return if this style is tightly spaced (scriptstyle/scriptscriptstyle)
+ */
+Style.prototype.isTight = function() {
+    return this.size >= 2;
+};
+
+// IDs of the different styles
+var D = 0;
+var Dc = 1;
+var T = 2;
+var Tc = 3;
+var S = 4;
+var Sc = 5;
+var SS = 6;
+var SSc = 7;
+
+// String names for the different sizes
+var sizeNames = [
+    "displaystyle textstyle",
+    "textstyle",
+    "scriptstyle",
+    "scriptscriptstyle"
+];
+
+// Reset names for the different sizes
+var resetNames = [
+    "reset-textstyle",
+    "reset-textstyle",
+    "reset-scriptstyle",
+    "reset-scriptscriptstyle"
+];
+
+// Instances of the different styles
+var styles = [
+    new Style(D, 0, 1.0, false),
+    new Style(Dc, 0, 1.0, true),
+    new Style(T, 1, 1.0, false),
+    new Style(Tc, 1, 1.0, true),
+    new Style(S, 2, 0.7, false),
+    new Style(Sc, 2, 0.7, true),
+    new Style(SS, 3, 0.5, false),
+    new Style(SSc, 3, 0.5, true)
+];
+
+// Lookup tables for switching from one style to another
+var sup = [S, Sc, S, Sc, SS, SSc, SS, SSc];
+var sub = [Sc, Sc, Sc, Sc, SSc, SSc, SSc, SSc];
+var fracNum = [T, Tc, S, Sc, SS, SSc, SS, SSc];
+var fracDen = [Tc, Tc, Sc, Sc, SSc, SSc, SSc, SSc];
+var cramp = [Dc, Dc, Tc, Tc, Sc, Sc, SSc, SSc];
+
+// We only export some of the styles. Also, we don't export the `Style` class so
+// no more styles can be generated.
+module.exports = {
+    DISPLAY: styles[D],
+    TEXT: styles[T],
+    SCRIPT: styles[S],
+    SCRIPTSCRIPT: styles[SS]
+};
+
+},{"./fontMetrics.js":17}],10:[function(require,module,exports){
+/* eslint no-console:0 */
+/**
+ * This module contains general functions that can be used for building
+ * different kinds of domTree nodes in a consistent manner.
+ */
+
+var domTree = require("./domTree");
+var fontMetrics = require("./fontMetrics");
+var symbols = require("./symbols");
+var utils = require("./utils");
+
+var greekCapitals = [
+    "\\Gamma",
+    "\\Delta",
+    "\\Theta",
+    "\\Lambda",
+    "\\Xi",
+    "\\Pi",
+    "\\Sigma",
+    "\\Upsilon",
+    "\\Phi",
+    "\\Psi",
+    "\\Omega"
+];
+
+// The following have to be loaded from Main-Italic font, using class mainit
+var mainitLetters = [
+    "\u0131",   // dotless i, \imath
+    "\u0237",   // dotless j, \jmath
+    "\u00a3"   // \pounds
+];
+
+/**
+ * Makes a symbolNode after translation via the list of symbols in symbols.js.
+ * Correctly pulls out metrics for the character, and optionally takes a list of
+ * classes to be attached to the node.
+ *
+ * TODO: make argument order closer to makeSpan
+ * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which
+ * should if present come first in `classes`.
+ */
+var makeSymbol = function(value, fontFamily, mode, options, classes) {
+    // Replace the value with its replaced value from symbol.js
+    if (symbols[mode][value] && symbols[mode][value].replace) {
+        value = symbols[mode][value].replace;
+    }
+
+    var metrics = fontMetrics.getCharacterMetrics(value, fontFamily);
+
+    var symbolNode;
+    if (metrics) {
+        var italic = metrics.italic;
+        if (mode === "text") {
+            italic = 0;
+        }
+        symbolNode = new domTree.symbolNode(
+            value, metrics.height, metrics.depth, italic, metrics.skew,
+            classes);
+    } else {
+        // TODO(emily): Figure out a good way to only print this in development
+        typeof console !== "undefined" && console.warn(
+            "No character metrics for '" + value + "' in style '" +
+                fontFamily + "'");
+        symbolNode = new domTree.symbolNode(value, 0, 0, 0, 0, classes);
+    }
+
+    if (options) {
+        if (options.style.isTight()) {
+            symbolNode.classes.push("mtight");
+        }
+        if (options.getColor()) {
+            symbolNode.style.color = options.getColor();
+        }
+    }
+
+    return symbolNode;
+};
+
+/**
+ * Makes a symbol in Main-Regular or AMS-Regular.
+ * Used for rel, bin, open, close, inner, and punct.
+ */
+var mathsym = function(value, mode, options, classes) {
+    // Decide what font to render the symbol in by its entry in the symbols
+    // table.
+    // Have a special case for when the value = \ because the \ is used as a
+    // textord in unsupported command errors but cannot be parsed as a regular
+    // text ordinal and is therefore not present as a symbol in the symbols
+    // table for text
+    if (value === "\\" || symbols[mode][value].font === "main") {
+        return makeSymbol(value, "Main-Regular", mode, options, classes);
+    } else {
+        return makeSymbol(
+            value, "AMS-Regular", mode, options, classes.concat(["amsrm"]));
+    }
+};
+
+/**
+ * Makes a symbol in the default font for mathords and textords.
+ */
+var mathDefault = function(value, mode, options, classes, type) {
+    if (type === "mathord") {
+        return mathit(value, mode, options, classes);
+    } else if (type === "textord") {
+        return makeSymbol(
+            value, "Main-Regular", mode, options, classes.concat(["mathrm"]));
+    } else {
+        throw new Error("unexpected type: " + type + " in mathDefault");
+    }
+};
+
+/**
+ * Makes a symbol in the italic math font.
+ */
+var mathit = function(value, mode, options, classes) {
+    if (/[0-9]/.test(value.charAt(0)) ||
+            // glyphs for \imath and \jmath do not exist in Math-Italic so we
+            // need to use Main-Italic instead
+            utils.contains(mainitLetters, value) ||
+            utils.contains(greekCapitals, value)) {
+        return makeSymbol(
+            value, "Main-Italic", mode, options, classes.concat(["mainit"]));
+    } else {
+        return makeSymbol(
+            value, "Math-Italic", mode, options, classes.concat(["mathit"]));
+    }
+};
+
+/**
+ * Makes either a mathord or textord in the correct font and color.
+ */
+var makeOrd = function(group, options, type) {
+    var mode = group.mode;
+    var value = group.value;
+    if (symbols[mode][value] && symbols[mode][value].replace) {
+        value = symbols[mode][value].replace;
+    }
+
+    var classes = ["mord"];
+
+    var font = options.font;
+    if (font) {
+        if (font === "mathit" || utils.contains(mainitLetters, value)) {
+            return mathit(value, mode, options, classes);
+        } else {
+            var fontName = fontMap[font].fontName;
+            if (fontMetrics.getCharacterMetrics(value, fontName)) {
+                return makeSymbol(
+                    value, fontName, mode, options, classes.concat([font]));
+            } else {
+                return mathDefault(value, mode, options, classes, type);
+            }
+        }
+    } else {
+        return mathDefault(value, mode, options, classes, type);
+    }
+};
+
+/**
+ * Calculate the height, depth, and maxFontSize of an element based on its
+ * children.
+ */
+var sizeElementFromChildren = function(elem) {
+    var height = 0;
+    var depth = 0;
+    var maxFontSize = 0;
+
+    if (elem.children) {
+        for (var i = 0; i < elem.children.length; i++) {
+            if (elem.children[i].height > height) {
+                height = elem.children[i].height;
+            }
+            if (elem.children[i].depth > depth) {
+                depth = elem.children[i].depth;
+            }
+            if (elem.children[i].maxFontSize > maxFontSize) {
+                maxFontSize = elem.children[i].maxFontSize;
+            }
+        }
+    }
+
+    elem.height = height;
+    elem.depth = depth;
+    elem.maxFontSize = maxFontSize;
+};
+
+/**
+ * Makes a span with the given list of classes, list of children, and options.
+ *
+ * TODO: Ensure that `options` is always provided (currently some call sites
+ * don't pass it).
+ * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which
+ * should if present come first in `classes`.
+ */
+var makeSpan = function(classes, children, options) {
+    var span = new domTree.span(classes, children, options);
+
+    sizeElementFromChildren(span);
+
+    return span;
+};
+
+/**
+ * Prepends the given children to the given span, updating height, depth, and
+ * maxFontSize.
+ */
+var prependChildren = function(span, children) {
+    span.children = children.concat(span.children);
+
+    sizeElementFromChildren(span);
+};
+
+/**
+ * Makes a document fragment with the given list of children.
+ */
+var makeFragment = function(children) {
+    var fragment = new domTree.documentFragment(children);
+
+    sizeElementFromChildren(fragment);
+
+    return fragment;
+};
+
+/**
+ * Makes an element placed in each of the vlist elements to ensure that each
+ * element has the same max font size. To do this, we create a zero-width space
+ * with the correct font size.
+ */
+var makeFontSizer = function(options, fontSize) {
+    var fontSizeInner = makeSpan([], [new domTree.symbolNode("\u200b")]);
+    fontSizeInner.style.fontSize =
+        (fontSize / options.style.sizeMultiplier) + "em";
+
+    var fontSizer = makeSpan(
+        ["fontsize-ensurer", "reset-" + options.size, "size5"],
+        [fontSizeInner]);
+
+    return fontSizer;
+};
+
+/**
+ * Makes a vertical list by stacking elements and kerns on top of each other.
+ * Allows for many different ways of specifying the positioning method.
+ *
+ * Arguments:
+ *  - children: A list of child or kern nodes to be stacked on top of each other
+ *              (i.e. the first element will be at the bottom, and the last at
+ *              the top). Element nodes are specified as
+ *                {type: "elem", elem: node}
+ *              while kern nodes are specified as
+ *                {type: "kern", size: size}
+ *  - positionType: The method by which the vlist should be positioned. Valid
+ *                  values are:
+ *                   - "individualShift": The children list only contains elem
+ *                                        nodes, and each node contains an extra
+ *                                        "shift" value of how much it should be
+ *                                        shifted (note that shifting is always
+ *                                        moving downwards). positionData is
+ *                                        ignored.
+ *                   - "top": The positionData specifies the topmost point of
+ *                            the vlist (note this is expected to be a height,
+ *                            so positive values move up)
+ *                   - "bottom": The positionData specifies the bottommost point
+ *                               of the vlist (note this is expected to be a
+ *                               depth, so positive values move down
+ *                   - "shift": The vlist will be positioned such that its
+ *                              baseline is positionData away from the baseline
+ *                              of the first child. Positive values move
+ *                              downwards.
+ *                   - "firstBaseline": The vlist will be positioned such that
+ *                                      its baseline is aligned with the
+ *                                      baseline of the first child.
+ *                                      positionData is ignored. (this is
+ *                                      equivalent to "shift" with
+ *                                      positionData=0)
+ *  - positionData: Data used in different ways depending on positionType
+ *  - options: An Options object
+ *
+ */
+var makeVList = function(children, positionType, positionData, options) {
+    var depth;
+    var currPos;
+    var i;
+    if (positionType === "individualShift") {
+        var oldChildren = children;
+        children = [oldChildren[0]];
+
+        // Add in kerns to the list of children to get each element to be
+        // shifted to the correct specified shift
+        depth = -oldChildren[0].shift - oldChildren[0].elem.depth;
+        currPos = depth;
+        for (i = 1; i < oldChildren.length; i++) {
+            var diff = -oldChildren[i].shift - currPos -
+                oldChildren[i].elem.depth;
+            var size = diff -
+                (oldChildren[i - 1].elem.height +
+                 oldChildren[i - 1].elem.depth);
+
+            currPos = currPos + diff;
+
+            children.push({type: "kern", size: size});
+            children.push(oldChildren[i]);
+        }
+    } else if (positionType === "top") {
+        // We always start at the bottom, so calculate the bottom by adding up
+        // all the sizes
+        var bottom = positionData;
+        for (i = 0; i < children.length; i++) {
+            if (children[i].type === "kern") {
+                bottom -= children[i].size;
+            } else {
+                bottom -= children[i].elem.height + children[i].elem.depth;
+            }
+        }
+        depth = bottom;
+    } else if (positionType === "bottom") {
+        depth = -positionData;
+    } else if (positionType === "shift") {
+        depth = -children[0].elem.depth - positionData;
+    } else if (positionType === "firstBaseline") {
+        depth = -children[0].elem.depth;
+    } else {
+        depth = 0;
+    }
+
+    // Make the fontSizer
+    var maxFontSize = 0;
+    for (i = 0; i < children.length; i++) {
+        if (children[i].type === "elem") {
+            maxFontSize = Math.max(maxFontSize, children[i].elem.maxFontSize);
+        }
+    }
+    var fontSizer = makeFontSizer(options, maxFontSize);
+
+    // Create a new list of actual children at the correct offsets
+    var realChildren = [];
+    currPos = depth;
+    for (i = 0; i < children.length; i++) {
+        if (children[i].type === "kern") {
+            currPos += children[i].size;
+        } else {
+            var child = children[i].elem;
+
+            var shift = -child.depth - currPos;
+            currPos += child.height + child.depth;
+
+            var childWrap = makeSpan([], [fontSizer, child]);
+            childWrap.height -= shift;
+            childWrap.depth += shift;
+            childWrap.style.top = shift + "em";
+
+            realChildren.push(childWrap);
+        }
+    }
+
+    // Add in an element at the end with no offset to fix the calculation of
+    // baselines in some browsers (namely IE, sometimes safari)
+    var baselineFix = makeSpan(
+        ["baseline-fix"], [fontSizer, new domTree.symbolNode("\u200b")]);
+    realChildren.push(baselineFix);
+
+    var vlist = makeSpan(["vlist"], realChildren);
+    // Fix the final height and depth, in case there were kerns at the ends
+    // since the makeSpan calculation won't take that in to account.
+    vlist.height = Math.max(currPos, vlist.height);
+    vlist.depth = Math.max(-depth, vlist.depth);
+    return vlist;
+};
+
+// A table of size -> font size for the different sizing functions
+var sizingMultiplier = {
+    size1: 0.5,
+    size2: 0.7,
+    size3: 0.8,
+    size4: 0.9,
+    size5: 1.0,
+    size6: 1.2,
+    size7: 1.44,
+    size8: 1.73,
+    size9: 2.07,
+    size10: 2.49
+};
+
+// A map of spacing functions to their attributes, like size and corresponding
+// CSS class
+var spacingFunctions = {
+    "\\qquad": {
+        size: "2em",
+        className: "qquad"
+    },
+    "\\quad": {
+        size: "1em",
+        className: "quad"
+    },
+    "\\enspace": {
+        size: "0.5em",
+        className: "enspace"
+    },
+    "\\;": {
+        size: "0.277778em",
+        className: "thickspace"
+    },
+    "\\:": {
+        size: "0.22222em",
+        className: "mediumspace"
+    },
+    "\\,": {
+        size: "0.16667em",
+        className: "thinspace"
+    },
+    "\\!": {
+        size: "-0.16667em",
+        className: "negativethinspace"
+    }
+};
+
+/**
+ * Maps TeX font commands to objects containing:
+ * - variant: string used for "mathvariant" attribute in buildMathML.js
+ * - fontName: the "style" parameter to fontMetrics.getCharacterMetrics
+ */
+// A map between tex font commands an MathML mathvariant attribute values
+var fontMap = {
+    // styles
+    "mathbf": {
+        variant: "bold",
+        fontName: "Main-Bold"
+    },
+    "mathrm": {
+        variant: "normal",
+        fontName: "Main-Regular"
+    },
+    "textit": {
+        variant: "italic",
+        fontName: "Main-Italic"
+    },
+
+    // "mathit" is missing because it requires the use of two fonts: Main-Italic
+    // and Math-Italic.  This is handled by a special case in makeOrd which ends
+    // up calling mathit.
+
+    // families
+    "mathbb": {
+        variant: "double-struck",
+        fontName: "AMS-Regular"
+    },
+    "mathcal": {
+        variant: "script",
+        fontName: "Caligraphic-Regular"
+    },
+    "mathfrak": {
+        variant: "fraktur",
+        fontName: "Fraktur-Regular"
+    },
+    "mathscr": {
+        variant: "script",
+        fontName: "Script-Regular"
+    },
+    "mathsf": {
+        variant: "sans-serif",
+        fontName: "SansSerif-Regular"
+    },
+    "mathtt": {
+        variant: "monospace",
+        fontName: "Typewriter-Regular"
+    }
+};
+
+module.exports = {
+    fontMap: fontMap,
+    makeSymbol: makeSymbol,
+    mathsym: mathsym,
+    makeSpan: makeSpan,
+    makeFragment: makeFragment,
+    makeVList: makeVList,
+    makeOrd: makeOrd,
+    prependChildren: prependChildren,
+    sizingMultiplier: sizingMultiplier,
+    spacingFunctions: spacingFunctions
+};
+
+},{"./domTree":15,"./fontMetrics":17,"./symbols":23,"./utils":25}],11:[function(require,module,exports){
+/* eslint no-console:0 */
+/**
+ * This file does the main work of building a domTree structure from a parse
+ * tree. The entry point is the `buildHTML` function, which takes a parse tree.
+ * Then, the buildExpression, buildGroup, and various groupTypes functions are
+ * called, to produce a final HTML tree.
+ */
+
+var ParseError = require("./ParseError");
+var Style = require("./Style");
+
+var buildCommon = require("./buildCommon");
+var delimiter = require("./delimiter");
+var domTree = require("./domTree");
+var fontMetrics = require("./fontMetrics");
+var utils = require("./utils");
+
+var makeSpan = buildCommon.makeSpan;
+
+var isSpace = function(node) {
+    return node instanceof domTree.span && node.classes[0] === "mspace";
+};
+
+// Binary atoms (first class `mbin`) change into ordinary atoms (`mord`)
+// depending on their surroundings. See TeXbook pg. 442-446, Rules 5 and 6,
+// and the text before Rule 19.
+
+var isBin = function(node) {
+    return node && node.classes[0] === "mbin";
+};
+
+var isBinLeftCanceller = function(node, isRealGroup) {
+    // TODO: This code assumes that a node's math class is the first element
+    // of its `classes` array. A later cleanup should ensure this, for
+    // instance by changing the signature of `makeSpan`.
+    if (node) {
+        return utils.contains(["mbin", "mopen", "mrel", "mop", "mpunct"],
+                              node.classes[0]);
+    } else {
+        return isRealGroup;
+    }
+};
+
+var isBinRightCanceller = function(node, isRealGroup) {
+    if (node) {
+        return utils.contains(["mrel", "mclose", "mpunct"], node.classes[0]);
+    } else {
+        return isRealGroup;
+    }
+};
+
+/**
+ * Take a list of nodes, build them in order, and return a list of the built
+ * nodes. documentFragments are flattened into their contents, so the
+ * returned list contains no fragments. `isRealGroup` is true if `expression`
+ * is a real group (no atoms will be added on either side), as opposed to
+ * a partial group (e.g. one created by \color).
+ */
+var buildExpression = function(expression, options, isRealGroup) {
+    // Parse expressions into `groups`.
+    var groups = [];
+    for (var i = 0; i < expression.length; i++) {
+        var group = expression[i];
+        var output = buildGroup(group, options);
+        if (output instanceof domTree.documentFragment) {
+            Array.prototype.push.apply(groups, output.children);
+        } else {
+            groups.push(output);
+        }
+    }
+    // At this point `groups` consists entirely of `symbolNode`s and `span`s.
+
+    // Explicit spaces (e.g., \;, \,) should be ignored with respect to atom
+    // spacing (e.g., "add thick space between mord and mrel"). Since CSS
+    // adjacency rules implement atom spacing, spaces should be invisible to
+    // CSS. So we splice them out of `groups` and into the atoms themselves.
+    var spaces = null;
+    for (i = 0; i < groups.length; i++) {
+        if (isSpace(groups[i])) {
+            spaces = spaces || [];
+            spaces.push(groups[i]);
+            groups.splice(i, 1);
+            i--;
+        } else if (spaces) {
+            if (groups[i] instanceof domTree.symbolNode) {
+                groups[i] = makeSpan([].concat(groups[i].classes), [groups[i]]);
+            }
+            buildCommon.prependChildren(groups[i], spaces);
+            spaces = null;
+        }
+    }
+    if (spaces) {
+        Array.prototype.push.apply(groups, spaces);
+    }
+
+    // Binary operators change to ordinary symbols in some contexts.
+    for (i = 0; i < groups.length; i++) {
+        if (isBin(groups[i])
+            && (isBinLeftCanceller(groups[i - 1], isRealGroup)
+                || isBinRightCanceller(groups[i + 1], isRealGroup))) {
+            groups[i].classes[0] = "mord";
+        }
+    }
+
+    return groups;
+};
+
+// Return math atom class (mclass) of a domTree.
+var getTypeOfDomTree = function(node) {
+    if (node instanceof domTree.documentFragment) {
+        if (node.children.length) {
+            return getTypeOfDomTree(
+                node.children[node.children.length - 1]);
+        }
+    } else {
+        if (utils.contains(["mord", "mop", "mbin", "mrel", "mopen", "mclose",
+            "mpunct", "minner"], node.classes[0])) {
+            return node.classes[0];
+        }
+    }
+    return null;
+};
+
+/**
+ * Sometimes, groups perform special rules when they have superscripts or
+ * subscripts attached to them. This function lets the `supsub` group know that
+ * its inner element should handle the superscripts and subscripts instead of
+ * handling them itself.
+ */
+var shouldHandleSupSub = function(group, options) {
+    if (!group) {
+        return false;
+    } else if (group.type === "op") {
+        // Operators handle supsubs differently when they have limits
+        // (e.g. `\displaystyle\sum_2^3`)
+        return group.value.limits &&
+            (options.style.size === Style.DISPLAY.size ||
+            group.value.alwaysHandleSupSub);
+    } else if (group.type === "accent") {
+        return isCharacterBox(group.value.base);
+    } else {
+        return null;
+    }
+};
+
+/**
+ * Sometimes we want to pull out the innermost element of a group. In most
+ * cases, this will just be the group itself, but when ordgroups and colors have
+ * a single element, we want to pull that out.
+ */
+var getBaseElem = function(group) {
+    if (!group) {
+        return false;
+    } else if (group.type === "ordgroup") {
+        if (group.value.length === 1) {
+            return getBaseElem(group.value[0]);
+        } else {
+            return group;
+        }
+    } else if (group.type === "color") {
+        if (group.value.value.length === 1) {
+            return getBaseElem(group.value.value[0]);
+        } else {
+            return group;
+        }
+    } else if (group.type === "font") {
+        return getBaseElem(group.value.body);
+    } else {
+        return group;
+    }
+};
+
+/**
+ * TeXbook algorithms often reference "character boxes", which are simply groups
+ * with a single character in them. To decide if something is a character box,
+ * we find its innermost group, and see if it is a single character.
+ */
+var isCharacterBox = function(group) {
+    var baseElem = getBaseElem(group);
+
+    // These are all they types of groups which hold single characters
+    return baseElem.type === "mathord" ||
+        baseElem.type === "textord" ||
+        baseElem.type === "bin" ||
+        baseElem.type === "rel" ||
+        baseElem.type === "inner" ||
+        baseElem.type === "open" ||
+        baseElem.type === "close" ||
+        baseElem.type === "punct";
+};
+
+var makeNullDelimiter = function(options, classes) {
+    return makeSpan(classes.concat([
+        "sizing", "reset-" + options.size, "size5",
+        options.style.reset(), Style.TEXT.cls(),
+        "nulldelimiter"]));
+};
+
+/**
+ * This is a map of group types to the function used to handle that type.
+ * Simpler types come at the beginning, while complicated types come afterwards.
+ */
+var groupTypes = {};
+
+groupTypes.mathord = function(group, options) {
+    return buildCommon.makeOrd(group, options, "mathord");
+};
+
+groupTypes.textord = function(group, options) {
+    return buildCommon.makeOrd(group, options, "textord");
+};
+
+groupTypes.bin = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mbin"]);
+};
+
+groupTypes.rel = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mrel"]);
+};
+
+groupTypes.open = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mopen"]);
+};
+
+groupTypes.close = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mclose"]);
+};
+
+groupTypes.inner = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["minner"]);
+};
+
+groupTypes.punct = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mpunct"]);
+};
+
+groupTypes.ordgroup = function(group, options) {
+    return makeSpan(
+        ["mord", options.style.cls()],
+        buildExpression(group.value, options.reset(), true),
+        options
+    );
+};
+
+groupTypes.text = function(group, options) {
+    var newOptions = options.withFont(group.value.style);
+    var inner = buildExpression(group.value.body, newOptions, true);
+    for (var i = 0; i < inner.length - 1; i++) {
+        if (inner[i].tryCombine(inner[i + 1])) {
+            inner.splice(i + 1, 1);
+            i--;
+        }
+    }
+    return makeSpan(["mord", "text", newOptions.style.cls()],
+        inner, newOptions);
+};
+
+groupTypes.color = function(group, options) {
+    var elements = buildExpression(
+        group.value.value,
+        options.withColor(group.value.color),
+        false
+    );
+
+    // \color isn't supposed to affect the type of the elements it contains.
+    // To accomplish this, we wrap the results in a fragment, so the inner
+    // elements will be able to directly interact with their neighbors. For
+    // example, `\color{red}{2 +} 3` has the same spacing as `2 + 3`
+    return new buildCommon.makeFragment(elements);
+};
+
+groupTypes.supsub = function(group, options) {
+    // Superscript and subscripts are handled in the TeXbook on page
+    // 445-446, rules 18(a-f).
+
+    // Here is where we defer to the inner group if it should handle
+    // superscripts and subscripts itself.
+    if (shouldHandleSupSub(group.value.base, options)) {
+        return groupTypes[group.value.base.type](group, options);
+    }
+
+    var base = buildGroup(group.value.base, options.reset());
+    var supmid;
+    var submid;
+    var sup;
+    var sub;
+
+    var style = options.style;
+    var newOptions;
+
+    if (group.value.sup) {
+        newOptions = options.withStyle(style.sup());
+        sup = buildGroup(group.value.sup, newOptions);
+        supmid = makeSpan([style.reset(), style.sup().cls()],
+            [sup], newOptions);
+    }
+
+    if (group.value.sub) {
+        newOptions = options.withStyle(style.sub());
+        sub = buildGroup(group.value.sub, newOptions);
+        submid = makeSpan([style.reset(), style.sub().cls()],
+            [sub], newOptions);
+    }
+
+    // Rule 18a
+    var supShift;
+    var subShift;
+    if (isCharacterBox(group.value.base)) {
+        supShift = 0;
+        subShift = 0;
+    } else {
+        supShift = base.height - style.metrics.supDrop;
+        subShift = base.depth + style.metrics.subDrop;
+    }
+
+    // Rule 18c
+    var minSupShift;
+    if (style === Style.DISPLAY) {
+        minSupShift = style.metrics.sup1;
+    } else if (style.cramped) {
+        minSupShift = style.metrics.sup3;
+    } else {
+        minSupShift = style.metrics.sup2;
+    }
+
+    // scriptspace is a font-size-independent size, so scale it
+    // appropriately
+    var multiplier = Style.TEXT.sizeMultiplier *
+            style.sizeMultiplier;
+    var scriptspace =
+        (0.5 / fontMetrics.metrics.ptPerEm) / multiplier + "em";
+
+    var supsub;
+    if (!group.value.sup) {
+        // Rule 18b
+        subShift = Math.max(
+            subShift, style.metrics.sub1,
+            sub.height - 0.8 * style.metrics.xHeight);
+
+        supsub = buildCommon.makeVList([
+            {type: "elem", elem: submid}
+        ], "shift", subShift, options);
+
+        supsub.children[0].style.marginRight = scriptspace;
+
+        // Subscripts shouldn't be shifted by the base's italic correction.
+        // Account for that by shifting the subscript back the appropriate
+        // amount. Note we only do this when the base is a single symbol.
+        if (base instanceof domTree.symbolNode) {
+            supsub.children[0].style.marginLeft = -base.italic + "em";
+        }
+    } else if (!group.value.sub) {
+        // Rule 18c, d
+        supShift = Math.max(supShift, minSupShift,
+            sup.depth + 0.25 * style.metrics.xHeight);
+
+        supsub = buildCommon.makeVList([
+            {type: "elem", elem: supmid}
+        ], "shift", -supShift, options);
+
+        supsub.children[0].style.marginRight = scriptspace;
+    } else {
+        supShift = Math.max(
+            supShift, minSupShift, sup.depth + 0.25 * style.metrics.xHeight);
+        subShift = Math.max(subShift, style.metrics.sub2);
+
+        var ruleWidth = fontMetrics.metrics.defaultRuleThickness;
+
+        // Rule 18e
+        if ((supShift - sup.depth) - (sub.height - subShift) <
+                4 * ruleWidth) {
+            subShift = 4 * ruleWidth - (supShift - sup.depth) + sub.height;
+            var psi = 0.8 * style.metrics.xHeight - (supShift - sup.depth);
+            if (psi > 0) {
+                supShift += psi;
+                subShift -= psi;
+            }
+        }
+
+        supsub = buildCommon.makeVList([
+            {type: "elem", elem: submid, shift: subShift},
+            {type: "elem", elem: supmid, shift: -supShift}
+        ], "individualShift", null, options);
+
+        // See comment above about subscripts not being shifted
+        if (base instanceof domTree.symbolNode) {
+            supsub.children[0].style.marginLeft = -base.italic + "em";
+        }
+
+        supsub.children[0].style.marginRight = scriptspace;
+        supsub.children[1].style.marginRight = scriptspace;
+    }
+
+    // We ensure to wrap the supsub vlist in a span.msupsub to reset text-align
+    var mclass = getTypeOfDomTree(base) || "mord";
+    return makeSpan([mclass],
+        [base, makeSpan(["msupsub"], [supsub])],
+        options);
+};
+
+groupTypes.genfrac = function(group, options) {
+    // Fractions are handled in the TeXbook on pages 444-445, rules 15(a-e).
+    // Figure out what style this fraction should be in based on the
+    // function used
+    var style = options.style;
+    if (group.value.size === "display") {
+        style = Style.DISPLAY;
+    } else if (group.value.size === "text") {
+        style = Style.TEXT;
+    }
+
+    var nstyle = style.fracNum();
+    var dstyle = style.fracDen();
+    var newOptions;
+
+    newOptions = options.withStyle(nstyle);
+    var numer = buildGroup(group.value.numer, newOptions);
+    var numerreset = makeSpan([style.reset(), nstyle.cls()],
+        [numer], newOptions);
+
+    newOptions = options.withStyle(dstyle);
+    var denom = buildGroup(group.value.denom, newOptions);
+    var denomreset = makeSpan([style.reset(), dstyle.cls()],
+        [denom], newOptions);
+
+    var ruleWidth;
+    if (group.value.hasBarLine) {
+        ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+            options.style.sizeMultiplier;
+    } else {
+        ruleWidth = 0;
+    }
+
+    // Rule 15b
+    var numShift;
+    var clearance;
+    var denomShift;
+    if (style.size === Style.DISPLAY.size) {
+        numShift = style.metrics.num1;
+        if (ruleWidth > 0) {
+            clearance = 3 * ruleWidth;
+        } else {
+            clearance = 7 * fontMetrics.metrics.defaultRuleThickness;
+        }
+        denomShift = style.metrics.denom1;
+    } else {
+        if (ruleWidth > 0) {
+            numShift = style.metrics.num2;
+            clearance = ruleWidth;
+        } else {
+            numShift = style.metrics.num3;
+            clearance = 3 * fontMetrics.metrics.defaultRuleThickness;
+        }
+        denomShift = style.metrics.denom2;
+    }
+
+    var frac;
+    if (ruleWidth === 0) {
+        // Rule 15c
+        var candidateClearance =
+            (numShift - numer.depth) - (denom.height - denomShift);
+        if (candidateClearance < clearance) {
+            numShift += 0.5 * (clearance - candidateClearance);
+            denomShift += 0.5 * (clearance - candidateClearance);
+        }
+
+        frac = buildCommon.makeVList([
+            {type: "elem", elem: denomreset, shift: denomShift},
+            {type: "elem", elem: numerreset, shift: -numShift}
+        ], "individualShift", null, options);
+    } else {
+        // Rule 15d
+        var axisHeight = style.metrics.axisHeight;
+
+        if ((numShift - numer.depth) - (axisHeight + 0.5 * ruleWidth) <
+                clearance) {
+            numShift +=
+                clearance - ((numShift - numer.depth) -
+                             (axisHeight + 0.5 * ruleWidth));
+        }
+
+        if ((axisHeight - 0.5 * ruleWidth) - (denom.height - denomShift) <
+                clearance) {
+            denomShift +=
+                clearance - ((axisHeight - 0.5 * ruleWidth) -
+                             (denom.height - denomShift));
+        }
+
+        var mid = makeSpan(
+            [options.style.reset(), Style.TEXT.cls(), "frac-line"]);
+        // Manually set the height of the line because its height is
+        // created in CSS
+        mid.height = ruleWidth;
+
+        var midShift = -(axisHeight - 0.5 * ruleWidth);
+
+        frac = buildCommon.makeVList([
+            {type: "elem", elem: denomreset, shift: denomShift},
+            {type: "elem", elem: mid,        shift: midShift},
+            {type: "elem", elem: numerreset, shift: -numShift}
+        ], "individualShift", null, options);
+    }
+
+    // Since we manually change the style sometimes (with \dfrac or \tfrac),
+    // account for the possible size change here.
+    frac.height *= style.sizeMultiplier / options.style.sizeMultiplier;
+    frac.depth *= style.sizeMultiplier / options.style.sizeMultiplier;
+
+    // Rule 15e
+    var delimSize;
+    if (style.size === Style.DISPLAY.size) {
+        delimSize = style.metrics.delim1;
+    } else {
+        delimSize = style.metrics.delim2;
+    }
+
+    var leftDelim;
+    var rightDelim;
+    if (group.value.leftDelim == null) {
+        leftDelim = makeNullDelimiter(options, ["mopen"]);
+    } else {
+        leftDelim = delimiter.customSizedDelim(
+            group.value.leftDelim, delimSize, true,
+            options.withStyle(style), group.mode, ["mopen"]);
+    }
+    if (group.value.rightDelim == null) {
+        rightDelim = makeNullDelimiter(options, ["mclose"]);
+    } else {
+        rightDelim = delimiter.customSizedDelim(
+            group.value.rightDelim, delimSize, true,
+            options.withStyle(style), group.mode, ["mclose"]);
+    }
+
+    return makeSpan(
+        ["mord", options.style.reset(), style.cls()],
+        [leftDelim, makeSpan(["mfrac"], [frac]), rightDelim],
+        options);
+};
+
+var calculateSize = function(sizeValue, style) {
+    var x = sizeValue.number;
+    if (sizeValue.unit === "ex") {
+        x *= style.metrics.emPerEx;
+    } else if (sizeValue.unit === "mu") {
+        x /= 18;
+    }
+    return x;
+};
+
+groupTypes.array = function(group, options) {
+    var r;
+    var c;
+    var nr = group.value.body.length;
+    var nc = 0;
+    var body = new Array(nr);
+
+    var style = options.style;
+
+    // Horizontal spacing
+    var pt = 1 / fontMetrics.metrics.ptPerEm;
+    var arraycolsep = 5 * pt; // \arraycolsep in article.cls
+
+    // Vertical spacing
+    var baselineskip = 12 * pt; // see size10.clo
+    // Default \arraystretch from lttab.dtx
+    // TODO(gagern): may get redefined once we have user-defined macros
+    var arraystretch = utils.deflt(group.value.arraystretch, 1);
+    var arrayskip = arraystretch * baselineskip;
+    var arstrutHeight = 0.7 * arrayskip; // \strutbox in ltfsstrc.dtx and
+    var arstrutDepth = 0.3 * arrayskip;  // \@arstrutbox in lttab.dtx
+
+    var totalHeight = 0;
+    for (r = 0; r < group.value.body.length; ++r) {
+        var inrow = group.value.body[r];
+        var height = arstrutHeight; // \@array adds an \@arstrut
+        var depth = arstrutDepth;   // to each tow (via the template)
+
+        if (nc < inrow.length) {
+            nc = inrow.length;
+        }
+
+        var outrow = new Array(inrow.length);
+        for (c = 0; c < inrow.length; ++c) {
+            var elt = buildGroup(inrow[c], options);
+            if (depth < elt.depth) {
+                depth = elt.depth;
+            }
+            if (height < elt.height) {
+                height = elt.height;
+            }
+            outrow[c] = elt;
+        }
+
+        var gap = 0;
+        if (group.value.rowGaps[r]) {
+            gap = calculateSize(group.value.rowGaps[r].value, style);
+            if (gap > 0) { // \@argarraycr
+                gap += arstrutDepth;
+                if (depth < gap) {
+                    depth = gap; // \@xargarraycr
+                }
+                gap = 0;
+            }
+        }
+
+        outrow.height = height;
+        outrow.depth = depth;
+        totalHeight += height;
+        outrow.pos = totalHeight;
+        totalHeight += depth + gap; // \@yargarraycr
+        body[r] = outrow;
+    }
+
+    var offset = totalHeight / 2 + style.metrics.axisHeight;
+    var colDescriptions = group.value.cols || [];
+    var cols = [];
+    var colSep;
+    var colDescrNum;
+    for (c = 0, colDescrNum = 0;
+         // Continue while either there are more columns or more column
+         // descriptions, so trailing separators don't get lost.
+         c < nc || colDescrNum < colDescriptions.length;
+         ++c, ++colDescrNum) {
+
+        var colDescr = colDescriptions[colDescrNum] || {};
+
+        var firstSeparator = true;
+        while (colDescr.type === "separator") {
+            // If there is more than one separator in a row, add a space
+            // between them.
+            if (!firstSeparator) {
+                colSep = makeSpan(["arraycolsep"], []);
+                colSep.style.width =
+                    fontMetrics.metrics.doubleRuleSep + "em";
+                cols.push(colSep);
+            }
+
+            if (colDescr.separator === "|") {
+                var separator = makeSpan(
+                    ["vertical-separator"],
+                    []);
+                separator.style.height = totalHeight + "em";
+                separator.style.verticalAlign =
+                    -(totalHeight - offset) + "em";
+
+                cols.push(separator);
+            } else {
+                throw new ParseError(
+                    "Invalid separator type: " + colDescr.separator);
+            }
+
+            colDescrNum++;
+            colDescr = colDescriptions[colDescrNum] || {};
+            firstSeparator = false;
+        }
+
+        if (c >= nc) {
+            continue;
+        }
+
+        var sepwidth;
+        if (c > 0 || group.value.hskipBeforeAndAfter) {
+            sepwidth = utils.deflt(colDescr.pregap, arraycolsep);
+            if (sepwidth !== 0) {
+                colSep = makeSpan(["arraycolsep"], []);
+                colSep.style.width = sepwidth + "em";
+                cols.push(colSep);
+            }
+        }
+
+        var col = [];
+        for (r = 0; r < nr; ++r) {
+            var row = body[r];
+            var elem = row[c];
+            if (!elem) {
+                continue;
+            }
+            var shift = row.pos - offset;
+            elem.depth = row.depth;
+            elem.height = row.height;
+            col.push({type: "elem", elem: elem, shift: shift});
+        }
+
+        col = buildCommon.makeVList(col, "individualShift", null, options);
+        col = makeSpan(
+            ["col-align-" + (colDescr.align || "c")],
+            [col]);
+        cols.push(col);
+
+        if (c < nc - 1 || group.value.hskipBeforeAndAfter) {
+            sepwidth = utils.deflt(colDescr.postgap, arraycolsep);
+            if (sepwidth !== 0) {
+                colSep = makeSpan(["arraycolsep"], []);
+                colSep.style.width = sepwidth + "em";
+                cols.push(colSep);
+            }
+        }
+    }
+    body = makeSpan(["mtable"], cols);
+    return makeSpan(["mord"], [body], options);
+};
+
+groupTypes.spacing = function(group, options) {
+    if (group.value === "\\ " || group.value === "\\space" ||
+        group.value === " " || group.value === "~") {
+        // Spaces are generated by adding an actual space. Each of these
+        // things has an entry in the symbols table, so these will be turned
+        // into appropriate outputs.
+        if (group.mode === "text") {
+            return buildCommon.makeOrd(group, options, "textord");
+        } else {
+            return makeSpan(["mspace"],
+                [buildCommon.mathsym(group.value, group.mode, options)],
+                options);
+        }
+    } else {
+        // Other kinds of spaces are of arbitrary width. We use CSS to
+        // generate these.
+        return makeSpan(
+            ["mspace",
+                buildCommon.spacingFunctions[group.value].className],
+            [], options);
+    }
+};
+
+groupTypes.llap = function(group, options) {
+    var inner = makeSpan(
+        ["inner"], [buildGroup(group.value.body, options.reset())]);
+    var fix = makeSpan(["fix"], []);
+    return makeSpan(
+        ["mord", "llap", options.style.cls()], [inner, fix], options);
+};
+
+groupTypes.rlap = function(group, options) {
+    var inner = makeSpan(
+        ["inner"], [buildGroup(group.value.body, options.reset())]);
+    var fix = makeSpan(["fix"], []);
+    return makeSpan(
+        ["mord", "rlap", options.style.cls()], [inner, fix], options);
+};
+
+groupTypes.op = function(group, options) {
+    // Operators are handled in the TeXbook pg. 443-444, rule 13(a).
+    var supGroup;
+    var subGroup;
+    var hasLimits = false;
+    if (group.type === "supsub") {
+        // If we have limits, supsub will pass us its group to handle. Pull
+        // out the superscript and subscript and set the group to the op in
+        // its base.
+        supGroup = group.value.sup;
+        subGroup = group.value.sub;
+        group = group.value.base;
+        hasLimits = true;
+    }
+
+    var style = options.style;
+
+    // Most operators have a large successor symbol, but these don't.
+    var noSuccessor = [
+        "\\smallint"
+    ];
+
+    var large = false;
+    if (style.size === Style.DISPLAY.size &&
+        group.value.symbol &&
+        !utils.contains(noSuccessor, group.value.body)) {
+
+        // Most symbol operators get larger in displaystyle (rule 13)
+        large = true;
+    }
+
+    var base;
+    var baseShift = 0;
+    var slant = 0;
+    if (group.value.symbol) {
+        // If this is a symbol, create the symbol.
+        var fontName = large ? "Size2-Regular" : "Size1-Regular";
+        base = buildCommon.makeSymbol(
+            group.value.body, fontName, "math", options,
+            ["mop", "op-symbol", large ? "large-op" : "small-op"]);
+
+        // Shift the symbol so its center lies on the axis (rule 13). It
+        // appears that our fonts have the centers of the symbols already
+        // almost on the axis, so these numbers are very small. Note we
+        // don't actually apply this here, but instead it is used either in
+        // the vlist creation or separately when there are no limits.
+        baseShift = (base.height - base.depth) / 2 -
+            style.metrics.axisHeight * style.sizeMultiplier;
+
+        // The slant of the symbol is just its italic correction.
+        slant = base.italic;
+    } else if (group.value.value) {
+        // If this is a list, compose that list.
+        var inner = buildExpression(group.value.value, options, true);
+
+        base = makeSpan(["mop"], inner, options);
+    } else {
+        // Otherwise, this is a text operator. Build the text from the
+        // operator's name.
+        // TODO(emily): Add a space in the middle of some of these
+        // operators, like \limsup
+        var output = [];
+        for (var i = 1; i < group.value.body.length; i++) {
+            output.push(buildCommon.mathsym(group.value.body[i], group.mode));
+        }
+        base = makeSpan(["mop"], output, options);
+    }
+
+    if (hasLimits) {
+        // IE 8 clips \int if it is in a display: inline-block. We wrap it
+        // in a new span so it is an inline, and works.
+        base = makeSpan([], [base]);
+
+        var supmid;
+        var supKern;
+        var submid;
+        var subKern;
+        var newOptions;
+        // We manually have to handle the superscripts and subscripts. This,
+        // aside from the kern calculations, is copied from supsub.
+        if (supGroup) {
+            newOptions = options.withStyle(style.sup());
+            var sup = buildGroup(supGroup, newOptions);
+            supmid = makeSpan([style.reset(), style.sup().cls()],
+                [sup], newOptions);
+
+            supKern = Math.max(
+                fontMetrics.metrics.bigOpSpacing1,
+                fontMetrics.metrics.bigOpSpacing3 - sup.depth);
+        }
+
+        if (subGroup) {
+            newOptions = options.withStyle(style.sub());
+            var sub = buildGroup(subGroup, newOptions);
+            submid = makeSpan([style.reset(), style.sub().cls()],
+                [sub], newOptions);
+
+            subKern = Math.max(
+                fontMetrics.metrics.bigOpSpacing2,
+                fontMetrics.metrics.bigOpSpacing4 - sub.height);
+        }
+
+        // Build the final group as a vlist of the possible subscript, base,
+        // and possible superscript.
+        var finalGroup;
+        var top;
+        var bottom;
+        if (!supGroup) {
+            top = base.height - baseShift;
+
+            finalGroup = buildCommon.makeVList([
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5},
+                {type: "elem", elem: submid},
+                {type: "kern", size: subKern},
+                {type: "elem", elem: base}
+            ], "top", top, options);
+
+            // Here, we shift the limits by the slant of the symbol. Note
+            // that we are supposed to shift the limits by 1/2 of the slant,
+            // but since we are centering the limits adding a full slant of
+            // margin will shift by 1/2 that.
+            finalGroup.children[0].style.marginLeft = -slant + "em";
+        } else if (!subGroup) {
+            bottom = base.depth + baseShift;
+
+            finalGroup = buildCommon.makeVList([
+                {type: "elem", elem: base},
+                {type: "kern", size: supKern},
+                {type: "elem", elem: supmid},
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5}
+            ], "bottom", bottom, options);
+
+            // See comment above about slants
+            finalGroup.children[1].style.marginLeft = slant + "em";
+        } else if (!supGroup && !subGroup) {
+            // This case probably shouldn't occur (this would mean the
+            // supsub was sending us a group with no superscript or
+            // subscript) but be safe.
+            return base;
+        } else {
+            bottom = fontMetrics.metrics.bigOpSpacing5 +
+                submid.height + submid.depth +
+                subKern +
+                base.depth + baseShift;
+
+            finalGroup = buildCommon.makeVList([
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5},
+                {type: "elem", elem: submid},
+                {type: "kern", size: subKern},
+                {type: "elem", elem: base},
+                {type: "kern", size: supKern},
+                {type: "elem", elem: supmid},
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5}
+            ], "bottom", bottom, options);
+
+            // See comment above about slants
+            finalGroup.children[0].style.marginLeft = -slant + "em";
+            finalGroup.children[2].style.marginLeft = slant + "em";
+        }
+
+        return makeSpan(["mop", "op-limits"], [finalGroup], options);
+    } else {
+        if (group.value.symbol) {
+            base.style.top = baseShift + "em";
+        }
+
+        return base;
+    }
+};
+
+groupTypes.mod = function(group, options) {
+    var inner = [];
+
+    if (group.value.modType === "bmod") {
+        // “\nonscript\mskip-\medmuskip\mkern5mu”
+        if (!options.style.isTight()) {
+            inner.push(makeSpan(
+                ["mspace", "negativemediumspace"], [], options));
+        }
+        inner.push(makeSpan(["mspace", "thickspace"], [], options));
+    } else if (options.style.size === Style.DISPLAY.size) {
+        inner.push(makeSpan(["mspace", "quad"], [], options));
+    } else if (group.value.modType === "mod") {
+        inner.push(makeSpan(["mspace", "twelvemuspace"], [], options));
+    } else {
+        inner.push(makeSpan(["mspace", "eightmuspace"], [], options));
+    }
+
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(buildCommon.mathsym("(", group.mode));
+    }
+
+    if (group.value.modType !== "pod") {
+        var modInner = [
+            buildCommon.mathsym("m", group.mode),
+            buildCommon.mathsym("o", group.mode),
+            buildCommon.mathsym("d", group.mode)];
+        if (group.value.modType === "bmod") {
+            inner.push(makeSpan(["mbin"], modInner, options));
+            // “\mkern5mu\nonscript\mskip-\medmuskip”
+            inner.push(makeSpan(["mspace", "thickspace"], [], options));
+            if (!options.style.isTight()) {
+                inner.push(makeSpan(
+                    ["mspace", "negativemediumspace"], [], options));
+            }
+        } else {
+            Array.prototype.push.apply(inner, modInner);
+            inner.push(makeSpan(["mspace", "sixmuspace"], [], options));
+        }
+    }
+
+    if (group.value.value) {
+        Array.prototype.push.apply(inner,
+            buildExpression(group.value.value, options, false));
+    }
+
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(buildCommon.mathsym(")", group.mode));
+    }
+
+    return buildCommon.makeFragment(inner);
+};
+
+groupTypes.katex = function(group, options) {
+    // The KaTeX logo. The offsets for the K and a were chosen to look
+    // good, but the offsets for the T, E, and X were taken from the
+    // definition of \TeX in TeX (see TeXbook pg. 356)
+    var k = makeSpan(
+        ["k"], [buildCommon.mathsym("K", group.mode)], options);
+    var a = makeSpan(
+        ["a"], [buildCommon.mathsym("A", group.mode)], options);
+
+    a.height = (a.height + 0.2) * 0.75;
+    a.depth = (a.height - 0.2) * 0.75;
+
+    var t = makeSpan(
+        ["t"], [buildCommon.mathsym("T", group.mode)], options);
+    var e = makeSpan(
+        ["e"], [buildCommon.mathsym("E", group.mode)], options);
+
+    e.height = (e.height - 0.2155);
+    e.depth = (e.depth + 0.2155);
+
+    var x = makeSpan(
+        ["x"], [buildCommon.mathsym("X", group.mode)], options);
+
+    return makeSpan(
+        ["mord", "katex-logo"], [k, a, t, e, x], options);
+};
+
+groupTypes.overline = function(group, options) {
+    // Overlines are handled in the TeXbook pg 443, Rule 9.
+    var style = options.style;
+
+    // Build the inner group in the cramped style.
+    var innerGroup = buildGroup(group.value.body,
+            options.withStyle(style.cramp()));
+
+    var ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+        style.sizeMultiplier;
+
+    // Create the line above the body
+    var line = makeSpan(
+        [style.reset(), Style.TEXT.cls(), "overline-line"]);
+    line.height = ruleWidth;
+    line.maxFontSize = 1.0;
+
+    // Generate the vlist, with the appropriate kerns
+    var vlist = buildCommon.makeVList([
+        {type: "elem", elem: innerGroup},
+        {type: "kern", size: 3 * ruleWidth},
+        {type: "elem", elem: line},
+        {type: "kern", size: ruleWidth}
+    ], "firstBaseline", null, options);
+
+    return makeSpan(["mord", "overline"], [vlist], options);
+};
+
+groupTypes.underline = function(group, options) {
+    // Underlines are handled in the TeXbook pg 443, Rule 10.
+    var style = options.style;
+
+    // Build the inner group.
+    var innerGroup = buildGroup(group.value.body, options);
+
+    var ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+        style.sizeMultiplier;
+
+    // Create the line above the body
+    var line = makeSpan([style.reset(), Style.TEXT.cls(), "underline-line"]);
+    line.height = ruleWidth;
+    line.maxFontSize = 1.0;
+
+    // Generate the vlist, with the appropriate kerns
+    var vlist = buildCommon.makeVList([
+        {type: "kern", size: ruleWidth},
+        {type: "elem", elem: line},
+        {type: "kern", size: 3 * ruleWidth},
+        {type: "elem", elem: innerGroup}
+    ], "top", innerGroup.height, options);
+
+    return makeSpan(["mord", "underline"], [vlist], options);
+};
+
+groupTypes.sqrt = function(group, options) {
+    // Square roots are handled in the TeXbook pg. 443, Rule 11.
+    var style = options.style;
+
+    // First, we do the same steps as in overline to build the inner group
+    // and line
+    var inner = buildGroup(group.value.body, options.withStyle(style.cramp()));
+
+    var ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+        style.sizeMultiplier;
+
+    var line = makeSpan(
+        [style.reset(), Style.TEXT.cls(), "sqrt-line"], [],
+        options);
+    line.height = ruleWidth;
+    line.maxFontSize = 1.0;
+
+    var phi = ruleWidth;
+    if (style.id < Style.TEXT.id) {
+        phi = style.metrics.xHeight;
+    }
+
+    // Calculate the clearance between the body and line
+    var lineClearance = ruleWidth + phi / 4;
+
+    var innerHeight = (inner.height + inner.depth) * style.sizeMultiplier;
+    var minDelimiterHeight = innerHeight + lineClearance + ruleWidth;
+
+    // Create a \surd delimiter of the required minimum size
+    var delim = makeSpan(["sqrt-sign"], [
+        delimiter.customSizedDelim("\\surd", minDelimiterHeight,
+                                   false, options, group.mode)],
+                         options);
+
+    var delimDepth = (delim.height + delim.depth) - ruleWidth;
+
+    // Adjust the clearance based on the delimiter size
+    if (delimDepth > inner.height + inner.depth + lineClearance) {
+        lineClearance =
+            (lineClearance + delimDepth - inner.height - inner.depth) / 2;
+    }
+
+    // Shift the delimiter so that its top lines up with the top of the line
+    var delimShift = -(inner.height + lineClearance + ruleWidth) + delim.height;
+    delim.style.top = delimShift + "em";
+    delim.height -= delimShift;
+    delim.depth += delimShift;
+
+    // We add a special case here, because even when `inner` is empty, we
+    // still get a line. So, we use a simple heuristic to decide if we
+    // should omit the body entirely. (note this doesn't work for something
+    // like `\sqrt{\rlap{x}}`, but if someone is doing that they deserve for
+    // it not to work.
+    var body;
+    if (inner.height === 0 && inner.depth === 0) {
+        body = makeSpan();
+    } else {
+        body = buildCommon.makeVList([
+            {type: "elem", elem: inner},
+            {type: "kern", size: lineClearance},
+            {type: "elem", elem: line},
+            {type: "kern", size: ruleWidth}
+        ], "firstBaseline", null, options);
+    }
+
+    if (!group.value.index) {
+        return makeSpan(["mord", "sqrt"], [delim, body], options);
+    } else {
+        // Handle the optional root index
+
+        // The index is always in scriptscript style
+        var newOptions = options.withStyle(Style.SCRIPTSCRIPT);
+        var root = buildGroup(group.value.index, newOptions);
+        var rootWrap = makeSpan(
+            [style.reset(), Style.SCRIPTSCRIPT.cls()],
+            [root],
+            newOptions);
+
+        // Figure out the height and depth of the inner part
+        var innerRootHeight = Math.max(delim.height, body.height);
+        var innerRootDepth = Math.max(delim.depth, body.depth);
+
+        // The amount the index is shifted by. This is taken from the TeX
+        // source, in the definition of `\r@@t`.
+        var toShift = 0.6 * (innerRootHeight - innerRootDepth);
+
+        // Build a VList with the superscript shifted up correctly
+        var rootVList = buildCommon.makeVList(
+            [{type: "elem", elem: rootWrap}],
+            "shift", -toShift, options);
+        // Add a class surrounding it so we can add on the appropriate
+        // kerning
+        var rootVListWrap = makeSpan(["root"], [rootVList]);
+
+        return makeSpan(["mord", "sqrt"],
+            [rootVListWrap, delim, body], options);
+    }
+};
+
+groupTypes.sizing = function(group, options) {
+    // Handle sizing operators like \Huge. Real TeX doesn't actually allow
+    // these functions inside of math expressions, so we do some special
+    // handling.
+    var inner = buildExpression(group.value.value,
+            options.withSize(group.value.size), false);
+
+    // Compute the correct maxFontSize.
+    var style = options.style;
+    var fontSize = buildCommon.sizingMultiplier[group.value.size];
+    fontSize = fontSize * style.sizeMultiplier;
+
+    // Add size-resetting classes to the inner list and set maxFontSize
+    // manually. Handle nested size changes.
+    for (var i = 0; i < inner.length; i++) {
+        var pos = utils.indexOf(inner[i].classes, "sizing");
+        if (pos < 0) {
+            inner[i].classes.push("sizing", "reset-" + options.size,
+                                  group.value.size, style.cls());
+            inner[i].maxFontSize = fontSize;
+        } else if (inner[i].classes[pos + 1] === "reset-" + group.value.size) {
+            // This is a nested size change: e.g., inner[i] is the "b" in
+            // `\Huge a \small b`. Override the old size (the `reset-` class)
+            // but not the new size.
+            inner[i].classes[pos + 1] = "reset-" + options.size;
+        }
+    }
+
+    return buildCommon.makeFragment(inner);
+};
+
+groupTypes.styling = function(group, options) {
+    // Style changes are handled in the TeXbook on pg. 442, Rule 3.
+
+    // Figure out what style we're changing to.
+    var styleMap = {
+        "display": Style.DISPLAY,
+        "text": Style.TEXT,
+        "script": Style.SCRIPT,
+        "scriptscript": Style.SCRIPTSCRIPT
+    };
+
+    var newStyle = styleMap[group.value.style];
+    var newOptions = options.withStyle(newStyle);
+
+    // Build the inner expression in the new style.
+    var inner = buildExpression(
+        group.value.value, newOptions, false);
+
+    // Add style-resetting classes to the inner list. Handle nested changes.
+    for (var i = 0; i < inner.length; i++) {
+        var pos = utils.indexOf(inner[i].classes, newStyle.reset());
+        if (pos < 0) {
+            inner[i].classes.push(options.style.reset(), newStyle.cls());
+        } else {
+            // This is a nested style change, as `\textstyle a\scriptstyle b`.
+            // Only override the old style (the reset class).
+            inner[i].classes[pos] = options.style.reset();
+        }
+    }
+
+    return new buildCommon.makeFragment(inner);
+};
+
+groupTypes.font = function(group, options) {
+    var font = group.value.font;
+    return buildGroup(group.value.body, options.withFont(font));
+};
+
+groupTypes.delimsizing = function(group, options) {
+    var delim = group.value.value;
+
+    if (delim === ".") {
+        // Empty delimiters still count as elements, even though they don't
+        // show anything.
+        return makeSpan([group.value.mclass]);
+    }
+
+    // Use delimiter.sizedDelim to generate the delimiter.
+    return delimiter.sizedDelim(
+            delim, group.value.size, options, group.mode,
+            [group.value.mclass]);
+};
+
+groupTypes.leftright = function(group, options) {
+    // Build the inner expression
+    var inner = buildExpression(group.value.body, options.reset(), true);
+
+    var innerHeight = 0;
+    var innerDepth = 0;
+    var hadMiddle = false;
+
+    // Calculate its height and depth
+    for (var i = 0; i < inner.length; i++) {
+        if (inner[i].isMiddle) {
+            hadMiddle = true;
+        } else {
+            innerHeight = Math.max(inner[i].height, innerHeight);
+            innerDepth = Math.max(inner[i].depth, innerDepth);
+        }
+    }
+
+    var style = options.style;
+
+    // The size of delimiters is the same, regardless of what style we are
+    // in. Thus, to correctly calculate the size of delimiter we need around
+    // a group, we scale down the inner size based on the size.
+    innerHeight *= style.sizeMultiplier;
+    innerDepth *= style.sizeMultiplier;
+
+    var leftDelim;
+    if (group.value.left === ".") {
+        // Empty delimiters in \left and \right make null delimiter spaces.
+        leftDelim = makeNullDelimiter(options, ["mopen"]);
+    } else {
+        // Otherwise, use leftRightDelim to generate the correct sized
+        // delimiter.
+        leftDelim = delimiter.leftRightDelim(
+            group.value.left, innerHeight, innerDepth, options,
+            group.mode, ["mopen"]);
+    }
+    // Add it to the beginning of the expression
+    inner.unshift(leftDelim);
+
+    // Handle middle delimiters
+    if (hadMiddle) {
+        for (i = 1; i < inner.length; i++) {
+            if (inner[i].isMiddle) {
+                // Apply the options that were active when \middle was called
+                inner[i] = delimiter.leftRightDelim(
+                    inner[i].isMiddle.value, innerHeight, innerDepth,
+                    inner[i].isMiddle.options, group.mode, []);
+            }
+        }
+    }
+
+    var rightDelim;
+    // Same for the right delimiter
+    if (group.value.right === ".") {
+        rightDelim = makeNullDelimiter(options, ["mclose"]);
+    } else {
+        rightDelim = delimiter.leftRightDelim(
+            group.value.right, innerHeight, innerDepth, options,
+            group.mode, ["mclose"]);
+    }
+    // Add it to the end of the expression.
+    inner.push(rightDelim);
+
+    return makeSpan(
+        ["minner", style.cls()], inner, options);
+};
+
+groupTypes.middle = function(group, options) {
+    var middleDelim;
+    if (group.value.value === ".") {
+        middleDelim = makeNullDelimiter(options, []);
+    } else {
+        middleDelim = delimiter.sizedDelim(
+            group.value.value, 1, options,
+            group.mode, []);
+        middleDelim.isMiddle = {value: group.value.value, options: options};
+    }
+    return middleDelim;
+};
+
+groupTypes.rule = function(group, options) {
+    // Make an empty span for the rule
+    var rule = makeSpan(["mord", "rule"], [], options);
+    var style = options.style;
+
+    // Calculate the shift, width, and height of the rule, and account for units
+    var shift = 0;
+    if (group.value.shift) {
+        shift = calculateSize(group.value.shift, style);
+    }
+
+    var width = calculateSize(group.value.width, style);
+    var height = calculateSize(group.value.height, style);
+
+    // The sizes of rules are absolute, so make it larger if we are in a
+    // smaller style.
+    shift /= style.sizeMultiplier;
+    width /= style.sizeMultiplier;
+    height /= style.sizeMultiplier;
+
+    // Style the rule to the right size
+    rule.style.borderRightWidth = width + "em";
+    rule.style.borderTopWidth = height + "em";
+    rule.style.bottom = shift + "em";
+
+    // Record the height and width
+    rule.width = width;
+    rule.height = height + shift;
+    rule.depth = -shift;
+
+    return rule;
+};
+
+groupTypes.kern = function(group, options) {
+    // Make an empty span for the rule
+    var rule = makeSpan(["mord", "rule"], [], options);
+    var style = options.style;
+
+    var dimension = 0;
+    if (group.value.dimension) {
+        dimension = calculateSize(group.value.dimension, style);
+    }
+
+    dimension /= style.sizeMultiplier;
+
+    rule.style.marginLeft = dimension + "em";
+
+    return rule;
+};
+
+groupTypes.accent = function(group, options) {
+    // Accents are handled in the TeXbook pg. 443, rule 12.
+    var base = group.value.base;
+    var style = options.style;
+
+    var supsubGroup;
+    if (group.type === "supsub") {
+        // If our base is a character box, and we have superscripts and
+        // subscripts, the supsub will defer to us. In particular, we want
+        // to attach the superscripts and subscripts to the inner body (so
+        // that the position of the superscripts and subscripts won't be
+        // affected by the height of the accent). We accomplish this by
+        // sticking the base of the accent into the base of the supsub, and
+        // rendering that, while keeping track of where the accent is.
+
+        // The supsub group is the group that was passed in
+        var supsub = group;
+        // The real accent group is the base of the supsub group
+        group = supsub.value.base;
+        // The character box is the base of the accent group
+        base = group.value.base;
+        // Stick the character box into the base of the supsub group
+        supsub.value.base = base;
+
+        // Rerender the supsub group with its new base, and store that
+        // result.
+        supsubGroup = buildGroup(
+            supsub, options.reset());
+    }
+
+    // Build the base group
+    var body = buildGroup(
+        base, options.withStyle(style.cramp()));
+
+    // Calculate the skew of the accent. This is based on the line "If the
+    // nucleus is not a single character, let s = 0; otherwise set s to the
+    // kern amount for the nucleus followed by the \skewchar of its font."
+    // Note that our skew metrics are just the kern between each character
+    // and the skewchar.
+    var skew;
+    if (isCharacterBox(base)) {
+        // If the base is a character box, then we want the skew of the
+        // innermost character. To do that, we find the innermost character:
+        var baseChar = getBaseElem(base);
+        // Then, we render its group to get the symbol inside it
+        var baseGroup = buildGroup(
+            baseChar, options.withStyle(style.cramp()));
+        // Finally, we pull the skew off of the symbol.
+        skew = baseGroup.skew;
+        // Note that we now throw away baseGroup, because the layers we
+        // removed with getBaseElem might contain things like \color which
+        // we can't get rid of.
+        // TODO(emily): Find a better way to get the skew
+    } else {
+        skew = 0;
+    }
+
+    // calculate the amount of space between the body and the accent
+    var clearance = Math.min(
+        body.height,
+        style.metrics.xHeight);
+
+    // Build the accent
+    var accent = buildCommon.makeSymbol(
+        group.value.accent, "Main-Regular", "math", options);
+    // Remove the italic correction of the accent, because it only serves to
+    // shift the accent over to a place we don't want.
+    accent.italic = 0;
+
+    // The \vec character that the fonts use is a combining character, and
+    // thus shows up much too far to the left. To account for this, we add a
+    // specific class which shifts the accent over to where we want it.
+    // TODO(emily): Fix this in a better way, like by changing the font
+    var vecClass = group.value.accent === "\\vec" ? "accent-vec" : null;
+
+    var accentBody = makeSpan(["accent-body", vecClass], [
+        makeSpan([], [accent])]);
+
+    accentBody = buildCommon.makeVList([
+        {type: "elem", elem: body},
+        {type: "kern", size: -clearance},
+        {type: "elem", elem: accentBody}
+    ], "firstBaseline", null, options);
+
+    // Shift the accent over by the skew. Note we shift by twice the skew
+    // because we are centering the accent, so by adding 2*skew to the left,
+    // we shift it to the right by 1*skew.
+    accentBody.children[1].style.marginLeft = 2 * skew + "em";
+
+    var accentWrap = makeSpan(["mord", "accent"], [accentBody], options);
+
+    if (supsubGroup) {
+        // Here, we replace the "base" child of the supsub with our newly
+        // generated accent.
+        supsubGroup.children[0] = accentWrap;
+
+        // Since we don't rerun the height calculation after replacing the
+        // accent, we manually recalculate height.
+        supsubGroup.height = Math.max(accentWrap.height, supsubGroup.height);
+
+        // Accents should always be ords, even when their innards are not.
+        supsubGroup.classes[0] = "mord";
+
+        return supsubGroup;
+    } else {
+        return accentWrap;
+    }
+};
+
+groupTypes.phantom = function(group, options) {
+    var elements = buildExpression(
+        group.value.value,
+        options.withPhantom(),
+        false
+    );
+
+    // \phantom isn't supposed to affect the elements it contains.
+    // See "color" for more details.
+    return new buildCommon.makeFragment(elements);
+};
+
+groupTypes.mclass = function(group, options) {
+    var elements = buildExpression(group.value.value, options, true);
+
+    return makeSpan([group.value.mclass], elements, options);
+};
+
+/**
+ * buildGroup is the function that takes a group and calls the correct groupType
+ * function for it. It also handles the interaction of size and style changes
+ * between parents and children.
+ */
+var buildGroup = function(group, options) {
+    if (!group) {
+        return makeSpan();
+    }
+
+    if (groupTypes[group.type]) {
+        // Call the groupTypes function
+        var groupNode = groupTypes[group.type](group, options);
+        var multiplier;
+
+        // If the style changed between the parent and the current group,
+        // account for the size difference
+        if (options.style !== options.parentStyle) {
+            multiplier = options.style.sizeMultiplier /
+                    options.parentStyle.sizeMultiplier;
+
+            groupNode.height *= multiplier;
+            groupNode.depth *= multiplier;
+        }
+
+        // If the size changed between the parent and the current group, account
+        // for that size difference.
+        if (options.size !== options.parentSize) {
+            multiplier = buildCommon.sizingMultiplier[options.size] /
+                    buildCommon.sizingMultiplier[options.parentSize];
+
+            groupNode.height *= multiplier;
+            groupNode.depth *= multiplier;
+        }
+
+        return groupNode;
+    } else {
+        throw new ParseError(
+            "Got group of unknown type: '" + group.type + "'");
+    }
+};
+
+/**
+ * Take an entire parse tree, and build it into an appropriate set of HTML
+ * nodes.
+ */
+var buildHTML = function(tree, options) {
+    // buildExpression is destructive, so we need to make a clone
+    // of the incoming tree so that it isn't accidentally changed
+    tree = JSON.parse(JSON.stringify(tree));
+
+    // Build the expression contained in the tree
+    var expression = buildExpression(tree, options, true);
+    var body = makeSpan(["base", options.style.cls()], expression, options);
+
+    // Add struts, which ensure that the top of the HTML element falls at the
+    // height of the expression, and the bottom of the HTML element falls at the
+    // depth of the expression.
+    var topStrut = makeSpan(["strut"]);
+    var bottomStrut = makeSpan(["strut", "bottom"]);
+
+    topStrut.style.height = body.height + "em";
+    bottomStrut.style.height = (body.height + body.depth) + "em";
+    // We'd like to use `vertical-align: top` but in IE 9 this lowers the
+    // baseline of the box to the bottom of this strut (instead staying in the
+    // normal place) so we use an absolute value for vertical-align instead
+    bottomStrut.style.verticalAlign = -body.depth + "em";
+
+    // Wrap the struts and body together
+    var htmlNode = makeSpan(["katex-html"], [topStrut, bottomStrut, body]);
+
+    htmlNode.setAttribute("aria-hidden", "true");
+
+    return htmlNode;
+};
+
+module.exports = buildHTML;
+
+},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./delimiter":14,"./domTree":15,"./fontMetrics":17,"./utils":25}],12:[function(require,module,exports){
+/**
+ * This file converts a parse tree into a cooresponding MathML tree. The main
+ * entry point is the `buildMathML` function, which takes a parse tree from the
+ * parser.
+ */
+
+var buildCommon = require("./buildCommon");
+var fontMetrics = require("./fontMetrics");
+var mathMLTree = require("./mathMLTree");
+var ParseError = require("./ParseError");
+var symbols = require("./symbols");
+var utils = require("./utils");
+
+var makeSpan = buildCommon.makeSpan;
+var fontMap = buildCommon.fontMap;
+
+/**
+ * Takes a symbol and converts it into a MathML text node after performing
+ * optional replacement from symbols.js.
+ */
+var makeText = function(text, mode) {
+    if (symbols[mode][text] && symbols[mode][text].replace) {
+        text = symbols[mode][text].replace;
+    }
+
+    return new mathMLTree.TextNode(text);
+};
+
+/**
+ * Returns the math variant as a string or null if none is required.
+ */
+var getVariant = function(group, options) {
+    var font = options.font;
+    if (!font) {
+        return null;
+    }
+
+    var mode = group.mode;
+    if (font === "mathit") {
+        return "italic";
+    }
+
+    var value = group.value;
+    if (utils.contains(["\\imath", "\\jmath"], value)) {
+        return null;
+    }
+
+    if (symbols[mode][value] && symbols[mode][value].replace) {
+        value = symbols[mode][value].replace;
+    }
+
+    var fontName = fontMap[font].fontName;
+    if (fontMetrics.getCharacterMetrics(value, fontName)) {
+        return fontMap[options.font].variant;
+    }
+
+    return null;
+};
+
+/**
+ * Functions for handling the different types of groups found in the parse
+ * tree. Each function should take a parse group and return a MathML node.
+ */
+var groupTypes = {};
+
+groupTypes.mathord = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mi",
+        [makeText(group.value, group.mode)]);
+
+    var variant = getVariant(group, options);
+    if (variant) {
+        node.setAttribute("mathvariant", variant);
+    }
+    return node;
+};
+
+groupTypes.textord = function(group, options) {
+    var text = makeText(group.value, group.mode);
+
+    var variant = getVariant(group, options) || "normal";
+
+    var node;
+    if (/[0-9]/.test(group.value)) {
+        // TODO(kevinb) merge adjacent <mn> nodes
+        // do it as a post processing step
+        node = new mathMLTree.MathNode("mn", [text]);
+        if (options.font) {
+            node.setAttribute("mathvariant", variant);
+        }
+    } else {
+        node = new mathMLTree.MathNode("mi", [text]);
+        node.setAttribute("mathvariant", variant);
+    }
+
+    return node;
+};
+
+groupTypes.bin = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.rel = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.open = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.close = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.inner = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.punct = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    node.setAttribute("separator", "true");
+
+    return node;
+};
+
+groupTypes.ordgroup = function(group, options) {
+    var inner = buildExpression(group.value, options);
+
+    var node = new mathMLTree.MathNode("mrow", inner);
+
+    return node;
+};
+
+groupTypes.text = function(group, options) {
+    var inner = buildExpression(group.value.body, options);
+
+    var node = new mathMLTree.MathNode("mtext", inner);
+
+    return node;
+};
+
+groupTypes.color = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+
+    var node = new mathMLTree.MathNode("mstyle", inner);
+
+    node.setAttribute("mathcolor", group.value.color);
+
+    return node;
+};
+
+groupTypes.supsub = function(group, options) {
+    var children = [buildGroup(group.value.base, options)];
+
+    if (group.value.sub) {
+        children.push(buildGroup(group.value.sub, options));
+    }
+
+    if (group.value.sup) {
+        children.push(buildGroup(group.value.sup, options));
+    }
+
+    var nodeType;
+    if (!group.value.sub) {
+        nodeType = "msup";
+    } else if (!group.value.sup) {
+        nodeType = "msub";
+    } else {
+        nodeType = "msubsup";
+    }
+
+    var node = new mathMLTree.MathNode(nodeType, children);
+
+    return node;
+};
+
+groupTypes.genfrac = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mfrac",
+        [buildGroup(group.value.numer, options),
+            buildGroup(group.value.denom, options)]);
+
+    if (!group.value.hasBarLine) {
+        node.setAttribute("linethickness", "0px");
+    }
+
+    if (group.value.leftDelim != null || group.value.rightDelim != null) {
+        var withDelims = [];
+
+        if (group.value.leftDelim != null) {
+            var leftOp = new mathMLTree.MathNode(
+                "mo", [new mathMLTree.TextNode(group.value.leftDelim)]);
+
+            leftOp.setAttribute("fence", "true");
+
+            withDelims.push(leftOp);
+        }
+
+        withDelims.push(node);
+
+        if (group.value.rightDelim != null) {
+            var rightOp = new mathMLTree.MathNode(
+                "mo", [new mathMLTree.TextNode(group.value.rightDelim)]);
+
+            rightOp.setAttribute("fence", "true");
+
+            withDelims.push(rightOp);
+        }
+
+        var outerNode = new mathMLTree.MathNode("mrow", withDelims);
+
+        return outerNode;
+    }
+
+    return node;
+};
+
+groupTypes.array = function(group, options) {
+    return new mathMLTree.MathNode(
+        "mtable", group.value.body.map(function(row) {
+            return new mathMLTree.MathNode(
+                "mtr", row.map(function(cell) {
+                    return new mathMLTree.MathNode(
+                        "mtd", [buildGroup(cell, options)]);
+                }));
+        }));
+};
+
+groupTypes.sqrt = function(group, options) {
+    var node;
+    if (group.value.index) {
+        node = new mathMLTree.MathNode(
+            "mroot", [
+                buildGroup(group.value.body, options),
+                buildGroup(group.value.index, options)
+            ]);
+    } else {
+        node = new mathMLTree.MathNode(
+            "msqrt", [buildGroup(group.value.body, options)]);
+    }
+
+    return node;
+};
+
+groupTypes.leftright = function(group, options) {
+    var inner = buildExpression(group.value.body, options);
+
+    if (group.value.left !== ".") {
+        var leftNode = new mathMLTree.MathNode(
+            "mo", [makeText(group.value.left, group.mode)]);
+
+        leftNode.setAttribute("fence", "true");
+
+        inner.unshift(leftNode);
+    }
+
+    if (group.value.right !== ".") {
+        var rightNode = new mathMLTree.MathNode(
+            "mo", [makeText(group.value.right, group.mode)]);
+
+        rightNode.setAttribute("fence", "true");
+
+        inner.push(rightNode);
+    }
+
+    var outerNode = new mathMLTree.MathNode("mrow", inner);
+
+    return outerNode;
+};
+
+groupTypes.middle = function(group, options) {
+    var middleNode = new mathMLTree.MathNode(
+        "mo", [makeText(group.value.middle, group.mode)]);
+    middleNode.setAttribute("fence", "true");
+    return middleNode;
+};
+
+groupTypes.accent = function(group, options) {
+    var accentNode = new mathMLTree.MathNode(
+        "mo", [makeText(group.value.accent, group.mode)]);
+
+    var node = new mathMLTree.MathNode(
+        "mover",
+        [buildGroup(group.value.base, options),
+            accentNode]);
+
+    node.setAttribute("accent", "true");
+
+    return node;
+};
+
+groupTypes.spacing = function(group) {
+    var node;
+
+    if (group.value === "\\ " || group.value === "\\space" ||
+        group.value === " " || group.value === "~") {
+        node = new mathMLTree.MathNode(
+            "mtext", [new mathMLTree.TextNode("\u00a0")]);
+    } else {
+        node = new mathMLTree.MathNode("mspace");
+
+        node.setAttribute(
+            "width", buildCommon.spacingFunctions[group.value].size);
+    }
+
+    return node;
+};
+
+groupTypes.op = function(group, options) {
+    var node;
+
+    // TODO(emily): handle big operators using the `largeop` attribute
+
+    if (group.value.symbol) {
+        // This is a symbol. Just add the symbol.
+        node = new mathMLTree.MathNode(
+            "mo", [makeText(group.value.body, group.mode)]);
+    } else if (group.value.value) {
+        // This is an operator with children. Add them.
+        node = new mathMLTree.MathNode(
+            "mo", buildExpression(group.value.value, options));
+    } else {
+        // This is a text operator. Add all of the characters from the
+        // operator's name.
+        // TODO(emily): Add a space in the middle of some of these
+        // operators, like \limsup.
+        node = new mathMLTree.MathNode(
+            "mi", [new mathMLTree.TextNode(group.value.body.slice(1))]);
+    }
+
+    return node;
+};
+
+groupTypes.mod = function(group, options) {
+    var inner = [];
+
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(new mathMLTree.MathNode(
+            "mo", [makeText("(", group.mode)]));
+    }
+    if (group.value.modType !== "pod") {
+        inner.push(new mathMLTree.MathNode(
+            "mo", [makeText("mod", group.mode)]));
+    }
+    if (group.value.value) {
+        var space = new mathMLTree.MathNode("mspace");
+        space.setAttribute("width", "0.333333em");
+        inner.push(space);
+        inner = inner.concat(buildExpression(group.value.value, options));
+    }
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(new mathMLTree.MathNode(
+            "mo", [makeText(")", group.mode)]));
+    }
+
+    return new mathMLTree.MathNode("mo", inner);
+};
+
+groupTypes.katex = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mtext", [new mathMLTree.TextNode("KaTeX")]);
+
+    return node;
+};
+
+groupTypes.font = function(group, options) {
+    var font = group.value.font;
+    return buildGroup(group.value.body, options.withFont(font));
+};
+
+groupTypes.delimsizing = function(group) {
+    var children = [];
+
+    if (group.value.value !== ".") {
+        children.push(makeText(group.value.value, group.mode));
+    }
+
+    var node = new mathMLTree.MathNode("mo", children);
+
+    if (group.value.mclass === "mopen" ||
+        group.value.mclass === "mclose") {
+        // Only some of the delimsizing functions act as fences, and they
+        // return "mopen" or "mclose" mclass.
+        node.setAttribute("fence", "true");
+    } else {
+        // Explicitly disable fencing if it's not a fence, to override the
+        // defaults.
+        node.setAttribute("fence", "false");
+    }
+
+    return node;
+};
+
+groupTypes.styling = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+
+    var node = new mathMLTree.MathNode("mstyle", inner);
+
+    var styleAttributes = {
+        "display": ["0", "true"],
+        "text": ["0", "false"],
+        "script": ["1", "false"],
+        "scriptscript": ["2", "false"]
+    };
+
+    var attr = styleAttributes[group.value.style];
+
+    node.setAttribute("scriptlevel", attr[0]);
+    node.setAttribute("displaystyle", attr[1]);
+
+    return node;
+};
+
+groupTypes.sizing = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+
+    var node = new mathMLTree.MathNode("mstyle", inner);
+
+    // TODO(emily): This doesn't produce the correct size for nested size
+    // changes, because we don't keep state of what style we're currently
+    // in, so we can't reset the size to normal before changing it.  Now
+    // that we're passing an options parameter we should be able to fix
+    // this.
+    node.setAttribute(
+        "mathsize", buildCommon.sizingMultiplier[group.value.size] + "em");
+
+    return node;
+};
+
+groupTypes.overline = function(group, options) {
+    var operator = new mathMLTree.MathNode(
+        "mo", [new mathMLTree.TextNode("\u203e")]);
+    operator.setAttribute("stretchy", "true");
+
+    var node = new mathMLTree.MathNode(
+        "mover",
+        [buildGroup(group.value.body, options),
+            operator]);
+    node.setAttribute("accent", "true");
+
+    return node;
+};
+
+groupTypes.underline = function(group, options) {
+    var operator = new mathMLTree.MathNode(
+        "mo", [new mathMLTree.TextNode("\u203e")]);
+    operator.setAttribute("stretchy", "true");
+
+    var node = new mathMLTree.MathNode(
+        "munder",
+        [buildGroup(group.value.body, options),
+            operator]);
+    node.setAttribute("accentunder", "true");
+
+    return node;
+};
+
+groupTypes.rule = function(group) {
+    // TODO(emily): Figure out if there's an actual way to draw black boxes
+    // in MathML.
+    var node = new mathMLTree.MathNode("mrow");
+
+    return node;
+};
+
+groupTypes.kern = function(group) {
+    // TODO(kevin): Figure out if there's a way to add space in MathML
+    var node = new mathMLTree.MathNode("mrow");
+
+    return node;
+};
+
+groupTypes.llap = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mpadded", [buildGroup(group.value.body, options)]);
+
+    node.setAttribute("lspace", "-1width");
+    node.setAttribute("width", "0px");
+
+    return node;
+};
+
+groupTypes.rlap = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mpadded", [buildGroup(group.value.body, options)]);
+
+    node.setAttribute("width", "0px");
+
+    return node;
+};
+
+groupTypes.phantom = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+    return new mathMLTree.MathNode("mphantom", inner);
+};
+
+groupTypes.mclass = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+    return new mathMLTree.MathNode("mstyle", inner);
+};
+
+/**
+ * Takes a list of nodes, builds them, and returns a list of the generated
+ * MathML nodes. A little simpler than the HTML version because we don't do any
+ * previous-node handling.
+ */
+var buildExpression = function(expression, options) {
+    var groups = [];
+    for (var i = 0; i < expression.length; i++) {
+        var group = expression[i];
+        groups.push(buildGroup(group, options));
+    }
+    return groups;
+};
+
+/**
+ * Takes a group from the parser and calls the appropriate groupTypes function
+ * on it to produce a MathML node.
+ */
+var buildGroup = function(group, options) {
+    if (!group) {
+        return new mathMLTree.MathNode("mrow");
+    }
+
+    if (groupTypes[group.type]) {
+        // Call the groupTypes function
+        return groupTypes[group.type](group, options);
+    } else {
+        throw new ParseError(
+            "Got group of unknown type: '" + group.type + "'");
+    }
+};
+
+/**
+ * Takes a full parse tree and settings and builds a MathML representation of
+ * it. In particular, we put the elements from building the parse tree into a
+ * <semantics> tag so we can also include that TeX source as an annotation.
+ *
+ * Note that we actually return a domTree element with a `<math>` inside it so
+ * we can do appropriate styling.
+ */
+var buildMathML = function(tree, texExpression, options) {
+    var expression = buildExpression(tree, options);
+
+    // Wrap up the expression in an mrow so it is presented in the semantics
+    // tag correctly.
+    var wrapper = new mathMLTree.MathNode("mrow", expression);
+
+    // Build a TeX annotation of the source
+    var annotation = new mathMLTree.MathNode(
+        "annotation", [new mathMLTree.TextNode(texExpression)]);
+
+    annotation.setAttribute("encoding", "application/x-tex");
+
+    var semantics = new mathMLTree.MathNode(
+        "semantics", [wrapper, annotation]);
+
+    var math = new mathMLTree.MathNode("math", [semantics]);
+
+    // You can't style <math> nodes, so we wrap the node in a span.
+    return makeSpan(["katex-mathml"], [math]);
+};
+
+module.exports = buildMathML;
+
+},{"./ParseError":6,"./buildCommon":10,"./fontMetrics":17,"./mathMLTree":20,"./symbols":23,"./utils":25}],13:[function(require,module,exports){
+var buildHTML = require("./buildHTML");
+var buildMathML = require("./buildMathML");
+var buildCommon = require("./buildCommon");
+var Options = require("./Options");
+var Settings = require("./Settings");
+var Style = require("./Style");
+
+var makeSpan = buildCommon.makeSpan;
+
+var buildTree = function(tree, expression, settings) {
+    settings = settings || new Settings({});
+
+    var startStyle = Style.TEXT;
+    if (settings.displayMode) {
+        startStyle = Style.DISPLAY;
+    }
+
+    // Setup the default options
+    var options = new Options({
+        style: startStyle,
+        size: "size5"
+    });
+
+    // `buildHTML` sometimes messes with the parse tree (like turning bins ->
+    // ords), so we build the MathML version first.
+    var mathMLNode = buildMathML(tree, expression, options);
+    var htmlNode = buildHTML(tree, options);
+
+    var katexNode = makeSpan(["katex"], [
+        mathMLNode, htmlNode
+    ]);
+
+    if (settings.displayMode) {
+        return makeSpan(["katex-display"], [katexNode]);
+    } else {
+        return katexNode;
+    }
+};
+
+module.exports = buildTree;
+
+},{"./Options":5,"./Settings":8,"./Style":9,"./buildCommon":10,"./buildHTML":11,"./buildMathML":12}],14:[function(require,module,exports){
+/**
+ * This file deals with creating delimiters of various sizes. The TeXbook
+ * discusses these routines on page 441-442, in the "Another subroutine sets box
+ * x to a specified variable delimiter" paragraph.
+ *
+ * There are three main routines here. `makeSmallDelim` makes a delimiter in the
+ * normal font, but in either text, script, or scriptscript style.
+ * `makeLargeDelim` makes a delimiter in textstyle, but in one of the Size1,
+ * Size2, Size3, or Size4 fonts. `makeStackedDelim` makes a delimiter out of
+ * smaller pieces that are stacked on top of one another.
+ *
+ * The functions take a parameter `center`, which determines if the delimiter
+ * should be centered around the axis.
+ *
+ * Then, there are three exposed functions. `sizedDelim` makes a delimiter in
+ * one of the given sizes. This is used for things like `\bigl`.
+ * `customSizedDelim` makes a delimiter with a given total height+depth. It is
+ * called in places like `\sqrt`. `leftRightDelim` makes an appropriate
+ * delimiter which surrounds an expression of a given height an depth. It is
+ * used in `\left` and `\right`.
+ */
+
+var ParseError = require("./ParseError");
+var Style = require("./Style");
+
+var buildCommon = require("./buildCommon");
+var fontMetrics = require("./fontMetrics");
+var symbols = require("./symbols");
+var utils = require("./utils");
+
+var makeSpan = buildCommon.makeSpan;
+
+/**
+ * Get the metrics for a given symbol and font, after transformation (i.e.
+ * after following replacement from symbols.js)
+ */
+var getMetrics = function(symbol, font) {
+    if (symbols.math[symbol] && symbols.math[symbol].replace) {
+        return fontMetrics.getCharacterMetrics(
+            symbols.math[symbol].replace, font);
+    } else {
+        return fontMetrics.getCharacterMetrics(
+            symbol, font);
+    }
+};
+
+/**
+ * Builds a symbol in the given font size (note size is an integer)
+ */
+var mathrmSize = function(value, size, mode, options) {
+    return buildCommon.makeSymbol(value, "Size" + size + "-Regular",
+        mode, options);
+};
+
+/**
+ * Puts a delimiter span in a given style, and adds appropriate height, depth,
+ * and maxFontSizes.
+ */
+var styleWrap = function(delim, toStyle, options, classes) {
+    classes = classes || [];
+    var span = makeSpan(
+        classes.concat(["style-wrap", options.style.reset(), toStyle.cls()]),
+        [delim], options);
+
+    var multiplier = toStyle.sizeMultiplier / options.style.sizeMultiplier;
+
+    span.height *= multiplier;
+    span.depth *= multiplier;
+    span.maxFontSize = toStyle.sizeMultiplier;
+
+    return span;
+};
+
+/**
+ * Makes a small delimiter. This is a delimiter that comes in the Main-Regular
+ * font, but is restyled to either be in textstyle, scriptstyle, or
+ * scriptscriptstyle.
+ */
+var makeSmallDelim = function(delim, style, center, options, mode, classes) {
+    var text = buildCommon.makeSymbol(delim, "Main-Regular", mode, options);
+
+    var span = styleWrap(text, style, options, classes);
+
+    if (center) {
+        var shift =
+            (1 - options.style.sizeMultiplier / style.sizeMultiplier) *
+            options.style.metrics.axisHeight;
+
+        span.style.top = shift + "em";
+        span.height -= shift;
+        span.depth += shift;
+    }
+
+    return span;
+};
+
+/**
+ * Makes a large delimiter. This is a delimiter that comes in the Size1, Size2,
+ * Size3, or Size4 fonts. It is always rendered in textstyle.
+ */
+var makeLargeDelim = function(delim, size, center, options, mode, classes) {
+    var inner = mathrmSize(delim, size, mode, options);
+
+    var span = styleWrap(
+        makeSpan(["delimsizing", "size" + size], [inner], options),
+        Style.TEXT, options, classes);
+
+    if (center) {
+        var shift = (1 - options.style.sizeMultiplier) *
+            options.style.metrics.axisHeight;
+
+        span.style.top = shift + "em";
+        span.height -= shift;
+        span.depth += shift;
+    }
+
+    return span;
+};
+
+/**
+ * Make an inner span with the given offset and in the given font. This is used
+ * in `makeStackedDelim` to make the stacking pieces for the delimiter.
+ */
+var makeInner = function(symbol, font, mode) {
+    var sizeClass;
+    // Apply the correct CSS class to choose the right font.
+    if (font === "Size1-Regular") {
+        sizeClass = "delim-size1";
+    } else if (font === "Size4-Regular") {
+        sizeClass = "delim-size4";
+    }
+
+    var inner = makeSpan(
+        ["delimsizinginner", sizeClass],
+        [makeSpan([], [buildCommon.makeSymbol(symbol, font, mode)])]);
+
+    // Since this will be passed into `makeVList` in the end, wrap the element
+    // in the appropriate tag that VList uses.
+    return {type: "elem", elem: inner};
+};
+
+/**
+ * Make a stacked delimiter out of a given delimiter, with the total height at
+ * least `heightTotal`. This routine is mentioned on page 442 of the TeXbook.
+ */
+var makeStackedDelim = function(delim, heightTotal, center, options, mode,
+                                classes) {
+    // There are four parts, the top, an optional middle, a repeated part, and a
+    // bottom.
+    var top;
+    var middle;
+    var repeat;
+    var bottom;
+    top = repeat = bottom = delim;
+    middle = null;
+    // Also keep track of what font the delimiters are in
+    var font = "Size1-Regular";
+
+    // We set the parts and font based on the symbol. Note that we use
+    // '\u23d0' instead of '|' and '\u2016' instead of '\\|' for the
+    // repeats of the arrows
+    if (delim === "\\uparrow") {
+        repeat = bottom = "\u23d0";
+    } else if (delim === "\\Uparrow") {
+        repeat = bottom = "\u2016";
+    } else if (delim === "\\downarrow") {
+        top = repeat = "\u23d0";
+    } else if (delim === "\\Downarrow") {
+        top = repeat = "\u2016";
+    } else if (delim === "\\updownarrow") {
+        top = "\\uparrow";
+        repeat = "\u23d0";
+        bottom = "\\downarrow";
+    } else if (delim === "\\Updownarrow") {
+        top = "\\Uparrow";
+        repeat = "\u2016";
+        bottom = "\\Downarrow";
+    } else if (delim === "[" || delim === "\\lbrack") {
+        top = "\u23a1";
+        repeat = "\u23a2";
+        bottom = "\u23a3";
+        font = "Size4-Regular";
+    } else if (delim === "]" || delim === "\\rbrack") {
+        top = "\u23a4";
+        repeat = "\u23a5";
+        bottom = "\u23a6";
+        font = "Size4-Regular";
+    } else if (delim === "\\lfloor") {
+        repeat = top = "\u23a2";
+        bottom = "\u23a3";
+        font = "Size4-Regular";
+    } else if (delim === "\\lceil") {
+        top = "\u23a1";
+        repeat = bottom = "\u23a2";
+        font = "Size4-Regular";
+    } else if (delim === "\\rfloor") {
+        repeat = top = "\u23a5";
+        bottom = "\u23a6";
+        font = "Size4-Regular";
+    } else if (delim === "\\rceil") {
+        top = "\u23a4";
+        repeat = bottom = "\u23a5";
+        font = "Size4-Regular";
+    } else if (delim === "(") {
+        top = "\u239b";
+        repeat = "\u239c";
+        bottom = "\u239d";
+        font = "Size4-Regular";
+    } else if (delim === ")") {
+        top = "\u239e";
+        repeat = "\u239f";
+        bottom = "\u23a0";
+        font = "Size4-Regular";
+    } else if (delim === "\\{" || delim === "\\lbrace") {
+        top = "\u23a7";
+        middle = "\u23a8";
+        bottom = "\u23a9";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\}" || delim === "\\rbrace") {
+        top = "\u23ab";
+        middle = "\u23ac";
+        bottom = "\u23ad";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\lgroup") {
+        top = "\u23a7";
+        bottom = "\u23a9";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\rgroup") {
+        top = "\u23ab";
+        bottom = "\u23ad";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\lmoustache") {
+        top = "\u23a7";
+        bottom = "\u23ad";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\rmoustache") {
+        top = "\u23ab";
+        bottom = "\u23a9";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\surd") {
+        top = "\ue001";
+        bottom = "\u23b7";
+        repeat = "\ue000";
+        font = "Size4-Regular";
+    }
+
+    // Get the metrics of the four sections
+    var topMetrics = getMetrics(top, font);
+    var topHeightTotal = topMetrics.height + topMetrics.depth;
+    var repeatMetrics = getMetrics(repeat, font);
+    var repeatHeightTotal = repeatMetrics.height + repeatMetrics.depth;
+    var bottomMetrics = getMetrics(bottom, font);
+    var bottomHeightTotal = bottomMetrics.height + bottomMetrics.depth;
+    var middleHeightTotal = 0;
+    var middleFactor = 1;
+    if (middle !== null) {
+        var middleMetrics = getMetrics(middle, font);
+        middleHeightTotal = middleMetrics.height + middleMetrics.depth;
+        middleFactor = 2; // repeat symmetrically above and below middle
+    }
+
+    // Calcuate the minimal height that the delimiter can have.
+    // It is at least the size of the top, bottom, and optional middle combined.
+    var minHeight = topHeightTotal + bottomHeightTotal + middleHeightTotal;
+
+    // Compute the number of copies of the repeat symbol we will need
+    var repeatCount = Math.ceil(
+        (heightTotal - minHeight) / (middleFactor * repeatHeightTotal));
+
+    // Compute the total height of the delimiter including all the symbols
+    var realHeightTotal =
+        minHeight + repeatCount * middleFactor * repeatHeightTotal;
+
+    // The center of the delimiter is placed at the center of the axis. Note
+    // that in this context, "center" means that the delimiter should be
+    // centered around the axis in the current style, while normally it is
+    // centered around the axis in textstyle.
+    var axisHeight = options.style.metrics.axisHeight;
+    if (center) {
+        axisHeight *= options.style.sizeMultiplier;
+    }
+    // Calculate the depth
+    var depth = realHeightTotal / 2 - axisHeight;
+
+    // Now, we start building the pieces that will go into the vlist
+
+    // Keep a list of the inner pieces
+    var inners = [];
+
+    // Add the bottom symbol
+    inners.push(makeInner(bottom, font, mode));
+
+    var i;
+    if (middle === null) {
+        // Add that many symbols
+        for (i = 0; i < repeatCount; i++) {
+            inners.push(makeInner(repeat, font, mode));
+        }
+    } else {
+        // When there is a middle bit, we need the middle part and two repeated
+        // sections
+        for (i = 0; i < repeatCount; i++) {
+            inners.push(makeInner(repeat, font, mode));
+        }
+        inners.push(makeInner(middle, font, mode));
+        for (i = 0; i < repeatCount; i++) {
+            inners.push(makeInner(repeat, font, mode));
+        }
+    }
+
+    // Add the top symbol
+    inners.push(makeInner(top, font, mode));
+
+    // Finally, build the vlist
+    var inner = buildCommon.makeVList(inners, "bottom", depth, options);
+
+    return styleWrap(
+        makeSpan(["delimsizing", "mult"], [inner], options),
+        Style.TEXT, options, classes);
+};
+
+// There are three kinds of delimiters, delimiters that stack when they become
+// too large
+var stackLargeDelimiters = [
+    "(", ")", "[", "\\lbrack", "]", "\\rbrack",
+    "\\{", "\\lbrace", "\\}", "\\rbrace",
+    "\\lfloor", "\\rfloor", "\\lceil", "\\rceil",
+    "\\surd"
+];
+
+// delimiters that always stack
+var stackAlwaysDelimiters = [
+    "\\uparrow", "\\downarrow", "\\updownarrow",
+    "\\Uparrow", "\\Downarrow", "\\Updownarrow",
+    "|", "\\|", "\\vert", "\\Vert",
+    "\\lvert", "\\rvert", "\\lVert", "\\rVert",
+    "\\lgroup", "\\rgroup", "\\lmoustache", "\\rmoustache"
+];
+
+// and delimiters that never stack
+var stackNeverDelimiters = [
+    "<", ">", "\\langle", "\\rangle", "/", "\\backslash", "\\lt", "\\gt"
+];
+
+// Metrics of the different sizes. Found by looking at TeX's output of
+// $\bigl| // \Bigl| \biggl| \Biggl| \showlists$
+// Used to create stacked delimiters of appropriate sizes in makeSizedDelim.
+var sizeToMaxHeight = [0, 1.2, 1.8, 2.4, 3.0];
+
+/**
+ * Used to create a delimiter of a specific size, where `size` is 1, 2, 3, or 4.
+ */
+var makeSizedDelim = function(delim, size, options, mode, classes) {
+    // < and > turn into \langle and \rangle in delimiters
+    if (delim === "<" || delim === "\\lt") {
+        delim = "\\langle";
+    } else if (delim === ">" || delim === "\\gt") {
+        delim = "\\rangle";
+    }
+
+    // Sized delimiters are never centered.
+    if (utils.contains(stackLargeDelimiters, delim) ||
+        utils.contains(stackNeverDelimiters, delim)) {
+        return makeLargeDelim(delim, size, false, options, mode, classes);
+    } else if (utils.contains(stackAlwaysDelimiters, delim)) {
+        return makeStackedDelim(
+            delim, sizeToMaxHeight[size], false, options, mode, classes);
+    } else {
+        throw new ParseError("Illegal delimiter: '" + delim + "'");
+    }
+};
+
+/**
+ * There are three different sequences of delimiter sizes that the delimiters
+ * follow depending on the kind of delimiter. This is used when creating custom
+ * sized delimiters to decide whether to create a small, large, or stacked
+ * delimiter.
+ *
+ * In real TeX, these sequences aren't explicitly defined, but are instead
+ * defined inside the font metrics. Since there are only three sequences that
+ * are possible for the delimiters that TeX defines, it is easier to just encode
+ * them explicitly here.
+ */
+
+// Delimiters that never stack try small delimiters and large delimiters only
+var stackNeverDelimiterSequence = [
+    {type: "small", style: Style.SCRIPTSCRIPT},
+    {type: "small", style: Style.SCRIPT},
+    {type: "small", style: Style.TEXT},
+    {type: "large", size: 1},
+    {type: "large", size: 2},
+    {type: "large", size: 3},
+    {type: "large", size: 4}
+];
+
+// Delimiters that always stack try the small delimiters first, then stack
+var stackAlwaysDelimiterSequence = [
+    {type: "small", style: Style.SCRIPTSCRIPT},
+    {type: "small", style: Style.SCRIPT},
+    {type: "small", style: Style.TEXT},
+    {type: "stack"}
+];
+
+// Delimiters that stack when large try the small and then large delimiters, and
+// stack afterwards
+var stackLargeDelimiterSequence = [
+    {type: "small", style: Style.SCRIPTSCRIPT},
+    {type: "small", style: Style.SCRIPT},
+    {type: "small", style: Style.TEXT},
+    {type: "large", size: 1},
+    {type: "large", size: 2},
+    {type: "large", size: 3},
+    {type: "large", size: 4},
+    {type: "stack"}
+];
+
+/**
+ * Get the font used in a delimiter based on what kind of delimiter it is.
+ */
+var delimTypeToFont = function(type) {
+    if (type.type === "small") {
+        return "Main-Regular";
+    } else if (type.type === "large") {
+        return "Size" + type.size + "-Regular";
+    } else if (type.type === "stack") {
+        return "Size4-Regular";
+    }
+};
+
+/**
+ * Traverse a sequence of types of delimiters to decide what kind of delimiter
+ * should be used to create a delimiter of the given height+depth.
+ */
+var traverseSequence = function(delim, height, sequence, options) {
+    // Here, we choose the index we should start at in the sequences. In smaller
+    // sizes (which correspond to larger numbers in style.size) we start earlier
+    // in the sequence. Thus, scriptscript starts at index 3-3=0, script starts
+    // at index 3-2=1, text starts at 3-1=2, and display starts at min(2,3-0)=2
+    var start = Math.min(2, 3 - options.style.size);
+    for (var i = start; i < sequence.length; i++) {
+        if (sequence[i].type === "stack") {
+            // This is always the last delimiter, so we just break the loop now.
+            break;
+        }
+
+        var metrics = getMetrics(delim, delimTypeToFont(sequence[i]));
+        var heightDepth = metrics.height + metrics.depth;
+
+        // Small delimiters are scaled down versions of the same font, so we
+        // account for the style change size.
+
+        if (sequence[i].type === "small") {
+            heightDepth *= sequence[i].style.sizeMultiplier;
+        }
+
+        // Check if the delimiter at this size works for the given height.
+        if (heightDepth > height) {
+            return sequence[i];
+        }
+    }
+
+    // If we reached the end of the sequence, return the last sequence element.
+    return sequence[sequence.length - 1];
+};
+
+/**
+ * Make a delimiter of a given height+depth, with optional centering. Here, we
+ * traverse the sequences, and create a delimiter that the sequence tells us to.
+ */
+var makeCustomSizedDelim = function(delim, height, center, options, mode,
+                                    classes) {
+    if (delim === "<" || delim === "\\lt") {
+        delim = "\\langle";
+    } else if (delim === ">" || delim === "\\gt") {
+        delim = "\\rangle";
+    }
+
+    // Decide what sequence to use
+    var sequence;
+    if (utils.contains(stackNeverDelimiters, delim)) {
+        sequence = stackNeverDelimiterSequence;
+    } else if (utils.contains(stackLargeDelimiters, delim)) {
+        sequence = stackLargeDelimiterSequence;
+    } else {
+        sequence = stackAlwaysDelimiterSequence;
+    }
+
+    // Look through the sequence
+    var delimType = traverseSequence(delim, height, sequence, options);
+
+    // Depending on the sequence element we decided on, call the appropriate
+    // function.
+    if (delimType.type === "small") {
+        return makeSmallDelim(delim, delimType.style, center, options, mode,
+                              classes);
+    } else if (delimType.type === "large") {
+        return makeLargeDelim(delim, delimType.size, center, options, mode,
+                              classes);
+    } else if (delimType.type === "stack") {
+        return makeStackedDelim(delim, height, center, options, mode, classes);
+    }
+};
+
+/**
+ * Make a delimiter for use with `\left` and `\right`, given a height and depth
+ * of an expression that the delimiters surround.
+ */
+var makeLeftRightDelim = function(delim, height, depth, options, mode,
+                                  classes) {
+    // We always center \left/\right delimiters, so the axis is always shifted
+    var axisHeight =
+        options.style.metrics.axisHeight * options.style.sizeMultiplier;
+
+    // Taken from TeX source, tex.web, function make_left_right
+    var delimiterFactor = 901;
+    var delimiterExtend = 5.0 / fontMetrics.metrics.ptPerEm;
+
+    var maxDistFromAxis = Math.max(
+        height - axisHeight, depth + axisHeight);
+
+    var totalHeight = Math.max(
+        // In real TeX, calculations are done using integral values which are
+        // 65536 per pt, or 655360 per em. So, the division here truncates in
+        // TeX but doesn't here, producing different results. If we wanted to
+        // exactly match TeX's calculation, we could do
+        //   Math.floor(655360 * maxDistFromAxis / 500) *
+        //    delimiterFactor / 655360
+        // (To see the difference, compare
+        //    x^{x^{\left(\rule{0.1em}{0.68em}\right)}}
+        // in TeX and KaTeX)
+        maxDistFromAxis / 500 * delimiterFactor,
+        2 * maxDistFromAxis - delimiterExtend);
+
+    // Finally, we defer to `makeCustomSizedDelim` with our calculated total
+    // height
+    return makeCustomSizedDelim(delim, totalHeight, true, options, mode,
+                                classes);
+};
+
+module.exports = {
+    sizedDelim: makeSizedDelim,
+    customSizedDelim: makeCustomSizedDelim,
+    leftRightDelim: makeLeftRightDelim
+};
+
+},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./fontMetrics":17,"./symbols":23,"./utils":25}],15:[function(require,module,exports){
+/**
+ * These objects store the data about the DOM nodes we create, as well as some
+ * extra data. They can then be transformed into real DOM nodes with the
+ * `toNode` function or HTML markup using `toMarkup`. They are useful for both
+ * storing extra properties on the nodes, as well as providing a way to easily
+ * work with the DOM.
+ *
+ * Similar functions for working with MathML nodes exist in mathMLTree.js.
+ */
+var unicodeRegexes = require("./unicodeRegexes");
+var utils = require("./utils");
+
+/**
+ * Create an HTML className based on a list of classes. In addition to joining
+ * with spaces, we also remove null or empty classes.
+ */
+var createClass = function(classes) {
+    classes = classes.slice();
+    for (var i = classes.length - 1; i >= 0; i--) {
+        if (!classes[i]) {
+            classes.splice(i, 1);
+        }
+    }
+
+    return classes.join(" ");
+};
+
+/**
+ * This node represents a span node, with a className, a list of children, and
+ * an inline style. It also contains information about its height, depth, and
+ * maxFontSize.
+ */
+function span(classes, children, options) {
+    this.classes = classes || [];
+    this.children = children || [];
+    this.height = 0;
+    this.depth = 0;
+    this.maxFontSize = 0;
+    this.style = {};
+    this.attributes = {};
+    if (options) {
+        if (options.style.isTight()) {
+            this.classes.push("mtight");
+        }
+        if (options.getColor()) {
+            this.style.color = options.getColor();
+        }
+    }
+}
+
+/**
+ * Sets an arbitrary attribute on the span. Warning: use this wisely. Not all
+ * browsers support attributes the same, and having too many custom attributes
+ * is probably bad.
+ */
+span.prototype.setAttribute = function(attribute, value) {
+    this.attributes[attribute] = value;
+};
+
+span.prototype.tryCombine = function(sibling) {
+    return false;
+};
+
+/**
+ * Convert the span into an HTML node
+ */
+span.prototype.toNode = function() {
+    var span = document.createElement("span");
+
+    // Apply the class
+    span.className = createClass(this.classes);
+
+    // Apply inline styles
+    for (var style in this.style) {
+        if (Object.prototype.hasOwnProperty.call(this.style, style)) {
+            span.style[style] = this.style[style];
+        }
+    }
+
+    // Apply attributes
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            span.setAttribute(attr, this.attributes[attr]);
+        }
+    }
+
+    // Append the children, also as HTML nodes
+    for (var i = 0; i < this.children.length; i++) {
+        span.appendChild(this.children[i].toNode());
+    }
+
+    return span;
+};
+
+/**
+ * Convert the span into an HTML markup string
+ */
+span.prototype.toMarkup = function() {
+    var markup = "<span";
+
+    // Add the class
+    if (this.classes.length) {
+        markup += " class=\"";
+        markup += utils.escape(createClass(this.classes));
+        markup += "\"";
+    }
+
+    var styles = "";
+
+    // Add the styles, after hyphenation
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)) {
+            styles += utils.hyphenate(style) + ":" + this.style[style] + ";";
+        }
+    }
+
+    if (styles) {
+        markup += " style=\"" + utils.escape(styles) + "\"";
+    }
+
+    // Add the attributes
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            markup += " " + attr + "=\"";
+            markup += utils.escape(this.attributes[attr]);
+            markup += "\"";
+        }
+    }
+
+    markup += ">";
+
+    // Add the markup of the children, also as markup
+    for (var i = 0; i < this.children.length; i++) {
+        markup += this.children[i].toMarkup();
+    }
+
+    markup += "</span>";
+
+    return markup;
+};
+
+/**
+ * This node represents a document fragment, which contains elements, but when
+ * placed into the DOM doesn't have any representation itself. Thus, it only
+ * contains children and doesn't have any HTML properties. It also keeps track
+ * of a height, depth, and maxFontSize.
+ */
+function documentFragment(children) {
+    this.children = children || [];
+    this.height = 0;
+    this.depth = 0;
+    this.maxFontSize = 0;
+}
+
+/**
+ * Convert the fragment into a node
+ */
+documentFragment.prototype.toNode = function() {
+    // Create a fragment
+    var frag = document.createDocumentFragment();
+
+    // Append the children
+    for (var i = 0; i < this.children.length; i++) {
+        frag.appendChild(this.children[i].toNode());
+    }
+
+    return frag;
+};
+
+/**
+ * Convert the fragment into HTML markup
+ */
+documentFragment.prototype.toMarkup = function() {
+    var markup = "";
+
+    // Simply concatenate the markup for the children together
+    for (var i = 0; i < this.children.length; i++) {
+        markup += this.children[i].toMarkup();
+    }
+
+    return markup;
+};
+
+var iCombinations = {
+    'î': '\u0131\u0302',
+    'ï': '\u0131\u0308',
+    'í': '\u0131\u0301',
+    // 'ī': '\u0131\u0304', // enable when we add Extended Latin
+    'ì': '\u0131\u0300'
+};
+
+/**
+ * A symbol node contains information about a single symbol. It either renders
+ * to a single text node, or a span with a single text node in it, depending on
+ * whether it has CSS classes, styles, or needs italic correction.
+ */
+function symbolNode(value, height, depth, italic, skew, classes, style) {
+    this.value = value || "";
+    this.height = height || 0;
+    this.depth = depth || 0;
+    this.italic = italic || 0;
+    this.skew = skew || 0;
+    this.classes = classes || [];
+    this.style = style || {};
+    this.maxFontSize = 0;
+
+    // Mark CJK characters with specific classes so that we can specify which
+    // fonts to use.  This allows us to render these characters with a serif
+    // font in situations where the browser would either default to a sans serif
+    // or render a placeholder character.
+    if (unicodeRegexes.cjkRegex.test(value)) {
+        // I couldn't find any fonts that contained Hangul as well as all of
+        // the other characters we wanted to test there for it gets its own
+        // CSS class.
+        if (unicodeRegexes.hangulRegex.test(value)) {
+            this.classes.push('hangul_fallback');
+        } else {
+            this.classes.push('cjk_fallback');
+        }
+    }
+
+    if (/[îïíì]/.test(this.value)) {    // add ī when we add Extended Latin
+        this.value = iCombinations[this.value];
+    }
+}
+
+symbolNode.prototype.tryCombine = function(sibling) {
+    if (!sibling
+        || !(sibling instanceof symbolNode)
+        || this.italic > 0
+        || createClass(this.classes) !== createClass(sibling.classes)
+        || this.skew !== sibling.skew
+        || this.maxFontSize !== sibling.maxFontSize) {
+        return false;
+    }
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)
+            && this.style[style] !== sibling.style[style]) {
+            return false;
+        }
+    }
+    for (style in sibling.style) {
+        if (sibling.style.hasOwnProperty(style)
+            && this.style[style] !== sibling.style[style]) {
+            return false;
+        }
+    }
+    this.value += sibling.value;
+    this.height = Math.max(this.height, sibling.height);
+    this.depth = Math.max(this.depth, sibling.depth);
+    this.italic = sibling.italic;
+    return true;
+};
+
+/**
+ * Creates a text node or span from a symbol node. Note that a span is only
+ * created if it is needed.
+ */
+symbolNode.prototype.toNode = function() {
+    var node = document.createTextNode(this.value);
+    var span = null;
+
+    if (this.italic > 0) {
+        span = document.createElement("span");
+        span.style.marginRight = this.italic + "em";
+    }
+
+    if (this.classes.length > 0) {
+        span = span || document.createElement("span");
+        span.className = createClass(this.classes);
+    }
+
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)) {
+            span = span || document.createElement("span");
+            span.style[style] = this.style[style];
+        }
+    }
+
+    if (span) {
+        span.appendChild(node);
+        return span;
+    } else {
+        return node;
+    }
+};
+
+/**
+ * Creates markup for a symbol node.
+ */
+symbolNode.prototype.toMarkup = function() {
+    // TODO(alpert): More duplication than I'd like from
+    // span.prototype.toMarkup and symbolNode.prototype.toNode...
+    var needsSpan = false;
+
+    var markup = "<span";
+
+    if (this.classes.length) {
+        needsSpan = true;
+        markup += " class=\"";
+        markup += utils.escape(createClass(this.classes));
+        markup += "\"";
+    }
+
+    var styles = "";
+
+    if (this.italic > 0) {
+        styles += "margin-right:" + this.italic + "em;";
+    }
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)) {
+            styles += utils.hyphenate(style) + ":" + this.style[style] + ";";
+        }
+    }
+
+    if (styles) {
+        needsSpan = true;
+        markup += " style=\"" + utils.escape(styles) + "\"";
+    }
+
+    var escaped = utils.escape(this.value);
+    if (needsSpan) {
+        markup += ">";
+        markup += escaped;
+        markup += "</span>";
+        return markup;
+    } else {
+        return escaped;
+    }
+};
+
+module.exports = {
+    span: span,
+    documentFragment: documentFragment,
+    symbolNode: symbolNode
+};
+
+},{"./unicodeRegexes":24,"./utils":25}],16:[function(require,module,exports){
+/* eslint no-constant-condition:0 */
+var parseData = require("./parseData");
+var ParseError = require("./ParseError");
+var Style = require("./Style");
+
+var ParseNode = parseData.ParseNode;
+
+/**
+ * Parse the body of the environment, with rows delimited by \\ and
+ * columns delimited by &, and create a nested list in row-major order
+ * with one group per cell.
+ */
+function parseArray(parser, result) {
+    var row = [];
+    var body = [row];
+    var rowGaps = [];
+    while (true) {
+        var cell = parser.parseExpression(false, null);
+        row.push(new ParseNode("ordgroup", cell, parser.mode));
+        var next = parser.nextToken.text;
+        if (next === "&") {
+            parser.consume();
+        } else if (next === "\\end") {
+            break;
+        } else if (next === "\\\\" || next === "\\cr") {
+            var cr = parser.parseFunction();
+            rowGaps.push(cr.value.size);
+            row = [];
+            body.push(row);
+        } else {
+            throw new ParseError("Expected & or \\\\ or \\end",
+                                 parser.nextToken);
+        }
+    }
+    result.body = body;
+    result.rowGaps = rowGaps;
+    return new ParseNode(result.type, result, parser.mode);
+}
+
+/*
+ * An environment definition is very similar to a function definition:
+ * it is declared with a name or a list of names, a set of properties
+ * and a handler containing the actual implementation.
+ *
+ * The properties include:
+ *  - numArgs: The number of arguments after the \begin{name} function.
+ *  - argTypes: (optional) Just like for a function
+ *  - allowedInText: (optional) Whether or not the environment is allowed inside
+ *                   text mode (default false) (not enforced yet)
+ *  - numOptionalArgs: (optional) Just like for a function
+ * A bare number instead of that object indicates the numArgs value.
+ *
+ * The handler function will receive two arguments
+ *  - context: information and references provided by the parser
+ *  - args: an array of arguments passed to \begin{name}
+ * The context contains the following properties:
+ *  - envName: the name of the environment, one of the listed names.
+ *  - parser: the parser object
+ *  - lexer: the lexer object
+ *  - positions: the positions associated with these arguments from args.
+ * The handler must return a ParseResult.
+ */
+
+function defineEnvironment(names, props, handler) {
+    if (typeof names === "string") {
+        names = [names];
+    }
+    if (typeof props === "number") {
+        props = { numArgs: props };
+    }
+    // Set default values of environments
+    var data = {
+        numArgs: props.numArgs || 0,
+        argTypes: props.argTypes,
+        greediness: 1,
+        allowedInText: !!props.allowedInText,
+        numOptionalArgs: props.numOptionalArgs || 0,
+        handler: handler
+    };
+    for (var i = 0; i < names.length; ++i) {
+        module.exports[names[i]] = data;
+    }
+}
+
+// Arrays are part of LaTeX, defined in lttab.dtx so its documentation
+// is part of the source2e.pdf file of LaTeX2e source documentation.
+defineEnvironment("array", {
+    numArgs: 1
+}, function(context, args) {
+    var colalign = args[0];
+    colalign = colalign.value.map ? colalign.value : [colalign];
+    var cols = colalign.map(function(node) {
+        var ca = node.value;
+        if ("lcr".indexOf(ca) !== -1) {
+            return {
+                type: "align",
+                align: ca
+            };
+        } else if (ca === "|") {
+            return {
+                type: "separator",
+                separator: "|"
+            };
+        }
+        throw new ParseError(
+            "Unknown column alignment: " + node.value,
+            node);
+    });
+    var res = {
+        type: "array",
+        cols: cols,
+        hskipBeforeAndAfter: true // \@preamble in lttab.dtx
+    };
+    res = parseArray(context.parser, res);
+    return res;
+});
+
+// The matrix environments of amsmath builds on the array environment
+// of LaTeX, which is discussed above.
+defineEnvironment([
+    "matrix",
+    "pmatrix",
+    "bmatrix",
+    "Bmatrix",
+    "vmatrix",
+    "Vmatrix"
+], {
+}, function(context) {
+    var delimiters = {
+        "matrix": null,
+        "pmatrix": ["(", ")"],
+        "bmatrix": ["[", "]"],
+        "Bmatrix": ["\\{", "\\}"],
+        "vmatrix": ["|", "|"],
+        "Vmatrix": ["\\Vert", "\\Vert"]
+    }[context.envName];
+    var res = {
+        type: "array",
+        hskipBeforeAndAfter: false // \hskip -\arraycolsep in amsmath
+    };
+    res = parseArray(context.parser, res);
+    if (delimiters) {
+        res = new ParseNode("leftright", {
+            body: [res],
+            left: delimiters[0],
+            right: delimiters[1]
+        }, context.mode);
+    }
+    return res;
+});
+
+// A cases environment (in amsmath.sty) is almost equivalent to
+// \def\arraystretch{1.2}%
+// \left\{\begin{array}{@{}l@{\quad}l@{}} … \end{array}\right.
+defineEnvironment("cases", {
+}, function(context) {
+    var res = {
+        type: "array",
+        arraystretch: 1.2,
+        cols: [{
+            type: "align",
+            align: "l",
+            pregap: 0,
+            // TODO(kevinb) get the current style.
+            // For now we use the metrics for TEXT style which is what we were
+            // doing before.  Before attempting to get the current style we
+            // should look at TeX's behavior especially for \over and matrices.
+            postgap: Style.TEXT.metrics.quad
+        }, {
+            type: "align",
+            align: "l",
+            pregap: 0,
+            postgap: 0
+        }]
+    };
+    res = parseArray(context.parser, res);
+    res = new ParseNode("leftright", {
+        body: [res],
+        left: "\\{",
+        right: "."
+    }, context.mode);
+    return res;
+});
+
+// An aligned environment is like the align* environment
+// except it operates within math mode.
+// Note that we assume \nomallineskiplimit to be zero,
+// so that \strut@ is the same as \strut.
+defineEnvironment("aligned", {
+}, function(context) {
+    var res = {
+        type: "array",
+        cols: []
+    };
+    res = parseArray(context.parser, res);
+    var emptyGroup = new ParseNode("ordgroup", [], context.mode);
+    var numCols = 0;
+    res.value.body.forEach(function(row) {
+        var i;
+        for (i = 1; i < row.length; i += 2) {
+            row[i].value.unshift(emptyGroup);
+        }
+        if (numCols < row.length) {
+            numCols = row.length;
+        }
+    });
+    for (var i = 0; i < numCols; ++i) {
+        var align = "r";
+        var pregap = 0;
+        if (i % 2 === 1) {
+            align = "l";
+        } else if (i > 0) {
+            pregap = 2; // one \qquad between columns
+        }
+        res.value.cols[i] = {
+            type: "align",
+            align: align,
+            pregap: pregap,
+            postgap: 0
+        };
+    }
+    return res;
+});
+
+},{"./ParseError":6,"./Style":9,"./parseData":21}],17:[function(require,module,exports){
+/* eslint no-unused-vars:0 */
+
+var Style = require("./Style");
+var cjkRegex = require("./unicodeRegexes").cjkRegex;
+
+/**
+ * This file contains metrics regarding fonts and individual symbols. The sigma
+ * and xi variables, as well as the metricMap map contain data extracted from
+ * TeX, TeX font metrics, and the TTF files. These data are then exposed via the
+ * `metrics` variable and the getCharacterMetrics function.
+ */
+
+// In TeX, there are actually three sets of dimensions, one for each of
+// textstyle, scriptstyle, and scriptscriptstyle.  These are provided in the
+// the arrays below, in that order.
+//
+// The font metrics are stored in fonts cmsy10, cmsy7, and cmsy5 respsectively.
+// This was determined by running the folllowing script:
+//
+//     latex -interaction=nonstopmode \
+//     '\documentclass{article}\usepackage{amsmath}\begin{document}' \
+//     '$a$ \expandafter\show\the\textfont2' \
+//     '\expandafter\show\the\scriptfont2' \
+//     '\expandafter\show\the\scriptscriptfont2' \
+//     '\stop'
+//
+// The metrics themselves were retreived using the following commands:
+//
+//     tftopl cmsy10
+//     tftopl cmsy7
+//     tftopl cmsy5
+//
+// The output of each of these commands is quite lengthy.  The only part we
+// care about is the FONTDIMEN section. Each value is measured in EMs.
+var sigmas = {
+    slant: [0.250, 0.250, 0.250],       // sigma1
+    space: [0.000, 0.000, 0.000],       // sigma2
+    stretch: [0.000, 0.000, 0.000],     // sigma3
+    shrink: [0.000, 0.000, 0.000],      // sigma4
+    xHeight: [0.431, 0.431, 0.431],     // sigma5
+    quad: [1.000, 1.171, 1.472],        // sigma6
+    extraSpace: [0.000, 0.000, 0.000],  // sigma7
+    num1: [0.677, 0.732, 0.925],        // sigma8
+    num2: [0.394, 0.384, 0.387],        // sigma9
+    num3: [0.444, 0.471, 0.504],        // sigma10
+    denom1: [0.686, 0.752, 1.025],      // sigma11
+    denom2: [0.345, 0.344, 0.532],      // sigma12
+    sup1: [0.413, 0.503, 0.504],        // sigma13
+    sup2: [0.363, 0.431, 0.404],        // sigma14
+    sup3: [0.289, 0.286, 0.294],        // sigma15
+    sub1: [0.150, 0.143, 0.200],        // sigma16
+    sub2: [0.247, 0.286, 0.400],        // sigma17
+    supDrop: [0.386, 0.353, 0.494],     // sigma18
+    subDrop: [0.050, 0.071, 0.100],     // sigma19
+    delim1: [2.390, 1.700, 1.980],      // sigma20
+    delim2: [1.010, 1.157, 1.420],      // sigma21
+    axisHeight: [0.250, 0.250, 0.250]  // sigma22
+};
+
+// These font metrics are extracted from TeX by using
+// \font\a=cmex10
+// \showthe\fontdimenX\a
+// where X is the corresponding variable number. These correspond to the font
+// parameters of the extension fonts (family 3). See the TeXbook, page 441.
+var xi1 = 0;
+var xi2 = 0;
+var xi3 = 0;
+var xi4 = 0;
+var xi5 = 0.431;
+var xi6 = 1;
+var xi7 = 0;
+var xi8 = 0.04;
+var xi9 = 0.111;
+var xi10 = 0.166;
+var xi11 = 0.2;
+var xi12 = 0.6;
+var xi13 = 0.1;
+
+// This value determines how large a pt is, for metrics which are defined in
+// terms of pts.
+// This value is also used in katex.less; if you change it make sure the values
+// match.
+var ptPerEm = 10.0;
+
+// The space between adjacent `|` columns in an array definition. From
+// `\showthe\doublerulesep` in LaTeX.
+var doubleRuleSep = 2.0 / ptPerEm;
+
+/**
+ * This is just a mapping from common names to real metrics
+ */
+var metrics = {
+    defaultRuleThickness: xi8,
+    bigOpSpacing1: xi9,
+    bigOpSpacing2: xi10,
+    bigOpSpacing3: xi11,
+    bigOpSpacing4: xi12,
+    bigOpSpacing5: xi13,
+    ptPerEm: ptPerEm,
+    doubleRuleSep: doubleRuleSep
+};
+
+// This map contains a mapping from font name and character code to character
+// metrics, including height, depth, italic correction, and skew (kern from the
+// character to the corresponding \skewchar)
+// This map is generated via `make metrics`. It should not be changed manually.
+var metricMap = require("./fontMetricsData");
+
+// These are very rough approximations.  We default to Times New Roman which
+// should have Latin-1 and Cyrillic characters, but may not depending on the
+// operating system.  The metrics do not account for extra height from the
+// accents.  In the case of Cyrillic characters which have both ascenders and
+// descenders we prefer approximations with ascenders, primarily to prevent
+// the fraction bar or root line from intersecting the glyph.
+// TODO(kevinb) allow union of multiple glyph metrics for better accuracy.
+var extraCharacterMap = {
+    // Latin-1
+    'À': 'A',
+    'Á': 'A',
+    'Â': 'A',
+    'Ã': 'A',
+    'Ä': 'A',
+    'Å': 'A',
+    'Æ': 'A',
+    'Ç': 'C',
+    'È': 'E',
+    'É': 'E',
+    'Ê': 'E',
+    'Ë': 'E',
+    'Ì': 'I',
+    'Í': 'I',
+    'Î': 'I',
+    'Ï': 'I',
+    'Ð': 'D',
+    'Ñ': 'N',
+    'Ò': 'O',
+    'Ó': 'O',
+    'Ô': 'O',
+    'Õ': 'O',
+    'Ö': 'O',
+    'Ø': 'O',
+    'Ù': 'U',
+    'Ú': 'U',
+    'Û': 'U',
+    'Ü': 'U',
+    'Ý': 'Y',
+    'Þ': 'o',
+    'ß': 'B',
+    'à': 'a',
+    'á': 'a',
+    'â': 'a',
+    'ã': 'a',
+    'ä': 'a',
+    'å': 'a',
+    'æ': 'a',
+    'ç': 'c',
+    'è': 'e',
+    'é': 'e',
+    'ê': 'e',
+    'ë': 'e',
+    'ì': 'i',
+    'í': 'i',
+    'î': 'i',
+    'ï': 'i',
+    'ð': 'd',
+    'ñ': 'n',
+    'ò': 'o',
+    'ó': 'o',
+    'ô': 'o',
+    'õ': 'o',
+    'ö': 'o',
+    'ø': 'o',
+    'ù': 'u',
+    'ú': 'u',
+    'û': 'u',
+    'ü': 'u',
+    'ý': 'y',
+    'þ': 'o',
+    'ÿ': 'y',
+
+    // Cyrillic
+    'А': 'A',
+    'Б': 'B',
+    'В': 'B',
+    'Г': 'F',
+    'Д': 'A',
+    'Е': 'E',
+    'Ж': 'K',
+    'З': '3',
+    'И': 'N',
+    'Й': 'N',
+    'К': 'K',
+    'Л': 'N',
+    'М': 'M',
+    'Н': 'H',
+    'О': 'O',
+    'П': 'N',
+    'Р': 'P',
+    'С': 'C',
+    'Т': 'T',
+    'У': 'y',
+    'Ф': 'O',
+    'Х': 'X',
+    'Ц': 'U',
+    'Ч': 'h',
+    'Ш': 'W',
+    'Щ': 'W',
+    'Ъ': 'B',
+    'Ы': 'X',
+    'Ь': 'B',
+    'Э': '3',
+    'Ю': 'X',
+    'Я': 'R',
+    'а': 'a',
+    'б': 'b',
+    'в': 'a',
+    'г': 'r',
+    'д': 'y',
+    'е': 'e',
+    'ж': 'm',
+    'з': 'e',
+    'и': 'n',
+    'й': 'n',
+    'к': 'n',
+    'л': 'n',
+    'м': 'm',
+    'н': 'n',
+    'о': 'o',
+    'п': 'n',
+    'р': 'p',
+    'с': 'c',
+    'т': 'o',
+    'у': 'y',
+    'ф': 'b',
+    'х': 'x',
+    'ц': 'n',
+    'ч': 'n',
+    'ш': 'w',
+    'щ': 'w',
+    'ъ': 'a',
+    'ы': 'm',
+    'ь': 'a',
+    'э': 'e',
+    'ю': 'm',
+    'я': 'r'
+};
+
+/**
+ * This function is a convenience function for looking up information in the
+ * metricMap table. It takes a character as a string, and a style.
+ *
+ * Note: the `width` property may be undefined if fontMetricsData.js wasn't
+ * built using `Make extended_metrics`.
+ */
+var getCharacterMetrics = function(character, style) {
+    var ch = character.charCodeAt(0);
+    if (character[0] in extraCharacterMap) {
+        ch = extraCharacterMap[character[0]].charCodeAt(0);
+    } else if (cjkRegex.test(character[0])) {
+        ch = 'M'.charCodeAt(0);
+    }
+    var metrics = metricMap[style][ch];
+    if (metrics) {
+        return {
+            depth: metrics[0],
+            height: metrics[1],
+            italic: metrics[2],
+            skew: metrics[3],
+            width: metrics[4]
+        };
+    }
+};
+
+module.exports = {
+    metrics: metrics,
+    sigmas: sigmas,
+    getCharacterMetrics: getCharacterMetrics
+};
+
+},{"./Style":9,"./fontMetricsData":18,"./unicodeRegexes":24}],18:[function(require,module,exports){
+module.exports = {
+    "AMS-Regular": {
+        "65": [0, 0.68889, 0, 0],
+        "66": [0, 0.68889, 0, 0],
+        "67": [0, 0.68889, 0, 0],
+        "68": [0, 0.68889, 0, 0],
+        "69": [0, 0.68889, 0, 0],
+        "70": [0, 0.68889, 0, 0],
+        "71": [0, 0.68889, 0, 0],
+        "72": [0, 0.68889, 0, 0],
+        "73": [0, 0.68889, 0, 0],
+        "74": [0.16667, 0.68889, 0, 0],
+        "75": [0, 0.68889, 0, 0],
+        "76": [0, 0.68889, 0, 0],
+        "77": [0, 0.68889, 0, 0],
+        "78": [0, 0.68889, 0, 0],
+        "79": [0.16667, 0.68889, 0, 0],
+        "80": [0, 0.68889, 0, 0],
+        "81": [0.16667, 0.68889, 0, 0],
+        "82": [0, 0.68889, 0, 0],
+        "83": [0, 0.68889, 0, 0],
+        "84": [0, 0.68889, 0, 0],
+        "85": [0, 0.68889, 0, 0],
+        "86": [0, 0.68889, 0, 0],
+        "87": [0, 0.68889, 0, 0],
+        "88": [0, 0.68889, 0, 0],
+        "89": [0, 0.68889, 0, 0],
+        "90": [0, 0.68889, 0, 0],
+        "107": [0, 0.68889, 0, 0],
+        "165": [0, 0.675, 0.025, 0],
+        "174": [0.15559, 0.69224, 0, 0],
+        "240": [0, 0.68889, 0, 0],
+        "295": [0, 0.68889, 0, 0],
+        "710": [0, 0.825, 0, 0],
+        "732": [0, 0.9, 0, 0],
+        "770": [0, 0.825, 0, 0],
+        "771": [0, 0.9, 0, 0],
+        "989": [0.08167, 0.58167, 0, 0],
+        "1008": [0, 0.43056, 0.04028, 0],
+        "8245": [0, 0.54986, 0, 0],
+        "8463": [0, 0.68889, 0, 0],
+        "8487": [0, 0.68889, 0, 0],
+        "8498": [0, 0.68889, 0, 0],
+        "8502": [0, 0.68889, 0, 0],
+        "8503": [0, 0.68889, 0, 0],
+        "8504": [0, 0.68889, 0, 0],
+        "8513": [0, 0.68889, 0, 0],
+        "8592": [-0.03598, 0.46402, 0, 0],
+        "8594": [-0.03598, 0.46402, 0, 0],
+        "8602": [-0.13313, 0.36687, 0, 0],
+        "8603": [-0.13313, 0.36687, 0, 0],
+        "8606": [0.01354, 0.52239, 0, 0],
+        "8608": [0.01354, 0.52239, 0, 0],
+        "8610": [0.01354, 0.52239, 0, 0],
+        "8611": [0.01354, 0.52239, 0, 0],
+        "8619": [0, 0.54986, 0, 0],
+        "8620": [0, 0.54986, 0, 0],
+        "8621": [-0.13313, 0.37788, 0, 0],
+        "8622": [-0.13313, 0.36687, 0, 0],
+        "8624": [0, 0.69224, 0, 0],
+        "8625": [0, 0.69224, 0, 0],
+        "8630": [0, 0.43056, 0, 0],
+        "8631": [0, 0.43056, 0, 0],
+        "8634": [0.08198, 0.58198, 0, 0],
+        "8635": [0.08198, 0.58198, 0, 0],
+        "8638": [0.19444, 0.69224, 0, 0],
+        "8639": [0.19444, 0.69224, 0, 0],
+        "8642": [0.19444, 0.69224, 0, 0],
+        "8643": [0.19444, 0.69224, 0, 0],
+        "8644": [0.1808, 0.675, 0, 0],
+        "8646": [0.1808, 0.675, 0, 0],
+        "8647": [0.1808, 0.675, 0, 0],
+        "8648": [0.19444, 0.69224, 0, 0],
+        "8649": [0.1808, 0.675, 0, 0],
+        "8650": [0.19444, 0.69224, 0, 0],
+        "8651": [0.01354, 0.52239, 0, 0],
+        "8652": [0.01354, 0.52239, 0, 0],
+        "8653": [-0.13313, 0.36687, 0, 0],
+        "8654": [-0.13313, 0.36687, 0, 0],
+        "8655": [-0.13313, 0.36687, 0, 0],
+        "8666": [0.13667, 0.63667, 0, 0],
+        "8667": [0.13667, 0.63667, 0, 0],
+        "8669": [-0.13313, 0.37788, 0, 0],
+        "8672": [-0.064, 0.437, 0, 0],
+        "8674": [-0.064, 0.437, 0, 0],
+        "8705": [0, 0.825, 0, 0],
+        "8708": [0, 0.68889, 0, 0],
+        "8709": [0.08167, 0.58167, 0, 0],
+        "8717": [0, 0.43056, 0, 0],
+        "8722": [-0.03598, 0.46402, 0, 0],
+        "8724": [0.08198, 0.69224, 0, 0],
+        "8726": [0.08167, 0.58167, 0, 0],
+        "8733": [0, 0.69224, 0, 0],
+        "8736": [0, 0.69224, 0, 0],
+        "8737": [0, 0.69224, 0, 0],
+        "8738": [0.03517, 0.52239, 0, 0],
+        "8739": [0.08167, 0.58167, 0, 0],
+        "8740": [0.25142, 0.74111, 0, 0],
+        "8741": [0.08167, 0.58167, 0, 0],
+        "8742": [0.25142, 0.74111, 0, 0],
+        "8756": [0, 0.69224, 0, 0],
+        "8757": [0, 0.69224, 0, 0],
+        "8764": [-0.13313, 0.36687, 0, 0],
+        "8765": [-0.13313, 0.37788, 0, 0],
+        "8769": [-0.13313, 0.36687, 0, 0],
+        "8770": [-0.03625, 0.46375, 0, 0],
+        "8774": [0.30274, 0.79383, 0, 0],
+        "8776": [-0.01688, 0.48312, 0, 0],
+        "8778": [0.08167, 0.58167, 0, 0],
+        "8782": [0.06062, 0.54986, 0, 0],
+        "8783": [0.06062, 0.54986, 0, 0],
+        "8785": [0.08198, 0.58198, 0, 0],
+        "8786": [0.08198, 0.58198, 0, 0],
+        "8787": [0.08198, 0.58198, 0, 0],
+        "8790": [0, 0.69224, 0, 0],
+        "8791": [0.22958, 0.72958, 0, 0],
+        "8796": [0.08198, 0.91667, 0, 0],
+        "8806": [0.25583, 0.75583, 0, 0],
+        "8807": [0.25583, 0.75583, 0, 0],
+        "8808": [0.25142, 0.75726, 0, 0],
+        "8809": [0.25142, 0.75726, 0, 0],
+        "8812": [0.25583, 0.75583, 0, 0],
+        "8814": [0.20576, 0.70576, 0, 0],
+        "8815": [0.20576, 0.70576, 0, 0],
+        "8816": [0.30274, 0.79383, 0, 0],
+        "8817": [0.30274, 0.79383, 0, 0],
+        "8818": [0.22958, 0.72958, 0, 0],
+        "8819": [0.22958, 0.72958, 0, 0],
+        "8822": [0.1808, 0.675, 0, 0],
+        "8823": [0.1808, 0.675, 0, 0],
+        "8828": [0.13667, 0.63667, 0, 0],
+        "8829": [0.13667, 0.63667, 0, 0],
+        "8830": [0.22958, 0.72958, 0, 0],
+        "8831": [0.22958, 0.72958, 0, 0],
+        "8832": [0.20576, 0.70576, 0, 0],
+        "8833": [0.20576, 0.70576, 0, 0],
+        "8840": [0.30274, 0.79383, 0, 0],
+        "8841": [0.30274, 0.79383, 0, 0],
+        "8842": [0.13597, 0.63597, 0, 0],
+        "8843": [0.13597, 0.63597, 0, 0],
+        "8847": [0.03517, 0.54986, 0, 0],
+        "8848": [0.03517, 0.54986, 0, 0],
+        "8858": [0.08198, 0.58198, 0, 0],
+        "8859": [0.08198, 0.58198, 0, 0],
+        "8861": [0.08198, 0.58198, 0, 0],
+        "8862": [0, 0.675, 0, 0],
+        "8863": [0, 0.675, 0, 0],
+        "8864": [0, 0.675, 0, 0],
+        "8865": [0, 0.675, 0, 0],
+        "8872": [0, 0.69224, 0, 0],
+        "8873": [0, 0.69224, 0, 0],
+        "8874": [0, 0.69224, 0, 0],
+        "8876": [0, 0.68889, 0, 0],
+        "8877": [0, 0.68889, 0, 0],
+        "8878": [0, 0.68889, 0, 0],
+        "8879": [0, 0.68889, 0, 0],
+        "8882": [0.03517, 0.54986, 0, 0],
+        "8883": [0.03517, 0.54986, 0, 0],
+        "8884": [0.13667, 0.63667, 0, 0],
+        "8885": [0.13667, 0.63667, 0, 0],
+        "8888": [0, 0.54986, 0, 0],
+        "8890": [0.19444, 0.43056, 0, 0],
+        "8891": [0.19444, 0.69224, 0, 0],
+        "8892": [0.19444, 0.69224, 0, 0],
+        "8901": [0, 0.54986, 0, 0],
+        "8903": [0.08167, 0.58167, 0, 0],
+        "8905": [0.08167, 0.58167, 0, 0],
+        "8906": [0.08167, 0.58167, 0, 0],
+        "8907": [0, 0.69224, 0, 0],
+        "8908": [0, 0.69224, 0, 0],
+        "8909": [-0.03598, 0.46402, 0, 0],
+        "8910": [0, 0.54986, 0, 0],
+        "8911": [0, 0.54986, 0, 0],
+        "8912": [0.03517, 0.54986, 0, 0],
+        "8913": [0.03517, 0.54986, 0, 0],
+        "8914": [0, 0.54986, 0, 0],
+        "8915": [0, 0.54986, 0, 0],
+        "8916": [0, 0.69224, 0, 0],
+        "8918": [0.0391, 0.5391, 0, 0],
+        "8919": [0.0391, 0.5391, 0, 0],
+        "8920": [0.03517, 0.54986, 0, 0],
+        "8921": [0.03517, 0.54986, 0, 0],
+        "8922": [0.38569, 0.88569, 0, 0],
+        "8923": [0.38569, 0.88569, 0, 0],
+        "8926": [0.13667, 0.63667, 0, 0],
+        "8927": [0.13667, 0.63667, 0, 0],
+        "8928": [0.30274, 0.79383, 0, 0],
+        "8929": [0.30274, 0.79383, 0, 0],
+        "8934": [0.23222, 0.74111, 0, 0],
+        "8935": [0.23222, 0.74111, 0, 0],
+        "8936": [0.23222, 0.74111, 0, 0],
+        "8937": [0.23222, 0.74111, 0, 0],
+        "8938": [0.20576, 0.70576, 0, 0],
+        "8939": [0.20576, 0.70576, 0, 0],
+        "8940": [0.30274, 0.79383, 0, 0],
+        "8941": [0.30274, 0.79383, 0, 0],
+        "8994": [0.19444, 0.69224, 0, 0],
+        "8995": [0.19444, 0.69224, 0, 0],
+        "9416": [0.15559, 0.69224, 0, 0],
+        "9484": [0, 0.69224, 0, 0],
+        "9488": [0, 0.69224, 0, 0],
+        "9492": [0, 0.37788, 0, 0],
+        "9496": [0, 0.37788, 0, 0],
+        "9585": [0.19444, 0.68889, 0, 0],
+        "9586": [0.19444, 0.74111, 0, 0],
+        "9632": [0, 0.675, 0, 0],
+        "9633": [0, 0.675, 0, 0],
+        "9650": [0, 0.54986, 0, 0],
+        "9651": [0, 0.54986, 0, 0],
+        "9654": [0.03517, 0.54986, 0, 0],
+        "9660": [0, 0.54986, 0, 0],
+        "9661": [0, 0.54986, 0, 0],
+        "9664": [0.03517, 0.54986, 0, 0],
+        "9674": [0.11111, 0.69224, 0, 0],
+        "9733": [0.19444, 0.69224, 0, 0],
+        "10003": [0, 0.69224, 0, 0],
+        "10016": [0, 0.69224, 0, 0],
+        "10731": [0.11111, 0.69224, 0, 0],
+        "10846": [0.19444, 0.75583, 0, 0],
+        "10877": [0.13667, 0.63667, 0, 0],
+        "10878": [0.13667, 0.63667, 0, 0],
+        "10885": [0.25583, 0.75583, 0, 0],
+        "10886": [0.25583, 0.75583, 0, 0],
+        "10887": [0.13597, 0.63597, 0, 0],
+        "10888": [0.13597, 0.63597, 0, 0],
+        "10889": [0.26167, 0.75726, 0, 0],
+        "10890": [0.26167, 0.75726, 0, 0],
+        "10891": [0.48256, 0.98256, 0, 0],
+        "10892": [0.48256, 0.98256, 0, 0],
+        "10901": [0.13667, 0.63667, 0, 0],
+        "10902": [0.13667, 0.63667, 0, 0],
+        "10933": [0.25142, 0.75726, 0, 0],
+        "10934": [0.25142, 0.75726, 0, 0],
+        "10935": [0.26167, 0.75726, 0, 0],
+        "10936": [0.26167, 0.75726, 0, 0],
+        "10937": [0.26167, 0.75726, 0, 0],
+        "10938": [0.26167, 0.75726, 0, 0],
+        "10949": [0.25583, 0.75583, 0, 0],
+        "10950": [0.25583, 0.75583, 0, 0],
+        "10955": [0.28481, 0.79383, 0, 0],
+        "10956": [0.28481, 0.79383, 0, 0],
+        "57350": [0.08167, 0.58167, 0, 0],
+        "57351": [0.08167, 0.58167, 0, 0],
+        "57352": [0.08167, 0.58167, 0, 0],
+        "57353": [0, 0.43056, 0.04028, 0],
+        "57356": [0.25142, 0.75726, 0, 0],
+        "57357": [0.25142, 0.75726, 0, 0],
+        "57358": [0.41951, 0.91951, 0, 0],
+        "57359": [0.30274, 0.79383, 0, 0],
+        "57360": [0.30274, 0.79383, 0, 0],
+        "57361": [0.41951, 0.91951, 0, 0],
+        "57366": [0.25142, 0.75726, 0, 0],
+        "57367": [0.25142, 0.75726, 0, 0],
+        "57368": [0.25142, 0.75726, 0, 0],
+        "57369": [0.25142, 0.75726, 0, 0],
+        "57370": [0.13597, 0.63597, 0, 0],
+        "57371": [0.13597, 0.63597, 0, 0]
+    },
+    "Caligraphic-Regular": {
+        "48": [0, 0.43056, 0, 0],
+        "49": [0, 0.43056, 0, 0],
+        "50": [0, 0.43056, 0, 0],
+        "51": [0.19444, 0.43056, 0, 0],
+        "52": [0.19444, 0.43056, 0, 0],
+        "53": [0.19444, 0.43056, 0, 0],
+        "54": [0, 0.64444, 0, 0],
+        "55": [0.19444, 0.43056, 0, 0],
+        "56": [0, 0.64444, 0, 0],
+        "57": [0.19444, 0.43056, 0, 0],
+        "65": [0, 0.68333, 0, 0.19445],
+        "66": [0, 0.68333, 0.03041, 0.13889],
+        "67": [0, 0.68333, 0.05834, 0.13889],
+        "68": [0, 0.68333, 0.02778, 0.08334],
+        "69": [0, 0.68333, 0.08944, 0.11111],
+        "70": [0, 0.68333, 0.09931, 0.11111],
+        "71": [0.09722, 0.68333, 0.0593, 0.11111],
+        "72": [0, 0.68333, 0.00965, 0.11111],
+        "73": [0, 0.68333, 0.07382, 0],
+        "74": [0.09722, 0.68333, 0.18472, 0.16667],
+        "75": [0, 0.68333, 0.01445, 0.05556],
+        "76": [0, 0.68333, 0, 0.13889],
+        "77": [0, 0.68333, 0, 0.13889],
+        "78": [0, 0.68333, 0.14736, 0.08334],
+        "79": [0, 0.68333, 0.02778, 0.11111],
+        "80": [0, 0.68333, 0.08222, 0.08334],
+        "81": [0.09722, 0.68333, 0, 0.11111],
+        "82": [0, 0.68333, 0, 0.08334],
+        "83": [0, 0.68333, 0.075, 0.13889],
+        "84": [0, 0.68333, 0.25417, 0],
+        "85": [0, 0.68333, 0.09931, 0.08334],
+        "86": [0, 0.68333, 0.08222, 0],
+        "87": [0, 0.68333, 0.08222, 0.08334],
+        "88": [0, 0.68333, 0.14643, 0.13889],
+        "89": [0.09722, 0.68333, 0.08222, 0.08334],
+        "90": [0, 0.68333, 0.07944, 0.13889]
+    },
+    "Fraktur-Regular": {
+        "33": [0, 0.69141, 0, 0],
+        "34": [0, 0.69141, 0, 0],
+        "38": [0, 0.69141, 0, 0],
+        "39": [0, 0.69141, 0, 0],
+        "40": [0.24982, 0.74947, 0, 0],
+        "41": [0.24982, 0.74947, 0, 0],
+        "42": [0, 0.62119, 0, 0],
+        "43": [0.08319, 0.58283, 0, 0],
+        "44": [0, 0.10803, 0, 0],
+        "45": [0.08319, 0.58283, 0, 0],
+        "46": [0, 0.10803, 0, 0],
+        "47": [0.24982, 0.74947, 0, 0],
+        "48": [0, 0.47534, 0, 0],
+        "49": [0, 0.47534, 0, 0],
+        "50": [0, 0.47534, 0, 0],
+        "51": [0.18906, 0.47534, 0, 0],
+        "52": [0.18906, 0.47534, 0, 0],
+        "53": [0.18906, 0.47534, 0, 0],
+        "54": [0, 0.69141, 0, 0],
+        "55": [0.18906, 0.47534, 0, 0],
+        "56": [0, 0.69141, 0, 0],
+        "57": [0.18906, 0.47534, 0, 0],
+        "58": [0, 0.47534, 0, 0],
+        "59": [0.12604, 0.47534, 0, 0],
+        "61": [-0.13099, 0.36866, 0, 0],
+        "63": [0, 0.69141, 0, 0],
+        "65": [0, 0.69141, 0, 0],
+        "66": [0, 0.69141, 0, 0],
+        "67": [0, 0.69141, 0, 0],
+        "68": [0, 0.69141, 0, 0],
+        "69": [0, 0.69141, 0, 0],
+        "70": [0.12604, 0.69141, 0, 0],
+        "71": [0, 0.69141, 0, 0],
+        "72": [0.06302, 0.69141, 0, 0],
+        "73": [0, 0.69141, 0, 0],
+        "74": [0.12604, 0.69141, 0, 0],
+        "75": [0, 0.69141, 0, 0],
+        "76": [0, 0.69141, 0, 0],
+        "77": [0, 0.69141, 0, 0],
+        "78": [0, 0.69141, 0, 0],
+        "79": [0, 0.69141, 0, 0],
+        "80": [0.18906, 0.69141, 0, 0],
+        "81": [0.03781, 0.69141, 0, 0],
+        "82": [0, 0.69141, 0, 0],
+        "83": [0, 0.69141, 0, 0],
+        "84": [0, 0.69141, 0, 0],
+        "85": [0, 0.69141, 0, 0],
+        "86": [0, 0.69141, 0, 0],
+        "87": [0, 0.69141, 0, 0],
+        "88": [0, 0.69141, 0, 0],
+        "89": [0.18906, 0.69141, 0, 0],
+        "90": [0.12604, 0.69141, 0, 0],
+        "91": [0.24982, 0.74947, 0, 0],
+        "93": [0.24982, 0.74947, 0, 0],
+        "94": [0, 0.69141, 0, 0],
+        "97": [0, 0.47534, 0, 0],
+        "98": [0, 0.69141, 0, 0],
+        "99": [0, 0.47534, 0, 0],
+        "100": [0, 0.62119, 0, 0],
+        "101": [0, 0.47534, 0, 0],
+        "102": [0.18906, 0.69141, 0, 0],
+        "103": [0.18906, 0.47534, 0, 0],
+        "104": [0.18906, 0.69141, 0, 0],
+        "105": [0, 0.69141, 0, 0],
+        "106": [0, 0.69141, 0, 0],
+        "107": [0, 0.69141, 0, 0],
+        "108": [0, 0.69141, 0, 0],
+        "109": [0, 0.47534, 0, 0],
+        "110": [0, 0.47534, 0, 0],
+        "111": [0, 0.47534, 0, 0],
+        "112": [0.18906, 0.52396, 0, 0],
+        "113": [0.18906, 0.47534, 0, 0],
+        "114": [0, 0.47534, 0, 0],
+        "115": [0, 0.47534, 0, 0],
+        "116": [0, 0.62119, 0, 0],
+        "117": [0, 0.47534, 0, 0],
+        "118": [0, 0.52396, 0, 0],
+        "119": [0, 0.52396, 0, 0],
+        "120": [0.18906, 0.47534, 0, 0],
+        "121": [0.18906, 0.47534, 0, 0],
+        "122": [0.18906, 0.47534, 0, 0],
+        "8216": [0, 0.69141, 0, 0],
+        "8217": [0, 0.69141, 0, 0],
+        "58112": [0, 0.62119, 0, 0],
+        "58113": [0, 0.62119, 0, 0],
+        "58114": [0.18906, 0.69141, 0, 0],
+        "58115": [0.18906, 0.69141, 0, 0],
+        "58116": [0.18906, 0.47534, 0, 0],
+        "58117": [0, 0.69141, 0, 0],
+        "58118": [0, 0.62119, 0, 0],
+        "58119": [0, 0.47534, 0, 0]
+    },
+    "Main-Bold": {
+        "33": [0, 0.69444, 0, 0],
+        "34": [0, 0.69444, 0, 0],
+        "35": [0.19444, 0.69444, 0, 0],
+        "36": [0.05556, 0.75, 0, 0],
+        "37": [0.05556, 0.75, 0, 0],
+        "38": [0, 0.69444, 0, 0],
+        "39": [0, 0.69444, 0, 0],
+        "40": [0.25, 0.75, 0, 0],
+        "41": [0.25, 0.75, 0, 0],
+        "42": [0, 0.75, 0, 0],
+        "43": [0.13333, 0.63333, 0, 0],
+        "44": [0.19444, 0.15556, 0, 0],
+        "45": [0, 0.44444, 0, 0],
+        "46": [0, 0.15556, 0, 0],
+        "47": [0.25, 0.75, 0, 0],
+        "48": [0, 0.64444, 0, 0],
+        "49": [0, 0.64444, 0, 0],
+        "50": [0, 0.64444, 0, 0],
+        "51": [0, 0.64444, 0, 0],
+        "52": [0, 0.64444, 0, 0],
+        "53": [0, 0.64444, 0, 0],
+        "54": [0, 0.64444, 0, 0],
+        "55": [0, 0.64444, 0, 0],
+        "56": [0, 0.64444, 0, 0],
+        "57": [0, 0.64444, 0, 0],
+        "58": [0, 0.44444, 0, 0],
+        "59": [0.19444, 0.44444, 0, 0],
+        "60": [0.08556, 0.58556, 0, 0],
+        "61": [-0.10889, 0.39111, 0, 0],
+        "62": [0.08556, 0.58556, 0, 0],
+        "63": [0, 0.69444, 0, 0],
+        "64": [0, 0.69444, 0, 0],
+        "65": [0, 0.68611, 0, 0],
+        "66": [0, 0.68611, 0, 0],
+        "67": [0, 0.68611, 0, 0],
+        "68": [0, 0.68611, 0, 0],
+        "69": [0, 0.68611, 0, 0],
+        "70": [0, 0.68611, 0, 0],
+        "71": [0, 0.68611, 0, 0],
+        "72": [0, 0.68611, 0, 0],
+        "73": [0, 0.68611, 0, 0],
+        "74": [0, 0.68611, 0, 0],
+        "75": [0, 0.68611, 0, 0],
+        "76": [0, 0.68611, 0, 0],
+        "77": [0, 0.68611, 0, 0],
+        "78": [0, 0.68611, 0, 0],
+        "79": [0, 0.68611, 0, 0],
+        "80": [0, 0.68611, 0, 0],
+        "81": [0.19444, 0.68611, 0, 0],
+        "82": [0, 0.68611, 0, 0],
+        "83": [0, 0.68611, 0, 0],
+        "84": [0, 0.68611, 0, 0],
+        "85": [0, 0.68611, 0, 0],
+        "86": [0, 0.68611, 0.01597, 0],
+        "87": [0, 0.68611, 0.01597, 0],
+        "88": [0, 0.68611, 0, 0],
+        "89": [0, 0.68611, 0.02875, 0],
+        "90": [0, 0.68611, 0, 0],
+        "91": [0.25, 0.75, 0, 0],
+        "92": [0.25, 0.75, 0, 0],
+        "93": [0.25, 0.75, 0, 0],
+        "94": [0, 0.69444, 0, 0],
+        "95": [0.31, 0.13444, 0.03194, 0],
+        "96": [0, 0.69444, 0, 0],
+        "97": [0, 0.44444, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.44444, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.44444, 0, 0],
+        "102": [0, 0.69444, 0.10903, 0],
+        "103": [0.19444, 0.44444, 0.01597, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.69444, 0, 0],
+        "106": [0.19444, 0.69444, 0, 0],
+        "107": [0, 0.69444, 0, 0],
+        "108": [0, 0.69444, 0, 0],
+        "109": [0, 0.44444, 0, 0],
+        "110": [0, 0.44444, 0, 0],
+        "111": [0, 0.44444, 0, 0],
+        "112": [0.19444, 0.44444, 0, 0],
+        "113": [0.19444, 0.44444, 0, 0],
+        "114": [0, 0.44444, 0, 0],
+        "115": [0, 0.44444, 0, 0],
+        "116": [0, 0.63492, 0, 0],
+        "117": [0, 0.44444, 0, 0],
+        "118": [0, 0.44444, 0.01597, 0],
+        "119": [0, 0.44444, 0.01597, 0],
+        "120": [0, 0.44444, 0, 0],
+        "121": [0.19444, 0.44444, 0.01597, 0],
+        "122": [0, 0.44444, 0, 0],
+        "123": [0.25, 0.75, 0, 0],
+        "124": [0.25, 0.75, 0, 0],
+        "125": [0.25, 0.75, 0, 0],
+        "126": [0.35, 0.34444, 0, 0],
+        "168": [0, 0.69444, 0, 0],
+        "172": [0, 0.44444, 0, 0],
+        "175": [0, 0.59611, 0, 0],
+        "176": [0, 0.69444, 0, 0],
+        "177": [0.13333, 0.63333, 0, 0],
+        "180": [0, 0.69444, 0, 0],
+        "215": [0.13333, 0.63333, 0, 0],
+        "247": [0.13333, 0.63333, 0, 0],
+        "305": [0, 0.44444, 0, 0],
+        "567": [0.19444, 0.44444, 0, 0],
+        "710": [0, 0.69444, 0, 0],
+        "711": [0, 0.63194, 0, 0],
+        "713": [0, 0.59611, 0, 0],
+        "714": [0, 0.69444, 0, 0],
+        "715": [0, 0.69444, 0, 0],
+        "728": [0, 0.69444, 0, 0],
+        "729": [0, 0.69444, 0, 0],
+        "730": [0, 0.69444, 0, 0],
+        "732": [0, 0.69444, 0, 0],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0, 0],
+        "770": [0, 0.69444, 0, 0],
+        "771": [0, 0.69444, 0, 0],
+        "772": [0, 0.59611, 0, 0],
+        "774": [0, 0.69444, 0, 0],
+        "775": [0, 0.69444, 0, 0],
+        "776": [0, 0.69444, 0, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0, 0],
+        "780": [0, 0.63194, 0, 0],
+        "824": [0.19444, 0.69444, 0, 0],
+        "915": [0, 0.68611, 0, 0],
+        "916": [0, 0.68611, 0, 0],
+        "920": [0, 0.68611, 0, 0],
+        "923": [0, 0.68611, 0, 0],
+        "926": [0, 0.68611, 0, 0],
+        "928": [0, 0.68611, 0, 0],
+        "931": [0, 0.68611, 0, 0],
+        "933": [0, 0.68611, 0, 0],
+        "934": [0, 0.68611, 0, 0],
+        "936": [0, 0.68611, 0, 0],
+        "937": [0, 0.68611, 0, 0],
+        "8211": [0, 0.44444, 0.03194, 0],
+        "8212": [0, 0.44444, 0.03194, 0],
+        "8216": [0, 0.69444, 0, 0],
+        "8217": [0, 0.69444, 0, 0],
+        "8220": [0, 0.69444, 0, 0],
+        "8221": [0, 0.69444, 0, 0],
+        "8224": [0.19444, 0.69444, 0, 0],
+        "8225": [0.19444, 0.69444, 0, 0],
+        "8242": [0, 0.55556, 0, 0],
+        "8407": [0, 0.72444, 0.15486, 0],
+        "8463": [0, 0.69444, 0, 0],
+        "8465": [0, 0.69444, 0, 0],
+        "8467": [0, 0.69444, 0, 0],
+        "8472": [0.19444, 0.44444, 0, 0],
+        "8476": [0, 0.69444, 0, 0],
+        "8501": [0, 0.69444, 0, 0],
+        "8592": [-0.10889, 0.39111, 0, 0],
+        "8593": [0.19444, 0.69444, 0, 0],
+        "8594": [-0.10889, 0.39111, 0, 0],
+        "8595": [0.19444, 0.69444, 0, 0],
+        "8596": [-0.10889, 0.39111, 0, 0],
+        "8597": [0.25, 0.75, 0, 0],
+        "8598": [0.19444, 0.69444, 0, 0],
+        "8599": [0.19444, 0.69444, 0, 0],
+        "8600": [0.19444, 0.69444, 0, 0],
+        "8601": [0.19444, 0.69444, 0, 0],
+        "8636": [-0.10889, 0.39111, 0, 0],
+        "8637": [-0.10889, 0.39111, 0, 0],
+        "8640": [-0.10889, 0.39111, 0, 0],
+        "8641": [-0.10889, 0.39111, 0, 0],
+        "8656": [-0.10889, 0.39111, 0, 0],
+        "8657": [0.19444, 0.69444, 0, 0],
+        "8658": [-0.10889, 0.39111, 0, 0],
+        "8659": [0.19444, 0.69444, 0, 0],
+        "8660": [-0.10889, 0.39111, 0, 0],
+        "8661": [0.25, 0.75, 0, 0],
+        "8704": [0, 0.69444, 0, 0],
+        "8706": [0, 0.69444, 0.06389, 0],
+        "8707": [0, 0.69444, 0, 0],
+        "8709": [0.05556, 0.75, 0, 0],
+        "8711": [0, 0.68611, 0, 0],
+        "8712": [0.08556, 0.58556, 0, 0],
+        "8715": [0.08556, 0.58556, 0, 0],
+        "8722": [0.13333, 0.63333, 0, 0],
+        "8723": [0.13333, 0.63333, 0, 0],
+        "8725": [0.25, 0.75, 0, 0],
+        "8726": [0.25, 0.75, 0, 0],
+        "8727": [-0.02778, 0.47222, 0, 0],
+        "8728": [-0.02639, 0.47361, 0, 0],
+        "8729": [-0.02639, 0.47361, 0, 0],
+        "8730": [0.18, 0.82, 0, 0],
+        "8733": [0, 0.44444, 0, 0],
+        "8734": [0, 0.44444, 0, 0],
+        "8736": [0, 0.69224, 0, 0],
+        "8739": [0.25, 0.75, 0, 0],
+        "8741": [0.25, 0.75, 0, 0],
+        "8743": [0, 0.55556, 0, 0],
+        "8744": [0, 0.55556, 0, 0],
+        "8745": [0, 0.55556, 0, 0],
+        "8746": [0, 0.55556, 0, 0],
+        "8747": [0.19444, 0.69444, 0.12778, 0],
+        "8764": [-0.10889, 0.39111, 0, 0],
+        "8768": [0.19444, 0.69444, 0, 0],
+        "8771": [0.00222, 0.50222, 0, 0],
+        "8776": [0.02444, 0.52444, 0, 0],
+        "8781": [0.00222, 0.50222, 0, 0],
+        "8801": [0.00222, 0.50222, 0, 0],
+        "8804": [0.19667, 0.69667, 0, 0],
+        "8805": [0.19667, 0.69667, 0, 0],
+        "8810": [0.08556, 0.58556, 0, 0],
+        "8811": [0.08556, 0.58556, 0, 0],
+        "8826": [0.08556, 0.58556, 0, 0],
+        "8827": [0.08556, 0.58556, 0, 0],
+        "8834": [0.08556, 0.58556, 0, 0],
+        "8835": [0.08556, 0.58556, 0, 0],
+        "8838": [0.19667, 0.69667, 0, 0],
+        "8839": [0.19667, 0.69667, 0, 0],
+        "8846": [0, 0.55556, 0, 0],
+        "8849": [0.19667, 0.69667, 0, 0],
+        "8850": [0.19667, 0.69667, 0, 0],
+        "8851": [0, 0.55556, 0, 0],
+        "8852": [0, 0.55556, 0, 0],
+        "8853": [0.13333, 0.63333, 0, 0],
+        "8854": [0.13333, 0.63333, 0, 0],
+        "8855": [0.13333, 0.63333, 0, 0],
+        "8856": [0.13333, 0.63333, 0, 0],
+        "8857": [0.13333, 0.63333, 0, 0],
+        "8866": [0, 0.69444, 0, 0],
+        "8867": [0, 0.69444, 0, 0],
+        "8868": [0, 0.69444, 0, 0],
+        "8869": [0, 0.69444, 0, 0],
+        "8900": [-0.02639, 0.47361, 0, 0],
+        "8901": [-0.02639, 0.47361, 0, 0],
+        "8902": [-0.02778, 0.47222, 0, 0],
+        "8968": [0.25, 0.75, 0, 0],
+        "8969": [0.25, 0.75, 0, 0],
+        "8970": [0.25, 0.75, 0, 0],
+        "8971": [0.25, 0.75, 0, 0],
+        "8994": [-0.13889, 0.36111, 0, 0],
+        "8995": [-0.13889, 0.36111, 0, 0],
+        "9651": [0.19444, 0.69444, 0, 0],
+        "9657": [-0.02778, 0.47222, 0, 0],
+        "9661": [0.19444, 0.69444, 0, 0],
+        "9667": [-0.02778, 0.47222, 0, 0],
+        "9711": [0.19444, 0.69444, 0, 0],
+        "9824": [0.12963, 0.69444, 0, 0],
+        "9825": [0.12963, 0.69444, 0, 0],
+        "9826": [0.12963, 0.69444, 0, 0],
+        "9827": [0.12963, 0.69444, 0, 0],
+        "9837": [0, 0.75, 0, 0],
+        "9838": [0.19444, 0.69444, 0, 0],
+        "9839": [0.19444, 0.69444, 0, 0],
+        "10216": [0.25, 0.75, 0, 0],
+        "10217": [0.25, 0.75, 0, 0],
+        "10815": [0, 0.68611, 0, 0],
+        "10927": [0.19667, 0.69667, 0, 0],
+        "10928": [0.19667, 0.69667, 0, 0]
+    },
+    "Main-Italic": {
+        "33": [0, 0.69444, 0.12417, 0],
+        "34": [0, 0.69444, 0.06961, 0],
+        "35": [0.19444, 0.69444, 0.06616, 0],
+        "37": [0.05556, 0.75, 0.13639, 0],
+        "38": [0, 0.69444, 0.09694, 0],
+        "39": [0, 0.69444, 0.12417, 0],
+        "40": [0.25, 0.75, 0.16194, 0],
+        "41": [0.25, 0.75, 0.03694, 0],
+        "42": [0, 0.75, 0.14917, 0],
+        "43": [0.05667, 0.56167, 0.03694, 0],
+        "44": [0.19444, 0.10556, 0, 0],
+        "45": [0, 0.43056, 0.02826, 0],
+        "46": [0, 0.10556, 0, 0],
+        "47": [0.25, 0.75, 0.16194, 0],
+        "48": [0, 0.64444, 0.13556, 0],
+        "49": [0, 0.64444, 0.13556, 0],
+        "50": [0, 0.64444, 0.13556, 0],
+        "51": [0, 0.64444, 0.13556, 0],
+        "52": [0.19444, 0.64444, 0.13556, 0],
+        "53": [0, 0.64444, 0.13556, 0],
+        "54": [0, 0.64444, 0.13556, 0],
+        "55": [0.19444, 0.64444, 0.13556, 0],
+        "56": [0, 0.64444, 0.13556, 0],
+        "57": [0, 0.64444, 0.13556, 0],
+        "58": [0, 0.43056, 0.0582, 0],
+        "59": [0.19444, 0.43056, 0.0582, 0],
+        "61": [-0.13313, 0.36687, 0.06616, 0],
+        "63": [0, 0.69444, 0.1225, 0],
+        "64": [0, 0.69444, 0.09597, 0],
+        "65": [0, 0.68333, 0, 0],
+        "66": [0, 0.68333, 0.10257, 0],
+        "67": [0, 0.68333, 0.14528, 0],
+        "68": [0, 0.68333, 0.09403, 0],
+        "69": [0, 0.68333, 0.12028, 0],
+        "70": [0, 0.68333, 0.13305, 0],
+        "71": [0, 0.68333, 0.08722, 0],
+        "72": [0, 0.68333, 0.16389, 0],
+        "73": [0, 0.68333, 0.15806, 0],
+        "74": [0, 0.68333, 0.14028, 0],
+        "75": [0, 0.68333, 0.14528, 0],
+        "76": [0, 0.68333, 0, 0],
+        "77": [0, 0.68333, 0.16389, 0],
+        "78": [0, 0.68333, 0.16389, 0],
+        "79": [0, 0.68333, 0.09403, 0],
+        "80": [0, 0.68333, 0.10257, 0],
+        "81": [0.19444, 0.68333, 0.09403, 0],
+        "82": [0, 0.68333, 0.03868, 0],
+        "83": [0, 0.68333, 0.11972, 0],
+        "84": [0, 0.68333, 0.13305, 0],
+        "85": [0, 0.68333, 0.16389, 0],
+        "86": [0, 0.68333, 0.18361, 0],
+        "87": [0, 0.68333, 0.18361, 0],
+        "88": [0, 0.68333, 0.15806, 0],
+        "89": [0, 0.68333, 0.19383, 0],
+        "90": [0, 0.68333, 0.14528, 0],
+        "91": [0.25, 0.75, 0.1875, 0],
+        "93": [0.25, 0.75, 0.10528, 0],
+        "94": [0, 0.69444, 0.06646, 0],
+        "95": [0.31, 0.12056, 0.09208, 0],
+        "97": [0, 0.43056, 0.07671, 0],
+        "98": [0, 0.69444, 0.06312, 0],
+        "99": [0, 0.43056, 0.05653, 0],
+        "100": [0, 0.69444, 0.10333, 0],
+        "101": [0, 0.43056, 0.07514, 0],
+        "102": [0.19444, 0.69444, 0.21194, 0],
+        "103": [0.19444, 0.43056, 0.08847, 0],
+        "104": [0, 0.69444, 0.07671, 0],
+        "105": [0, 0.65536, 0.1019, 0],
+        "106": [0.19444, 0.65536, 0.14467, 0],
+        "107": [0, 0.69444, 0.10764, 0],
+        "108": [0, 0.69444, 0.10333, 0],
+        "109": [0, 0.43056, 0.07671, 0],
+        "110": [0, 0.43056, 0.07671, 0],
+        "111": [0, 0.43056, 0.06312, 0],
+        "112": [0.19444, 0.43056, 0.06312, 0],
+        "113": [0.19444, 0.43056, 0.08847, 0],
+        "114": [0, 0.43056, 0.10764, 0],
+        "115": [0, 0.43056, 0.08208, 0],
+        "116": [0, 0.61508, 0.09486, 0],
+        "117": [0, 0.43056, 0.07671, 0],
+        "118": [0, 0.43056, 0.10764, 0],
+        "119": [0, 0.43056, 0.10764, 0],
+        "120": [0, 0.43056, 0.12042, 0],
+        "121": [0.19444, 0.43056, 0.08847, 0],
+        "122": [0, 0.43056, 0.12292, 0],
+        "126": [0.35, 0.31786, 0.11585, 0],
+        "163": [0, 0.69444, 0, 0],
+        "305": [0, 0.43056, 0, 0.02778],
+        "567": [0.19444, 0.43056, 0, 0.08334],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0.09694, 0],
+        "770": [0, 0.69444, 0.06646, 0],
+        "771": [0, 0.66786, 0.11585, 0],
+        "772": [0, 0.56167, 0.10333, 0],
+        "774": [0, 0.69444, 0.10806, 0],
+        "775": [0, 0.66786, 0.11752, 0],
+        "776": [0, 0.66786, 0.10474, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0.1225, 0],
+        "780": [0, 0.62847, 0.08295, 0],
+        "915": [0, 0.68333, 0.13305, 0],
+        "916": [0, 0.68333, 0, 0],
+        "920": [0, 0.68333, 0.09403, 0],
+        "923": [0, 0.68333, 0, 0],
+        "926": [0, 0.68333, 0.15294, 0],
+        "928": [0, 0.68333, 0.16389, 0],
+        "931": [0, 0.68333, 0.12028, 0],
+        "933": [0, 0.68333, 0.11111, 0],
+        "934": [0, 0.68333, 0.05986, 0],
+        "936": [0, 0.68333, 0.11111, 0],
+        "937": [0, 0.68333, 0.10257, 0],
+        "8211": [0, 0.43056, 0.09208, 0],
+        "8212": [0, 0.43056, 0.09208, 0],
+        "8216": [0, 0.69444, 0.12417, 0],
+        "8217": [0, 0.69444, 0.12417, 0],
+        "8220": [0, 0.69444, 0.1685, 0],
+        "8221": [0, 0.69444, 0.06961, 0],
+        "8463": [0, 0.68889, 0, 0]
+    },
+    "Main-Regular": {
+        "32": [0, 0, 0, 0],
+        "33": [0, 0.69444, 0, 0],
+        "34": [0, 0.69444, 0, 0],
+        "35": [0.19444, 0.69444, 0, 0],
+        "36": [0.05556, 0.75, 0, 0],
+        "37": [0.05556, 0.75, 0, 0],
+        "38": [0, 0.69444, 0, 0],
+        "39": [0, 0.69444, 0, 0],
+        "40": [0.25, 0.75, 0, 0],
+        "41": [0.25, 0.75, 0, 0],
+        "42": [0, 0.75, 0, 0],
+        "43": [0.08333, 0.58333, 0, 0],
+        "44": [0.19444, 0.10556, 0, 0],
+        "45": [0, 0.43056, 0, 0],
+        "46": [0, 0.10556, 0, 0],
+        "47": [0.25, 0.75, 0, 0],
+        "48": [0, 0.64444, 0, 0],
+        "49": [0, 0.64444, 0, 0],
+        "50": [0, 0.64444, 0, 0],
+        "51": [0, 0.64444, 0, 0],
+        "52": [0, 0.64444, 0, 0],
+        "53": [0, 0.64444, 0, 0],
+        "54": [0, 0.64444, 0, 0],
+        "55": [0, 0.64444, 0, 0],
+        "56": [0, 0.64444, 0, 0],
+        "57": [0, 0.64444, 0, 0],
+        "58": [0, 0.43056, 0, 0],
+        "59": [0.19444, 0.43056, 0, 0],
+        "60": [0.0391, 0.5391, 0, 0],
+        "61": [-0.13313, 0.36687, 0, 0],
+        "62": [0.0391, 0.5391, 0, 0],
+        "63": [0, 0.69444, 0, 0],
+        "64": [0, 0.69444, 0, 0],
+        "65": [0, 0.68333, 0, 0],
+        "66": [0, 0.68333, 0, 0],
+        "67": [0, 0.68333, 0, 0],
+        "68": [0, 0.68333, 0, 0],
+        "69": [0, 0.68333, 0, 0],
+        "70": [0, 0.68333, 0, 0],
+        "71": [0, 0.68333, 0, 0],
+        "72": [0, 0.68333, 0, 0],
+        "73": [0, 0.68333, 0, 0],
+        "74": [0, 0.68333, 0, 0],
+        "75": [0, 0.68333, 0, 0],
+        "76": [0, 0.68333, 0, 0],
+        "77": [0, 0.68333, 0, 0],
+        "78": [0, 0.68333, 0, 0],
+        "79": [0, 0.68333, 0, 0],
+        "80": [0, 0.68333, 0, 0],
+        "81": [0.19444, 0.68333, 0, 0],
+        "82": [0, 0.68333, 0, 0],
+        "83": [0, 0.68333, 0, 0],
+        "84": [0, 0.68333, 0, 0],
+        "85": [0, 0.68333, 0, 0],
+        "86": [0, 0.68333, 0.01389, 0],
+        "87": [0, 0.68333, 0.01389, 0],
+        "88": [0, 0.68333, 0, 0],
+        "89": [0, 0.68333, 0.025, 0],
+        "90": [0, 0.68333, 0, 0],
+        "91": [0.25, 0.75, 0, 0],
+        "92": [0.25, 0.75, 0, 0],
+        "93": [0.25, 0.75, 0, 0],
+        "94": [0, 0.69444, 0, 0],
+        "95": [0.31, 0.12056, 0.02778, 0],
+        "96": [0, 0.69444, 0, 0],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.43056, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.43056, 0, 0],
+        "102": [0, 0.69444, 0.07778, 0],
+        "103": [0.19444, 0.43056, 0.01389, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.66786, 0, 0],
+        "106": [0.19444, 0.66786, 0, 0],
+        "107": [0, 0.69444, 0, 0],
+        "108": [0, 0.69444, 0, 0],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0],
+        "112": [0.19444, 0.43056, 0, 0],
+        "113": [0.19444, 0.43056, 0, 0],
+        "114": [0, 0.43056, 0, 0],
+        "115": [0, 0.43056, 0, 0],
+        "116": [0, 0.61508, 0, 0],
+        "117": [0, 0.43056, 0, 0],
+        "118": [0, 0.43056, 0.01389, 0],
+        "119": [0, 0.43056, 0.01389, 0],
+        "120": [0, 0.43056, 0, 0],
+        "121": [0.19444, 0.43056, 0.01389, 0],
+        "122": [0, 0.43056, 0, 0],
+        "123": [0.25, 0.75, 0, 0],
+        "124": [0.25, 0.75, 0, 0],
+        "125": [0.25, 0.75, 0, 0],
+        "126": [0.35, 0.31786, 0, 0],
+        "160": [0, 0, 0, 0],
+        "168": [0, 0.66786, 0, 0],
+        "172": [0, 0.43056, 0, 0],
+        "175": [0, 0.56778, 0, 0],
+        "176": [0, 0.69444, 0, 0],
+        "177": [0.08333, 0.58333, 0, 0],
+        "180": [0, 0.69444, 0, 0],
+        "215": [0.08333, 0.58333, 0, 0],
+        "247": [0.08333, 0.58333, 0, 0],
+        "305": [0, 0.43056, 0, 0],
+        "567": [0.19444, 0.43056, 0, 0],
+        "710": [0, 0.69444, 0, 0],
+        "711": [0, 0.62847, 0, 0],
+        "713": [0, 0.56778, 0, 0],
+        "714": [0, 0.69444, 0, 0],
+        "715": [0, 0.69444, 0, 0],
+        "728": [0, 0.69444, 0, 0],
+        "729": [0, 0.66786, 0, 0],
+        "730": [0, 0.69444, 0, 0],
+        "732": [0, 0.66786, 0, 0],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0, 0],
+        "770": [0, 0.69444, 0, 0],
+        "771": [0, 0.66786, 0, 0],
+        "772": [0, 0.56778, 0, 0],
+        "774": [0, 0.69444, 0, 0],
+        "775": [0, 0.66786, 0, 0],
+        "776": [0, 0.66786, 0, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0, 0],
+        "780": [0, 0.62847, 0, 0],
+        "824": [0.19444, 0.69444, 0, 0],
+        "915": [0, 0.68333, 0, 0],
+        "916": [0, 0.68333, 0, 0],
+        "920": [0, 0.68333, 0, 0],
+        "923": [0, 0.68333, 0, 0],
+        "926": [0, 0.68333, 0, 0],
+        "928": [0, 0.68333, 0, 0],
+        "931": [0, 0.68333, 0, 0],
+        "933": [0, 0.68333, 0, 0],
+        "934": [0, 0.68333, 0, 0],
+        "936": [0, 0.68333, 0, 0],
+        "937": [0, 0.68333, 0, 0],
+        "8211": [0, 0.43056, 0.02778, 0],
+        "8212": [0, 0.43056, 0.02778, 0],
+        "8216": [0, 0.69444, 0, 0],
+        "8217": [0, 0.69444, 0, 0],
+        "8220": [0, 0.69444, 0, 0],
+        "8221": [0, 0.69444, 0, 0],
+        "8224": [0.19444, 0.69444, 0, 0],
+        "8225": [0.19444, 0.69444, 0, 0],
+        "8230": [0, 0.12, 0, 0],
+        "8242": [0, 0.55556, 0, 0],
+        "8407": [0, 0.71444, 0.15382, 0],
+        "8463": [0, 0.68889, 0, 0],
+        "8465": [0, 0.69444, 0, 0],
+        "8467": [0, 0.69444, 0, 0.11111],
+        "8472": [0.19444, 0.43056, 0, 0.11111],
+        "8476": [0, 0.69444, 0, 0],
+        "8501": [0, 0.69444, 0, 0],
+        "8592": [-0.13313, 0.36687, 0, 0],
+        "8593": [0.19444, 0.69444, 0, 0],
+        "8594": [-0.13313, 0.36687, 0, 0],
+        "8595": [0.19444, 0.69444, 0, 0],
+        "8596": [-0.13313, 0.36687, 0, 0],
+        "8597": [0.25, 0.75, 0, 0],
+        "8598": [0.19444, 0.69444, 0, 0],
+        "8599": [0.19444, 0.69444, 0, 0],
+        "8600": [0.19444, 0.69444, 0, 0],
+        "8601": [0.19444, 0.69444, 0, 0],
+        "8614": [0.011, 0.511, 0, 0],
+        "8617": [0.011, 0.511, 0, 0],
+        "8618": [0.011, 0.511, 0, 0],
+        "8636": [-0.13313, 0.36687, 0, 0],
+        "8637": [-0.13313, 0.36687, 0, 0],
+        "8640": [-0.13313, 0.36687, 0, 0],
+        "8641": [-0.13313, 0.36687, 0, 0],
+        "8652": [0.011, 0.671, 0, 0],
+        "8656": [-0.13313, 0.36687, 0, 0],
+        "8657": [0.19444, 0.69444, 0, 0],
+        "8658": [-0.13313, 0.36687, 0, 0],
+        "8659": [0.19444, 0.69444, 0, 0],
+        "8660": [-0.13313, 0.36687, 0, 0],
+        "8661": [0.25, 0.75, 0, 0],
+        "8704": [0, 0.69444, 0, 0],
+        "8706": [0, 0.69444, 0.05556, 0.08334],
+        "8707": [0, 0.69444, 0, 0],
+        "8709": [0.05556, 0.75, 0, 0],
+        "8711": [0, 0.68333, 0, 0],
+        "8712": [0.0391, 0.5391, 0, 0],
+        "8715": [0.0391, 0.5391, 0, 0],
+        "8722": [0.08333, 0.58333, 0, 0],
+        "8723": [0.08333, 0.58333, 0, 0],
+        "8725": [0.25, 0.75, 0, 0],
+        "8726": [0.25, 0.75, 0, 0],
+        "8727": [-0.03472, 0.46528, 0, 0],
+        "8728": [-0.05555, 0.44445, 0, 0],
+        "8729": [-0.05555, 0.44445, 0, 0],
+        "8730": [0.2, 0.8, 0, 0],
+        "8733": [0, 0.43056, 0, 0],
+        "8734": [0, 0.43056, 0, 0],
+        "8736": [0, 0.69224, 0, 0],
+        "8739": [0.25, 0.75, 0, 0],
+        "8741": [0.25, 0.75, 0, 0],
+        "8743": [0, 0.55556, 0, 0],
+        "8744": [0, 0.55556, 0, 0],
+        "8745": [0, 0.55556, 0, 0],
+        "8746": [0, 0.55556, 0, 0],
+        "8747": [0.19444, 0.69444, 0.11111, 0],
+        "8764": [-0.13313, 0.36687, 0, 0],
+        "8768": [0.19444, 0.69444, 0, 0],
+        "8771": [-0.03625, 0.46375, 0, 0],
+        "8773": [-0.022, 0.589, 0, 0],
+        "8776": [-0.01688, 0.48312, 0, 0],
+        "8781": [-0.03625, 0.46375, 0, 0],
+        "8784": [-0.133, 0.67, 0, 0],
+        "8800": [0.215, 0.716, 0, 0],
+        "8801": [-0.03625, 0.46375, 0, 0],
+        "8804": [0.13597, 0.63597, 0, 0],
+        "8805": [0.13597, 0.63597, 0, 0],
+        "8810": [0.0391, 0.5391, 0, 0],
+        "8811": [0.0391, 0.5391, 0, 0],
+        "8826": [0.0391, 0.5391, 0, 0],
+        "8827": [0.0391, 0.5391, 0, 0],
+        "8834": [0.0391, 0.5391, 0, 0],
+        "8835": [0.0391, 0.5391, 0, 0],
+        "8838": [0.13597, 0.63597, 0, 0],
+        "8839": [0.13597, 0.63597, 0, 0],
+        "8846": [0, 0.55556, 0, 0],
+        "8849": [0.13597, 0.63597, 0, 0],
+        "8850": [0.13597, 0.63597, 0, 0],
+        "8851": [0, 0.55556, 0, 0],
+        "8852": [0, 0.55556, 0, 0],
+        "8853": [0.08333, 0.58333, 0, 0],
+        "8854": [0.08333, 0.58333, 0, 0],
+        "8855": [0.08333, 0.58333, 0, 0],
+        "8856": [0.08333, 0.58333, 0, 0],
+        "8857": [0.08333, 0.58333, 0, 0],
+        "8866": [0, 0.69444, 0, 0],
+        "8867": [0, 0.69444, 0, 0],
+        "8868": [0, 0.69444, 0, 0],
+        "8869": [0, 0.69444, 0, 0],
+        "8872": [0.249, 0.75, 0, 0],
+        "8900": [-0.05555, 0.44445, 0, 0],
+        "8901": [-0.05555, 0.44445, 0, 0],
+        "8902": [-0.03472, 0.46528, 0, 0],
+        "8904": [0.005, 0.505, 0, 0],
+        "8942": [0.03, 0.9, 0, 0],
+        "8943": [-0.19, 0.31, 0, 0],
+        "8945": [-0.1, 0.82, 0, 0],
+        "8968": [0.25, 0.75, 0, 0],
+        "8969": [0.25, 0.75, 0, 0],
+        "8970": [0.25, 0.75, 0, 0],
+        "8971": [0.25, 0.75, 0, 0],
+        "8994": [-0.14236, 0.35764, 0, 0],
+        "8995": [-0.14236, 0.35764, 0, 0],
+        "9136": [0.244, 0.744, 0, 0],
+        "9137": [0.244, 0.744, 0, 0],
+        "9651": [0.19444, 0.69444, 0, 0],
+        "9657": [-0.03472, 0.46528, 0, 0],
+        "9661": [0.19444, 0.69444, 0, 0],
+        "9667": [-0.03472, 0.46528, 0, 0],
+        "9711": [0.19444, 0.69444, 0, 0],
+        "9824": [0.12963, 0.69444, 0, 0],
+        "9825": [0.12963, 0.69444, 0, 0],
+        "9826": [0.12963, 0.69444, 0, 0],
+        "9827": [0.12963, 0.69444, 0, 0],
+        "9837": [0, 0.75, 0, 0],
+        "9838": [0.19444, 0.69444, 0, 0],
+        "9839": [0.19444, 0.69444, 0, 0],
+        "10216": [0.25, 0.75, 0, 0],
+        "10217": [0.25, 0.75, 0, 0],
+        "10222": [0.244, 0.744, 0, 0],
+        "10223": [0.244, 0.744, 0, 0],
+        "10229": [0.011, 0.511, 0, 0],
+        "10230": [0.011, 0.511, 0, 0],
+        "10231": [0.011, 0.511, 0, 0],
+        "10232": [0.024, 0.525, 0, 0],
+        "10233": [0.024, 0.525, 0, 0],
+        "10234": [0.024, 0.525, 0, 0],
+        "10236": [0.011, 0.511, 0, 0],
+        "10815": [0, 0.68333, 0, 0],
+        "10927": [0.13597, 0.63597, 0, 0],
+        "10928": [0.13597, 0.63597, 0, 0]
+    },
+    "Math-BoldItalic": {
+        "47": [0.19444, 0.69444, 0, 0],
+        "65": [0, 0.68611, 0, 0],
+        "66": [0, 0.68611, 0.04835, 0],
+        "67": [0, 0.68611, 0.06979, 0],
+        "68": [0, 0.68611, 0.03194, 0],
+        "69": [0, 0.68611, 0.05451, 0],
+        "70": [0, 0.68611, 0.15972, 0],
+        "71": [0, 0.68611, 0, 0],
+        "72": [0, 0.68611, 0.08229, 0],
+        "73": [0, 0.68611, 0.07778, 0],
+        "74": [0, 0.68611, 0.10069, 0],
+        "75": [0, 0.68611, 0.06979, 0],
+        "76": [0, 0.68611, 0, 0],
+        "77": [0, 0.68611, 0.11424, 0],
+        "78": [0, 0.68611, 0.11424, 0],
+        "79": [0, 0.68611, 0.03194, 0],
+        "80": [0, 0.68611, 0.15972, 0],
+        "81": [0.19444, 0.68611, 0, 0],
+        "82": [0, 0.68611, 0.00421, 0],
+        "83": [0, 0.68611, 0.05382, 0],
+        "84": [0, 0.68611, 0.15972, 0],
+        "85": [0, 0.68611, 0.11424, 0],
+        "86": [0, 0.68611, 0.25555, 0],
+        "87": [0, 0.68611, 0.15972, 0],
+        "88": [0, 0.68611, 0.07778, 0],
+        "89": [0, 0.68611, 0.25555, 0],
+        "90": [0, 0.68611, 0.06979, 0],
+        "97": [0, 0.44444, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.44444, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.44444, 0, 0],
+        "102": [0.19444, 0.69444, 0.11042, 0],
+        "103": [0.19444, 0.44444, 0.03704, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.69326, 0, 0],
+        "106": [0.19444, 0.69326, 0.0622, 0],
+        "107": [0, 0.69444, 0.01852, 0],
+        "108": [0, 0.69444, 0.0088, 0],
+        "109": [0, 0.44444, 0, 0],
+        "110": [0, 0.44444, 0, 0],
+        "111": [0, 0.44444, 0, 0],
+        "112": [0.19444, 0.44444, 0, 0],
+        "113": [0.19444, 0.44444, 0.03704, 0],
+        "114": [0, 0.44444, 0.03194, 0],
+        "115": [0, 0.44444, 0, 0],
+        "116": [0, 0.63492, 0, 0],
+        "117": [0, 0.44444, 0, 0],
+        "118": [0, 0.44444, 0.03704, 0],
+        "119": [0, 0.44444, 0.02778, 0],
+        "120": [0, 0.44444, 0, 0],
+        "121": [0.19444, 0.44444, 0.03704, 0],
+        "122": [0, 0.44444, 0.04213, 0],
+        "915": [0, 0.68611, 0.15972, 0],
+        "916": [0, 0.68611, 0, 0],
+        "920": [0, 0.68611, 0.03194, 0],
+        "923": [0, 0.68611, 0, 0],
+        "926": [0, 0.68611, 0.07458, 0],
+        "928": [0, 0.68611, 0.08229, 0],
+        "931": [0, 0.68611, 0.05451, 0],
+        "933": [0, 0.68611, 0.15972, 0],
+        "934": [0, 0.68611, 0, 0],
+        "936": [0, 0.68611, 0.11653, 0],
+        "937": [0, 0.68611, 0.04835, 0],
+        "945": [0, 0.44444, 0, 0],
+        "946": [0.19444, 0.69444, 0.03403, 0],
+        "947": [0.19444, 0.44444, 0.06389, 0],
+        "948": [0, 0.69444, 0.03819, 0],
+        "949": [0, 0.44444, 0, 0],
+        "950": [0.19444, 0.69444, 0.06215, 0],
+        "951": [0.19444, 0.44444, 0.03704, 0],
+        "952": [0, 0.69444, 0.03194, 0],
+        "953": [0, 0.44444, 0, 0],
+        "954": [0, 0.44444, 0, 0],
+        "955": [0, 0.69444, 0, 0],
+        "956": [0.19444, 0.44444, 0, 0],
+        "957": [0, 0.44444, 0.06898, 0],
+        "958": [0.19444, 0.69444, 0.03021, 0],
+        "959": [0, 0.44444, 0, 0],
+        "960": [0, 0.44444, 0.03704, 0],
+        "961": [0.19444, 0.44444, 0, 0],
+        "962": [0.09722, 0.44444, 0.07917, 0],
+        "963": [0, 0.44444, 0.03704, 0],
+        "964": [0, 0.44444, 0.13472, 0],
+        "965": [0, 0.44444, 0.03704, 0],
+        "966": [0.19444, 0.44444, 0, 0],
+        "967": [0.19444, 0.44444, 0, 0],
+        "968": [0.19444, 0.69444, 0.03704, 0],
+        "969": [0, 0.44444, 0.03704, 0],
+        "977": [0, 0.69444, 0, 0],
+        "981": [0.19444, 0.69444, 0, 0],
+        "982": [0, 0.44444, 0.03194, 0],
+        "1009": [0.19444, 0.44444, 0, 0],
+        "1013": [0, 0.44444, 0, 0]
+    },
+    "Math-Italic": {
+        "47": [0.19444, 0.69444, 0, 0],
+        "65": [0, 0.68333, 0, 0.13889],
+        "66": [0, 0.68333, 0.05017, 0.08334],
+        "67": [0, 0.68333, 0.07153, 0.08334],
+        "68": [0, 0.68333, 0.02778, 0.05556],
+        "69": [0, 0.68333, 0.05764, 0.08334],
+        "70": [0, 0.68333, 0.13889, 0.08334],
+        "71": [0, 0.68333, 0, 0.08334],
+        "72": [0, 0.68333, 0.08125, 0.05556],
+        "73": [0, 0.68333, 0.07847, 0.11111],
+        "74": [0, 0.68333, 0.09618, 0.16667],
+        "75": [0, 0.68333, 0.07153, 0.05556],
+        "76": [0, 0.68333, 0, 0.02778],
+        "77": [0, 0.68333, 0.10903, 0.08334],
+        "78": [0, 0.68333, 0.10903, 0.08334],
+        "79": [0, 0.68333, 0.02778, 0.08334],
+        "80": [0, 0.68333, 0.13889, 0.08334],
+        "81": [0.19444, 0.68333, 0, 0.08334],
+        "82": [0, 0.68333, 0.00773, 0.08334],
+        "83": [0, 0.68333, 0.05764, 0.08334],
+        "84": [0, 0.68333, 0.13889, 0.08334],
+        "85": [0, 0.68333, 0.10903, 0.02778],
+        "86": [0, 0.68333, 0.22222, 0],
+        "87": [0, 0.68333, 0.13889, 0],
+        "88": [0, 0.68333, 0.07847, 0.08334],
+        "89": [0, 0.68333, 0.22222, 0],
+        "90": [0, 0.68333, 0.07153, 0.08334],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.43056, 0, 0.05556],
+        "100": [0, 0.69444, 0, 0.16667],
+        "101": [0, 0.43056, 0, 0.05556],
+        "102": [0.19444, 0.69444, 0.10764, 0.16667],
+        "103": [0.19444, 0.43056, 0.03588, 0.02778],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.65952, 0, 0],
+        "106": [0.19444, 0.65952, 0.05724, 0],
+        "107": [0, 0.69444, 0.03148, 0],
+        "108": [0, 0.69444, 0.01968, 0.08334],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0.05556],
+        "112": [0.19444, 0.43056, 0, 0.08334],
+        "113": [0.19444, 0.43056, 0.03588, 0.08334],
+        "114": [0, 0.43056, 0.02778, 0.05556],
+        "115": [0, 0.43056, 0, 0.05556],
+        "116": [0, 0.61508, 0, 0.08334],
+        "117": [0, 0.43056, 0, 0.02778],
+        "118": [0, 0.43056, 0.03588, 0.02778],
+        "119": [0, 0.43056, 0.02691, 0.08334],
+        "120": [0, 0.43056, 0, 0.02778],
+        "121": [0.19444, 0.43056, 0.03588, 0.05556],
+        "122": [0, 0.43056, 0.04398, 0.05556],
+        "915": [0, 0.68333, 0.13889, 0.08334],
+        "916": [0, 0.68333, 0, 0.16667],
+        "920": [0, 0.68333, 0.02778, 0.08334],
+        "923": [0, 0.68333, 0, 0.16667],
+        "926": [0, 0.68333, 0.07569, 0.08334],
+        "928": [0, 0.68333, 0.08125, 0.05556],
+        "931": [0, 0.68333, 0.05764, 0.08334],
+        "933": [0, 0.68333, 0.13889, 0.05556],
+        "934": [0, 0.68333, 0, 0.08334],
+        "936": [0, 0.68333, 0.11, 0.05556],
+        "937": [0, 0.68333, 0.05017, 0.08334],
+        "945": [0, 0.43056, 0.0037, 0.02778],
+        "946": [0.19444, 0.69444, 0.05278, 0.08334],
+        "947": [0.19444, 0.43056, 0.05556, 0],
+        "948": [0, 0.69444, 0.03785, 0.05556],
+        "949": [0, 0.43056, 0, 0.08334],
+        "950": [0.19444, 0.69444, 0.07378, 0.08334],
+        "951": [0.19444, 0.43056, 0.03588, 0.05556],
+        "952": [0, 0.69444, 0.02778, 0.08334],
+        "953": [0, 0.43056, 0, 0.05556],
+        "954": [0, 0.43056, 0, 0],
+        "955": [0, 0.69444, 0, 0],
+        "956": [0.19444, 0.43056, 0, 0.02778],
+        "957": [0, 0.43056, 0.06366, 0.02778],
+        "958": [0.19444, 0.69444, 0.04601, 0.11111],
+        "959": [0, 0.43056, 0, 0.05556],
+        "960": [0, 0.43056, 0.03588, 0],
+        "961": [0.19444, 0.43056, 0, 0.08334],
+        "962": [0.09722, 0.43056, 0.07986, 0.08334],
+        "963": [0, 0.43056, 0.03588, 0],
+        "964": [0, 0.43056, 0.1132, 0.02778],
+        "965": [0, 0.43056, 0.03588, 0.02778],
+        "966": [0.19444, 0.43056, 0, 0.08334],
+        "967": [0.19444, 0.43056, 0, 0.05556],
+        "968": [0.19444, 0.69444, 0.03588, 0.11111],
+        "969": [0, 0.43056, 0.03588, 0],
+        "977": [0, 0.69444, 0, 0.08334],
+        "981": [0.19444, 0.69444, 0, 0.08334],
+        "982": [0, 0.43056, 0.02778, 0],
+        "1009": [0.19444, 0.43056, 0, 0.08334],
+        "1013": [0, 0.43056, 0, 0.05556]
+    },
+    "Math-Regular": {
+        "65": [0, 0.68333, 0, 0.13889],
+        "66": [0, 0.68333, 0.05017, 0.08334],
+        "67": [0, 0.68333, 0.07153, 0.08334],
+        "68": [0, 0.68333, 0.02778, 0.05556],
+        "69": [0, 0.68333, 0.05764, 0.08334],
+        "70": [0, 0.68333, 0.13889, 0.08334],
+        "71": [0, 0.68333, 0, 0.08334],
+        "72": [0, 0.68333, 0.08125, 0.05556],
+        "73": [0, 0.68333, 0.07847, 0.11111],
+        "74": [0, 0.68333, 0.09618, 0.16667],
+        "75": [0, 0.68333, 0.07153, 0.05556],
+        "76": [0, 0.68333, 0, 0.02778],
+        "77": [0, 0.68333, 0.10903, 0.08334],
+        "78": [0, 0.68333, 0.10903, 0.08334],
+        "79": [0, 0.68333, 0.02778, 0.08334],
+        "80": [0, 0.68333, 0.13889, 0.08334],
+        "81": [0.19444, 0.68333, 0, 0.08334],
+        "82": [0, 0.68333, 0.00773, 0.08334],
+        "83": [0, 0.68333, 0.05764, 0.08334],
+        "84": [0, 0.68333, 0.13889, 0.08334],
+        "85": [0, 0.68333, 0.10903, 0.02778],
+        "86": [0, 0.68333, 0.22222, 0],
+        "87": [0, 0.68333, 0.13889, 0],
+        "88": [0, 0.68333, 0.07847, 0.08334],
+        "89": [0, 0.68333, 0.22222, 0],
+        "90": [0, 0.68333, 0.07153, 0.08334],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.43056, 0, 0.05556],
+        "100": [0, 0.69444, 0, 0.16667],
+        "101": [0, 0.43056, 0, 0.05556],
+        "102": [0.19444, 0.69444, 0.10764, 0.16667],
+        "103": [0.19444, 0.43056, 0.03588, 0.02778],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.65952, 0, 0],
+        "106": [0.19444, 0.65952, 0.05724, 0],
+        "107": [0, 0.69444, 0.03148, 0],
+        "108": [0, 0.69444, 0.01968, 0.08334],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0.05556],
+        "112": [0.19444, 0.43056, 0, 0.08334],
+        "113": [0.19444, 0.43056, 0.03588, 0.08334],
+        "114": [0, 0.43056, 0.02778, 0.05556],
+        "115": [0, 0.43056, 0, 0.05556],
+        "116": [0, 0.61508, 0, 0.08334],
+        "117": [0, 0.43056, 0, 0.02778],
+        "118": [0, 0.43056, 0.03588, 0.02778],
+        "119": [0, 0.43056, 0.02691, 0.08334],
+        "120": [0, 0.43056, 0, 0.02778],
+        "121": [0.19444, 0.43056, 0.03588, 0.05556],
+        "122": [0, 0.43056, 0.04398, 0.05556],
+        "915": [0, 0.68333, 0.13889, 0.08334],
+        "916": [0, 0.68333, 0, 0.16667],
+        "920": [0, 0.68333, 0.02778, 0.08334],
+        "923": [0, 0.68333, 0, 0.16667],
+        "926": [0, 0.68333, 0.07569, 0.08334],
+        "928": [0, 0.68333, 0.08125, 0.05556],
+        "931": [0, 0.68333, 0.05764, 0.08334],
+        "933": [0, 0.68333, 0.13889, 0.05556],
+        "934": [0, 0.68333, 0, 0.08334],
+        "936": [0, 0.68333, 0.11, 0.05556],
+        "937": [0, 0.68333, 0.05017, 0.08334],
+        "945": [0, 0.43056, 0.0037, 0.02778],
+        "946": [0.19444, 0.69444, 0.05278, 0.08334],
+        "947": [0.19444, 0.43056, 0.05556, 0],
+        "948": [0, 0.69444, 0.03785, 0.05556],
+        "949": [0, 0.43056, 0, 0.08334],
+        "950": [0.19444, 0.69444, 0.07378, 0.08334],
+        "951": [0.19444, 0.43056, 0.03588, 0.05556],
+        "952": [0, 0.69444, 0.02778, 0.08334],
+        "953": [0, 0.43056, 0, 0.05556],
+        "954": [0, 0.43056, 0, 0],
+        "955": [0, 0.69444, 0, 0],
+        "956": [0.19444, 0.43056, 0, 0.02778],
+        "957": [0, 0.43056, 0.06366, 0.02778],
+        "958": [0.19444, 0.69444, 0.04601, 0.11111],
+        "959": [0, 0.43056, 0, 0.05556],
+        "960": [0, 0.43056, 0.03588, 0],
+        "961": [0.19444, 0.43056, 0, 0.08334],
+        "962": [0.09722, 0.43056, 0.07986, 0.08334],
+        "963": [0, 0.43056, 0.03588, 0],
+        "964": [0, 0.43056, 0.1132, 0.02778],
+        "965": [0, 0.43056, 0.03588, 0.02778],
+        "966": [0.19444, 0.43056, 0, 0.08334],
+        "967": [0.19444, 0.43056, 0, 0.05556],
+        "968": [0.19444, 0.69444, 0.03588, 0.11111],
+        "969": [0, 0.43056, 0.03588, 0],
+        "977": [0, 0.69444, 0, 0.08334],
+        "981": [0.19444, 0.69444, 0, 0.08334],
+        "982": [0, 0.43056, 0.02778, 0],
+        "1009": [0.19444, 0.43056, 0, 0.08334],
+        "1013": [0, 0.43056, 0, 0.05556]
+    },
+    "SansSerif-Regular": {
+        "33": [0, 0.69444, 0, 0],
+        "34": [0, 0.69444, 0, 0],
+        "35": [0.19444, 0.69444, 0, 0],
+        "36": [0.05556, 0.75, 0, 0],
+        "37": [0.05556, 0.75, 0, 0],
+        "38": [0, 0.69444, 0, 0],
+        "39": [0, 0.69444, 0, 0],
+        "40": [0.25, 0.75, 0, 0],
+        "41": [0.25, 0.75, 0, 0],
+        "42": [0, 0.75, 0, 0],
+        "43": [0.08333, 0.58333, 0, 0],
+        "44": [0.125, 0.08333, 0, 0],
+        "45": [0, 0.44444, 0, 0],
+        "46": [0, 0.08333, 0, 0],
+        "47": [0.25, 0.75, 0, 0],
+        "48": [0, 0.65556, 0, 0],
+        "49": [0, 0.65556, 0, 0],
+        "50": [0, 0.65556, 0, 0],
+        "51": [0, 0.65556, 0, 0],
+        "52": [0, 0.65556, 0, 0],
+        "53": [0, 0.65556, 0, 0],
+        "54": [0, 0.65556, 0, 0],
+        "55": [0, 0.65556, 0, 0],
+        "56": [0, 0.65556, 0, 0],
+        "57": [0, 0.65556, 0, 0],
+        "58": [0, 0.44444, 0, 0],
+        "59": [0.125, 0.44444, 0, 0],
+        "61": [-0.13, 0.37, 0, 0],
+        "63": [0, 0.69444, 0, 0],
+        "64": [0, 0.69444, 0, 0],
+        "65": [0, 0.69444, 0, 0],
+        "66": [0, 0.69444, 0, 0],
+        "67": [0, 0.69444, 0, 0],
+        "68": [0, 0.69444, 0, 0],
+        "69": [0, 0.69444, 0, 0],
+        "70": [0, 0.69444, 0, 0],
+        "71": [0, 0.69444, 0, 0],
+        "72": [0, 0.69444, 0, 0],
+        "73": [0, 0.69444, 0, 0],
+        "74": [0, 0.69444, 0, 0],
+        "75": [0, 0.69444, 0, 0],
+        "76": [0, 0.69444, 0, 0],
+        "77": [0, 0.69444, 0, 0],
+        "78": [0, 0.69444, 0, 0],
+        "79": [0, 0.69444, 0, 0],
+        "80": [0, 0.69444, 0, 0],
+        "81": [0.125, 0.69444, 0, 0],
+        "82": [0, 0.69444, 0, 0],
+        "83": [0, 0.69444, 0, 0],
+        "84": [0, 0.69444, 0, 0],
+        "85": [0, 0.69444, 0, 0],
+        "86": [0, 0.69444, 0.01389, 0],
+        "87": [0, 0.69444, 0.01389, 0],
+        "88": [0, 0.69444, 0, 0],
+        "89": [0, 0.69444, 0.025, 0],
+        "90": [0, 0.69444, 0, 0],
+        "91": [0.25, 0.75, 0, 0],
+        "93": [0.25, 0.75, 0, 0],
+        "94": [0, 0.69444, 0, 0],
+        "95": [0.35, 0.09444, 0.02778, 0],
+        "97": [0, 0.44444, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.44444, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.44444, 0, 0],
+        "102": [0, 0.69444, 0.06944, 0],
+        "103": [0.19444, 0.44444, 0.01389, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.67937, 0, 0],
+        "106": [0.19444, 0.67937, 0, 0],
+        "107": [0, 0.69444, 0, 0],
+        "108": [0, 0.69444, 0, 0],
+        "109": [0, 0.44444, 0, 0],
+        "110": [0, 0.44444, 0, 0],
+        "111": [0, 0.44444, 0, 0],
+        "112": [0.19444, 0.44444, 0, 0],
+        "113": [0.19444, 0.44444, 0, 0],
+        "114": [0, 0.44444, 0.01389, 0],
+        "115": [0, 0.44444, 0, 0],
+        "116": [0, 0.57143, 0, 0],
+        "117": [0, 0.44444, 0, 0],
+        "118": [0, 0.44444, 0.01389, 0],
+        "119": [0, 0.44444, 0.01389, 0],
+        "120": [0, 0.44444, 0, 0],
+        "121": [0.19444, 0.44444, 0.01389, 0],
+        "122": [0, 0.44444, 0, 0],
+        "126": [0.35, 0.32659, 0, 0],
+        "305": [0, 0.44444, 0, 0],
+        "567": [0.19444, 0.44444, 0, 0],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0, 0],
+        "770": [0, 0.69444, 0, 0],
+        "771": [0, 0.67659, 0, 0],
+        "772": [0, 0.60889, 0, 0],
+        "774": [0, 0.69444, 0, 0],
+        "775": [0, 0.67937, 0, 0],
+        "776": [0, 0.67937, 0, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0, 0],
+        "780": [0, 0.63194, 0, 0],
+        "915": [0, 0.69444, 0, 0],
+        "916": [0, 0.69444, 0, 0],
+        "920": [0, 0.69444, 0, 0],
+        "923": [0, 0.69444, 0, 0],
+        "926": [0, 0.69444, 0, 0],
+        "928": [0, 0.69444, 0, 0],
+        "931": [0, 0.69444, 0, 0],
+        "933": [0, 0.69444, 0, 0],
+        "934": [0, 0.69444, 0, 0],
+        "936": [0, 0.69444, 0, 0],
+        "937": [0, 0.69444, 0, 0],
+        "8211": [0, 0.44444, 0.02778, 0],
+        "8212": [0, 0.44444, 0.02778, 0],
+        "8216": [0, 0.69444, 0, 0],
+        "8217": [0, 0.69444, 0, 0],
+        "8220": [0, 0.69444, 0, 0],
+        "8221": [0, 0.69444, 0, 0]
+    },
+    "Script-Regular": {
+        "65": [0, 0.7, 0.22925, 0],
+        "66": [0, 0.7, 0.04087, 0],
+        "67": [0, 0.7, 0.1689, 0],
+        "68": [0, 0.7, 0.09371, 0],
+        "69": [0, 0.7, 0.18583, 0],
+        "70": [0, 0.7, 0.13634, 0],
+        "71": [0, 0.7, 0.17322, 0],
+        "72": [0, 0.7, 0.29694, 0],
+        "73": [0, 0.7, 0.19189, 0],
+        "74": [0.27778, 0.7, 0.19189, 0],
+        "75": [0, 0.7, 0.31259, 0],
+        "76": [0, 0.7, 0.19189, 0],
+        "77": [0, 0.7, 0.15981, 0],
+        "78": [0, 0.7, 0.3525, 0],
+        "79": [0, 0.7, 0.08078, 0],
+        "80": [0, 0.7, 0.08078, 0],
+        "81": [0, 0.7, 0.03305, 0],
+        "82": [0, 0.7, 0.06259, 0],
+        "83": [0, 0.7, 0.19189, 0],
+        "84": [0, 0.7, 0.29087, 0],
+        "85": [0, 0.7, 0.25815, 0],
+        "86": [0, 0.7, 0.27523, 0],
+        "87": [0, 0.7, 0.27523, 0],
+        "88": [0, 0.7, 0.26006, 0],
+        "89": [0, 0.7, 0.2939, 0],
+        "90": [0, 0.7, 0.24037, 0]
+    },
+    "Size1-Regular": {
+        "40": [0.35001, 0.85, 0, 0],
+        "41": [0.35001, 0.85, 0, 0],
+        "47": [0.35001, 0.85, 0, 0],
+        "91": [0.35001, 0.85, 0, 0],
+        "92": [0.35001, 0.85, 0, 0],
+        "93": [0.35001, 0.85, 0, 0],
+        "123": [0.35001, 0.85, 0, 0],
+        "125": [0.35001, 0.85, 0, 0],
+        "710": [0, 0.72222, 0, 0],
+        "732": [0, 0.72222, 0, 0],
+        "770": [0, 0.72222, 0, 0],
+        "771": [0, 0.72222, 0, 0],
+        "8214": [-0.00099, 0.601, 0, 0],
+        "8593": [1e-05, 0.6, 0, 0],
+        "8595": [1e-05, 0.6, 0, 0],
+        "8657": [1e-05, 0.6, 0, 0],
+        "8659": [1e-05, 0.6, 0, 0],
+        "8719": [0.25001, 0.75, 0, 0],
+        "8720": [0.25001, 0.75, 0, 0],
+        "8721": [0.25001, 0.75, 0, 0],
+        "8730": [0.35001, 0.85, 0, 0],
+        "8739": [-0.00599, 0.606, 0, 0],
+        "8741": [-0.00599, 0.606, 0, 0],
+        "8747": [0.30612, 0.805, 0.19445, 0],
+        "8748": [0.306, 0.805, 0.19445, 0],
+        "8749": [0.306, 0.805, 0.19445, 0],
+        "8750": [0.30612, 0.805, 0.19445, 0],
+        "8896": [0.25001, 0.75, 0, 0],
+        "8897": [0.25001, 0.75, 0, 0],
+        "8898": [0.25001, 0.75, 0, 0],
+        "8899": [0.25001, 0.75, 0, 0],
+        "8968": [0.35001, 0.85, 0, 0],
+        "8969": [0.35001, 0.85, 0, 0],
+        "8970": [0.35001, 0.85, 0, 0],
+        "8971": [0.35001, 0.85, 0, 0],
+        "9168": [-0.00099, 0.601, 0, 0],
+        "10216": [0.35001, 0.85, 0, 0],
+        "10217": [0.35001, 0.85, 0, 0],
+        "10752": [0.25001, 0.75, 0, 0],
+        "10753": [0.25001, 0.75, 0, 0],
+        "10754": [0.25001, 0.75, 0, 0],
+        "10756": [0.25001, 0.75, 0, 0],
+        "10758": [0.25001, 0.75, 0, 0]
+    },
+    "Size2-Regular": {
+        "40": [0.65002, 1.15, 0, 0],
+        "41": [0.65002, 1.15, 0, 0],
+        "47": [0.65002, 1.15, 0, 0],
+        "91": [0.65002, 1.15, 0, 0],
+        "92": [0.65002, 1.15, 0, 0],
+        "93": [0.65002, 1.15, 0, 0],
+        "123": [0.65002, 1.15, 0, 0],
+        "125": [0.65002, 1.15, 0, 0],
+        "710": [0, 0.75, 0, 0],
+        "732": [0, 0.75, 0, 0],
+        "770": [0, 0.75, 0, 0],
+        "771": [0, 0.75, 0, 0],
+        "8719": [0.55001, 1.05, 0, 0],
+        "8720": [0.55001, 1.05, 0, 0],
+        "8721": [0.55001, 1.05, 0, 0],
+        "8730": [0.65002, 1.15, 0, 0],
+        "8747": [0.86225, 1.36, 0.44445, 0],
+        "8748": [0.862, 1.36, 0.44445, 0],
+        "8749": [0.862, 1.36, 0.44445, 0],
+        "8750": [0.86225, 1.36, 0.44445, 0],
+        "8896": [0.55001, 1.05, 0, 0],
+        "8897": [0.55001, 1.05, 0, 0],
+        "8898": [0.55001, 1.05, 0, 0],
+        "8899": [0.55001, 1.05, 0, 0],
+        "8968": [0.65002, 1.15, 0, 0],
+        "8969": [0.65002, 1.15, 0, 0],
+        "8970": [0.65002, 1.15, 0, 0],
+        "8971": [0.65002, 1.15, 0, 0],
+        "10216": [0.65002, 1.15, 0, 0],
+        "10217": [0.65002, 1.15, 0, 0],
+        "10752": [0.55001, 1.05, 0, 0],
+        "10753": [0.55001, 1.05, 0, 0],
+        "10754": [0.55001, 1.05, 0, 0],
+        "10756": [0.55001, 1.05, 0, 0],
+        "10758": [0.55001, 1.05, 0, 0]
+    },
+    "Size3-Regular": {
+        "40": [0.95003, 1.45, 0, 0],
+        "41": [0.95003, 1.45, 0, 0],
+        "47": [0.95003, 1.45, 0, 0],
+        "91": [0.95003, 1.45, 0, 0],
+        "92": [0.95003, 1.45, 0, 0],
+        "93": [0.95003, 1.45, 0, 0],
+        "123": [0.95003, 1.45, 0, 0],
+        "125": [0.95003, 1.45, 0, 0],
+        "710": [0, 0.75, 0, 0],
+        "732": [0, 0.75, 0, 0],
+        "770": [0, 0.75, 0, 0],
+        "771": [0, 0.75, 0, 0],
+        "8730": [0.95003, 1.45, 0, 0],
+        "8968": [0.95003, 1.45, 0, 0],
+        "8969": [0.95003, 1.45, 0, 0],
+        "8970": [0.95003, 1.45, 0, 0],
+        "8971": [0.95003, 1.45, 0, 0],
+        "10216": [0.95003, 1.45, 0, 0],
+        "10217": [0.95003, 1.45, 0, 0]
+    },
+    "Size4-Regular": {
+        "40": [1.25003, 1.75, 0, 0],
+        "41": [1.25003, 1.75, 0, 0],
+        "47": [1.25003, 1.75, 0, 0],
+        "91": [1.25003, 1.75, 0, 0],
+        "92": [1.25003, 1.75, 0, 0],
+        "93": [1.25003, 1.75, 0, 0],
+        "123": [1.25003, 1.75, 0, 0],
+        "125": [1.25003, 1.75, 0, 0],
+        "710": [0, 0.825, 0, 0],
+        "732": [0, 0.825, 0, 0],
+        "770": [0, 0.825, 0, 0],
+        "771": [0, 0.825, 0, 0],
+        "8730": [1.25003, 1.75, 0, 0],
+        "8968": [1.25003, 1.75, 0, 0],
+        "8969": [1.25003, 1.75, 0, 0],
+        "8970": [1.25003, 1.75, 0, 0],
+        "8971": [1.25003, 1.75, 0, 0],
+        "9115": [0.64502, 1.155, 0, 0],
+        "9116": [1e-05, 0.6, 0, 0],
+        "9117": [0.64502, 1.155, 0, 0],
+        "9118": [0.64502, 1.155, 0, 0],
+        "9119": [1e-05, 0.6, 0, 0],
+        "9120": [0.64502, 1.155, 0, 0],
+        "9121": [0.64502, 1.155, 0, 0],
+        "9122": [-0.00099, 0.601, 0, 0],
+        "9123": [0.64502, 1.155, 0, 0],
+        "9124": [0.64502, 1.155, 0, 0],
+        "9125": [-0.00099, 0.601, 0, 0],
+        "9126": [0.64502, 1.155, 0, 0],
+        "9127": [1e-05, 0.9, 0, 0],
+        "9128": [0.65002, 1.15, 0, 0],
+        "9129": [0.90001, 0, 0, 0],
+        "9130": [0, 0.3, 0, 0],
+        "9131": [1e-05, 0.9, 0, 0],
+        "9132": [0.65002, 1.15, 0, 0],
+        "9133": [0.90001, 0, 0, 0],
+        "9143": [0.88502, 0.915, 0, 0],
+        "10216": [1.25003, 1.75, 0, 0],
+        "10217": [1.25003, 1.75, 0, 0],
+        "57344": [-0.00499, 0.605, 0, 0],
+        "57345": [-0.00499, 0.605, 0, 0],
+        "57680": [0, 0.12, 0, 0],
+        "57681": [0, 0.12, 0, 0],
+        "57682": [0, 0.12, 0, 0],
+        "57683": [0, 0.12, 0, 0]
+    },
+    "Typewriter-Regular": {
+        "33": [0, 0.61111, 0, 0],
+        "34": [0, 0.61111, 0, 0],
+        "35": [0, 0.61111, 0, 0],
+        "36": [0.08333, 0.69444, 0, 0],
+        "37": [0.08333, 0.69444, 0, 0],
+        "38": [0, 0.61111, 0, 0],
+        "39": [0, 0.61111, 0, 0],
+        "40": [0.08333, 0.69444, 0, 0],
+        "41": [0.08333, 0.69444, 0, 0],
+        "42": [0, 0.52083, 0, 0],
+        "43": [-0.08056, 0.53055, 0, 0],
+        "44": [0.13889, 0.125, 0, 0],
+        "45": [-0.08056, 0.53055, 0, 0],
+        "46": [0, 0.125, 0, 0],
+        "47": [0.08333, 0.69444, 0, 0],
+        "48": [0, 0.61111, 0, 0],
+        "49": [0, 0.61111, 0, 0],
+        "50": [0, 0.61111, 0, 0],
+        "51": [0, 0.61111, 0, 0],
+        "52": [0, 0.61111, 0, 0],
+        "53": [0, 0.61111, 0, 0],
+        "54": [0, 0.61111, 0, 0],
+        "55": [0, 0.61111, 0, 0],
+        "56": [0, 0.61111, 0, 0],
+        "57": [0, 0.61111, 0, 0],
+        "58": [0, 0.43056, 0, 0],
+        "59": [0.13889, 0.43056, 0, 0],
+        "60": [-0.05556, 0.55556, 0, 0],
+        "61": [-0.19549, 0.41562, 0, 0],
+        "62": [-0.05556, 0.55556, 0, 0],
+        "63": [0, 0.61111, 0, 0],
+        "64": [0, 0.61111, 0, 0],
+        "65": [0, 0.61111, 0, 0],
+        "66": [0, 0.61111, 0, 0],
+        "67": [0, 0.61111, 0, 0],
+        "68": [0, 0.61111, 0, 0],
+        "69": [0, 0.61111, 0, 0],
+        "70": [0, 0.61111, 0, 0],
+        "71": [0, 0.61111, 0, 0],
+        "72": [0, 0.61111, 0, 0],
+        "73": [0, 0.61111, 0, 0],
+        "74": [0, 0.61111, 0, 0],
+        "75": [0, 0.61111, 0, 0],
+        "76": [0, 0.61111, 0, 0],
+        "77": [0, 0.61111, 0, 0],
+        "78": [0, 0.61111, 0, 0],
+        "79": [0, 0.61111, 0, 0],
+        "80": [0, 0.61111, 0, 0],
+        "81": [0.13889, 0.61111, 0, 0],
+        "82": [0, 0.61111, 0, 0],
+        "83": [0, 0.61111, 0, 0],
+        "84": [0, 0.61111, 0, 0],
+        "85": [0, 0.61111, 0, 0],
+        "86": [0, 0.61111, 0, 0],
+        "87": [0, 0.61111, 0, 0],
+        "88": [0, 0.61111, 0, 0],
+        "89": [0, 0.61111, 0, 0],
+        "90": [0, 0.61111, 0, 0],
+        "91": [0.08333, 0.69444, 0, 0],
+        "92": [0.08333, 0.69444, 0, 0],
+        "93": [0.08333, 0.69444, 0, 0],
+        "94": [0, 0.61111, 0, 0],
+        "95": [0.09514, 0, 0, 0],
+        "96": [0, 0.61111, 0, 0],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.61111, 0, 0],
+        "99": [0, 0.43056, 0, 0],
+        "100": [0, 0.61111, 0, 0],
+        "101": [0, 0.43056, 0, 0],
+        "102": [0, 0.61111, 0, 0],
+        "103": [0.22222, 0.43056, 0, 0],
+        "104": [0, 0.61111, 0, 0],
+        "105": [0, 0.61111, 0, 0],
+        "106": [0.22222, 0.61111, 0, 0],
+        "107": [0, 0.61111, 0, 0],
+        "108": [0, 0.61111, 0, 0],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0],
+        "112": [0.22222, 0.43056, 0, 0],
+        "113": [0.22222, 0.43056, 0, 0],
+        "114": [0, 0.43056, 0, 0],
+        "115": [0, 0.43056, 0, 0],
+        "116": [0, 0.55358, 0, 0],
+        "117": [0, 0.43056, 0, 0],
+        "118": [0, 0.43056, 0, 0],
+        "119": [0, 0.43056, 0, 0],
+        "120": [0, 0.43056, 0, 0],
+        "121": [0.22222, 0.43056, 0, 0],
+        "122": [0, 0.43056, 0, 0],
+        "123": [0.08333, 0.69444, 0, 0],
+        "124": [0.08333, 0.69444, 0, 0],
+        "125": [0.08333, 0.69444, 0, 0],
+        "126": [0, 0.61111, 0, 0],
+        "127": [0, 0.61111, 0, 0],
+        "305": [0, 0.43056, 0, 0],
+        "567": [0.22222, 0.43056, 0, 0],
+        "768": [0, 0.61111, 0, 0],
+        "769": [0, 0.61111, 0, 0],
+        "770": [0, 0.61111, 0, 0],
+        "771": [0, 0.61111, 0, 0],
+        "772": [0, 0.56555, 0, 0],
+        "774": [0, 0.61111, 0, 0],
+        "776": [0, 0.61111, 0, 0],
+        "778": [0, 0.61111, 0, 0],
+        "780": [0, 0.56597, 0, 0],
+        "915": [0, 0.61111, 0, 0],
+        "916": [0, 0.61111, 0, 0],
+        "920": [0, 0.61111, 0, 0],
+        "923": [0, 0.61111, 0, 0],
+        "926": [0, 0.61111, 0, 0],
+        "928": [0, 0.61111, 0, 0],
+        "931": [0, 0.61111, 0, 0],
+        "933": [0, 0.61111, 0, 0],
+        "934": [0, 0.61111, 0, 0],
+        "936": [0, 0.61111, 0, 0],
+        "937": [0, 0.61111, 0, 0],
+        "2018": [0, 0.61111, 0, 0],
+        "2019": [0, 0.61111, 0, 0],
+        "8242": [0, 0.61111, 0, 0]
+    }
+};
+
+},{}],19:[function(require,module,exports){
+var utils = require("./utils");
+var ParseError = require("./ParseError");
+var parseData = require("./parseData");
+var ParseNode = parseData.ParseNode;
+
+/* This file contains a list of functions that we parse, identified by
+ * the calls to defineFunction.
+ *
+ * The first argument to defineFunction is a single name or a list of names.
+ * All functions named in such a list will share a single implementation.
+ *
+ * Each declared function can have associated properties, which
+ * include the following:
+ *
+ *  - numArgs: The number of arguments the function takes.
+ *             If this is the only property, it can be passed as a number
+ *             instead of an element of a properties object.
+ *  - argTypes: (optional) An array corresponding to each argument of the
+ *              function, giving the type of argument that should be parsed. Its
+ *              length should be equal to `numArgs + numOptionalArgs`. Valid
+ *              types:
+ *               - "size": A size-like thing, such as "1em" or "5ex"
+ *               - "color": An html color, like "#abc" or "blue"
+ *               - "original": The same type as the environment that the
+ *                             function being parsed is in (e.g. used for the
+ *                             bodies of functions like \color where the first
+ *                             argument is special and the second argument is
+ *                             parsed normally)
+ *              Other possible types (probably shouldn't be used)
+ *               - "text": Text-like (e.g. \text)
+ *               - "math": Normal math
+ *              If undefined, this will be treated as an appropriate length
+ *              array of "original" strings
+ *  - greediness: (optional) The greediness of the function to use ungrouped
+ *                arguments.
+ *
+ *                E.g. if you have an expression
+ *                  \sqrt \frac 1 2
+ *                since \frac has greediness=2 vs \sqrt's greediness=1, \frac
+ *                will use the two arguments '1' and '2' as its two arguments,
+ *                then that whole function will be used as the argument to
+ *                \sqrt. On the other hand, the expressions
+ *                  \frac \frac 1 2 3
+ *                and
+ *                  \frac \sqrt 1 2
+ *                will fail because \frac and \frac have equal greediness
+ *                and \sqrt has a lower greediness than \frac respectively. To
+ *                make these parse, we would have to change them to:
+ *                  \frac {\frac 1 2} 3
+ *                and
+ *                  \frac {\sqrt 1} 2
+ *
+ *                The default value is `1`
+ *  - allowedInText: (optional) Whether or not the function is allowed inside
+ *                   text mode (default false)
+ *  - numOptionalArgs: (optional) The number of optional arguments the function
+ *                     should parse. If the optional arguments aren't found,
+ *                     `null` will be passed to the handler in their place.
+ *                     (default 0)
+ *  - infix: (optional) Must be true if the function is an infix operator.
+ *
+ * The last argument is that implementation, the handler for the function(s).
+ * It is called to handle these functions and their arguments.
+ * It receives two arguments:
+ *  - context contains information and references provided by the parser
+ *  - args is an array of arguments obtained from TeX input
+ * The context contains the following properties:
+ *  - funcName: the text (i.e. name) of the function, including \
+ *  - parser: the parser object
+ *  - lexer: the lexer object
+ *  - positions: the positions in the overall string of the function
+ *               and the arguments.
+ * The latter three should only be used to produce error messages.
+ *
+ * The function should return an object with the following keys:
+ *  - type: The type of element that this is. This is then used in
+ *          buildHTML/buildMathML to determine which function
+ *          should be called to build this node into a DOM node
+ * Any other data can be added to the object, which will be passed
+ * in to the function in buildHTML/buildMathML as `group.value`.
+ */
+
+function defineFunction(names, props, handler) {
+    if (typeof names === "string") {
+        names = [names];
+    }
+    if (typeof props === "number") {
+        props = { numArgs: props };
+    }
+    // Set default values of functions
+    var data = {
+        numArgs: props.numArgs,
+        argTypes: props.argTypes,
+        greediness: (props.greediness === undefined) ? 1 : props.greediness,
+        allowedInText: !!props.allowedInText,
+        numOptionalArgs: props.numOptionalArgs || 0,
+        infix: !!props.infix,
+        handler: handler
+    };
+    for (var i = 0; i < names.length; ++i) {
+        module.exports[names[i]] = data;
+    }
+}
+
+// Since the corresponding buildHTML/buildMathML function expects a
+// list of elements, we normalize for different kinds of arguments
+var ordargument = function(arg) {
+    if (arg.type === "ordgroup") {
+        return arg.value;
+    } else {
+        return [arg];
+    }
+};
+
+// A normal square root
+defineFunction("\\sqrt", {
+    numArgs: 1,
+    numOptionalArgs: 1
+}, function(context, args) {
+    var index = args[0];
+    var body = args[1];
+    return {
+        type: "sqrt",
+        body: body,
+        index: index
+    };
+});
+
+// Non-mathy text, possibly in a font
+var textFunctionStyles = {
+    "\\text": undefined, "\\textrm": "mathrm", "\\textsf": "mathsf",
+    "\\texttt": "mathtt", "\\textnormal": "mathrm", "\\textbf": "mathbf",
+    "\\textit": "textit"
+};
+
+defineFunction([
+    "\\text", "\\textrm", "\\textsf", "\\texttt", "\\textnormal",
+    "\\textbf", "\\textit"
+], {
+    numArgs: 1,
+    argTypes: ["text"],
+    greediness: 2,
+    allowedInText: true
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "text",
+        body: ordargument(body),
+        style: textFunctionStyles[context.funcName]
+    };
+});
+
+// A two-argument custom color
+defineFunction("\\color", {
+    numArgs: 2,
+    allowedInText: true,
+    greediness: 3,
+    argTypes: ["color", "original"]
+}, function(context, args) {
+    var color = args[0];
+    var body = args[1];
+    return {
+        type: "color",
+        color: color.value,
+        value: ordargument(body)
+    };
+});
+
+// An overline
+defineFunction("\\overline", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "overline",
+        body: body
+    };
+});
+
+// An underline
+defineFunction("\\underline", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "underline",
+        body: body
+    };
+});
+
+// A box of the width and height
+defineFunction("\\rule", {
+    numArgs: 2,
+    numOptionalArgs: 1,
+    argTypes: ["size", "size", "size"]
+}, function(context, args) {
+    var shift = args[0];
+    var width = args[1];
+    var height = args[2];
+    return {
+        type: "rule",
+        shift: shift && shift.value,
+        width: width.value,
+        height: height.value
+    };
+});
+
+// TODO: In TeX, \mkern only accepts mu-units, and \kern does not accept
+// mu-units. In current KaTeX we relax this; both commands accept any unit.
+defineFunction(["\\kern", "\\mkern"], {
+    numArgs: 1,
+    argTypes: ["size"]
+}, function(context, args) {
+    return {
+        type: "kern",
+        dimension: args[0].value
+    };
+});
+
+// A KaTeX logo
+defineFunction("\\KaTeX", {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "katex"
+    };
+});
+
+defineFunction("\\phantom", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "phantom",
+        value: ordargument(body)
+    };
+});
+
+// Math class commands except \mathop
+defineFunction([
+    "\\mathord", "\\mathbin", "\\mathrel", "\\mathopen",
+    "\\mathclose", "\\mathpunct", "\\mathinner"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "mclass",
+        mclass: "m" + context.funcName.substr(5),
+        value: ordargument(body)
+    };
+});
+
+// Build a relation by placing one symbol on top of another
+defineFunction("\\stackrel", {
+    numArgs: 2
+}, function(context, args) {
+    var top = args[0];
+    var bottom = args[1];
+
+    var bottomop = new ParseNode("op", {
+        type: "op",
+        limits: true,
+        alwaysHandleSupSub: true,
+        symbol: false,
+        value: ordargument(bottom)
+    }, bottom.mode);
+
+    var supsub = new ParseNode("supsub", {
+        base: bottomop,
+        sup: top,
+        sub: null
+    }, top.mode);
+
+    return {
+        type: "mclass",
+        mclass: "mrel",
+        value: [supsub]
+    };
+});
+
+// \mod-type functions
+defineFunction("\\bmod", {
+    numArgs: 0
+}, function(context, args) {
+    return {
+        type: "mod",
+        modType: "bmod",
+        value: null
+    };
+});
+
+defineFunction(["\\pod", "\\pmod", "\\mod"], {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "mod",
+        modType: context.funcName.substr(1),
+        value: ordargument(body)
+    };
+});
+
+// Extra data needed for the delimiter handler down below
+var delimiterSizes = {
+    "\\bigl" : {mclass: "mopen",    size: 1},
+    "\\Bigl" : {mclass: "mopen",    size: 2},
+    "\\biggl": {mclass: "mopen",    size: 3},
+    "\\Biggl": {mclass: "mopen",    size: 4},
+    "\\bigr" : {mclass: "mclose",   size: 1},
+    "\\Bigr" : {mclass: "mclose",   size: 2},
+    "\\biggr": {mclass: "mclose",   size: 3},
+    "\\Biggr": {mclass: "mclose",   size: 4},
+    "\\bigm" : {mclass: "mrel",     size: 1},
+    "\\Bigm" : {mclass: "mrel",     size: 2},
+    "\\biggm": {mclass: "mrel",     size: 3},
+    "\\Biggm": {mclass: "mrel",     size: 4},
+    "\\big"  : {mclass: "mord",     size: 1},
+    "\\Big"  : {mclass: "mord",     size: 2},
+    "\\bigg" : {mclass: "mord",     size: 3},
+    "\\Bigg" : {mclass: "mord",     size: 4}
+};
+
+var delimiters = [
+    "(", ")", "[", "\\lbrack", "]", "\\rbrack",
+    "\\{", "\\lbrace", "\\}", "\\rbrace",
+    "\\lfloor", "\\rfloor", "\\lceil", "\\rceil",
+    "<", ">", "\\langle", "\\rangle", "\\lt", "\\gt",
+    "\\lvert", "\\rvert", "\\lVert", "\\rVert",
+    "\\lgroup", "\\rgroup", "\\lmoustache", "\\rmoustache",
+    "/", "\\backslash",
+    "|", "\\vert", "\\|", "\\Vert",
+    "\\uparrow", "\\Uparrow",
+    "\\downarrow", "\\Downarrow",
+    "\\updownarrow", "\\Updownarrow",
+    "."
+];
+
+var fontAliases = {
+    "\\Bbb": "\\mathbb",
+    "\\bold": "\\mathbf",
+    "\\frak": "\\mathfrak"
+};
+
+// Single-argument color functions
+defineFunction([
+    "\\blue", "\\orange", "\\pink", "\\red",
+    "\\green", "\\gray", "\\purple",
+    "\\blueA", "\\blueB", "\\blueC", "\\blueD", "\\blueE",
+    "\\tealA", "\\tealB", "\\tealC", "\\tealD", "\\tealE",
+    "\\greenA", "\\greenB", "\\greenC", "\\greenD", "\\greenE",
+    "\\goldA", "\\goldB", "\\goldC", "\\goldD", "\\goldE",
+    "\\redA", "\\redB", "\\redC", "\\redD", "\\redE",
+    "\\maroonA", "\\maroonB", "\\maroonC", "\\maroonD", "\\maroonE",
+    "\\purpleA", "\\purpleB", "\\purpleC", "\\purpleD", "\\purpleE",
+    "\\mintA", "\\mintB", "\\mintC",
+    "\\grayA", "\\grayB", "\\grayC", "\\grayD", "\\grayE",
+    "\\grayF", "\\grayG", "\\grayH", "\\grayI",
+    "\\kaBlue", "\\kaGreen"
+], {
+    numArgs: 1,
+    allowedInText: true,
+    greediness: 3
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "color",
+        color: "katex-" + context.funcName.slice(1),
+        value: ordargument(body)
+    };
+});
+
+// There are 2 flags for operators; whether they produce limits in
+// displaystyle, and whether they are symbols and should grow in
+// displaystyle. These four groups cover the four possible choices.
+
+// No limits, not symbols
+defineFunction([
+    "\\arcsin", "\\arccos", "\\arctan", "\\arg", "\\cos", "\\cosh",
+    "\\cot", "\\coth", "\\csc", "\\deg", "\\dim", "\\exp", "\\hom",
+    "\\ker", "\\lg", "\\ln", "\\log", "\\sec", "\\sin", "\\sinh",
+    "\\tan", "\\tanh"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: false,
+        symbol: false,
+        body: context.funcName
+    };
+});
+
+// Limits, not symbols
+defineFunction([
+    "\\det", "\\gcd", "\\inf", "\\lim", "\\liminf", "\\limsup", "\\max",
+    "\\min", "\\Pr", "\\sup"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: true,
+        symbol: false,
+        body: context.funcName
+    };
+});
+
+// No limits, symbols
+defineFunction([
+    "\\int", "\\iint", "\\iiint", "\\oint"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: false,
+        symbol: true,
+        body: context.funcName
+    };
+});
+
+// Limits, symbols
+defineFunction([
+    "\\coprod", "\\bigvee", "\\bigwedge", "\\biguplus", "\\bigcap",
+    "\\bigcup", "\\intop", "\\prod", "\\sum", "\\bigotimes",
+    "\\bigoplus", "\\bigodot", "\\bigsqcup", "\\smallint"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: true,
+        symbol: true,
+        body: context.funcName
+    };
+});
+
+// \mathop class command
+defineFunction("\\mathop", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "op",
+        limits: false,
+        symbol: false,
+        value: ordargument(body)
+    };
+});
+
+// Fractions
+defineFunction([
+    "\\dfrac", "\\frac", "\\tfrac",
+    "\\dbinom", "\\binom", "\\tbinom",
+    "\\\\atopfrac" // can’t be entered directly
+], {
+    numArgs: 2,
+    greediness: 2
+}, function(context, args) {
+    var numer = args[0];
+    var denom = args[1];
+    var hasBarLine;
+    var leftDelim = null;
+    var rightDelim = null;
+    var size = "auto";
+
+    switch (context.funcName) {
+        case "\\dfrac":
+        case "\\frac":
+        case "\\tfrac":
+            hasBarLine = true;
+            break;
+        case "\\\\atopfrac":
+            hasBarLine = false;
+            break;
+        case "\\dbinom":
+        case "\\binom":
+        case "\\tbinom":
+            hasBarLine = false;
+            leftDelim = "(";
+            rightDelim = ")";
+            break;
+        default:
+            throw new Error("Unrecognized genfrac command");
+    }
+
+    switch (context.funcName) {
+        case "\\dfrac":
+        case "\\dbinom":
+            size = "display";
+            break;
+        case "\\tfrac":
+        case "\\tbinom":
+            size = "text";
+            break;
+    }
+
+    return {
+        type: "genfrac",
+        numer: numer,
+        denom: denom,
+        hasBarLine: hasBarLine,
+        leftDelim: leftDelim,
+        rightDelim: rightDelim,
+        size: size
+    };
+});
+
+// Left and right overlap functions
+defineFunction(["\\llap", "\\rlap"], {
+    numArgs: 1,
+    allowedInText: true
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: context.funcName.slice(1),
+        body: body
+    };
+});
+
+// Delimiter functions
+var checkDelimiter = function(delim, context) {
+    if (utils.contains(delimiters, delim.value)) {
+        return delim;
+    } else {
+        throw new ParseError(
+            "Invalid delimiter: '" + delim.value + "' after '" +
+            context.funcName + "'", delim);
+    }
+};
+
+defineFunction([
+    "\\bigl", "\\Bigl", "\\biggl", "\\Biggl",
+    "\\bigr", "\\Bigr", "\\biggr", "\\Biggr",
+    "\\bigm", "\\Bigm", "\\biggm", "\\Biggm",
+    "\\big",  "\\Big",  "\\bigg",  "\\Bigg"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var delim = checkDelimiter(args[0], context);
+
+    return {
+        type: "delimsizing",
+        size: delimiterSizes[context.funcName].size,
+        mclass: delimiterSizes[context.funcName].mclass,
+        value: delim.value
+    };
+});
+
+defineFunction([
+    "\\left", "\\right"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var delim = checkDelimiter(args[0], context);
+
+    // \left and \right are caught somewhere in Parser.js, which is
+    // why this data doesn't match what is in buildHTML.
+    return {
+        type: "leftright",
+        value: delim.value
+    };
+});
+
+defineFunction("\\middle", {
+    numArgs: 1
+}, function(context, args) {
+    var delim = checkDelimiter(args[0], context);
+    if (!context.parser.leftrightDepth) {
+        throw new ParseError("\\middle without preceding \\left", delim);
+    }
+
+    return {
+        type: "middle",
+        value: delim.value
+    };
+});
+
+// Sizing functions (handled in Parser.js explicitly, hence no handler)
+defineFunction([
+    "\\tiny", "\\scriptsize", "\\footnotesize", "\\small",
+    "\\normalsize", "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"
+], 0, null);
+
+// Style changing functions (handled in Parser.js explicitly, hence no
+// handler)
+defineFunction([
+    "\\displaystyle", "\\textstyle", "\\scriptstyle",
+    "\\scriptscriptstyle"
+], 0, null);
+
+defineFunction([
+    // styles
+    "\\mathrm", "\\mathit", "\\mathbf",
+
+    // families
+    "\\mathbb", "\\mathcal", "\\mathfrak", "\\mathscr", "\\mathsf",
+    "\\mathtt",
+
+    // aliases
+    "\\Bbb", "\\bold", "\\frak"
+], {
+    numArgs: 1,
+    greediness: 2
+}, function(context, args) {
+    var body = args[0];
+    var func = context.funcName;
+    if (func in fontAliases) {
+        func = fontAliases[func];
+    }
+    return {
+        type: "font",
+        font: func.slice(1),
+        body: body
+    };
+});
+
+// Accents
+defineFunction([
+    "\\acute", "\\grave", "\\ddot", "\\tilde", "\\bar", "\\breve",
+    "\\check", "\\hat", "\\vec", "\\dot"
+    // We don't support expanding accents yet
+    // "\\widetilde", "\\widehat"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var base = args[0];
+    return {
+        type: "accent",
+        accent: context.funcName,
+        base: base
+    };
+});
+
+// Infix generalized fractions
+defineFunction(["\\over", "\\choose", "\\atop"], {
+    numArgs: 0,
+    infix: true
+}, function(context) {
+    var replaceWith;
+    switch (context.funcName) {
+        case "\\over":
+            replaceWith = "\\frac";
+            break;
+        case "\\choose":
+            replaceWith = "\\binom";
+            break;
+        case "\\atop":
+            replaceWith = "\\\\atopfrac";
+            break;
+        default:
+            throw new Error("Unrecognized infix genfrac command");
+    }
+    return {
+        type: "infix",
+        replaceWith: replaceWith,
+        token: context.token
+    };
+});
+
+// Row breaks for aligned data
+defineFunction(["\\\\", "\\cr"], {
+    numArgs: 0,
+    numOptionalArgs: 1,
+    argTypes: ["size"]
+}, function(context, args) {
+    var size = args[0];
+    return {
+        type: "cr",
+        size: size
+    };
+});
+
+// Environment delimiters
+defineFunction(["\\begin", "\\end"], {
+    numArgs: 1,
+    argTypes: ["text"]
+}, function(context, args) {
+    var nameGroup = args[0];
+    if (nameGroup.type !== "ordgroup") {
+        throw new ParseError("Invalid environment name", nameGroup);
+    }
+    var name = "";
+    for (var i = 0; i < nameGroup.value.length; ++i) {
+        name += nameGroup.value[i].value;
+    }
+    return {
+        type: "environment",
+        name: name,
+        nameGroup: nameGroup
+    };
+});
+
+},{"./ParseError":6,"./parseData":21,"./utils":25}],20:[function(require,module,exports){
+/**
+ * These objects store data about MathML nodes. This is the MathML equivalent
+ * of the types in domTree.js. Since MathML handles its own rendering, and
+ * since we're mainly using MathML to improve accessibility, we don't manage
+ * any of the styling state that the plain DOM nodes do.
+ *
+ * The `toNode` and `toMarkup` functions work simlarly to how they do in
+ * domTree.js, creating namespaced DOM nodes and HTML text markup respectively.
+ */
+
+var utils = require("./utils");
+
+/**
+ * This node represents a general purpose MathML node of any type. The
+ * constructor requires the type of node to create (for example, `"mo"` or
+ * `"mspace"`, corresponding to `<mo>` and `<mspace>` tags).
+ */
+function MathNode(type, children) {
+    this.type = type;
+    this.attributes = {};
+    this.children = children || [];
+}
+
+/**
+ * Sets an attribute on a MathML node. MathML depends on attributes to convey a
+ * semantic content, so this is used heavily.
+ */
+MathNode.prototype.setAttribute = function(name, value) {
+    this.attributes[name] = value;
+};
+
+/**
+ * Converts the math node into a MathML-namespaced DOM element.
+ */
+MathNode.prototype.toNode = function() {
+    var node = document.createElementNS(
+        "http://www.w3.org/1998/Math/MathML", this.type);
+
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            node.setAttribute(attr, this.attributes[attr]);
+        }
+    }
+
+    for (var i = 0; i < this.children.length; i++) {
+        node.appendChild(this.children[i].toNode());
+    }
+
+    return node;
+};
+
+/**
+ * Converts the math node into an HTML markup string.
+ */
+MathNode.prototype.toMarkup = function() {
+    var markup = "<" + this.type;
+
+    // Add the attributes
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            markup += " " + attr + "=\"";
+            markup += utils.escape(this.attributes[attr]);
+            markup += "\"";
+        }
+    }
+
+    markup += ">";
+
+    for (var i = 0; i < this.children.length; i++) {
+        markup += this.children[i].toMarkup();
+    }
+
+    markup += "</" + this.type + ">";
+
+    return markup;
+};
+
+/**
+ * This node represents a piece of text.
+ */
+function TextNode(text) {
+    this.text = text;
+}
+
+/**
+ * Converts the text node into a DOM text node.
+ */
+TextNode.prototype.toNode = function() {
+    return document.createTextNode(this.text);
+};
+
+/**
+ * Converts the text node into HTML markup (which is just the text itself).
+ */
+TextNode.prototype.toMarkup = function() {
+    return utils.escape(this.text);
+};
+
+module.exports = {
+    MathNode: MathNode,
+    TextNode: TextNode
+};
+
+},{"./utils":25}],21:[function(require,module,exports){
+/**
+ * The resulting parse tree nodes of the parse tree.
+ *
+ * It is possible to provide position information, so that a ParseNode can
+ * fulfil a role similar to a Token in error reporting.
+ * For details on the corresponding properties see Token constructor.
+ * Providing such information can lead to better error reporting.
+ *
+ * @param {string}  type       type of node, like e.g. "ordgroup"
+ * @param {?object} value      type-specific representation of the node
+ * @param {string}  mode       parse mode in action for this node,
+ *                             "math" or "text"
+ * @param {Token=} firstToken  first token of the input for this node,
+ *                             will omit position information if unset
+ * @param {Token=} lastToken   last token of the input for this node,
+ *                             will default to firstToken if unset
+ */
+function ParseNode(type, value, mode, firstToken, lastToken) {
+    this.type = type;
+    this.value = value;
+    this.mode = mode;
+    if (firstToken && (!lastToken || lastToken.lexer === firstToken.lexer)) {
+        this.lexer = firstToken.lexer;
+        this.start = firstToken.start;
+        this.end = (lastToken || firstToken).end;
+    }
+}
+
+module.exports = {
+    ParseNode: ParseNode
+};
+
+
+},{}],22:[function(require,module,exports){
+/**
+ * Provides a single function for parsing an expression using a Parser
+ * TODO(emily): Remove this
+ */
+
+var Parser = require("./Parser");
+
+/**
+ * Parses an expression using a Parser, then returns the parsed result.
+ */
+var parseTree = function(toParse, settings) {
+    if (!(typeof toParse === 'string' || toParse instanceof String)) {
+        throw new TypeError('KaTeX can only parse string typed expression');
+    }
+    var parser = new Parser(toParse, settings);
+
+    return parser.parse();
+};
+
+module.exports = parseTree;
+
+},{"./Parser":7}],23:[function(require,module,exports){
+/**
+ * This file holds a list of all no-argument functions and single-character
+ * symbols (like 'a' or ';').
+ *
+ * For each of the symbols, there are three properties they can have:
+ * - font (required): the font to be used for this symbol. Either "main" (the
+     normal font), or "ams" (the ams fonts).
+ * - group (required): the ParseNode group type the symbol should have (i.e.
+     "textord", "mathord", etc).
+     See https://github.com/Khan/KaTeX/wiki/Examining-TeX#group-types
+ * - replace: the character that this symbol or function should be
+ *   replaced with (i.e. "\phi" has a replace value of "\u03d5", the phi
+ *   character in the main font).
+ *
+ * The outermost map in the table indicates what mode the symbols should be
+ * accepted in (e.g. "math" or "text").
+ */
+
+module.exports = {
+    math: {},
+    text: {}
+};
+
+function defineSymbol(mode, font, group, replace, name) {
+    module.exports[mode][name] = {
+        font: font,
+        group: group,
+        replace: replace
+    };
+}
+
+// Some abbreviations for commonly used strings.
+// This helps minify the code, and also spotting typos using jshint.
+
+// modes:
+var math = "math";
+var text = "text";
+
+// fonts:
+var main = "main";
+var ams = "ams";
+
+// groups:
+var accent = "accent";
+var bin = "bin";
+var close = "close";
+var inner = "inner";
+var mathord = "mathord";
+var op = "op";
+var open = "open";
+var punct = "punct";
+var rel = "rel";
+var spacing = "spacing";
+var textord = "textord";
+
+// Now comes the symbol table
+
+// Relation Symbols
+defineSymbol(math, main, rel, "\u2261", "\\equiv");
+defineSymbol(math, main, rel, "\u227a", "\\prec");
+defineSymbol(math, main, rel, "\u227b", "\\succ");
+defineSymbol(math, main, rel, "\u223c", "\\sim");
+defineSymbol(math, main, rel, "\u22a5", "\\perp");
+defineSymbol(math, main, rel, "\u2aaf", "\\preceq");
+defineSymbol(math, main, rel, "\u2ab0", "\\succeq");
+defineSymbol(math, main, rel, "\u2243", "\\simeq");
+defineSymbol(math, main, rel, "\u2223", "\\mid");
+defineSymbol(math, main, rel, "\u226a", "\\ll");
+defineSymbol(math, main, rel, "\u226b", "\\gg");
+defineSymbol(math, main, rel, "\u224d", "\\asymp");
+defineSymbol(math, main, rel, "\u2225", "\\parallel");
+defineSymbol(math, main, rel, "\u22c8", "\\bowtie");
+defineSymbol(math, main, rel, "\u2323", "\\smile");
+defineSymbol(math, main, rel, "\u2291", "\\sqsubseteq");
+defineSymbol(math, main, rel, "\u2292", "\\sqsupseteq");
+defineSymbol(math, main, rel, "\u2250", "\\doteq");
+defineSymbol(math, main, rel, "\u2322", "\\frown");
+defineSymbol(math, main, rel, "\u220b", "\\ni");
+defineSymbol(math, main, rel, "\u221d", "\\propto");
+defineSymbol(math, main, rel, "\u22a2", "\\vdash");
+defineSymbol(math, main, rel, "\u22a3", "\\dashv");
+defineSymbol(math, main, rel, "\u220b", "\\owns");
+
+// Punctuation
+defineSymbol(math, main, punct, "\u002e", "\\ldotp");
+defineSymbol(math, main, punct, "\u22c5", "\\cdotp");
+
+// Misc Symbols
+defineSymbol(math, main, textord, "\u0023", "\\#");
+defineSymbol(text, main, textord, "\u0023", "\\#");
+defineSymbol(math, main, textord, "\u0026", "\\&");
+defineSymbol(text, main, textord, "\u0026", "\\&");
+defineSymbol(math, main, textord, "\u2135", "\\aleph");
+defineSymbol(math, main, textord, "\u2200", "\\forall");
+defineSymbol(math, main, textord, "\u210f", "\\hbar");
+defineSymbol(math, main, textord, "\u2203", "\\exists");
+defineSymbol(math, main, textord, "\u2207", "\\nabla");
+defineSymbol(math, main, textord, "\u266d", "\\flat");
+defineSymbol(math, main, textord, "\u2113", "\\ell");
+defineSymbol(math, main, textord, "\u266e", "\\natural");
+defineSymbol(math, main, textord, "\u2663", "\\clubsuit");
+defineSymbol(math, main, textord, "\u2118", "\\wp");
+defineSymbol(math, main, textord, "\u266f", "\\sharp");
+defineSymbol(math, main, textord, "\u2662", "\\diamondsuit");
+defineSymbol(math, main, textord, "\u211c", "\\Re");
+defineSymbol(math, main, textord, "\u2661", "\\heartsuit");
+defineSymbol(math, main, textord, "\u2111", "\\Im");
+defineSymbol(math, main, textord, "\u2660", "\\spadesuit");
+
+// Math and Text
+defineSymbol(math, main, textord, "\u2020", "\\dag");
+defineSymbol(math, main, textord, "\u2021", "\\ddag");
+
+// Large Delimiters
+defineSymbol(math, main, close, "\u23b1", "\\rmoustache");
+defineSymbol(math, main, open, "\u23b0", "\\lmoustache");
+defineSymbol(math, main, close, "\u27ef", "\\rgroup");
+defineSymbol(math, main, open, "\u27ee", "\\lgroup");
+
+// Binary Operators
+defineSymbol(math, main, bin, "\u2213", "\\mp");
+defineSymbol(math, main, bin, "\u2296", "\\ominus");
+defineSymbol(math, main, bin, "\u228e", "\\uplus");
+defineSymbol(math, main, bin, "\u2293", "\\sqcap");
+defineSymbol(math, main, bin, "\u2217", "\\ast");
+defineSymbol(math, main, bin, "\u2294", "\\sqcup");
+defineSymbol(math, main, bin, "\u25ef", "\\bigcirc");
+defineSymbol(math, main, bin, "\u2219", "\\bullet");
+defineSymbol(math, main, bin, "\u2021", "\\ddagger");
+defineSymbol(math, main, bin, "\u2240", "\\wr");
+defineSymbol(math, main, bin, "\u2a3f", "\\amalg");
+
+// Arrow Symbols
+defineSymbol(math, main, rel, "\u27f5", "\\longleftarrow");
+defineSymbol(math, main, rel, "\u21d0", "\\Leftarrow");
+defineSymbol(math, main, rel, "\u27f8", "\\Longleftarrow");
+defineSymbol(math, main, rel, "\u27f6", "\\longrightarrow");
+defineSymbol(math, main, rel, "\u21d2", "\\Rightarrow");
+defineSymbol(math, main, rel, "\u27f9", "\\Longrightarrow");
+defineSymbol(math, main, rel, "\u2194", "\\leftrightarrow");
+defineSymbol(math, main, rel, "\u27f7", "\\longleftrightarrow");
+defineSymbol(math, main, rel, "\u21d4", "\\Leftrightarrow");
+defineSymbol(math, main, rel, "\u27fa", "\\Longleftrightarrow");
+defineSymbol(math, main, rel, "\u21a6", "\\mapsto");
+defineSymbol(math, main, rel, "\u27fc", "\\longmapsto");
+defineSymbol(math, main, rel, "\u2197", "\\nearrow");
+defineSymbol(math, main, rel, "\u21a9", "\\hookleftarrow");
+defineSymbol(math, main, rel, "\u21aa", "\\hookrightarrow");
+defineSymbol(math, main, rel, "\u2198", "\\searrow");
+defineSymbol(math, main, rel, "\u21bc", "\\leftharpoonup");
+defineSymbol(math, main, rel, "\u21c0", "\\rightharpoonup");
+defineSymbol(math, main, rel, "\u2199", "\\swarrow");
+defineSymbol(math, main, rel, "\u21bd", "\\leftharpoondown");
+defineSymbol(math, main, rel, "\u21c1", "\\rightharpoondown");
+defineSymbol(math, main, rel, "\u2196", "\\nwarrow");
+defineSymbol(math, main, rel, "\u21cc", "\\rightleftharpoons");
+
+// AMS Negated Binary Relations
+defineSymbol(math, ams, rel, "\u226e", "\\nless");
+defineSymbol(math, ams, rel, "\ue010", "\\nleqslant");
+defineSymbol(math, ams, rel, "\ue011", "\\nleqq");
+defineSymbol(math, ams, rel, "\u2a87", "\\lneq");
+defineSymbol(math, ams, rel, "\u2268", "\\lneqq");
+defineSymbol(math, ams, rel, "\ue00c", "\\lvertneqq");
+defineSymbol(math, ams, rel, "\u22e6", "\\lnsim");
+defineSymbol(math, ams, rel, "\u2a89", "\\lnapprox");
+defineSymbol(math, ams, rel, "\u2280", "\\nprec");
+defineSymbol(math, ams, rel, "\u22e0", "\\npreceq");
+defineSymbol(math, ams, rel, "\u22e8", "\\precnsim");
+defineSymbol(math, ams, rel, "\u2ab9", "\\precnapprox");
+defineSymbol(math, ams, rel, "\u2241", "\\nsim");
+defineSymbol(math, ams, rel, "\ue006", "\\nshortmid");
+defineSymbol(math, ams, rel, "\u2224", "\\nmid");
+defineSymbol(math, ams, rel, "\u22ac", "\\nvdash");
+defineSymbol(math, ams, rel, "\u22ad", "\\nvDash");
+defineSymbol(math, ams, rel, "\u22ea", "\\ntriangleleft");
+defineSymbol(math, ams, rel, "\u22ec", "\\ntrianglelefteq");
+defineSymbol(math, ams, rel, "\u228a", "\\subsetneq");
+defineSymbol(math, ams, rel, "\ue01a", "\\varsubsetneq");
+defineSymbol(math, ams, rel, "\u2acb", "\\subsetneqq");
+defineSymbol(math, ams, rel, "\ue017", "\\varsubsetneqq");
+defineSymbol(math, ams, rel, "\u226f", "\\ngtr");
+defineSymbol(math, ams, rel, "\ue00f", "\\ngeqslant");
+defineSymbol(math, ams, rel, "\ue00e", "\\ngeqq");
+defineSymbol(math, ams, rel, "\u2a88", "\\gneq");
+defineSymbol(math, ams, rel, "\u2269", "\\gneqq");
+defineSymbol(math, ams, rel, "\ue00d", "\\gvertneqq");
+defineSymbol(math, ams, rel, "\u22e7", "\\gnsim");
+defineSymbol(math, ams, rel, "\u2a8a", "\\gnapprox");
+defineSymbol(math, ams, rel, "\u2281", "\\nsucc");
+defineSymbol(math, ams, rel, "\u22e1", "\\nsucceq");
+defineSymbol(math, ams, rel, "\u22e9", "\\succnsim");
+defineSymbol(math, ams, rel, "\u2aba", "\\succnapprox");
+defineSymbol(math, ams, rel, "\u2246", "\\ncong");
+defineSymbol(math, ams, rel, "\ue007", "\\nshortparallel");
+defineSymbol(math, ams, rel, "\u2226", "\\nparallel");
+defineSymbol(math, ams, rel, "\u22af", "\\nVDash");
+defineSymbol(math, ams, rel, "\u22eb", "\\ntriangleright");
+defineSymbol(math, ams, rel, "\u22ed", "\\ntrianglerighteq");
+defineSymbol(math, ams, rel, "\ue018", "\\nsupseteqq");
+defineSymbol(math, ams, rel, "\u228b", "\\supsetneq");
+defineSymbol(math, ams, rel, "\ue01b", "\\varsupsetneq");
+defineSymbol(math, ams, rel, "\u2acc", "\\supsetneqq");
+defineSymbol(math, ams, rel, "\ue019", "\\varsupsetneqq");
+defineSymbol(math, ams, rel, "\u22ae", "\\nVdash");
+defineSymbol(math, ams, rel, "\u2ab5", "\\precneqq");
+defineSymbol(math, ams, rel, "\u2ab6", "\\succneqq");
+defineSymbol(math, ams, rel, "\ue016", "\\nsubseteqq");
+defineSymbol(math, ams, bin, "\u22b4", "\\unlhd");
+defineSymbol(math, ams, bin, "\u22b5", "\\unrhd");
+
+// AMS Negated Arrows
+defineSymbol(math, ams, rel, "\u219a", "\\nleftarrow");
+defineSymbol(math, ams, rel, "\u219b", "\\nrightarrow");
+defineSymbol(math, ams, rel, "\u21cd", "\\nLeftarrow");
+defineSymbol(math, ams, rel, "\u21cf", "\\nRightarrow");
+defineSymbol(math, ams, rel, "\u21ae", "\\nleftrightarrow");
+defineSymbol(math, ams, rel, "\u21ce", "\\nLeftrightarrow");
+
+// AMS Misc
+defineSymbol(math, ams, rel, "\u25b3", "\\vartriangle");
+defineSymbol(math, ams, textord, "\u210f", "\\hslash");
+defineSymbol(math, ams, textord, "\u25bd", "\\triangledown");
+defineSymbol(math, ams, textord, "\u25ca", "\\lozenge");
+defineSymbol(math, ams, textord, "\u24c8", "\\circledS");
+defineSymbol(math, ams, textord, "\u00ae", "\\circledR");
+defineSymbol(math, ams, textord, "\u2221", "\\measuredangle");
+defineSymbol(math, ams, textord, "\u2204", "\\nexists");
+defineSymbol(math, ams, textord, "\u2127", "\\mho");
+defineSymbol(math, ams, textord, "\u2132", "\\Finv");
+defineSymbol(math, ams, textord, "\u2141", "\\Game");
+defineSymbol(math, ams, textord, "\u006b", "\\Bbbk");
+defineSymbol(math, ams, textord, "\u2035", "\\backprime");
+defineSymbol(math, ams, textord, "\u25b2", "\\blacktriangle");
+defineSymbol(math, ams, textord, "\u25bc", "\\blacktriangledown");
+defineSymbol(math, ams, textord, "\u25a0", "\\blacksquare");
+defineSymbol(math, ams, textord, "\u29eb", "\\blacklozenge");
+defineSymbol(math, ams, textord, "\u2605", "\\bigstar");
+defineSymbol(math, ams, textord, "\u2222", "\\sphericalangle");
+defineSymbol(math, ams, textord, "\u2201", "\\complement");
+defineSymbol(math, ams, textord, "\u00f0", "\\eth");
+defineSymbol(math, ams, textord, "\u2571", "\\diagup");
+defineSymbol(math, ams, textord, "\u2572", "\\diagdown");
+defineSymbol(math, ams, textord, "\u25a1", "\\square");
+defineSymbol(math, ams, textord, "\u25a1", "\\Box");
+defineSymbol(math, ams, textord, "\u25ca", "\\Diamond");
+defineSymbol(math, ams, textord, "\u00a5", "\\yen");
+defineSymbol(math, ams, textord, "\u2713", "\\checkmark");
+
+// AMS Hebrew
+defineSymbol(math, ams, textord, "\u2136", "\\beth");
+defineSymbol(math, ams, textord, "\u2138", "\\daleth");
+defineSymbol(math, ams, textord, "\u2137", "\\gimel");
+
+// AMS Greek
+defineSymbol(math, ams, textord, "\u03dd", "\\digamma");
+defineSymbol(math, ams, textord, "\u03f0", "\\varkappa");
+
+// AMS Delimiters
+defineSymbol(math, ams, open, "\u250c", "\\ulcorner");
+defineSymbol(math, ams, close, "\u2510", "\\urcorner");
+defineSymbol(math, ams, open, "\u2514", "\\llcorner");
+defineSymbol(math, ams, close, "\u2518", "\\lrcorner");
+
+// AMS Binary Relations
+defineSymbol(math, ams, rel, "\u2266", "\\leqq");
+defineSymbol(math, ams, rel, "\u2a7d", "\\leqslant");
+defineSymbol(math, ams, rel, "\u2a95", "\\eqslantless");
+defineSymbol(math, ams, rel, "\u2272", "\\lesssim");
+defineSymbol(math, ams, rel, "\u2a85", "\\lessapprox");
+defineSymbol(math, ams, rel, "\u224a", "\\approxeq");
+defineSymbol(math, ams, bin, "\u22d6", "\\lessdot");
+defineSymbol(math, ams, rel, "\u22d8", "\\lll");
+defineSymbol(math, ams, rel, "\u2276", "\\lessgtr");
+defineSymbol(math, ams, rel, "\u22da", "\\lesseqgtr");
+defineSymbol(math, ams, rel, "\u2a8b", "\\lesseqqgtr");
+defineSymbol(math, ams, rel, "\u2251", "\\doteqdot");
+defineSymbol(math, ams, rel, "\u2253", "\\risingdotseq");
+defineSymbol(math, ams, rel, "\u2252", "\\fallingdotseq");
+defineSymbol(math, ams, rel, "\u223d", "\\backsim");
+defineSymbol(math, ams, rel, "\u22cd", "\\backsimeq");
+defineSymbol(math, ams, rel, "\u2ac5", "\\subseteqq");
+defineSymbol(math, ams, rel, "\u22d0", "\\Subset");
+defineSymbol(math, ams, rel, "\u228f", "\\sqsubset");
+defineSymbol(math, ams, rel, "\u227c", "\\preccurlyeq");
+defineSymbol(math, ams, rel, "\u22de", "\\curlyeqprec");
+defineSymbol(math, ams, rel, "\u227e", "\\precsim");
+defineSymbol(math, ams, rel, "\u2ab7", "\\precapprox");
+defineSymbol(math, ams, rel, "\u22b2", "\\vartriangleleft");
+defineSymbol(math, ams, rel, "\u22b4", "\\trianglelefteq");
+defineSymbol(math, ams, rel, "\u22a8", "\\vDash");
+defineSymbol(math, ams, rel, "\u22aa", "\\Vvdash");
+defineSymbol(math, ams, rel, "\u2323", "\\smallsmile");
+defineSymbol(math, ams, rel, "\u2322", "\\smallfrown");
+defineSymbol(math, ams, rel, "\u224f", "\\bumpeq");
+defineSymbol(math, ams, rel, "\u224e", "\\Bumpeq");
+defineSymbol(math, ams, rel, "\u2267", "\\geqq");
+defineSymbol(math, ams, rel, "\u2a7e", "\\geqslant");
+defineSymbol(math, ams, rel, "\u2a96", "\\eqslantgtr");
+defineSymbol(math, ams, rel, "\u2273", "\\gtrsim");
+defineSymbol(math, ams, rel, "\u2a86", "\\gtrapprox");
+defineSymbol(math, ams, bin, "\u22d7", "\\gtrdot");
+defineSymbol(math, ams, rel, "\u22d9", "\\ggg");
+defineSymbol(math, ams, rel, "\u2277", "\\gtrless");
+defineSymbol(math, ams, rel, "\u22db", "\\gtreqless");
+defineSymbol(math, ams, rel, "\u2a8c", "\\gtreqqless");
+defineSymbol(math, ams, rel, "\u2256", "\\eqcirc");
+defineSymbol(math, ams, rel, "\u2257", "\\circeq");
+defineSymbol(math, ams, rel, "\u225c", "\\triangleq");
+defineSymbol(math, ams, rel, "\u223c", "\\thicksim");
+defineSymbol(math, ams, rel, "\u2248", "\\thickapprox");
+defineSymbol(math, ams, rel, "\u2ac6", "\\supseteqq");
+defineSymbol(math, ams, rel, "\u22d1", "\\Supset");
+defineSymbol(math, ams, rel, "\u2290", "\\sqsupset");
+defineSymbol(math, ams, rel, "\u227d", "\\succcurlyeq");
+defineSymbol(math, ams, rel, "\u22df", "\\curlyeqsucc");
+defineSymbol(math, ams, rel, "\u227f", "\\succsim");
+defineSymbol(math, ams, rel, "\u2ab8", "\\succapprox");
+defineSymbol(math, ams, rel, "\u22b3", "\\vartriangleright");
+defineSymbol(math, ams, rel, "\u22b5", "\\trianglerighteq");
+defineSymbol(math, ams, rel, "\u22a9", "\\Vdash");
+defineSymbol(math, ams, rel, "\u2223", "\\shortmid");
+defineSymbol(math, ams, rel, "\u2225", "\\shortparallel");
+defineSymbol(math, ams, rel, "\u226c", "\\between");
+defineSymbol(math, ams, rel, "\u22d4", "\\pitchfork");
+defineSymbol(math, ams, rel, "\u221d", "\\varpropto");
+defineSymbol(math, ams, rel, "\u25c0", "\\blacktriangleleft");
+defineSymbol(math, ams, rel, "\u2234", "\\therefore");
+defineSymbol(math, ams, rel, "\u220d", "\\backepsilon");
+defineSymbol(math, ams, rel, "\u25b6", "\\blacktriangleright");
+defineSymbol(math, ams, rel, "\u2235", "\\because");
+defineSymbol(math, ams, rel, "\u22d8", "\\llless");
+defineSymbol(math, ams, rel, "\u22d9", "\\gggtr");
+defineSymbol(math, ams, bin, "\u22b2", "\\lhd");
+defineSymbol(math, ams, bin, "\u22b3", "\\rhd");
+defineSymbol(math, ams, rel, "\u2242", "\\eqsim");
+defineSymbol(math, main, rel, "\u22c8", "\\Join");
+defineSymbol(math, ams, rel, "\u2251", "\\Doteq");
+
+// AMS Binary Operators
+defineSymbol(math, ams, bin, "\u2214", "\\dotplus");
+defineSymbol(math, ams, bin, "\u2216", "\\smallsetminus");
+defineSymbol(math, ams, bin, "\u22d2", "\\Cap");
+defineSymbol(math, ams, bin, "\u22d3", "\\Cup");
+defineSymbol(math, ams, bin, "\u2a5e", "\\doublebarwedge");
+defineSymbol(math, ams, bin, "\u229f", "\\boxminus");
+defineSymbol(math, ams, bin, "\u229e", "\\boxplus");
+defineSymbol(math, ams, bin, "\u22c7", "\\divideontimes");
+defineSymbol(math, ams, bin, "\u22c9", "\\ltimes");
+defineSymbol(math, ams, bin, "\u22ca", "\\rtimes");
+defineSymbol(math, ams, bin, "\u22cb", "\\leftthreetimes");
+defineSymbol(math, ams, bin, "\u22cc", "\\rightthreetimes");
+defineSymbol(math, ams, bin, "\u22cf", "\\curlywedge");
+defineSymbol(math, ams, bin, "\u22ce", "\\curlyvee");
+defineSymbol(math, ams, bin, "\u229d", "\\circleddash");
+defineSymbol(math, ams, bin, "\u229b", "\\circledast");
+defineSymbol(math, ams, bin, "\u22c5", "\\centerdot");
+defineSymbol(math, ams, bin, "\u22ba", "\\intercal");
+defineSymbol(math, ams, bin, "\u22d2", "\\doublecap");
+defineSymbol(math, ams, bin, "\u22d3", "\\doublecup");
+defineSymbol(math, ams, bin, "\u22a0", "\\boxtimes");
+
+// AMS Arrows
+defineSymbol(math, ams, rel, "\u21e2", "\\dashrightarrow");
+defineSymbol(math, ams, rel, "\u21e0", "\\dashleftarrow");
+defineSymbol(math, ams, rel, "\u21c7", "\\leftleftarrows");
+defineSymbol(math, ams, rel, "\u21c6", "\\leftrightarrows");
+defineSymbol(math, ams, rel, "\u21da", "\\Lleftarrow");
+defineSymbol(math, ams, rel, "\u219e", "\\twoheadleftarrow");
+defineSymbol(math, ams, rel, "\u21a2", "\\leftarrowtail");
+defineSymbol(math, ams, rel, "\u21ab", "\\looparrowleft");
+defineSymbol(math, ams, rel, "\u21cb", "\\leftrightharpoons");
+defineSymbol(math, ams, rel, "\u21b6", "\\curvearrowleft");
+defineSymbol(math, ams, rel, "\u21ba", "\\circlearrowleft");
+defineSymbol(math, ams, rel, "\u21b0", "\\Lsh");
+defineSymbol(math, ams, rel, "\u21c8", "\\upuparrows");
+defineSymbol(math, ams, rel, "\u21bf", "\\upharpoonleft");
+defineSymbol(math, ams, rel, "\u21c3", "\\downharpoonleft");
+defineSymbol(math, ams, rel, "\u22b8", "\\multimap");
+defineSymbol(math, ams, rel, "\u21ad", "\\leftrightsquigarrow");
+defineSymbol(math, ams, rel, "\u21c9", "\\rightrightarrows");
+defineSymbol(math, ams, rel, "\u21c4", "\\rightleftarrows");
+defineSymbol(math, ams, rel, "\u21a0", "\\twoheadrightarrow");
+defineSymbol(math, ams, rel, "\u21a3", "\\rightarrowtail");
+defineSymbol(math, ams, rel, "\u21ac", "\\looparrowright");
+defineSymbol(math, ams, rel, "\u21b7", "\\curvearrowright");
+defineSymbol(math, ams, rel, "\u21bb", "\\circlearrowright");
+defineSymbol(math, ams, rel, "\u21b1", "\\Rsh");
+defineSymbol(math, ams, rel, "\u21ca", "\\downdownarrows");
+defineSymbol(math, ams, rel, "\u21be", "\\upharpoonright");
+defineSymbol(math, ams, rel, "\u21c2", "\\downharpoonright");
+defineSymbol(math, ams, rel, "\u21dd", "\\rightsquigarrow");
+defineSymbol(math, ams, rel, "\u21dd", "\\leadsto");
+defineSymbol(math, ams, rel, "\u21db", "\\Rrightarrow");
+defineSymbol(math, ams, rel, "\u21be", "\\restriction");
+
+defineSymbol(math, main, textord, "\u2018", "`");
+defineSymbol(math, main, textord, "$", "\\$");
+defineSymbol(text, main, textord, "$", "\\$");
+defineSymbol(math, main, textord, "%", "\\%");
+defineSymbol(text, main, textord, "%", "\\%");
+defineSymbol(math, main, textord, "_", "\\_");
+defineSymbol(text, main, textord, "_", "\\_");
+defineSymbol(math, main, textord, "\u2220", "\\angle");
+defineSymbol(math, main, textord, "\u221e", "\\infty");
+defineSymbol(math, main, textord, "\u2032", "\\prime");
+defineSymbol(math, main, textord, "\u25b3", "\\triangle");
+defineSymbol(math, main, textord, "\u0393", "\\Gamma");
+defineSymbol(math, main, textord, "\u0394", "\\Delta");
+defineSymbol(math, main, textord, "\u0398", "\\Theta");
+defineSymbol(math, main, textord, "\u039b", "\\Lambda");
+defineSymbol(math, main, textord, "\u039e", "\\Xi");
+defineSymbol(math, main, textord, "\u03a0", "\\Pi");
+defineSymbol(math, main, textord, "\u03a3", "\\Sigma");
+defineSymbol(math, main, textord, "\u03a5", "\\Upsilon");
+defineSymbol(math, main, textord, "\u03a6", "\\Phi");
+defineSymbol(math, main, textord, "\u03a8", "\\Psi");
+defineSymbol(math, main, textord, "\u03a9", "\\Omega");
+defineSymbol(math, main, textord, "\u00ac", "\\neg");
+defineSymbol(math, main, textord, "\u00ac", "\\lnot");
+defineSymbol(math, main, textord, "\u22a4", "\\top");
+defineSymbol(math, main, textord, "\u22a5", "\\bot");
+defineSymbol(math, main, textord, "\u2205", "\\emptyset");
+defineSymbol(math, ams, textord, "\u2205", "\\varnothing");
+defineSymbol(math, main, mathord, "\u03b1", "\\alpha");
+defineSymbol(math, main, mathord, "\u03b2", "\\beta");
+defineSymbol(math, main, mathord, "\u03b3", "\\gamma");
+defineSymbol(math, main, mathord, "\u03b4", "\\delta");
+defineSymbol(math, main, mathord, "\u03f5", "\\epsilon");
+defineSymbol(math, main, mathord, "\u03b6", "\\zeta");
+defineSymbol(math, main, mathord, "\u03b7", "\\eta");
+defineSymbol(math, main, mathord, "\u03b8", "\\theta");
+defineSymbol(math, main, mathord, "\u03b9", "\\iota");
+defineSymbol(math, main, mathord, "\u03ba", "\\kappa");
+defineSymbol(math, main, mathord, "\u03bb", "\\lambda");
+defineSymbol(math, main, mathord, "\u03bc", "\\mu");
+defineSymbol(math, main, mathord, "\u03bd", "\\nu");
+defineSymbol(math, main, mathord, "\u03be", "\\xi");
+defineSymbol(math, main, mathord, "o", "\\omicron");
+defineSymbol(math, main, mathord, "\u03c0", "\\pi");
+defineSymbol(math, main, mathord, "\u03c1", "\\rho");
+defineSymbol(math, main, mathord, "\u03c3", "\\sigma");
+defineSymbol(math, main, mathord, "\u03c4", "\\tau");
+defineSymbol(math, main, mathord, "\u03c5", "\\upsilon");
+defineSymbol(math, main, mathord, "\u03d5", "\\phi");
+defineSymbol(math, main, mathord, "\u03c7", "\\chi");
+defineSymbol(math, main, mathord, "\u03c8", "\\psi");
+defineSymbol(math, main, mathord, "\u03c9", "\\omega");
+defineSymbol(math, main, mathord, "\u03b5", "\\varepsilon");
+defineSymbol(math, main, mathord, "\u03d1", "\\vartheta");
+defineSymbol(math, main, mathord, "\u03d6", "\\varpi");
+defineSymbol(math, main, mathord, "\u03f1", "\\varrho");
+defineSymbol(math, main, mathord, "\u03c2", "\\varsigma");
+defineSymbol(math, main, mathord, "\u03c6", "\\varphi");
+defineSymbol(math, main, bin, "\u2217", "*");
+defineSymbol(math, main, bin, "+", "+");
+defineSymbol(math, main, bin, "\u2212", "-");
+defineSymbol(math, main, bin, "\u22c5", "\\cdot");
+defineSymbol(math, main, bin, "\u2218", "\\circ");
+defineSymbol(math, main, bin, "\u00f7", "\\div");
+defineSymbol(math, main, bin, "\u00b1", "\\pm");
+defineSymbol(math, main, bin, "\u00d7", "\\times");
+defineSymbol(math, main, bin, "\u2229", "\\cap");
+defineSymbol(math, main, bin, "\u222a", "\\cup");
+defineSymbol(math, main, bin, "\u2216", "\\setminus");
+defineSymbol(math, main, bin, "\u2227", "\\land");
+defineSymbol(math, main, bin, "\u2228", "\\lor");
+defineSymbol(math, main, bin, "\u2227", "\\wedge");
+defineSymbol(math, main, bin, "\u2228", "\\vee");
+defineSymbol(math, main, textord, "\u221a", "\\surd");
+defineSymbol(math, main, open, "(", "(");
+defineSymbol(math, main, open, "[", "[");
+defineSymbol(math, main, open, "\u27e8", "\\langle");
+defineSymbol(math, main, open, "\u2223", "\\lvert");
+defineSymbol(math, main, open, "\u2225", "\\lVert");
+defineSymbol(math, main, close, ")", ")");
+defineSymbol(math, main, close, "]", "]");
+defineSymbol(math, main, close, "?", "?");
+defineSymbol(math, main, close, "!", "!");
+defineSymbol(math, main, close, "\u27e9", "\\rangle");
+defineSymbol(math, main, close, "\u2223", "\\rvert");
+defineSymbol(math, main, close, "\u2225", "\\rVert");
+defineSymbol(math, main, rel, "=", "=");
+defineSymbol(math, main, rel, "<", "<");
+defineSymbol(math, main, rel, ">", ">");
+defineSymbol(math, main, rel, ":", ":");
+defineSymbol(math, main, rel, "\u2248", "\\approx");
+defineSymbol(math, main, rel, "\u2245", "\\cong");
+defineSymbol(math, main, rel, "\u2265", "\\ge");
+defineSymbol(math, main, rel, "\u2265", "\\geq");
+defineSymbol(math, main, rel, "\u2190", "\\gets");
+defineSymbol(math, main, rel, ">", "\\gt");
+defineSymbol(math, main, rel, "\u2208", "\\in");
+defineSymbol(math, main, rel, "\u2209", "\\notin");
+defineSymbol(math, main, rel, "\u2282", "\\subset");
+defineSymbol(math, main, rel, "\u2283", "\\supset");
+defineSymbol(math, main, rel, "\u2286", "\\subseteq");
+defineSymbol(math, main, rel, "\u2287", "\\supseteq");
+defineSymbol(math, ams, rel, "\u2288", "\\nsubseteq");
+defineSymbol(math, ams, rel, "\u2289", "\\nsupseteq");
+defineSymbol(math, main, rel, "\u22a8", "\\models");
+defineSymbol(math, main, rel, "\u2190", "\\leftarrow");
+defineSymbol(math, main, rel, "\u2264", "\\le");
+defineSymbol(math, main, rel, "\u2264", "\\leq");
+defineSymbol(math, main, rel, "<", "\\lt");
+defineSymbol(math, main, rel, "\u2260", "\\ne");
+defineSymbol(math, main, rel, "\u2260", "\\neq");
+defineSymbol(math, main, rel, "\u2192", "\\rightarrow");
+defineSymbol(math, main, rel, "\u2192", "\\to");
+defineSymbol(math, ams, rel, "\u2271", "\\ngeq");
+defineSymbol(math, ams, rel, "\u2270", "\\nleq");
+defineSymbol(math, main, spacing, null, "\\!");
+defineSymbol(math, main, spacing, "\u00a0", "\\ ");
+defineSymbol(math, main, spacing, "\u00a0", "~");
+defineSymbol(math, main, spacing, null, "\\,");
+defineSymbol(math, main, spacing, null, "\\:");
+defineSymbol(math, main, spacing, null, "\\;");
+defineSymbol(math, main, spacing, null, "\\enspace");
+defineSymbol(math, main, spacing, null, "\\qquad");
+defineSymbol(math, main, spacing, null, "\\quad");
+defineSymbol(math, main, spacing, "\u00a0", "\\space");
+defineSymbol(math, main, punct, ",", ",");
+defineSymbol(math, main, punct, ";", ";");
+defineSymbol(math, main, punct, ":", "\\colon");
+defineSymbol(math, ams, bin, "\u22bc", "\\barwedge");
+defineSymbol(math, ams, bin, "\u22bb", "\\veebar");
+defineSymbol(math, main, bin, "\u2299", "\\odot");
+defineSymbol(math, main, bin, "\u2295", "\\oplus");
+defineSymbol(math, main, bin, "\u2297", "\\otimes");
+defineSymbol(math, main, textord, "\u2202", "\\partial");
+defineSymbol(math, main, bin, "\u2298", "\\oslash");
+defineSymbol(math, ams, bin, "\u229a", "\\circledcirc");
+defineSymbol(math, ams, bin, "\u22a1", "\\boxdot");
+defineSymbol(math, main, bin, "\u25b3", "\\bigtriangleup");
+defineSymbol(math, main, bin, "\u25bd", "\\bigtriangledown");
+defineSymbol(math, main, bin, "\u2020", "\\dagger");
+defineSymbol(math, main, bin, "\u22c4", "\\diamond");
+defineSymbol(math, main, bin, "\u22c6", "\\star");
+defineSymbol(math, main, bin, "\u25c3", "\\triangleleft");
+defineSymbol(math, main, bin, "\u25b9", "\\triangleright");
+defineSymbol(math, main, open, "{", "\\{");
+defineSymbol(text, main, textord, "{", "\\{");
+defineSymbol(math, main, close, "}", "\\}");
+defineSymbol(text, main, textord, "}", "\\}");
+defineSymbol(math, main, open, "{", "\\lbrace");
+defineSymbol(math, main, close, "}", "\\rbrace");
+defineSymbol(math, main, open, "[", "\\lbrack");
+defineSymbol(math, main, close, "]", "\\rbrack");
+defineSymbol(math, main, open, "\u230a", "\\lfloor");
+defineSymbol(math, main, close, "\u230b", "\\rfloor");
+defineSymbol(math, main, open, "\u2308", "\\lceil");
+defineSymbol(math, main, close, "\u2309", "\\rceil");
+defineSymbol(math, main, textord, "\\", "\\backslash");
+defineSymbol(math, main, textord, "\u2223", "|");
+defineSymbol(math, main, textord, "\u2223", "\\vert");
+defineSymbol(math, main, textord, "\u2225", "\\|");
+defineSymbol(math, main, textord, "\u2225", "\\Vert");
+defineSymbol(math, main, rel, "\u2191", "\\uparrow");
+defineSymbol(math, main, rel, "\u21d1", "\\Uparrow");
+defineSymbol(math, main, rel, "\u2193", "\\downarrow");
+defineSymbol(math, main, rel, "\u21d3", "\\Downarrow");
+defineSymbol(math, main, rel, "\u2195", "\\updownarrow");
+defineSymbol(math, main, rel, "\u21d5", "\\Updownarrow");
+defineSymbol(math, math, op, "\u2210", "\\coprod");
+defineSymbol(math, math, op, "\u22c1", "\\bigvee");
+defineSymbol(math, math, op, "\u22c0", "\\bigwedge");
+defineSymbol(math, math, op, "\u2a04", "\\biguplus");
+defineSymbol(math, math, op, "\u22c2", "\\bigcap");
+defineSymbol(math, math, op, "\u22c3", "\\bigcup");
+defineSymbol(math, math, op, "\u222b", "\\int");
+defineSymbol(math, math, op, "\u222b", "\\intop");
+defineSymbol(math, math, op, "\u222c", "\\iint");
+defineSymbol(math, math, op, "\u222d", "\\iiint");
+defineSymbol(math, math, op, "\u220f", "\\prod");
+defineSymbol(math, math, op, "\u2211", "\\sum");
+defineSymbol(math, math, op, "\u2a02", "\\bigotimes");
+defineSymbol(math, math, op, "\u2a01", "\\bigoplus");
+defineSymbol(math, math, op, "\u2a00", "\\bigodot");
+defineSymbol(math, math, op, "\u222e", "\\oint");
+defineSymbol(math, math, op, "\u2a06", "\\bigsqcup");
+defineSymbol(math, math, op, "\u222b", "\\smallint");
+defineSymbol(text, main, inner, "\u2026", "\\textellipsis");
+defineSymbol(math, main, inner, "\u2026", "\\mathellipsis");
+defineSymbol(text, main, inner, "\u2026", "\\ldots");
+defineSymbol(math, main, inner, "\u2026", "\\ldots");
+defineSymbol(math, main, inner, "\u22ef", "\\cdots");
+defineSymbol(math, main, inner, "\u22f1", "\\ddots");
+defineSymbol(math, main, textord, "\u22ee", "\\vdots");
+defineSymbol(math, main, accent, "\u00b4", "\\acute");
+defineSymbol(math, main, accent, "\u0060", "\\grave");
+defineSymbol(math, main, accent, "\u00a8", "\\ddot");
+defineSymbol(math, main, accent, "\u007e", "\\tilde");
+defineSymbol(math, main, accent, "\u00af", "\\bar");
+defineSymbol(math, main, accent, "\u02d8", "\\breve");
+defineSymbol(math, main, accent, "\u02c7", "\\check");
+defineSymbol(math, main, accent, "\u005e", "\\hat");
+defineSymbol(math, main, accent, "\u20d7", "\\vec");
+defineSymbol(math, main, accent, "\u02d9", "\\dot");
+defineSymbol(math, main, mathord, "\u0131", "\\imath");
+defineSymbol(math, main, mathord, "\u0237", "\\jmath");
+
+defineSymbol(text, main, textord, "\u2013", "--");
+defineSymbol(text, main, textord, "\u2014", "---");
+defineSymbol(text, main, textord, "\u2018", "`");
+defineSymbol(text, main, textord, "\u2019", "'");
+defineSymbol(text, main, textord, "\u201c", "``");
+defineSymbol(text, main, textord, "\u201d", "''");
+defineSymbol(math, main, textord, "\u00b0", "\\degree");
+defineSymbol(text, main, textord, "\u00b0", "\\degree");
+defineSymbol(math, main, mathord, "\u00a3", "\\pounds");
+defineSymbol(math, ams, textord, "\u2720", "\\maltese");
+defineSymbol(text, ams, textord, "\u2720", "\\maltese");
+
+defineSymbol(text, main, spacing, "\u00a0", "\\ ");
+defineSymbol(text, main, spacing, "\u00a0", " ");
+defineSymbol(text, main, spacing, "\u00a0", "~");
+
+// There are lots of symbols which are the same, so we add them in afterwards.
+var i;
+var ch;
+
+// All of these are textords in math mode
+var mathTextSymbols = "0123456789/@.\"";
+for (i = 0; i < mathTextSymbols.length; i++) {
+    ch = mathTextSymbols.charAt(i);
+    defineSymbol(math, main, textord, ch, ch);
+}
+
+// All of these are textords in text mode
+var textSymbols = "0123456789!@*()-=+[]\";:?/.,";
+for (i = 0; i < textSymbols.length; i++) {
+    ch = textSymbols.charAt(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// All of these are textords in text mode, and mathords in math mode
+var letters = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
+for (i = 0; i < letters.length; i++) {
+    ch = letters.charAt(i);
+    defineSymbol(math, main, mathord, ch, ch);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// Latin-1 letters
+for (i = 0x00C0; i <= 0x00D6; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+for (i = 0x00D8; i <= 0x00F6; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+for (i = 0x00F8; i <= 0x00FF; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// Cyrillic
+for (i = 0x0410; i <= 0x044F; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// Unicode versions of existing characters
+defineSymbol(text, main, textord, "\u2013", "–");
+defineSymbol(text, main, textord, "\u2014", "—");
+defineSymbol(text, main, textord, "\u2018", "‘");
+defineSymbol(text, main, textord, "\u2019", "’");
+defineSymbol(text, main, textord, "\u201c", "“");
+defineSymbol(text, main, textord, "\u201d", "”");
+
+},{}],24:[function(require,module,exports){
+var hangulRegex = /[\uAC00-\uD7AF]/;
+
+// This regex combines
+// - Hiragana: [\u3040-\u309F]
+// - Katakana: [\u30A0-\u30FF]
+// - CJK ideograms: [\u4E00-\u9FAF]
+// - Hangul syllables: [\uAC00-\uD7AF]
+// Notably missing are halfwidth Katakana and Romanji glyphs.
+var cjkRegex =
+    /[\u3040-\u309F]|[\u30A0-\u30FF]|[\u4E00-\u9FAF]|[\uAC00-\uD7AF]/;
+
+module.exports = {
+    cjkRegex: cjkRegex,
+    hangulRegex: hangulRegex
+};
+
+},{}],25:[function(require,module,exports){
+/**
+ * This file contains a list of utility functions which are useful in other
+ * files.
+ */
+
+/**
+ * Provide an `indexOf` function which works in IE8, but defers to native if
+ * possible.
+ */
+var nativeIndexOf = Array.prototype.indexOf;
+var indexOf = function(list, elem) {
+    if (list == null) {
+        return -1;
+    }
+    if (nativeIndexOf && list.indexOf === nativeIndexOf) {
+        return list.indexOf(elem);
+    }
+    var i = 0;
+    var l = list.length;
+    for (; i < l; i++) {
+        if (list[i] === elem) {
+            return i;
+        }
+    }
+    return -1;
+};
+
+/**
+ * Return whether an element is contained in a list
+ */
+var contains = function(list, elem) {
+    return indexOf(list, elem) !== -1;
+};
+
+/**
+ * Provide a default value if a setting is undefined
+ */
+var deflt = function(setting, defaultIfUndefined) {
+    return setting === undefined ? defaultIfUndefined : setting;
+};
+
+// hyphenate and escape adapted from Facebook's React under Apache 2 license
+
+var uppercase = /([A-Z])/g;
+var hyphenate = function(str) {
+    return str.replace(uppercase, "-$1").toLowerCase();
+};
+
+var ESCAPE_LOOKUP = {
+    "&": "&amp;",
+    ">": "&gt;",
+    "<": "&lt;",
+    "\"": "&quot;",
+    "'": "&#x27;"
+};
+
+var ESCAPE_REGEX = /[&><"']/g;
+
+function escaper(match) {
+    return ESCAPE_LOOKUP[match];
+}
+
+/**
+ * Escapes text to prevent scripting attacks.
+ *
+ * @param {*} text Text value to escape.
+ * @return {string} An escaped string.
+ */
+function escape(text) {
+    return ("" + text).replace(ESCAPE_REGEX, escaper);
+}
+
+/**
+ * A function to set the text content of a DOM element in all supported
+ * browsers. Note that we don't define this if there is no document.
+ */
+var setTextContent;
+if (typeof document !== "undefined") {
+    var testNode = document.createElement("span");
+    if ("textContent" in testNode) {
+        setTextContent = function(node, text) {
+            node.textContent = text;
+        };
+    } else {
+        setTextContent = function(node, text) {
+            node.innerText = text;
+        };
+    }
+}
+
+/**
+ * A function to clear a node.
+ */
+function clearNode(node) {
+    setTextContent(node, "");
+}
+
+module.exports = {
+    contains: contains,
+    deflt: deflt,
+    escape: escape,
+    hyphenate: hyphenate,
+    indexOf: indexOf,
+    setTextContent: setTextContent,
+    clearNode: clearNode
+};
+
+},{}]},{},[1])(1)
+});
\ No newline at end of file
diff --git a/specs/es/3.2/katex/katex.min.css b/specs/es/3.2/katex/katex.min.css
new file mode 100644
index 0000000..d6fb837
--- /dev/null
+++ b/specs/es/3.2/katex/katex.min.css
@@ -0,0 +1 @@
+@font-face{font-family:KaTeX_AMS;src:url(fonts/KaTeX_AMS-Regular.eot);src:url(fonts/KaTeX_AMS-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_AMS-Regular.woff2) format('woff2'),url(fonts/KaTeX_AMS-Regular.woff) format('woff'),url(fonts/KaTeX_AMS-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Caligraphic;src:url(fonts/KaTeX_Caligraphic-Bold.eot);src:url(fonts/KaTeX_Caligraphic-Bold.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Caligraphic-Bold.woff2) format('woff2'),url(fonts/KaTeX_Caligraphic-Bold.woff) format('woff'),url(fonts/KaTeX_Caligraphic-Bold.ttf) format('truetype');font-weight:700;font-style:normal}@font-face{font-family:KaTeX_Caligraphic;src:url(fonts/KaTeX_Caligraphic-Regular.eot);src:url(fonts/KaTeX_Caligraphic-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Caligraphic-Regular.woff2) format('woff2'),url(fonts/KaTeX_Caligraphic-Regular.woff) format('woff'),url(fonts/KaTeX_Caligraphic-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Fraktur;src:url(fonts/KaTeX_Fraktur-Bold.eot);src:url(fonts/KaTeX_Fraktur-Bold.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Fraktur-Bold.woff2) format('woff2'),url(fonts/KaTeX_Fraktur-Bold.woff) format('woff'),url(fonts/KaTeX_Fraktur-Bold.ttf) format('truetype');font-weight:700;font-style:normal}@font-face{font-family:KaTeX_Fraktur;src:url(fonts/KaTeX_Fraktur-Regular.eot);src:url(fonts/KaTeX_Fraktur-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Fraktur-Regular.woff2) format('woff2'),url(fonts/KaTeX_Fraktur-Regular.woff) format('woff'),url(fonts/KaTeX_Fraktur-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Main;src:url(fonts/KaTeX_Main-Bold.eot);src:url(fonts/KaTeX_Main-Bold.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Main-Bold.woff2) format('woff2'),url(fonts/KaTeX_Main-Bold.woff) format('woff'),url(fonts/KaTeX_Main-Bold.ttf) format('truetype');font-weight:700;font-style:normal}@font-face{font-family:KaTeX_Main;src:url(fonts/KaTeX_Main-Italic.eot);src:url(fonts/KaTeX_Main-Italic.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Main-Italic.woff2) format('woff2'),url(fonts/KaTeX_Main-Italic.woff) format('woff'),url(fonts/KaTeX_Main-Italic.ttf) format('truetype');font-weight:400;font-style:italic}@font-face{font-family:KaTeX_Main;src:url(fonts/KaTeX_Main-Regular.eot);src:url(fonts/KaTeX_Main-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Main-Regular.woff2) format('woff2'),url(fonts/KaTeX_Main-Regular.woff) format('woff'),url(fonts/KaTeX_Main-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Math;src:url(fonts/KaTeX_Math-Italic.eot);src:url(fonts/KaTeX_Math-Italic.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Math-Italic.woff2) format('woff2'),url(fonts/KaTeX_Math-Italic.woff) format('woff'),url(fonts/KaTeX_Math-Italic.ttf) format('truetype');font-weight:400;font-style:italic}@font-face{font-family:KaTeX_SansSerif;src:url(fonts/KaTeX_SansSerif-Regular.eot);src:url(fonts/KaTeX_SansSerif-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_SansSerif-Regular.woff2) format('woff2'),url(fonts/KaTeX_SansSerif-Regular.woff) format('woff'),url(fonts/KaTeX_SansSerif-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Script;src:url(fonts/KaTeX_Script-Regular.eot);src:url(fonts/KaTeX_Script-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Script-Regular.woff2) format('woff2'),url(fonts/KaTeX_Script-Regular.woff) format('woff'),url(fonts/KaTeX_Script-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size1;src:url(fonts/KaTeX_Size1-Regular.eot);src:url(fonts/KaTeX_Size1-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size1-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size1-Regular.woff) format('woff'),url(fonts/KaTeX_Size1-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size2;src:url(fonts/KaTeX_Size2-Regular.eot);src:url(fonts/KaTeX_Size2-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size2-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size2-Regular.woff) format('woff'),url(fonts/KaTeX_Size2-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size3;src:url(fonts/KaTeX_Size3-Regular.eot);src:url(fonts/KaTeX_Size3-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size3-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size3-Regular.woff) format('woff'),url(fonts/KaTeX_Size3-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size4;src:url(fonts/KaTeX_Size4-Regular.eot);src:url(fonts/KaTeX_Size4-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size4-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size4-Regular.woff) format('woff'),url(fonts/KaTeX_Size4-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Typewriter;src:url(fonts/KaTeX_Typewriter-Regular.eot);src:url(fonts/KaTeX_Typewriter-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Typewriter-Regular.woff2) format('woff2'),url(fonts/KaTeX_Typewriter-Regular.woff) format('woff'),url(fonts/KaTeX_Typewriter-Regular.ttf) format('truetype');font-weight:400;font-style:normal}.katex-display{display:block;margin:1em 0;text-align:center}.katex-display>.katex{display:inline-block;text-align:initial}.katex{font:400 1.21em KaTeX_Main,Times New Roman,serif;line-height:1.2;white-space:nowrap;text-indent:0}.katex .katex-html{display:inline-block}.katex .katex-mathml{position:absolute;clip:rect(1px,1px,1px,1px);padding:0;border:0;height:1px;width:1px;overflow:hidden}.katex .base,.katex .strut{display:inline-block}.katex .mathrm{font-style:normal}.katex .textit{font-style:italic}.katex .mathit{font-family:KaTeX_Math;font-style:italic}.katex .mathbf{font-family:KaTeX_Main;font-weight:700}.katex .amsrm,.katex .mathbb{font-family:KaTeX_AMS}.katex .mathcal{font-family:KaTeX_Caligraphic}.katex .mathfrak{font-family:KaTeX_Fraktur}.katex .mathtt{font-family:KaTeX_Typewriter}.katex .mathscr{font-family:KaTeX_Script}.katex .mathsf{font-family:KaTeX_SansSerif}.katex .mainit{font-family:KaTeX_Main;font-style:italic}.katex .mord+.mop{margin-left:.16667em}.katex .mord+.mbin{margin-left:.22222em}.katex .mord+.mrel{margin-left:.27778em}.katex .mop+.mop,.katex .mop+.mord,.katex .mord+.minner{margin-left:.16667em}.katex .mop+.mrel{margin-left:.27778em}.katex .mop+.minner{margin-left:.16667em}.katex .mbin+.minner,.katex .mbin+.mop,.katex .mbin+.mopen,.katex .mbin+.mord{margin-left:.22222em}.katex .mrel+.minner,.katex .mrel+.mop,.katex .mrel+.mopen,.katex .mrel+.mord{margin-left:.27778em}.katex .mclose+.mop{margin-left:.16667em}.katex .mclose+.mbin{margin-left:.22222em}.katex .mclose+.mrel{margin-left:.27778em}.katex .mclose+.minner,.katex .minner+.mop,.katex .minner+.mord,.katex .mpunct+.mclose,.katex .mpunct+.minner,.katex .mpunct+.mop,.katex .mpunct+.mopen,.katex .mpunct+.mord,.katex .mpunct+.mpunct,.katex .mpunct+.mrel{margin-left:.16667em}.katex .minner+.mbin{margin-left:.22222em}.katex .minner+.mrel{margin-left:.27778em}.katex .minner+.minner,.katex .minner+.mopen,.katex .minner+.mpunct{margin-left:.16667em}.katex .mbin.mtight,.katex .mclose.mtight,.katex .minner.mtight,.katex .mop.mtight,.katex .mopen.mtight,.katex .mord.mtight,.katex .mpunct.mtight,.katex .mrel.mtight{margin-left:0}.katex .mclose+.mop.mtight,.katex .minner+.mop.mtight,.katex .mop+.mop.mtight,.katex .mop+.mord.mtight,.katex .mord+.mop.mtight{margin-left:.16667em}.katex .reset-textstyle.textstyle{font-size:1em}.katex .reset-textstyle.scriptstyle{font-size:.7em}.katex .reset-textstyle.scriptscriptstyle{font-size:.5em}.katex .reset-scriptstyle.textstyle{font-size:1.42857em}.katex .reset-scriptstyle.scriptstyle{font-size:1em}.katex .reset-scriptstyle.scriptscriptstyle{font-size:.71429em}.katex .reset-scriptscriptstyle.textstyle{font-size:2em}.katex .reset-scriptscriptstyle.scriptstyle{font-size:1.4em}.katex .reset-scriptscriptstyle.scriptscriptstyle{font-size:1em}.katex .style-wrap{position:relative}.katex .vlist{display:inline-block}.katex .vlist>span{display:block;height:0;position:relative}.katex .vlist>span>span{display:inline-block}.katex .vlist .baseline-fix{display:inline-table;table-layout:fixed}.katex .msupsub{text-align:left}.katex .mfrac>span>span{text-align:center}.katex .mfrac .frac-line{width:100%}.katex .mfrac .frac-line:before{border-bottom-style:solid;border-bottom-width:1px;content:"";display:block}.katex .mfrac .frac-line:after{border-bottom-style:solid;border-bottom-width:.04em;content:"";display:block;margin-top:-1px}.katex .mspace{display:inline-block}.katex .mspace.negativethinspace{margin-left:-.16667em}.katex .mspace.thinspace{width:.16667em}.katex .mspace.negativemediumspace{margin-left:-.22222em}.katex .mspace.mediumspace{width:.22222em}.katex .mspace.thickspace{width:.27778em}.katex .mspace.sixmuspace{width:.333333em}.katex .mspace.eightmuspace{width:.444444em}.katex .mspace.enspace{width:.5em}.katex .mspace.twelvemuspace{width:.666667em}.katex .mspace.quad{width:1em}.katex .mspace.qquad{width:2em}.katex .llap,.katex .rlap{width:0;position:relative}.katex .llap>.inner,.katex .rlap>.inner{position:absolute}.katex .llap>.fix,.katex .rlap>.fix{display:inline-block}.katex .llap>.inner{right:0}.katex .rlap>.inner{left:0}.katex .katex-logo .a{font-size:.75em;margin-left:-.32em;position:relative;top:-.2em}.katex .katex-logo .t{margin-left:-.23em}.katex .katex-logo .e{margin-left:-.1667em;position:relative;top:.2155em}.katex .katex-logo .x{margin-left:-.125em}.katex .rule{display:inline-block;border:0 solid;position:relative}.katex .overline .overline-line,.katex .underline .underline-line{width:100%}.katex .overline .overline-line:before,.katex .underline .underline-line:before{border-bottom-style:solid;border-bottom-width:1px;content:"";display:block}.katex .overline .overline-line:after,.katex .underline .underline-line:after{border-bottom-style:solid;border-bottom-width:.04em;content:"";display:block;margin-top:-1px}.katex .sqrt>.sqrt-sign{position:relative}.katex .sqrt .sqrt-line{width:100%}.katex .sqrt .sqrt-line:before{border-bottom-style:solid;border-bottom-width:1px;content:"";display:block}.katex .sqrt .sqrt-line:after{border-bottom-style:solid;border-bottom-width:.04em;content:"";display:block;margin-top:-1px}.katex .sqrt>.root{margin-left:.27777778em;margin-right:-.55555556em}.katex .fontsize-ensurer,.katex .sizing{display:inline-block}.katex .fontsize-ensurer.reset-size1.size1,.katex .sizing.reset-size1.size1{font-size:1em}.katex .fontsize-ensurer.reset-size1.size2,.katex .sizing.reset-size1.size2{font-size:1.4em}.katex .fontsize-ensurer.reset-size1.size3,.katex .sizing.reset-size1.size3{font-size:1.6em}.katex .fontsize-ensurer.reset-size1.size4,.katex .sizing.reset-size1.size4{font-size:1.8em}.katex .fontsize-ensurer.reset-size1.size5,.katex .sizing.reset-size1.size5{font-size:2em}.katex .fontsize-ensurer.reset-size1.size6,.katex .sizing.reset-size1.size6{font-size:2.4em}.katex .fontsize-ensurer.reset-size1.size7,.katex .sizing.reset-size1.size7{font-size:2.88em}.katex .fontsize-ensurer.reset-size1.size8,.katex .sizing.reset-size1.size8{font-size:3.46em}.katex .fontsize-ensurer.reset-size1.size9,.katex .sizing.reset-size1.size9{font-size:4.14em}.katex .fontsize-ensurer.reset-size1.size10,.katex .sizing.reset-size1.size10{font-size:4.98em}.katex .fontsize-ensurer.reset-size2.size1,.katex .sizing.reset-size2.size1{font-size:.71428571em}.katex .fontsize-ensurer.reset-size2.size2,.katex .sizing.reset-size2.size2{font-size:1em}.katex .fontsize-ensurer.reset-size2.size3,.katex .sizing.reset-size2.size3{font-size:1.14285714em}.katex .fontsize-ensurer.reset-size2.size4,.katex .sizing.reset-size2.size4{font-size:1.28571429em}.katex .fontsize-ensurer.reset-size2.size5,.katex .sizing.reset-size2.size5{font-size:1.42857143em}.katex .fontsize-ensurer.reset-size2.size6,.katex .sizing.reset-size2.size6{font-size:1.71428571em}.katex .fontsize-ensurer.reset-size2.size7,.katex .sizing.reset-size2.size7{font-size:2.05714286em}.katex .fontsize-ensurer.reset-size2.size8,.katex .sizing.reset-size2.size8{font-size:2.47142857em}.katex .fontsize-ensurer.reset-size2.size9,.katex .sizing.reset-size2.size9{font-size:2.95714286em}.katex .fontsize-ensurer.reset-size2.size10,.katex .sizing.reset-size2.size10{font-size:3.55714286em}.katex .fontsize-ensurer.reset-size3.size1,.katex .sizing.reset-size3.size1{font-size:.625em}.katex .fontsize-ensurer.reset-size3.size2,.katex .sizing.reset-size3.size2{font-size:.875em}.katex .fontsize-ensurer.reset-size3.size3,.katex .sizing.reset-size3.size3{font-size:1em}.katex .fontsize-ensurer.reset-size3.size4,.katex .sizing.reset-size3.size4{font-size:1.125em}.katex .fontsize-ensurer.reset-size3.size5,.katex .sizing.reset-size3.size5{font-size:1.25em}.katex .fontsize-ensurer.reset-size3.size6,.katex .sizing.reset-size3.size6{font-size:1.5em}.katex .fontsize-ensurer.reset-size3.size7,.katex .sizing.reset-size3.size7{font-size:1.8em}.katex .fontsize-ensurer.reset-size3.size8,.katex .sizing.reset-size3.size8{font-size:2.1625em}.katex .fontsize-ensurer.reset-size3.size9,.katex .sizing.reset-size3.size9{font-size:2.5875em}.katex .fontsize-ensurer.reset-size3.size10,.katex .sizing.reset-size3.size10{font-size:3.1125em}.katex .fontsize-ensurer.reset-size4.size1,.katex .sizing.reset-size4.size1{font-size:.55555556em}.katex .fontsize-ensurer.reset-size4.size2,.katex .sizing.reset-size4.size2{font-size:.77777778em}.katex .fontsize-ensurer.reset-size4.size3,.katex .sizing.reset-size4.size3{font-size:.88888889em}.katex .fontsize-ensurer.reset-size4.size4,.katex .sizing.reset-size4.size4{font-size:1em}.katex .fontsize-ensurer.reset-size4.size5,.katex .sizing.reset-size4.size5{font-size:1.11111111em}.katex .fontsize-ensurer.reset-size4.size6,.katex .sizing.reset-size4.size6{font-size:1.33333333em}.katex .fontsize-ensurer.reset-size4.size7,.katex .sizing.reset-size4.size7{font-size:1.6em}.katex .fontsize-ensurer.reset-size4.size8,.katex .sizing.reset-size4.size8{font-size:1.92222222em}.katex .fontsize-ensurer.reset-size4.size9,.katex .sizing.reset-size4.size9{font-size:2.3em}.katex .fontsize-ensurer.reset-size4.size10,.katex .sizing.reset-size4.size10{font-size:2.76666667em}.katex .fontsize-ensurer.reset-size5.size1,.katex .sizing.reset-size5.size1{font-size:.5em}.katex .fontsize-ensurer.reset-size5.size2,.katex .sizing.reset-size5.size2{font-size:.7em}.katex .fontsize-ensurer.reset-size5.size3,.katex .sizing.reset-size5.size3{font-size:.8em}.katex .fontsize-ensurer.reset-size5.size4,.katex .sizing.reset-size5.size4{font-size:.9em}.katex .fontsize-ensurer.reset-size5.size5,.katex .sizing.reset-size5.size5{font-size:1em}.katex .fontsize-ensurer.reset-size5.size6,.katex .sizing.reset-size5.size6{font-size:1.2em}.katex .fontsize-ensurer.reset-size5.size7,.katex .sizing.reset-size5.size7{font-size:1.44em}.katex .fontsize-ensurer.reset-size5.size8,.katex .sizing.reset-size5.size8{font-size:1.73em}.katex .fontsize-ensurer.reset-size5.size9,.katex .sizing.reset-size5.size9{font-size:2.07em}.katex .fontsize-ensurer.reset-size5.size10,.katex .sizing.reset-size5.size10{font-size:2.49em}.katex .fontsize-ensurer.reset-size6.size1,.katex .sizing.reset-size6.size1{font-size:.41666667em}.katex .fontsize-ensurer.reset-size6.size2,.katex .sizing.reset-size6.size2{font-size:.58333333em}.katex .fontsize-ensurer.reset-size6.size3,.katex .sizing.reset-size6.size3{font-size:.66666667em}.katex .fontsize-ensurer.reset-size6.size4,.katex .sizing.reset-size6.size4{font-size:.75em}.katex .fontsize-ensurer.reset-size6.size5,.katex .sizing.reset-size6.size5{font-size:.83333333em}.katex .fontsize-ensurer.reset-size6.size6,.katex .sizing.reset-size6.size6{font-size:1em}.katex .fontsize-ensurer.reset-size6.size7,.katex .sizing.reset-size6.size7{font-size:1.2em}.katex .fontsize-ensurer.reset-size6.size8,.katex .sizing.reset-size6.size8{font-size:1.44166667em}.katex .fontsize-ensurer.reset-size6.size9,.katex .sizing.reset-size6.size9{font-size:1.725em}.katex .fontsize-ensurer.reset-size6.size10,.katex .sizing.reset-size6.size10{font-size:2.075em}.katex .fontsize-ensurer.reset-size7.size1,.katex .sizing.reset-size7.size1{font-size:.34722222em}.katex .fontsize-ensurer.reset-size7.size2,.katex .sizing.reset-size7.size2{font-size:.48611111em}.katex .fontsize-ensurer.reset-size7.size3,.katex .sizing.reset-size7.size3{font-size:.55555556em}.katex .fontsize-ensurer.reset-size7.size4,.katex .sizing.reset-size7.size4{font-size:.625em}.katex .fontsize-ensurer.reset-size7.size5,.katex .sizing.reset-size7.size5{font-size:.69444444em}.katex .fontsize-ensurer.reset-size7.size6,.katex .sizing.reset-size7.size6{font-size:.83333333em}.katex .fontsize-ensurer.reset-size7.size7,.katex .sizing.reset-size7.size7{font-size:1em}.katex .fontsize-ensurer.reset-size7.size8,.katex .sizing.reset-size7.size8{font-size:1.20138889em}.katex .fontsize-ensurer.reset-size7.size9,.katex .sizing.reset-size7.size9{font-size:1.4375em}.katex .fontsize-ensurer.reset-size7.size10,.katex .sizing.reset-size7.size10{font-size:1.72916667em}.katex .fontsize-ensurer.reset-size8.size1,.katex .sizing.reset-size8.size1{font-size:.28901734em}.katex .fontsize-ensurer.reset-size8.size2,.katex .sizing.reset-size8.size2{font-size:.40462428em}.katex .fontsize-ensurer.reset-size8.size3,.katex .sizing.reset-size8.size3{font-size:.46242775em}.katex .fontsize-ensurer.reset-size8.size4,.katex .sizing.reset-size8.size4{font-size:.52023121em}.katex .fontsize-ensurer.reset-size8.size5,.katex .sizing.reset-size8.size5{font-size:.57803468em}.katex .fontsize-ensurer.reset-size8.size6,.katex .sizing.reset-size8.size6{font-size:.69364162em}.katex .fontsize-ensurer.reset-size8.size7,.katex .sizing.reset-size8.size7{font-size:.83236994em}.katex .fontsize-ensurer.reset-size8.size8,.katex .sizing.reset-size8.size8{font-size:1em}.katex .fontsize-ensurer.reset-size8.size9,.katex .sizing.reset-size8.size9{font-size:1.19653179em}.katex .fontsize-ensurer.reset-size8.size10,.katex .sizing.reset-size8.size10{font-size:1.43930636em}.katex .fontsize-ensurer.reset-size9.size1,.katex .sizing.reset-size9.size1{font-size:.24154589em}.katex .fontsize-ensurer.reset-size9.size2,.katex .sizing.reset-size9.size2{font-size:.33816425em}.katex .fontsize-ensurer.reset-size9.size3,.katex .sizing.reset-size9.size3{font-size:.38647343em}.katex .fontsize-ensurer.reset-size9.size4,.katex .sizing.reset-size9.size4{font-size:.43478261em}.katex .fontsize-ensurer.reset-size9.size5,.katex .sizing.reset-size9.size5{font-size:.48309179em}.katex .fontsize-ensurer.reset-size9.size6,.katex .sizing.reset-size9.size6{font-size:.57971014em}.katex .fontsize-ensurer.reset-size9.size7,.katex .sizing.reset-size9.size7{font-size:.69565217em}.katex .fontsize-ensurer.reset-size9.size8,.katex .sizing.reset-size9.size8{font-size:.83574879em}.katex .fontsize-ensurer.reset-size9.size9,.katex .sizing.reset-size9.size9{font-size:1em}.katex .fontsize-ensurer.reset-size9.size10,.katex .sizing.reset-size9.size10{font-size:1.20289855em}.katex .fontsize-ensurer.reset-size10.size1,.katex .sizing.reset-size10.size1{font-size:.20080321em}.katex .fontsize-ensurer.reset-size10.size2,.katex .sizing.reset-size10.size2{font-size:.2811245em}.katex .fontsize-ensurer.reset-size10.size3,.katex .sizing.reset-size10.size3{font-size:.32128514em}.katex .fontsize-ensurer.reset-size10.size4,.katex .sizing.reset-size10.size4{font-size:.36144578em}.katex .fontsize-ensurer.reset-size10.size5,.katex .sizing.reset-size10.size5{font-size:.40160643em}.katex .fontsize-ensurer.reset-size10.size6,.katex .sizing.reset-size10.size6{font-size:.48192771em}.katex .fontsize-ensurer.reset-size10.size7,.katex .sizing.reset-size10.size7{font-size:.57831325em}.katex .fontsize-ensurer.reset-size10.size8,.katex .sizing.reset-size10.size8{font-size:.69477912em}.katex .fontsize-ensurer.reset-size10.size9,.katex .sizing.reset-size10.size9{font-size:.8313253em}.katex .fontsize-ensurer.reset-size10.size10,.katex .sizing.reset-size10.size10{font-size:1em}.katex .delimsizing.size1{font-family:KaTeX_Size1}.katex .delimsizing.size2{font-family:KaTeX_Size2}.katex .delimsizing.size3{font-family:KaTeX_Size3}.katex .delimsizing.size4{font-family:KaTeX_Size4}.katex .delimsizing.mult .delim-size1>span{font-family:KaTeX_Size1}.katex .delimsizing.mult .delim-size4>span{font-family:KaTeX_Size4}.katex .nulldelimiter{display:inline-block;width:.12em}.katex .op-symbol{position:relative}.katex .op-symbol.small-op{font-family:KaTeX_Size1}.katex .op-symbol.large-op{font-family:KaTeX_Size2}.katex .accent>.vlist>span,.katex .op-limits>.vlist>span{text-align:center}.katex .accent .accent-body>span{width:0}.katex .accent .accent-body.accent-vec>span{position:relative;left:.326em}.katex .mtable .vertical-separator{display:inline-block;margin:0 -.025em;border-right:.05em solid #000}.katex .mtable .arraycolsep{display:inline-block}.katex .mtable .col-align-c>.vlist{text-align:center}.katex .mtable .col-align-l>.vlist{text-align:left}.katex .mtable .col-align-r>.vlist{text-align:right}
\ No newline at end of file
diff --git a/specs/es/3.2/katex/katex.min.js b/specs/es/3.2/katex/katex.min.js
new file mode 100644
index 0000000..66c0821
--- /dev/null
+++ b/specs/es/3.2/katex/katex.min.js
@@ -0,0 +1,4 @@
+(function(e){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=e()}else if(typeof define==="function"&&define.amd){define([],e)}else{var t;if(typeof window!=="undefined"){t=window}else if(typeof global!=="undefined"){t=global}else if(typeof self!=="undefined"){t=self}else{t=this}t.katex=e()}})(function(){var e,t,r;return function a(e,t,r){function i(s,l){if(!t[s]){if(!e[s]){var o=typeof require=="function"&&require;if(!l&&o)return o(s,!0);if(n)return n(s,!0);var u=new Error("Cannot find module '"+s+"'");throw u.code="MODULE_NOT_FOUND",u}var p=t[s]={exports:{}};e[s][0].call(p.exports,function(t){var r=e[s][1][t];return i(r?r:t)},p,p.exports,a,e,t,r)}return t[s].exports}var n=typeof require=="function"&&require;for(var s=0;s<r.length;s++)i(r[s]);return i}({1:[function(e,t,r){var a=e("./src/ParseError");var i=e("./src/Settings");var n=e("./src/buildTree");var s=e("./src/parseTree");var l=e("./src/utils");var o=function(e,t,r){l.clearNode(t);var a=new i(r);var o=s(e,a);var u=n(o,e,a).toNode();t.appendChild(u)};if(typeof document!=="undefined"){if(document.compatMode!=="CSS1Compat"){typeof console!=="undefined"&&console.warn("Warning: KaTeX doesn't work in quirks mode. Make sure your "+"website has a suitable doctype.");o=function(){throw new a("KaTeX doesn't work in quirks mode.")}}}var u=function(e,t){var r=new i(t);var a=s(e,r);return n(a,e,r).toMarkup()};var p=function(e,t){var r=new i(t);return s(e,r)};t.exports={render:o,renderToString:u,__parse:p,ParseError:a}},{"./src/ParseError":6,"./src/Settings":8,"./src/buildTree":13,"./src/parseTree":22,"./src/utils":25}],2:[function(e,t,r){"use strict";function a(e){if(!e.__matchAtRelocatable){var t=e.source+"|()";var r="g"+(e.ignoreCase?"i":"")+(e.multiline?"m":"")+(e.unicode?"u":"");e.__matchAtRelocatable=new RegExp(t,r)}return e.__matchAtRelocatable}function i(e,t,r){if(e.global||e.sticky){throw new Error("matchAt(...): Only non-global regexes are supported")}var i=a(e);i.lastIndex=r;var n=i.exec(t);if(n[n.length-1]==null){n.length=n.length-1;return n}else{return null}}t.exports=i},{}],3:[function(e,t,r){var a=e("match-at");var i=e("./ParseError");function n(e){this.input=e;this.pos=0}function s(e,t,r,a){this.text=e;this.start=t;this.end=r;this.lexer=a}s.prototype.range=function(e,t){if(e.lexer!==this.lexer){return new s(t)}return new s(t,this.start,e.end,this.lexer)};var l=new RegExp("([ \r\n	]+)|"+"([!-\\[\\]-\u2027\u202a-\ud7ff\uf900-\uffff]"+"|[\ud800-\udbff][\udc00-\udfff]"+"|\\\\(?:[a-zA-Z]+|[^\ud800-\udfff])"+")");n.prototype.lex=function(){var e=this.input;var t=this.pos;if(t===e.length){return new s("EOF",t,t,this)}var r=a(l,e,t);if(r===null){throw new i("Unexpected character: '"+e[t]+"'",new s(e[t],t,t+1,this))}var n=r[2]||" ";var o=this.pos;this.pos+=r[0].length;var u=this.pos;return new s(n,o,u,this)};t.exports=n},{"./ParseError":6,"match-at":2}],4:[function(e,t,r){var a=e("./Lexer");function i(e,t){this.lexer=new a(e);this.macros=t;this.stack=[];this.discardedWhiteSpace=[]}i.prototype.nextToken=function(){for(;;){if(this.stack.length===0){this.stack.push(this.lexer.lex())}var e=this.stack.pop();var t=e.text;if(!(t.charAt(0)==="\\"&&this.macros.hasOwnProperty(t))){return e}var r=this.macros[t];if(typeof r==="string"){var i=new a(r);r=[];var n=i.lex();while(n.text!=="EOF"){r.push(n);n=i.lex()}r.reverse();this.macros[t]=r}this.stack=this.stack.concat(r)}};i.prototype.get=function(e){this.discardedWhiteSpace=[];var t=this.nextToken();if(e){while(t.text===" "){this.discardedWhiteSpace.push(t);t=this.nextToken()}}return t};i.prototype.unget=function(e){this.stack.push(e);while(this.discardedWhiteSpace.length!==0){this.stack.push(this.discardedWhiteSpace.pop())}};t.exports=i},{"./Lexer":3}],5:[function(e,t,r){function a(e){this.style=e.style;this.color=e.color;this.size=e.size;this.phantom=e.phantom;this.font=e.font;if(e.parentStyle===undefined){this.parentStyle=e.style}else{this.parentStyle=e.parentStyle}if(e.parentSize===undefined){this.parentSize=e.size}else{this.parentSize=e.parentSize}}a.prototype.extend=function(e){var t={style:this.style,size:this.size,color:this.color,parentStyle:this.style,parentSize:this.size,phantom:this.phantom,font:this.font};for(var r in e){if(e.hasOwnProperty(r)){t[r]=e[r]}}return new a(t)};a.prototype.withStyle=function(e){return this.extend({style:e})};a.prototype.withSize=function(e){return this.extend({size:e})};a.prototype.withColor=function(e){return this.extend({color:e})};a.prototype.withPhantom=function(){return this.extend({phantom:true})};a.prototype.withFont=function(e){return this.extend({font:e||this.font})};a.prototype.reset=function(){return this.extend({})};var i={"katex-blue":"#6495ed","katex-orange":"#ffa500","katex-pink":"#ff00af","katex-red":"#df0030","katex-green":"#28ae7b","katex-gray":"gray","katex-purple":"#9d38bd","katex-blueA":"#ccfaff","katex-blueB":"#80f6ff","katex-blueC":"#63d9ea","katex-blueD":"#11accd","katex-blueE":"#0c7f99","katex-tealA":"#94fff5","katex-tealB":"#26edd5","katex-tealC":"#01d1c1","katex-tealD":"#01a995","katex-tealE":"#208170","katex-greenA":"#b6ffb0","katex-greenB":"#8af281","katex-greenC":"#74cf70","katex-greenD":"#1fab54","katex-greenE":"#0d923f","katex-goldA":"#ffd0a9","katex-goldB":"#ffbb71","katex-goldC":"#ff9c39","katex-goldD":"#e07d10","katex-goldE":"#a75a05","katex-redA":"#fca9a9","katex-redB":"#ff8482","katex-redC":"#f9685d","katex-redD":"#e84d39","katex-redE":"#bc2612","katex-maroonA":"#ffbde0","katex-maroonB":"#ff92c6","katex-maroonC":"#ed5fa6","katex-maroonD":"#ca337c","katex-maroonE":"#9e034e","katex-purpleA":"#ddd7ff","katex-purpleB":"#c6b9fc","katex-purpleC":"#aa87ff","katex-purpleD":"#7854ab","katex-purpleE":"#543b78","katex-mintA":"#f5f9e8","katex-mintB":"#edf2df","katex-mintC":"#e0e5cc","katex-grayA":"#f6f7f7","katex-grayB":"#f0f1f2","katex-grayC":"#e3e5e6","katex-grayD":"#d6d8da","katex-grayE":"#babec2","katex-grayF":"#888d93","katex-grayG":"#626569","katex-grayH":"#3b3e40","katex-grayI":"#21242c","katex-kaBlue":"#314453","katex-kaGreen":"#71B307"};a.prototype.getColor=function(){if(this.phantom){return"transparent"}else{return i[this.color]||this.color}};t.exports=a},{}],6:[function(e,t,r){function a(e,t){var r="KaTeX parse error: "+e;var i;var n;if(t&&t.lexer&&t.start<=t.end){var s=t.lexer.input;i=t.start;n=t.end;if(i===s.length){r+=" at end of input: "}else{r+=" at position "+(i+1)+": "}var l=s.slice(i,n).replace(/[^]/g,"$&\u0332");var o;if(i>15){o="\u2026"+s.slice(i-15,i)}else{o=s.slice(0,i)}var u;if(n+15<s.length){u=s.slice(n,n+15)+"\u2026"}else{u=s.slice(n)}r+=o+l+u}var p=new Error(r);p.name="ParseError";p.__proto__=a.prototype;p.position=i;return p}a.prototype.__proto__=Error.prototype;t.exports=a},{}],7:[function(e,t,r){var a=e("./functions");var i=e("./environments");var n=e("./MacroExpander");var s=e("./symbols");var l=e("./utils");var o=e("./unicodeRegexes").cjkRegex;var u=e("./parseData");var p=e("./ParseError");function h(e,t){this.gullet=new n(e,t.macros);this.settings=t;this.leftrightDepth=0}var c=u.ParseNode;function m(e,t,r){this.result=e;this.isFunction=t;this.token=r}h.prototype.expect=function(e,t){if(this.nextToken.text!==e){throw new p("Expected '"+e+"', got '"+this.nextToken.text+"'",this.nextToken)}if(t!==false){this.consume()}};h.prototype.consume=function(){this.nextToken=this.gullet.get(this.mode==="math")};h.prototype.switchMode=function(e){this.gullet.unget(this.nextToken);this.mode=e;this.consume()};h.prototype.parse=function(){this.mode="math";this.consume();var e=this.parseInput();return e};h.prototype.parseInput=function(){var e=this.parseExpression(false);this.expect("EOF",false);return e};var f=["}","\\end","\\right","&","\\\\","\\cr"];h.prototype.parseExpression=function(e,t){var r=[];while(true){var i=this.nextToken;if(f.indexOf(i.text)!==-1){break}if(t&&i.text===t){break}if(e&&a[i.text]&&a[i.text].infix){break}var n=this.parseAtom();if(!n){if(!this.settings.throwOnError&&i.text[0]==="\\"){var s=this.handleUnsupportedCmd();r.push(s);continue}break}r.push(n)}return this.handleInfixNodes(r)};h.prototype.handleInfixNodes=function(e){var t=-1;var r;for(var a=0;a<e.length;a++){var i=e[a];if(i.type==="infix"){if(t!==-1){throw new p("only one infix operator per group",i.value.token)}t=a;r=i.value.replaceWith}}if(t!==-1){var n;var s;var l=e.slice(0,t);var o=e.slice(t+1);if(l.length===1&&l[0].type==="ordgroup"){n=l[0]}else{n=new c("ordgroup",l,this.mode)}if(o.length===1&&o[0].type==="ordgroup"){s=o[0]}else{s=new c("ordgroup",o,this.mode)}var u=this.callFunction(r,[n,s],null);return[new c(u.type,u,this.mode)]}else{return e}};var v=1;h.prototype.handleSupSubscript=function(e){var t=this.nextToken;var r=t.text;this.consume();var i=this.parseGroup();if(!i){if(!this.settings.throwOnError&&this.nextToken.text[0]==="\\"){return this.handleUnsupportedCmd()}else{throw new p("Expected group after '"+r+"'",t)}}else if(i.isFunction){var n=a[i.result].greediness;if(n>v){return this.parseFunction(i)}else{throw new p("Got function '"+i.result+"' with no arguments "+"as "+e,t)}}else{return i.result}};h.prototype.handleUnsupportedCmd=function(){var e=this.nextToken.text;var t=[];for(var r=0;r<e.length;r++){t.push(new c("textord",e[r],"text"))}var a=new c("text",{body:t,type:"text"},this.mode);var i=new c("color",{color:this.settings.errorColor,value:[a],type:"color"},this.mode);this.consume();return i};h.prototype.parseAtom=function(){var e=this.parseImplicitGroup();if(this.mode==="text"){return e}var t;var r;while(true){var a=this.nextToken;if(a.text==="\\limits"||a.text==="\\nolimits"){if(!e||e.type!=="op"){throw new p("Limit controls must follow a math operator",a)}else{var i=a.text==="\\limits";e.value.limits=i;e.value.alwaysHandleSupSub=true}this.consume()}else if(a.text==="^"){if(t){throw new p("Double superscript",a)}t=this.handleSupSubscript("superscript")}else if(a.text==="_"){if(r){throw new p("Double subscript",a)}r=this.handleSupSubscript("subscript")}else if(a.text==="'"){var n=new c("textord","\\prime",this.mode);var s=[n];this.consume();while(this.nextToken.text==="'"){s.push(n);this.consume()}t=new c("ordgroup",s,this.mode)}else{break}}if(t||r){return new c("supsub",{base:e,sup:t,sub:r},this.mode)}else{return e}};var d=["\\tiny","\\scriptsize","\\footnotesize","\\small","\\normalsize","\\large","\\Large","\\LARGE","\\huge","\\Huge"];var g=["\\displaystyle","\\textstyle","\\scriptstyle","\\scriptscriptstyle"];h.prototype.parseImplicitGroup=function(){var e=this.parseSymbol();if(e==null){return this.parseFunction()}var t=e.result;var r;if(t==="\\left"){var a=this.parseFunction(e);++this.leftrightDepth;r=this.parseExpression(false);--this.leftrightDepth;this.expect("\\right",false);var n=this.parseFunction();return new c("leftright",{body:r,left:a.value.value,right:n.value.value},this.mode)}else if(t==="\\begin"){var s=this.parseFunction(e);var o=s.value.name;if(!i.hasOwnProperty(o)){throw new p("No such environment: "+o,s.value.nameGroup)}var u=i[o];var h=this.parseArguments("\\begin{"+o+"}",u);var m={mode:this.mode,envName:o,parser:this,positions:h.pop()};var f=u.handler(m,h);this.expect("\\end",false);var v=this.nextToken;var y=this.parseFunction();if(y.value.name!==o){throw new p("Mismatch: \\begin{"+o+"} matched "+"by \\end{"+y.value.name+"}",v)}f.position=y.position;return f}else if(l.contains(d,t)){r=this.parseExpression(false);return new c("sizing",{size:"size"+(l.indexOf(d,t)+1),value:r},this.mode)}else if(l.contains(g,t)){r=this.parseExpression(true);return new c("styling",{style:t.slice(1,t.length-5),value:r},this.mode)}else{return this.parseFunction(e)}};h.prototype.parseFunction=function(e){if(!e){e=this.parseGroup()}if(e){if(e.isFunction){var t=e.result;var r=a[t];if(this.mode==="text"&&!r.allowedInText){throw new p("Can't use function '"+t+"' in text mode",e.token)}var i=this.parseArguments(t,r);var n=e.token;var s=this.callFunction(t,i,i.pop(),n);return new c(s.type,s,this.mode)}else{return e.result}}else{return null}};h.prototype.callFunction=function(e,t,r,i){var n={funcName:e,parser:this,positions:r,token:i};return a[e].handler(n,t)};h.prototype.parseArguments=function(e,t){var r=t.numArgs+t.numOptionalArgs;if(r===0){return[[this.pos]]}var i=t.greediness;var n=[this.pos];var s=[];for(var l=0;l<r;l++){var o=this.nextToken;var u=t.argTypes&&t.argTypes[l];var h;if(l<t.numOptionalArgs){if(u){h=this.parseGroupOfType(u,true)}else{h=this.parseGroup(true)}if(!h){s.push(null);n.push(this.pos);continue}}else{if(u){h=this.parseGroupOfType(u)}else{h=this.parseGroup()}if(!h){if(!this.settings.throwOnError&&this.nextToken.text[0]==="\\"){h=new m(this.handleUnsupportedCmd(this.nextToken.text),false)}else{throw new p("Expected group after '"+e+"'",o)}}}var c;if(h.isFunction){var f=a[h.result].greediness;if(f>i){c=this.parseFunction(h)}else{throw new p("Got function '"+h.result+"' as "+"argument to '"+e+"'",o)}}else{c=h.result}s.push(c);n.push(this.pos)}s.push(n);return s};h.prototype.parseGroupOfType=function(e,t){var r=this.mode;if(e==="original"){e=r}if(e==="color"){return this.parseColorGroup(t)}if(e==="size"){return this.parseSizeGroup(t)}this.switchMode(e);if(e==="text"){while(this.nextToken.text===" "){this.consume()}}var a=this.parseGroup(t);this.switchMode(r);return a};h.prototype.parseStringGroup=function(e,t){if(t&&this.nextToken.text!=="["){return null}var r=this.mode;this.mode="text";this.expect(t?"[":"{");var a="";var i=this.nextToken;var n=i;while(this.nextToken.text!==(t?"]":"}")){if(this.nextToken.text==="EOF"){throw new p("Unexpected end of input in "+e,i.range(this.nextToken,a))}n=this.nextToken;a+=n.text;this.consume()}this.mode=r;this.expect(t?"]":"}");return i.range(n,a)};h.prototype.parseRegexGroup=function(e,t){var r=this.mode;this.mode="text";var a=this.nextToken;var i=a;var n="";while(this.nextToken.text!=="EOF"&&e.test(n+this.nextToken.text)){i=this.nextToken;n+=i.text;this.consume()}if(n===""){throw new p("Invalid "+t+": '"+a.text+"'",a)}this.mode=r;return a.range(i,n)};h.prototype.parseColorGroup=function(e){var t=this.parseStringGroup("color",e);if(!t){return null}var r=/^(#[a-z0-9]+|[a-z]+)$/i.exec(t.text);if(!r){throw new p("Invalid color: '"+t.text+"'",t)}return new m(new c("color",r[0],this.mode),false)};h.prototype.parseSizeGroup=function(e){var t;if(!e&&this.nextToken.text!=="{"){t=this.parseRegexGroup(/^[-+]? *(?:$|\d+|\d+\.\d*|\.\d*) *[a-z]{0,2}$/,"size")}else{t=this.parseStringGroup("size",e)}if(!t){return null}var r=/([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/.exec(t.text);if(!r){throw new p("Invalid size: '"+t.text+"'",t)}var a={number:+(r[1]+r[2]),unit:r[3]};if(a.unit!=="em"&&a.unit!=="ex"&&a.unit!=="mu"){throw new p("Invalid unit: '"+a.unit+"'",t)}return new m(new c("color",a,this.mode),false)};h.prototype.parseGroup=function(e){var t=this.nextToken;if(this.nextToken.text===(e?"[":"{")){this.consume();var r=this.parseExpression(false,e?"]":null);var a=this.nextToken;this.expect(e?"]":"}");if(this.mode==="text"){this.formLigatures(r)}return new m(new c("ordgroup",r,this.mode,t,a),false)}else{return e?null:this.parseSymbol()}};h.prototype.formLigatures=function(e){var t;var r=e.length-1;for(t=0;t<r;++t){var a=e[t];var i=a.value;if(i==="-"&&e[t+1].value==="-"){if(t+1<r&&e[t+2].value==="-"){e.splice(t,3,new c("textord","---","text",a,e[t+2]));r-=2}else{e.splice(t,2,new c("textord","--","text",a,e[t+1]));r-=1}}if((i==="'"||i==="`")&&e[t+1].value===i){e.splice(t,2,new c("textord",i+i,"text",a,e[t+1]));r-=1}}};h.prototype.parseSymbol=function(){var e=this.nextToken;if(a[e.text]){this.consume();return new m(e.text,true,e)}else if(s[this.mode][e.text]){this.consume();return new m(new c(s[this.mode][e.text].group,e.text,this.mode,e),false,e)}else if(this.mode==="text"&&o.test(e.text)){this.consume();return new m(new c("textord",e.text,this.mode,e),false,e)}else{return null}};h.prototype.ParseNode=c;t.exports=h},{"./MacroExpander":4,"./ParseError":6,"./environments":16,"./functions":19,"./parseData":21,"./symbols":23,"./unicodeRegexes":24,"./utils":25}],8:[function(e,t,r){function a(e,t){return e===undefined?t:e}function i(e){e=e||{};this.displayMode=a(e.displayMode,false);this.throwOnError=a(e.throwOnError,true);this.errorColor=a(e.errorColor,"#cc0000");this.macros=e.macros||{}}t.exports=i},{}],9:[function(e,t,r){var a=e("./fontMetrics.js").sigmas;var i=[{},{},{}];var n;for(var s in a){if(a.hasOwnProperty(s)){for(n=0;n<3;n++){i[n][s]=a[s][n]}}}for(n=0;n<3;n++){i[n].emPerEx=a.xHeight[n]/a.quad[n]}function l(e,t,r,a){this.id=e;this.size=t;this.cramped=a;this.sizeMultiplier=r;this.metrics=i[t>0?t-1:0]}l.prototype.sup=function(){return y[x[this.id]]};l.prototype.sub=function(){return y[b[this.id]]};l.prototype.fracNum=function(){return y[w[this.id]]};l.prototype.fracDen=function(){return y[k[this.id]]};l.prototype.cramp=function(){return y[z[this.id]]};l.prototype.cls=function(){return d[this.size]+(this.cramped?" cramped":" uncramped")};l.prototype.reset=function(){return g[this.size]};l.prototype.isTight=function(){return this.size>=2};var o=0;var u=1;var p=2;var h=3;var c=4;var m=5;var f=6;var v=7;var d=["displaystyle textstyle","textstyle","scriptstyle","scriptscriptstyle"];var g=["reset-textstyle","reset-textstyle","reset-scriptstyle","reset-scriptscriptstyle"];var y=[new l(o,0,1,false),new l(u,0,1,true),new l(p,1,1,false),new l(h,1,1,true),new l(c,2,.7,false),new l(m,2,.7,true),new l(f,3,.5,false),new l(v,3,.5,true)];var x=[c,m,c,m,f,v,f,v];var b=[m,m,m,m,v,v,v,v];var w=[p,h,c,m,f,v,f,v];var k=[h,h,m,m,v,v,v,v];var z=[u,u,h,h,m,m,v,v];t.exports={DISPLAY:y[o],TEXT:y[p],SCRIPT:y[c],SCRIPTSCRIPT:y[f]}},{"./fontMetrics.js":17}],10:[function(e,t,r){var a=e("./domTree");var i=e("./fontMetrics");var n=e("./symbols");var s=e("./utils");var l=["\\Gamma","\\Delta","\\Theta","\\Lambda","\\Xi","\\Pi","\\Sigma","\\Upsilon","\\Phi","\\Psi","\\Omega"];var o=["\u0131","\u0237","\xa3"];var u=function(e,t,r,s,l){if(n[r][e]&&n[r][e].replace){e=n[r][e].replace}var o=i.getCharacterMetrics(e,t);var u;if(o){var p=o.italic;if(r==="text"){p=0}u=new a.symbolNode(e,o.height,o.depth,p,o.skew,l)}else{typeof console!=="undefined"&&console.warn("No character metrics for '"+e+"' in style '"+t+"'");u=new a.symbolNode(e,0,0,0,0,l)}if(s){if(s.style.isTight()){u.classes.push("mtight")}if(s.getColor()){u.style.color=s.getColor()}}return u};var p=function(e,t,r,a){if(e==="\\"||n[t][e].font==="main"){return u(e,"Main-Regular",t,r,a)}else{return u(e,"AMS-Regular",t,r,a.concat(["amsrm"]))}};var h=function(e,t,r,a,i){if(i==="mathord"){return c(e,t,r,a)}else if(i==="textord"){return u(e,"Main-Regular",t,r,a.concat(["mathrm"]))}else{throw new Error("unexpected type: "+i+" in mathDefault")}};var c=function(e,t,r,a){if(/[0-9]/.test(e.charAt(0))||s.contains(o,e)||s.contains(l,e)){return u(e,"Main-Italic",t,r,a.concat(["mainit"]))}else{return u(e,"Math-Italic",t,r,a.concat(["mathit"]))}};var m=function(e,t,r){var a=e.mode;var l=e.value;if(n[a][l]&&n[a][l].replace){l=n[a][l].replace}var p=["mord"];var m=t.font;if(m){if(m==="mathit"||s.contains(o,l)){return c(l,a,t,p)}else{var f=k[m].fontName;if(i.getCharacterMetrics(l,f)){return u(l,f,a,t,p.concat([m]))}else{return h(l,a,t,p,r)}}}else{return h(l,a,t,p,r)}};var f=function(e){var t=0;var r=0;var a=0;if(e.children){for(var i=0;i<e.children.length;i++){if(e.children[i].height>t){t=e.children[i].height}if(e.children[i].depth>r){r=e.children[i].depth}if(e.children[i].maxFontSize>a){a=e.children[i].maxFontSize}}}e.height=t;e.depth=r;e.maxFontSize=a};var v=function(e,t,r){var i=new a.span(e,t,r);f(i);return i};var d=function(e,t){e.children=t.concat(e.children);f(e)};var g=function(e){var t=new a.documentFragment(e);f(t);return t};var y=function(e,t){var r=v([],[new a.symbolNode("\u200b")]);r.style.fontSize=t/e.style.sizeMultiplier+"em";var i=v(["fontsize-ensurer","reset-"+e.size,"size5"],[r]);return i};var x=function(e,t,r,i){var n;var s;var l;if(t==="individualShift"){var o=e;e=[o[0]];n=-o[0].shift-o[0].elem.depth;s=n;for(l=1;l<o.length;l++){var u=-o[l].shift-s-o[l].elem.depth;var p=u-(o[l-1].elem.height+o[l-1].elem.depth);s=s+u;e.push({type:"kern",size:p});e.push(o[l])}}else if(t==="top"){var h=r;for(l=0;l<e.length;l++){if(e[l].type==="kern"){h-=e[l].size}else{h-=e[l].elem.height+e[l].elem.depth}}n=h}else if(t==="bottom"){n=-r}else if(t==="shift"){n=-e[0].elem.depth-r}else if(t==="firstBaseline"){n=-e[0].elem.depth}else{n=0}var c=0;for(l=0;l<e.length;l++){if(e[l].type==="elem"){c=Math.max(c,e[l].elem.maxFontSize)}}var m=y(i,c);var f=[];s=n;for(l=0;l<e.length;l++){if(e[l].type==="kern"){s+=e[l].size}else{var d=e[l].elem;var g=-d.depth-s;s+=d.height+d.depth;var x=v([],[m,d]);x.height-=g;x.depth+=g;x.style.top=g+"em";f.push(x)}}var b=v(["baseline-fix"],[m,new a.symbolNode("\u200b")]);f.push(b);var w=v(["vlist"],f);w.height=Math.max(s,w.height);w.depth=Math.max(-n,w.depth);return w};var b={size1:.5,size2:.7,size3:.8,size4:.9,size5:1,size6:1.2,size7:1.44,size8:1.73,size9:2.07,size10:2.49};var w={"\\qquad":{size:"2em",className:"qquad"},"\\quad":{size:"1em",className:"quad"},"\\enspace":{size:"0.5em",className:"enspace"},"\\;":{size:"0.277778em",className:"thickspace"},"\\:":{size:"0.22222em",className:"mediumspace"},"\\,":{size:"0.16667em",className:"thinspace"},"\\!":{size:"-0.16667em",className:"negativethinspace"}};var k={mathbf:{variant:"bold",fontName:"Main-Bold"},mathrm:{variant:"normal",fontName:"Main-Regular"},textit:{variant:"italic",fontName:"Main-Italic"},mathbb:{variant:"double-struck",fontName:"AMS-Regular"},mathcal:{variant:"script",fontName:"Caligraphic-Regular"},mathfrak:{variant:"fraktur",fontName:"Fraktur-Regular"},mathscr:{variant:"script",fontName:"Script-Regular"},mathsf:{variant:"sans-serif",fontName:"SansSerif-Regular"},mathtt:{variant:"monospace",fontName:"Typewriter-Regular"}};t.exports={fontMap:k,makeSymbol:u,mathsym:p,makeSpan:v,makeFragment:g,makeVList:x,makeOrd:m,prependChildren:d,sizingMultiplier:b,spacingFunctions:w}},{"./domTree":15,"./fontMetrics":17,"./symbols":23,"./utils":25}],11:[function(e,t,r){var a=e("./ParseError");var i=e("./Style");var n=e("./buildCommon");var s=e("./delimiter");var l=e("./domTree");var o=e("./fontMetrics");var u=e("./utils");var p=n.makeSpan;var h=function(e){return e instanceof l.span&&e.classes[0]==="mspace"};var c=function(e){return e&&e.classes[0]==="mbin"};var m=function(e,t){if(e){return u.contains(["mbin","mopen","mrel","mop","mpunct"],e.classes[0])}else{return t}};var f=function(e,t){if(e){return u.contains(["mrel","mclose","mpunct"],e.classes[0])}else{return t}};var v=function(e,t,r){var a=[];for(var i=0;i<e.length;i++){var s=e[i];var o=z(s,t);if(o instanceof l.documentFragment){Array.prototype.push.apply(a,o.children)}else{a.push(o)}}var u=null;for(i=0;i<a.length;i++){if(h(a[i])){u=u||[];u.push(a[i]);a.splice(i,1);i--}else if(u){if(a[i]instanceof l.symbolNode){a[i]=p([].concat(a[i].classes),[a[i]])}n.prependChildren(a[i],u);u=null}}if(u){Array.prototype.push.apply(a,u)}for(i=0;i<a.length;i++){if(c(a[i])&&(m(a[i-1],r)||f(a[i+1],r))){a[i].classes[0]="mord"}}return a};var d=function(e){if(e instanceof l.documentFragment){if(e.children.length){return d(e.children[e.children.length-1])}}else{if(u.contains(["mord","mop","mbin","mrel","mopen","mclose","mpunct","minner"],e.classes[0])){return e.classes[0]}}return null};var g=function(e,t){if(!e){return false}else if(e.type==="op"){return e.value.limits&&(t.style.size===i.DISPLAY.size||e.value.alwaysHandleSupSub)}else if(e.type==="accent"){return x(e.value.base)}else{return null}};var y=function(e){if(!e){return false}else if(e.type==="ordgroup"){if(e.value.length===1){return y(e.value[0])}else{return e}}else if(e.type==="color"){if(e.value.value.length===1){return y(e.value.value[0])}else{return e}}else if(e.type==="font"){return y(e.value.body)}else{return e}};var x=function(e){var t=y(e);return t.type==="mathord"||t.type==="textord"||t.type==="bin"||t.type==="rel"||t.type==="inner"||t.type==="open"||t.type==="close"||t.type==="punct"};var b=function(e,t){return p(t.concat(["sizing","reset-"+e.size,"size5",e.style.reset(),i.TEXT.cls(),"nulldelimiter"]))};var w={};w.mathord=function(e,t){return n.makeOrd(e,t,"mathord")};w.textord=function(e,t){return n.makeOrd(e,t,"textord")};w.bin=function(e,t){return n.mathsym(e.value,e.mode,t,["mbin"])};w.rel=function(e,t){return n.mathsym(e.value,e.mode,t,["mrel"])};w.open=function(e,t){return n.mathsym(e.value,e.mode,t,["mopen"])};w.close=function(e,t){return n.mathsym(e.value,e.mode,t,["mclose"])};w.inner=function(e,t){return n.mathsym(e.value,e.mode,t,["minner"])};w.punct=function(e,t){return n.mathsym(e.value,e.mode,t,["mpunct"])};w.ordgroup=function(e,t){return p(["mord",t.style.cls()],v(e.value,t.reset(),true),t)};w.text=function(e,t){var r=t.withFont(e.value.style);var a=v(e.value.body,r,true);for(var i=0;i<a.length-1;i++){if(a[i].tryCombine(a[i+1])){a.splice(i+1,1);i--}}return p(["mord","text",r.style.cls()],a,r)};w.color=function(e,t){var r=v(e.value.value,t.withColor(e.value.color),false);return new n.makeFragment(r)};w.supsub=function(e,t){if(g(e.value.base,t)){return w[e.value.base.type](e,t)}var r=z(e.value.base,t.reset());var a;var s;var u;var h;var c=t.style;var m;if(e.value.sup){m=t.withStyle(c.sup());u=z(e.value.sup,m);a=p([c.reset(),c.sup().cls()],[u],m)}if(e.value.sub){m=t.withStyle(c.sub());h=z(e.value.sub,m);s=p([c.reset(),c.sub().cls()],[h],m)}var f;var v;if(x(e.value.base)){f=0;v=0}else{f=r.height-c.metrics.supDrop;v=r.depth+c.metrics.subDrop}var y;if(c===i.DISPLAY){y=c.metrics.sup1}else if(c.cramped){y=c.metrics.sup3}else{y=c.metrics.sup2}var b=i.TEXT.sizeMultiplier*c.sizeMultiplier;var k=.5/o.metrics.ptPerEm/b+"em";var S;if(!e.value.sup){v=Math.max(v,c.metrics.sub1,h.height-.8*c.metrics.xHeight);S=n.makeVList([{type:"elem",elem:s}],"shift",v,t);S.children[0].style.marginRight=k;if(r instanceof l.symbolNode){S.children[0].style.marginLeft=-r.italic+"em"}}else if(!e.value.sub){f=Math.max(f,y,u.depth+.25*c.metrics.xHeight);S=n.makeVList([{type:"elem",elem:a}],"shift",-f,t);S.children[0].style.marginRight=k}else{f=Math.max(f,y,u.depth+.25*c.metrics.xHeight);v=Math.max(v,c.metrics.sub2);var M=o.metrics.defaultRuleThickness;if(f-u.depth-(h.height-v)<4*M){v=4*M-(f-u.depth)+h.height;var T=.8*c.metrics.xHeight-(f-u.depth);if(T>0){f+=T;v-=T}}S=n.makeVList([{type:"elem",elem:s,shift:v},{type:"elem",elem:a,shift:-f}],"individualShift",null,t);if(r instanceof l.symbolNode){S.children[0].style.marginLeft=-r.italic+"em"}S.children[0].style.marginRight=k;S.children[1].style.marginRight=k}var A=d(r)||"mord";return p([A],[r,p(["msupsub"],[S])],t)};w.genfrac=function(e,t){var r=t.style;if(e.value.size==="display"){r=i.DISPLAY}else if(e.value.size==="text"){r=i.TEXT}var a=r.fracNum();var l=r.fracDen();var u;u=t.withStyle(a);var h=z(e.value.numer,u);var c=p([r.reset(),a.cls()],[h],u);u=t.withStyle(l);var m=z(e.value.denom,u);var f=p([r.reset(),l.cls()],[m],u);var v;if(e.value.hasBarLine){v=o.metrics.defaultRuleThickness/t.style.sizeMultiplier}else{v=0}var d;var g;var y;if(r.size===i.DISPLAY.size){d=r.metrics.num1;if(v>0){g=3*v}else{g=7*o.metrics.defaultRuleThickness}y=r.metrics.denom1}else{if(v>0){d=r.metrics.num2;g=v}else{d=r.metrics.num3;g=3*o.metrics.defaultRuleThickness}y=r.metrics.denom2}var x;if(v===0){var w=d-h.depth-(m.height-y);if(w<g){d+=.5*(g-w);y+=.5*(g-w)}x=n.makeVList([{type:"elem",elem:f,shift:y},{type:"elem",elem:c,shift:-d}],"individualShift",null,t)}else{var k=r.metrics.axisHeight;if(d-h.depth-(k+.5*v)<g){d+=g-(d-h.depth-(k+.5*v))}if(k-.5*v-(m.height-y)<g){y+=g-(k-.5*v-(m.height-y))}var S=p([t.style.reset(),i.TEXT.cls(),"frac-line"]);S.height=v;var M=-(k-.5*v);x=n.makeVList([{type:"elem",elem:f,shift:y},{type:"elem",elem:S,shift:M},{type:"elem",elem:c,shift:-d}],"individualShift",null,t)}x.height*=r.sizeMultiplier/t.style.sizeMultiplier;x.depth*=r.sizeMultiplier/t.style.sizeMultiplier;var T;if(r.size===i.DISPLAY.size){T=r.metrics.delim1}else{T=r.metrics.delim2}var A;var N;if(e.value.leftDelim==null){A=b(t,["mopen"])}else{A=s.customSizedDelim(e.value.leftDelim,T,true,t.withStyle(r),e.mode,["mopen"])}if(e.value.rightDelim==null){N=b(t,["mclose"])}else{N=s.customSizedDelim(e.value.rightDelim,T,true,t.withStyle(r),e.mode,["mclose"])}return p(["mord",t.style.reset(),r.cls()],[A,p(["mfrac"],[x]),N],t)};var k=function(e,t){var r=e.number;if(e.unit==="ex"){r*=t.metrics.emPerEx}else if(e.unit==="mu"){r/=18}return r};w.array=function(e,t){var r;var i;var s=e.value.body.length;var l=0;var h=new Array(s);var c=t.style;var m=1/o.metrics.ptPerEm;var f=5*m;var v=12*m;var d=u.deflt(e.value.arraystretch,1);var g=d*v;var y=.7*g;var x=.3*g;var b=0;for(r=0;r<e.value.body.length;++r){var w=e.value.body[r];var S=y;var M=x;if(l<w.length){l=w.length}var T=new Array(w.length);for(i=0;i<w.length;++i){var A=z(w[i],t);if(M<A.depth){M=A.depth}if(S<A.height){S=A.height}T[i]=A}var N=0;if(e.value.rowGaps[r]){N=k(e.value.rowGaps[r].value,c);if(N>0){N+=x;if(M<N){M=N}N=0}}T.height=S;T.depth=M;b+=S;T.pos=b;b+=M+N;h[r]=T}var q=b/2+c.metrics.axisHeight;var R=e.value.cols||[];var E=[];var C;var D;for(i=0,D=0;i<l||D<R.length;++i,++D){var O=R[D]||{};var P=true;while(O.type==="separator"){if(!P){C=p(["arraycolsep"],[]);C.style.width=o.metrics.doubleRuleSep+"em";E.push(C)}if(O.separator==="|"){var F=p(["vertical-separator"],[]);F.style.height=b+"em";F.style.verticalAlign=-(b-q)+"em";E.push(F)}else{throw new a("Invalid separator type: "+O.separator)}D++;O=R[D]||{};P=false}if(i>=l){continue}var I;if(i>0||e.value.hskipBeforeAndAfter){I=u.deflt(O.pregap,f);if(I!==0){C=p(["arraycolsep"],[]);C.style.width=I+"em";E.push(C)}}var L=[];for(r=0;r<s;++r){var B=h[r];var G=B[i];if(!G){continue}var V=B.pos-q;G.depth=B.depth;G.height=B.height;L.push({type:"elem",elem:G,shift:V})}L=n.makeVList(L,"individualShift",null,t);L=p(["col-align-"+(O.align||"c")],[L]);E.push(L);if(i<l-1||e.value.hskipBeforeAndAfter){I=u.deflt(O.postgap,f);if(I!==0){C=p(["arraycolsep"],[]);C.style.width=I+"em";E.push(C)}}}h=p(["mtable"],E);return p(["mord"],[h],t)};w.spacing=function(e,t){if(e.value==="\\ "||e.value==="\\space"||e.value===" "||e.value==="~"){if(e.mode==="text"){return n.makeOrd(e,t,"textord")}else{return p(["mspace"],[n.mathsym(e.value,e.mode,t)],t)}}else{return p(["mspace",n.spacingFunctions[e.value].className],[],t)}};w.llap=function(e,t){var r=p(["inner"],[z(e.value.body,t.reset())]);var a=p(["fix"],[]);return p(["mord","llap",t.style.cls()],[r,a],t)};w.rlap=function(e,t){var r=p(["inner"],[z(e.value.body,t.reset())]);var a=p(["fix"],[]);return p(["mord","rlap",t.style.cls()],[r,a],t)};w.op=function(e,t){var r;var a;var s=false;if(e.type==="supsub"){r=e.value.sup;a=e.value.sub;e=e.value.base;s=true}var l=t.style;var h=["\\smallint"];var c=false;if(l.size===i.DISPLAY.size&&e.value.symbol&&!u.contains(h,e.value.body)){c=true}var m;var f=0;var d=0;if(e.value.symbol){var g=c?"Size2-Regular":"Size1-Regular";m=n.makeSymbol(e.value.body,g,"math",t,["mop","op-symbol",c?"large-op":"small-op"]);f=(m.height-m.depth)/2-l.metrics.axisHeight*l.sizeMultiplier;d=m.italic}else if(e.value.value){var y=v(e.value.value,t,true);m=p(["mop"],y,t)}else{var x=[];for(var b=1;b<e.value.body.length;b++){x.push(n.mathsym(e.value.body[b],e.mode))}m=p(["mop"],x,t)}if(s){m=p([],[m]);var w;var k;var S;var M;var T;if(r){T=t.withStyle(l.sup());var A=z(r,T);w=p([l.reset(),l.sup().cls()],[A],T);k=Math.max(o.metrics.bigOpSpacing1,o.metrics.bigOpSpacing3-A.depth)}if(a){T=t.withStyle(l.sub());var N=z(a,T);S=p([l.reset(),l.sub().cls()],[N],T);M=Math.max(o.metrics.bigOpSpacing2,o.metrics.bigOpSpacing4-N.height)}var q;var R;var E;if(!r){R=m.height-f;q=n.makeVList([{type:"kern",size:o.metrics.bigOpSpacing5},{type:"elem",elem:S},{type:"kern",size:M},{type:"elem",elem:m}],"top",R,t);q.children[0].style.marginLeft=-d+"em"}else if(!a){E=m.depth+f;q=n.makeVList([{type:"elem",elem:m},{type:"kern",size:k},{type:"elem",elem:w},{type:"kern",size:o.metrics.bigOpSpacing5}],"bottom",E,t);q.children[1].style.marginLeft=d+"em"}else if(!r&&!a){return m}else{E=o.metrics.bigOpSpacing5+S.height+S.depth+M+m.depth+f;
+q=n.makeVList([{type:"kern",size:o.metrics.bigOpSpacing5},{type:"elem",elem:S},{type:"kern",size:M},{type:"elem",elem:m},{type:"kern",size:k},{type:"elem",elem:w},{type:"kern",size:o.metrics.bigOpSpacing5}],"bottom",E,t);q.children[0].style.marginLeft=-d+"em";q.children[2].style.marginLeft=d+"em"}return p(["mop","op-limits"],[q],t)}else{if(e.value.symbol){m.style.top=f+"em"}return m}};w.mod=function(e,t){var r=[];if(e.value.modType==="bmod"){if(!t.style.isTight()){r.push(p(["mspace","negativemediumspace"],[],t))}r.push(p(["mspace","thickspace"],[],t))}else if(t.style.size===i.DISPLAY.size){r.push(p(["mspace","quad"],[],t))}else if(e.value.modType==="mod"){r.push(p(["mspace","twelvemuspace"],[],t))}else{r.push(p(["mspace","eightmuspace"],[],t))}if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(n.mathsym("(",e.mode))}if(e.value.modType!=="pod"){var a=[n.mathsym("m",e.mode),n.mathsym("o",e.mode),n.mathsym("d",e.mode)];if(e.value.modType==="bmod"){r.push(p(["mbin"],a,t));r.push(p(["mspace","thickspace"],[],t));if(!t.style.isTight()){r.push(p(["mspace","negativemediumspace"],[],t))}}else{Array.prototype.push.apply(r,a);r.push(p(["mspace","sixmuspace"],[],t))}}if(e.value.value){Array.prototype.push.apply(r,v(e.value.value,t,false))}if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(n.mathsym(")",e.mode))}return n.makeFragment(r)};w.katex=function(e,t){var r=p(["k"],[n.mathsym("K",e.mode)],t);var a=p(["a"],[n.mathsym("A",e.mode)],t);a.height=(a.height+.2)*.75;a.depth=(a.height-.2)*.75;var i=p(["t"],[n.mathsym("T",e.mode)],t);var s=p(["e"],[n.mathsym("E",e.mode)],t);s.height=s.height-.2155;s.depth=s.depth+.2155;var l=p(["x"],[n.mathsym("X",e.mode)],t);return p(["mord","katex-logo"],[r,a,i,s,l],t)};w.overline=function(e,t){var r=t.style;var a=z(e.value.body,t.withStyle(r.cramp()));var s=o.metrics.defaultRuleThickness/r.sizeMultiplier;var l=p([r.reset(),i.TEXT.cls(),"overline-line"]);l.height=s;l.maxFontSize=1;var u=n.makeVList([{type:"elem",elem:a},{type:"kern",size:3*s},{type:"elem",elem:l},{type:"kern",size:s}],"firstBaseline",null,t);return p(["mord","overline"],[u],t)};w.underline=function(e,t){var r=t.style;var a=z(e.value.body,t);var s=o.metrics.defaultRuleThickness/r.sizeMultiplier;var l=p([r.reset(),i.TEXT.cls(),"underline-line"]);l.height=s;l.maxFontSize=1;var u=n.makeVList([{type:"kern",size:s},{type:"elem",elem:l},{type:"kern",size:3*s},{type:"elem",elem:a}],"top",a.height,t);return p(["mord","underline"],[u],t)};w.sqrt=function(e,t){var r=t.style;var a=z(e.value.body,t.withStyle(r.cramp()));var l=o.metrics.defaultRuleThickness/r.sizeMultiplier;var u=p([r.reset(),i.TEXT.cls(),"sqrt-line"],[],t);u.height=l;u.maxFontSize=1;var h=l;if(r.id<i.TEXT.id){h=r.metrics.xHeight}var c=l+h/4;var m=(a.height+a.depth)*r.sizeMultiplier;var f=m+c+l;var v=p(["sqrt-sign"],[s.customSizedDelim("\\surd",f,false,t,e.mode)],t);var d=v.height+v.depth-l;if(d>a.height+a.depth+c){c=(c+d-a.height-a.depth)/2}var g=-(a.height+c+l)+v.height;v.style.top=g+"em";v.height-=g;v.depth+=g;var y;if(a.height===0&&a.depth===0){y=p()}else{y=n.makeVList([{type:"elem",elem:a},{type:"kern",size:c},{type:"elem",elem:u},{type:"kern",size:l}],"firstBaseline",null,t)}if(!e.value.index){return p(["mord","sqrt"],[v,y],t)}else{var x=t.withStyle(i.SCRIPTSCRIPT);var b=z(e.value.index,x);var w=p([r.reset(),i.SCRIPTSCRIPT.cls()],[b],x);var k=Math.max(v.height,y.height);var S=Math.max(v.depth,y.depth);var M=.6*(k-S);var T=n.makeVList([{type:"elem",elem:w}],"shift",-M,t);var A=p(["root"],[T]);return p(["mord","sqrt"],[A,v,y],t)}};w.sizing=function(e,t){var r=v(e.value.value,t.withSize(e.value.size),false);var a=t.style;var i=n.sizingMultiplier[e.value.size];i=i*a.sizeMultiplier;for(var s=0;s<r.length;s++){var l=u.indexOf(r[s].classes,"sizing");if(l<0){r[s].classes.push("sizing","reset-"+t.size,e.value.size,a.cls());r[s].maxFontSize=i}else if(r[s].classes[l+1]==="reset-"+e.value.size){r[s].classes[l+1]="reset-"+t.size}}return n.makeFragment(r)};w.styling=function(e,t){var r={display:i.DISPLAY,text:i.TEXT,script:i.SCRIPT,scriptscript:i.SCRIPTSCRIPT};var a=r[e.value.style];var s=t.withStyle(a);var l=v(e.value.value,s,false);for(var o=0;o<l.length;o++){var p=u.indexOf(l[o].classes,a.reset());if(p<0){l[o].classes.push(t.style.reset(),a.cls())}else{l[o].classes[p]=t.style.reset()}}return new n.makeFragment(l)};w.font=function(e,t){var r=e.value.font;return z(e.value.body,t.withFont(r))};w.delimsizing=function(e,t){var r=e.value.value;if(r==="."){return p([e.value.mclass])}return s.sizedDelim(r,e.value.size,t,e.mode,[e.value.mclass])};w.leftright=function(e,t){var r=v(e.value.body,t.reset(),true);var a=0;var i=0;var n=false;for(var l=0;l<r.length;l++){if(r[l].isMiddle){n=true}else{a=Math.max(r[l].height,a);i=Math.max(r[l].depth,i)}}var o=t.style;a*=o.sizeMultiplier;i*=o.sizeMultiplier;var u;if(e.value.left==="."){u=b(t,["mopen"])}else{u=s.leftRightDelim(e.value.left,a,i,t,e.mode,["mopen"])}r.unshift(u);if(n){for(l=1;l<r.length;l++){if(r[l].isMiddle){r[l]=s.leftRightDelim(r[l].isMiddle.value,a,i,r[l].isMiddle.options,e.mode,[])}}}var h;if(e.value.right==="."){h=b(t,["mclose"])}else{h=s.leftRightDelim(e.value.right,a,i,t,e.mode,["mclose"])}r.push(h);return p(["minner",o.cls()],r,t)};w.middle=function(e,t){var r;if(e.value.value==="."){r=b(t,[])}else{r=s.sizedDelim(e.value.value,1,t,e.mode,[]);r.isMiddle={value:e.value.value,options:t}}return r};w.rule=function(e,t){var r=p(["mord","rule"],[],t);var a=t.style;var i=0;if(e.value.shift){i=k(e.value.shift,a)}var n=k(e.value.width,a);var s=k(e.value.height,a);i/=a.sizeMultiplier;n/=a.sizeMultiplier;s/=a.sizeMultiplier;r.style.borderRightWidth=n+"em";r.style.borderTopWidth=s+"em";r.style.bottom=i+"em";r.width=n;r.height=s+i;r.depth=-i;return r};w.kern=function(e,t){var r=p(["mord","rule"],[],t);var a=t.style;var i=0;if(e.value.dimension){i=k(e.value.dimension,a)}i/=a.sizeMultiplier;r.style.marginLeft=i+"em";return r};w.accent=function(e,t){var r=e.value.base;var a=t.style;var i;if(e.type==="supsub"){var s=e;e=s.value.base;r=e.value.base;s.value.base=r;i=z(s,t.reset())}var l=z(r,t.withStyle(a.cramp()));var o;if(x(r)){var u=y(r);var h=z(u,t.withStyle(a.cramp()));o=h.skew}else{o=0}var c=Math.min(l.height,a.metrics.xHeight);var m=n.makeSymbol(e.value.accent,"Main-Regular","math",t);m.italic=0;var f=e.value.accent==="\\vec"?"accent-vec":null;var v=p(["accent-body",f],[p([],[m])]);v=n.makeVList([{type:"elem",elem:l},{type:"kern",size:-c},{type:"elem",elem:v}],"firstBaseline",null,t);v.children[1].style.marginLeft=2*o+"em";var d=p(["mord","accent"],[v],t);if(i){i.children[0]=d;i.height=Math.max(d.height,i.height);i.classes[0]="mord";return i}else{return d}};w.phantom=function(e,t){var r=v(e.value.value,t.withPhantom(),false);return new n.makeFragment(r)};w.mclass=function(e,t){var r=v(e.value.value,t,true);return p([e.value.mclass],r,t)};var z=function(e,t){if(!e){return p()}if(w[e.type]){var r=w[e.type](e,t);var i;if(t.style!==t.parentStyle){i=t.style.sizeMultiplier/t.parentStyle.sizeMultiplier;r.height*=i;r.depth*=i}if(t.size!==t.parentSize){i=n.sizingMultiplier[t.size]/n.sizingMultiplier[t.parentSize];r.height*=i;r.depth*=i}return r}else{throw new a("Got group of unknown type: '"+e.type+"'")}};var S=function(e,t){e=JSON.parse(JSON.stringify(e));var r=v(e,t,true);var a=p(["base",t.style.cls()],r,t);var i=p(["strut"]);var n=p(["strut","bottom"]);i.style.height=a.height+"em";n.style.height=a.height+a.depth+"em";n.style.verticalAlign=-a.depth+"em";var s=p(["katex-html"],[i,n,a]);s.setAttribute("aria-hidden","true");return s};t.exports=S},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./delimiter":14,"./domTree":15,"./fontMetrics":17,"./utils":25}],12:[function(e,t,r){var a=e("./buildCommon");var i=e("./fontMetrics");var n=e("./mathMLTree");var s=e("./ParseError");var l=e("./symbols");var o=e("./utils");var u=a.makeSpan;var p=a.fontMap;var h=function(e,t){if(l[t][e]&&l[t][e].replace){e=l[t][e].replace}return new n.TextNode(e)};var c=function(e,t){var r=t.font;if(!r){return null}var a=e.mode;if(r==="mathit"){return"italic"}var n=e.value;if(o.contains(["\\imath","\\jmath"],n)){return null}if(l[a][n]&&l[a][n].replace){n=l[a][n].replace}var s=p[r].fontName;if(i.getCharacterMetrics(n,s)){return p[t.font].variant}return null};var m={};m.mathord=function(e,t){var r=new n.MathNode("mi",[h(e.value,e.mode)]);var a=c(e,t);if(a){r.setAttribute("mathvariant",a)}return r};m.textord=function(e,t){var r=h(e.value,e.mode);var a=c(e,t)||"normal";var i;if(/[0-9]/.test(e.value)){i=new n.MathNode("mn",[r]);if(t.font){i.setAttribute("mathvariant",a)}}else{i=new n.MathNode("mi",[r]);i.setAttribute("mathvariant",a)}return i};m.bin=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.rel=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.open=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.close=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.inner=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.punct=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);t.setAttribute("separator","true");return t};m.ordgroup=function(e,t){var r=f(e.value,t);var a=new n.MathNode("mrow",r);return a};m.text=function(e,t){var r=f(e.value.body,t);var a=new n.MathNode("mtext",r);return a};m.color=function(e,t){var r=f(e.value.value,t);var a=new n.MathNode("mstyle",r);a.setAttribute("mathcolor",e.value.color);return a};m.supsub=function(e,t){var r=[v(e.value.base,t)];if(e.value.sub){r.push(v(e.value.sub,t))}if(e.value.sup){r.push(v(e.value.sup,t))}var a;if(!e.value.sub){a="msup"}else if(!e.value.sup){a="msub"}else{a="msubsup"}var i=new n.MathNode(a,r);return i};m.genfrac=function(e,t){var r=new n.MathNode("mfrac",[v(e.value.numer,t),v(e.value.denom,t)]);if(!e.value.hasBarLine){r.setAttribute("linethickness","0px")}if(e.value.leftDelim!=null||e.value.rightDelim!=null){var a=[];if(e.value.leftDelim!=null){var i=new n.MathNode("mo",[new n.TextNode(e.value.leftDelim)]);i.setAttribute("fence","true");a.push(i)}a.push(r);if(e.value.rightDelim!=null){var s=new n.MathNode("mo",[new n.TextNode(e.value.rightDelim)]);s.setAttribute("fence","true");a.push(s)}var l=new n.MathNode("mrow",a);return l}return r};m.array=function(e,t){return new n.MathNode("mtable",e.value.body.map(function(e){return new n.MathNode("mtr",e.map(function(e){return new n.MathNode("mtd",[v(e,t)])}))}))};m.sqrt=function(e,t){var r;if(e.value.index){r=new n.MathNode("mroot",[v(e.value.body,t),v(e.value.index,t)])}else{r=new n.MathNode("msqrt",[v(e.value.body,t)])}return r};m.leftright=function(e,t){var r=f(e.value.body,t);if(e.value.left!=="."){var a=new n.MathNode("mo",[h(e.value.left,e.mode)]);a.setAttribute("fence","true");r.unshift(a)}if(e.value.right!=="."){var i=new n.MathNode("mo",[h(e.value.right,e.mode)]);i.setAttribute("fence","true");r.push(i)}var s=new n.MathNode("mrow",r);return s};m.middle=function(e,t){var r=new n.MathNode("mo",[h(e.value.middle,e.mode)]);r.setAttribute("fence","true");return r};m.accent=function(e,t){var r=new n.MathNode("mo",[h(e.value.accent,e.mode)]);var a=new n.MathNode("mover",[v(e.value.base,t),r]);a.setAttribute("accent","true");return a};m.spacing=function(e){var t;if(e.value==="\\ "||e.value==="\\space"||e.value===" "||e.value==="~"){t=new n.MathNode("mtext",[new n.TextNode("\xa0")])}else{t=new n.MathNode("mspace");t.setAttribute("width",a.spacingFunctions[e.value].size)}return t};m.op=function(e,t){var r;if(e.value.symbol){r=new n.MathNode("mo",[h(e.value.body,e.mode)])}else if(e.value.value){r=new n.MathNode("mo",f(e.value.value,t))}else{r=new n.MathNode("mi",[new n.TextNode(e.value.body.slice(1))])}return r};m.mod=function(e,t){var r=[];if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(new n.MathNode("mo",[h("(",e.mode)]))}if(e.value.modType!=="pod"){r.push(new n.MathNode("mo",[h("mod",e.mode)]))}if(e.value.value){var a=new n.MathNode("mspace");a.setAttribute("width","0.333333em");r.push(a);r=r.concat(f(e.value.value,t))}if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(new n.MathNode("mo",[h(")",e.mode)]))}return new n.MathNode("mo",r)};m.katex=function(e){var t=new n.MathNode("mtext",[new n.TextNode("KaTeX")]);return t};m.font=function(e,t){var r=e.value.font;return v(e.value.body,t.withFont(r))};m.delimsizing=function(e){var t=[];if(e.value.value!=="."){t.push(h(e.value.value,e.mode))}var r=new n.MathNode("mo",t);if(e.value.mclass==="mopen"||e.value.mclass==="mclose"){r.setAttribute("fence","true")}else{r.setAttribute("fence","false")}return r};m.styling=function(e,t){var r=f(e.value.value,t);var a=new n.MathNode("mstyle",r);var i={display:["0","true"],text:["0","false"],script:["1","false"],scriptscript:["2","false"]};var s=i[e.value.style];a.setAttribute("scriptlevel",s[0]);a.setAttribute("displaystyle",s[1]);return a};m.sizing=function(e,t){var r=f(e.value.value,t);var i=new n.MathNode("mstyle",r);i.setAttribute("mathsize",a.sizingMultiplier[e.value.size]+"em");return i};m.overline=function(e,t){var r=new n.MathNode("mo",[new n.TextNode("\u203e")]);r.setAttribute("stretchy","true");var a=new n.MathNode("mover",[v(e.value.body,t),r]);a.setAttribute("accent","true");return a};m.underline=function(e,t){var r=new n.MathNode("mo",[new n.TextNode("\u203e")]);r.setAttribute("stretchy","true");var a=new n.MathNode("munder",[v(e.value.body,t),r]);a.setAttribute("accentunder","true");return a};m.rule=function(e){var t=new n.MathNode("mrow");return t};m.kern=function(e){var t=new n.MathNode("mrow");return t};m.llap=function(e,t){var r=new n.MathNode("mpadded",[v(e.value.body,t)]);r.setAttribute("lspace","-1width");r.setAttribute("width","0px");return r};m.rlap=function(e,t){var r=new n.MathNode("mpadded",[v(e.value.body,t)]);r.setAttribute("width","0px");return r};m.phantom=function(e,t){var r=f(e.value.value,t);return new n.MathNode("mphantom",r)};m.mclass=function(e,t){var r=f(e.value.value,t);return new n.MathNode("mstyle",r)};var f=function(e,t){var r=[];for(var a=0;a<e.length;a++){var i=e[a];r.push(v(i,t))}return r};var v=function(e,t){if(!e){return new n.MathNode("mrow")}if(m[e.type]){return m[e.type](e,t)}else{throw new s("Got group of unknown type: '"+e.type+"'")}};var d=function(e,t,r){var a=f(e,r);var i=new n.MathNode("mrow",a);var s=new n.MathNode("annotation",[new n.TextNode(t)]);s.setAttribute("encoding","application/x-tex");var l=new n.MathNode("semantics",[i,s]);var o=new n.MathNode("math",[l]);return u(["katex-mathml"],[o])};t.exports=d},{"./ParseError":6,"./buildCommon":10,"./fontMetrics":17,"./mathMLTree":20,"./symbols":23,"./utils":25}],13:[function(e,t,r){var a=e("./buildHTML");var i=e("./buildMathML");var n=e("./buildCommon");var s=e("./Options");var l=e("./Settings");var o=e("./Style");var u=n.makeSpan;var p=function(e,t,r){r=r||new l({});var n=o.TEXT;if(r.displayMode){n=o.DISPLAY}var p=new s({style:n,size:"size5"});var h=i(e,t,p);var c=a(e,p);var m=u(["katex"],[h,c]);if(r.displayMode){return u(["katex-display"],[m])}else{return m}};t.exports=p},{"./Options":5,"./Settings":8,"./Style":9,"./buildCommon":10,"./buildHTML":11,"./buildMathML":12}],14:[function(e,t,r){var a=e("./ParseError");var i=e("./Style");var n=e("./buildCommon");var s=e("./fontMetrics");var l=e("./symbols");var o=e("./utils");var u=n.makeSpan;var p=function(e,t){if(l.math[e]&&l.math[e].replace){return s.getCharacterMetrics(l.math[e].replace,t)}else{return s.getCharacterMetrics(e,t)}};var h=function(e,t,r,a){return n.makeSymbol(e,"Size"+t+"-Regular",r,a)};var c=function(e,t,r,a){a=a||[];var i=u(a.concat(["style-wrap",r.style.reset(),t.cls()]),[e],r);var n=t.sizeMultiplier/r.style.sizeMultiplier;i.height*=n;i.depth*=n;i.maxFontSize=t.sizeMultiplier;return i};var m=function(e,t,r,a,i,s){var l=n.makeSymbol(e,"Main-Regular",i,a);var o=c(l,t,a,s);if(r){var u=(1-a.style.sizeMultiplier/t.sizeMultiplier)*a.style.metrics.axisHeight;o.style.top=u+"em";o.height-=u;o.depth+=u}return o};var f=function(e,t,r,a,n,s){var l=h(e,t,n,a);var o=c(u(["delimsizing","size"+t],[l],a),i.TEXT,a,s);if(r){var p=(1-a.style.sizeMultiplier)*a.style.metrics.axisHeight;o.style.top=p+"em";o.height-=p;o.depth+=p}return o};var v=function(e,t,r){var a;if(t==="Size1-Regular"){a="delim-size1"}else if(t==="Size4-Regular"){a="delim-size4"}var i=u(["delimsizinginner",a],[u([],[n.makeSymbol(e,t,r)])]);return{type:"elem",elem:i}};var d=function(e,t,r,a,s,l){var o;var h;var m;var f;o=m=f=e;h=null;var d="Size1-Regular";if(e==="\\uparrow"){m=f="\u23d0"}else if(e==="\\Uparrow"){m=f="\u2016"}else if(e==="\\downarrow"){o=m="\u23d0"}else if(e==="\\Downarrow"){o=m="\u2016"}else if(e==="\\updownarrow"){o="\\uparrow";m="\u23d0";f="\\downarrow"}else if(e==="\\Updownarrow"){o="\\Uparrow";m="\u2016";f="\\Downarrow"}else if(e==="["||e==="\\lbrack"){o="\u23a1";m="\u23a2";f="\u23a3";d="Size4-Regular"}else if(e==="]"||e==="\\rbrack"){o="\u23a4";m="\u23a5";f="\u23a6";d="Size4-Regular"}else if(e==="\\lfloor"){m=o="\u23a2";f="\u23a3";d="Size4-Regular"}else if(e==="\\lceil"){o="\u23a1";m=f="\u23a2";d="Size4-Regular"}else if(e==="\\rfloor"){m=o="\u23a5";f="\u23a6";d="Size4-Regular"}else if(e==="\\rceil"){o="\u23a4";m=f="\u23a5";d="Size4-Regular"}else if(e==="("){o="\u239b";m="\u239c";f="\u239d";d="Size4-Regular"}else if(e===")"){o="\u239e";m="\u239f";f="\u23a0";d="Size4-Regular"}else if(e==="\\{"||e==="\\lbrace"){o="\u23a7";h="\u23a8";f="\u23a9";m="\u23aa";d="Size4-Regular"}else if(e==="\\}"||e==="\\rbrace"){o="\u23ab";h="\u23ac";f="\u23ad";m="\u23aa";d="Size4-Regular"}else if(e==="\\lgroup"){o="\u23a7";f="\u23a9";m="\u23aa";d="Size4-Regular"}else if(e==="\\rgroup"){o="\u23ab";f="\u23ad";m="\u23aa";d="Size4-Regular"}else if(e==="\\lmoustache"){o="\u23a7";f="\u23ad";m="\u23aa";d="Size4-Regular"}else if(e==="\\rmoustache"){o="\u23ab";f="\u23a9";m="\u23aa";d="Size4-Regular"}else if(e==="\\surd"){o="\ue001";f="\u23b7";m="\ue000";d="Size4-Regular"}var g=p(o,d);var y=g.height+g.depth;var x=p(m,d);var b=x.height+x.depth;var w=p(f,d);var k=w.height+w.depth;var z=0;var S=1;if(h!==null){var M=p(h,d);z=M.height+M.depth;S=2}var T=y+k+z;var A=Math.ceil((t-T)/(S*b));var N=T+A*S*b;var q=a.style.metrics.axisHeight;if(r){q*=a.style.sizeMultiplier}var R=N/2-q;var E=[];E.push(v(f,d,s));var C;if(h===null){for(C=0;C<A;C++){E.push(v(m,d,s))}}else{for(C=0;C<A;C++){E.push(v(m,d,s))}E.push(v(h,d,s));for(C=0;C<A;C++){E.push(v(m,d,s))}}E.push(v(o,d,s));var D=n.makeVList(E,"bottom",R,a);return c(u(["delimsizing","mult"],[D],a),i.TEXT,a,l)};var g=["(",")","[","\\lbrack","]","\\rbrack","\\{","\\lbrace","\\}","\\rbrace","\\lfloor","\\rfloor","\\lceil","\\rceil","\\surd"];var y=["\\uparrow","\\downarrow","\\updownarrow","\\Uparrow","\\Downarrow","\\Updownarrow","|","\\|","\\vert","\\Vert","\\lvert","\\rvert","\\lVert","\\rVert","\\lgroup","\\rgroup","\\lmoustache","\\rmoustache"];var x=["<",">","\\langle","\\rangle","/","\\backslash","\\lt","\\gt"];var b=[0,1.2,1.8,2.4,3];var w=function(e,t,r,i,n){if(e==="<"||e==="\\lt"){e="\\langle"}else if(e===">"||e==="\\gt"){e="\\rangle"}if(o.contains(g,e)||o.contains(x,e)){return f(e,t,false,r,i,n)}else if(o.contains(y,e)){return d(e,b[t],false,r,i,n)}else{throw new a("Illegal delimiter: '"+e+"'")}};var k=[{type:"small",style:i.SCRIPTSCRIPT},{type:"small",style:i.SCRIPT},{type:"small",style:i.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4}];var z=[{type:"small",style:i.SCRIPTSCRIPT},{type:"small",style:i.SCRIPT},{type:"small",style:i.TEXT},{type:"stack"}];var S=[{type:"small",style:i.SCRIPTSCRIPT},{type:"small",style:i.SCRIPT},{type:"small",style:i.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4},{type:"stack"}];var M=function(e){if(e.type==="small"){return"Main-Regular"}else if(e.type==="large"){return"Size"+e.size+"-Regular"}else if(e.type==="stack"){return"Size4-Regular"}};var T=function(e,t,r,a){var i=Math.min(2,3-a.style.size);for(var n=i;n<r.length;n++){if(r[n].type==="stack"){break}var s=p(e,M(r[n]));var l=s.height+s.depth;if(r[n].type==="small"){l*=r[n].style.sizeMultiplier}if(l>t){return r[n]}}return r[r.length-1]};var A=function(e,t,r,a,i,n){if(e==="<"||e==="\\lt"){e="\\langle"}else if(e===">"||e==="\\gt"){e="\\rangle"}var s;if(o.contains(x,e)){s=k}else if(o.contains(g,e)){s=S}else{s=z}var l=T(e,t,s,a);if(l.type==="small"){return m(e,l.style,r,a,i,n)}else if(l.type==="large"){return f(e,l.size,r,a,i,n)}else if(l.type==="stack"){return d(e,t,r,a,i,n)}};var N=function(e,t,r,a,i,n){var l=a.style.metrics.axisHeight*a.style.sizeMultiplier;var o=901;var u=5/s.metrics.ptPerEm;var p=Math.max(t-l,r+l);var h=Math.max(p/500*o,2*p-u);return A(e,h,true,a,i,n)};t.exports={sizedDelim:w,customSizedDelim:A,leftRightDelim:N}},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./fontMetrics":17,"./symbols":23,"./utils":25}],15:[function(e,t,r){var a=e("./unicodeRegexes");var i=e("./utils");var n=function(e){e=e.slice();for(var t=e.length-1;t>=0;t--){if(!e[t]){e.splice(t,1)}}return e.join(" ")};function s(e,t,r){this.classes=e||[];this.children=t||[];this.height=0;this.depth=0;this.maxFontSize=0;this.style={};this.attributes={};if(r){if(r.style.isTight()){this.classes.push("mtight")}if(r.getColor()){this.style.color=r.getColor()}}}s.prototype.setAttribute=function(e,t){this.attributes[e]=t};s.prototype.tryCombine=function(e){return false};s.prototype.toNode=function(){var e=document.createElement("span");e.className=n(this.classes);for(var t in this.style){if(Object.prototype.hasOwnProperty.call(this.style,t)){e.style[t]=this.style[t]}}for(var r in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,r)){e.setAttribute(r,this.attributes[r])}}for(var a=0;a<this.children.length;a++){e.appendChild(this.children[a].toNode())}return e};s.prototype.toMarkup=function(){var e="<span";if(this.classes.length){e+=' class="';e+=i.escape(n(this.classes));e+='"'}var t="";for(var r in this.style){if(this.style.hasOwnProperty(r)){t+=i.hyphenate(r)+":"+this.style[r]+";"}}if(t){e+=' style="'+i.escape(t)+'"'}for(var a in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,a)){e+=" "+a+'="';e+=i.escape(this.attributes[a]);e+='"'}}e+=">";for(var s=0;s<this.children.length;s++){e+=this.children[s].toMarkup()}e+="</span>";return e};function l(e){this.children=e||[];this.height=0;this.depth=0;this.maxFontSize=0}l.prototype.toNode=function(){var e=document.createDocumentFragment();for(var t=0;t<this.children.length;t++){e.appendChild(this.children[t].toNode())}return e};l.prototype.toMarkup=function(){var e="";for(var t=0;t<this.children.length;t++){e+=this.children[t].toMarkup()}return e};var o={"\xee":"\u0131\u0302","\xef":"\u0131\u0308","\xed":"\u0131\u0301","\xec":"\u0131\u0300"};function u(e,t,r,i,n,s,l){this.value=e||"";this.height=t||0;this.depth=r||0;this.italic=i||0;this.skew=n||0;this.classes=s||[];this.style=l||{};this.maxFontSize=0;if(a.cjkRegex.test(e)){if(a.hangulRegex.test(e)){this.classes.push("hangul_fallback")}else{this.classes.push("cjk_fallback")}}if(/[\xee\xef\xed\xec]/.test(this.value)){this.value=o[this.value]}}u.prototype.tryCombine=function(e){if(!e||!(e instanceof u)||this.italic>0||n(this.classes)!==n(e.classes)||this.skew!==e.skew||this.maxFontSize!==e.maxFontSize){return false}for(var t in this.style){if(this.style.hasOwnProperty(t)&&this.style[t]!==e.style[t]){return false}}for(t in e.style){if(e.style.hasOwnProperty(t)&&this.style[t]!==e.style[t]){return false}}this.value+=e.value;this.height=Math.max(this.height,e.height);this.depth=Math.max(this.depth,e.depth);this.italic=e.italic;return true};u.prototype.toNode=function(){var e=document.createTextNode(this.value);var t=null;if(this.italic>0){t=document.createElement("span");t.style.marginRight=this.italic+"em"}if(this.classes.length>0){t=t||document.createElement("span");t.className=n(this.classes)}for(var r in this.style){if(this.style.hasOwnProperty(r)){t=t||document.createElement("span");t.style[r]=this.style[r]}}if(t){t.appendChild(e);return t}else{return e}};u.prototype.toMarkup=function(){var e=false;var t="<span";if(this.classes.length){e=true;t+=' class="';t+=i.escape(n(this.classes));t+='"'}var r="";if(this.italic>0){r+="margin-right:"+this.italic+"em;"}for(var a in this.style){if(this.style.hasOwnProperty(a)){r+=i.hyphenate(a)+":"+this.style[a]+";"}}if(r){e=true;t+=' style="'+i.escape(r)+'"'}var s=i.escape(this.value);if(e){t+=">";t+=s;t+="</span>";return t}else{return s}};t.exports={span:s,documentFragment:l,symbolNode:u}},{"./unicodeRegexes":24,"./utils":25}],16:[function(e,t,r){var a=e("./parseData");var i=e("./ParseError");var n=e("./Style");var s=a.ParseNode;function l(e,t){var r=[];var a=[r];var n=[];while(true){var l=e.parseExpression(false,null);r.push(new s("ordgroup",l,e.mode));var o=e.nextToken.text;if(o==="&"){e.consume()}else if(o==="\\end"){break}else if(o==="\\\\"||o==="\\cr"){var u=e.parseFunction();n.push(u.value.size);r=[];a.push(r)}else{throw new i("Expected & or \\\\ or \\end",e.nextToken)}}t.body=a;t.rowGaps=n;return new s(t.type,t,e.mode)}function o(e,r,a){if(typeof e==="string"){e=[e]}if(typeof r==="number"){r={numArgs:r}}var i={numArgs:r.numArgs||0,argTypes:r.argTypes,greediness:1,allowedInText:!!r.allowedInText,numOptionalArgs:r.numOptionalArgs||0,handler:a};for(var n=0;n<e.length;++n){t.exports[e[n]]=i}}o("array",{numArgs:1},function(e,t){var r=t[0];r=r.value.map?r.value:[r];var a=r.map(function(e){var t=e.value;if("lcr".indexOf(t)!==-1){return{type:"align",align:t}}else if(t==="|"){return{type:"separator",separator:"|"}}throw new i("Unknown column alignment: "+e.value,e)});var n={type:"array",cols:a,hskipBeforeAndAfter:true};n=l(e.parser,n);return n});o(["matrix","pmatrix","bmatrix","Bmatrix","vmatrix","Vmatrix"],{},function(e){var t={matrix:null,pmatrix:["(",")"],bmatrix:["[","]"],Bmatrix:["\\{","\\}"],vmatrix:["|","|"],Vmatrix:["\\Vert","\\Vert"]}[e.envName];var r={type:"array",hskipBeforeAndAfter:false};r=l(e.parser,r);if(t){r=new s("leftright",{body:[r],left:t[0],right:t[1]},e.mode)}return r});o("cases",{},function(e){var t={type:"array",arraystretch:1.2,cols:[{type:"align",align:"l",pregap:0,postgap:n.TEXT.metrics.quad},{type:"align",align:"l",pregap:0,postgap:0}]};t=l(e.parser,t);t=new s("leftright",{body:[t],left:"\\{",right:"."},e.mode);return t});o("aligned",{},function(e){var t={type:"array",cols:[]};t=l(e.parser,t);var r=new s("ordgroup",[],e.mode);var a=0;t.value.body.forEach(function(e){var t;for(t=1;t<e.length;t+=2){e[t].value.unshift(r)}if(a<e.length){a=e.length}});for(var i=0;i<a;++i){var n="r";var o=0;if(i%2===1){n="l"}else if(i>0){o=2}t.value.cols[i]={type:"align",align:n,pregap:o,postgap:0}}return t})},{"./ParseError":6,"./Style":9,"./parseData":21}],17:[function(e,t,r){var a=e("./Style");var i=e("./unicodeRegexes").cjkRegex;var n={slant:[.25,.25,.25],space:[0,0,0],stretch:[0,0,0],shrink:[0,0,0],xHeight:[.431,.431,.431],quad:[1,1.171,1.472],extraSpace:[0,0,0],num1:[.677,.732,.925],num2:[.394,.384,.387],num3:[.444,.471,.504],denom1:[.686,.752,1.025],denom2:[.345,.344,.532],sup1:[.413,.503,.504],sup2:[.363,.431,.404],sup3:[.289,.286,.294],sub1:[.15,.143,.2],sub2:[.247,.286,.4],supDrop:[.386,.353,.494],subDrop:[.05,.071,.1],delim1:[2.39,1.7,1.98],delim2:[1.01,1.157,1.42],axisHeight:[.25,.25,.25]};var s=0;var l=0;var o=0;var u=0;var p=.431;var h=1;var c=0;var m=.04;var f=.111;var v=.166;var d=.2;var g=.6;var y=.1;var x=10;var b=2/x;var w={defaultRuleThickness:m,bigOpSpacing1:f,bigOpSpacing2:v,bigOpSpacing3:d,bigOpSpacing4:g,bigOpSpacing5:y,ptPerEm:x,doubleRuleSep:b};var k=e("./fontMetricsData");var z={"\xc0":"A","\xc1":"A","\xc2":"A","\xc3":"A","\xc4":"A","\xc5":"A","\xc6":"A","\xc7":"C","\xc8":"E","\xc9":"E","\xca":"E","\xcb":"E","\xcc":"I","\xcd":"I","\xce":"I","\xcf":"I","\xd0":"D","\xd1":"N","\xd2":"O","\xd3":"O","\xd4":"O","\xd5":"O","\xd6":"O","\xd8":"O","\xd9":"U","\xda":"U","\xdb":"U","\xdc":"U","\xdd":"Y","\xde":"o","\xdf":"B","\xe0":"a","\xe1":"a","\xe2":"a","\xe3":"a","\xe4":"a","\xe5":"a","\xe6":"a","\xe7":"c","\xe8":"e","\xe9":"e","\xea":"e","\xeb":"e","\xec":"i","\xed":"i","\xee":"i","\xef":"i","\xf0":"d","\xf1":"n","\xf2":"o","\xf3":"o","\xf4":"o","\xf5":"o","\xf6":"o","\xf8":"o","\xf9":"u","\xfa":"u","\xfb":"u","\xfc":"u","\xfd":"y","\xfe":"o","\xff":"y","\u0410":"A","\u0411":"B","\u0412":"B","\u0413":"F","\u0414":"A","\u0415":"E","\u0416":"K","\u0417":"3","\u0418":"N","\u0419":"N","\u041a":"K","\u041b":"N","\u041c":"M","\u041d":"H","\u041e":"O","\u041f":"N","\u0420":"P","\u0421":"C","\u0422":"T","\u0423":"y","\u0424":"O","\u0425":"X","\u0426":"U","\u0427":"h","\u0428":"W","\u0429":"W","\u042a":"B","\u042b":"X","\u042c":"B","\u042d":"3","\u042e":"X","\u042f":"R","\u0430":"a","\u0431":"b","\u0432":"a","\u0433":"r","\u0434":"y","\u0435":"e","\u0436":"m","\u0437":"e","\u0438":"n","\u0439":"n","\u043a":"n","\u043b":"n","\u043c":"m","\u043d":"n","\u043e":"o","\u043f":"n","\u0440":"p","\u0441":"c","\u0442":"o","\u0443":"y","\u0444":"b","\u0445":"x","\u0446":"n","\u0447":"n","\u0448":"w","\u0449":"w","\u044a":"a","\u044b":"m","\u044c":"a","\u044d":"e","\u044e":"m","\u044f":"r"};var S=function(e,t){var r=e.charCodeAt(0);if(e[0]in z){r=z[e[0]].charCodeAt(0)}else if(i.test(e[0])){r="M".charCodeAt(0)}var a=k[t][r];if(a){return{depth:a[0],height:a[1],italic:a[2],skew:a[3],width:a[4]}}};t.exports={metrics:w,sigmas:n,getCharacterMetrics:S}},{"./Style":9,"./fontMetricsData":18,"./unicodeRegexes":24}],18:[function(e,t,r){t.exports={"AMS-Regular":{65:[0,.68889,0,0],66:[0,.68889,0,0],67:[0,.68889,0,0],68:[0,.68889,0,0],69:[0,.68889,0,0],70:[0,.68889,0,0],71:[0,.68889,0,0],72:[0,.68889,0,0],73:[0,.68889,0,0],74:[.16667,.68889,0,0],75:[0,.68889,0,0],76:[0,.68889,0,0],77:[0,.68889,0,0],78:[0,.68889,0,0],79:[.16667,.68889,0,0],80:[0,.68889,0,0],81:[.16667,.68889,0,0],82:[0,.68889,0,0],83:[0,.68889,0,0],84:[0,.68889,0,0],85:[0,.68889,0,0],86:[0,.68889,0,0],87:[0,.68889,0,0],88:[0,.68889,0,0],89:[0,.68889,0,0],90:[0,.68889,0,0],107:[0,.68889,0,0],165:[0,.675,.025,0],174:[.15559,.69224,0,0],240:[0,.68889,0,0],295:[0,.68889,0,0],710:[0,.825,0,0],732:[0,.9,0,0],770:[0,.825,0,0],771:[0,.9,0,0],989:[.08167,.58167,0,0],1008:[0,.43056,.04028,0],8245:[0,.54986,0,0],8463:[0,.68889,0,0],8487:[0,.68889,0,0],8498:[0,.68889,0,0],8502:[0,.68889,0,0],8503:[0,.68889,0,0],8504:[0,.68889,0,0],8513:[0,.68889,0,0],8592:[-.03598,.46402,0,0],8594:[-.03598,.46402,0,0],8602:[-.13313,.36687,0,0],8603:[-.13313,.36687,0,0],8606:[.01354,.52239,0,0],8608:[.01354,.52239,0,0],8610:[.01354,.52239,0,0],8611:[.01354,.52239,0,0],8619:[0,.54986,0,0],8620:[0,.54986,0,0],8621:[-.13313,.37788,0,0],8622:[-.13313,.36687,0,0],8624:[0,.69224,0,0],8625:[0,.69224,0,0],8630:[0,.43056,0,0],8631:[0,.43056,0,0],8634:[.08198,.58198,0,0],8635:[.08198,.58198,0,0],8638:[.19444,.69224,0,0],8639:[.19444,.69224,0,0],8642:[.19444,.69224,0,0],8643:[.19444,.69224,0,0],8644:[.1808,.675,0,0],8646:[.1808,.675,0,0],8647:[.1808,.675,0,0],8648:[.19444,.69224,0,0],8649:[.1808,.675,0,0],8650:[.19444,.69224,0,0],8651:[.01354,.52239,0,0],8652:[.01354,.52239,0,0],8653:[-.13313,.36687,0,0],8654:[-.13313,.36687,0,0],8655:[-.13313,.36687,0,0],8666:[.13667,.63667,0,0],8667:[.13667,.63667,0,0],8669:[-.13313,.37788,0,0],8672:[-.064,.437,0,0],8674:[-.064,.437,0,0],8705:[0,.825,0,0],8708:[0,.68889,0,0],8709:[.08167,.58167,0,0],8717:[0,.43056,0,0],8722:[-.03598,.46402,0,0],8724:[.08198,.69224,0,0],8726:[.08167,.58167,0,0],8733:[0,.69224,0,0],8736:[0,.69224,0,0],8737:[0,.69224,0,0],8738:[.03517,.52239,0,0],8739:[.08167,.58167,0,0],8740:[.25142,.74111,0,0],8741:[.08167,.58167,0,0],8742:[.25142,.74111,0,0],8756:[0,.69224,0,0],8757:[0,.69224,0,0],8764:[-.13313,.36687,0,0],8765:[-.13313,.37788,0,0],8769:[-.13313,.36687,0,0],8770:[-.03625,.46375,0,0],8774:[.30274,.79383,0,0],8776:[-.01688,.48312,0,0],8778:[.08167,.58167,0,0],8782:[.06062,.54986,0,0],8783:[.06062,.54986,0,0],8785:[.08198,.58198,0,0],8786:[.08198,.58198,0,0],8787:[.08198,.58198,0,0],8790:[0,.69224,0,0],8791:[.22958,.72958,0,0],8796:[.08198,.91667,0,0],8806:[.25583,.75583,0,0],
+8807:[.25583,.75583,0,0],8808:[.25142,.75726,0,0],8809:[.25142,.75726,0,0],8812:[.25583,.75583,0,0],8814:[.20576,.70576,0,0],8815:[.20576,.70576,0,0],8816:[.30274,.79383,0,0],8817:[.30274,.79383,0,0],8818:[.22958,.72958,0,0],8819:[.22958,.72958,0,0],8822:[.1808,.675,0,0],8823:[.1808,.675,0,0],8828:[.13667,.63667,0,0],8829:[.13667,.63667,0,0],8830:[.22958,.72958,0,0],8831:[.22958,.72958,0,0],8832:[.20576,.70576,0,0],8833:[.20576,.70576,0,0],8840:[.30274,.79383,0,0],8841:[.30274,.79383,0,0],8842:[.13597,.63597,0,0],8843:[.13597,.63597,0,0],8847:[.03517,.54986,0,0],8848:[.03517,.54986,0,0],8858:[.08198,.58198,0,0],8859:[.08198,.58198,0,0],8861:[.08198,.58198,0,0],8862:[0,.675,0,0],8863:[0,.675,0,0],8864:[0,.675,0,0],8865:[0,.675,0,0],8872:[0,.69224,0,0],8873:[0,.69224,0,0],8874:[0,.69224,0,0],8876:[0,.68889,0,0],8877:[0,.68889,0,0],8878:[0,.68889,0,0],8879:[0,.68889,0,0],8882:[.03517,.54986,0,0],8883:[.03517,.54986,0,0],8884:[.13667,.63667,0,0],8885:[.13667,.63667,0,0],8888:[0,.54986,0,0],8890:[.19444,.43056,0,0],8891:[.19444,.69224,0,0],8892:[.19444,.69224,0,0],8901:[0,.54986,0,0],8903:[.08167,.58167,0,0],8905:[.08167,.58167,0,0],8906:[.08167,.58167,0,0],8907:[0,.69224,0,0],8908:[0,.69224,0,0],8909:[-.03598,.46402,0,0],8910:[0,.54986,0,0],8911:[0,.54986,0,0],8912:[.03517,.54986,0,0],8913:[.03517,.54986,0,0],8914:[0,.54986,0,0],8915:[0,.54986,0,0],8916:[0,.69224,0,0],8918:[.0391,.5391,0,0],8919:[.0391,.5391,0,0],8920:[.03517,.54986,0,0],8921:[.03517,.54986,0,0],8922:[.38569,.88569,0,0],8923:[.38569,.88569,0,0],8926:[.13667,.63667,0,0],8927:[.13667,.63667,0,0],8928:[.30274,.79383,0,0],8929:[.30274,.79383,0,0],8934:[.23222,.74111,0,0],8935:[.23222,.74111,0,0],8936:[.23222,.74111,0,0],8937:[.23222,.74111,0,0],8938:[.20576,.70576,0,0],8939:[.20576,.70576,0,0],8940:[.30274,.79383,0,0],8941:[.30274,.79383,0,0],8994:[.19444,.69224,0,0],8995:[.19444,.69224,0,0],9416:[.15559,.69224,0,0],9484:[0,.69224,0,0],9488:[0,.69224,0,0],9492:[0,.37788,0,0],9496:[0,.37788,0,0],9585:[.19444,.68889,0,0],9586:[.19444,.74111,0,0],9632:[0,.675,0,0],9633:[0,.675,0,0],9650:[0,.54986,0,0],9651:[0,.54986,0,0],9654:[.03517,.54986,0,0],9660:[0,.54986,0,0],9661:[0,.54986,0,0],9664:[.03517,.54986,0,0],9674:[.11111,.69224,0,0],9733:[.19444,.69224,0,0],10003:[0,.69224,0,0],10016:[0,.69224,0,0],10731:[.11111,.69224,0,0],10846:[.19444,.75583,0,0],10877:[.13667,.63667,0,0],10878:[.13667,.63667,0,0],10885:[.25583,.75583,0,0],10886:[.25583,.75583,0,0],10887:[.13597,.63597,0,0],10888:[.13597,.63597,0,0],10889:[.26167,.75726,0,0],10890:[.26167,.75726,0,0],10891:[.48256,.98256,0,0],10892:[.48256,.98256,0,0],10901:[.13667,.63667,0,0],10902:[.13667,.63667,0,0],10933:[.25142,.75726,0,0],10934:[.25142,.75726,0,0],10935:[.26167,.75726,0,0],10936:[.26167,.75726,0,0],10937:[.26167,.75726,0,0],10938:[.26167,.75726,0,0],10949:[.25583,.75583,0,0],10950:[.25583,.75583,0,0],10955:[.28481,.79383,0,0],10956:[.28481,.79383,0,0],57350:[.08167,.58167,0,0],57351:[.08167,.58167,0,0],57352:[.08167,.58167,0,0],57353:[0,.43056,.04028,0],57356:[.25142,.75726,0,0],57357:[.25142,.75726,0,0],57358:[.41951,.91951,0,0],57359:[.30274,.79383,0,0],57360:[.30274,.79383,0,0],57361:[.41951,.91951,0,0],57366:[.25142,.75726,0,0],57367:[.25142,.75726,0,0],57368:[.25142,.75726,0,0],57369:[.25142,.75726,0,0],57370:[.13597,.63597,0,0],57371:[.13597,.63597,0,0]},"Caligraphic-Regular":{48:[0,.43056,0,0],49:[0,.43056,0,0],50:[0,.43056,0,0],51:[.19444,.43056,0,0],52:[.19444,.43056,0,0],53:[.19444,.43056,0,0],54:[0,.64444,0,0],55:[.19444,.43056,0,0],56:[0,.64444,0,0],57:[.19444,.43056,0,0],65:[0,.68333,0,.19445],66:[0,.68333,.03041,.13889],67:[0,.68333,.05834,.13889],68:[0,.68333,.02778,.08334],69:[0,.68333,.08944,.11111],70:[0,.68333,.09931,.11111],71:[.09722,.68333,.0593,.11111],72:[0,.68333,.00965,.11111],73:[0,.68333,.07382,0],74:[.09722,.68333,.18472,.16667],75:[0,.68333,.01445,.05556],76:[0,.68333,0,.13889],77:[0,.68333,0,.13889],78:[0,.68333,.14736,.08334],79:[0,.68333,.02778,.11111],80:[0,.68333,.08222,.08334],81:[.09722,.68333,0,.11111],82:[0,.68333,0,.08334],83:[0,.68333,.075,.13889],84:[0,.68333,.25417,0],85:[0,.68333,.09931,.08334],86:[0,.68333,.08222,0],87:[0,.68333,.08222,.08334],88:[0,.68333,.14643,.13889],89:[.09722,.68333,.08222,.08334],90:[0,.68333,.07944,.13889]},"Fraktur-Regular":{33:[0,.69141,0,0],34:[0,.69141,0,0],38:[0,.69141,0,0],39:[0,.69141,0,0],40:[.24982,.74947,0,0],41:[.24982,.74947,0,0],42:[0,.62119,0,0],43:[.08319,.58283,0,0],44:[0,.10803,0,0],45:[.08319,.58283,0,0],46:[0,.10803,0,0],47:[.24982,.74947,0,0],48:[0,.47534,0,0],49:[0,.47534,0,0],50:[0,.47534,0,0],51:[.18906,.47534,0,0],52:[.18906,.47534,0,0],53:[.18906,.47534,0,0],54:[0,.69141,0,0],55:[.18906,.47534,0,0],56:[0,.69141,0,0],57:[.18906,.47534,0,0],58:[0,.47534,0,0],59:[.12604,.47534,0,0],61:[-.13099,.36866,0,0],63:[0,.69141,0,0],65:[0,.69141,0,0],66:[0,.69141,0,0],67:[0,.69141,0,0],68:[0,.69141,0,0],69:[0,.69141,0,0],70:[.12604,.69141,0,0],71:[0,.69141,0,0],72:[.06302,.69141,0,0],73:[0,.69141,0,0],74:[.12604,.69141,0,0],75:[0,.69141,0,0],76:[0,.69141,0,0],77:[0,.69141,0,0],78:[0,.69141,0,0],79:[0,.69141,0,0],80:[.18906,.69141,0,0],81:[.03781,.69141,0,0],82:[0,.69141,0,0],83:[0,.69141,0,0],84:[0,.69141,0,0],85:[0,.69141,0,0],86:[0,.69141,0,0],87:[0,.69141,0,0],88:[0,.69141,0,0],89:[.18906,.69141,0,0],90:[.12604,.69141,0,0],91:[.24982,.74947,0,0],93:[.24982,.74947,0,0],94:[0,.69141,0,0],97:[0,.47534,0,0],98:[0,.69141,0,0],99:[0,.47534,0,0],100:[0,.62119,0,0],101:[0,.47534,0,0],102:[.18906,.69141,0,0],103:[.18906,.47534,0,0],104:[.18906,.69141,0,0],105:[0,.69141,0,0],106:[0,.69141,0,0],107:[0,.69141,0,0],108:[0,.69141,0,0],109:[0,.47534,0,0],110:[0,.47534,0,0],111:[0,.47534,0,0],112:[.18906,.52396,0,0],113:[.18906,.47534,0,0],114:[0,.47534,0,0],115:[0,.47534,0,0],116:[0,.62119,0,0],117:[0,.47534,0,0],118:[0,.52396,0,0],119:[0,.52396,0,0],120:[.18906,.47534,0,0],121:[.18906,.47534,0,0],122:[.18906,.47534,0,0],8216:[0,.69141,0,0],8217:[0,.69141,0,0],58112:[0,.62119,0,0],58113:[0,.62119,0,0],58114:[.18906,.69141,0,0],58115:[.18906,.69141,0,0],58116:[.18906,.47534,0,0],58117:[0,.69141,0,0],58118:[0,.62119,0,0],58119:[0,.47534,0,0]},"Main-Bold":{33:[0,.69444,0,0],34:[0,.69444,0,0],35:[.19444,.69444,0,0],36:[.05556,.75,0,0],37:[.05556,.75,0,0],38:[0,.69444,0,0],39:[0,.69444,0,0],40:[.25,.75,0,0],41:[.25,.75,0,0],42:[0,.75,0,0],43:[.13333,.63333,0,0],44:[.19444,.15556,0,0],45:[0,.44444,0,0],46:[0,.15556,0,0],47:[.25,.75,0,0],48:[0,.64444,0,0],49:[0,.64444,0,0],50:[0,.64444,0,0],51:[0,.64444,0,0],52:[0,.64444,0,0],53:[0,.64444,0,0],54:[0,.64444,0,0],55:[0,.64444,0,0],56:[0,.64444,0,0],57:[0,.64444,0,0],58:[0,.44444,0,0],59:[.19444,.44444,0,0],60:[.08556,.58556,0,0],61:[-.10889,.39111,0,0],62:[.08556,.58556,0,0],63:[0,.69444,0,0],64:[0,.69444,0,0],65:[0,.68611,0,0],66:[0,.68611,0,0],67:[0,.68611,0,0],68:[0,.68611,0,0],69:[0,.68611,0,0],70:[0,.68611,0,0],71:[0,.68611,0,0],72:[0,.68611,0,0],73:[0,.68611,0,0],74:[0,.68611,0,0],75:[0,.68611,0,0],76:[0,.68611,0,0],77:[0,.68611,0,0],78:[0,.68611,0,0],79:[0,.68611,0,0],80:[0,.68611,0,0],81:[.19444,.68611,0,0],82:[0,.68611,0,0],83:[0,.68611,0,0],84:[0,.68611,0,0],85:[0,.68611,0,0],86:[0,.68611,.01597,0],87:[0,.68611,.01597,0],88:[0,.68611,0,0],89:[0,.68611,.02875,0],90:[0,.68611,0,0],91:[.25,.75,0,0],92:[.25,.75,0,0],93:[.25,.75,0,0],94:[0,.69444,0,0],95:[.31,.13444,.03194,0],96:[0,.69444,0,0],97:[0,.44444,0,0],98:[0,.69444,0,0],99:[0,.44444,0,0],100:[0,.69444,0,0],101:[0,.44444,0,0],102:[0,.69444,.10903,0],103:[.19444,.44444,.01597,0],104:[0,.69444,0,0],105:[0,.69444,0,0],106:[.19444,.69444,0,0],107:[0,.69444,0,0],108:[0,.69444,0,0],109:[0,.44444,0,0],110:[0,.44444,0,0],111:[0,.44444,0,0],112:[.19444,.44444,0,0],113:[.19444,.44444,0,0],114:[0,.44444,0,0],115:[0,.44444,0,0],116:[0,.63492,0,0],117:[0,.44444,0,0],118:[0,.44444,.01597,0],119:[0,.44444,.01597,0],120:[0,.44444,0,0],121:[.19444,.44444,.01597,0],122:[0,.44444,0,0],123:[.25,.75,0,0],124:[.25,.75,0,0],125:[.25,.75,0,0],126:[.35,.34444,0,0],168:[0,.69444,0,0],172:[0,.44444,0,0],175:[0,.59611,0,0],176:[0,.69444,0,0],177:[.13333,.63333,0,0],180:[0,.69444,0,0],215:[.13333,.63333,0,0],247:[.13333,.63333,0,0],305:[0,.44444,0,0],567:[.19444,.44444,0,0],710:[0,.69444,0,0],711:[0,.63194,0,0],713:[0,.59611,0,0],714:[0,.69444,0,0],715:[0,.69444,0,0],728:[0,.69444,0,0],729:[0,.69444,0,0],730:[0,.69444,0,0],732:[0,.69444,0,0],768:[0,.69444,0,0],769:[0,.69444,0,0],770:[0,.69444,0,0],771:[0,.69444,0,0],772:[0,.59611,0,0],774:[0,.69444,0,0],775:[0,.69444,0,0],776:[0,.69444,0,0],778:[0,.69444,0,0],779:[0,.69444,0,0],780:[0,.63194,0,0],824:[.19444,.69444,0,0],915:[0,.68611,0,0],916:[0,.68611,0,0],920:[0,.68611,0,0],923:[0,.68611,0,0],926:[0,.68611,0,0],928:[0,.68611,0,0],931:[0,.68611,0,0],933:[0,.68611,0,0],934:[0,.68611,0,0],936:[0,.68611,0,0],937:[0,.68611,0,0],8211:[0,.44444,.03194,0],8212:[0,.44444,.03194,0],8216:[0,.69444,0,0],8217:[0,.69444,0,0],8220:[0,.69444,0,0],8221:[0,.69444,0,0],8224:[.19444,.69444,0,0],8225:[.19444,.69444,0,0],8242:[0,.55556,0,0],8407:[0,.72444,.15486,0],8463:[0,.69444,0,0],8465:[0,.69444,0,0],8467:[0,.69444,0,0],8472:[.19444,.44444,0,0],8476:[0,.69444,0,0],8501:[0,.69444,0,0],8592:[-.10889,.39111,0,0],8593:[.19444,.69444,0,0],8594:[-.10889,.39111,0,0],8595:[.19444,.69444,0,0],8596:[-.10889,.39111,0,0],8597:[.25,.75,0,0],8598:[.19444,.69444,0,0],8599:[.19444,.69444,0,0],8600:[.19444,.69444,0,0],8601:[.19444,.69444,0,0],8636:[-.10889,.39111,0,0],8637:[-.10889,.39111,0,0],8640:[-.10889,.39111,0,0],8641:[-.10889,.39111,0,0],8656:[-.10889,.39111,0,0],8657:[.19444,.69444,0,0],8658:[-.10889,.39111,0,0],8659:[.19444,.69444,0,0],8660:[-.10889,.39111,0,0],8661:[.25,.75,0,0],8704:[0,.69444,0,0],8706:[0,.69444,.06389,0],8707:[0,.69444,0,0],8709:[.05556,.75,0,0],8711:[0,.68611,0,0],8712:[.08556,.58556,0,0],8715:[.08556,.58556,0,0],8722:[.13333,.63333,0,0],8723:[.13333,.63333,0,0],8725:[.25,.75,0,0],8726:[.25,.75,0,0],8727:[-.02778,.47222,0,0],8728:[-.02639,.47361,0,0],8729:[-.02639,.47361,0,0],8730:[.18,.82,0,0],8733:[0,.44444,0,0],8734:[0,.44444,0,0],8736:[0,.69224,0,0],8739:[.25,.75,0,0],8741:[.25,.75,0,0],8743:[0,.55556,0,0],8744:[0,.55556,0,0],8745:[0,.55556,0,0],8746:[0,.55556,0,0],8747:[.19444,.69444,.12778,0],8764:[-.10889,.39111,0,0],8768:[.19444,.69444,0,0],8771:[.00222,.50222,0,0],8776:[.02444,.52444,0,0],8781:[.00222,.50222,0,0],8801:[.00222,.50222,0,0],8804:[.19667,.69667,0,0],8805:[.19667,.69667,0,0],8810:[.08556,.58556,0,0],8811:[.08556,.58556,0,0],8826:[.08556,.58556,0,0],8827:[.08556,.58556,0,0],8834:[.08556,.58556,0,0],8835:[.08556,.58556,0,0],8838:[.19667,.69667,0,0],8839:[.19667,.69667,0,0],8846:[0,.55556,0,0],8849:[.19667,.69667,0,0],8850:[.19667,.69667,0,0],8851:[0,.55556,0,0],8852:[0,.55556,0,0],8853:[.13333,.63333,0,0],8854:[.13333,.63333,0,0],8855:[.13333,.63333,0,0],8856:[.13333,.63333,0,0],8857:[.13333,.63333,0,0],8866:[0,.69444,0,0],8867:[0,.69444,0,0],8868:[0,.69444,0,0],8869:[0,.69444,0,0],8900:[-.02639,.47361,0,0],8901:[-.02639,.47361,0,0],8902:[-.02778,.47222,0,0],8968:[.25,.75,0,0],8969:[.25,.75,0,0],8970:[.25,.75,0,0],8971:[.25,.75,0,0],8994:[-.13889,.36111,0,0],8995:[-.13889,.36111,0,0],9651:[.19444,.69444,0,0],9657:[-.02778,.47222,0,0],9661:[.19444,.69444,0,0],9667:[-.02778,.47222,0,0],9711:[.19444,.69444,0,0],9824:[.12963,.69444,0,0],9825:[.12963,.69444,0,0],9826:[.12963,.69444,0,0],9827:[.12963,.69444,0,0],9837:[0,.75,0,0],9838:[.19444,.69444,0,0],9839:[.19444,.69444,0,0],10216:[.25,.75,0,0],10217:[.25,.75,0,0],10815:[0,.68611,0,0],10927:[.19667,.69667,0,0],10928:[.19667,.69667,0,0]},"Main-Italic":{33:[0,.69444,.12417,0],34:[0,.69444,.06961,0],35:[.19444,.69444,.06616,0],37:[.05556,.75,.13639,0],38:[0,.69444,.09694,0],39:[0,.69444,.12417,0],40:[.25,.75,.16194,0],41:[.25,.75,.03694,0],42:[0,.75,.14917,0],43:[.05667,.56167,.03694,0],44:[.19444,.10556,0,0],45:[0,.43056,.02826,0],46:[0,.10556,0,0],47:[.25,.75,.16194,0],48:[0,.64444,.13556,0],49:[0,.64444,.13556,0],50:[0,.64444,.13556,0],51:[0,.64444,.13556,0],52:[.19444,.64444,.13556,0],53:[0,.64444,.13556,0],54:[0,.64444,.13556,0],55:[.19444,.64444,.13556,0],56:[0,.64444,.13556,0],57:[0,.64444,.13556,0],58:[0,.43056,.0582,0],59:[.19444,.43056,.0582,0],61:[-.13313,.36687,.06616,0],63:[0,.69444,.1225,0],64:[0,.69444,.09597,0],65:[0,.68333,0,0],66:[0,.68333,.10257,0],67:[0,.68333,.14528,0],68:[0,.68333,.09403,0],69:[0,.68333,.12028,0],70:[0,.68333,.13305,0],71:[0,.68333,.08722,0],72:[0,.68333,.16389,0],73:[0,.68333,.15806,0],74:[0,.68333,.14028,0],75:[0,.68333,.14528,0],76:[0,.68333,0,0],77:[0,.68333,.16389,0],78:[0,.68333,.16389,0],79:[0,.68333,.09403,0],80:[0,.68333,.10257,0],81:[.19444,.68333,.09403,0],82:[0,.68333,.03868,0],83:[0,.68333,.11972,0],84:[0,.68333,.13305,0],85:[0,.68333,.16389,0],86:[0,.68333,.18361,0],87:[0,.68333,.18361,0],88:[0,.68333,.15806,0],89:[0,.68333,.19383,0],90:[0,.68333,.14528,0],91:[.25,.75,.1875,0],93:[.25,.75,.10528,0],94:[0,.69444,.06646,0],95:[.31,.12056,.09208,0],97:[0,.43056,.07671,0],98:[0,.69444,.06312,0],99:[0,.43056,.05653,0],100:[0,.69444,.10333,0],101:[0,.43056,.07514,0],102:[.19444,.69444,.21194,0],103:[.19444,.43056,.08847,0],104:[0,.69444,.07671,0],105:[0,.65536,.1019,0],106:[.19444,.65536,.14467,0],107:[0,.69444,.10764,0],108:[0,.69444,.10333,0],109:[0,.43056,.07671,0],110:[0,.43056,.07671,0],111:[0,.43056,.06312,0],112:[.19444,.43056,.06312,0],113:[.19444,.43056,.08847,0],114:[0,.43056,.10764,0],115:[0,.43056,.08208,0],116:[0,.61508,.09486,0],117:[0,.43056,.07671,0],118:[0,.43056,.10764,0],119:[0,.43056,.10764,0],120:[0,.43056,.12042,0],121:[.19444,.43056,.08847,0],122:[0,.43056,.12292,0],126:[.35,.31786,.11585,0],163:[0,.69444,0,0],305:[0,.43056,0,.02778],567:[.19444,.43056,0,.08334],768:[0,.69444,0,0],769:[0,.69444,.09694,0],770:[0,.69444,.06646,0],771:[0,.66786,.11585,0],772:[0,.56167,.10333,0],774:[0,.69444,.10806,0],775:[0,.66786,.11752,0],776:[0,.66786,.10474,0],778:[0,.69444,0,0],779:[0,.69444,.1225,0],780:[0,.62847,.08295,0],915:[0,.68333,.13305,0],916:[0,.68333,0,0],920:[0,.68333,.09403,0],923:[0,.68333,0,0],926:[0,.68333,.15294,0],928:[0,.68333,.16389,0],931:[0,.68333,.12028,0],933:[0,.68333,.11111,0],934:[0,.68333,.05986,0],936:[0,.68333,.11111,0],937:[0,.68333,.10257,0],8211:[0,.43056,.09208,0],8212:[0,.43056,.09208,0],8216:[0,.69444,.12417,0],8217:[0,.69444,.12417,0],8220:[0,.69444,.1685,0],8221:[0,.69444,.06961,0],8463:[0,.68889,0,0]},"Main-Regular":{32:[0,0,0,0],33:[0,.69444,0,0],34:[0,.69444,0,0],35:[.19444,.69444,0,0],36:[.05556,.75,0,0],37:[.05556,.75,0,0],38:[0,.69444,0,0],39:[0,.69444,0,0],40:[.25,.75,0,0],41:[.25,.75,0,0],42:[0,.75,0,0],43:[.08333,.58333,0,0],44:[.19444,.10556,0,0],45:[0,.43056,0,0],46:[0,.10556,0,0],47:[.25,.75,0,0],48:[0,.64444,0,0],49:[0,.64444,0,0],50:[0,.64444,0,0],51:[0,.64444,0,0],52:[0,.64444,0,0],53:[0,.64444,0,0],54:[0,.64444,0,0],55:[0,.64444,0,0],56:[0,.64444,0,0],57:[0,.64444,0,0],58:[0,.43056,0,0],59:[.19444,.43056,0,0],60:[.0391,.5391,0,0],61:[-.13313,.36687,0,0],62:[.0391,.5391,0,0],63:[0,.69444,0,0],64:[0,.69444,0,0],65:[0,.68333,0,0],66:[0,.68333,0,0],67:[0,.68333,0,0],68:[0,.68333,0,0],69:[0,.68333,0,0],70:[0,.68333,0,0],71:[0,.68333,0,0],72:[0,.68333,0,0],73:[0,.68333,0,0],74:[0,.68333,0,0],75:[0,.68333,0,0],76:[0,.68333,0,0],77:[0,.68333,0,0],78:[0,.68333,0,0],79:[0,.68333,0,0],80:[0,.68333,0,0],81:[.19444,.68333,0,0],82:[0,.68333,0,0],83:[0,.68333,0,0],84:[0,.68333,0,0],85:[0,.68333,0,0],86:[0,.68333,.01389,0],87:[0,.68333,.01389,0],88:[0,.68333,0,0],89:[0,.68333,.025,0],90:[0,.68333,0,0],91:[.25,.75,0,0],92:[.25,.75,0,0],93:[.25,.75,0,0],94:[0,.69444,0,0],95:[.31,.12056,.02778,0],96:[0,.69444,0,0],97:[0,.43056,0,0],98:[0,.69444,0,0],99:[0,.43056,0,0],100:[0,.69444,0,0],101:[0,.43056,0,0],102:[0,.69444,.07778,0],103:[.19444,.43056,.01389,0],104:[0,.69444,0,0],105:[0,.66786,0,0],106:[.19444,.66786,0,0],107:[0,.69444,0,0],108:[0,.69444,0,0],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,0],112:[.19444,.43056,0,0],113:[.19444,.43056,0,0],114:[0,.43056,0,0],115:[0,.43056,0,0],116:[0,.61508,0,0],117:[0,.43056,0,0],118:[0,.43056,.01389,0],119:[0,.43056,.01389,0],120:[0,.43056,0,0],121:[.19444,.43056,.01389,0],122:[0,.43056,0,0],123:[.25,.75,0,0],124:[.25,.75,0,0],125:[.25,.75,0,0],126:[.35,.31786,0,0],160:[0,0,0,0],168:[0,.66786,0,0],172:[0,.43056,0,0],175:[0,.56778,0,0],176:[0,.69444,0,0],177:[.08333,.58333,0,0],180:[0,.69444,0,0],215:[.08333,.58333,0,0],247:[.08333,.58333,0,0],305:[0,.43056,0,0],567:[.19444,.43056,0,0],710:[0,.69444,0,0],711:[0,.62847,0,0],713:[0,.56778,0,0],714:[0,.69444,0,0],715:[0,.69444,0,0],728:[0,.69444,0,0],729:[0,.66786,0,0],730:[0,.69444,0,0],732:[0,.66786,0,0],768:[0,.69444,0,0],769:[0,.69444,0,0],770:[0,.69444,0,0],771:[0,.66786,0,0],772:[0,.56778,0,0],774:[0,.69444,0,0],775:[0,.66786,0,0],776:[0,.66786,0,0],778:[0,.69444,0,0],779:[0,.69444,0,0],780:[0,.62847,0,0],824:[.19444,.69444,0,0],915:[0,.68333,0,0],916:[0,.68333,0,0],920:[0,.68333,0,0],923:[0,.68333,0,0],926:[0,.68333,0,0],928:[0,.68333,0,0],931:[0,.68333,0,0],933:[0,.68333,0,0],934:[0,.68333,0,0],936:[0,.68333,0,0],937:[0,.68333,0,0],8211:[0,.43056,.02778,0],8212:[0,.43056,.02778,0],8216:[0,.69444,0,0],8217:[0,.69444,0,0],8220:[0,.69444,0,0],8221:[0,.69444,0,0],8224:[.19444,.69444,0,0],8225:[.19444,.69444,0,0],8230:[0,.12,0,0],8242:[0,.55556,0,0],8407:[0,.71444,.15382,0],8463:[0,.68889,0,0],8465:[0,.69444,0,0],8467:[0,.69444,0,.11111],8472:[.19444,.43056,0,.11111],8476:[0,.69444,0,0],8501:[0,.69444,0,0],8592:[-.13313,.36687,0,0],8593:[.19444,.69444,0,0],8594:[-.13313,.36687,0,0],8595:[.19444,.69444,0,0],8596:[-.13313,.36687,0,0],8597:[.25,.75,0,0],8598:[.19444,.69444,0,0],8599:[.19444,.69444,0,0],8600:[.19444,.69444,0,0],8601:[.19444,.69444,0,0],8614:[.011,.511,0,0],8617:[.011,.511,0,0],8618:[.011,.511,0,0],8636:[-.13313,.36687,0,0],8637:[-.13313,.36687,0,0],8640:[-.13313,.36687,0,0],8641:[-.13313,.36687,0,0],8652:[.011,.671,0,0],8656:[-.13313,.36687,0,0],8657:[.19444,.69444,0,0],8658:[-.13313,.36687,0,0],8659:[.19444,.69444,0,0],8660:[-.13313,.36687,0,0],8661:[.25,.75,0,0],8704:[0,.69444,0,0],8706:[0,.69444,.05556,.08334],8707:[0,.69444,0,0],8709:[.05556,.75,0,0],8711:[0,.68333,0,0],8712:[.0391,.5391,0,0],8715:[.0391,.5391,0,0],8722:[.08333,.58333,0,0],8723:[.08333,.58333,0,0],8725:[.25,.75,0,0],8726:[.25,.75,0,0],8727:[-.03472,.46528,0,0],8728:[-.05555,.44445,0,0],8729:[-.05555,.44445,0,0],8730:[.2,.8,0,0],8733:[0,.43056,0,0],8734:[0,.43056,0,0],8736:[0,.69224,0,0],8739:[.25,.75,0,0],8741:[.25,.75,0,0],8743:[0,.55556,0,0],8744:[0,.55556,0,0],8745:[0,.55556,0,0],8746:[0,.55556,0,0],8747:[.19444,.69444,.11111,0],8764:[-.13313,.36687,0,0],8768:[.19444,.69444,0,0],8771:[-.03625,.46375,0,0],8773:[-.022,.589,0,0],8776:[-.01688,.48312,0,0],8781:[-.03625,.46375,0,0],8784:[-.133,.67,0,0],8800:[.215,.716,0,0],8801:[-.03625,.46375,0,0],8804:[.13597,.63597,0,0],8805:[.13597,.63597,0,0],8810:[.0391,.5391,0,0],8811:[.0391,.5391,0,0],8826:[.0391,.5391,0,0],8827:[.0391,.5391,0,0],8834:[.0391,.5391,0,0],8835:[.0391,.5391,0,0],8838:[.13597,.63597,0,0],8839:[.13597,.63597,0,0],8846:[0,.55556,0,0],8849:[.13597,.63597,0,0],8850:[.13597,.63597,0,0],8851:[0,.55556,0,0],8852:[0,.55556,0,0],8853:[.08333,.58333,0,0],8854:[.08333,.58333,0,0],8855:[.08333,.58333,0,0],8856:[.08333,.58333,0,0],8857:[.08333,.58333,0,0],8866:[0,.69444,0,0],8867:[0,.69444,0,0],8868:[0,.69444,0,0],8869:[0,.69444,0,0],8872:[.249,.75,0,0],8900:[-.05555,.44445,0,0],8901:[-.05555,.44445,0,0],8902:[-.03472,.46528,0,0],8904:[.005,.505,0,0],8942:[.03,.9,0,0],8943:[-.19,.31,0,0],8945:[-.1,.82,0,0],8968:[.25,.75,0,0],8969:[.25,.75,0,0],8970:[.25,.75,0,0],8971:[.25,.75,0,0],8994:[-.14236,.35764,0,0],8995:[-.14236,.35764,0,0],9136:[.244,.744,0,0],9137:[.244,.744,0,0],9651:[.19444,.69444,0,0],9657:[-.03472,.46528,0,0],9661:[.19444,.69444,0,0],9667:[-.03472,.46528,0,0],9711:[.19444,.69444,0,0],9824:[.12963,.69444,0,0],9825:[.12963,.69444,0,0],9826:[.12963,.69444,0,0],9827:[.12963,.69444,0,0],9837:[0,.75,0,0],9838:[.19444,.69444,0,0],9839:[.19444,.69444,0,0],10216:[.25,.75,0,0],10217:[.25,.75,0,0],10222:[.244,.744,0,0],10223:[.244,.744,0,0],10229:[.011,.511,0,0],10230:[.011,.511,0,0],10231:[.011,.511,0,0],10232:[.024,.525,0,0],10233:[.024,.525,0,0],10234:[.024,.525,0,0],10236:[.011,.511,0,0],10815:[0,.68333,0,0],10927:[.13597,.63597,0,0],10928:[.13597,.63597,0,0]},"Math-BoldItalic":{47:[.19444,.69444,0,0],65:[0,.68611,0,0],66:[0,.68611,.04835,0],67:[0,.68611,.06979,0],68:[0,.68611,.03194,0],69:[0,.68611,.05451,0],70:[0,.68611,.15972,0],71:[0,.68611,0,0],72:[0,.68611,.08229,0],73:[0,.68611,.07778,0],74:[0,.68611,.10069,0],75:[0,.68611,.06979,0],76:[0,.68611,0,0],77:[0,.68611,.11424,0],78:[0,.68611,.11424,0],79:[0,.68611,.03194,0],80:[0,.68611,.15972,0],81:[.19444,.68611,0,0],82:[0,.68611,.00421,0],83:[0,.68611,.05382,0],84:[0,.68611,.15972,0],85:[0,.68611,.11424,0],86:[0,.68611,.25555,0],87:[0,.68611,.15972,0],88:[0,.68611,.07778,0],89:[0,.68611,.25555,0],90:[0,.68611,.06979,0],97:[0,.44444,0,0],98:[0,.69444,0,0],99:[0,.44444,0,0],100:[0,.69444,0,0],101:[0,.44444,0,0],102:[.19444,.69444,.11042,0],103:[.19444,.44444,.03704,0],104:[0,.69444,0,0],105:[0,.69326,0,0],106:[.19444,.69326,.0622,0],107:[0,.69444,.01852,0],108:[0,.69444,.0088,0],109:[0,.44444,0,0],110:[0,.44444,0,0],111:[0,.44444,0,0],112:[.19444,.44444,0,0],113:[.19444,.44444,.03704,0],114:[0,.44444,.03194,0],115:[0,.44444,0,0],116:[0,.63492,0,0],117:[0,.44444,0,0],118:[0,.44444,.03704,0],119:[0,.44444,.02778,0],120:[0,.44444,0,0],121:[.19444,.44444,.03704,0],122:[0,.44444,.04213,0],915:[0,.68611,.15972,0],916:[0,.68611,0,0],920:[0,.68611,.03194,0],923:[0,.68611,0,0],926:[0,.68611,.07458,0],928:[0,.68611,.08229,0],931:[0,.68611,.05451,0],933:[0,.68611,.15972,0],934:[0,.68611,0,0],936:[0,.68611,.11653,0],937:[0,.68611,.04835,0],945:[0,.44444,0,0],946:[.19444,.69444,.03403,0],947:[.19444,.44444,.06389,0],948:[0,.69444,.03819,0],949:[0,.44444,0,0],950:[.19444,.69444,.06215,0],951:[.19444,.44444,.03704,0],952:[0,.69444,.03194,0],953:[0,.44444,0,0],954:[0,.44444,0,0],955:[0,.69444,0,0],956:[.19444,.44444,0,0],957:[0,.44444,.06898,0],958:[.19444,.69444,.03021,0],959:[0,.44444,0,0],960:[0,.44444,.03704,0],961:[.19444,.44444,0,0],962:[.09722,.44444,.07917,0],963:[0,.44444,.03704,0],964:[0,.44444,.13472,0],965:[0,.44444,.03704,0],966:[.19444,.44444,0,0],967:[.19444,.44444,0,0],968:[.19444,.69444,.03704,0],969:[0,.44444,.03704,0],977:[0,.69444,0,0],981:[.19444,.69444,0,0],982:[0,.44444,.03194,0],1009:[.19444,.44444,0,0],1013:[0,.44444,0,0]},"Math-Italic":{47:[.19444,.69444,0,0],65:[0,.68333,0,.13889],66:[0,.68333,.05017,.08334],67:[0,.68333,.07153,.08334],68:[0,.68333,.02778,.05556],69:[0,.68333,.05764,.08334],70:[0,.68333,.13889,.08334],71:[0,.68333,0,.08334],72:[0,.68333,.08125,.05556],73:[0,.68333,.07847,.11111],74:[0,.68333,.09618,.16667],75:[0,.68333,.07153,.05556],76:[0,.68333,0,.02778],77:[0,.68333,.10903,.08334],78:[0,.68333,.10903,.08334],79:[0,.68333,.02778,.08334],80:[0,.68333,.13889,.08334],81:[.19444,.68333,0,.08334],82:[0,.68333,.00773,.08334],83:[0,.68333,.05764,.08334],84:[0,.68333,.13889,.08334],85:[0,.68333,.10903,.02778],86:[0,.68333,.22222,0],87:[0,.68333,.13889,0],88:[0,.68333,.07847,.08334],89:[0,.68333,.22222,0],90:[0,.68333,.07153,.08334],97:[0,.43056,0,0],98:[0,.69444,0,0],99:[0,.43056,0,.05556],100:[0,.69444,0,.16667],101:[0,.43056,0,.05556],102:[.19444,.69444,.10764,.16667],103:[.19444,.43056,.03588,.02778],104:[0,.69444,0,0],105:[0,.65952,0,0],106:[.19444,.65952,.05724,0],107:[0,.69444,.03148,0],108:[0,.69444,.01968,.08334],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,.05556],112:[.19444,.43056,0,.08334],113:[.19444,.43056,.03588,.08334],114:[0,.43056,.02778,.05556],115:[0,.43056,0,.05556],116:[0,.61508,0,.08334],117:[0,.43056,0,.02778],118:[0,.43056,.03588,.02778],119:[0,.43056,.02691,.08334],120:[0,.43056,0,.02778],121:[.19444,.43056,.03588,.05556],122:[0,.43056,.04398,.05556],915:[0,.68333,.13889,.08334],916:[0,.68333,0,.16667],920:[0,.68333,.02778,.08334],923:[0,.68333,0,.16667],926:[0,.68333,.07569,.08334],928:[0,.68333,.08125,.05556],931:[0,.68333,.05764,.08334],933:[0,.68333,.13889,.05556],934:[0,.68333,0,.08334],936:[0,.68333,.11,.05556],937:[0,.68333,.05017,.08334],945:[0,.43056,.0037,.02778],946:[.19444,.69444,.05278,.08334],947:[.19444,.43056,.05556,0],948:[0,.69444,.03785,.05556],949:[0,.43056,0,.08334],950:[.19444,.69444,.07378,.08334],951:[.19444,.43056,.03588,.05556],952:[0,.69444,.02778,.08334],953:[0,.43056,0,.05556],954:[0,.43056,0,0],955:[0,.69444,0,0],956:[.19444,.43056,0,.02778],957:[0,.43056,.06366,.02778],958:[.19444,.69444,.04601,.11111],959:[0,.43056,0,.05556],960:[0,.43056,.03588,0],961:[.19444,.43056,0,.08334],962:[.09722,.43056,.07986,.08334],963:[0,.43056,.03588,0],964:[0,.43056,.1132,.02778],965:[0,.43056,.03588,.02778],966:[.19444,.43056,0,.08334],967:[.19444,.43056,0,.05556],968:[.19444,.69444,.03588,.11111],969:[0,.43056,.03588,0],977:[0,.69444,0,.08334],981:[.19444,.69444,0,.08334],982:[0,.43056,.02778,0],1009:[.19444,.43056,0,.08334],1013:[0,.43056,0,.05556]},"Math-Regular":{65:[0,.68333,0,.13889],66:[0,.68333,.05017,.08334],67:[0,.68333,.07153,.08334],68:[0,.68333,.02778,.05556],69:[0,.68333,.05764,.08334],70:[0,.68333,.13889,.08334],71:[0,.68333,0,.08334],72:[0,.68333,.08125,.05556],73:[0,.68333,.07847,.11111],74:[0,.68333,.09618,.16667],75:[0,.68333,.07153,.05556],76:[0,.68333,0,.02778],77:[0,.68333,.10903,.08334],78:[0,.68333,.10903,.08334],79:[0,.68333,.02778,.08334],80:[0,.68333,.13889,.08334],81:[.19444,.68333,0,.08334],82:[0,.68333,.00773,.08334],83:[0,.68333,.05764,.08334],84:[0,.68333,.13889,.08334],85:[0,.68333,.10903,.02778],86:[0,.68333,.22222,0],87:[0,.68333,.13889,0],88:[0,.68333,.07847,.08334],89:[0,.68333,.22222,0],90:[0,.68333,.07153,.08334],97:[0,.43056,0,0],98:[0,.69444,0,0],99:[0,.43056,0,.05556],100:[0,.69444,0,.16667],101:[0,.43056,0,.05556],102:[.19444,.69444,.10764,.16667],103:[.19444,.43056,.03588,.02778],104:[0,.69444,0,0],105:[0,.65952,0,0],106:[.19444,.65952,.05724,0],107:[0,.69444,.03148,0],108:[0,.69444,.01968,.08334],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,.05556],112:[.19444,.43056,0,.08334],113:[.19444,.43056,.03588,.08334],114:[0,.43056,.02778,.05556],115:[0,.43056,0,.05556],116:[0,.61508,0,.08334],117:[0,.43056,0,.02778],118:[0,.43056,.03588,.02778],119:[0,.43056,.02691,.08334],120:[0,.43056,0,.02778],121:[.19444,.43056,.03588,.05556],122:[0,.43056,.04398,.05556],915:[0,.68333,.13889,.08334],916:[0,.68333,0,.16667],920:[0,.68333,.02778,.08334],923:[0,.68333,0,.16667],926:[0,.68333,.07569,.08334],928:[0,.68333,.08125,.05556],931:[0,.68333,.05764,.08334],933:[0,.68333,.13889,.05556],934:[0,.68333,0,.08334],936:[0,.68333,.11,.05556],937:[0,.68333,.05017,.08334],945:[0,.43056,.0037,.02778],946:[.19444,.69444,.05278,.08334],947:[.19444,.43056,.05556,0],948:[0,.69444,.03785,.05556],949:[0,.43056,0,.08334],950:[.19444,.69444,.07378,.08334],951:[.19444,.43056,.03588,.05556],952:[0,.69444,.02778,.08334],953:[0,.43056,0,.05556],954:[0,.43056,0,0],955:[0,.69444,0,0],956:[.19444,.43056,0,.02778],957:[0,.43056,.06366,.02778],958:[.19444,.69444,.04601,.11111],959:[0,.43056,0,.05556],960:[0,.43056,.03588,0],961:[.19444,.43056,0,.08334],962:[.09722,.43056,.07986,.08334],963:[0,.43056,.03588,0],964:[0,.43056,.1132,.02778],965:[0,.43056,.03588,.02778],966:[.19444,.43056,0,.08334],967:[.19444,.43056,0,.05556],968:[.19444,.69444,.03588,.11111],969:[0,.43056,.03588,0],977:[0,.69444,0,.08334],981:[.19444,.69444,0,.08334],982:[0,.43056,.02778,0],1009:[.19444,.43056,0,.08334],1013:[0,.43056,0,.05556]},"SansSerif-Regular":{33:[0,.69444,0,0],34:[0,.69444,0,0],35:[.19444,.69444,0,0],36:[.05556,.75,0,0],37:[.05556,.75,0,0],38:[0,.69444,0,0],39:[0,.69444,0,0],40:[.25,.75,0,0],41:[.25,.75,0,0],42:[0,.75,0,0],43:[.08333,.58333,0,0],44:[.125,.08333,0,0],45:[0,.44444,0,0],46:[0,.08333,0,0],47:[.25,.75,0,0],48:[0,.65556,0,0],49:[0,.65556,0,0],50:[0,.65556,0,0],51:[0,.65556,0,0],52:[0,.65556,0,0],53:[0,.65556,0,0],54:[0,.65556,0,0],55:[0,.65556,0,0],56:[0,.65556,0,0],57:[0,.65556,0,0],58:[0,.44444,0,0],59:[.125,.44444,0,0],61:[-.13,.37,0,0],63:[0,.69444,0,0],64:[0,.69444,0,0],65:[0,.69444,0,0],66:[0,.69444,0,0],67:[0,.69444,0,0],68:[0,.69444,0,0],69:[0,.69444,0,0],70:[0,.69444,0,0],71:[0,.69444,0,0],72:[0,.69444,0,0],73:[0,.69444,0,0],74:[0,.69444,0,0],75:[0,.69444,0,0],76:[0,.69444,0,0],77:[0,.69444,0,0],78:[0,.69444,0,0],79:[0,.69444,0,0],80:[0,.69444,0,0],81:[.125,.69444,0,0],82:[0,.69444,0,0],83:[0,.69444,0,0],84:[0,.69444,0,0],85:[0,.69444,0,0],86:[0,.69444,.01389,0],87:[0,.69444,.01389,0],88:[0,.69444,0,0],89:[0,.69444,.025,0],90:[0,.69444,0,0],91:[.25,.75,0,0],93:[.25,.75,0,0],94:[0,.69444,0,0],95:[.35,.09444,.02778,0],97:[0,.44444,0,0],98:[0,.69444,0,0],99:[0,.44444,0,0],100:[0,.69444,0,0],101:[0,.44444,0,0],102:[0,.69444,.06944,0],103:[.19444,.44444,.01389,0],104:[0,.69444,0,0],105:[0,.67937,0,0],106:[.19444,.67937,0,0],107:[0,.69444,0,0],108:[0,.69444,0,0],109:[0,.44444,0,0],110:[0,.44444,0,0],111:[0,.44444,0,0],112:[.19444,.44444,0,0],113:[.19444,.44444,0,0],114:[0,.44444,.01389,0],115:[0,.44444,0,0],116:[0,.57143,0,0],117:[0,.44444,0,0],118:[0,.44444,.01389,0],119:[0,.44444,.01389,0],120:[0,.44444,0,0],121:[.19444,.44444,.01389,0],122:[0,.44444,0,0],126:[.35,.32659,0,0],305:[0,.44444,0,0],567:[.19444,.44444,0,0],768:[0,.69444,0,0],769:[0,.69444,0,0],770:[0,.69444,0,0],771:[0,.67659,0,0],772:[0,.60889,0,0],774:[0,.69444,0,0],775:[0,.67937,0,0],776:[0,.67937,0,0],778:[0,.69444,0,0],779:[0,.69444,0,0],780:[0,.63194,0,0],915:[0,.69444,0,0],916:[0,.69444,0,0],920:[0,.69444,0,0],923:[0,.69444,0,0],926:[0,.69444,0,0],928:[0,.69444,0,0],931:[0,.69444,0,0],933:[0,.69444,0,0],934:[0,.69444,0,0],936:[0,.69444,0,0],937:[0,.69444,0,0],8211:[0,.44444,.02778,0],8212:[0,.44444,.02778,0],8216:[0,.69444,0,0],8217:[0,.69444,0,0],8220:[0,.69444,0,0],8221:[0,.69444,0,0]},"Script-Regular":{65:[0,.7,.22925,0],66:[0,.7,.04087,0],67:[0,.7,.1689,0],68:[0,.7,.09371,0],69:[0,.7,.18583,0],70:[0,.7,.13634,0],71:[0,.7,.17322,0],72:[0,.7,.29694,0],73:[0,.7,.19189,0],74:[.27778,.7,.19189,0],75:[0,.7,.31259,0],76:[0,.7,.19189,0],77:[0,.7,.15981,0],78:[0,.7,.3525,0],79:[0,.7,.08078,0],80:[0,.7,.08078,0],81:[0,.7,.03305,0],82:[0,.7,.06259,0],83:[0,.7,.19189,0],84:[0,.7,.29087,0],85:[0,.7,.25815,0],86:[0,.7,.27523,0],87:[0,.7,.27523,0],88:[0,.7,.26006,0],89:[0,.7,.2939,0],90:[0,.7,.24037,0]},"Size1-Regular":{40:[.35001,.85,0,0],41:[.35001,.85,0,0],47:[.35001,.85,0,0],91:[.35001,.85,0,0],92:[.35001,.85,0,0],93:[.35001,.85,0,0],123:[.35001,.85,0,0],125:[.35001,.85,0,0],710:[0,.72222,0,0],732:[0,.72222,0,0],770:[0,.72222,0,0],771:[0,.72222,0,0],8214:[-99e-5,.601,0,0],8593:[1e-5,.6,0,0],8595:[1e-5,.6,0,0],8657:[1e-5,.6,0,0],8659:[1e-5,.6,0,0],8719:[.25001,.75,0,0],8720:[.25001,.75,0,0],8721:[.25001,.75,0,0],8730:[.35001,.85,0,0],8739:[-.00599,.606,0,0],8741:[-.00599,.606,0,0],8747:[.30612,.805,.19445,0],8748:[.306,.805,.19445,0],8749:[.306,.805,.19445,0],8750:[.30612,.805,.19445,0],8896:[.25001,.75,0,0],8897:[.25001,.75,0,0],8898:[.25001,.75,0,0],8899:[.25001,.75,0,0],8968:[.35001,.85,0,0],8969:[.35001,.85,0,0],8970:[.35001,.85,0,0],8971:[.35001,.85,0,0],9168:[-99e-5,.601,0,0],10216:[.35001,.85,0,0],10217:[.35001,.85,0,0],10752:[.25001,.75,0,0],10753:[.25001,.75,0,0],10754:[.25001,.75,0,0],10756:[.25001,.75,0,0],10758:[.25001,.75,0,0]},"Size2-Regular":{40:[.65002,1.15,0,0],41:[.65002,1.15,0,0],47:[.65002,1.15,0,0],91:[.65002,1.15,0,0],92:[.65002,1.15,0,0],93:[.65002,1.15,0,0],123:[.65002,1.15,0,0],125:[.65002,1.15,0,0],710:[0,.75,0,0],732:[0,.75,0,0],770:[0,.75,0,0],771:[0,.75,0,0],8719:[.55001,1.05,0,0],8720:[.55001,1.05,0,0],8721:[.55001,1.05,0,0],8730:[.65002,1.15,0,0],8747:[.86225,1.36,.44445,0],8748:[.862,1.36,.44445,0],8749:[.862,1.36,.44445,0],8750:[.86225,1.36,.44445,0],8896:[.55001,1.05,0,0],8897:[.55001,1.05,0,0],8898:[.55001,1.05,0,0],8899:[.55001,1.05,0,0],8968:[.65002,1.15,0,0],8969:[.65002,1.15,0,0],8970:[.65002,1.15,0,0],8971:[.65002,1.15,0,0],10216:[.65002,1.15,0,0],10217:[.65002,1.15,0,0],10752:[.55001,1.05,0,0],10753:[.55001,1.05,0,0],10754:[.55001,1.05,0,0],
+10756:[.55001,1.05,0,0],10758:[.55001,1.05,0,0]},"Size3-Regular":{40:[.95003,1.45,0,0],41:[.95003,1.45,0,0],47:[.95003,1.45,0,0],91:[.95003,1.45,0,0],92:[.95003,1.45,0,0],93:[.95003,1.45,0,0],123:[.95003,1.45,0,0],125:[.95003,1.45,0,0],710:[0,.75,0,0],732:[0,.75,0,0],770:[0,.75,0,0],771:[0,.75,0,0],8730:[.95003,1.45,0,0],8968:[.95003,1.45,0,0],8969:[.95003,1.45,0,0],8970:[.95003,1.45,0,0],8971:[.95003,1.45,0,0],10216:[.95003,1.45,0,0],10217:[.95003,1.45,0,0]},"Size4-Regular":{40:[1.25003,1.75,0,0],41:[1.25003,1.75,0,0],47:[1.25003,1.75,0,0],91:[1.25003,1.75,0,0],92:[1.25003,1.75,0,0],93:[1.25003,1.75,0,0],123:[1.25003,1.75,0,0],125:[1.25003,1.75,0,0],710:[0,.825,0,0],732:[0,.825,0,0],770:[0,.825,0,0],771:[0,.825,0,0],8730:[1.25003,1.75,0,0],8968:[1.25003,1.75,0,0],8969:[1.25003,1.75,0,0],8970:[1.25003,1.75,0,0],8971:[1.25003,1.75,0,0],9115:[.64502,1.155,0,0],9116:[1e-5,.6,0,0],9117:[.64502,1.155,0,0],9118:[.64502,1.155,0,0],9119:[1e-5,.6,0,0],9120:[.64502,1.155,0,0],9121:[.64502,1.155,0,0],9122:[-99e-5,.601,0,0],9123:[.64502,1.155,0,0],9124:[.64502,1.155,0,0],9125:[-99e-5,.601,0,0],9126:[.64502,1.155,0,0],9127:[1e-5,.9,0,0],9128:[.65002,1.15,0,0],9129:[.90001,0,0,0],9130:[0,.3,0,0],9131:[1e-5,.9,0,0],9132:[.65002,1.15,0,0],9133:[.90001,0,0,0],9143:[.88502,.915,0,0],10216:[1.25003,1.75,0,0],10217:[1.25003,1.75,0,0],57344:[-.00499,.605,0,0],57345:[-.00499,.605,0,0],57680:[0,.12,0,0],57681:[0,.12,0,0],57682:[0,.12,0,0],57683:[0,.12,0,0]},"Typewriter-Regular":{33:[0,.61111,0,0],34:[0,.61111,0,0],35:[0,.61111,0,0],36:[.08333,.69444,0,0],37:[.08333,.69444,0,0],38:[0,.61111,0,0],39:[0,.61111,0,0],40:[.08333,.69444,0,0],41:[.08333,.69444,0,0],42:[0,.52083,0,0],43:[-.08056,.53055,0,0],44:[.13889,.125,0,0],45:[-.08056,.53055,0,0],46:[0,.125,0,0],47:[.08333,.69444,0,0],48:[0,.61111,0,0],49:[0,.61111,0,0],50:[0,.61111,0,0],51:[0,.61111,0,0],52:[0,.61111,0,0],53:[0,.61111,0,0],54:[0,.61111,0,0],55:[0,.61111,0,0],56:[0,.61111,0,0],57:[0,.61111,0,0],58:[0,.43056,0,0],59:[.13889,.43056,0,0],60:[-.05556,.55556,0,0],61:[-.19549,.41562,0,0],62:[-.05556,.55556,0,0],63:[0,.61111,0,0],64:[0,.61111,0,0],65:[0,.61111,0,0],66:[0,.61111,0,0],67:[0,.61111,0,0],68:[0,.61111,0,0],69:[0,.61111,0,0],70:[0,.61111,0,0],71:[0,.61111,0,0],72:[0,.61111,0,0],73:[0,.61111,0,0],74:[0,.61111,0,0],75:[0,.61111,0,0],76:[0,.61111,0,0],77:[0,.61111,0,0],78:[0,.61111,0,0],79:[0,.61111,0,0],80:[0,.61111,0,0],81:[.13889,.61111,0,0],82:[0,.61111,0,0],83:[0,.61111,0,0],84:[0,.61111,0,0],85:[0,.61111,0,0],86:[0,.61111,0,0],87:[0,.61111,0,0],88:[0,.61111,0,0],89:[0,.61111,0,0],90:[0,.61111,0,0],91:[.08333,.69444,0,0],92:[.08333,.69444,0,0],93:[.08333,.69444,0,0],94:[0,.61111,0,0],95:[.09514,0,0,0],96:[0,.61111,0,0],97:[0,.43056,0,0],98:[0,.61111,0,0],99:[0,.43056,0,0],100:[0,.61111,0,0],101:[0,.43056,0,0],102:[0,.61111,0,0],103:[.22222,.43056,0,0],104:[0,.61111,0,0],105:[0,.61111,0,0],106:[.22222,.61111,0,0],107:[0,.61111,0,0],108:[0,.61111,0,0],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,0],112:[.22222,.43056,0,0],113:[.22222,.43056,0,0],114:[0,.43056,0,0],115:[0,.43056,0,0],116:[0,.55358,0,0],117:[0,.43056,0,0],118:[0,.43056,0,0],119:[0,.43056,0,0],120:[0,.43056,0,0],121:[.22222,.43056,0,0],122:[0,.43056,0,0],123:[.08333,.69444,0,0],124:[.08333,.69444,0,0],125:[.08333,.69444,0,0],126:[0,.61111,0,0],127:[0,.61111,0,0],305:[0,.43056,0,0],567:[.22222,.43056,0,0],768:[0,.61111,0,0],769:[0,.61111,0,0],770:[0,.61111,0,0],771:[0,.61111,0,0],772:[0,.56555,0,0],774:[0,.61111,0,0],776:[0,.61111,0,0],778:[0,.61111,0,0],780:[0,.56597,0,0],915:[0,.61111,0,0],916:[0,.61111,0,0],920:[0,.61111,0,0],923:[0,.61111,0,0],926:[0,.61111,0,0],928:[0,.61111,0,0],931:[0,.61111,0,0],933:[0,.61111,0,0],934:[0,.61111,0,0],936:[0,.61111,0,0],937:[0,.61111,0,0],2018:[0,.61111,0,0],2019:[0,.61111,0,0],8242:[0,.61111,0,0]}}},{}],19:[function(e,t,r){var a=e("./utils");var i=e("./ParseError");var n=e("./parseData");var s=n.ParseNode;function l(e,r,a){if(typeof e==="string"){e=[e]}if(typeof r==="number"){r={numArgs:r}}var i={numArgs:r.numArgs,argTypes:r.argTypes,greediness:r.greediness===undefined?1:r.greediness,allowedInText:!!r.allowedInText,numOptionalArgs:r.numOptionalArgs||0,infix:!!r.infix,handler:a};for(var n=0;n<e.length;++n){t.exports[e[n]]=i}}var o=function(e){if(e.type==="ordgroup"){return e.value}else{return[e]}};l("\\sqrt",{numArgs:1,numOptionalArgs:1},function(e,t){var r=t[0];var a=t[1];return{type:"sqrt",body:a,index:r}});var u={"\\text":undefined,"\\textrm":"mathrm","\\textsf":"mathsf","\\texttt":"mathtt","\\textnormal":"mathrm","\\textbf":"mathbf","\\textit":"textit"};l(["\\text","\\textrm","\\textsf","\\texttt","\\textnormal","\\textbf","\\textit"],{numArgs:1,argTypes:["text"],greediness:2,allowedInText:true},function(e,t){var r=t[0];return{type:"text",body:o(r),style:u[e.funcName]}});l("\\color",{numArgs:2,allowedInText:true,greediness:3,argTypes:["color","original"]},function(e,t){var r=t[0];var a=t[1];return{type:"color",color:r.value,value:o(a)}});l("\\overline",{numArgs:1},function(e,t){var r=t[0];return{type:"overline",body:r}});l("\\underline",{numArgs:1},function(e,t){var r=t[0];return{type:"underline",body:r}});l("\\rule",{numArgs:2,numOptionalArgs:1,argTypes:["size","size","size"]},function(e,t){var r=t[0];var a=t[1];var i=t[2];return{type:"rule",shift:r&&r.value,width:a.value,height:i.value}});l(["\\kern","\\mkern"],{numArgs:1,argTypes:["size"]},function(e,t){return{type:"kern",dimension:t[0].value}});l("\\KaTeX",{numArgs:0},function(e){return{type:"katex"}});l("\\phantom",{numArgs:1},function(e,t){var r=t[0];return{type:"phantom",value:o(r)}});l(["\\mathord","\\mathbin","\\mathrel","\\mathopen","\\mathclose","\\mathpunct","\\mathinner"],{numArgs:1},function(e,t){var r=t[0];return{type:"mclass",mclass:"m"+e.funcName.substr(5),value:o(r)}});l("\\stackrel",{numArgs:2},function(e,t){var r=t[0];var a=t[1];var i=new s("op",{type:"op",limits:true,alwaysHandleSupSub:true,symbol:false,value:o(a)},a.mode);var n=new s("supsub",{base:i,sup:r,sub:null},r.mode);return{type:"mclass",mclass:"mrel",value:[n]}});l("\\bmod",{numArgs:0},function(e,t){return{type:"mod",modType:"bmod",value:null}});l(["\\pod","\\pmod","\\mod"],{numArgs:1},function(e,t){var r=t[0];return{type:"mod",modType:e.funcName.substr(1),value:o(r)}});var p={"\\bigl":{mclass:"mopen",size:1},"\\Bigl":{mclass:"mopen",size:2},"\\biggl":{mclass:"mopen",size:3},"\\Biggl":{mclass:"mopen",size:4},"\\bigr":{mclass:"mclose",size:1},"\\Bigr":{mclass:"mclose",size:2},"\\biggr":{mclass:"mclose",size:3},"\\Biggr":{mclass:"mclose",size:4},"\\bigm":{mclass:"mrel",size:1},"\\Bigm":{mclass:"mrel",size:2},"\\biggm":{mclass:"mrel",size:3},"\\Biggm":{mclass:"mrel",size:4},"\\big":{mclass:"mord",size:1},"\\Big":{mclass:"mord",size:2},"\\bigg":{mclass:"mord",size:3},"\\Bigg":{mclass:"mord",size:4}};var h=["(",")","[","\\lbrack","]","\\rbrack","\\{","\\lbrace","\\}","\\rbrace","\\lfloor","\\rfloor","\\lceil","\\rceil","<",">","\\langle","\\rangle","\\lt","\\gt","\\lvert","\\rvert","\\lVert","\\rVert","\\lgroup","\\rgroup","\\lmoustache","\\rmoustache","/","\\backslash","|","\\vert","\\|","\\Vert","\\uparrow","\\Uparrow","\\downarrow","\\Downarrow","\\updownarrow","\\Updownarrow","."];var c={"\\Bbb":"\\mathbb","\\bold":"\\mathbf","\\frak":"\\mathfrak"};l(["\\blue","\\orange","\\pink","\\red","\\green","\\gray","\\purple","\\blueA","\\blueB","\\blueC","\\blueD","\\blueE","\\tealA","\\tealB","\\tealC","\\tealD","\\tealE","\\greenA","\\greenB","\\greenC","\\greenD","\\greenE","\\goldA","\\goldB","\\goldC","\\goldD","\\goldE","\\redA","\\redB","\\redC","\\redD","\\redE","\\maroonA","\\maroonB","\\maroonC","\\maroonD","\\maroonE","\\purpleA","\\purpleB","\\purpleC","\\purpleD","\\purpleE","\\mintA","\\mintB","\\mintC","\\grayA","\\grayB","\\grayC","\\grayD","\\grayE","\\grayF","\\grayG","\\grayH","\\grayI","\\kaBlue","\\kaGreen"],{numArgs:1,allowedInText:true,greediness:3},function(e,t){var r=t[0];return{type:"color",color:"katex-"+e.funcName.slice(1),value:o(r)}});l(["\\arcsin","\\arccos","\\arctan","\\arg","\\cos","\\cosh","\\cot","\\coth","\\csc","\\deg","\\dim","\\exp","\\hom","\\ker","\\lg","\\ln","\\log","\\sec","\\sin","\\sinh","\\tan","\\tanh"],{numArgs:0},function(e){return{type:"op",limits:false,symbol:false,body:e.funcName}});l(["\\det","\\gcd","\\inf","\\lim","\\liminf","\\limsup","\\max","\\min","\\Pr","\\sup"],{numArgs:0},function(e){return{type:"op",limits:true,symbol:false,body:e.funcName}});l(["\\int","\\iint","\\iiint","\\oint"],{numArgs:0},function(e){return{type:"op",limits:false,symbol:true,body:e.funcName}});l(["\\coprod","\\bigvee","\\bigwedge","\\biguplus","\\bigcap","\\bigcup","\\intop","\\prod","\\sum","\\bigotimes","\\bigoplus","\\bigodot","\\bigsqcup","\\smallint"],{numArgs:0},function(e){return{type:"op",limits:true,symbol:true,body:e.funcName}});l("\\mathop",{numArgs:1},function(e,t){var r=t[0];return{type:"op",limits:false,symbol:false,value:o(r)}});l(["\\dfrac","\\frac","\\tfrac","\\dbinom","\\binom","\\tbinom","\\\\atopfrac"],{numArgs:2,greediness:2},function(e,t){var r=t[0];var a=t[1];var i;var n=null;var s=null;var l="auto";switch(e.funcName){case"\\dfrac":case"\\frac":case"\\tfrac":i=true;break;case"\\\\atopfrac":i=false;break;case"\\dbinom":case"\\binom":case"\\tbinom":i=false;n="(";s=")";break;default:throw new Error("Unrecognized genfrac command")}switch(e.funcName){case"\\dfrac":case"\\dbinom":l="display";break;case"\\tfrac":case"\\tbinom":l="text";break}return{type:"genfrac",numer:r,denom:a,hasBarLine:i,leftDelim:n,rightDelim:s,size:l}});l(["\\llap","\\rlap"],{numArgs:1,allowedInText:true},function(e,t){var r=t[0];return{type:e.funcName.slice(1),body:r}});var m=function(e,t){if(a.contains(h,e.value)){return e}else{throw new i("Invalid delimiter: '"+e.value+"' after '"+t.funcName+"'",e)}};l(["\\bigl","\\Bigl","\\biggl","\\Biggl","\\bigr","\\Bigr","\\biggr","\\Biggr","\\bigm","\\Bigm","\\biggm","\\Biggm","\\big","\\Big","\\bigg","\\Bigg"],{numArgs:1},function(e,t){var r=m(t[0],e);return{type:"delimsizing",size:p[e.funcName].size,mclass:p[e.funcName].mclass,value:r.value}});l(["\\left","\\right"],{numArgs:1},function(e,t){var r=m(t[0],e);return{type:"leftright",value:r.value}});l("\\middle",{numArgs:1},function(e,t){var r=m(t[0],e);if(!e.parser.leftrightDepth){throw new i("\\middle without preceding \\left",r)}return{type:"middle",value:r.value}});l(["\\tiny","\\scriptsize","\\footnotesize","\\small","\\normalsize","\\large","\\Large","\\LARGE","\\huge","\\Huge"],0,null);l(["\\displaystyle","\\textstyle","\\scriptstyle","\\scriptscriptstyle"],0,null);l(["\\mathrm","\\mathit","\\mathbf","\\mathbb","\\mathcal","\\mathfrak","\\mathscr","\\mathsf","\\mathtt","\\Bbb","\\bold","\\frak"],{numArgs:1,greediness:2},function(e,t){var r=t[0];var a=e.funcName;if(a in c){a=c[a]}return{type:"font",font:a.slice(1),body:r}});l(["\\acute","\\grave","\\ddot","\\tilde","\\bar","\\breve","\\check","\\hat","\\vec","\\dot"],{numArgs:1},function(e,t){var r=t[0];return{type:"accent",accent:e.funcName,base:r}});l(["\\over","\\choose","\\atop"],{numArgs:0,infix:true},function(e){var t;switch(e.funcName){case"\\over":t="\\frac";break;case"\\choose":t="\\binom";break;case"\\atop":t="\\\\atopfrac";break;default:throw new Error("Unrecognized infix genfrac command")}return{type:"infix",replaceWith:t,token:e.token}});l(["\\\\","\\cr"],{numArgs:0,numOptionalArgs:1,argTypes:["size"]},function(e,t){var r=t[0];return{type:"cr",size:r}});l(["\\begin","\\end"],{numArgs:1,argTypes:["text"]},function(e,t){var r=t[0];if(r.type!=="ordgroup"){throw new i("Invalid environment name",r)}var a="";for(var n=0;n<r.value.length;++n){a+=r.value[n].value}return{type:"environment",name:a,nameGroup:r}})},{"./ParseError":6,"./parseData":21,"./utils":25}],20:[function(e,t,r){var a=e("./utils");function i(e,t){this.type=e;this.attributes={};this.children=t||[]}i.prototype.setAttribute=function(e,t){this.attributes[e]=t};i.prototype.toNode=function(){var e=document.createElementNS("http://www.w3.org/1998/Math/MathML",this.type);for(var t in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,t)){e.setAttribute(t,this.attributes[t])}}for(var r=0;r<this.children.length;r++){e.appendChild(this.children[r].toNode())}return e};i.prototype.toMarkup=function(){var e="<"+this.type;for(var t in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,t)){e+=" "+t+'="';e+=a.escape(this.attributes[t]);e+='"'}}e+=">";for(var r=0;r<this.children.length;r++){e+=this.children[r].toMarkup()}e+="</"+this.type+">";return e};function n(e){this.text=e}n.prototype.toNode=function(){return document.createTextNode(this.text)};n.prototype.toMarkup=function(){return a.escape(this.text)};t.exports={MathNode:i,TextNode:n}},{"./utils":25}],21:[function(e,t,r){function a(e,t,r,a,i){this.type=e;this.value=t;this.mode=r;if(a&&(!i||i.lexer===a.lexer)){this.lexer=a.lexer;this.start=a.start;this.end=(i||a).end}}t.exports={ParseNode:a}},{}],22:[function(e,t,r){var a=e("./Parser");var i=function(e,t){if(!(typeof e==="string"||e instanceof String)){throw new TypeError("KaTeX can only parse string typed expression")}var r=new a(e,t);return r.parse()};t.exports=i},{"./Parser":7}],23:[function(e,t,r){t.exports={math:{},text:{}};function a(e,r,a,i,n){t.exports[e][n]={font:r,group:a,replace:i}}var i="math";var n="text";var s="main";var l="ams";var o="accent";var u="bin";var p="close";var h="inner";var c="mathord";var m="op";var f="open";var v="punct";var d="rel";var g="spacing";var y="textord";a(i,s,d,"\u2261","\\equiv");a(i,s,d,"\u227a","\\prec");a(i,s,d,"\u227b","\\succ");a(i,s,d,"\u223c","\\sim");a(i,s,d,"\u22a5","\\perp");a(i,s,d,"\u2aaf","\\preceq");a(i,s,d,"\u2ab0","\\succeq");a(i,s,d,"\u2243","\\simeq");a(i,s,d,"\u2223","\\mid");a(i,s,d,"\u226a","\\ll");a(i,s,d,"\u226b","\\gg");a(i,s,d,"\u224d","\\asymp");a(i,s,d,"\u2225","\\parallel");a(i,s,d,"\u22c8","\\bowtie");a(i,s,d,"\u2323","\\smile");a(i,s,d,"\u2291","\\sqsubseteq");a(i,s,d,"\u2292","\\sqsupseteq");a(i,s,d,"\u2250","\\doteq");a(i,s,d,"\u2322","\\frown");a(i,s,d,"\u220b","\\ni");a(i,s,d,"\u221d","\\propto");a(i,s,d,"\u22a2","\\vdash");a(i,s,d,"\u22a3","\\dashv");a(i,s,d,"\u220b","\\owns");a(i,s,v,".","\\ldotp");a(i,s,v,"\u22c5","\\cdotp");a(i,s,y,"#","\\#");a(n,s,y,"#","\\#");a(i,s,y,"&","\\&");a(n,s,y,"&","\\&");a(i,s,y,"\u2135","\\aleph");a(i,s,y,"\u2200","\\forall");a(i,s,y,"\u210f","\\hbar");a(i,s,y,"\u2203","\\exists");a(i,s,y,"\u2207","\\nabla");a(i,s,y,"\u266d","\\flat");a(i,s,y,"\u2113","\\ell");a(i,s,y,"\u266e","\\natural");a(i,s,y,"\u2663","\\clubsuit");a(i,s,y,"\u2118","\\wp");a(i,s,y,"\u266f","\\sharp");a(i,s,y,"\u2662","\\diamondsuit");a(i,s,y,"\u211c","\\Re");a(i,s,y,"\u2661","\\heartsuit");a(i,s,y,"\u2111","\\Im");a(i,s,y,"\u2660","\\spadesuit");a(i,s,y,"\u2020","\\dag");a(i,s,y,"\u2021","\\ddag");a(i,s,p,"\u23b1","\\rmoustache");a(i,s,f,"\u23b0","\\lmoustache");a(i,s,p,"\u27ef","\\rgroup");a(i,s,f,"\u27ee","\\lgroup");a(i,s,u,"\u2213","\\mp");a(i,s,u,"\u2296","\\ominus");a(i,s,u,"\u228e","\\uplus");a(i,s,u,"\u2293","\\sqcap");a(i,s,u,"\u2217","\\ast");a(i,s,u,"\u2294","\\sqcup");a(i,s,u,"\u25ef","\\bigcirc");a(i,s,u,"\u2219","\\bullet");a(i,s,u,"\u2021","\\ddagger");a(i,s,u,"\u2240","\\wr");a(i,s,u,"\u2a3f","\\amalg");a(i,s,d,"\u27f5","\\longleftarrow");a(i,s,d,"\u21d0","\\Leftarrow");a(i,s,d,"\u27f8","\\Longleftarrow");a(i,s,d,"\u27f6","\\longrightarrow");a(i,s,d,"\u21d2","\\Rightarrow");a(i,s,d,"\u27f9","\\Longrightarrow");a(i,s,d,"\u2194","\\leftrightarrow");a(i,s,d,"\u27f7","\\longleftrightarrow");a(i,s,d,"\u21d4","\\Leftrightarrow");a(i,s,d,"\u27fa","\\Longleftrightarrow");a(i,s,d,"\u21a6","\\mapsto");a(i,s,d,"\u27fc","\\longmapsto");a(i,s,d,"\u2197","\\nearrow");a(i,s,d,"\u21a9","\\hookleftarrow");a(i,s,d,"\u21aa","\\hookrightarrow");a(i,s,d,"\u2198","\\searrow");a(i,s,d,"\u21bc","\\leftharpoonup");a(i,s,d,"\u21c0","\\rightharpoonup");a(i,s,d,"\u2199","\\swarrow");a(i,s,d,"\u21bd","\\leftharpoondown");a(i,s,d,"\u21c1","\\rightharpoondown");a(i,s,d,"\u2196","\\nwarrow");a(i,s,d,"\u21cc","\\rightleftharpoons");a(i,l,d,"\u226e","\\nless");a(i,l,d,"\ue010","\\nleqslant");a(i,l,d,"\ue011","\\nleqq");a(i,l,d,"\u2a87","\\lneq");a(i,l,d,"\u2268","\\lneqq");a(i,l,d,"\ue00c","\\lvertneqq");a(i,l,d,"\u22e6","\\lnsim");a(i,l,d,"\u2a89","\\lnapprox");a(i,l,d,"\u2280","\\nprec");a(i,l,d,"\u22e0","\\npreceq");a(i,l,d,"\u22e8","\\precnsim");a(i,l,d,"\u2ab9","\\precnapprox");a(i,l,d,"\u2241","\\nsim");a(i,l,d,"\ue006","\\nshortmid");a(i,l,d,"\u2224","\\nmid");a(i,l,d,"\u22ac","\\nvdash");a(i,l,d,"\u22ad","\\nvDash");a(i,l,d,"\u22ea","\\ntriangleleft");a(i,l,d,"\u22ec","\\ntrianglelefteq");a(i,l,d,"\u228a","\\subsetneq");a(i,l,d,"\ue01a","\\varsubsetneq");a(i,l,d,"\u2acb","\\subsetneqq");a(i,l,d,"\ue017","\\varsubsetneqq");a(i,l,d,"\u226f","\\ngtr");a(i,l,d,"\ue00f","\\ngeqslant");a(i,l,d,"\ue00e","\\ngeqq");a(i,l,d,"\u2a88","\\gneq");a(i,l,d,"\u2269","\\gneqq");a(i,l,d,"\ue00d","\\gvertneqq");a(i,l,d,"\u22e7","\\gnsim");a(i,l,d,"\u2a8a","\\gnapprox");a(i,l,d,"\u2281","\\nsucc");a(i,l,d,"\u22e1","\\nsucceq");a(i,l,d,"\u22e9","\\succnsim");a(i,l,d,"\u2aba","\\succnapprox");a(i,l,d,"\u2246","\\ncong");a(i,l,d,"\ue007","\\nshortparallel");a(i,l,d,"\u2226","\\nparallel");a(i,l,d,"\u22af","\\nVDash");a(i,l,d,"\u22eb","\\ntriangleright");a(i,l,d,"\u22ed","\\ntrianglerighteq");a(i,l,d,"\ue018","\\nsupseteqq");a(i,l,d,"\u228b","\\supsetneq");a(i,l,d,"\ue01b","\\varsupsetneq");a(i,l,d,"\u2acc","\\supsetneqq");a(i,l,d,"\ue019","\\varsupsetneqq");a(i,l,d,"\u22ae","\\nVdash");a(i,l,d,"\u2ab5","\\precneqq");a(i,l,d,"\u2ab6","\\succneqq");a(i,l,d,"\ue016","\\nsubseteqq");a(i,l,u,"\u22b4","\\unlhd");a(i,l,u,"\u22b5","\\unrhd");a(i,l,d,"\u219a","\\nleftarrow");a(i,l,d,"\u219b","\\nrightarrow");a(i,l,d,"\u21cd","\\nLeftarrow");a(i,l,d,"\u21cf","\\nRightarrow");a(i,l,d,"\u21ae","\\nleftrightarrow");a(i,l,d,"\u21ce","\\nLeftrightarrow");a(i,l,d,"\u25b3","\\vartriangle");a(i,l,y,"\u210f","\\hslash");a(i,l,y,"\u25bd","\\triangledown");a(i,l,y,"\u25ca","\\lozenge");a(i,l,y,"\u24c8","\\circledS");a(i,l,y,"\xae","\\circledR");a(i,l,y,"\u2221","\\measuredangle");a(i,l,y,"\u2204","\\nexists");a(i,l,y,"\u2127","\\mho");a(i,l,y,"\u2132","\\Finv");a(i,l,y,"\u2141","\\Game");a(i,l,y,"k","\\Bbbk");a(i,l,y,"\u2035","\\backprime");a(i,l,y,"\u25b2","\\blacktriangle");a(i,l,y,"\u25bc","\\blacktriangledown");a(i,l,y,"\u25a0","\\blacksquare");a(i,l,y,"\u29eb","\\blacklozenge");a(i,l,y,"\u2605","\\bigstar");a(i,l,y,"\u2222","\\sphericalangle");a(i,l,y,"\u2201","\\complement");a(i,l,y,"\xf0","\\eth");a(i,l,y,"\u2571","\\diagup");a(i,l,y,"\u2572","\\diagdown");a(i,l,y,"\u25a1","\\square");a(i,l,y,"\u25a1","\\Box");a(i,l,y,"\u25ca","\\Diamond");a(i,l,y,"\xa5","\\yen");a(i,l,y,"\u2713","\\checkmark");a(i,l,y,"\u2136","\\beth");a(i,l,y,"\u2138","\\daleth");a(i,l,y,"\u2137","\\gimel");a(i,l,y,"\u03dd","\\digamma");a(i,l,y,"\u03f0","\\varkappa");a(i,l,f,"\u250c","\\ulcorner");a(i,l,p,"\u2510","\\urcorner");a(i,l,f,"\u2514","\\llcorner");a(i,l,p,"\u2518","\\lrcorner");a(i,l,d,"\u2266","\\leqq");a(i,l,d,"\u2a7d","\\leqslant");a(i,l,d,"\u2a95","\\eqslantless");a(i,l,d,"\u2272","\\lesssim");a(i,l,d,"\u2a85","\\lessapprox");a(i,l,d,"\u224a","\\approxeq");a(i,l,u,"\u22d6","\\lessdot");a(i,l,d,"\u22d8","\\lll");a(i,l,d,"\u2276","\\lessgtr");a(i,l,d,"\u22da","\\lesseqgtr");a(i,l,d,"\u2a8b","\\lesseqqgtr");a(i,l,d,"\u2251","\\doteqdot");a(i,l,d,"\u2253","\\risingdotseq");a(i,l,d,"\u2252","\\fallingdotseq");a(i,l,d,"\u223d","\\backsim");a(i,l,d,"\u22cd","\\backsimeq");a(i,l,d,"\u2ac5","\\subseteqq");a(i,l,d,"\u22d0","\\Subset");a(i,l,d,"\u228f","\\sqsubset");a(i,l,d,"\u227c","\\preccurlyeq");a(i,l,d,"\u22de","\\curlyeqprec");a(i,l,d,"\u227e","\\precsim");a(i,l,d,"\u2ab7","\\precapprox");a(i,l,d,"\u22b2","\\vartriangleleft");a(i,l,d,"\u22b4","\\trianglelefteq");a(i,l,d,"\u22a8","\\vDash");a(i,l,d,"\u22aa","\\Vvdash");a(i,l,d,"\u2323","\\smallsmile");a(i,l,d,"\u2322","\\smallfrown");a(i,l,d,"\u224f","\\bumpeq");a(i,l,d,"\u224e","\\Bumpeq");a(i,l,d,"\u2267","\\geqq");a(i,l,d,"\u2a7e","\\geqslant");a(i,l,d,"\u2a96","\\eqslantgtr");a(i,l,d,"\u2273","\\gtrsim");a(i,l,d,"\u2a86","\\gtrapprox");a(i,l,u,"\u22d7","\\gtrdot");a(i,l,d,"\u22d9","\\ggg");a(i,l,d,"\u2277","\\gtrless");a(i,l,d,"\u22db","\\gtreqless");a(i,l,d,"\u2a8c","\\gtreqqless");a(i,l,d,"\u2256","\\eqcirc");a(i,l,d,"\u2257","\\circeq");a(i,l,d,"\u225c","\\triangleq");a(i,l,d,"\u223c","\\thicksim");a(i,l,d,"\u2248","\\thickapprox");a(i,l,d,"\u2ac6","\\supseteqq");a(i,l,d,"\u22d1","\\Supset");a(i,l,d,"\u2290","\\sqsupset");a(i,l,d,"\u227d","\\succcurlyeq");a(i,l,d,"\u22df","\\curlyeqsucc");a(i,l,d,"\u227f","\\succsim");a(i,l,d,"\u2ab8","\\succapprox");a(i,l,d,"\u22b3","\\vartriangleright");a(i,l,d,"\u22b5","\\trianglerighteq");a(i,l,d,"\u22a9","\\Vdash");a(i,l,d,"\u2223","\\shortmid");a(i,l,d,"\u2225","\\shortparallel");a(i,l,d,"\u226c","\\between");a(i,l,d,"\u22d4","\\pitchfork");a(i,l,d,"\u221d","\\varpropto");a(i,l,d,"\u25c0","\\blacktriangleleft");a(i,l,d,"\u2234","\\therefore");a(i,l,d,"\u220d","\\backepsilon");a(i,l,d,"\u25b6","\\blacktriangleright");a(i,l,d,"\u2235","\\because");a(i,l,d,"\u22d8","\\llless");a(i,l,d,"\u22d9","\\gggtr");a(i,l,u,"\u22b2","\\lhd");a(i,l,u,"\u22b3","\\rhd");a(i,l,d,"\u2242","\\eqsim");a(i,s,d,"\u22c8","\\Join");a(i,l,d,"\u2251","\\Doteq");a(i,l,u,"\u2214","\\dotplus");a(i,l,u,"\u2216","\\smallsetminus");a(i,l,u,"\u22d2","\\Cap");a(i,l,u,"\u22d3","\\Cup");a(i,l,u,"\u2a5e","\\doublebarwedge");a(i,l,u,"\u229f","\\boxminus");a(i,l,u,"\u229e","\\boxplus");a(i,l,u,"\u22c7","\\divideontimes");a(i,l,u,"\u22c9","\\ltimes");a(i,l,u,"\u22ca","\\rtimes");a(i,l,u,"\u22cb","\\leftthreetimes");a(i,l,u,"\u22cc","\\rightthreetimes");a(i,l,u,"\u22cf","\\curlywedge");a(i,l,u,"\u22ce","\\curlyvee");a(i,l,u,"\u229d","\\circleddash");a(i,l,u,"\u229b","\\circledast");a(i,l,u,"\u22c5","\\centerdot");a(i,l,u,"\u22ba","\\intercal");a(i,l,u,"\u22d2","\\doublecap");a(i,l,u,"\u22d3","\\doublecup");a(i,l,u,"\u22a0","\\boxtimes");a(i,l,d,"\u21e2","\\dashrightarrow");a(i,l,d,"\u21e0","\\dashleftarrow");a(i,l,d,"\u21c7","\\leftleftarrows");a(i,l,d,"\u21c6","\\leftrightarrows");a(i,l,d,"\u21da","\\Lleftarrow");a(i,l,d,"\u219e","\\twoheadleftarrow");a(i,l,d,"\u21a2","\\leftarrowtail");a(i,l,d,"\u21ab","\\looparrowleft");a(i,l,d,"\u21cb","\\leftrightharpoons");a(i,l,d,"\u21b6","\\curvearrowleft");a(i,l,d,"\u21ba","\\circlearrowleft");a(i,l,d,"\u21b0","\\Lsh");a(i,l,d,"\u21c8","\\upuparrows");a(i,l,d,"\u21bf","\\upharpoonleft");a(i,l,d,"\u21c3","\\downharpoonleft");a(i,l,d,"\u22b8","\\multimap");a(i,l,d,"\u21ad","\\leftrightsquigarrow");a(i,l,d,"\u21c9","\\rightrightarrows");a(i,l,d,"\u21c4","\\rightleftarrows");a(i,l,d,"\u21a0","\\twoheadrightarrow");a(i,l,d,"\u21a3","\\rightarrowtail");a(i,l,d,"\u21ac","\\looparrowright");a(i,l,d,"\u21b7","\\curvearrowright");a(i,l,d,"\u21bb","\\circlearrowright");a(i,l,d,"\u21b1","\\Rsh");a(i,l,d,"\u21ca","\\downdownarrows");a(i,l,d,"\u21be","\\upharpoonright");a(i,l,d,"\u21c2","\\downharpoonright");a(i,l,d,"\u21dd","\\rightsquigarrow");a(i,l,d,"\u21dd","\\leadsto");a(i,l,d,"\u21db","\\Rrightarrow");a(i,l,d,"\u21be","\\restriction");a(i,s,y,"\u2018","`");a(i,s,y,"$","\\$");a(n,s,y,"$","\\$");a(i,s,y,"%","\\%");a(n,s,y,"%","\\%");a(i,s,y,"_","\\_");a(n,s,y,"_","\\_");a(i,s,y,"\u2220","\\angle");a(i,s,y,"\u221e","\\infty");a(i,s,y,"\u2032","\\prime");a(i,s,y,"\u25b3","\\triangle");a(i,s,y,"\u0393","\\Gamma");a(i,s,y,"\u0394","\\Delta");a(i,s,y,"\u0398","\\Theta");a(i,s,y,"\u039b","\\Lambda");a(i,s,y,"\u039e","\\Xi");a(i,s,y,"\u03a0","\\Pi");a(i,s,y,"\u03a3","\\Sigma");a(i,s,y,"\u03a5","\\Upsilon");a(i,s,y,"\u03a6","\\Phi");a(i,s,y,"\u03a8","\\Psi");a(i,s,y,"\u03a9","\\Omega");a(i,s,y,"\xac","\\neg");a(i,s,y,"\xac","\\lnot");a(i,s,y,"\u22a4","\\top");a(i,s,y,"\u22a5","\\bot");a(i,s,y,"\u2205","\\emptyset");a(i,l,y,"\u2205","\\varnothing");a(i,s,c,"\u03b1","\\alpha");a(i,s,c,"\u03b2","\\beta");a(i,s,c,"\u03b3","\\gamma");a(i,s,c,"\u03b4","\\delta");a(i,s,c,"\u03f5","\\epsilon");a(i,s,c,"\u03b6","\\zeta");a(i,s,c,"\u03b7","\\eta");a(i,s,c,"\u03b8","\\theta");a(i,s,c,"\u03b9","\\iota");a(i,s,c,"\u03ba","\\kappa");a(i,s,c,"\u03bb","\\lambda");a(i,s,c,"\u03bc","\\mu");a(i,s,c,"\u03bd","\\nu");a(i,s,c,"\u03be","\\xi");a(i,s,c,"o","\\omicron");a(i,s,c,"\u03c0","\\pi");a(i,s,c,"\u03c1","\\rho");a(i,s,c,"\u03c3","\\sigma");a(i,s,c,"\u03c4","\\tau");a(i,s,c,"\u03c5","\\upsilon");a(i,s,c,"\u03d5","\\phi");a(i,s,c,"\u03c7","\\chi");a(i,s,c,"\u03c8","\\psi");a(i,s,c,"\u03c9","\\omega");a(i,s,c,"\u03b5","\\varepsilon");a(i,s,c,"\u03d1","\\vartheta");a(i,s,c,"\u03d6","\\varpi");a(i,s,c,"\u03f1","\\varrho");a(i,s,c,"\u03c2","\\varsigma");a(i,s,c,"\u03c6","\\varphi");a(i,s,u,"\u2217","*");a(i,s,u,"+","+");a(i,s,u,"\u2212","-");a(i,s,u,"\u22c5","\\cdot");a(i,s,u,"\u2218","\\circ");a(i,s,u,"\xf7","\\div");a(i,s,u,"\xb1","\\pm");a(i,s,u,"\xd7","\\times");a(i,s,u,"\u2229","\\cap");a(i,s,u,"\u222a","\\cup");a(i,s,u,"\u2216","\\setminus");a(i,s,u,"\u2227","\\land");a(i,s,u,"\u2228","\\lor");a(i,s,u,"\u2227","\\wedge");a(i,s,u,"\u2228","\\vee");a(i,s,y,"\u221a","\\surd");a(i,s,f,"(","(");a(i,s,f,"[","[");a(i,s,f,"\u27e8","\\langle");a(i,s,f,"\u2223","\\lvert");a(i,s,f,"\u2225","\\lVert");a(i,s,p,")",")");a(i,s,p,"]","]");a(i,s,p,"?","?");a(i,s,p,"!","!");a(i,s,p,"\u27e9","\\rangle");a(i,s,p,"\u2223","\\rvert");a(i,s,p,"\u2225","\\rVert");a(i,s,d,"=","=");a(i,s,d,"<","<");a(i,s,d,">",">");a(i,s,d,":",":");a(i,s,d,"\u2248","\\approx");a(i,s,d,"\u2245","\\cong");a(i,s,d,"\u2265","\\ge");a(i,s,d,"\u2265","\\geq");a(i,s,d,"\u2190","\\gets");a(i,s,d,">","\\gt");a(i,s,d,"\u2208","\\in");a(i,s,d,"\u2209","\\notin");a(i,s,d,"\u2282","\\subset");a(i,s,d,"\u2283","\\supset");a(i,s,d,"\u2286","\\subseteq");a(i,s,d,"\u2287","\\supseteq");a(i,l,d,"\u2288","\\nsubseteq");a(i,l,d,"\u2289","\\nsupseteq");a(i,s,d,"\u22a8","\\models");a(i,s,d,"\u2190","\\leftarrow");a(i,s,d,"\u2264","\\le");a(i,s,d,"\u2264","\\leq");a(i,s,d,"<","\\lt");a(i,s,d,"\u2260","\\ne");a(i,s,d,"\u2260","\\neq");a(i,s,d,"\u2192","\\rightarrow");a(i,s,d,"\u2192","\\to");a(i,l,d,"\u2271","\\ngeq");a(i,l,d,"\u2270","\\nleq");a(i,s,g,null,"\\!");a(i,s,g,"\xa0","\\ ");a(i,s,g,"\xa0","~");a(i,s,g,null,"\\,");a(i,s,g,null,"\\:");a(i,s,g,null,"\\;");a(i,s,g,null,"\\enspace");a(i,s,g,null,"\\qquad");a(i,s,g,null,"\\quad");a(i,s,g,"\xa0","\\space");a(i,s,v,",",",");a(i,s,v,";",";");a(i,s,v,":","\\colon");a(i,l,u,"\u22bc","\\barwedge");a(i,l,u,"\u22bb","\\veebar");a(i,s,u,"\u2299","\\odot");a(i,s,u,"\u2295","\\oplus");a(i,s,u,"\u2297","\\otimes");a(i,s,y,"\u2202","\\partial");a(i,s,u,"\u2298","\\oslash");a(i,l,u,"\u229a","\\circledcirc");a(i,l,u,"\u22a1","\\boxdot");a(i,s,u,"\u25b3","\\bigtriangleup");a(i,s,u,"\u25bd","\\bigtriangledown");a(i,s,u,"\u2020","\\dagger");a(i,s,u,"\u22c4","\\diamond");a(i,s,u,"\u22c6","\\star");a(i,s,u,"\u25c3","\\triangleleft");a(i,s,u,"\u25b9","\\triangleright");a(i,s,f,"{","\\{");a(n,s,y,"{","\\{");a(i,s,p,"}","\\}");a(n,s,y,"}","\\}");a(i,s,f,"{","\\lbrace");a(i,s,p,"}","\\rbrace");a(i,s,f,"[","\\lbrack");a(i,s,p,"]","\\rbrack");a(i,s,f,"\u230a","\\lfloor");a(i,s,p,"\u230b","\\rfloor");a(i,s,f,"\u2308","\\lceil");a(i,s,p,"\u2309","\\rceil");a(i,s,y,"\\","\\backslash");a(i,s,y,"\u2223","|");a(i,s,y,"\u2223","\\vert");a(i,s,y,"\u2225","\\|");a(i,s,y,"\u2225","\\Vert");a(i,s,d,"\u2191","\\uparrow");a(i,s,d,"\u21d1","\\Uparrow");a(i,s,d,"\u2193","\\downarrow");a(i,s,d,"\u21d3","\\Downarrow");a(i,s,d,"\u2195","\\updownarrow");a(i,s,d,"\u21d5","\\Updownarrow");a(i,i,m,"\u2210","\\coprod");a(i,i,m,"\u22c1","\\bigvee");a(i,i,m,"\u22c0","\\bigwedge");a(i,i,m,"\u2a04","\\biguplus");a(i,i,m,"\u22c2","\\bigcap");a(i,i,m,"\u22c3","\\bigcup");a(i,i,m,"\u222b","\\int");a(i,i,m,"\u222b","\\intop");a(i,i,m,"\u222c","\\iint");a(i,i,m,"\u222d","\\iiint");a(i,i,m,"\u220f","\\prod");a(i,i,m,"\u2211","\\sum");a(i,i,m,"\u2a02","\\bigotimes");a(i,i,m,"\u2a01","\\bigoplus");a(i,i,m,"\u2a00","\\bigodot");a(i,i,m,"\u222e","\\oint");a(i,i,m,"\u2a06","\\bigsqcup");a(i,i,m,"\u222b","\\smallint");a(n,s,h,"\u2026","\\textellipsis");a(i,s,h,"\u2026","\\mathellipsis");a(n,s,h,"\u2026","\\ldots");a(i,s,h,"\u2026","\\ldots");a(i,s,h,"\u22ef","\\cdots");a(i,s,h,"\u22f1","\\ddots");a(i,s,y,"\u22ee","\\vdots");a(i,s,o,"\xb4","\\acute");a(i,s,o,"`","\\grave");a(i,s,o,"\xa8","\\ddot");a(i,s,o,"~","\\tilde");a(i,s,o,"\xaf","\\bar");a(i,s,o,"\u02d8","\\breve");a(i,s,o,"\u02c7","\\check");a(i,s,o,"^","\\hat");a(i,s,o,"\u20d7","\\vec");a(i,s,o,"\u02d9","\\dot");a(i,s,c,"\u0131","\\imath");a(i,s,c,"\u0237","\\jmath");a(n,s,y,"\u2013","--");a(n,s,y,"\u2014","---");a(n,s,y,"\u2018","`");a(n,s,y,"\u2019","'");a(n,s,y,"\u201c","``");a(n,s,y,"\u201d","''");a(i,s,y,"\xb0","\\degree");a(n,s,y,"\xb0","\\degree");a(i,s,c,"\xa3","\\pounds");a(i,l,y,"\u2720","\\maltese");a(n,l,y,"\u2720","\\maltese");a(n,s,g,"\xa0","\\ ");a(n,s,g,"\xa0"," ");a(n,s,g,"\xa0","~");var x;var b;var w='0123456789/@."';for(x=0;x<w.length;x++){b=w.charAt(x);a(i,s,y,b,b)}var k='0123456789!@*()-=+[]";:?/.,';for(x=0;x<k.length;x++){b=k.charAt(x);a(n,s,y,b,b)}var z="abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";for(x=0;x<z.length;x++){b=z.charAt(x);a(i,s,c,b,b);a(n,s,y,b,b)}for(x=192;x<=214;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}for(x=216;x<=246;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}for(x=248;x<=255;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}for(x=1040;x<=1103;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}a(n,s,y,"\u2013","\u2013");a(n,s,y,"\u2014","\u2014");a(n,s,y,"\u2018","\u2018");a(n,s,y,"\u2019","\u2019");a(n,s,y,"\u201c","\u201c");a(n,s,y,"\u201d","\u201d")},{}],24:[function(e,t,r){var a=/[\uAC00-\uD7AF]/;var i=/[\u3040-\u309F]|[\u30A0-\u30FF]|[\u4E00-\u9FAF]|[\uAC00-\uD7AF]/;t.exports={cjkRegex:i,hangulRegex:a}},{}],25:[function(e,t,r){var a=Array.prototype.indexOf;var i=function(e,t){if(e==null){return-1}if(a&&e.indexOf===a){return e.indexOf(t)}var r=0;var i=e.length;for(;r<i;r++){if(e[r]===t){return r}}return-1};var n=function(e,t){return i(e,t)!==-1};var s=function(e,t){return e===undefined?t:e};var l=/([A-Z])/g;var o=function(e){return e.replace(l,"-$1").toLowerCase()};var u={"&":"&amp;",">":"&gt;","<":"&lt;",'"':"&quot;","'":"&#x27;"};var p=/[&><"']/g;function h(e){return u[e]}function c(e){return(""+e).replace(p,h)}var m;if(typeof document!=="undefined"){var f=document.createElement("span");if("textContent"in f){m=function(e,t){e.textContent=t}}else{m=function(e,t){e.innerText=t}}}function v(e){m(e,"")}t.exports={contains:n,deflt:s,escape:c,hyphenate:o,indexOf:i,setTextContent:m,clearNode:v}},{}]},{},[1])(1)});
diff --git a/specs/gl/GLSLangSpec.4.60.html b/specs/gl/GLSLangSpec.4.60.html
new file mode 100644
index 0000000..e289efb
--- /dev/null
+++ b/specs/gl/GLSLangSpec.4.60.html
@@ -0,0 +1,16882 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8">
+<!--[if IE]><meta http-equiv="X-UA-Compatible" content="IE=edge"><![endif]-->
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="generator" content="Asciidoctor 1.5.7.1">
+<meta name="author" content="John Kessenich, Google (Editor and Author) ; Dave Baldwin and Randi Rost (Version 1.1 Authors)">
+<title>The OpenGL&#174; Shading Language, Version 4.60.6</title>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700">
+<style>
+/* Asciidoctor default stylesheet | MIT License | http://asciidoctor.org */
+/* Uncomment @import statement below to use as custom stylesheet */
+/*@import "https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700";*/
+article,aside,details,figcaption,figure,footer,header,hgroup,main,nav,section,summary{display:block}
+audio,canvas,video{display:inline-block}
+audio:not([controls]){display:none;height:0}
+script{display:none!important}
+html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}
+a{background:transparent}
+a:focus{outline:thin dotted}
+a:active,a:hover{outline:0}
+h1{font-size:2em;margin:.67em 0}
+abbr[title]{border-bottom:1px dotted}
+b,strong{font-weight:bold}
+dfn{font-style:italic}
+hr{-moz-box-sizing:content-box;box-sizing:content-box;height:0}
+mark{background:#ff0;color:#000}
+code,kbd,pre,samp{font-family:monospace;font-size:1em}
+pre{white-space:pre-wrap}
+q{quotes:"\201C" "\201D" "\2018" "\2019"}
+small{font-size:80%}
+sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}
+sup{top:-.5em}
+sub{bottom:-.25em}
+img{border:0}
+svg:not(:root){overflow:hidden}
+figure{margin:0}
+fieldset{border:1px solid silver;margin:0 2px;padding:.35em .625em .75em}
+legend{border:0;padding:0}
+button,input,select,textarea{font-family:inherit;font-size:100%;margin:0}
+button,input{line-height:normal}
+button,select{text-transform:none}
+button,html input[type="button"],input[type="reset"],input[type="submit"]{-webkit-appearance:button;cursor:pointer}
+button[disabled],html input[disabled]{cursor:default}
+input[type="checkbox"],input[type="radio"]{box-sizing:border-box;padding:0}
+button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}
+textarea{overflow:auto;vertical-align:top}
+table{border-collapse:collapse;border-spacing:0}
+*,*::before,*::after{-moz-box-sizing:border-box;-webkit-box-sizing:border-box;box-sizing:border-box}
+html,body{font-size:100%}
+body{background:#fff;color:rgba(0,0,0,.8);padding:0;margin:0;font-family:"Noto Serif","DejaVu Serif",serif;font-weight:400;font-style:normal;line-height:1;position:relative;cursor:auto;tab-size:4;-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased}
+a:hover{cursor:pointer}
+img,object,embed{max-width:100%;height:auto}
+object,embed{height:100%}
+img{-ms-interpolation-mode:bicubic}
+.left{float:left!important}
+.right{float:right!important}
+.text-left{text-align:left!important}
+.text-right{text-align:right!important}
+.text-center{text-align:center!important}
+.text-justify{text-align:justify!important}
+.hide{display:none}
+img,object,svg{display:inline-block;vertical-align:middle}
+textarea{height:auto;min-height:50px}
+select{width:100%}
+.center{margin-left:auto;margin-right:auto}
+.stretch{width:100%}
+.subheader,.admonitionblock td.content>.title,.audioblock>.title,.exampleblock>.title,.imageblock>.title,.listingblock>.title,.literalblock>.title,.stemblock>.title,.openblock>.title,.paragraph>.title,.quoteblock>.title,table.tableblock>.title,.verseblock>.title,.videoblock>.title,.dlist>.title,.olist>.title,.ulist>.title,.qlist>.title,.hdlist>.title{line-height:1.45;color:#7a2518;font-weight:400;margin-top:0;margin-bottom:.25em}
+div,dl,dt,dd,ul,ol,li,h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6,pre,form,p,blockquote,th,td{margin:0;padding:0;direction:ltr}
+a{color:#2156a5;text-decoration:underline;line-height:inherit}
+a:hover,a:focus{color:#1d4b8f}
+a img{border:none}
+p{font-family:inherit;font-weight:400;font-size:1em;line-height:1.6;margin-bottom:1.25em;text-rendering:optimizeLegibility}
+p aside{font-size:.875em;line-height:1.35;font-style:italic}
+h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{font-family:"Open Sans","DejaVu Sans",sans-serif;font-weight:300;font-style:normal;color:#ba3925;text-rendering:optimizeLegibility;margin-top:1em;margin-bottom:.5em;line-height:1.0125em}
+h1 small,h2 small,h3 small,#toctitle small,.sidebarblock>.content>.title small,h4 small,h5 small,h6 small{font-size:60%;color:#e99b8f;line-height:0}
+h1{font-size:2.125em}
+h2{font-size:1.6875em}
+h3,#toctitle,.sidebarblock>.content>.title{font-size:1.375em}
+h4,h5{font-size:1.125em}
+h6{font-size:1em}
+hr{border:solid #ddddd8;border-width:1px 0 0;clear:both;margin:1.25em 0 1.1875em;height:0}
+em,i{font-style:italic;line-height:inherit}
+strong,b{font-weight:bold;line-height:inherit}
+small{font-size:60%;line-height:inherit}
+code{font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;font-weight:400;color:rgba(0,0,0,.9)}
+ul,ol,dl{font-size:1em;line-height:1.6;margin-bottom:1.25em;list-style-position:outside;font-family:inherit}
+ul,ol{margin-left:1.5em}
+ul li ul,ul li ol{margin-left:1.25em;margin-bottom:0;font-size:1em}
+ul.square li ul,ul.circle li ul,ul.disc li ul{list-style:inherit}
+ul.square{list-style-type:square}
+ul.circle{list-style-type:circle}
+ul.disc{list-style-type:disc}
+ol li ul,ol li ol{margin-left:1.25em;margin-bottom:0}
+dl dt{margin-bottom:.3125em;font-weight:bold}
+dl dd{margin-bottom:1.25em}
+abbr,acronym{text-transform:uppercase;font-size:90%;color:rgba(0,0,0,.8);border-bottom:1px dotted #ddd;cursor:help}
+abbr{text-transform:none}
+blockquote{margin:0 0 1.25em;padding:.5625em 1.25em 0 1.1875em;border-left:1px solid #ddd}
+blockquote cite{display:block;font-size:.9375em;color:rgba(0,0,0,.6)}
+blockquote cite::before{content:"\2014 \0020"}
+blockquote cite a,blockquote cite a:visited{color:rgba(0,0,0,.6)}
+blockquote,blockquote p{line-height:1.6;color:rgba(0,0,0,.85)}
+@media screen and (min-width:768px){h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{line-height:1.2}
+h1{font-size:2.75em}
+h2{font-size:2.3125em}
+h3,#toctitle,.sidebarblock>.content>.title{font-size:1.6875em}
+h4{font-size:1.4375em}}
+table{background:#fff;margin-bottom:1.25em;border:solid 1px #dedede}
+table thead,table tfoot{background:#f7f8f7}
+table thead tr th,table thead tr td,table tfoot tr th,table tfoot tr td{padding:.5em .625em .625em;font-size:inherit;color:rgba(0,0,0,.8);text-align:left}
+table tr th,table tr td{padding:.5625em .625em;font-size:inherit;color:rgba(0,0,0,.8)}
+table tr.even,table tr.alt,table tr:nth-of-type(even){background:#f8f8f7}
+table thead tr th,table tfoot tr th,table tbody tr td,table tr td,table tfoot tr td{display:table-cell;line-height:1.6}
+h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{line-height:1.2;word-spacing:-.05em}
+h1 strong,h2 strong,h3 strong,#toctitle strong,.sidebarblock>.content>.title strong,h4 strong,h5 strong,h6 strong{font-weight:400}
+.clearfix::before,.clearfix::after,.float-group::before,.float-group::after{content:" ";display:table}
+.clearfix::after,.float-group::after{clear:both}
+*:not(pre)>code{font-size:.9375em;font-style:normal!important;letter-spacing:0;padding:.1em .5ex;word-spacing:-.15em;background-color:#f7f7f8;-webkit-border-radius:4px;border-radius:4px;line-height:1.45;text-rendering:optimizeSpeed;word-wrap:break-word}
+*:not(pre)>code.nobreak{word-wrap:normal}
+*:not(pre)>code.nowrap{white-space:nowrap}
+pre,pre>code{line-height:1.45;color:rgba(0,0,0,.9);font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;font-weight:400;text-rendering:optimizeSpeed}
+em em{font-style:normal}
+strong strong{font-weight:400}
+.keyseq{color:rgba(51,51,51,.8)}
+kbd{font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;display:inline-block;color:rgba(0,0,0,.8);font-size:.65em;line-height:1.45;background-color:#f7f7f7;border:1px solid #ccc;-webkit-border-radius:3px;border-radius:3px;-webkit-box-shadow:0 1px 0 rgba(0,0,0,.2),0 0 0 .1em white inset;box-shadow:0 1px 0 rgba(0,0,0,.2),0 0 0 .1em #fff inset;margin:0 .15em;padding:.2em .5em;vertical-align:middle;position:relative;top:-.1em;white-space:nowrap}
+.keyseq kbd:first-child{margin-left:0}
+.keyseq kbd:last-child{margin-right:0}
+.menuseq,.menuref{color:#000}
+.menuseq b:not(.caret),.menuref{font-weight:inherit}
+.menuseq{word-spacing:-.02em}
+.menuseq b.caret{font-size:1.25em;line-height:.8}
+.menuseq i.caret{font-weight:bold;text-align:center;width:.45em}
+b.button::before,b.button::after{position:relative;top:-1px;font-weight:400}
+b.button::before{content:"[";padding:0 3px 0 2px}
+b.button::after{content:"]";padding:0 2px 0 3px}
+p a>code:hover{color:rgba(0,0,0,.9)}
+#header,#content,#footnotes,#footer{width:100%;margin-left:auto;margin-right:auto;margin-top:0;margin-bottom:0;max-width:62.5em;*zoom:1;position:relative;padding-left:.9375em;padding-right:.9375em}
+#header::before,#header::after,#content::before,#content::after,#footnotes::before,#footnotes::after,#footer::before,#footer::after{content:" ";display:table}
+#header::after,#content::after,#footnotes::after,#footer::after{clear:both}
+#content{margin-top:1.25em}
+#content::before{content:none}
+#header>h1:first-child{color:rgba(0,0,0,.85);margin-top:2.25rem;margin-bottom:0}
+#header>h1:first-child+#toc{margin-top:8px;border-top:1px solid #ddddd8}
+#header>h1:only-child,body.toc2 #header>h1:nth-last-child(2){border-bottom:1px solid #ddddd8;padding-bottom:8px}
+#header .details{border-bottom:1px solid #ddddd8;line-height:1.45;padding-top:.25em;padding-bottom:.25em;padding-left:.25em;color:rgba(0,0,0,.6);display:-ms-flexbox;display:-webkit-flex;display:flex;-ms-flex-flow:row wrap;-webkit-flex-flow:row wrap;flex-flow:row wrap}
+#header .details span:first-child{margin-left:-.125em}
+#header .details span.email a{color:rgba(0,0,0,.85)}
+#header .details br{display:none}
+#header .details br+span::before{content:"\00a0\2013\00a0"}
+#header .details br+span.author::before{content:"\00a0\22c5\00a0";color:rgba(0,0,0,.85)}
+#header .details br+span#revremark::before{content:"\00a0|\00a0"}
+#header #revnumber{text-transform:capitalize}
+#header #revnumber::after{content:"\00a0"}
+#content>h1:first-child:not([class]){color:rgba(0,0,0,.85);border-bottom:1px solid #ddddd8;padding-bottom:8px;margin-top:0;padding-top:1rem;margin-bottom:1.25rem}
+#toc{border-bottom:1px solid #efefed;padding-bottom:.5em}
+#toc>ul{margin-left:.125em}
+#toc ul.sectlevel0>li>a{font-style:italic}
+#toc ul.sectlevel0 ul.sectlevel1{margin:.5em 0}
+#toc ul{font-family:"Open Sans","DejaVu Sans",sans-serif;list-style-type:none}
+#toc li{line-height:1.3334;margin-top:.3334em}
+#toc a{text-decoration:none}
+#toc a:active{text-decoration:underline}
+#toctitle{color:#7a2518;font-size:1.2em}
+@media screen and (min-width:768px){#toctitle{font-size:1.375em}
+body.toc2{padding-left:15em;padding-right:0}
+#toc.toc2{margin-top:0!important;background-color:#f8f8f7;position:fixed;width:15em;left:0;top:0;border-right:1px solid #efefed;border-top-width:0!important;border-bottom-width:0!important;z-index:1000;padding:1.25em 1em;height:100%;overflow:auto}
+#toc.toc2 #toctitle{margin-top:0;margin-bottom:.8rem;font-size:1.2em}
+#toc.toc2>ul{font-size:.9em;margin-bottom:0}
+#toc.toc2 ul ul{margin-left:0;padding-left:1em}
+#toc.toc2 ul.sectlevel0 ul.sectlevel1{padding-left:0;margin-top:.5em;margin-bottom:.5em}
+body.toc2.toc-right{padding-left:0;padding-right:15em}
+body.toc2.toc-right #toc.toc2{border-right-width:0;border-left:1px solid #efefed;left:auto;right:0}}
+@media screen and (min-width:1280px){body.toc2{padding-left:20em;padding-right:0}
+#toc.toc2{width:20em}
+#toc.toc2 #toctitle{font-size:1.375em}
+#toc.toc2>ul{font-size:.95em}
+#toc.toc2 ul ul{padding-left:1.25em}
+body.toc2.toc-right{padding-left:0;padding-right:20em}}
+#content #toc{border-style:solid;border-width:1px;border-color:#e0e0dc;margin-bottom:1.25em;padding:1.25em;background:#f8f8f7;-webkit-border-radius:4px;border-radius:4px}
+#content #toc>:first-child{margin-top:0}
+#content #toc>:last-child{margin-bottom:0}
+#footer{max-width:100%;background-color:rgba(0,0,0,.8);padding:1.25em}
+#footer-text{color:rgba(255,255,255,.8);line-height:1.44}
+#content{margin-bottom:.625em}
+.sect1{padding-bottom:.625em}
+@media screen and (min-width:768px){#content{margin-bottom:1.25em}
+.sect1{padding-bottom:1.25em}}
+.sect1:last-child{padding-bottom:0}
+.sect1+.sect1{border-top:1px solid #efefed}
+#content h1>a.anchor,h2>a.anchor,h3>a.anchor,#toctitle>a.anchor,.sidebarblock>.content>.title>a.anchor,h4>a.anchor,h5>a.anchor,h6>a.anchor{position:absolute;z-index:1001;width:1.5ex;margin-left:-1.5ex;display:block;text-decoration:none!important;visibility:hidden;text-align:center;font-weight:400}
+#content h1>a.anchor::before,h2>a.anchor::before,h3>a.anchor::before,#toctitle>a.anchor::before,.sidebarblock>.content>.title>a.anchor::before,h4>a.anchor::before,h5>a.anchor::before,h6>a.anchor::before{content:"\00A7";font-size:.85em;display:block;padding-top:.1em}
+#content h1:hover>a.anchor,#content h1>a.anchor:hover,h2:hover>a.anchor,h2>a.anchor:hover,h3:hover>a.anchor,#toctitle:hover>a.anchor,.sidebarblock>.content>.title:hover>a.anchor,h3>a.anchor:hover,#toctitle>a.anchor:hover,.sidebarblock>.content>.title>a.anchor:hover,h4:hover>a.anchor,h4>a.anchor:hover,h5:hover>a.anchor,h5>a.anchor:hover,h6:hover>a.anchor,h6>a.anchor:hover{visibility:visible}
+#content h1>a.link,h2>a.link,h3>a.link,#toctitle>a.link,.sidebarblock>.content>.title>a.link,h4>a.link,h5>a.link,h6>a.link{color:#ba3925;text-decoration:none}
+#content h1>a.link:hover,h2>a.link:hover,h3>a.link:hover,#toctitle>a.link:hover,.sidebarblock>.content>.title>a.link:hover,h4>a.link:hover,h5>a.link:hover,h6>a.link:hover{color:#a53221}
+.audioblock,.imageblock,.literalblock,.listingblock,.stemblock,.videoblock{margin-bottom:1.25em}
+.admonitionblock td.content>.title,.audioblock>.title,.exampleblock>.title,.imageblock>.title,.listingblock>.title,.literalblock>.title,.stemblock>.title,.openblock>.title,.paragraph>.title,.quoteblock>.title,table.tableblock>.title,.verseblock>.title,.videoblock>.title,.dlist>.title,.olist>.title,.ulist>.title,.qlist>.title,.hdlist>.title{text-rendering:optimizeLegibility;text-align:left;font-family:"Noto Serif","DejaVu Serif",serif;font-size:1rem;font-style:italic}
+table.tableblock.fit-content>caption.title{white-space:nowrap;width:0}
+.paragraph.lead>p,#preamble>.sectionbody>[class="paragraph"]:first-of-type p{font-size:1.21875em;line-height:1.6;color:rgba(0,0,0,.85)}
+table.tableblock #preamble>.sectionbody>[class="paragraph"]:first-of-type p{font-size:inherit}
+.admonitionblock>table{border-collapse:separate;border:0;background:none;width:100%}
+.admonitionblock>table td.icon{text-align:center;width:80px}
+.admonitionblock>table td.icon img{max-width:none}
+.admonitionblock>table td.icon .title{font-weight:bold;font-family:"Open Sans","DejaVu Sans",sans-serif;text-transform:uppercase}
+.admonitionblock>table td.content{padding-left:1.125em;padding-right:1.25em;border-left:1px solid #ddddd8;color:rgba(0,0,0,.6)}
+.admonitionblock>table td.content>:last-child>:last-child{margin-bottom:0}
+.exampleblock>.content{border-style:solid;border-width:1px;border-color:#e6e6e6;margin-bottom:1.25em;padding:1.25em;background:#fff;-webkit-border-radius:4px;border-radius:4px}
+.exampleblock>.content>:first-child{margin-top:0}
+.exampleblock>.content>:last-child{margin-bottom:0}
+.sidebarblock{border-style:solid;border-width:1px;border-color:#e0e0dc;margin-bottom:1.25em;padding:1.25em;background:#f8f8f7;-webkit-border-radius:4px;border-radius:4px}
+.sidebarblock>:first-child{margin-top:0}
+.sidebarblock>:last-child{margin-bottom:0}
+.sidebarblock>.content>.title{color:#7a2518;margin-top:0;text-align:center}
+.exampleblock>.content>:last-child>:last-child,.exampleblock>.content .olist>ol>li:last-child>:last-child,.exampleblock>.content .ulist>ul>li:last-child>:last-child,.exampleblock>.content .qlist>ol>li:last-child>:last-child,.sidebarblock>.content>:last-child>:last-child,.sidebarblock>.content .olist>ol>li:last-child>:last-child,.sidebarblock>.content .ulist>ul>li:last-child>:last-child,.sidebarblock>.content .qlist>ol>li:last-child>:last-child{margin-bottom:0}
+.literalblock pre,.listingblock pre:not(.highlight),.listingblock pre[class="highlight"],.listingblock pre[class^="highlight "],.listingblock pre.CodeRay,.listingblock pre.prettyprint{background:#f7f7f8}
+.sidebarblock .literalblock pre,.sidebarblock .listingblock pre:not(.highlight),.sidebarblock .listingblock pre[class="highlight"],.sidebarblock .listingblock pre[class^="highlight "],.sidebarblock .listingblock pre.CodeRay,.sidebarblock .listingblock pre.prettyprint{background:#f2f1f1}
+.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{-webkit-border-radius:4px;border-radius:4px;word-wrap:break-word;padding:1em;font-size:.8125em}
+.literalblock pre.nowrap,.literalblock pre[class].nowrap,.listingblock pre.nowrap,.listingblock pre[class].nowrap{overflow-x:auto;white-space:pre;word-wrap:normal}
+@media screen and (min-width:768px){.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{font-size:.90625em}}
+@media screen and (min-width:1280px){.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{font-size:1em}}
+.literalblock.output pre{color:#f7f7f8;background-color:rgba(0,0,0,.9)}
+.listingblock pre.highlightjs{padding:0}
+.listingblock pre.highlightjs>code{padding:1em;-webkit-border-radius:4px;border-radius:4px}
+.listingblock pre.prettyprint{border-width:0}
+.listingblock>.content{position:relative}
+.listingblock code[data-lang]::before{display:none;content:attr(data-lang);position:absolute;font-size:.75em;top:.425rem;right:.5rem;line-height:1;text-transform:uppercase;color:#999}
+.listingblock:hover code[data-lang]::before{display:block}
+.listingblock.terminal pre .command::before{content:attr(data-prompt);padding-right:.5em;color:#999}
+.listingblock.terminal pre .command:not([data-prompt])::before{content:"$"}
+table.pyhltable{border-collapse:separate;border:0;margin-bottom:0;background:none}
+table.pyhltable td{vertical-align:top;padding-top:0;padding-bottom:0;line-height:1.45}
+table.pyhltable td.code{padding-left:.75em;padding-right:0}
+pre.pygments .lineno,table.pyhltable td:not(.code){color:#999;padding-left:0;padding-right:.5em;border-right:1px solid #ddddd8}
+pre.pygments .lineno{display:inline-block;margin-right:.25em}
+table.pyhltable .linenodiv{background:none!important;padding-right:0!important}
+.quoteblock{margin:0 1em 1.25em 1.5em;display:table}
+.quoteblock>.title{margin-left:-1.5em;margin-bottom:.75em}
+.quoteblock blockquote,.quoteblock blockquote p{color:rgba(0,0,0,.85);font-size:1.15rem;line-height:1.75;word-spacing:.1em;letter-spacing:0;font-style:italic;text-align:justify}
+.quoteblock blockquote{margin:0;padding:0;border:0}
+.quoteblock blockquote::before{content:"\201c";float:left;font-size:2.75em;font-weight:bold;line-height:.6em;margin-left:-.6em;color:#7a2518;text-shadow:0 1px 2px rgba(0,0,0,.1)}
+.quoteblock blockquote>.paragraph:last-child p{margin-bottom:0}
+.quoteblock .attribution{margin-top:.5em;margin-right:.5ex;text-align:right}
+.quoteblock .quoteblock{margin-left:0;margin-right:0;padding:.5em 0;border-left:3px solid rgba(0,0,0,.6)}
+.quoteblock .quoteblock blockquote{padding:0 0 0 .75em}
+.quoteblock .quoteblock blockquote::before{display:none}
+.verseblock{margin:0 1em 1.25em}
+.verseblock pre{font-family:"Open Sans","DejaVu Sans",sans;font-size:1.15rem;color:rgba(0,0,0,.85);font-weight:300;text-rendering:optimizeLegibility}
+.verseblock pre strong{font-weight:400}
+.verseblock .attribution{margin-top:1.25rem;margin-left:.5ex}
+.quoteblock .attribution,.verseblock .attribution{font-size:.9375em;line-height:1.45;font-style:italic}
+.quoteblock .attribution br,.verseblock .attribution br{display:none}
+.quoteblock .attribution cite,.verseblock .attribution cite{display:block;letter-spacing:-.025em;color:rgba(0,0,0,.6)}
+.quoteblock.abstract{margin:0 1em 1.25em;display:block}
+.quoteblock.abstract>.title{margin:0 0 .375em;font-size:1.15em;text-align:center}
+.quoteblock.abstract blockquote,.quoteblock.abstract blockquote p{word-spacing:0;line-height:1.6}
+.quoteblock.abstract blockquote::before,.quoteblock.abstract p::before{display:none}
+table.tableblock{max-width:100%;border-collapse:separate}
+p.tableblock:last-child{margin-bottom:0}
+td.tableblock>.content{margin-bottom:-1.25em}
+table.tableblock,th.tableblock,td.tableblock{border:0 solid #dedede}
+table.grid-all>thead>tr>.tableblock,table.grid-all>tbody>tr>.tableblock{border-width:0 1px 1px 0}
+table.grid-all>tfoot>tr>.tableblock{border-width:1px 1px 0 0}
+table.grid-cols>*>tr>.tableblock{border-width:0 1px 0 0}
+table.grid-rows>thead>tr>.tableblock,table.grid-rows>tbody>tr>.tableblock{border-width:0 0 1px}
+table.grid-rows>tfoot>tr>.tableblock{border-width:1px 0 0}
+table.grid-all>*>tr>.tableblock:last-child,table.grid-cols>*>tr>.tableblock:last-child{border-right-width:0}
+table.grid-all>tbody>tr:last-child>.tableblock,table.grid-all>thead:last-child>tr>.tableblock,table.grid-rows>tbody>tr:last-child>.tableblock,table.grid-rows>thead:last-child>tr>.tableblock{border-bottom-width:0}
+table.frame-all{border-width:1px}
+table.frame-sides{border-width:0 1px}
+table.frame-topbot,table.frame-ends{border-width:1px 0}
+table.stripes-all tr,table.stripes-odd tr:nth-of-type(odd){background:#f8f8f7}
+table.stripes-none tr,table.stripes-odd tr:nth-of-type(even){background:none}
+th.halign-left,td.halign-left{text-align:left}
+th.halign-right,td.halign-right{text-align:right}
+th.halign-center,td.halign-center{text-align:center}
+th.valign-top,td.valign-top{vertical-align:top}
+th.valign-bottom,td.valign-bottom{vertical-align:bottom}
+th.valign-middle,td.valign-middle{vertical-align:middle}
+table thead th,table tfoot th{font-weight:bold}
+tbody tr th{display:table-cell;line-height:1.6;background:#f7f8f7}
+tbody tr th,tbody tr th p,tfoot tr th,tfoot tr th p{color:rgba(0,0,0,.8);font-weight:bold}
+p.tableblock>code:only-child{background:none;padding:0}
+p.tableblock{font-size:1em}
+td>div.verse{white-space:pre}
+ol{margin-left:1.75em}
+ul li ol{margin-left:1.5em}
+dl dd{margin-left:1.125em}
+dl dd:last-child,dl dd:last-child>:last-child{margin-bottom:0}
+ol>li p,ul>li p,ul dd,ol dd,.olist .olist,.ulist .ulist,.ulist .olist,.olist .ulist{margin-bottom:.625em}
+ul.checklist,ul.none,ol.none,ul.no-bullet,ol.no-bullet,ol.unnumbered,ul.unstyled,ol.unstyled{list-style-type:none}
+ul.no-bullet,ol.no-bullet,ol.unnumbered{margin-left:.625em}
+ul.unstyled,ol.unstyled{margin-left:0}
+ul.checklist{margin-left:.625em}
+ul.checklist li>p:first-child>.fa-square-o:first-child,ul.checklist li>p:first-child>.fa-check-square-o:first-child{width:1.25em;font-size:.8em;position:relative;bottom:.125em}
+ul.checklist li>p:first-child>input[type="checkbox"]:first-child{margin-right:.25em}
+ul.inline{display:-ms-flexbox;display:-webkit-box;display:flex;-ms-flex-flow:row wrap;-webkit-flex-flow:row wrap;flex-flow:row wrap;list-style:none;margin:0 0 .625em -1.25em}
+ul.inline>li{margin-left:1.25em}
+.unstyled dl dt{font-weight:400;font-style:normal}
+ol.arabic{list-style-type:decimal}
+ol.decimal{list-style-type:decimal-leading-zero}
+ol.loweralpha{list-style-type:lower-alpha}
+ol.upperalpha{list-style-type:upper-alpha}
+ol.lowerroman{list-style-type:lower-roman}
+ol.upperroman{list-style-type:upper-roman}
+ol.lowergreek{list-style-type:lower-greek}
+.hdlist>table,.colist>table{border:0;background:none}
+.hdlist>table>tbody>tr,.colist>table>tbody>tr{background:none}
+td.hdlist1,td.hdlist2{vertical-align:top;padding:0 .625em}
+td.hdlist1{font-weight:bold;padding-bottom:1.25em}
+.literalblock+.colist,.listingblock+.colist{margin-top:-.5em}
+.colist td:not([class]):first-child{padding:.4em .75em 0;line-height:1;vertical-align:top}
+.colist td:not([class]):first-child img{max-width:none}
+.colist td:not([class]):last-child{padding:.25em 0}
+.thumb,.th{line-height:0;display:inline-block;border:solid 4px #fff;-webkit-box-shadow:0 0 0 1px #ddd;box-shadow:0 0 0 1px #ddd}
+.imageblock.left,.imageblock[style*="float: left"]{margin:.25em .625em 1.25em 0}
+.imageblock.right,.imageblock[style*="float: right"]{margin:.25em 0 1.25em .625em}
+.imageblock>.title{margin-bottom:0}
+.imageblock.thumb,.imageblock.th{border-width:6px}
+.imageblock.thumb>.title,.imageblock.th>.title{padding:0 .125em}
+.image.left,.image.right{margin-top:.25em;margin-bottom:.25em;display:inline-block;line-height:0}
+.image.left{margin-right:.625em}
+.image.right{margin-left:.625em}
+a.image{text-decoration:none;display:inline-block}
+a.image object{pointer-events:none}
+sup.footnote,sup.footnoteref{font-size:.875em;position:static;vertical-align:super}
+sup.footnote a,sup.footnoteref a{text-decoration:none}
+sup.footnote a:active,sup.footnoteref a:active{text-decoration:underline}
+#footnotes{padding-top:.75em;padding-bottom:.75em;margin-bottom:.625em}
+#footnotes hr{width:20%;min-width:6.25em;margin:-.25em 0 .75em;border-width:1px 0 0}
+#footnotes .footnote{padding:0 .375em 0 .225em;line-height:1.3334;font-size:.875em;margin-left:1.2em;margin-bottom:.2em}
+#footnotes .footnote a:first-of-type{font-weight:bold;text-decoration:none;margin-left:-1.05em}
+#footnotes .footnote:last-of-type{margin-bottom:0}
+#content #footnotes{margin-top:-.625em;margin-bottom:0;padding:.75em 0}
+.gist .file-data>table{border:0;background:#fff;width:100%;margin-bottom:0}
+.gist .file-data>table td.line-data{width:99%}
+div.unbreakable{page-break-inside:avoid}
+.big{font-size:larger}
+.small{font-size:smaller}
+.underline{text-decoration:underline}
+.overline{text-decoration:overline}
+.line-through{text-decoration:line-through}
+.aqua{color:#00bfbf}
+.aqua-background{background-color:#00fafa}
+.black{color:#000}
+.black-background{background-color:#000}
+.blue{color:#0000bf}
+.blue-background{background-color:#0000fa}
+.fuchsia{color:#bf00bf}
+.fuchsia-background{background-color:#fa00fa}
+.gray{color:#606060}
+.gray-background{background-color:#7d7d7d}
+.green{color:#006000}
+.green-background{background-color:#007d00}
+.lime{color:#00bf00}
+.lime-background{background-color:#00fa00}
+.maroon{color:#600000}
+.maroon-background{background-color:#7d0000}
+.navy{color:#000060}
+.navy-background{background-color:#00007d}
+.olive{color:#606000}
+.olive-background{background-color:#7d7d00}
+.purple{color:#600060}
+.purple-background{background-color:#7d007d}
+.red{color:#bf0000}
+.red-background{background-color:#fa0000}
+.silver{color:#909090}
+.silver-background{background-color:#bcbcbc}
+.teal{color:#006060}
+.teal-background{background-color:#007d7d}
+.white{color:#bfbfbf}
+.white-background{background-color:#fafafa}
+.yellow{color:#bfbf00}
+.yellow-background{background-color:#fafa00}
+span.icon>.fa{cursor:default}
+a span.icon>.fa{cursor:inherit}
+.admonitionblock td.icon [class^="fa icon-"]{font-size:2.5em;text-shadow:1px 1px 2px rgba(0,0,0,.5);cursor:default}
+.admonitionblock td.icon .icon-note::before{content:"\f05a";color:#19407c}
+.admonitionblock td.icon .icon-tip::before{content:"\f0eb";text-shadow:1px 1px 2px rgba(155,155,0,.8);color:#111}
+.admonitionblock td.icon .icon-warning::before{content:"\f071";color:#bf6900}
+.admonitionblock td.icon .icon-caution::before{content:"\f06d";color:#bf3400}
+.admonitionblock td.icon .icon-important::before{content:"\f06a";color:#bf0000}
+.conum[data-value]{display:inline-block;color:#fff!important;background-color:rgba(0,0,0,.8);-webkit-border-radius:100px;border-radius:100px;text-align:center;font-size:.75em;width:1.67em;height:1.67em;line-height:1.67em;font-family:"Open Sans","DejaVu Sans",sans-serif;font-style:normal;font-weight:bold}
+.conum[data-value] *{color:#fff!important}
+.conum[data-value]+b{display:none}
+.conum[data-value]::after{content:attr(data-value)}
+pre .conum[data-value]{position:relative;top:-.125em}
+b.conum *{color:inherit!important}
+.conum:not([data-value]):empty{display:none}
+dt,th.tableblock,td.content,div.footnote{text-rendering:optimizeLegibility}
+h1,h2,p,td.content,span.alt{letter-spacing:-.01em}
+p strong,td.content strong,div.footnote strong{letter-spacing:-.005em}
+p,blockquote,dt,td.content,span.alt{font-size:1.0625rem}
+p{margin-bottom:1.25rem}
+.sidebarblock p,.sidebarblock dt,.sidebarblock td.content,p.tableblock{font-size:1em}
+.exampleblock>.content{background-color:#fffef7;border-color:#e0e0dc;-webkit-box-shadow:0 1px 4px #e0e0dc;box-shadow:0 1px 4px #e0e0dc}
+.print-only{display:none!important}
+@page{margin:1.25cm .75cm}
+@media print{*{-webkit-box-shadow:none!important;box-shadow:none!important;text-shadow:none!important}
+html{font-size:80%}
+a{color:inherit!important;text-decoration:underline!important}
+a.bare,a[href^="#"],a[href^="mailto:"]{text-decoration:none!important}
+a[href^="http:"]:not(.bare)::after,a[href^="https:"]:not(.bare)::after{content:"(" attr(href) ")";display:inline-block;font-size:.875em;padding-left:.25em}
+abbr[title]::after{content:" (" attr(title) ")"}
+pre,blockquote,tr,img,object,svg{page-break-inside:avoid}
+thead{display:table-header-group}
+svg{max-width:100%}
+p,blockquote,dt,td.content{font-size:1em;orphans:3;widows:3}
+h2,h3,#toctitle,.sidebarblock>.content>.title{page-break-after:avoid}
+#toc,.sidebarblock,.exampleblock>.content{background:none!important}
+#toc{border-bottom:1px solid #ddddd8!important;padding-bottom:0!important}
+body.book #header{text-align:center}
+body.book #header>h1:first-child{border:0!important;margin:2.5em 0 1em}
+body.book #header .details{border:0!important;display:block;padding:0!important}
+body.book #header .details span:first-child{margin-left:0!important}
+body.book #header .details br{display:block}
+body.book #header .details br+span::before{content:none!important}
+body.book #toc{border:0!important;text-align:left!important;padding:0!important;margin:0!important}
+body.book #toc,body.book #preamble,body.book h1.sect0,body.book .sect1>h2{page-break-before:always}
+.listingblock code[data-lang]::before{display:block}
+#footer{padding:0 .9375em}
+.hide-on-print{display:none!important}
+.print-only{display:block!important}
+.hide-for-print{display:none!important}
+.show-for-print{display:inherit!important}}
+@media print,amzn-kf8{#header>h1:first-child{margin-top:1.25rem}
+.sect1{padding:0!important}
+.sect1+.sect1{border:0}
+#footer{background:none}
+#footer-text{color:rgba(0,0,0,.6);font-size:.9em}}
+@media amzn-kf8{#header,#content,#footnotes,#footer{padding:0}}
+</style>
+<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
+<style>
+/* Stylesheet for CodeRay to match GitHub theme | MIT License | http://foundation.zurb.com */
+/*pre.CodeRay {background-color:#f7f7f8;}*/
+.CodeRay .line-numbers{border-right:1px solid #d8d8d8;padding:0 0.5em 0 .25em}
+.CodeRay span.line-numbers{display:inline-block;margin-right:.5em;color:rgba(0,0,0,.3)}
+.CodeRay .line-numbers strong{color:rgba(0,0,0,.4)}
+table.CodeRay{border-collapse:separate;border-spacing:0;margin-bottom:0;border:0;background:none}
+table.CodeRay td{vertical-align: top;line-height:1.45}
+table.CodeRay td.line-numbers{text-align:right}
+table.CodeRay td.line-numbers>pre{padding:0;color:rgba(0,0,0,.3)}
+table.CodeRay td.code{padding:0 0 0 .5em}
+table.CodeRay td.code>pre{padding:0}
+.CodeRay .debug{color:#fff !important;background:#000080 !important}
+.CodeRay .annotation{color:#007}
+.CodeRay .attribute-name{color:#000080}
+.CodeRay .attribute-value{color:#700}
+.CodeRay .binary{color:#509}
+.CodeRay .comment{color:#998;font-style:italic}
+.CodeRay .char{color:#04d}
+.CodeRay .char .content{color:#04d}
+.CodeRay .char .delimiter{color:#039}
+.CodeRay .class{color:#458;font-weight:bold}
+.CodeRay .complex{color:#a08}
+.CodeRay .constant,.CodeRay .predefined-constant{color:#008080}
+.CodeRay .color{color:#099}
+.CodeRay .class-variable{color:#369}
+.CodeRay .decorator{color:#b0b}
+.CodeRay .definition{color:#099}
+.CodeRay .delimiter{color:#000}
+.CodeRay .doc{color:#970}
+.CodeRay .doctype{color:#34b}
+.CodeRay .doc-string{color:#d42}
+.CodeRay .escape{color:#666}
+.CodeRay .entity{color:#800}
+.CodeRay .error{color:#808}
+.CodeRay .exception{color:inherit}
+.CodeRay .filename{color:#099}
+.CodeRay .function{color:#900;font-weight:bold}
+.CodeRay .global-variable{color:#008080}
+.CodeRay .hex{color:#058}
+.CodeRay .integer,.CodeRay .float{color:#099}
+.CodeRay .include{color:#555}
+.CodeRay .inline{color:#000}
+.CodeRay .inline .inline{background:#ccc}
+.CodeRay .inline .inline .inline{background:#bbb}
+.CodeRay .inline .inline-delimiter{color:#d14}
+.CodeRay .inline-delimiter{color:#d14}
+.CodeRay .important{color:#555;font-weight:bold}
+.CodeRay .interpreted{color:#b2b}
+.CodeRay .instance-variable{color:#008080}
+.CodeRay .label{color:#970}
+.CodeRay .local-variable{color:#963}
+.CodeRay .octal{color:#40e}
+.CodeRay .predefined{color:#369}
+.CodeRay .preprocessor{color:#579}
+.CodeRay .pseudo-class{color:#555}
+.CodeRay .directive{font-weight:bold}
+.CodeRay .type{font-weight:bold}
+.CodeRay .predefined-type{color:inherit}
+.CodeRay .reserved,.CodeRay .keyword {color:#000;font-weight:bold}
+.CodeRay .key{color:#808}
+.CodeRay .key .delimiter{color:#606}
+.CodeRay .key .char{color:#80f}
+.CodeRay .value{color:#088}
+.CodeRay .regexp .delimiter{color:#808}
+.CodeRay .regexp .content{color:#808}
+.CodeRay .regexp .modifier{color:#808}
+.CodeRay .regexp .char{color:#d14}
+.CodeRay .regexp .function{color:#404;font-weight:bold}
+.CodeRay .string{color:#d20}
+.CodeRay .string .string .string{background:#ffd0d0}
+.CodeRay .string .content{color:#d14}
+.CodeRay .string .char{color:#d14}
+.CodeRay .string .delimiter{color:#d14}
+.CodeRay .shell{color:#d14}
+.CodeRay .shell .delimiter{color:#d14}
+.CodeRay .symbol{color:#990073}
+.CodeRay .symbol .content{color:#a60}
+.CodeRay .symbol .delimiter{color:#630}
+.CodeRay .tag{color:#008080}
+.CodeRay .tag-special{color:#d70}
+.CodeRay .variable{color:#036}
+.CodeRay .insert{background:#afa}
+.CodeRay .delete{background:#faa}
+.CodeRay .change{color:#aaf;background:#007}
+.CodeRay .head{color:#f8f;background:#505}
+.CodeRay .insert .insert{color:#080}
+.CodeRay .delete .delete{color:#800}
+.CodeRay .change .change{color:#66f}
+.CodeRay .head .head{color:#f4f}
+</style>
+<link rel="stylesheet" href="../katex/katex.min.css">
+<script src="../katex/katex.min.js"></script>
+<script src="../katex/contrib/auto-render.min.js"></script>
+    <!-- Use KaTeX to render math once document is loaded, see
+         https://github.com/Khan/KaTeX/tree/master/contrib/auto-render -->
+<script>
+    document.addEventListener("DOMContentLoaded", function () {
+        renderMathInElement(
+            document.body,
+            {
+                delimiters: [
+                    { left: "$$", right: "$$", display: true},
+                    { left: "\\[", right: "\\]", display: true},
+                    { left: "$", right: "$", display: false},
+                    { left: "\\(", right: "\\)", display: false}
+                ]
+            }
+        );
+    });
+</script></head>
+<body class="book toc2 toc-left" style="max-width: 100;">
+<div id="header">
+<h1>The OpenGL<sup>&#174;</sup> Shading Language, Version 4.60.6</h1>
+<div class="details">
+<span id="author" class="author">John Kessenich, Google (Editor and Author) ; Dave Baldwin and Randi Rost (Version 1.1 Authors)</span><br>
+<span id="revnumber">version 4.60.6,</span>
+<span id="revdate">Wed, 12 Dec 2018 23:37:49 +0000</span>
+<br><span id="revremark">Git branch information not available</span>
+</div>
+<div id="toc" class="toc2">
+<div id="toctitle">Table of Contents</div>
+<ul class="sectlevel1">
+<li><a href="#introduction">1. Introduction</a>
+<ul class="sectlevel2">
+<li><a href="#changes">1.1. Changes</a></li>
+<li><a href="#overview">1.2. Overview</a></li>
+<li><a href="#error-handling">1.3. Error Handling</a></li>
+<li><a href="#typographical-conventions">1.4. Typographical Conventions</a></li>
+<li><a href="#deprecation">1.5. Deprecation</a></li>
+</ul>
+</li>
+<li><a href="#overview-of-opengl-shading">2. Overview of OpenGL Shading</a>
+<ul class="sectlevel2">
+<li><a href="#vertex-processor">2.1. Vertex Processor</a></li>
+<li><a href="#tessellation-control-processor">2.2. Tessellation Control Processor</a></li>
+<li><a href="#tessellation-evaluation-processor">2.3. Tessellation Evaluation Processor</a></li>
+<li><a href="#geometry-processor">2.4. Geometry Processor</a></li>
+<li><a href="#fragment-processor">2.5. Fragment Processor</a></li>
+<li><a href="#compute-processor">2.6. Compute Processor</a></li>
+</ul>
+</li>
+<li><a href="#basics">3. Basics</a>
+<ul class="sectlevel2">
+<li><a href="#character-set">3.1. Character Set and Phases of Compilation</a></li>
+<li><a href="#source-strings">3.2. Source Strings</a></li>
+<li><a href="#preprocessor">3.3. Preprocessor</a></li>
+<li><a href="#comments">3.4. Comments</a></li>
+<li><a href="#tokens">3.5. Tokens</a></li>
+<li><a href="#keywords">3.6. Keywords</a></li>
+<li><a href="#identifiers">3.7. Identifiers</a></li>
+<li><a href="#definitions">3.8. Definitions</a></li>
+</ul>
+</li>
+<li><a href="#variables-and-types">4. Variables and Types</a>
+<ul class="sectlevel2">
+<li><a href="#basic-types">4.1. Basic Types</a></li>
+<li><a href="#scoping">4.2. Scoping</a></li>
+<li><a href="#storage-qualifiers">4.3. Storage Qualifiers</a></li>
+<li><a href="#layout-qualifiers">4.4. Layout Qualifiers</a></li>
+<li><a href="#interpolation-qualifiers">4.5. Interpolation Qualifiers</a></li>
+<li><a href="#parameter-qualifiers">4.6. Parameter Qualifiers</a></li>
+<li><a href="#precision-and-precision-qualifiers">4.7. Precision and Precision Qualifiers</a></li>
+<li><a href="#variance-and-the-invariant-qualifier">4.8. Variance and the Invariant Qualifier</a></li>
+<li><a href="#the-precise-qualifier">4.9. The Precise Qualifier</a></li>
+<li><a href="#memory-qualifiers">4.10. Memory Qualifiers</a></li>
+<li><a href="#specialization-constant-qualifier">4.11. Specialization-Constant Qualifier</a></li>
+<li><a href="#order-of-qualification">4.12. Order and Repetition of Qualification</a></li>
+<li><a href="#empty-declarations">4.13. Empty Declarations</a></li>
+</ul>
+</li>
+<li><a href="#operators-and-expressions">5. Operators and Expressions</a>
+<ul class="sectlevel2">
+<li><a href="#operators">5.1. Operators</a></li>
+<li><a href="#array-operations">5.2. Array Operations</a></li>
+<li><a href="#function-calls">5.3. Function Calls</a></li>
+<li><a href="#constructors">5.4. Constructors</a></li>
+<li><a href="#vector-components">5.5. Vector and Scalar Components and Length</a></li>
+<li><a href="#matrix-components">5.6. Matrix Components</a></li>
+<li><a href="#structure-and-array-operations">5.7. Structure and Array Operations</a></li>
+<li><a href="#assignments">5.8. Assignments</a></li>
+<li><a href="#expressions">5.9. Expressions</a></li>
+<li><a href="#vector-and-matrix-operations">5.10. Vector and Matrix Operations</a></li>
+<li><a href="#out-of-bounds-accesses">5.11. Out-of-Bounds Accesses</a></li>
+<li><a href="#specialization-constant-operations">5.12. Specialization Constant Operations</a></li>
+</ul>
+</li>
+<li><a href="#statements-and-structure">6. Statements and Structure</a>
+<ul class="sectlevel2">
+<li><a href="#function-definitions">6.1. Function Definitions</a></li>
+<li><a href="#selection">6.2. Selection</a></li>
+<li><a href="#iteration">6.3. Iteration</a></li>
+<li><a href="#jumps">6.4. Jumps</a></li>
+</ul>
+</li>
+<li><a href="#built-in-variables">7. Built-In Variables</a>
+<ul class="sectlevel2">
+<li><a href="#built-in-language-variables">7.1. Built-In Language Variables</a></li>
+<li><a href="#compatibility-profile-vertex-shader-built-in-inputs">7.2. Compatibility Profile Vertex Shader Built-In Inputs</a></li>
+<li><a href="#built-in-constants">7.3. Built-In Constants</a></li>
+<li><a href="#built-in-uniform-state">7.4. Built-In Uniform State</a></li>
+<li><a href="#redeclaring-built-in-blocks">7.5. Redeclaring Built-In Blocks</a></li>
+</ul>
+</li>
+<li><a href="#built-in-functions">8. Built-In Functions</a>
+<ul class="sectlevel2">
+<li><a href="#angle-and-trigonometry-functions">8.1. Angle and Trigonometry Functions</a></li>
+<li><a href="#exponential-functions">8.2. Exponential Functions</a></li>
+<li><a href="#common-functions">8.3. Common Functions</a></li>
+<li><a href="#floating-point-pack-and-unpack-functions">8.4. Floating-Point Pack and Unpack Functions</a></li>
+<li><a href="#geometric-functions">8.5. Geometric Functions</a></li>
+<li><a href="#matrix-functions">8.6. Matrix Functions</a></li>
+<li><a href="#vector-relational-functions">8.7. Vector Relational Functions</a></li>
+<li><a href="#integer-functions">8.8. Integer Functions</a></li>
+<li><a href="#texture-functions">8.9. Texture Functions</a></li>
+<li><a href="#atomic-counter-functions">8.10. Atomic Counter Functions</a></li>
+<li><a href="#atomic-memory-functions">8.11. Atomic Memory Functions</a></li>
+<li><a href="#image-functions">8.12. Image Functions</a></li>
+<li><a href="#geometry-shader-functions">8.13. Geometry Shader Functions</a></li>
+<li><a href="#fragment-processing-functions">8.14. Fragment Processing Functions</a></li>
+<li><a href="#noise-functions">8.15. Noise Functions</a></li>
+<li><a href="#shader-invocation-control-functions">8.16. Shader Invocation Control Functions</a></li>
+<li><a href="#shader-memory-control-functions">8.17. Shader Memory Control Functions</a></li>
+<li><a href="#shader-invocation-group-functions">8.18. Shader Invocation Group Functions</a></li>
+</ul>
+</li>
+<li><a href="#shading-language-grammar">9. Shading Language Grammar</a></li>
+<li><a href="#acknowledgments">10. Acknowledgments</a></li>
+<li><a href="#references">11. Normative References</a></li>
+</ul>
+</div>
+</div>
+<div id="content">
+<div id="preamble">
+<div class="sectionbody">
+<div style="page-break-after: always;"></div>
+<div class="paragraph">
+<p>Copyright &#169; 2008-2018 The Khronos Group Inc. All Rights Reserved.</p>
+</div>
+<div class="paragraph">
+<p>This specification is protected by copyright laws and contains material
+proprietary to the Khronos Group, Inc. It or any components may not be
+reproduced, republished, distributed, transmitted, displayed, broadcast,
+or otherwise exploited in any manner without the express prior written
+permission of Khronos Group. You may use this specification for
+implementing the functionality therein, without altering or removing any
+trademark, copyright or other notice from the specification, but the
+receipt or possession of this specification does not convey any rights
+to reproduce, disclose, or distribute its contents, or to manufacture,
+use, or sell anything that it may describe, in whole or in part.</p>
+</div>
+<div class="paragraph">
+<p>Khronos Group grants express permission to any current Promoter,
+Contributor or Adopter member of Khronos to copy and redistribute
+UNMODIFIED versions of this specification in any fashion, provided that
+NO CHARGE is made for the specification and the latest available update
+of the specification for any version of the API is used whenever
+possible. Such distributed specification may be reformatted AS LONG AS
+the contents of the specification are not changed in any way. The
+specification may be incorporated into a product that is sold as long as
+such product includes significant independent work developed by the
+seller. A link to the current version of this specification on the
+Khronos Group website should be included whenever possible with
+specification distributions.</p>
+</div>
+<div class="paragraph">
+<p>Khronos Group makes no, and expressly disclaims any, representations or
+warranties, express or implied, regarding this specification, including,
+without limitation, any implied warranties of merchantability or fitness
+for a particular purpose or noninfringement of any intellectual
+property. Khronos Group makes no, and expressly disclaims any,
+warranties, express or implied, regarding the correctness, accuracy,
+completeness, timeliness, and reliability of the specification. Under no
+circumstances will the Khronos Group, or any of its Promoters,
+Contributors or Members or their respective partners, officers,
+directors, employees, agents, or representatives be liable for any
+damages, whether direct, indirect, special or consequential damages for
+lost revenues, lost profits, or otherwise, arising from or in connection
+with these materials.</p>
+</div>
+<div class="paragraph">
+<p>Khronos, Vulkan, SYCL, SPIR, WebGL, EGL, COLLADA, StreamInput, OpenVX,
+OpenKCam, glTF, OpenKODE, OpenVG, OpenWF, OpenSL ES, OpenMAX, OpenMAX
+AL, OpenMAX IL and OpenMAX DL are trademarks and WebCL is a
+certification mark of the Khronos Group Inc. OpenCL is a trademark of
+Apple Inc. and OpenGL and OpenML are registered trademarks and the
+OpenGL ES and OpenGL SC logos are trademarks of Silicon Graphics
+International used under license by Khronos. All other product names,
+trademarks, and/or company names are used solely for identification and
+belong to their respective owners.</p>
+</div>
+<div style="page-break-after: always;"></div>
+<!-- toc disabled -->
+</div>
+</div>
+<div class="sect1">
+<h2 id="introduction">1. Introduction</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>This document specifies only version 4.60 of the OpenGL Shading Language.
+It requires __VERSION__ to substitute 460, and requires
+<strong>#version</strong> to accept only
+<code>460</code>.
+If <strong>#version</strong> is declared with a smaller number, the language accepted is a
+previous version of the shading language, which will be supported depending
+on the version and type of context in the OpenGL API.
+See the <a href="#references">OpenGL Specification</a> for details on what language versions are
+supported.</p>
+</div>
+<div class="paragraph">
+<p>Previous versions of the OpenGL Shading Language, as well as the OpenGL ES Shading Language,
+are not strict subsets of the version specified here, particularly with
+respect to precision, name-hiding rules, and treatment of interface
+variables.
+See the specification corresponding to a particular language version for
+details specific to that version of the language.</p>
+</div>
+<div class="paragraph">
+<p>The OpenGL API will specify the commands used to manipulate SPIR-V
+shaders.
+Independent offline tool chains will compile GLSL down to the SPIR-V
+intermediate language.
+SPIR-V generation is not enabled with a <strong>#extension</strong>, <strong>#version</strong>, or a
+profile.
+Instead, use of GLSL for SPIR-V is determined by offline tool-chain use.
+See the documentation of such tools to see how to request generation of
+SPIR-V for OpenGL.</p>
+</div>
+<div class="paragraph">
+<p>GLSL &#8594; SPIR-V compilers must be directed as to what SPIR-V <strong>Capabilities</strong>
+are legal at run-time and give errors for GLSL feature use outside those
+capabilities.
+This is also true for implementation-dependent limits that can be error
+checked by the front-end against built-in constants present in the GLSL
+source: the front-end can be informed of such limits, and report errors when
+they are exceeded.</p>
+</div>
+<div class="paragraph">
+<p>All references in this specification to the <a href="#references">OpenGL Specification</a> are to
+the Core profile of version 4.6, unless a different profile is
+specified.</p>
+</div>
+<div class="sect2">
+<h3 id="changes">1.1. Changes</h3>
+<div class="sect3">
+<h4 id="_changes_from_revision_5_of_glsl_4_6">1.1.1. Changes from Revision 5 of GLSL 4.6</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Private GLSL issue #34: Clarify/consolidate implicit conversion rules from int &#8594; uint
+to be the same as explicit construction.</p>
+</li>
+<li>
+<p>Private GLSL issue #24: Clarify that <strong>barrier</strong>() by itself is enough to synchronize
+both control flow and memory accesses to <strong>shared</strong> variables and tessellation
+control output variables. For other memory accesses an additional memory
+barrier is still required.</p>
+</li>
+<li>
+<p>Normatively reference IEEE-754 for definitions of floating-point formats.</p>
+</li>
+<li>
+<p>Private GLSL issue 36: <strong>refract</strong> function on <strong>double</strong> types requires eta
+argument to have type <strong>double</strong>.</p>
+</li>
+<li>
+<p>Clarify restrictions on input variables in tessellation and geometry stages.</p>
+</li>
+<li>
+<p>Private GLSL issue 15: Clarify the ordering of bindings for arrays of arrays.</p>
+</li>
+<li>
+<p>Private GLSL issue 14: Uniform variables need only match at link time if they
+are statically used.</p>
+</li>
+<li>
+<p>For <strong>precise</strong> computations, the controlling expressions for
+control flow and ternary operators (<strong>?:</strong>) are not included.</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="_changes_from_revision_4_of_glsl_4_6">1.1.2. Changes from Revision 4 of GLSL 4.6</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Private bug 13012: Clarified that builtin uniform variables might only
+be available in the fragment stage.</p>
+</li>
+<li>
+<p>Private bug 13837: Ternary and sequence operators may operate on <strong>void</strong> types.</p>
+</li>
+<li>
+<p>Clarified that errors arising from preprocessing must be returned at compile time.</p>
+</li>
+<li>
+<p>Clarified that access to any part of a variable constitutes a static use.</p>
+</li>
+<li>
+<p>Private GLSL issue 19: A statement is required following any label at the end of a <strong>switch</strong>.</p>
+</li>
+<li>
+<p>Private GLSL issue 26: <strong>noise</strong> is not valid when compiling for SPIR-V.</p>
+</li>
+<li>
+<p>Private GLSL issue 20: <strong>length</strong>() expressions returning a constant value may not
+contain side effects.</p>
+</li>
+<li>
+<p>Public OpenGL-API issue 7: Variables can be declared as both <strong>readonly</strong>
+and <strong>writeonly</strong>.</p>
+</li>
+<li>
+<p>Private GLSL issue 16: Use of constant expressions within <strong>#line</strong> directives is undefined.</p>
+</li>
+<li>
+<p>Corrected return type of <strong>imageAtomicExchange</strong> on <strong>float</strong> images.</p>
+</li>
+<li>
+<p>Private GLSL issue 32: Remove <strong>length</strong>() method contradiction:
+Non runtime-sized arrays only support <strong>length</strong>() on explicitly
+sized arrays.</p>
+</li>
+<li>
+<p>Private GLSL issue 21: Clarified the l-value restriction on <strong>interpolateAt</strong>.</p>
+</li>
+<li>
+<p>Private OpenGL-API issue 53: Clarified bit-width requirements for location aliasing.</p>
+</li>
+<li>
+<p>Public GLSL issue 15: <strong>gl_in</strong> can be redeclared using unsized-array syntax.</p>
+</li>
+<li>
+<p>Clarification of the formats needed for DEPTH_COMPONENT and
+STENCIL_COMPONENT for depth/stencil textures.</p>
+</li>
+<li>
+<p>Added image formats to the layout-qualifier table in the
+<a href="#layout-qualifiers">Layout Qualifiers</a> section.</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="_changes_from_revision_3_of_glsl_4_6">1.1.3. Changes from Revision 3 of GLSL 4.6</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Private GLSL issue 13: Fix misspelling of <strong>allInvocationsEqual</strong>().
+(The one in the table was incorrectly listed as <strong>anyInvocationsEqual</strong>(),
+other spellings were correct.)</p>
+</li>
+</ul>
+</div>
+</div>
+<div class="sect3">
+<h4 id="_summary_of_changes_from_revision_7_of_glsl_version_4_50">1.1.4. Summary of Changes from Revision 7 of GLSL Version 4.50</h4>
+<div class="ulist">
+<ul>
+<li>
+<p>Incorporated the GL_ARB_shader_atomic_counter_ops extension.</p>
+</li>
+<li>
+<p>Incorporated the GL_ARB_shader_draw_parameters extension.</p>
+</li>
+<li>
+<p>Incorporated the GL_ARB_shader_group_vote extension.</p>
+</li>
+<li>
+<p>Incorporated the GL_ARB_gl_spirv extension.</p>
+</li>
+<li>
+<p>Private Bug 16070: Allow extra semi-colons at global scope.</p>
+</li>
+<li>
+<p>Private GLSL Issue 5: Be explicit that &#8220;fail to link&#8221; is really
+&#8220;compile-time or link-time error&#8221;, for some forms of error.</p>
+</li>
+<li>
+<p>Private GLSL Issue 7: Change <em>gl_MaxComputeUniformComponents</em> to 1024.</p>
+</li>
+<li>
+<p>Private OpenGL API Issue 35: Require location on transparent individual
+uniform variables for SPIR-V.</p>
+</li>
+<li>
+<p>Private GLSL Issue 8: Be more clear an <strong>interpolateAt</strong>() interpolant can
+be a structure member.</p>
+</li>
+<li>
+<p>Private GLSL Issue 9: Specify how <strong>xfb_buffer</strong> interacts with a block
+array: the capturing buffer increments for each block array element.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="overview">1.2. Overview</h3>
+<div class="paragraph">
+<p>This document describes <em>The OpenGL Shading Language, version 4.60</em>.</p>
+</div>
+<div class="paragraph">
+<p>Independent compilation units written in this language are called <em>shaders</em>.
+A <em>program</em> is a set of shaders that are compiled and linked
+together,
+completely creating one or more of the programmable stages of the
+OpenGL pipeline.
+All the shaders for a single programmable stage must be within the same
+program.
+A complete set of programmable stages can be put into a single program or
+the stages can be partitioned across multiple programs.
+The aim of this document is to thoroughly specify the programming language.
+The <a href="#references">OpenGL Specification</a> will specify the OpenGL entry points used to
+manipulate and communicate with programs and shaders.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="error-handling">1.3. Error Handling</h3>
+<div class="paragraph">
+<p>Compilers, in general, accept programs that are ill-formed, due to the
+impossibility of detecting all ill-formed programs.
+Portability is only ensured for well-formed programs, which this
+specification describes.
+Compilers are encouraged to detect ill-formed programs and issue diagnostic
+messages, but are not required to do so for all cases.
+Compile-time errors must be returned for lexically or grammatically
+incorrect shaders.
+Other errors are reported at compile time or link time as indicated.
+Code that is &#8220;dead&#8221; must still be error checked.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">if</span> (<span class="predefined-constant">false</span>)     <span class="comment">// changing false to true cannot uncover additional errors</span>
+    statement; <span class="comment">// statement must be error checked regardless</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="typographical-conventions">1.4. Typographical Conventions</h3>
+<div class="paragraph">
+<p>Italic, bold, and font choices have been used in this specification
+primarily to improve readability.
+Code fragments use a fixed width font.
+Identifiers embedded in text are italicized.
+Keywords embedded in text are bold.
+Operators are called by their name, followed by their symbol in bold in
+parentheses.
+The clarifying grammar fragments in the text use bold for literals and
+italics for non-terminals.
+The official grammar in &#8220;<a href="#shading-language-grammar">Shading Language
+Grammar</a>&#8221; uses all capitals for terminals and lower case for
+non-terminals.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="deprecation">1.5. Deprecation</h3>
+<div class="paragraph">
+<p>The OpenGL Shading Language has deprecated some features.
+These are clearly called out in this specification as &#8220;deprecated&#8221;.
+They are still present in this version of the language, but are targeted for
+potential removal in a future version of the shading language.
+The OpenGL API has a forward compatibility mode that will disallow use of
+deprecated features.
+If compiling in a mode where use of deprecated features is disallowed, their
+use causes compile-time or link-time errors.
+See the <a href="#references">OpenGL Specification</a> for details on what causes deprecated
+language features to be accepted or to return an error.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="overview-of-opengl-shading">2. Overview of OpenGL Shading</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The OpenGL Shading Language is actually several closely related languages.
+These languages are used to create shaders for each of the programmable
+processors contained in the OpenGL processing pipeline.
+Currently, these processors are the vertex, tessellation control,
+tessellation evaluation, geometry, fragment, and compute processors.</p>
+</div>
+<div class="paragraph">
+<p>Unless otherwise noted in this paper, a language feature applies to all
+languages, and common usage will refer to these languages as a single
+language.
+The specific languages will be referred to by the name of the processor they
+target: vertex, tessellation control, tessellation evaluation, geometry,
+fragment, or compute.</p>
+</div>
+<div class="paragraph">
+<p>Most OpenGL state is not tracked or made available to shaders.
+Typically, user-defined variables will be used for communicating between
+different stages of the OpenGL pipeline.
+However, a small amount of state is still tracked and automatically made
+available to shaders, and there are a few built-in variables for interfaces
+between different stages of the OpenGL pipeline.</p>
+</div>
+<div class="sect2">
+<h3 id="vertex-processor">2.1. Vertex Processor</h3>
+<div class="paragraph">
+<p>The <em>vertex processor</em> is a programmable unit that operates on incoming
+vertices and their associated data.
+Compilation units written in the OpenGL Shading Language to run on this processor are called
+<em>vertex shaders</em>.
+When a set of vertex shaders are successfully compiled and linked, they
+result in a <em>vertex shader executable</em> that runs on the vertex processor.</p>
+</div>
+<div class="paragraph">
+<p>The vertex processor operates on one vertex at a time.
+It does not replace graphics operations that require knowledge of several
+vertices at a time.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="tessellation-control-processor">2.2. Tessellation Control Processor</h3>
+<div class="paragraph">
+<p>The <em>tessellation control processor</em> is a programmable unit that operates on
+a patch of incoming vertices and their associated data, emitting a new
+output patch.
+Compilation units written in the OpenGL Shading Language to run on this processor are called
+tessellation control shaders.
+When a set of tessellation control shaders are successfully compiled and
+linked, they result in a <em>tessellation control shader executable</em> that runs
+on the tessellation control processor.</p>
+</div>
+<div class="paragraph">
+<p>The tessellation control shader is invoked for each vertex of the output
+patch.
+Each invocation can read the attributes of any vertex in the input or output
+patches, but can only write per-vertex attributes for the corresponding
+output patch vertex.
+The shader invocations collectively produce a set of per-patch attributes
+for the output patch.</p>
+</div>
+<div class="paragraph">
+<p>After all tessellation control shader invocations have completed, the output
+vertices and per-patch attributes are assembled to form a patch to be used
+by subsequent pipeline stages.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control shader invocations run mostly independently, with
+undefined relative execution order.
+However, the built-in function <strong>barrier</strong>() can be used to control execution
+order by synchronizing invocations, effectively dividing tessellation
+control shader execution into a set of phases.
+Tessellation control shaders will get undefined results if one invocation
+reads from a per-vertex or per-patch attribute written by another invocation
+at any point during the same phase, or if two invocations attempt to write
+different values to the same per-patch output
+32-bit component
+in a single phase.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="tessellation-evaluation-processor">2.3. Tessellation Evaluation Processor</h3>
+<div class="paragraph">
+<p>The <em>tessellation evaluation processor</em> is a programmable unit that
+evaluates the position and other attributes of a vertex generated by the
+tessellation primitive generator, using a patch of incoming vertices and
+their associated data.
+Compilation units written in the OpenGL Shading Language to run on this processor are called
+tessellation evaluation shaders.
+When a set of tessellation evaluation shaders are successfully compiled and
+linked, they result in a <em>tessellation evaluation shader executable</em> that
+runs on the tessellation evaluation processor.</p>
+</div>
+<div class="paragraph">
+<p>Each invocation of the tessellation evaluation executable computes the
+position and attributes of a single vertex generated by the tessellation
+primitive generator.
+The executable can read the attributes of any vertex in the input patch,
+plus the tessellation coordinate, which is the relative location of the
+vertex in the primitive being tessellated.
+The executable writes the position and other attributes of the vertex.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="geometry-processor">2.4. Geometry Processor</h3>
+<div class="paragraph">
+<p>The <em>geometry processor</em> is a programmable unit that operates on data for
+incoming vertices for a primitive assembled after vertex processing and
+outputs a sequence of vertices forming output primitives.
+Compilation units written in the OpenGL Shading Language to run on this processor are called
+<em>geometry shaders</em>.
+When a set of geometry shaders are successfully compiled and linked, they
+result in a <em>geometry shader executable</em> that runs on the geometry
+processor.</p>
+</div>
+<div class="paragraph">
+<p>A single invocation of the geometry shader executable on the geometry
+processor will operate on a declared input primitive with a fixed number of
+vertices.
+This single invocation can emit a variable number of vertices that are
+assembled into primitives of a declared output primitive type and passed to
+subsequent pipeline stages.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="fragment-processor">2.5. Fragment Processor</h3>
+<div class="paragraph">
+<p>The <em>fragment processor</em> is a programmable unit that operates on fragment
+values and their associated data.
+Compilation units written in the OpenGL Shading Language to run on this processor are called
+<em>fragment shaders</em>.
+When a set of fragment shaders are successfully compiled and linked, they
+result in a <em>fragment shader executable</em> that runs on the fragment
+processor.</p>
+</div>
+<div class="paragraph">
+<p>A fragment shader cannot change a fragment&#8217;s (<em>x</em>, <em>y</em>) position.
+Access to neighboring fragments is not allowed.
+The values computed by the fragment shader are ultimately used to update
+framebuffer memory or texture memory, depending on the current OpenGL
+state and the OpenGL command that caused the fragments to be generated.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="compute-processor">2.6. Compute Processor</h3>
+<div class="paragraph">
+<p>The <em>compute processor</em> is a programmable unit that operates independently
+from the other shader processors.
+Compilation units written in the OpenGL Shading Language to run on this processor are called
+<em>compute shaders</em>.
+When a set of compute shaders are successfully compiled and linked, they
+result in a <em>compute shader executable</em> that runs on the compute processor.</p>
+</div>
+<div class="paragraph">
+<p>A compute shader has access to many of the same resources as fragment and
+other shader processors, such as textures, buffers, image variables, and
+atomic counters.
+It does not have fixed-function outputs.
+It is not part of the graphics pipeline and its visible side effects are
+through changes to images, storage buffers, and atomic counters.</p>
+</div>
+<div class="paragraph">
+<p>A compute shader operates on a group of work items called a <em>workgroup</em>.
+A workgroup is a collection of shader invocations that execute the same
+code, potentially in parallel.
+An invocation within a workgroup may share data with other members of the
+same workgroup through shared variables and issue memory and control flow
+barriers to synchronize with other members of the same workgroup.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="basics">3. Basics</h2>
+<div class="sectionbody">
+<div class="sect2">
+<h3 id="character-set">3.1. Character Set and Phases of Compilation</h3>
+<div class="paragraph">
+<p>The source character set used for the OpenGL Shading Language is Unicode in the UTF-8
+encoding scheme.</p>
+</div>
+<div class="paragraph">
+<p>After preprocessing, only the following characters are allowed in the
+resulting stream of GLSL tokens:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The letters <strong>a-z</strong>, <strong>A-Z</strong>, and the underscore (<strong>_</strong>).</p>
+</li>
+<li>
+<p>The numbers <strong>0-9</strong>.</p>
+</li>
+<li>
+<p>The symbols period (<strong>.</strong>), plus (<strong>+</strong>), dash (<strong>-</strong>), slash (<strong>/</strong>), asterisk
+(<strong>*</strong>), percent (<strong>%</strong>), angled brackets (<strong>&lt;</strong> and <strong>&gt;</strong>), square brackets
+(<strong>[</strong> and <strong>]</strong>), parentheses (<strong>(</strong> and <strong>)</strong>), braces (<strong>{</strong> and <strong>}</strong>), caret
+(<strong>^</strong>), vertical bar (<strong>|</strong>), ampersand (<strong>&amp;</strong>), tilde (<strong>~</strong>), equals (<strong>=</strong>),
+exclamation point (<strong>!</strong>), colon (<strong>:</strong>), semicolon (<strong>;</strong>), comma (<strong>,</strong>), and
+question mark (<strong>?</strong>).</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>A compile-time error will be given if any other character is used in a GLSL
+token.</p>
+</div>
+<div class="paragraph">
+<p>There are no digraphs or trigraphs.
+There are no escape sequences or other uses of the backslash beyond use as
+the line-continuation character.</p>
+</div>
+<div class="paragraph">
+<p>Lines are relevant for compiler diagnostic messages and the preprocessor.
+They are terminated by carriage-return or line-feed.
+If both are used together, it will count as only a single line termination.
+For the remainder of this document, any of these combinations is simply
+referred to as a new-line.
+Lines may be of arbitrary length.</p>
+</div>
+<div class="paragraph">
+<p>In general, the language&#8217;s use of this character set is case sensitive.</p>
+</div>
+<div class="paragraph">
+<p>There are no character or string data types, so no quoting characters are
+included.</p>
+</div>
+<div class="paragraph">
+<p>There is no end-of-file character.</p>
+</div>
+<div class="paragraph">
+<p>More formally, compilation happens as if the following logical phases were
+executed in order:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>Source strings are concatenated to form a single input.
+All provided new-lines are retained.</p>
+</li>
+<li>
+<p>Line numbering is noted, based on all present new-lines, and does not
+change when new-lines are later eliminated.</p>
+</li>
+<li>
+<p>Wherever a backslash ('\') occurs immediately before a new-line, both
+are eliminated.
+(Note no white space is substituted, allowing a single token to span a
+new-line.) Any newly formed backslash followed by a new-line is not
+eliminated; only those pairs originally occurring after phase 1 are
+eliminated.</p>
+</li>
+<li>
+<p>All comments are replaced with a single space.
+(Note that '//' style comments end before their terminating new-lines
+and white space is generally relevant to preprocessing.)</p>
+</li>
+<li>
+<p>Preprocessing is done, resulting in a sequence of GLSL tokens, formed
+from the character set stated above.</p>
+</li>
+<li>
+<p>GLSL processing is done on the sequence of GLSL tokens.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Details that fully define source strings, comments, line numbering, new-line
+elimination, and preprocessing are all discussed in upcoming sections.
+Sections beyond those describe GLSL processing.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="source-strings">3.2. Source Strings</h3>
+<div class="paragraph">
+<p>The source for a single shader is an array of strings of characters from the
+character set.
+A single shader is made from the concatenation of these strings.
+Each string can contain multiple lines, separated by new-lines.
+No new-lines need be present in a string; a single line can be formed from
+multiple strings.
+No new-lines or other characters are inserted by the implementation when it
+concatenates the strings to form a single shader.
+Multiple shaders can be linked together to form a single program.</p>
+</div>
+<div class="paragraph">
+<p>Diagnostic messages returned from compiling a shader must identify both the
+line number within a string and which source string the message applies to.
+Source strings are counted sequentially with the first string being string
+0.
+Line numbers are one more than the number of new-lines that have been
+processed, including counting the new-lines that will be removed by the
+line-continuation character (<strong>\</strong>).</p>
+</div>
+<div class="paragraph">
+<p>Lines separated by the line-continuation character preceding a new-line are
+concatenated together before either comment processing or preprocessing.
+This means that no white space is substituted for the line-continuation
+character.
+That is, a single token could be formed by the concatenation by taking the
+characters at the end of one line concatenating them with the characters at
+the beginning of the next line.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> f\
+oo;
+<span class="comment">// forms a single line equivalent to &quot;float foo;&quot;</span>
+<span class="comment">// (assuming '\' is the last character before the new-line and &quot;oo&quot; are</span>
+<span class="comment">// the first two characters of the next line)</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="preprocessor">3.3. Preprocessor</h3>
+<div class="paragraph">
+<p>There is a preprocessor that processes the source strings as part of the
+compilation process.
+Except as noted below, it behaves as the C++ standard preprocessor (see
+&#8220;<a href="#references">Normative References</a>&#8221;).</p>
+</div>
+<div class="paragraph">
+<p>The complete list of preprocessor directives is as follows.</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#<br>
+#define<br>
+#undef<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#if<br>
+#ifdef<br>
+#ifndef<br>
+#else<br>
+#elif<br>
+#endif<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#error<br>
+#pragma<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#extension<br>
+#version<br></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>#line</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The following
+operators are
+also available:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>defined<br>
+##</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Each number sign (<strong>#</strong>) can be preceded in its line only by spaces or
+horizontal tabs.
+It may also be followed by spaces and horizontal tabs, preceding the
+directive.
+Each directive is terminated by a new-line.
+Preprocessing does not change the number or relative location of new-lines
+in a source string.
+Preprocessing takes places after new-lines have been removed by the
+line-continuation character.</p>
+</div>
+<div class="paragraph">
+<p>The number sign (<strong>#</strong>) on a line by itself is ignored.
+Any directive not listed above will cause a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p><strong>#define</strong> and <strong>#undef</strong> functionality are defined as is standard for C++
+preprocessors for macro definitions both with and without macro parameters.</p>
+</div>
+<div class="paragraph">
+<p>The following predefined macros are available:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>__LINE__<br>
+__FILE__<br>
+__VERSION__<br></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>__LINE__ will substitute a decimal integer constant that is one more than
+the number of preceding new-lines in the current source string.</p>
+</div>
+<div class="paragraph">
+<p>__FILE__ will substitute a decimal integer constant that says which source
+string number is currently being processed.</p>
+</div>
+<div class="paragraph">
+<p>__VERSION__ will substitute a decimal integer reflecting the version
+number of the OpenGL Shading Language.
+The version of the shading language described in this document will have
+__VERSION__ substitute the decimal integer 460.</p>
+</div>
+<div class="paragraph">
+<p>By convention, all macro names containing two consecutive underscores (__)
+are reserved for use by underlying software layers.
+Defining
+or undefining
+such a name in a shader does not itself result in an error, but may
+result in unintended behaviors that stem from having multiple definitions of
+the same name.
+All macro names prefixed with &#8220;GL_&#8221; (&#8220;GL&#8221; followed by a single
+underscore) are also reserved, and defining
+or undefining
+such a name results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>Implementations must support macro-name lengths of up to 1024 characters.
+Implementations are allowed to generate an error for a macro name of length
+greater than 1024 characters, but are also allowed to support lengths
+greater than 1024.</p>
+</div>
+<div class="paragraph">
+<p><strong>#if</strong>, <strong>#ifdef</strong>, <strong>#ifndef</strong>, <strong>#else</strong>, <strong>#elif</strong>, and <strong>#endif</strong> are defined to
+operate as is standard for C++ preprocessors except for the following:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Expressions following <strong>#if</strong> and <strong>#elif</strong> are
+further restricted to
+expressions operating on literal integer constants, plus identifiers
+consumed by the <strong>defined</strong> operator.</p>
+</li>
+<li>
+<p>Character constants are not supported.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The operators available are as follows.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Precedence</th>
+<th class="tableblock halign-left valign-top">Operator class</th>
+<th class="tableblock halign-left valign-top">Operators</th>
+<th class="tableblock halign-left valign-top">Associativity</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1 (highest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">parenthetical grouping</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">( )</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">NA</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">unary</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">defined<br>
+                                         + - ~ !</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">multiplicative</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">* / %</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">additive</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">+ -</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise shift</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;&lt; &gt;&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">relational</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt; &gt; &lt;= &gt;=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">7</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">equality</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">== !=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">8</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">9</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise exclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">^</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">10</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">|</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">11</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">12 (lowest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">||</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The <strong>defined</strong> operator can be used in either of the following ways:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">defined identifier
+defined ( identifier )</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Two tokens in a macro can be concatenated into one token using the token
+pasting (<strong>##</strong>) operator, as is standard for C++ preprocessors.
+The result must be a valid single token, which will then be subject to macro
+expansion.
+That is, macro expansion happens only after token pasting.
+There are no other number sign based operators (e.g. no <strong>#</strong> or <strong>#@</strong>), nor is
+there a <strong>sizeof</strong> operator.</p>
+</div>
+<div class="paragraph">
+<p>The semantics of applying operators to integer literals in the preprocessor
+match those standard in the C++ preprocessor, not those in the OpenGL Shading Language.</p>
+</div>
+<div class="paragraph">
+<p>Preprocessor expressions will be evaluated according to the behavior of the
+host processor, not the processor targeted by the shader.</p>
+</div>
+<div class="paragraph">
+<p><strong>#error</strong> will cause the implementation to put a compile-time diagnostic message
+into the shader object&#8217;s information log (see section 7.12 &#8220;Shader, Program
+and Program Pipeline Queries&#8221; of the <a href="#references">OpenGL Specification</a> for how to
+access a shader object&#8217;s information log).
+The message will be the tokens following the <strong>#error</strong> directive, up to the
+first new-line.
+The implementation must treat the presence of a <strong>#error</strong> directive as a
+compile-time error.</p>
+</div>
+<div class="paragraph">
+<p><strong>#pragma</strong> allows implementation-dependent compiler control.
+Tokens following <strong>#pragma</strong> are not subject to preprocessor macro expansion.
+If an implementation does not recognize the tokens following <strong>#pragma</strong>, then
+it will ignore that pragma.
+The following pragmas are defined as part of the language.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> STDGL</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>STDGL</strong> pragma is used to reserve pragmas for use by future revisions of
+this language.
+No implementation may use a pragma whose first token is <strong>STDGL</strong>.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> optimize(on)
+<span class="preprocessor">#pragma</span> optimize(off)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>can be used to turn off optimizations as an aid in developing and debugging
+shaders.
+It can only be used outside function definitions.
+By default, optimization is turned on for all shaders.
+The debug pragma</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> debug(on)
+<span class="preprocessor">#pragma</span> debug(off)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>can be used to enable compiling and annotating a shader with debug
+information, so that it can be used with a debugger.
+It can only be used outside function definitions.
+By default, debug is turned off.</p>
+</div>
+<div class="paragraph">
+<p>Shaders should declare the version of the language they are written to.
+The language version a shader is written to is specified by</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#version</span> number profile_opt</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>number</em> must be a version of the language, following the same
+convention as __VERSION__ above.
+The directive &#8220;<strong>#version 460</strong>&#8221; is required in any shader that
+uses version 4.60 of the language.
+Any <em>number</em> representing a version of the language a compiler does not
+support will cause a compile-time error to be generated.
+Version 1.10 of the language does not require shaders to include this
+directive, and shaders that do not include a <strong>#version</strong> directive will be
+treated as targeting version 1.10.
+Shaders that specify <strong>#version</strong> 100 will be treated as targeting version
+1.00 of the OpenGL ES Shading Language.
+Shaders that specify <strong>#version</strong> 300 will be treated as targeting version
+3.00 of the OpenGL ES Shading Language.
+Shaders that specify <strong>#version</strong> 310 will be treated as targeting version
+3.10 of the OpenGL ES Shading Language.</p>
+</div>
+<div class="paragraph">
+<p>If the optional <em>profile</em> argument is provided, it must be the name of an
+OpenGL profile.
+Currently, there are three choices:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">core
+compatibility
+es</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A <em>profile</em> argument can only be used with version 150 or greater.
+If no profile argument is provided and the version is 150 or greater, the
+default is <strong>core</strong>.
+If version 300 or 310 is specified, the profile argument is not optional and
+must be <strong>es</strong>, or a compile-time error results.
+The Language Specification for the <strong>es</strong> profile is specified in The OpenGL
+ES Shading Language specification.</p>
+</div>
+<div class="paragraph">
+<p>Shaders for the <strong>core</strong> or <strong>compatibility</strong> profiles that declare different
+versions can be linked together.
+However, <strong>es</strong> profile shaders cannot be linked with non-<strong>es</strong> profile shaders
+or with <strong>es</strong> profile shaders of a different version, or a link-time error
+will result.
+When linking shaders of versions allowed by these rules, remaining link-time
+errors will be given as per the linking rules in the GLSL version
+corresponding to the version of the context the shaders are linked under.
+Shader compile-time errors must still be given strictly based on the version
+declared (or defaulted to) within each shader.</p>
+</div>
+<div class="paragraph">
+<p>Unless otherwise specified, this specification is documenting the core
+profile, and everything specified for the core profile is also available in
+the compatibility profile.
+Features specified as belonging specifically to the compatibility profile
+are not available in the core profile.
+Compatibility-profile features are not available when generating SPIR-V.</p>
+</div>
+<div class="paragraph">
+<p>There is a built-in macro definition for each profile the implementation
+supports.
+All implementations provide the following macro:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#define</span> GL_core_profile <span class="integer">1</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Implementations providing the <strong>compatibility</strong> profile provide the following
+macro:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#define</span> GL_compatibility_profile <span class="integer">1</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Implementations providing the <strong>es</strong> profile provide the following macro:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#define</span> GL_es_profile <span class="integer">1</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>#version</strong> directive must occur in a shader before anything else, except
+for comments and white space.</p>
+</div>
+<div class="paragraph">
+<p>By default, compilers of this language must issue compile-time
+lexical
+and
+grammatical errors for shaders that do not conform to this specification.
+Any extended behavior must first be enabled.
+Directives to control the behavior of the compiler with respect to
+extensions are declared with the <strong>#extension</strong> directive</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#extension</span> extension_name : behavior
+<span class="preprocessor">#extension</span> all : behavior</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>extension_name</em> is the name of an extension.
+Extension names are not documented in this specification.
+The token <strong>all</strong> means the behavior applies to all extensions supported by
+the compiler.
+The <em>behavior</em> can be one of the following:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Behavior</th>
+<th class="tableblock halign-left valign-top">Effect</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>require</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave as specified by the extension <em>extension_name</em>.<br>
+              Give a compile-time error on the <strong>#extension</strong> if the extension
+              <em>extension_name</em> is not supported, or if <strong>all</strong> is specified.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>enable</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave as specified by the extension <em>extension_name</em>.<br>
+              Warn on the <strong>#extension</strong> if the extension <em>extension_name</em> is
+              not supported.<br>
+              Give a compile-time error on the <strong>#extension</strong> if <strong>all</strong> is
+              specified.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>warn</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave as specified by the extension <em>extension_name</em>,
+              except issue warnings on any detectable use of that extension,
+              unless such use is supported by other enabled or required
+              extensions.<br>
+              If <strong>all</strong> is specified, then warn on all detectable uses of any
+              extension used.<br>
+              Warn on the <strong>#extension</strong> if the extension <em>extension_name</em> is
+              not supported.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>disable</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Behave (including issuing errors and warnings) as if the
+              extension <em>extension_name</em> is not part of the language
+              definition.<br>
+              If <strong>all</strong> is specified, then behavior must revert back to that
+              of the non-extended core version of the language being
+              compiled to.<br>
+              Warn on the <strong>#extension</strong> if the extension <em>extension_name</em> is
+              not supported.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The <strong>extension</strong> directive is a simple, low-level mechanism to set the
+behavior for each extension.
+It does not define policies such as which combinations are appropriate,
+those must be defined elsewhere.
+Order of directives matters in setting the behavior for each extension:
+Directives that occur later override those seen earlier.
+The <strong>all</strong> variant sets the behavior for all extensions, overriding all
+previously issued <strong>extension</strong> directives, but only for the <em>behaviors</em>
+<strong>warn</strong> and <strong>disable</strong>.</p>
+</div>
+<div class="paragraph">
+<p>The initial state of the compiler is as if the directive</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#extension</span> all : disable</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>was issued, telling the compiler that all error and warning reporting must
+be done according to this specification, ignoring any extensions.</p>
+</div>
+<div class="paragraph">
+<p>Each extension can define its allowed granularity of scope.
+If nothing is said, the granularity is a shader (that is, a single
+compilation unit), and the extension directives must occur before any
+non-preprocessor tokens.
+If necessary, the linker can enforce granularities larger than a single
+compilation unit, in which case each involved shader will have to contain
+the necessary extension directive.</p>
+</div>
+<div class="paragraph">
+<p>Macro expansion is not done on lines containing <strong>#extension</strong> and <strong>#version</strong>
+directives.</p>
+</div>
+<div class="paragraph">
+<p><strong>#line</strong> must have, after macro substitution, one of the following forms:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#line</span> line
+<span class="preprocessor">#line</span> line source-<span class="predefined-type">string</span>-number</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>line</em> and <em>source-string-number</em> are
+constant integer expressions.
+If these constant expressions are not integer literals then behavior is undefined.
+After processing this directive (including its new-line), the implementation
+will behave as if it is compiling at line number <em>line</em> and source string
+number <em>source-string-number</em>.
+Subsequent source strings will be numbered sequentially, until another
+<strong>#line</strong> directive overrides that numbering.</p>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="title">Note</div>
+<div class="paragraph">
+<p>Some implementations have allowed constant expressions in #line directives and
+some have not. Even where expressions are supported the grammar is ambiguous and so
+results are implementation dependent. For example,
++ #line +2 +2               // Line number set to 4, or file to 2 and line to 2</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="paragraph">
+<p>When shaders are compiled for OpenGL SPIR-V, the following predefined
+macro is available:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#define</span> GL_SPIRV <span class="integer">100</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="comments">3.4. Comments</h3>
+<div class="paragraph">
+<p>Comments are delimited by <strong>/*</strong> and <strong>*/</strong>, or by <strong>//</strong> and a new-line.
+The begin comment delimiters (/* or //) are not recognized as comment
+delimiters inside of a comment, hence comments cannot be nested.
+A <strong>/*</strong> comment includes its terminating delimiter (*/).
+However, a <strong>//</strong> comment does not include (or eliminate) its terminating new
+line.</p>
+</div>
+<div class="paragraph">
+<p>Inside comments, any byte values may be used, except a byte whose value is
+0.
+No errors will be given for the content of comments and no validation on the
+content of comments need be done.</p>
+</div>
+<div class="paragraph">
+<p>Removal of new-lines by the line-continuation character (<strong>\</strong>) logically
+occurs before comments are processed.
+That is, a single-line comment ending in the line-continuation character
+(<strong>\</strong>) includes the next line in the comment.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// a single-line comment containing the next line \
+a = b; // this is still in the first comment</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="tokens">3.5. Tokens</h3>
+<div class="paragraph">
+<p>The language, after preprocessing, is a sequence of tokens.
+A token can be</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>token</em> : </dt>
+<dd>
+<p><em>keyword</em><br>
+<em>identifier</em><br>
+<em>integer-constant</em><br>
+<em>floating-constant</em><br>
+<em>operator</em><br>
+<strong>;</strong> <strong>{</strong> <strong>}</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="keywords">3.6. Keywords</h3>
+<div class="paragraph">
+<p>The following are the keywords in the language and (after
+preprocessing) can only be used as described in this specification,
+or a compile-time error results:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>const</strong> <strong>uniform</strong> <strong>buffer</strong> <strong>shared</strong>
+<strong>attribute</strong> <strong>varying</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>coherent</strong> <strong>volatile</strong> <strong>restrict</strong> <strong>readonly</strong> <strong>writeonly</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>atomic_uint</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>layout</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>centroid</strong> <strong>flat</strong> <strong>smooth</strong>
+<strong>noperspective</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>patch</strong> <strong>sample</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>invariant</strong> <strong>precise</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>break</strong> <strong>continue</strong> <strong>do</strong> <strong>for</strong> <strong>while</strong> <strong>switch</strong> <strong>case</strong> <strong>default</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>if</strong> <strong>else</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>subroutine</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>in</strong> <strong>out</strong> <strong>inout</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>int</strong> <strong>void</strong> <strong>bool</strong> <strong>true</strong> <strong>false</strong> <strong>float</strong>
+<strong>double</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>discard</strong> <strong>return</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>vec2</strong> <strong>vec3</strong> <strong>vec4</strong> <strong>ivec2</strong> <strong>ivec3</strong> <strong>ivec4</strong> <strong>bvec2</strong> <strong>bvec3</strong> <strong>bvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>uint</strong> <strong>uvec2</strong> <strong>uvec3</strong> <strong>uvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dvec2</strong> <strong>dvec3</strong> <strong>dvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat2</strong> <strong>mat3</strong> <strong>mat4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat2x2</strong> <strong>mat2x3</strong> <strong>mat2x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat3x2</strong> <strong>mat3x3</strong> <strong>mat3x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>mat4x2</strong> <strong>mat4x3</strong> <strong>mat4x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat2</strong> <strong>dmat3</strong> <strong>dmat4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat2x2</strong> <strong>dmat2x3</strong> <strong>dmat2x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat3x2</strong> <strong>dmat3x3</strong> <strong>dmat3x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>dmat4x2</strong> <strong>dmat4x3</strong> <strong>dmat4x4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>lowp</strong> <strong>mediump</strong> <strong>highp</strong> <strong>precision</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler1D</strong> <strong>sampler1DShadow</strong> <strong>sampler1DArray</strong> <strong>sampler1DArrayShadow</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>isampler1D</strong> <strong>isampler1DArray</strong> <strong>usampler1D</strong> <strong>usampler1DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2D</strong> <strong>sampler2DShadow</strong> <strong>sampler2DArray</strong> <strong>sampler2DArrayShadow</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>isampler2D</strong> <strong>isampler2DArray</strong> <strong>usampler2D</strong> <strong>usampler2DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2DRect</strong> <strong>sampler2DRectShadow</strong> <strong>isampler2DRect</strong> <strong>usampler2DRect</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2DMS</strong> <strong>isampler2DMS</strong> <strong>usampler2DMS</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler2DMSArray</strong> <strong>isampler2DMSArray</strong> <strong>usampler2DMSArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler3D</strong> <strong>isampler3D</strong> <strong>usampler3D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>samplerCube</strong> <strong>samplerCubeShadow</strong> <strong>isamplerCube</strong> <strong>usamplerCube</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>samplerCubeArray</strong> <strong>samplerCubeArrayShadow</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>isamplerCubeArray</strong> <strong>usamplerCubeArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>samplerBuffer</strong> <strong>isamplerBuffer</strong> <strong>usamplerBuffer</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image1D</strong> <strong>iimage1D</strong> <strong>uimage1D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image1DArray</strong> <strong>iimage1DArray</strong> <strong>uimage1DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2D</strong> <strong>iimage2D</strong> <strong>uimage2D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DArray</strong> <strong>iimage2DArray</strong> <strong>uimage2DArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DRect</strong> <strong>iimage2DRect</strong> <strong>uimage2DRect</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DMS</strong> <strong>iimage2DMS</strong> <strong>uimage2DMS</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image2DMSArray</strong> <strong>iimage2DMSArray</strong> <strong>uimage2DMSArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>image3D</strong> <strong>iimage3D</strong> <strong>uimage3D</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>imageCube</strong> <strong>iimageCube</strong> <strong>uimageCube</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>imageCubeArray</strong> <strong>iimageCubeArray</strong> <strong>uimageCubeArray</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>imageBuffer</strong> <strong>iimageBuffer</strong> <strong>uimageBuffer</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>struct</strong></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The following are the keywords reserved for future use.
+Using them will result in a compile-time error:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>common</strong> <strong>partition</strong> <strong>active</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>asm</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>class</strong> <strong>union</strong> <strong>enum</strong> <strong>typedef</strong> <strong>template</strong> <strong>this</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>resource</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>goto</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>inline</strong> <strong>noinline</strong> <strong>public</strong> <strong>static</strong> <strong>extern</strong> <strong>external</strong> <strong>interface</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>long</strong> <strong>short</strong> <strong>half</strong> <strong>fixed</strong> <strong>unsigned</strong> <strong>superp</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>input</strong> <strong>output</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>hvec2</strong> <strong>hvec3</strong> <strong>hvec4</strong> <strong>fvec2</strong> <strong>fvec3</strong> <strong>fvec4</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>filter</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sizeof</strong> <strong>cast</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>namespace</strong> <strong>using</strong></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p><strong>sampler3DRect</strong></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>In addition, all identifiers containing two consecutive underscores (__)
+are reserved for use by underlying software layers.
+Defining such a name in a shader does not itself result in an error, but may
+result in unintended behaviors that stem from having multiple definitions of
+the same name.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="identifiers">3.7. Identifiers</h3>
+<div class="paragraph">
+<p>Identifiers are used for variable names, function names, structure names,
+and field selectors (field selectors select components of
+<code><a href="#vector-components">vectors</a></code> and <code><a href="#matrix-components">matrices</a></code>,
+similarly to structure members).
+Identifiers have the form:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>identifier</em> : </dt>
+<dd>
+<p><em>nondigit</em><br>
+<em>identifier</em> <em>nondigit</em><br>
+<em>identifier</em> <em>digit</em></p>
+</dd>
+<dt class="hdlist1"><em>nondigit</em> : one of </dt>
+<dd>
+<p><strong>_</strong> <strong>a b c d e f g h i j k l m n o p q r s t u v w x y z</strong><br>
+<strong>A B C D E F G H I J K L M N O P Q R S T U V W X Y Z</strong></p>
+</dd>
+<dt class="hdlist1"><em>digit</em> : one of </dt>
+<dd>
+<p><strong>0 1 2 3 4 5 6 7 8 9</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Identifiers starting with &#8220;gl_&#8221; are reserved for use by OpenGL, and
+in general, may not be declared in a shader;
+this results in a compile-time error.
+However, as noted in the specification, there are some cases where
+previously declared variables can be redeclared, and predeclared &#8220;gl_&#8221;
+names are allowed to be redeclared in a shader only for these specific
+purposes.</p>
+</div>
+<div class="paragraph">
+<p>Implementations must support identifier lengths of up to 1024 characters.
+Implementations are allowed to generate an error for an identifier of length
+greater than 1024 characters, but are also allowed to support lengths
+greater than 1024.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="definitions">3.8. Definitions</h3>
+<div class="paragraph">
+<p>Some language rules described below depend on the following definitions.</p>
+</div>
+<div class="sect3">
+<h4 id="static-use">3.8.1. Static Use</h4>
+<div class="paragraph">
+<p>A shader contains a <em>static use</em> of a variable <em>x</em> if, after preprocessing,
+the shader contains a statement that would access any part of <em>x</em>,
+whether or not flow of control will cause that statement to be executed.
+Such a variable is referred to as being <em>statically used</em>. If the access is a
+write then <em>x</em> is further said to be <em>statically assigned</em>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="dynamically-uniform-expressions-and-uniform-control-flow">3.8.2. Dynamically Uniform Expressions and Uniform Control Flow</h4>
+<div class="paragraph">
+<p>Some operations require an expression to be <em>dynamically uniform</em>, or that
+it be located in <em>uniform control flow</em>.
+These requirements are defined by the following set of definitions.</p>
+</div>
+<div class="paragraph">
+<p>An <em>invocation</em> is a single execution of <em>main()</em> for a particular stage,
+operating only on the amount of data explicitly exposed within that stage&#8217;s
+shaders.
+(Any implicit operation on additional instances of data would comprise
+additional invocations.) For example, in compute execution models, a single
+invocation operates only on a single work item, or, in a vertex execution
+model, a single invocation operates only on a single vertex.</p>
+</div>
+<div class="paragraph">
+<p>An <em>invocation group</em> is the complete set of invocations collectively
+processing a particular compute workgroup or graphical operation, where the
+scope of a "graphical operation" is implementation-dependent, but at least
+as large as a single triangle or patch, and at most as large as a single
+rendering command, as defined by the client API.</p>
+</div>
+<div class="paragraph">
+<p>Within a single invocation, a single shader statement can be executed
+multiple times, giving multiple <em>dynamic instances</em> of that instruction.
+This can happen when the instruction is executed in a loop, or in a function
+called from multiple call sites, or combinations of multiple of these.
+Different loop iterations and different dynamic function-call-site chains
+yield different dynamic instances of such an instruction.
+Dynamic instances are distinguished by their control-flow path within an
+invocation, not by which invocation executed it.
+That is, different invocations of <em>main()</em> execute the same dynamic
+instances of an instruction when they follow the same control-flow path.</p>
+</div>
+<div class="paragraph">
+<p>An expression is _dynamically uniform for a dynamic instance consuming it
+when its value is the same for all invocations (in the invocation group)
+that execute that dynamic instance.</p>
+</div>
+<div class="paragraph">
+<p><em>Uniform control flow</em> (or converged control flow) occurs when all
+invocations in the invocation group execute the same control-flow path (and
+hence the same sequence of dynamic instances of instructions).
+Uniform control flow is the initial state at the entry into <em>main()</em>, and
+lasts until a conditional branch takes different control paths for different
+invocations (non-uniform or divergent control flow).
+Such divergence can reconverge, with all the invocations once again
+executing the same control-flow path, and this re-establishes the existence
+of uniform control flow.
+If control flow is uniform upon entry into a selection or loop, and all
+invocations in the invocation group subsequently leave that selection or
+loop, then control flow reconverges to be uniform.</p>
+</div>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">main()
+{
+    <span class="predefined-type">float</span> a = ...; <span class="comment">// this is uniform control flow</span>
+    <span class="keyword">if</span> (a &lt; b) {   <span class="comment">// this expression is true for some fragments, not all</span>
+        ...;       <span class="comment">// non-uniform control flow</span>
+    } <span class="keyword">else</span> {
+        ...;       <span class="comment">// non-uniform control flow</span>
+    }
+    ...;           <span class="comment">// uniform control flow again</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Note that constant expressions are trivially dynamically uniform.
+It follows that typical loop counters based on these are also dynamically
+uniform.</p>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="variables-and-types">4. Variables and Types</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>All variables and functions must be declared before being used.
+Variable and function names are identifiers.</p>
+</div>
+<div class="paragraph">
+<p>There are no default types.
+All variable and function declarations must have a declared type, and
+optionally qualifiers.
+A variable is declared by specifying its type followed by one or more names
+separated by commas.
+In many cases, a variable can be initialized as part of its declaration by
+using the assignment operator (<strong>=</strong>).</p>
+</div>
+<div class="paragraph">
+<p>User-defined types may be defined using <strong>struct</strong> to aggregate a list of
+existing types into a single name.</p>
+</div>
+<div class="paragraph">
+<p>The OpenGL Shading Language is type safe.
+There are some implicit conversions between types.
+Exactly how and when this can occur is described in section
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; and as referenced by other
+sections in this specification.</p>
+</div>
+<div class="sect2">
+<h3 id="basic-types">4.1. Basic Types</h3>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>A <em>basic type</em> is a type defined by a keyword in the language.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The OpenGL Shading Language supports the following basic data types, grouped as follows.</p>
+</div>
+<div class="sect3">
+<h4 id="_transparent_types">4.1.1. Transparent Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>void</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for functions that do not return a value</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bool</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a conditional type, taking on values of true or false</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>int</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a signed integer</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uint</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">an unsigned integer</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>float</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point scalar</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>double</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point scalar</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component single-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component single-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component single-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dvec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component double-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dvec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component double-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dvec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component double-precision floating-point vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bvec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component Boolean vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bvec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component Boolean vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>bvec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component Boolean vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component signed integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component signed integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component signed integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a two-component unsigned integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a three-component unsigned integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a four-component unsigned integer vector</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 2 × 2 single-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 3 × 3 single-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 4 × 4 single-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>mat2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 2 columns and 3 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 2 columns and 4 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 3 columns and 2 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>mat3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 3 columns and 4 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 4 columns and 2 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a single-precision floating-point matrix with 4 columns and 3 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>mat4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 2 × 2 double-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 3 × 3 double-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a 4 × 4 double-precision floating-point matrix</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>dmat2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point matrix with 2 columns and 3 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point matrix with 2 columns and 4 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point matrix with 3 columns and 2 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>dmat3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point matrix with 3 columns and 4 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point matrix with 4 columns and 2 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a double-precision floating-point matrix with 4 columns and 3 rows</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as a <strong>dmat4</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Note that where the following tables say &#8220;accessing a texture&#8221;, the
+<strong>sampler*</strong> opaque types access textures, and the <strong>image*</strong> opaque types
+access images, of a specified type.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="_floating_point_opaque_types">4.1.2. Floating-Point Opaque Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler1D</strong><br>
+  <strong>image1D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 1D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler1DShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 1D depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler1DArray</strong><br>
+  <strong>image1DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 1D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler1DArrayShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 1D array depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2D</strong><br>
+  <strong>image2D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DArray</strong><br>
+  <strong>image2DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DArrayShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D array depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DMS</strong><br>
+  <strong>image2DMS</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D multisample texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DMSArray</strong><br>
+  <strong>image2DMSArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 2D multisample array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DRect</strong><br>
+  <strong>image2DRect</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a rectangle texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler2DRectShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a rectangle texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sampler3D</strong><br>
+  <strong>image3D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a 3D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCube</strong><br>
+  <strong>imageCube</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube mapped texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCubeShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube map depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCubeArray</strong><br>
+  <strong>imageCubeArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube map array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerCubeArrayShadow</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a cube map array depth texture with comparison</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>samplerBuffer</strong><br>
+  <strong>imageBuffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing a buffer texture</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="_signed_integer_opaque_types">4.1.3. Signed Integer Opaque Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler1D</strong><br>
+  <strong>iimage1D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 1D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler1DArray</strong><br>
+  <strong>iimage1DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 1D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2D</strong><br>
+  <strong>iimage2D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DArray</strong><br>
+  <strong>iimage2DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DMS</strong><br>
+  <strong>iimage2DMS</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D multisample texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DMSArray</strong><br>
+  <strong>iimage2DMSArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D multisample array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler2DRect</strong><br>
+  <strong>iimage2DRect</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 2D rectangle texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isampler3D</strong><br>
+  <strong>iimage3D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer 3D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isamplerCube</strong><br>
+  <strong>iimageCube</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer cube mapped texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isamplerCubeArray</strong><br>
+  <strong>iimageCubeArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer cube map array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>isamplerBuffer</strong><br>
+  <strong>iimageBuffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an integer buffer texture</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="_unsigned_integer_opaque_types">4.1.4. Unsigned Integer Opaque Types</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler1D</strong><br>
+  <strong>uimage1D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 1D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler1DArray</strong><br>
+  <strong>uimage1DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 1D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2D</strong><br>
+  <strong>uimage2D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DArray</strong><br>
+  <strong>uimage2DArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DMS</strong><br>
+  <strong>uimage2DMS</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D multisample texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DMSArray</strong><br>
+  <strong>uimage2DMSArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 2D multisample array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler2DRect</strong><br>
+  <strong>uimage2DRect</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer rectangle texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usampler3D</strong><br>
+  <strong>uimage3D</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer 3D texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usamplerCube</strong><br>
+  <strong>uimageCube</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer cube mapped texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usamplerCubeArray</strong><br>
+  <strong>uimageCubeArray</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer cube map array texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>usamplerBuffer</strong><br>
+  <strong>uimageBuffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer buffer texture</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>atomic_uint</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a handle for accessing an unsigned integer atomic counter</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>In addition, a shader can aggregate these basic types using arrays and
+structures to build more complex types.</p>
+</div>
+<div class="paragraph">
+<p>There are no pointer types.</p>
+</div>
+<div class="paragraph">
+<p>In this specification, an <em>aggregate</em> will mean a structure or array.
+(Matrices and vectors are not by themselves aggregates.) Aggregates,
+matrices, and vectors will collectively be referred to as <em>composites</em>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="void">4.1.5. Void</h4>
+<div class="paragraph">
+<p>Functions that do not return a value must be declared as <strong>void</strong>.
+There is no default function return type.
+The keyword <strong>void</strong> cannot be used in any other declarations (except for
+empty formal or actual parameter lists), or a compile-time error results.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="booleans">4.1.6. Booleans</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>A <em>boolean type</em> is any boolean scalar or vector type (<strong>bool</strong>, <strong>bvec2</strong>,
+<strong>bvec3</strong>, <strong>bvec4</strong>)</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>To make conditional execution of code easier to express, the type <strong>bool</strong> is
+supported.
+There is no expectation that hardware directly supports variables of this
+type.
+It is a genuine Boolean type, holding only one of two values meaning either
+true or false.
+Two keywords <strong>true</strong> and <strong>false</strong> can be used as literal Boolean constants.
+Booleans are declared and optionally initialized as in the follow example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">bool</span> success;      <span class="comment">// declare &quot;success&quot; to be a Boolean</span>
+<span class="predefined-type">bool</span> done = <span class="predefined-constant">false</span>; <span class="comment">// declare and initialize &quot;done&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Expressions used for conditional jumps (<strong>if</strong>, <strong>for</strong>, <strong>?:</strong>, <strong>while</strong>,
+<strong>do</strong>-<strong>while</strong>) must evaluate to the type <strong>bool</strong>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="integers">4.1.7. Integers</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definitions</dt>
+<dd>
+<p>An <em>integral type</em> is any signed or unsigned, scalar or vector integer type.
+It excludes arrays and structures.</p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>A <em>scalar integral type</em> is a scalar signed or unsigned integer type:</p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>A <em>vector integral type</em> is a vector of signed or unsigned integers:</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Signed and unsigned integer variables are fully supported.
+In this document, the term <em>integer</em> is meant to generally include both
+signed and unsigned integers.
+Unsigned
+integers have exactly 32 bits of precision.
+Signed
+integers use 32 bits, including a sign bit, in two&#8217;s complement form.</p>
+</div>
+<div class="paragraph">
+<p>Addition, subtraction, and shift
+operations resulting in overflow or
+underflow will not cause any exception, nor will they saturate, rather they
+will &#8220;wrap&#8221; to yield the low-order
+32 bits of the result.
+Division and multiplication operations resulting in overflow or underflow
+will not cause any exception but will result in an undefined value.</p>
+</div>
+<div class="paragraph">
+<p>Integers are declared and optionally initialized with integer expressions,
+as in the following example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> i, j = <span class="integer">42</span>; <span class="comment">// default integer literal type is int</span>
+uint k = <span class="integer">3</span>u;   <span class="comment">// &quot;u&quot; establishes the type as uint</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Literal integer constants can be expressed in decimal (base 10), octal (base
+8), or hexadecimal (base 16) as follows.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>integer-constant</em> : </dt>
+<dd>
+<p><em>decimal-constant</em> <em>integer-suffix<sub>opt</sub></em><br>
+<em>octal-constant</em> <em>integer-suffix<sub>opt</sub></em><br>
+<em>hexadecimal-constant</em> <em>integer-suffix<sub>opt</sub></em></p>
+</dd>
+<dt class="hdlist1"><em>integer-suffix</em> : one of </dt>
+<dd>
+<p><strong>u</strong> <strong>U</strong></p>
+</dd>
+<dt class="hdlist1"><em>decimal-constant</em> : </dt>
+<dd>
+<p><em>nonzero-digit</em><br>
+<em>decimal-constant</em> <em>digit</em></p>
+</dd>
+<dt class="hdlist1"><em>octal-constant</em> : </dt>
+<dd>
+<p><strong>0</strong><br>
+<em>octal-constant</em> <em>octal-digit</em></p>
+</dd>
+<dt class="hdlist1"><em>hexadecimal-constant</em> : </dt>
+<dd>
+<p><strong>0x</strong> <em>hexadecimal-digit</em><br>
+<strong>0X</strong> <em>hexadecimal-digit</em><br>
+<em>hexadecimal-constant</em> <em>hexadecimal-digit</em></p>
+</dd>
+<dt class="hdlist1"><em>digit</em> : </dt>
+<dd>
+<p><strong>0</strong><br>
+<em>nonzero-digit</em></p>
+</dd>
+<dt class="hdlist1"><em>nonzero-digit</em> : one of </dt>
+<dd>
+<p><strong>1 2 3 4 5 6 7 8 9</strong></p>
+</dd>
+<dt class="hdlist1"><em>octal-digit</em> : one of </dt>
+<dd>
+<p><strong>0 1 2 3 4 5 6 7</strong></p>
+</dd>
+<dt class="hdlist1"><em>hexadecimal-digit</em> : one of </dt>
+<dd>
+<p><strong>0 1 2 3 4 5 6 7 8 9<br>
+a b c d e f<br>
+A B C D E F</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>No white space is allowed between the digits of an integer constant,
+including after the leading <strong>0</strong> or after the leading <strong>0x</strong> or <strong>0X</strong> of a
+constant, or before the suffix <strong>u</strong> or <strong>U</strong>.
+When tokenizing, the maximal token matching the above will be recognized
+before a new token is started.
+When the suffix <strong>u</strong> or <strong>U</strong> is present, the literal has type <strong>uint</strong>,
+otherwise the type is <strong>int</strong>.
+A leading unary minus sign (-) is interpreted as an arithmetic unary
+negation, not as part of the constant.
+Hence, literals themselves are always expressed with non-negative syntax,
+though they could result in a negative value.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to provide a literal integer whose bit pattern
+cannot fit in 32 bits.
+The bit pattern of the literal is always used unmodified.
+So a signed literal whose bit pattern includes a set sign bit creates a
+negative value.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="integer">1</span>             <span class="comment">// OK. Signed integer, value 1</span>
+<span class="integer">1</span>u            <span class="comment">// OK. Unsigned integer, value 1</span>
+-<span class="integer">1</span>            <span class="comment">// OK. Unary minus applied to signed integer.</span>
+              <span class="comment">// result is a signed integer, value -1</span>
+-<span class="integer">1</span>u           <span class="comment">// OK. Unary minus applies to unsigned integer.</span>
+              <span class="comment">// Result is an unsigned integer, value 0xffffffff</span>
+<span class="hex">0xA0000000</span>    <span class="comment">// OK. 32-bit signed hexadecimal</span>
+<span class="hex">0xABcdEF00</span>u   <span class="comment">// OK. 32-bit unsigned hexadecimal</span>
+<span class="hex">0xffffffff</span>    <span class="comment">// OK. Signed integer, value -1</span>
+<span class="hex">0x80000000</span>    <span class="comment">// OK. Evaluates to -2147483648</span>
+<span class="hex">0xffffffff</span>u   <span class="comment">// OK. Unsigned integer, value 0xffffffff</span>
+<span class="hex">0xfffffffff</span>   <span class="comment">// Error: needs more than 32 bits</span>
+<span class="integer">3000000000</span>    <span class="comment">// OK. A signed decimal literal taking 32 bits.</span>
+              <span class="comment">// It evaluates to -1294967296</span>
+<span class="integer">2147483648</span>    <span class="comment">// OK. Evaluates to -2147483648 (the literal set the sign bit)</span>
+<span class="integer">5000000000</span>    <span class="comment">// Error: needs more than 32 bits</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="floats">4.1.8. Floats</h4>
+<div class="paragraph">
+<p>Single-precision and double-precision floating-point variables are available
+for use in a variety of scalar calculations.
+Generally, the term <em>floating-point</em> will refer to both single- and
+double-precision floating-point.
+Floating-point variables are defined as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a, b = <span class="float">1</span><span class="float">.5</span>;    <span class="comment">// single-precision floating-point</span>
+<span class="predefined-type">double</span> c, d = <span class="float">2</span><span class="float">.0</span>LF; <span class="comment">// double-precision floating-point</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>As an input value to one of the processing units, a single-precision or
+double-precision floating-point variable is expected to match the
+corresponding IEEE 754 floating-point definition for precision and dynamic
+range.
+Floating-point variables within a shader are also encoded according to the
+IEEE 754 specification for single-precision floating-point values</p>
+</div>
+<div class="paragraph">
+<p>(logically, not necessarily physically).
+While encodings are logically IEEE 754, operations (addition,
+multiplication, etc.) are not necessarily performed as required by IEEE 754.
+See &#8220;<a href="#range-and-precision">Range and Precision</a>&#8221; for more details on
+precision and usage of NaNs (Not a Number) and Infs (positive or negative
+infinities).</p>
+</div>
+<div class="paragraph">
+<p>Floating-point constants are defined as follows.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>floating-constant</em> : </dt>
+<dd>
+<p><em>fractional-constant</em> <em>exponent-part<sub>opt</sub></em> <em>floating-suffix<sub>opt</sub></em><br>
+<em>digit-sequence</em> <em>exponent-part</em> <em>floating-suffix<sub>opt</sub></em></p>
+</dd>
+<dt class="hdlist1"><em>fractional-constant</em> : </dt>
+<dd>
+<p><em>digit-sequence</em> <strong>.</strong> <em>digit-sequence</em><br>
+<em>digit-sequence</em> <strong>.</strong><br>
+<strong>.</strong> <em>digit-sequence</em></p>
+</dd>
+<dt class="hdlist1"><em>exponent-part</em> : </dt>
+<dd>
+<p><strong>e</strong> <em>sign<sub>opt</sub></em> <em>digit-sequence</em><br>
+<strong>E</strong> <em>sign<sub>opt</sub></em> <em>digit-sequence</em></p>
+</dd>
+<dt class="hdlist1"><em>sign</em> : one of </dt>
+<dd>
+<p><strong>+</strong> <strong>-</strong></p>
+</dd>
+<dt class="hdlist1"><em>digit-sequence</em> : </dt>
+<dd>
+<p><em>digit</em><br>
+<em>digit-sequence</em> <em>digit</em></p>
+</dd>
+<dt class="hdlist1"><em>floating-suffix</em> : one of </dt>
+<dd>
+<p>    <strong>f</strong> <strong>F</strong>
+<strong>lf</strong> <strong>LF</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>A decimal point (<strong>.</strong>) is not needed if the exponent part is present.
+No white space may appear anywhere within a floating-point constant,
+including before a suffix.
+When tokenizing, the maximal token matching the above will be recognized
+before a new token is started.
+When the suffix "lf" or "LF" is present, the literal has type <strong>double</strong>.
+Otherwise, the literal has type <strong>float</strong>.
+A leading unary minus sign (<strong>-</strong>) is interpreted as a unary operator and is
+not part of the floating-point constant.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="vectors">4.1.9. Vectors</h4>
+<div class="paragraph">
+<p>The OpenGL Shading Language includes data types for generic 2-, 3-, and 4-component vectors
+of floating-point values, integers, and Booleans.
+Floating-point vector variables can be used to store colors, normals,
+positions, texture coordinates, texture lookup results and the like.
+Boolean vectors can be used for component-wise comparisons of numeric
+vectors.
+Some examples of vector declarations are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec2 texcoord1, texcoord2;
+vec3 position;
+vec4 myRGBA;
+ivec2 textureLookup;
+bvec3 less;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Initialization of vectors can be done with constructors.
+See &#8220;<a href="#vector-and-matrix-constructors">Vector and Matrix Constructors</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="matrices">4.1.10. Matrices</h4>
+<div class="paragraph">
+<p>The OpenGL Shading Language has built-in types for 2 × 2, 2 × 3, 2 × 4, 3
+× 2, 3 × 3, 3 × 4, 4 × 2, 4 × 3, and 4 ×
+4 matrices of floating-point numbers.
+Matrix types beginning with "<strong>mat</strong>" have single-precision components while
+matrix types beginning with "<strong>dmat</strong>" have double-precision components.
+The first number in the type is the number of columns, the second is the
+number of rows.
+If there is only one number, the matrix is square.
+Example matrix declarations:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2 mat2D;
+mat3 optMatrix;
+mat4 view, projection;
+mat4x4 view; <span class="comment">// an alternate way of declaring a mat4</span>
+mat3x2 m;    <span class="comment">// a matrix with 3 columns and 2 rows</span>
+dmat4 highPrecisionMVP;
+dmat2x4 dm;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Initialization of matrix values is done with constructors (described in
+&#8220;<a href="#vector-and-matrix-constructors">Vector and Matrix Constructors</a>&#8221;) in
+column-major order.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="opaque-types">4.1.11. Opaque Types</h4>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">Definition</dt>
+<dd>
+<p>An <em>opaque type</em> is a type where the internal structure of the type is
+hidden from the language.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The opaque types, as listed in the following sections, declare variables
+that are effectively opaque handles to other objects.
+These objects are accessed through built-in functions, not through direct
+reading or writing of the declared variable.
+They can only be declared as function parameters or in <strong>uniform</strong>-qualified
+variables (see &#8220;<a href="#uniform-variables">Uniform Variables</a>&#8221;).
+The only opaque types that take memory qualifiers are the image types.
+Except for array indexing, structure member selection, and parentheses,
+opaque variables are not allowed to be operands in expressions; such use
+results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>Opaque variables cannot be treated as l-values; hence cannot be used as
+<strong>out</strong> or <strong>inout</strong> function parameters, nor can they be assigned into.
+Any such use results in a compile-time error.
+However, they can be passed as <strong>in</strong> parameters with matching types and
+memory qualifiers.
+They cannot be declared with an initializer.</p>
+</div>
+<div class="paragraph">
+<p>Because a single opaque type declaration effectively declares two objects,
+the opaque handle itself and the object it is a handle to, there is room for
+both a storage qualifier and a memory qualifier.
+The storage qualifier will qualify the opaque handle, while the memory
+qualifier will qualify the object it is a handle to.</p>
+</div>
+<div class="sect4">
+<h5 id="samplers">Samplers</h5>
+<div class="paragraph">
+<p>Sampler types (e.g. <strong>sampler2D</strong>) are opaque types, declared and behaving as
+described above for opaque types.
+When aggregated into arrays within a shader, samplers can only be indexed
+with a dynamically uniform integral expression, otherwise results are
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>Sampler variables are handles to
+one-,
+two-, and three- dimensional textures, cube maps, depth textures (shadowing),
+etc., as enumerated in the basic types tables.
+There are distinct sampler types for each texture target, and for each of
+float, integer, and unsigned integer data types.
+Texture accesses are done through built-in texture functions (described in
+&#8220;<a href="#texture-functions">Texture Functions</a>&#8221;) and samplers are used to
+specify which texture to access and how it is to be filtered.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="images">Images</h5>
+<div class="paragraph">
+<p>Image types are opaque types, declared and behaving as described above for
+opaque types.
+They can be further qualified with memory qualifiers.
+When aggregated into arrays within a shader, images can only be indexed with
+a dynamically uniform integral expression, otherwise results are undefined.</p>
+</div>
+<div class="paragraph">
+<p>Image variables are handles to
+one-,
+two-, or three-dimensional images
+corresponding to all or a portion of a single level of a texture image bound
+to an image unit.
+There are distinct image variable types for each texture target, and for
+each of float, integer, and unsigned integer data types.
+Image accesses should use an image type that matches the target of the
+texture whose level is bound to the image unit, or for non-layered bindings
+of 3D or array images should use the image type that matches the
+dimensionality of the layer of the image (i.e., a layer of 3D, 2DArray,
+Cube, or CubeArray should use
+<strong>image2D</strong>, a layer of 1DArray should use <strong>image1D</strong>, and a layer of 2DMSArray
+should use <strong>image2DMS</strong>).
+If the image target type does not match the bound image in this manner, if
+the data type does not match the bound image, or if the format layout
+qualifier does not match the image unit format as described in section
+8.25
+&#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL Specification</a>, the
+results of image accesses are undefined but cannot include program
+termination.</p>
+</div>
+<div class="paragraph">
+<p>Image variables are used in the image load, store, and atomic functions
+described in &#8220;<a href="#image-functions">Image Functions</a>&#8221; to specify an image to
+access.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="atomic-counters">Atomic Counters</h5>
+<div class="paragraph">
+<p>Atomic counter types (e.g. <strong>atomic_uint</strong>) are opaque handles to counters,
+declared and behaving as described above for opaque types.
+The variables they declare specify which counter to access when using the
+built-in atomic counter functions as described in
+&#8220;<a href="#atomic-counter-functions">Atomic Counter Functions</a>&#8221;.
+They are bound to buffers as described in
+&#8220;<a href="#atomic-counter-layout-qualifiers">Atomic Counter Layout Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Atomic counters aggregated into arrays within a shader can only be indexed
+with dynamically uniform integral expressions, otherwise results are
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>Members of structures cannot be declared as atomic counter types.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="structures">4.1.12. Structures</h4>
+<div class="paragraph">
+<p>User-defined types can be created by aggregating other already defined types
+into a structure using the <strong>struct</strong> keyword.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> light {
+    <span class="predefined-type">float</span> intensity;
+    vec3 position;
+} lightVar;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>In this example, <em>light</em> becomes the name of the new type, and <em>lightVar</em>
+becomes a variable of type <em>light</em>.
+To declare variables of the new type, use its name (without the keyword
+<strong>struct</strong>).</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">light lightVar2;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>More formally, structures are declared as follows.
+However, the definitive grammar is as given in
+&#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221;.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>struct-definition</em> : </dt>
+<dd>
+<p><em>qualifier<sub>opt</sub></em> <strong>struct</strong> name<sub>opt</sub>_ <strong>{</strong> <em>member-list</em> <strong>}</strong>
+<em>declarators<sub>opt</sub></em> <strong>;</strong></p>
+</dd>
+<dt class="hdlist1"><em>member-list</em> : </dt>
+<dd>
+<p><em>member-declaration</em> <strong>;</strong><br>
+<em>member-declaration</em> <em>member-list</em> <strong>;</strong></p>
+</dd>
+<dt class="hdlist1"><em>member-declaration</em> : </dt>
+<dd>
+<p><em>basic-type</em> <em>declarators</em> <strong>;</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>name</em> becomes the user-defined type, and can be used to declare
+variables to be of this new type.
+The <em>name</em> shares the same name space as other variables, types, and
+functions.
+All previously visible variables, types, constructors, or functions with
+that name are hidden.
+The optional <em>qualifier</em> only applies to any <em>declarators</em>, and is not part
+of the type being defined for <em>name</em>.</p>
+</div>
+<div class="paragraph">
+<p>Structures must have at least one member declaration.
+Member declarators may contain precision qualifiers, but use of any other
+qualifier results in a compile-time error.
+Bit fields are not supported.
+Member types must be already defined (there are no forward references).
+A compile-time error results if a member declaration contains an
+initializer.
+Member declarators can contain arrays.
+Such arrays must have a size specified, and the size must be a constant
+integral expression that&#8217;s greater than zero (see
+&#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;).
+Each level of structure has its own name space for names given in member
+declarators; such names need only be unique within that name space.</p>
+</div>
+<div class="paragraph">
+<p>Anonymous structures are not supported.
+Embedded structure definitions are not supported.
+These result in compile-time errors.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> S { <span class="predefined-type">float</span> f; }; <span class="comment">// Allowed: S is defined as a structure.</span>
+
+<span class="keyword">struct</span> T {
+    S;              <span class="comment">// Error: anonymous structures disallowed</span>
+    <span class="keyword">struct</span> { ... }; <span class="comment">// Error: embedded structures disallowed</span>
+    S s;            <span class="comment">// Allowed: nested structure with a name.</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Structures can be initialized at declaration time using constructors, as
+discussed in &#8220;<a href="#structure-constructors">Structure Constructors</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Any restrictions on the usage of a type or qualifier also apply to any
+structure that contains a member of that type or qualifier.
+This also applies to structure members that are structures, recursively.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="arrays">4.1.13. Arrays</h4>
+<div class="paragraph">
+<p>Variables of the same type can be aggregated into arrays by declaring a name
+followed by brackets (<strong>[ ]</strong>) enclosing an optional size.
+When an array size is specified in a declaration, it must be an integral
+constant expression (see &#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;)
+greater than zero.
+Except for the last declared member of a shader storage block (see section
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221;), the size of an array must be
+declared (<em>explicitly sized</em>) before it is indexed with anything other than
+a constant integral expression.
+The size of any array must be declared before passing it as an argument to a
+function.
+Violation of any of these rules result in compile-time errors.
+It is legal to declare an array without a size (<em>unsized</em>) and then later
+redeclare the same name as an array of the same type and specify a size, or
+index it only with constant integral expressions (<em>implicitly sized</em>).
+However, unless noted otherwise, blocks cannot be redeclared; an unsized
+array member in a user-declared block cannot be sized by a block redeclaration.
+It is a compile-time error to declare an array with a size, and then later
+(in the same shader) index the same array with a constant integral
+expression greater than or equal to the declared size.
+It is a compile-time error to redeclare an unsized array with a size equal
+to or smaller than any index used earlier in the shader to index the array.
+It is also a compile-time error to index an array with a negative constant
+expression.
+Arrays declared as formal parameters in a function declaration must specify
+a size.
+Undefined behavior results from indexing an array with a non-constant
+expression that&#8217;s greater than or equal to the array&#8217;s size or less than 0.
+Arrays only have a single dimension (a single entry within "[ ]"), however,
+arrays of arrays can be declared.
+All types (basic types, structures, arrays) can be formed into an array.</p>
+</div>
+<div class="paragraph">
+<p>All arrays are inherently homogeneous; made of elements all having the same
+type and size, with one exception.
+The exception is a shader storage block having an unsized array as its last
+member (<em>run-time sized</em>); an array can be formed from such a shader storage
+block, even if the storage blocks have differing lengths for their last
+member.</p>
+</div>
+<div class="paragraph">
+<p>Some examples are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> frequencies[<span class="integer">3</span>];
+uniform vec4 lightPosition[<span class="integer">4</span>];
+light lights[];
+<span class="directive">const</span> <span class="predefined-type">int</span> numLights = <span class="integer">2</span>;
+light lights[numLights];
+
+<span class="comment">// a shader storage block, introduced in section 4.3.7 &quot;Buffer Variables&quot;</span>
+buffer b {
+    <span class="predefined-type">float</span> u[]; <span class="comment">// an error, unless u gets statically sized by link time</span>
+    vec4 v[];  <span class="comment">// okay, v will be sized dynamically, if not statically</span>
+} name[<span class="integer">3</span>];     <span class="comment">// when the block is arrayed, all u will be the same size,</span>
+               <span class="comment">// but not necessarily all v, if sized dynamically</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>An array type can be formed by specifying non-array type followed by an
+array specifier.
+All dimensions of such an array specifier must include a size.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>]    <span class="comment">// an array of size [5] of float</span>
+<span class="predefined-type">float</span>[<span class="integer">2</span>][<span class="integer">3</span>] <span class="comment">// an array of size [2][3] of float, not size [3] of float[2]</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This type can be used anywhere any other type can be used, including as the
+return value from a function</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>] foo() { }</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>as a constructor of an array:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>as an unnamed parameter:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> foo(<span class="predefined-type">float</span>[<span class="integer">5</span>])</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and as an alternate way of declaring a variable or function parameter:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span>[<span class="integer">5</span>] a;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Arrays can have initializers formed from array constructors:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[<span class="integer">5</span>] = <span class="predefined-type">float</span>[<span class="integer">5</span>](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+<span class="predefined-type">float</span> a[<span class="integer">5</span>] = <span class="predefined-type">float</span>[](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);  <span class="comment">// same thing</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>An array of arrays can be declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 a[<span class="integer">3</span>][<span class="integer">2</span>]; <span class="comment">// size-3 array of size-2 array of vec4</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>which declares a one-dimensional array of size 3 of one-dimensional arrays
+of size 2 of <strong>vec4</strong>.
+The following declarations do the same thing:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4[<span class="integer">2</span>] a[<span class="integer">3</span>]; <span class="comment">// size-3 array of size-2 array of vec4</span>
+vec4[<span class="integer">3</span>][<span class="integer">2</span>] a; <span class="comment">// size-3 array of size-2 array of vec4</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When in transparent memory (like in a uniform block), the layout is that the
+inner-most (right-most in declaration) dimensions iterate faster than the
+outer dimensions.
+That is, for the above, the order in memory would be:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>Low address : a[0][0] : a[0][1] : a[1][0] : a[1][1] : a[2][0] : a[2][1]
+: High address</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The type of <em>a</em> needed for both constructors and nameless parameters is
+&#8220;vec4[3][2]&#8221;:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 b[<span class="integer">2</span>] = vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">0</span><span class="float">.1</span>));
+vec4[<span class="integer">3</span>][<span class="integer">2</span>] a = vec4[<span class="integer">3</span>][<span class="integer">2</span>](b, b, b);        <span class="comment">// constructor</span>
+<span class="directive">void</span> foo(vec4[<span class="integer">3</span>][<span class="integer">2</span>]); <span class="comment">// prototype with unnamed parameter</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Alternatively, the initializer-list syntax can be used to initialize an
+array of arrays:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 a[<span class="integer">3</span>][<span class="integer">2</span>] = { vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.0</span>)),
+                 vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.0</span>)),
+                 vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.0</span>)) };</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Unsized arrays can be explicitly sized by an initializer at declaration
+time:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[<span class="integer">5</span>];
+...
+<span class="predefined-type">float</span> b[] = a;  <span class="comment">// b is explicitly size 5</span>
+<span class="predefined-type">float</span> b[<span class="integer">5</span>] = a; <span class="comment">// means the same thing</span>
+<span class="predefined-type">float</span> b[] = <span class="predefined-type">float</span>[](<span class="integer">1</span>,<span class="integer">2</span>,<span class="integer">3</span>,<span class="integer">4</span>,<span class="integer">5</span>); <span class="comment">// also explicitly sizes to 5</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>However, it is a compile-time error to assign to an unsized array.
+Note, this is a rare case that initializers and assignments appear to have
+different semantics.
+For arrays of arrays, any unsized dimension is explicitly sized by the
+initializer:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 a[][] = { vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.0</span>)), <span class="comment">// okay, size to a[3][2]</span>
+               vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.0</span>)),
+               vec4[<span class="integer">2</span>](vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.0</span>)) };</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Arrays know the number of elements they contain.
+This can be obtained by using the <strong>length</strong>() method:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[<span class="integer">5</span>];
+a.length(); <span class="comment">// returns 5</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This returns a type <strong>int</strong>.
+If an array has been explicitly sized, the value returned by the <strong>length</strong>()
+method is a constant expression.
+If an array has not been explicitly sized and is the last declared member of
+a shader storage block, the value returned will not be a constant expression
+and will be determined at runtime based on the size of the buffer object
+providing storage for the block.
+Such arrays are runtime sized.
+For runtime-sized arrays, the value returned by the <strong>length</strong>() method will be
+undefined if the array is contained in an array of shader storage blocks
+that is indexed with a non-constant expression less than zero or greater
+than or equal to the number of blocks in the array.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>length</strong>() method cannot be called on an array that is not runtime sized
+and also has not yet been explicitly sized;
+this results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>When the <strong>length</strong>() method returns a compile-time constant, the expression the
+<strong>length</strong>() method is applied to cannot contain any side effects, such as writes
+to l-values within the expression, or function calls that themselves have side
+effects: only the compile-time constant length itself need be computed.
+Behavior and results, including any compile-time error reporting,
+are undefined if the expression contains other effects.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a, b;
+<span class="directive">const</span> <span class="predefined-type">int</span> s = <span class="predefined-type">float</span>[<span class="integer">2</span>](a=<span class="float">3</span><span class="float">.0</span>, ++b).length(); <span class="comment">// illegal side effects</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>length</strong>() method works equally well for arrays of arrays:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 a[<span class="integer">3</span>][<span class="integer">2</span>];
+a.length()    <span class="comment">// this is 3</span>
+a[x].length() <span class="comment">// this is 2</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When the <strong>length</strong>() method returns a compile-time constant, the expression
+in brackets (<em>x</em> above) will be parsed and subjected to the rules required for
+array indexes, but the array will not be dereferenced.
+Thus, behavior is well defined even if the run-time value of the expression
+is out of bounds, as long as the expression contains no side effects.</p>
+</div>
+<div class="paragraph">
+<p>When the <strong>length</strong>() method returns a run-time value
+(not a compile-time constant), the array will be
+dereferenced.
+E.g., if <em>x</em> is not a compile-time constant and is out of range, an undefined
+value results.
+More generally, all involved expressions are fully evaluated and executed.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// for a compile time-sized array b containing a member array a:</span>
+b[x+<span class="integer">3</span>].a.length(); <span class="comment">// b is never dereferenced, x+3 is evaluated and checked</span>
+b[++x].a.length(); <span class="comment">// not allowed; results are undefined</span>
+
+<span class="comment">// for an array s of a shader storage object (run-time sized) containing a member array a:</span>
+s[++x].a.length(); <span class="comment">// s is dereferenced; ++x needs to be a valid index</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For implicitly-sized or run-time-sized arrays, only the outer-most dimension
+can be lacking a size.
+A type that includes an unknown array size cannot be formed into an array
+until it gets an explicit size, except for shader storage blocks where the
+only unsized array member is the last member of the block.</p>
+</div>
+<div class="paragraph">
+<p>In a shader storage block, the last member may be declared without an
+explicit size.
+In this case, the effective array size is inferred at run-time from the size
+of the data store backing the interface block.
+Such run-time-sized arrays may be indexed with general integer expressions.
+However, it is a compile-time error to pass them as an argument to a
+function or index them with a negative constant expression.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="implicit-conversions">4.1.14. Implicit Conversions</h4>
+<div class="paragraph">
+<p>In some situations, an expression and its type will be implicitly converted
+to a different type.
+The following table shows all allowed implicit conversions:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Type of expression</th>
+<th class="tableblock halign-left valign-top">Can be implicitly converted to</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>int</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uint</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>int</strong><br>
+  <strong>uint</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>float</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>int</strong><br>
+  <strong>uint</strong><br>
+  <strong>float</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>double</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uvec4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec2</strong><br>
+  <strong>uvec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec3</strong><br>
+  <strong>uvec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec4</strong><br>
+  <strong>uvec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vec4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec2</strong><br>
+  <strong>uvec2</strong><br>
+  <strong>vec2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dvec2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec3</strong><br>
+  <strong>uvec3</strong><br>
+  <strong>vec3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dvec3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>ivec4</strong><br>
+  <strong>uvec4</strong><br>
+  <strong>vec4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dvec4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2x3</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat2x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat2x4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3x2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat3x4</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat3x4</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x2</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4x2</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mat4x3</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>dmat4x3</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>There are no implicit array or structure conversions.
+For example, an array of <strong>int</strong> cannot be implicitly converted to an array of
+<strong>float</strong>.</p>
+</div>
+<div class="paragraph">
+<p>When an implicit conversion is done, it is the same conversion that would be
+done under explicit conversion, using a constructor.
+The explicit conversions via constructors are described in
+<a href="#conversion-and-scalar-constructors">Conversion and Scalar Constructors</a>.</p>
+</div>
+<div class="paragraph">
+<p>When performing implicit conversion for binary operators, there may be
+multiple data types to which the two operands can be converted.
+For example, when adding an <strong>int</strong> value to a <strong>uint</strong> value, both values can
+be implicitly converted to <strong>uint</strong>, <strong>float</strong>, and <strong>double</strong>.
+In such cases, a floating-point type is chosen if either operand has a
+floating-point type.
+Otherwise, an unsigned integer type is chosen if either operand has an
+unsigned integer type.
+Otherwise, a signed integer type is chosen.
+If operands can be implicitly converted to multiple data types deriving from
+the same base data type, the type with the smallest component size is used.</p>
+</div>
+<div class="paragraph">
+<p>The conversions in the table above are done only as indicated by other
+sections of this specification.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="initializers">4.1.15. Initializers</h4>
+<div class="paragraph">
+<p>At declaration, an initial value for a variable may be provided, specified
+as an equals (=) followed by an initializer.
+The initializer is either an <em>assignment-expression</em> or a list of
+initializers enclosed in curly braces.
+The grammar for the initializer is:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>initializer</em> : </dt>
+<dd>
+<p><em>assignment-expression</em><br>
+<strong>{</strong> <em>initializer-list</em> <strong>}</strong><br>
+<strong>{</strong> <em>initializer-list</em> <strong>,</strong> <strong>}</strong></p>
+</dd>
+<dt class="hdlist1"><em>initializer-list</em> : </dt>
+<dd>
+<p><em>initializer</em><br>
+<em>initializer-list</em> , <em>initializer</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <em>assignment-expression</em> is a normal expression except that a comma (<strong>,</strong>)
+outside parentheses is interpreted as the end of the initializer, not as the
+sequence operator.
+As explained in more detail below, this allows creation of nested
+initializers: The variable type and its initializer must exactly match in
+terms of nesting, number of components/elements/members present at each
+level, and types of components/elements/members.
+An <em>assignment-expression</em> at global scope can include calls to user-defined
+functions.</p>
+</div>
+<div class="paragraph">
+<p>An <em>assignment-expression</em> in an initializer must be either the same type as
+the object it initializes or be a type that can be converted to the object&#8217;s
+type according to &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221;.
+Since these include constructors, a composite variable can be initialized by
+either a constructor or an initializer list; and an element in an
+initializer list can be a constructor.</p>
+</div>
+<div class="paragraph">
+<p>If an initializer is a list of initializers enclosed in curly braces, the
+variable being declared must be a vector, a matrix, an array, or a
+structure.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> i = { <span class="integer">1</span> }; <span class="comment">// illegal, i is not a composite</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A list of initializers enclosed in a matching set of curly braces is applied
+to one composite.
+This may be the variable being declared or a composite contained in the
+variable being declared.
+Individual initializers from the initializer list are applied to the
+elements/members of the composite, in order.</p>
+</div>
+<div class="paragraph">
+<p>If the composite has a vector type, initializers from the list are applied
+to the components of the vector, in order, starting with component 0.
+The number of initializers must match the number of components.</p>
+</div>
+<div class="paragraph">
+<p>If the composite has a matrix type, initializers from the list must be
+vector initializers and are applied to the columns of the matrix, in order,
+starting with column 0.
+The number of initializers must match the number of columns.</p>
+</div>
+<div class="paragraph">
+<p>If the composite has a structure type, initializers from the list are
+applied to the members of the structure, in the order declared in the
+structure, starting with the first member.
+The number of initializers must match the number of members.</p>
+</div>
+<div class="paragraph">
+<p>Applying these rules, the following matrix declarations are equivalent:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2x2 a = mat2(  vec2( <span class="float">1</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span> ), vec2( <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span> ) );
+mat2x2 b =      { vec2( <span class="float">1</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span> ), vec2( <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span> ) };
+mat2x2 c =      {     { <span class="float">1</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span> },     { <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span> } };</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>All of the following declarations result in a compile-time error.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[<span class="integer">2</span>] = { <span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span> };         <span class="comment">// illegal</span>
+vec2 b = { <span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span> };             <span class="comment">// illegal</span>
+mat3x3 c = { vec3(<span class="float">0</span><span class="float">.0</span>), vec3(<span class="float">1</span><span class="float">.0</span>), vec3(<span class="float">2</span><span class="float">.0</span>), vec3(<span class="float">3</span><span class="float">.0</span>) }; <span class="comment">// illegal</span>
+mat2x2 d = { <span class="float">1</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span> };      <span class="comment">// illegal, can't flatten nesting</span>
+<span class="keyword">struct</span> {
+    <span class="predefined-type">float</span> a;
+    <span class="predefined-type">int</span> b;
+} e = { <span class="float">1</span><span class="float">.2</span>, <span class="integer">2</span>, <span class="integer">3</span> };                    <span class="comment">// illegal</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>In all cases, the inner-most initializer (i.e., not a list of initializers
+enclosed in curly braces) applied to an object must have the same type as
+the object being initialized or be a type that can be converted to the
+object&#8217;s type according to &#8220;<a href="#implicit-conversions">Implicit
+Conversions</a>&#8221;.
+In the latter case, an implicit conversion will be done on the initializer
+before the assignment is done.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> {
+    <span class="predefined-type">float</span> a;
+    <span class="predefined-type">int</span> b;
+} e = { <span class="float">1</span><span class="float">.2</span>, <span class="integer">2</span> }; <span class="comment">// legal, all types match</span>
+<span class="keyword">struct</span> {
+    <span class="predefined-type">float</span> a;
+    <span class="predefined-type">int</span> b;
+} e = { <span class="integer">1</span>, <span class="integer">3</span> };   <span class="comment">// legal, first initializer is converted</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>All of the following declarations result in a compile-time error.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> a = <span class="predefined-constant">true</span>;                         <span class="comment">// illegal</span>
+vec4 b[<span class="integer">2</span>] = { vec4(<span class="float">0</span><span class="float">.0</span>), <span class="float">1</span><span class="float">.0</span> };       <span class="comment">// illegal</span>
+mat4x2 c = { vec3(<span class="float">0</span><span class="float">.0</span>), vec3(<span class="float">1</span><span class="float">.0</span>) };  <span class="comment">// illegal</span>
+
+<span class="keyword">struct</span> S1 {
+    vec4 a;
+    vec4 b;
+};
+
+<span class="keyword">struct</span> {
+    <span class="predefined-type">float</span> s;
+    <span class="predefined-type">float</span> t;
+} d[] = { S1(vec4(<span class="float">0</span><span class="float">.0</span>), vec4(<span class="float">1</span><span class="float">.1</span>)) }; <span class="comment">// illegal</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If an initializer (of either form) is provided for an unsized array, the
+size of the array is determined by the number of top-level (non-nested)
+initializers within the initializer.
+All of the following declarations create arrays explicitly sized with five
+elements:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> a[] = <span class="predefined-type">float</span>[](<span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+<span class="predefined-type">float</span> b[] = { <span class="float">3</span><span class="float">.4</span>, <span class="float">4</span><span class="float">.2</span>, <span class="float">5</span><span class="float">.0</span>, <span class="float">5</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span> };
+<span class="predefined-type">float</span> c[] = a;                          <span class="comment">// c is explicitly size 5</span>
+<span class="predefined-type">float</span> d[<span class="integer">5</span>] = b;                         <span class="comment">// means the same thing</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to have too few or too many initializers in an
+initializer list for the composite being initialized.
+That is, all elements of an array, all members of a structure, all columns
+of a matrix, and all components of a vector must have exactly one
+initializer expression present, with no unconsumed initializers.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="scoping">4.2. Scoping</h3>
+<div class="paragraph">
+<p>The scope of a variable is determined by where it is declared.
+If it is declared outside all function definitions, it has global scope,
+which starts from where it is declared and persists to the end of the shader
+it is declared in.
+If it is declared in a <strong>while</strong> test or a <strong>for</strong> statement, then it is scoped
+to the end of the following sub-statement.
+If it is declared in an <strong>if</strong> or <strong>else</strong> statement, it is scoped to the end of
+that statement.
+(See &#8220;<a href="#selection">Selection</a>&#8221; and &#8220;<a href="#iteration">Iteration</a>&#8221; for the
+location of statements and sub-statements.) Otherwise, if it is declared as
+a statement within a compound statement, it is scoped to the end of that
+compound statement.
+If it is declared as a parameter in a function definition, it is scoped
+until the end of that function definition.
+A function&#8217;s parameter declarations and body together form a single scope
+nested in the global scope.
+The <strong>if</strong> statement&#8217;s expression does not allow new variables to be declared,
+hence does not form a new scope.</p>
+</div>
+<div class="paragraph">
+<p>Within a declaration, the scope of a name starts immediately after the
+initializer if present or immediately after the name being declared if not.
+Several examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> x = <span class="integer">1</span>;
+{
+    <span class="predefined-type">int</span> x = <span class="integer">2</span>, y = x; <span class="comment">// y is initialized to 2</span>
+}
+
+<span class="keyword">struct</span> S
+{
+    <span class="predefined-type">int</span> x;
+};
+
+{
+    S S = S(<span class="integer">0</span>); <span class="comment">// 'S' is only visible as a struct and constructor</span>
+    S;          <span class="comment">// 'S' is now visible as a variable</span>
+}
+
+<span class="predefined-type">int</span> x = x; <span class="comment">// Error if x has not been previously defined.</span>
+           <span class="comment">// If the previous definition of x was in this</span>
+           <span class="comment">// same scope, this causes a redeclaration error.</span>
+
+<span class="predefined-type">int</span> f( <span class="comment">/* nested scope begins here */</span> <span class="predefined-type">int</span> k)
+{
+    <span class="predefined-type">int</span> k = k + <span class="integer">3</span>; <span class="comment">// redeclaration error of the name k</span>
+    ...
+}
+
+<span class="predefined-type">int</span> f(<span class="predefined-type">int</span> k)
+{
+    {
+        <span class="predefined-type">int</span> k = k + <span class="integer">3</span>; <span class="comment">// 2nd k is parameter, initializing nested first k</span>
+        <span class="predefined-type">int</span> m = k;     <span class="comment">// use of new k, which is hiding the parameter</span>
+    }
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For both <strong>for</strong> and <strong>while</strong> loops, the sub-statement itself does not
+introduce a new scope for variable names, so the following has a
+redeclaration compile-time error:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">for</span> ( <span class="comment">/* nested scope begins here */</span> <span class="predefined-type">int</span> i = <span class="integer">0</span>; i &lt; <span class="integer">10</span>; i++) {
+    <span class="predefined-type">int</span> i; <span class="comment">// redeclaration error</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The body of a <strong>do</strong>-<strong>while</strong> loop introduces a new scope lasting only between
+the <strong>do</strong> and <strong>while</strong> (not including the while test expression), whether or
+not the body is simple or compound:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span> i = <span class="integer">17</span>;
+<span class="keyword">do</span>
+    <span class="predefined-type">int</span> i = <span class="integer">4</span>;  <span class="comment">// okay, in nested scope_</span>
+<span class="keyword">while</span> (i == <span class="integer">0</span>); <span class="comment">// i is 17, scoped outside the do-while body</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The statement following a <strong>switch</strong> (&#8230;&#8203;) forms a nested scope.</p>
+</div>
+<div class="paragraph">
+<p>All variable names, structure type names, and function names in a given
+scope share the same name space.
+Function names can be redeclared in the same scope, with the same or
+different parameters, without error.
+An implicitly-sized array can be redeclared in the same scope as an array of
+the same base type.
+Otherwise, within one compilation unit, a declared name cannot be redeclared
+in the same scope; doing so results in a redeclaration compile-time error.
+If a nested scope redeclares a name used in an outer scope, it hides all
+existing uses of that name.
+There is no way to access the hidden name or make it unhidden, without
+exiting the scope that hid it.</p>
+</div>
+<div class="paragraph">
+<p>The built-in functions are scoped in a scope outside the global scope that
+users declare global variables in.
+That is, a shader&#8217;s global scope, available for user-defined functions and
+global variables, is nested inside the scope containing the built-in
+functions.
+When a function name is redeclared in a nested scope, it hides all functions
+declared with that name in the outer scope.
+Function declarations (prototypes) cannot occur inside of functions; they
+must be at global scope, or for the built-in functions, outside the global
+scope, otherwise a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>Shared globals are global variables declared with the same name in
+independently compiled units (shaders) within the same language (i.e., same
+stage, e.g. vertex) that are linked together when making a single program.
+(Globals forming the interface between two different shader languages are
+discussed in other sections.) Shared globals share the same name space, and
+must be declared with the same type.
+They will share the same storage.</p>
+</div>
+<div class="paragraph">
+<p>Shared global arrays must have the same base type and the same explicit
+size.
+An array implicitly sized in one shader can be explicitly sized by another
+shader in the same stage.
+If no shader in a stage has an explicit size for the array, the largest
+implicit size (one more than the largest index used) in that stage is used.
+There is no cross-stage array sizing.
+If there is no static access to an implicitly sized array within the stage
+declaring it, then the array is given a size of 1, which is relevant when
+the array is declared within an interface block that is shared with other
+stages or the application (other unused arrays might be eliminated by the
+optimizer).</p>
+</div>
+<div class="paragraph">
+<p>Shared global scalars must have exactly the same type name and type
+definition.
+Structures must have the same name, sequence of type names, and type
+definitions, and member names to be considered the same type.
+This rule applies recursively for nested or embedded types.
+If a shared global has multiple initializers, the initializers must all be
+constant expressions, and they must all have the same value.
+Otherwise, a link-time error will result.
+(A shared global having only one initializer does not require that
+initializer to be a constant expression.)</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="storage-qualifiers">4.3. Storage Qualifiers</h3>
+<div class="paragraph">
+<p>Variable declarations may have at most one storage qualifier specified in
+front of the type.
+These are summarized as</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Storage Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;none: default&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">local read/write memory, or an input parameter to a
+                      function</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>const</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">a variable whose value cannot be changed</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>in</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">linkage into a shader from a previous stage, variable
+                      is copied in</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>out</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">linkage out of a shader to a subsequent stage,
+                      variable is copied out</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>attribute</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compatibility profile only and vertex language only;
+                      same as <strong>in</strong> when in a vertex shader</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uniform</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">value does not change across the primitive being
+                      processed, uniforms form the linkage between a shader,
+                      OpenGL, and the application</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>varying</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compatibility profile only and vertex and fragment
+                      languages only; same as <strong>out</strong> when in a vertex shader
+                      and same as <strong>in</strong> when in a fragment shader</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>buffer</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">value is stored in a buffer object, and can be read or
+                      written both by shader invocations and the OpenGL
+                      API</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>shared</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compute shader only; variable storage is shared across
+                      all work items in a workgroup</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Some input and output qualified variables can be qualified with at most one
+additional auxiliary storage qualifier:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Auxiliary Storage Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>centroid</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">centroid-based interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sample</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">per-sample interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>patch</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">per-tessellation-patch attributes</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Not all combinations of qualification are allowed.
+Auxiliary storage qualifiers can only be used with the <strong>in</strong> or <strong>out</strong> storage
+qualifiers.
+Additional qualifier rules are defined in upcoming sections.</p>
+</div>
+<div class="paragraph">
+<p>Local variables can only use the <strong>const</strong> storage qualifier (or use no
+storage qualifier).</p>
+</div>
+<div class="paragraph">
+<p>Note that function parameters can use <strong>const</strong>, <strong>in</strong>, and <strong>out</strong> qualifiers,
+but as <em>parameter qualifiers</em>.
+Parameter qualifiers are discussed in
+&#8220;<a href="#function-calling-conventions">Function Calling Conventions</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Function return types and structure members do not use storage qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Initializers in global declarations may only be used in declarations of
+global variables with no storage qualifier, with a <strong>const</strong> qualifier, or
+with a <strong>uniform</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>Global variables without storage qualifiers that are not initialized in
+their declaration or by the application will not be initialized by
+OpenGL, but rather will enter <em>main()</em> with undefined values.</p>
+</div>
+<div class="paragraph">
+<p>When comparing an output from one shader stage to an input of a subsequent
+shader stage, the input and output don&#8217;t match if their auxiliary qualifiers
+(or lack thereof) are not the same.</p>
+</div>
+<div class="sect3">
+<h4 id="default-storage-qualifier">4.3.1. Default Storage Qualifier</h4>
+<div class="paragraph">
+<p>If no qualifier is present on a global variable, then the variable has no
+linkage to the application or shaders running on other pipeline stages.
+For either global or local unqualified variables, the declaration will
+appear to allocate memory associated with the processor it targets.
+This variable will provide read/write access to this allocated memory.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="constant-qualifier">4.3.2. Constant Qualifier</h4>
+<div class="paragraph">
+<p>Named compile-time constants
+or read-only variables
+can be declared using
+the <strong>const</strong> qualifier.
+The <strong>const</strong> qualifier can be used with any of the non-void transparent basic
+data types, as well as with structures and arrays of these.
+It is a compile-time error to write to a <strong>const</strong> variable outside of its
+declaration, so they must be initialized when declared.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> vec3 zAxis = vec3 (<span class="float">0</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span>);
+<span class="directive">const</span> <span class="predefined-type">float</span> ceiling = a + b; <span class="comment">// a and b not necessarily constants</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Structure members may not be qualified with <strong>const</strong>.
+Structure variables can be declared as <strong>const</strong>, and initialized with a
+structure
+constructor or initializer.</p>
+</div>
+<div class="paragraph">
+<p>Initializers for <strong>const</strong> declarations
+at global scope
+must be constant expressions, as defined in
+&#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="constant-expressions">4.3.3. Constant Expressions</h4>
+<div class="paragraph">
+<p>SPIR-V specialization constants are expressed in GLSL as <strong>const</strong> with the
+layout qualifier <strong>constant_id</strong>, as described in
+&#8220;<a href="#specialization-constant-qualifier">Specialization-Constant
+Qualifier.</a>&#8221;</p>
+</div>
+<div class="paragraph">
+<p>A <em>constant expression</em> is one of</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A literal value (e.g. <strong>5</strong> or <strong>true</strong>).</p>
+</li>
+<li>
+<p>A variable declared with the <strong>const</strong> qualifier and an initializer, where
+the initializer is a constant expression.
+This includes both <strong>const</strong> declared with a specialization-constant
+layout qualifier, e.g. <strong>layout</strong>(<strong>constant_id</strong> = &#8230;&#8203;), and those declared
+without a specialization-constant layout qualifier.</p>
+</li>
+<li>
+<p>An expression formed by an operator on operands that are all constant
+expressions, including getting an element of a constant array, or a
+member of a constant structure, or components of a constant vector.
+However, the lowest precedence operators of the sequence operator (<strong>,</strong>)
+and the assignment operators (<strong>=</strong>, <strong>+=</strong>, <strong>&#8230;&#8203;</strong>) are not included in the
+operators that can create a constant expression.
+Also, an array access with a specialization constant as an index does
+not result in a constant expression.</p>
+</li>
+<li>
+<p>Valid use of the <strong>length</strong>() method on an explicitly sized object,
+whether or not the object itself is constant (implicitly sized or
+run-time sized arrays do not return a constant expression).</p>
+</li>
+<li>
+<p>A constructor whose arguments are all constant expressions.</p>
+</li>
+<li>
+<p>For non-specialization constants only: the value returned by certain
+built-in function calls whose arguments are all constant expressions,
+including at least the list below.
+Any other built-in function that does not access memory (not the texture
+lookup functions, image access, atomic counter, etc.), that has a
+non-<strong>void</strong> return type, that has no <strong>out</strong> parameter, and is not a noise
+function might also be considered a constant.
+When a function is called with an argument that is a specialization
+constant, the result is not a constant expression.</p>
+<div class="ulist">
+<ul>
+<li>
+<p>Angle and Trigonometric Functions</p>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>radians</strong></p>
+</li>
+<li>
+<p><strong>degrees</strong></p>
+</li>
+<li>
+<p><strong>sin</strong></p>
+</li>
+<li>
+<p><strong>cos</strong></p>
+</li>
+<li>
+<p><strong>asin</strong></p>
+</li>
+<li>
+<p><strong>acos</strong></p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Exponential Functions</p>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>pow</strong></p>
+</li>
+<li>
+<p><strong>exp</strong></p>
+</li>
+<li>
+<p><strong>log</strong></p>
+</li>
+<li>
+<p><strong>exp2</strong></p>
+</li>
+<li>
+<p><strong>log2</strong></p>
+</li>
+<li>
+<p><strong>sqrt</strong></p>
+</li>
+<li>
+<p><strong>inversesqrt</strong></p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Common Functions</p>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>abs</strong></p>
+</li>
+<li>
+<p><strong>sign</strong></p>
+</li>
+<li>
+<p><strong>floor</strong></p>
+</li>
+<li>
+<p><strong>trunc</strong></p>
+</li>
+<li>
+<p><strong>round</strong></p>
+</li>
+<li>
+<p><strong>ceil</strong></p>
+</li>
+<li>
+<p><strong>mod</strong></p>
+</li>
+<li>
+<p><strong>min</strong></p>
+</li>
+<li>
+<p><strong>max</strong></p>
+</li>
+<li>
+<p><strong>clamp</strong></p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Geometric Functions</p>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>length</strong></p>
+</li>
+<li>
+<p><strong>dot</strong></p>
+</li>
+<li>
+<p><strong>normalize</strong></p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Function calls to user-defined functions (non-built-in functions) cannot
+be used to form constant expressions.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>A <em>constant integral expression</em> is a constant expression that evaluates to
+a scalar signed or unsigned integer.</p>
+</div>
+<div class="paragraph">
+<p>Constant expressions will be evaluated in an invariant way so as to create
+the same value in multiple shaders when the same constant expressions appear
+in those shaders.
+See &#8220;<a href="#the-invariant-qualifier">The Invariant Qualifier</a>&#8221; for more details
+on how to create invariant expressions and
+&#8220;<a href="#precision-qualifiers">Precision Qualifiers</a>&#8221; for detail on how
+expressions are evaluated.</p>
+</div>
+<div class="paragraph">
+<p>Constant expressions respect the <strong>precise</strong> and <strong>invariant</strong> qualifiers but
+will be always be evaluated in an invariant way, independent of the use of
+such qualification, so as to create the same value in multiple shaders when
+the same constant expressions appear in those shaders.
+See &#8220;<a href="#the-invariant-qualifier">The Invariant Qualifier</a>&#8221; and
+&#8220;<a href="#the-precise-qualifier">The Precise Qualifier</a>&#8221; for more details on how
+to create invariant expressions.</p>
+</div>
+<div class="paragraph">
+<p>Non-specialization constant
+expressions may be evaluated by the compiler&#8217;s
+host platform, and are therefore not required to compute the same value that
+the same expression would evaluate to on the shader execution target.
+However, the host must use the same or greater precision than the target
+would use.</p>
+</div>
+<div class="paragraph">
+<p>Specialization-constant expressions are never evaluated by the compiler
+front end, but instead retain the expression&#8217;s operations needed to evaluate
+them later on the host.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="input-variables">4.3.4. Input Variables</h4>
+<div class="paragraph">
+<p>Shader input variables are declared with the <strong>in</strong> storage qualifier.
+They form the input interface between previous stages of the OpenGL
+pipeline and the declaring shader.
+Input variables must be declared at global scope.
+Values from the previous pipeline stage are copied into input variables at
+the beginning of shader execution.
+It is a compile-time error to write to a variable declared as an input.</p>
+</div>
+<div class="paragraph">
+<p>Only the input variables that are
+statically
+read need to be written by the
+previous stage; it is allowed to have superfluous declarations of input
+variables.
+This is shown in the following table.</p>
+</div>
+<table class="tableblock frame-all grid-all fit-content">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top" colspan="2" rowspan="2"><p class="tableblock">Treatment of Mismatched Input Variables</p></td>
+<td class="tableblock halign-left valign-top" colspan="3"><p class="tableblock">Consuming Shader (input variables)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No Declaration</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declared but no Static Use</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declared and Static Use</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top" rowspan="3"><p class="tableblock">Generating Shader (output variables)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">No Declaration</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Link-Time Error</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declared but no Static Use</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed (values are undefined)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Declared and Static Use</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Allowed (values are potentially undefined)</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Consumption errors are based on static use only.
+Compilation may generate a warning, but not an error, for any dynamic use
+the compiler can deduce that might cause consumption of undefined values.</p>
+</div>
+<div class="paragraph">
+<p>See &#8220;<a href="#built-in-variables">Built-In Variables</a>&#8221; for a list of the built-in
+input names.</p>
+</div>
+<div class="paragraph">
+<p>Vertex shader input variables (or attributes) receive per-vertex data.
+It is a compile-time error to use auxiliary storage or interpolation qualifiers
+on a vertex shader input.
+The values copied in are established by the OpenGL API or through the use
+of the layout identifier <strong>location</strong>.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a vertex shader input with, or that
+contains, any of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>A structure</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Example declarations in a vertex shader:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 position;
+in vec3 normal;
+in vec2 texCoord[<span class="integer">4</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is expected that graphics hardware will have a small number of fixed
+vector locations for passing vertex inputs.
+Therefore, the OpenGL Shading Language defines each non-matrix input variable as taking up
+one such vector location.
+There is an implementation-dependent limit on the number of locations that
+can be used, and if this is exceeded it will cause a link-time error.
+(Declared input variables that are not statically used do not count against
+this limit.) A scalar input counts the same amount against this limit as a
+<strong>vec4</strong>, so applications may want to consider packing groups of four
+unrelated float inputs together into a vector to better utilize the
+capabilities of the underlying hardware.
+A matrix input will use up multiple locations.
+The number of locations used will equal the number of columns in the matrix.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control, evaluation, and geometry shader input variables get
+the per-vertex values written out by output variables of the same names in
+the previous active shader stage.
+For these inputs, <strong>centroid</strong> and interpolation qualifiers are allowed, but
+have no effect.
+Since tessellation control, tessellation evaluation, and geometry shaders
+operate on a set of vertices, each input variable (or input block, see
+interface blocks below) needs to be declared as an array.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in <span class="predefined-type">float</span> foo[]; <span class="comment">// geometry shader input for vertex &quot;out float foo&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Each element of such an array corresponds to one vertex of the primitive
+being processed.
+Each array can optionally have a size declared.
+For geometry shaders, the array size will be set by, (or if provided must be
+consistent with) the input <strong>layout</strong> declaration(s) establishing the type of
+input primitive, as described later in &#8220;<a href="#input-layout-qualifiers">Input
+Layout Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Some inputs and outputs are <em>arrayed</em>, meaning that for an interface between
+two shader stages either the input or output declaration requires an extra
+level of array indexing for the declarations to match.
+For example, with the interface between a vertex shader and a geometry
+shader, vertex shader output variables and geometry shader input variables
+of the same name must have matching types, except that the geometry shader
+will have one more array dimension than the vertex shader, to allow for
+vertex indexing.
+If such an arrayed interface variable is not declared with the necessary
+additional input or output array dimension, a link-time error will result.
+Geometry shader inputs, tessellation control shader inputs and outputs, and
+tessellation evaluation inputs all have an additional level of arrayness
+relative to other shader inputs and outputs.
+These inputs and outputs are known as <em>per-vertex-arrayed</em> inputs and
+outputs.
+Component limits for arrayed interfaces (e.g.
+<em>gl_MaxTessControlInputComponents</em>) are limits per vertex, not limits for
+the entire interface.</p>
+</div>
+<div class="paragraph">
+<p>For non-arrayed interfaces (meaning array dimensionally stays the same
+between stages), it is a link-time error if the input variable is not
+declared with the same type, including array dimensionality, as the matching
+output variable.</p>
+</div>
+<div class="paragraph">
+<p>The link-time type-matching rules apply to all declared input and output
+variables, whether or not they are used.</p>
+</div>
+<div class="paragraph">
+<p>Additionally, tessellation evaluation shaders support per-patch input
+variables declared with the <strong>patch</strong> and <strong>in</strong> qualifiers.
+Per-patch input variables are filled with the values of per-patch output
+variables written by the tessellation control shader.
+Per-patch inputs may be declared as one-dimensional arrays, but are not
+indexed by vertex number.
+Applying the <strong>patch</strong> qualifier to inputs can only be done in tessellation
+evaluation shaders.
+As with other input variables, per-patch inputs must be declared using the
+same type and qualification as per-patch outputs from the previous
+(tessellation control) shader stage.
+It is a compile-time error to use <strong>patch</strong> with inputs in any other stage.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a tessellation control, tessellation
+evaluation or geometry shader input with, or that contains, any of the
+following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Fragment shader inputs get per-fragment values, typically interpolated from
+a previous stage&#8217;s outputs.
+The auxiliary storage qualifiers <strong>centroid</strong> and <strong>sample</strong> can also be
+applied, as well as the interpolation qualifiers <strong>flat</strong>, <strong>noperspective</strong>,
+and <strong>smooth.</strong></p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a fragment shader input with, or that
+contains, any of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Fragment shader inputs that are, or contain, integral
+or double-precision floating-point
+types must be
+qualified with the interpolation qualifier <strong>flat</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Fragment inputs are declared as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec3 normal;
+centroid in vec2 TexCoord;
+invariant centroid in vec4 Color;
+noperspective in <span class="predefined-type">float</span> temperature;
+flat in vec3 myColor;
+noperspective centroid in vec2 myTexCoord;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The fragment shader inputs form an interface with the last active shader in
+the vertex processing pipeline.
+For this interface, the last active shader stage output variables and
+fragment shader input variables of the same name must match in type and
+qualification, with a few exceptions: The storage qualifiers must, of
+course, differ (one is <strong>in</strong> and one is <strong>out</strong>).
+Also,
+interpolation qualification (e.g. <strong>flat</strong>) and
+auxiliary qualification (e.g. <strong>centroid</strong>) may differ.
+These mismatches are allowed between any pair of stages.
+When
+interpolation or
+auxiliary qualifiers do not match, those provided in
+the fragment shader supersede those provided in previous stages.
+If any such qualifiers are completely missing in the fragment shaders, then
+the default is used, rather than any qualifiers that may have been declared
+in previous stages.
+That is, what matters is what is declared in the fragment shaders, not what
+is declared in shaders in previous stages.</p>
+</div>
+<div class="paragraph">
+<p>When an interface between shader stages is formed using shaders from two
+separate program objects, it is not possible to detect mismatches between
+inputs and outputs when the programs are linked.
+When there are mismatches between inputs and outputs on such interfaces,
+the values passed across the interface will be partially or completely
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>Shaders can ensure matches across such interfaces either by using input and
+output layout qualifiers (sections &#8220;<a href="#input-layout-qualifiers">Input Layout
+Qualifiers</a>&#8221; and &#8220;<a href="#output-layout-qualifiers">Output Layout
+Qualifiers</a>&#8221;) or by using identical input and output declarations of
+blocks or variables.
+Complete rules for interface matching are found in section 7.4.1 &#8220;Shader
+Interface Matching&#8221; of the <a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>Compute shaders do not permit user-defined input variables and do not form a
+formal interface with any other shader stage.
+See &#8220;<a href="#compute-shader-special-variables">Compute Shader Special
+Variables</a>&#8221; for a description of built-in compute shader input variables.
+All other input to a compute shader is retrieved explicitly through image
+loads, texture fetches, loads from uniforms or uniform buffers, or other
+user supplied code.
+Redeclaration of built-in input variables in compute shaders is not
+permitted.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-variables">4.3.5. Uniform Variables</h4>
+<div class="paragraph">
+<p>The <strong>uniform</strong> qualifier is used to declare global variables whose values are
+the same across the entire primitive being processed.
+All <strong>uniform</strong> variables are read-only and are initialized externally either
+at link time or through the API.
+The link-time initial value is either the value of the variable&#8217;s
+initializer, if present, or 0 if no initializer is present.
+Opaque types cannot have initializers, or a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>Example declarations are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform vec4 lightPosition;
+uniform vec3 color = vec3(<span class="float">0</span><span class="float">.7</span>, <span class="float">0</span><span class="float">.7</span>, <span class="float">0</span><span class="float">.2</span>); <span class="comment">// value assigned at link time</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>uniform</strong> qualifier can be used with any of the basic data types, or
+when declaring a variable whose type is a structure, or an array of any of
+these.</p>
+</div>
+<div class="paragraph">
+<p>There is an implementation-dependent limit on the amount of storage for
+uniforms that can be used for each type of shader and if this is exceeded it
+will cause a compile-time or link-time error.
+Uniform variables that are declared but not
+used do not count against this limit.
+The number of user-defined uniform variables and the number of built-in
+uniform variables that are used within a shader are added together to
+determine whether available uniform storage has been exceeded.</p>
+</div>
+<div class="paragraph">
+<p>Uniforms in shaders all share a single global name space when linked into a
+program or separable program.
+Hence, the types,
+initializers,
+and any location specifiers of all statically used uniform variables with the
+same name must match across all shaders that are linked into a single program.
+However it is not required to repeat the
+initializer or
+location specifier in all the linked shaders.
+While this single uniform name space is cross stage, a uniform variable
+name&#8217;s scope is per stage: If a uniform variable name is declared in one
+stage (e.g. a vertex shader) but not in another (e.g. a fragment shader),
+then that name is still available in the other stage for a different use.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="output-variables">4.3.6. Output Variables</h4>
+<div class="paragraph">
+<p>Shader output variables are declared with the <strong>out</strong> storage qualifier.
+They form the output interface between the declaring shader and the
+subsequent stages of the OpenGL pipeline.
+Output variables must be declared at global scope.
+During shader execution they will behave as normal unqualified global
+variables.
+Their values are copied out to the subsequent pipeline stage on shader exit.
+Only output variables that are read by the subsequent pipeline stage need to
+be written; it is allowed to have superfluous declarations of output
+variables.</p>
+</div>
+<div class="paragraph">
+<p>There is <em>not</em> an <strong>inout</strong> storage qualifier for declaring a single variable
+name as both input and output to a shader.
+Also, a variable cannot be declared with both the <strong>in</strong> and the <strong>out</strong>
+qualifiers, this will result in a compile-time or link-time error.
+Output variables must be declared with different names than input variables.
+However, nesting an input or output inside an interface block with an
+instance name allows the same names with one referenced through a block
+instance name.</p>
+</div>
+<div class="paragraph">
+<p>Vertex, tessellation evaluation, and geometry output variables output
+per-vertex data and are declared using the <strong>out</strong> storage qualifier.
+Applying <strong>patch</strong> to an output can only be done in a tessellation control
+shader.
+It is a compile-time error to use <strong>patch</strong> on outputs in any other stage.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to declare a vertex, tessellation evaluation,
+tessellation control, or geometry shader output with, or that contains, any
+of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Individual outputs are declared as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec3 normal;
+centroid out vec2 TexCoord;
+invariant centroid out vec4 Color;
+flat out vec3 myColor;
+sample out vec4 perSampleColor;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>These can also appear in interface blocks, as described in
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221;.
+Interface blocks allow simpler addition of arrays to the interface from
+vertex to geometry shader.
+They also allow a fragment shader to have the same input interface as a
+geometry shader for a given vertex shader.</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control shader output variables are used to output
+per-vertex and per-patch data.
+Per-vertex output variables are arrayed (see <em>arrayed</em> under
+&#8220;<a href="#input-variables">Input Variables</a>&#8221;) and declared using the <strong>out</strong>
+qualifier without the <strong>patch</strong> qualifier.
+Per-patch output variables are declared using the <strong>patch</strong> and <strong>out</strong>
+qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Since tessellation control shaders produce an arrayed primitive comprising
+multiple vertices, each per-vertex output variable (or output block, see
+interface blocks below) needs to be declared as an array.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out <span class="predefined-type">float</span> foo[]; <span class="comment">// feeds next stage input &quot;in float foo[]&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Each element of such an array corresponds to one vertex of the primitive
+being produced.
+Each array can optionally have a size declared.
+The array size will be set by (or if provided must be consistent with) the
+output layout declaration(s) establishing the number of vertices in the
+output patch, as described later in
+&#8220;<a href="#tessellation-control-outputs">Tessellation Control Outputs</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Each tessellation control shader invocation has a corresponding output patch
+vertex, and may assign values to per-vertex outputs only if they belong to
+that corresponding vertex.
+If a per-vertex output variable is used as an l-value, it is a compile-time
+or link-time error if the expression indicating the vertex index is not the
+identifier <em>gl_InvocationID</em>.</p>
+</div>
+<div class="paragraph">
+<p>The order of execution of a tessellation control shader invocation relative
+to the other invocations for the same input patch is undefined unless the
+built-in function <strong>barrier</strong>() is used.
+This provides some control over relative execution order.
+When a shader invocation calls <strong>barrier</strong>(), its execution pauses until all
+other invocations have reached the same point of execution.
+Output variable assignments performed by any invocation executed prior to
+calling <strong>barrier</strong>() will be visible to any other invocation after the call
+to <strong>barrier</strong>() returns.</p>
+</div>
+<div class="paragraph">
+<p>Because tessellation control shader invocations execute in undefined order
+between barriers, the values of per-vertex or per-patch output variables
+will sometimes be undefined.
+Consider the beginning and end of shader execution and each call to
+<strong>barrier</strong>() as synchronization points.
+The value of an output variable will be undefined in any of the three
+following cases:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>At the beginning of execution.</p>
+</li>
+<li>
+<p>At each synchronization point, unless</p>
+<div class="openblock">
+<div class="content">
+<div class="ulist">
+<ul>
+<li>
+<p>the value was well-defined after the previous synchronization point and
+was not written by any invocation since, or</p>
+</li>
+<li>
+<p>the value was written by exactly one shader invocation since the previous
+synchronization point, or</p>
+</li>
+<li>
+<p>the value was written by multiple shader invocations since the previous
+synchronization point, and the last write performed by all such
+invocations wrote the same value.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</li>
+<li>
+<p>When read by a shader invocation, if</p>
+<div class="openblock">
+<div class="content">
+<div class="ulist">
+<ul>
+<li>
+<p>the value was undefined at the previous synchronization point and has not
+been written by the same shader invocation since, or</p>
+</li>
+<li>
+<p>the output variable is written to by any other shader invocation between
+the previous and next synchronization points, even if that assignment
+occurs in code following the read.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Fragment outputs output per-fragment data and are declared using the <strong>out</strong>
+storage qualifier.
+It is a compile-time error to use auxiliary storage qualifiers or
+interpolation qualifiers in a fragment shader output declaration.
+It is a compile-time error to declare a fragment shader output with, or that
+contains, any of the following types:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>A <a href="#booleans">boolean type</a></p>
+</li>
+<li>
+<p>A double-precision scalar or vector (<strong>double</strong>, <strong>dvec2</strong>, <strong>dvec3</strong>,
+<strong>dvec4</strong>)</p>
+</li>
+<li>
+<p>An <a href="#opaque-types">opaque type</a></p>
+</li>
+<li>
+<p>A matrix type</p>
+</li>
+<li>
+<p>A structure</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Fragment outputs are declared as in the following examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec4 FragmentColor;
+out uint Luminosity;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Compute shaders have no built-in output variables, do not support
+user-defined output variables and do not form a formal interface with any
+other shader stage.
+All outputs from a compute shader take the form of the side effects such as
+image stores and operations on atomic counters.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="buffer-variables">4.3.7. Buffer Variables</h4>
+<div class="paragraph">
+<p>The <strong>buffer</strong> qualifier is used to declare global variables whose values are
+stored in the data store of a buffer object bound through the OpenGL API.
+Buffer variables can be read and written, with the underlying storage shared
+among all active shader invocations.
+Buffer variable memory reads and writes within a single shader invocation
+are processed in order.
+However, the order of reads and writes performed in one invocation relative
+to those performed by another invocation is largely undefined.
+Buffer variables may be qualified with memory qualifiers affecting how the
+underlying memory is accessed, as described in &#8220;<a href="#memory-qualifiers">Memory
+Qualifiers</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>buffer</strong> qualifier can be used to declare interface blocks (see
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221;), which are then referred to as
+shader storage blocks.
+It is a compile-time error to declare buffer variables outside a block.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// use buffer to create a buffer block (shader storage block)</span>
+buffer BufferName { <span class="comment">// externally visible name of buffer</span>
+    <span class="predefined-type">int</span> count;      <span class="comment">// typed, shared memory...</span>
+    ...             <span class="comment">// ...</span>
+    vec4 v[];       <span class="comment">// last member may be an array that is not sized</span>
+                    <span class="comment">// until after link time (dynamically sized)</span>
+} Name;             <span class="comment">// name of block within the shader</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There are implementation-dependent limits on the number of shader storage
+blocks used for each type of shader, the combined number of shader storage
+blocks used for a program, and the amount of storage required by each
+individual shader storage block.
+If any of these limits are exceeded, it will cause a compile-time or
+link-time error.</p>
+</div>
+<div class="paragraph">
+<p>If multiple shaders are linked together, then they will share a single
+global buffer variable name space.
+Hence, the types of all declared buffer variables with the same name must
+match across all shaders that are linked into a single program.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="shared-variables">4.3.8. Shared Variables</h4>
+<div class="paragraph">
+<p>The <strong>shared</strong> qualifier is used to declare global variables that have storage
+shared between all work items in a compute shader workgroup.
+Variables declared as <strong>shared</strong> may only be used in compute shaders (see
+&#8220;<a href="#compute-processor">Compute Processor</a>&#8221;).
+Any other declaration of a <strong>shared</strong> variable is a compile-time error.
+Shared variables are implicitly coherent (see
+&#8220;<a href="#memory-qualifiers">Memory Qualifiers</a>&#8221;).</p>
+</div>
+<div class="paragraph">
+<p>Variables declared as <strong>shared</strong> may not have initializers and their contents
+are undefined at the beginning of shader execution.
+Any data written to <strong>shared</strong> variables will be visible to other work items
+(executing the same shader) within the same workgroup.</p>
+</div>
+<div class="paragraph">
+<p>In the absence of synchronization, the order of reads and writes to the same
+<strong>shared</strong> variable by different invocations of a shader is not defined.</p>
+</div>
+<div class="paragraph">
+<p>In order to achieve ordering with respect to reads and writes to <strong>shared</strong>
+variables, control flow barriers must be employed using the <strong>barrier</strong>() function
+(see &#8220;<a href="#shader-invocation-control-functions">Shader Invocation Control
+Functions</a>&#8221;).</p>
+</div>
+<div class="paragraph">
+<p>There is a limit to the total size of all variables declared as <strong>shared</strong> in a
+single program.
+This limit, expressed in units of basic machine units may be determined by
+using the OpenGL API to query the value of
+MAX_COMPUTE_SHARED_MEMORY_SIZE.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="interface-blocks">4.3.9. Interface Blocks</h4>
+<div class="paragraph">
+<p>Input, output, uniform, and buffer variable declarations can be grouped into
+named interface blocks to provide coarser granularity backing than is
+achievable with individual declarations.
+They can have an optional instance name, used in the shader to reference
+their members.
+An output block of one programmable stage is backed by a corresponding input
+block in the subsequent programmable stage.
+A <em>uniform block</em> is backed by the application with a buffer object.
+A block of buffer variables, called a <em>shader storage block</em>, is also backed
+by the application with a buffer object.
+It is a compile-time error to have an input block in a vertex shader or an
+output block in a fragment shader.
+These uses are reserved for future use.</p>
+</div>
+<div class="paragraph">
+<p>An interface block is started by an <strong>in</strong>, <strong>out</strong>, <strong>uniform</strong>, or <strong>buffer</strong>
+keyword, followed by a block name, followed by an open curly brace (<strong>{</strong>) as
+follows:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>interface-block</em> : </dt>
+<dd>
+<p><em>layout-qualifier<sub>opt</sub></em> <em>interface-qualifier</em> <em>block-name</em> <strong>{</strong>
+<em>member-list</em> <strong>}</strong> <em>instance-name<sub>opt</sub></em> <strong>;</strong></p>
+</dd>
+</dl>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>interface-qualifier</em> : </dt>
+<dd>
+<p><strong>in</strong><br>
+<strong>out</strong><br>
+<strong>patch</strong> <strong>in</strong> // Note: Qualifiers can be in any order.<br>
+<strong>patch</strong> <strong>out</strong><br>
+<strong>uniform</strong><br>
+<strong>buffer</strong></p>
+</dd>
+</dl>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>member-list</em> : </dt>
+<dd>
+<p><em>member-declaration</em><br>
+<em>member-declaration</em> <em>member-list</em></p>
+</dd>
+<dt class="hdlist1"><em>member-declaration</em> : </dt>
+<dd>
+<p><em>layout-qualifier<sub>opt</sub></em> <em>qualifiers<sub>opt</sub></em> <em>type</em> <em>declarators</em> <strong>;</strong></p>
+</dd>
+</dl>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>instance-name</em> : </dt>
+<dd>
+<p><em>identifier</em><br>
+<em>identifier</em> <strong>[</strong> <strong>]</strong><br>
+<em>identifier</em> <strong>[</strong> <em>constant-integral-expression</em> <strong>]</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Each of the above elements is discussed below, with the exception of layout
+qualifiers (<em>layout-qualifier</em>), which are defined in the next section.</p>
+</div>
+<div class="paragraph">
+<p>First, an example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform Transform {
+    mat4 ModelViewMatrix;
+    mat4 ModelViewProjectionMatrix;
+    uniform mat3 NormalMatrix;      <span class="comment">// allowed restatement of qualifier</span>
+    <span class="predefined-type">float</span> Deformation;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The above establishes a uniform block named &#8220;Transform&#8221; with four uniforms
+grouped inside it.</p>
+</div>
+<div class="paragraph">
+<p>Types and declarators are the same as for other input, output, uniform, and
+buffer variable declarations outside blocks, with these exceptions:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Initializers are not allowed</p>
+</li>
+<li>
+<p>Opaque types are not allowed</p>
+</li>
+<li>
+<p>Structure definitions cannot be nested inside a block</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Any of these would result in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>If no optional qualifier is used in a member-declaration, the qualification
+of the member includes all <strong>in</strong>, <strong>out</strong>, <strong>patch</strong>, <strong>uniform</strong>, or <strong>buffer</strong> as
+determined by <em>interface-qualifier</em>.
+If optional qualifiers are used, they can include interpolation qualifiers,
+auxiliary storage qualifiers,
+and storage qualifiers and they must declare
+an input, output, or uniform member consistent with the interface qualifier
+of the block: Input variables, output variables, uniform variables, and
+<strong>buffer</strong> members can only be in <strong>in</strong> blocks, <strong>out</strong> blocks, <strong>uniform</strong> blocks,
+and shader storage blocks, respectively.</p>
+</div>
+<div class="paragraph">
+<p>Repeating the <strong>in</strong>, <strong>out</strong>, <strong>patch</strong>, <strong>uniform</strong>, or <strong>buffer</strong> interface
+qualifier for a member&#8217;s storage qualifier is optional.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in Material {
+    smooth in vec4 Color1; <span class="comment">// legal, input inside in block</span>
+    smooth vec4 Color2;    <span class="comment">// legal, 'in' inherited from 'in Material'</span>
+    vec2 TexCoord;         <span class="comment">// legal, TexCoord is an input</span>
+    uniform <span class="predefined-type">float</span> Atten;   <span class="comment">// illegal, mismatched storage qualifier</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A <em>shader interface</em> is defined to be one of these:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>All the uniform variables and uniform blocks declared in a program.
+This spans all compilation units linked together within one program.</p>
+</li>
+<li>
+<p>All the <strong>buffer</strong> blocks declared in a program.</p>
+</li>
+<li>
+<p>The boundary between adjacent programmable pipeline stages: This spans
+all the outputs declared in all compilation units of the first stage and
+all the inputs declared in all compilation units of the second stage.
+Note that for the purposes of this definition, the fragment shader and
+the preceding shader are considered to have a shared boundary even
+though in practice, all values passed to the fragment shader first pass
+through the rasterizer and interpolator.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The block name (<em>block-name</em>) is used to match within shader interfaces: an
+output block of one pipeline stage will be matched to an input block with
+the same name in the subsequent pipeline stage.
+For uniform or shader storage blocks, the application uses the block name to
+identify the block.
+Block names have no other use within a shader beyond interface matching; it
+is a compile-time error
+to use a block name at global scope for anything other than as a
+block name (e.g. use of a block name for a global variable name or function
+name is currently reserved).
+It is a compile-time error to use the same block name for more than one
+block declaration in the same shader interface (as defined above) within one
+shader, even if the block contents are identical.</p>
+</div>
+<div class="paragraph">
+<p>Matched block names within a shader interface (as defined above) must match
+in terms of having the same number of declarations with the same sequence of
+types and the same sequence of member names, as well as having matching
+member-wise layout qualification
+(see next section).
+Matched uniform or shader storage block names (but not input or output block
+names) must also either all be lacking an instance name or all having an
+instance name, putting their members at the same scoping level.
+When instance names are present on matched block names, it is allowed for
+the instance names to differ; they need not match for the blocks to match.
+Furthermore, if a matching block is declared as an array, then the array
+sizes must also match (or follow array matching rules for the shader
+interface between consecutive shader stages).
+Any mismatch will generate a link-time error.
+A block name is allowed to have different definitions in different shader
+interfaces within the same shader, allowing, for example, an input block and
+output block to have the same name.</p>
+</div>
+<div class="paragraph">
+<p>If an instance name (<em>instance-name</em>) is not used, the names declared inside
+the block are scoped at the global level and accessed as if they were
+declared outside the block.
+If an instance name (<em>instance-name</em>) is used, then it puts all the members
+inside a scope within its own name space, accessed with the field selector
+(<strong>.</strong>) operator (analogously to structures).
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in Light {
+    vec4 LightPos;
+    vec3 LightColor;
+};
+in ColoredTexture {
+    vec4 Color;
+    vec2 TexCoord;
+} Material;           <span class="comment">// instance name</span>
+vec3 Color;           <span class="comment">// different Color than Material.Color</span>
+vec4 LightPos;        <span class="comment">// illegal, already defined</span>
+...
+... = LightPos;       <span class="comment">// accessing LightPos</span>
+... = Material.Color; <span class="comment">// accessing Color in ColoredTexture block</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Outside the shading language (i.e., in the API), members are similarly
+identified except the block name is always used in place of the instance
+name (API accesses are to shader interfaces, not to shaders).
+If there is no instance name, then the API does not use the block name to
+access a member, just the member name.</p>
+</div>
+<div class="paragraph">
+<p>Within a shader interface, all declarations of the same global name must be
+for the same object and must match in type and in whether they declare a
+variable or member of a block with no instance name.
+The API also needs this name to uniquely identify an object in the shader
+interface.
+It is a link-time error if any particular shader interface contains</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>two different blocks, each having no instance name, and each having a
+member of the same name, or</p>
+</li>
+<li>
+<p>a variable outside a block, and a block with no instance name, where the
+variable has the same name as a member in the block.</p>
+</li>
+</ul>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out Vertex {
+    vec4 Position;  <span class="comment">// API transform/feedback will use &quot;Vertex.Position&quot;</span>
+    vec2 Texture;
+} Coords;           <span class="comment">// shader will use &quot;Coords.Position&quot;</span>
+out Vertex2 {
+    vec4 Color;     <span class="comment">// API will use &quot;Color&quot;</span>
+    <span class="predefined-type">float</span> Color2;
+};
+
+<span class="comment">// in same program as Vertex2 above:</span>
+out Vertex3 {
+    <span class="predefined-type">float</span> Intensity;
+    vec4 Color;     <span class="comment">// ERROR, name collision with Color in Vertex2</span>
+};
+<span class="predefined-type">float</span> Color2;       <span class="comment">// ERROR, collides with Color2 in Vertex2</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For blocks declared as arrays, the array index must also be included when
+accessing members, as in this example</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">uniform Transform { <span class="comment">// API uses &quot;Transform[2]&quot; to refer to instance 2</span>
+    mat4 ModelViewMatrix;
+    mat4 ModelViewProjectionMatrix;
+    vec4 a[]; <span class="comment">// array will get implicitly sized</span>
+    <span class="predefined-type">float</span> Deformation;
+} transforms[<span class="integer">4</span>];
+...
+... = transforms[<span class="integer">2</span>].ModelViewMatrix; <span class="comment">// shader access of instance 2</span>
+<span class="comment">// API uses &quot;Transform.ModelViewMatrix&quot; to query an offset or other query</span>
+transforms[x].a.length(); <span class="comment">// same length for 'a' for all x</span>
+Transform[x];             <span class="comment">// illegal, must use 'transforms'</span>
+Transform.a.length();     <span class="comment">// illegal, must use 'transforms'</span>
+...transforms[<span class="integer">2</span>].a[<span class="integer">3</span>]...  <span class="comment">// if these are the only two dereferences of 'a',</span>
+...transforms[<span class="integer">3</span>].a[<span class="integer">7</span>]...  <span class="comment">// then 'a' must be size 8, for all</span>
+transforms[x]</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For uniform or shader storage blocks declared as an array, each individual
+array element corresponds to a separate buffer object bind range, backing
+one instance of the block.
+As the array size indicates the number of buffer objects needed, uniform and
+shader storage block array declarations must specify an array size.
+A uniform or shader storage block array can only be indexed with a
+dynamically uniform integral expression, otherwise results are undefined.</p>
+</div>
+<div class="paragraph">
+<p>When using OpenGL API entry points to identify the name of an individual
+block in an array of blocks, the name string may include an array index
+(e.g. <em>Transform[2]</em>).
+When using OpenGL API entry points to refer to offsets or other
+characteristics of a block member, an array index must not be specified
+(e.g. <em>Transform.ModelViewMatrix</em>).</p>
+</div>
+<div class="paragraph">
+<p>Tessellation control, tessellation evaluation and geometry shader input
+blocks must be declared as arrays and follow the array declaration and
+linking rules for all shader inputs for the respective stages.
+All other input and output block arrays must specify an array size.</p>
+</div>
+<div class="paragraph">
+<p>There are implementation-dependent limits on the number of uniform blocks
+and the number of shader storage blocks that can be used per stage.
+If either limit is exceeded, it will cause a link-time error.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="layout-qualifiers">4.4. Layout Qualifiers</h3>
+<div class="paragraph">
+<p>Layout qualifiers can appear in several forms of declaration.
+They can appear as part of an interface block definition or block member, as
+shown in the grammar in the previous section.
+They can also appear with just an <em>interface-qualifier</em> to establish layouts
+of other declarations made with that qualifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="paragraph">
+<p><em>layout-qualifier</em> <em>interface-qualifier</em> <strong>;</strong></p>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Or, they can appear with an individual variable declared with an interface
+qualifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="paragraph">
+<p><em>layout-qualifier</em> <em>interface-qualifier</em> <em>declaration</em> <strong>;</strong></p>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Declarations of layouts can only be made at global scope or block members,
+and only where indicated in the following subsections; their details are
+specific to what the interface qualifier is, and are discussed individually.</p>
+</div>
+<div class="paragraph">
+<p>The <em>layout-qualifier</em> expands to:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier</em> : </dt>
+<dd>
+<p><strong>layout</strong> <strong>(</strong> <em>layout-qualifier-id-list</em> <strong>)</strong></p>
+</dd>
+<dt class="hdlist1"><em>layout-qualifier-id-list</em> : </dt>
+<dd>
+<p><em>layout-qualifier-id</em><br>
+<em>layout-qualifier-id</em> <strong>,</strong> <em>layout-qualifier-id-list</em></p>
+</dd>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><em>layout-qualifier-name</em><br>
+<em>layout-qualifier-name</em> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>shared</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-value</em> : </dt>
+<dd>
+<p><em>integer-constant-expression</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The tokens used for <em>layout-qualifier-name</em> are identifiers, not keywords,
+however, the <strong>shared</strong> keyword is allowed as a <em>layout-qualifier-id</em>.
+Generally, they can be listed in any order.
+Order-dependent meanings exist only if explicitly called out below.
+Similarly, these identifiers are not case sensitive, unless explicitly noted
+otherwise.</p>
+</div>
+<div class="paragraph">
+<p>More than one layout qualifier may appear in a single declaration.
+Additionally, the same <em>layout-qualifier-name</em> can occur multiple times
+within a layout qualifier or across multiple layout qualifiers in the same
+declaration.
+When the same <em>layout-qualifier-name</em> occurs multiple times, in a single
+declaration, the last occurrence overrides the former occurrence(s).
+Further, if such a <em>layout-qualifier-name</em> will affect subsequent
+declarations or other observable behavior, it is only the last occurrence
+that will have any effect, behaving as if the earlier occurrence(s) within
+the declaration are not present.
+This is also true for overriding <em>layout-qualifier-name</em>, where one
+overrides the other (e.g. <strong>row_major</strong> vs.
+<strong>column_major</strong>); only the last occurrence has any effect.</p>
+</div>
+<div class="paragraph">
+<p><em>integer-constant-expression</em> is defined in
+&#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221; as &#8220;_constant integral
+expression_&#8221;, with it being a compile-time error for
+<em>integer-constant-expression</em> to be a specialization constant.</p>
+</div>
+<div class="paragraph">
+<p>The following table summarizes the use of layout qualifiers.
+It shows for each one what kinds of declarations it may be applied to.
+These are all discussed in detail in the following sections.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.6666%;">
+<col style="width: 16.667%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Layout Qualifier</th>
+<th class="tableblock halign-left valign-top">Qualifier Only</th>
+<th class="tableblock halign-left valign-top">Individual Variable</th>
+<th class="tableblock halign-left valign-top">Block</th>
+<th class="tableblock halign-left valign-top">Block Member</th>
+<th class="tableblock halign-left valign-top">Allowed Interfaces</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>shared</strong><br>
+  <strong>packed</strong><br>
+  <strong>std140</strong><br>
+  <strong>std430</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top" rowspan="5"><p class="tableblock"><strong>uniform</strong> / <strong>buffer</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>row_major</strong><br>
+  <strong>column_major</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>binding</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">opaque types only</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>offset</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">atomic counters only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>align</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>location</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uniform</strong> / <strong>buffer</strong> and subroutine variables</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>location</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top" rowspan="2"><p class="tableblock">all <strong>in</strong> / <strong>out</strong>, except for compute</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>component</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>index</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">fragment <strong>out</strong> and subroutine functions</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>triangles</strong><br>
+  <strong>quads</strong><br>
+  <strong>isolines</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>equal_spacing</strong><br>
+  <strong>fractional_even_spacing</strong><br>
+  <strong>fractional_odd_spacing</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cw</strong><br>
+  <strong>ccw</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>point_mode</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation evaluation <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>points</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>in</strong>/<strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">[ <strong>points</strong> ]<br>
+  <strong>lines</strong><br>
+  <strong>lines_adjacency</strong><br>
+  <strong>triangles</strong><br>
+  <strong>triangles_adjacency</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>invocations</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">geometry <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>origin_upper_left</strong><br>
+  <strong>pixel_center_integer</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>gl_FragCoord</em> only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top" rowspan="2"><p class="tableblock">fragment <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>early_fragment_tests</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>local_size_x</strong> =<br>
+  <strong>local_size_y</strong> =<br>
+  <strong>local_size_z</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compute <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>local_size_x_id</strong> =<br>
+  <strong>local_size_y_id</strong> =<br>
+  <strong>local_size_z_id</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compute <strong>in</strong> (SPIR-V generation only)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>xfb_buffer</strong> =<br>
+  <strong>xfb_stride</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top" rowspan="2"><p class="tableblock">vertex, tessellation, and geometry <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>xfb_offset</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>vertices</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">tessellation control <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">[ <strong>points</strong> ]<br>
+  <strong>line_strip</strong><br>
+  <strong>triangle_strip</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top" rowspan="3"><p class="tableblock">geometry <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>max_vertices</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>stream</strong> =</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>depth_any</strong><br>
+  <strong>depth_greater</strong><br>
+  <strong>depth_less</strong><br>
+  <strong>depth_unchanged</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>gl_FragDepth</em> only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">fragment <strong>out</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>constant_id</strong> =</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">scalar only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>const</strong> (SPIR-V generation only)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>rgba32f</strong><br>
+  <strong>rgba16f</strong><br>
+  <strong>rg32f</strong><br>
+  <strong>rg16f</strong><br>
+  <strong>r11f_g11f_b10f</strong><br>
+  <strong>r32f</strong><br>
+  <strong>r16f</strong><br>
+  <strong>rgba16</strong><br>
+  <strong>rgb10_a2</strong><br>
+  <strong>rgba8</strong><br>
+  <strong>rg16</strong><br>
+  <strong>rg8</strong><br>
+  <strong>r16</strong><br>
+  <strong>r8</strong><br>
+  <strong>rgba16_snorm</strong><br>
+  <strong>rgba8_snorm</strong><br>
+  <strong>rg16_snorm</strong><br>
+  <strong>rg8_snorm</strong><br>
+  <strong>r16_snorm</strong><br>
+  <strong>r8_snorm</strong><br>
+  <strong>rgba32i</strong><br>
+  <strong>rgba16i</strong><br>
+  <strong>rgba8i</strong><br>
+  <strong>rg32i</strong><br>
+  <strong>rg16i</strong><br>
+  <strong>rg8i</strong><br>
+  <strong>r32i</strong><br>
+  <strong>r16i</strong><br>
+  <strong>r8i</strong><br>
+  <strong>rgba32ui</strong><br>
+  <strong>rgba16ui</strong><br>
+<strong>rgb10_a2ui</strong><br>
+  <strong>rgba8ui</strong><br>
+  <strong>rg32ui</strong><br>
+  <strong>rg16ui</strong><br>
+  <strong>rg8ui</strong><br>
+  <strong>r32ui</strong><br>
+  <strong>r16ui</strong><br>
+  <strong>r8ui</strong></p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">image types only</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>uniform</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="sect3">
+<h4 id="input-layout-qualifiers">4.4.1. Input Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Layout qualifiers specific to a particular shader language are discussed in
+separate sections below.</p>
+</div>
+<div class="paragraph">
+<p>All shaders except compute shaders allow <strong>location</strong> layout qualifiers on
+input variable declarations, input block declarations, and input block
+member declarations.
+Of these, variables and block members (but not blocks) additionally allow
+the <strong>component</strong> layout qualifier.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>location</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>component</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>) in vec4 normal;
+<span class="directive">const</span> <span class="predefined-type">int</span> start = <span class="integer">6</span>;
+layout(location = start + <span class="integer">2</span>) <span class="predefined-type">int</span> vec4 v;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the shader input <em>normal</em> is assigned to vector location
+number
+3 and <em>v</em> is assigned location number 8.
+For vertex shader inputs, the location specifies the number of the
+vertex attribute from which input values are taken.
+For inputs of all other shader types, the location specifies a vector number
+that can be used to match against outputs from a previous shader stage, even
+if that shader is in a different program object.</p>
+</div>
+<div class="paragraph">
+<p>The following language describes how many locations are consumed by a given
+type.
+However, geometry shader inputs, tessellation control shader inputs and
+outputs, and tessellation evaluation inputs all have an additional level of
+arrayness relative to other shader inputs and outputs.
+This outer array level is removed from the type before considering how many
+locations the type consumes.</p>
+</div>
+<div class="paragraph">
+<p>If a vertex shader input is any scalar or vector type, it will consume a
+single location.
+If a non-vertex shader input is a scalar or vector type other than <strong>dvec3</strong>
+or <strong>dvec4</strong>, it will consume a single location, while types <strong>dvec3</strong> or
+<strong>dvec4</strong> will consume two consecutive locations.
+Inputs of type <strong>double</strong> and <strong>dvec2</strong> will consume only a single location, in
+all stages.</p>
+</div>
+<div class="paragraph">
+<p>If the declared input (after potentially removing an outer array level as
+just described above) is an array of size <em>n</em> and each of the elements takes
+<em>m</em> locations, it will be assigned <em>m</em> * <em>n</em> consecutive locations starting
+with the location specified.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">6</span>) in vec4 colors[<span class="integer">3</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the shader input <em>colors</em> is assigned to vector location
+numbers 6, 7, and 8.</p>
+</div>
+<div class="paragraph">
+<p>If the declared input is an <em>n</em> × <em>m</em>
+matrix, it will be assigned multiple locations starting with the location
+specified.
+The number of locations assigned for each matrix will be the same as for an
+<em>n</em>-element array of <em>m</em>-component vectors.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">9</span>) in mat4 transforms[<span class="integer">2</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that shader input <em>transforms</em> is assigned to vector
+locations 9-16, with <em>transforms[0]</em> being assigned to locations 9-12, and
+<em>transforms[1]</em> being assigned to locations 13-16.</p>
+</div>
+<div class="paragraph">
+<p>If the declared input is a structure or block, its members will be assigned
+consecutive locations in their order of declaration, with the first member
+assigned the location provided in the layout qualifier.
+For a structure, this process applies to the entire structure.
+It is a compile-time error to use a <strong>location</strong> qualifier on a member of a
+structure.
+For a block, this process applies to the entire block, or until the first
+member is reached that has a <strong>location</strong> layout qualifier.</p>
+</div>
+<div class="paragraph">
+<p>When a block member is declared with a <strong>location</strong> qualifier, its location
+comes from that qualifier; the member&#8217;s <strong>location</strong> qualifier overrides the
+block-level declaration.
+Subsequent members are again assigned consecutive locations, based on the
+newest location, until the next member declared with a <strong>location</strong> qualifier.
+The values used for locations do not have to be declared in increasing
+order.</p>
+</div>
+<div class="paragraph">
+<p>If a block has no block-level <strong>location</strong> layout qualifier, it is required
+that either all or none of its members have a <strong>location</strong> layout qualifier,
+or a compile-time error results.
+For some blocks declared as arrays, the <strong>location</strong> can only be applied at
+the block level: When a block is declared as an array where additional
+locations are needed for each member for each block array element, it is a
+compile-time error to specify locations on the block members.
+That is, when locations would be under specified by applying them on block
+members, they are not allowed on block members.
+For <em>arrayed</em> interfaces (those generally having an extra level of arrayness
+due to interface expansion), the outer array is stripped before applying
+this rule.</p>
+</div>
+<div class="paragraph">
+<p>When generating SPIR-V, all <strong>in</strong> and <strong>out</strong> qualified user-declared (non
+built-in) variables and blocks (or all their members) must have a
+shader-specified <strong>location</strong>.
+Otherwise, a compile-time error is generated.</p>
+</div>
+<div class="paragraph">
+<p>The locations consumed by block and structure members are determined by
+applying the rules above recursively as though the structure member were
+declared as an input variable of the same type.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>) in <span class="keyword">struct</span> S
+{
+    vec3 a;                      <span class="comment">// gets location 3</span>
+    mat2 b;                      <span class="comment">// gets locations 4 and 5</span>
+    vec4 c[<span class="integer">2</span>];                   <span class="comment">// gets locations 6 and 7</span>
+    layout(location = <span class="integer">8</span>) vec2 A; <span class="comment">// ERROR, can't use on struct member</span>
+} s;
+layout(location = <span class="integer">4</span>) in block
+{
+    vec4 d;                      <span class="comment">// gets location 4</span>
+    vec4 e;                      <span class="comment">// gets location 5</span>
+    layout(location = <span class="integer">7</span>) vec4 f; <span class="comment">// gets location 7</span>
+    vec4 g;                      <span class="comment">// gets location 8</span>
+    layout(location = <span class="integer">1</span>) vec4 h; <span class="comment">// gets location 1</span>
+    vec4 i;                      <span class="comment">// gets location 2</span>
+    vec4 j;                      <span class="comment">// gets location 3</span>
+    vec4 k;                      <span class="comment">// ERROR, location 4 already used</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The number of input locations available to a shader is limited.
+For vertex shaders, the limit is the advertised number of vertex attributes.
+For all other shaders, the limit is implementation-dependent and must be no
+less than one fourth of the advertised maximum input component count.</p>
+</div>
+<div class="paragraph">
+<p>A program will fail to link if any attached shader uses a location greater
+than or equal to the number of supported locations, unless device-dependent
+optimizations are able to make the program fit within available hardware
+resources.</p>
+</div>
+<div class="paragraph">
+<p>A program will fail to link if explicit location assignments leave the
+linker unable to find space for other variables without explicit
+assignments.</p>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if a non-vertex input matches an output from
+a previous shader stage, the <strong>location</strong> layout qualifier (if any) must
+match.</p>
+</div>
+<div class="paragraph">
+<p>If a vertex shader input variable with no location assigned in the shader
+text has a location specified through the OpenGL API, the API-assigned
+location will be used.
+Otherwise, such variables will be assigned a location by the linker.
+See section 11.1.1 &#8220;Vertex Attributes&#8221; of the <a href="#references">OpenGL Specification</a> for
+more details.
+A link-time error will occur if an input variable is declared in multiple
+shaders of the same language with conflicting locations.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>component</strong> qualifier allows the location to be more finely specified
+for scalars and vectors, down to the individual components within a location
+that are consumed.
+It is a compile-time error to use <strong>component</strong> without also specifying the
+<strong>location</strong> qualifier (order does not matter).
+The components within a location are 0, 1, 2, and 3.
+A variable or block member starting at component <em>N</em> will consume components
+<em>N</em>, <em>N+1</em>, <em>N+2</em>, &#8230;&#8203;
+up through its size.
+It is a compile-time error if this sequence of components gets larger than
+3.
+A scalar <strong>double</strong> will consume two of these components, and a <strong>dvec2</strong> will
+consume all four components available within a location.
+A <strong>dvec3</strong> or <strong>dvec4</strong> can only be declared without specifying a <strong>component</strong>.
+A <strong>dvec3</strong> will consume all four components of the first location and
+components 0 and 1 of the second location.
+This leaves components 2 and 3 available for other component-qualified
+declarations.</p>
+</div>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// a consumes components 2 and 3 of location 4</span>
+layout(location = <span class="integer">4</span>, component = <span class="integer">2</span>) in vec2 a;
+
+<span class="comment">// b consumes component 1 of location 4</span>
+layout(location = <span class="integer">4</span>, component = <span class="integer">1</span>) in <span class="predefined-type">float</span> b;
+
+<span class="comment">// ERROR: c overflows component 3</span>
+layout(location = <span class="integer">3</span>, component = <span class="integer">2</span>) in vec3 c;
+
+<span class="comment">// d consumes components 2 and 3 of location 5</span>
+layout(location = <span class="integer">5</span>, component = <span class="integer">2</span>) in <span class="predefined-type">double</span> d;
+
+<span class="comment">// ERROR: e overflows component 3 of location 6</span>
+layout(location = <span class="integer">6</span>, component = <span class="integer">2</span>) in dvec2 e;
+
+<span class="comment">// ERROR: f overlaps with g</span>
+layout(location = <span class="integer">7</span>, component = <span class="integer">0</span>) <span class="predefined-type">double</span> f;
+layout(location = <span class="integer">7</span>, component = <span class="integer">1</span>) <span class="predefined-type">float</span> g;
+
+layout(location = <span class="integer">8</span>) in dvec3 h; <span class="comment">// components 0,1,2 and 3 of location 8</span>
+                                 <span class="comment">// and components 0 and 1 of location 9</span>
+layout(location = <span class="integer">9</span>, component = <span class="integer">2</span>) in <span class="predefined-type">float</span> i; <span class="comment">// okay, compts 2 and 3</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If the variable is an array, each element of the array, in order, is
+assigned to consecutive locations, but all at the same specified component
+within each location.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// component 3 in 6 locations are consumed</span>
+layout(location = <span class="integer">2</span>, component = <span class="integer">3</span>) in <span class="predefined-type">float</span> d[<span class="integer">6</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>That is, location 2 component 3 will hold <em>d[0]</em>, location 3 component 3
+will hold <em>d[1]</em>, &#8230;&#8203;, up through location 7 component 3 holding <em>d[5]</em>.</p>
+</div>
+<div class="paragraph">
+<p>This allows packing of two arrays into the same set of locations:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// e consumes beginning (components 0, 1 and 2) of each of 6 slots</span>
+layout(location = <span class="integer">0</span>, component = <span class="integer">0</span>) in vec3 e[<span class="integer">6</span>];
+
+<span class="comment">// f consumes last component of the same 6 slots</span>
+layout(location = <span class="integer">0</span>, component = <span class="integer">3</span>) in <span class="predefined-type">float</span> f[<span class="integer">6</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If applying this to an array of arrays, all levels of arrayness are removed
+to get to the elements that are assigned per location to the specified
+component.
+These non-arrayed elements will fill the locations in the order specified
+for arrays of arrays in &#8220;<a href="#arrays">Arrays</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to apply the <strong>component</strong> qualifier to a matrix, a
+structure, a block, or an array containing any of these.
+It is a compile-time error to use <strong>component</strong> 1 or 3 as the beginning of a
+<strong>double</strong> or <strong>dvec2</strong>.
+It is a link-time error to specify different components for the same
+variable within a program.</p>
+</div>
+<div class="paragraph">
+<p><em>Location aliasing</em> is causing two variables or block members to have the
+same location number.
+<em>Component aliasing</em> is assigning the same (or overlapping) component
+numbers for two location aliases.
+(Recall if <strong>component</strong> is not used, components are assigned starting with
+0.) With one exception, location aliasing is allowed only if it does not
+cause component aliasing; it is a compile-time or link-time error to cause
+component aliasing.
+Further, when location aliasing, the aliases sharing the location must have
+the same underlying numerical type and bit width  (floating-point or integer,
+32-bit versus 64-bit, etc.) and the same
+auxiliary storage and interpolation qualification.
+The one exception where component aliasing is permitted is for two input
+variables (not block members) to a vertex shader, which are allowed to have
+component aliasing.
+This vertex-variable component aliasing is intended only to support vertex
+shaders where each execution path accesses at most one input per each
+aliased component.
+Implementations are permitted, but not required, to generate link-time
+errors if they detect that every path through the vertex shader executable
+accesses multiple inputs aliased to any single component.</p>
+</div>
+<div class="sect4">
+<h5 id="tessellation-evaluation-inputs">Tessellation Evaluation Inputs</h5>
+<div class="paragraph">
+<p>Additional input layout qualifier identifiers allowed for tessellation
+evaluation shaders are described below.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><em>primitive_mode</em><br>
+<em>vertex_spacing</em><br>
+<em>ordering</em><br>
+<em>point_mode</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>primitive-mode</strong> is used to specify a tessellation primitive mode to be
+used by the tessellation primitive generator.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>primitive-mode</em>: </dt>
+<dd>
+<p><strong>triangles</strong><br>
+<strong>quads</strong><br>
+<strong>isolines</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>If present, the <em>primitive-mode</em> specifies that the tessellation primitive
+generator should subdivide a triangle into smaller triangles, a quad into
+triangles, or a quad into a collection of lines, respectively.</p>
+</div>
+<div class="paragraph">
+<p>A second group of layout identifiers, <em>vertex spacing</em>, is used to specify
+the spacing used by the tessellation primitive generator when subdividing an
+edge.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>vertex-spacing</em>: </dt>
+<dd>
+<p><strong>equal_spacing</strong><br>
+<strong>fractional_even_spacing</strong><br>
+<strong>fractional_odd_spacing</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p><strong>equal_spacing</strong> specifies that edges should be divided into a collection of
+equal-sized segments;</p>
+</div>
+<div class="paragraph">
+<p><strong>fractional_even_spacing</strong> specifies that edges should be divided into an
+even number of equal-length segments plus two additional shorter
+&#8220;fractional&#8221; segments; or</p>
+</div>
+<div class="paragraph">
+<p><strong>fractional_odd_spacing</strong> specifies that edges should be divided into an odd
+number of equal-length segments plus two additional shorter &#8220;fractional&#8221;
+segments.</p>
+</div>
+<div class="paragraph">
+<p>A third group of layout identifiers, <em>ordering</em>, specifies whether the
+tessellation primitive generator produces triangles in clockwise or
+counter-clockwise order, according to the coordinate system depicted in the
+<a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>ordering</em>: </dt>
+<dd>
+<p><strong>cw</strong><br>
+<strong>ccw</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifiers <strong>cw</strong> and <strong>ccw</strong> indicate clockwise and counter-clockwise
+triangles, respectively.
+If the tessellation primitive generator does not produce triangles, the
+order is ignored.</p>
+</div>
+<div class="paragraph">
+<p>Finally, <em>point mode</em> indicates that the tessellation primitive generator
+should produce one point for each distinct vertex in the subdivided
+primitive, rather than generating lines or triangles.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>point-mode</em>: </dt>
+<dd>
+<p><strong>point_mode</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Any or all of these identifiers may be specified one or more times in a
+single input layout declaration.
+If primitive mode, vertex spacing, or ordering is declared more than once in
+the tessellation evaluation shaders of a program, all such declarations must
+use the same identifier.</p>
+</div>
+<div class="paragraph">
+<p>At least one tessellation evaluation shader (compilation unit) in a program
+must declare a primitive mode in its input layout.
+Declaring vertex spacing, ordering, or point mode identifiers is optional.
+It is not required that all tessellation evaluation shaders in a program
+declare a primitive mode.
+If spacing or vertex ordering declarations are omitted, the tessellation
+primitive generator will use equal spacing or counter-clockwise vertex
+ordering, respectively.
+If a point mode declaration is omitted, the tessellation primitive generator
+will produce lines or triangles according to the primitive mode.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-shader-inputs">Geometry Shader Inputs</h5>
+<div class="paragraph">
+<p>Additional layout qualifier identifiers for geometry shader inputs include
+<em>primitive</em> identifiers and an <em>invocation count</em> identifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>points</strong><br>
+<strong>lines</strong><br>
+<strong>lines_adjacency</strong><br>
+<strong>triangles</strong><br>
+<strong>triangles_adjacency</strong><br>
+<strong>invocations</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifiers <strong>points</strong>, <strong>lines</strong>, <strong>lines_adjacency</strong>, <strong>triangles</strong>, and
+<strong>triangles_adjacency</strong> are used to specify the type of input primitive
+accepted by the geometry shader, and only one of these is accepted.
+At least one geometry shader (compilation unit) in a program must declare
+this input primitive layout, and all geometry shader input layout
+declarations in a program must declare the same layout.
+It is not required that all geometry shaders in a program declare an input
+primitive layout.</p>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>invocations</strong> is used to specify the number of times the
+geometry shader executable is invoked for each input primitive received.
+Invocation count declarations are optional.
+If no invocation count is declared in any geometry shader in a program, the
+geometry shader will be run once for each input primitive.
+If an invocation count is declared, all such declarations must specify the
+same count.
+If a shader specifies an invocation count greater than the
+implementation-dependent maximum, or less than or equal to zero,
+a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(triangles, invocations = <span class="integer">6</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that all inputs to the geometry shader are triangles and that
+the geometry shader executable is run six times for each triangle processed.</p>
+</div>
+<div class="paragraph">
+<p>All geometry shader input unsized array declarations will be sized by an
+earlier input primitive layout qualifier, when present, as per the following
+table.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Layout</th>
+<th class="tableblock halign-left valign-top">Size of Input Arrays</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>points</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lines</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lines_adjacency</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>triangles</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>triangles_adjacency</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The intrinsically declared input array <em>gl_in[]</em> will also be sized by any
+input primitive-layout declaration.
+Hence, the expression</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_in.length()</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will return the value from the table above.</p>
+</div>
+<div class="paragraph">
+<p>For inputs declared without an array size, including intrinsically declared
+inputs (i.e., <em>gl_in</em>), a layout must be declared before any use of the
+method <strong>length</strong>() or other any array use that requires the array size to be
+known.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error if a layout declaration&#8217;s array size (from the
+table above) does not match all the explicit array sizes specified in
+declarations of an input variables in the same shader.
+The following includes examples of compile-time errors:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// code sequence within one shader...</span>
+in vec4 Color1[];     <span class="comment">// legal, size still unknown</span>
+in vec4 Color2[<span class="integer">2</span>];    <span class="comment">// legal, size is 2</span>
+in vec4 Color3[<span class="integer">3</span>];    <span class="comment">// illegal, input sizes are inconsistent</span>
+layout(lines) in;     <span class="comment">// legal for Color2, input size is 2, matching Color2</span>
+in vec4 Color4[<span class="integer">3</span>];    <span class="comment">// illegal, contradicts layout of lines</span>
+layout(lines) in;     <span class="comment">// legal, matches other layout() declaration</span>
+layout(triangles) in; <span class="comment">// illegal, does not match earlier layout() declaration</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is a link-time error if not all provided sizes (sized input arrays and
+layout size) match across all geometry shaders in a program.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="fragment-shader-inputs">Fragment Shader Inputs</h5>
+<div class="paragraph">
+<p>Additional fragment layout qualifier identifiers include the following for
+<em>gl_FragCoord</em> :</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>origin_upper_left</strong><br>
+<strong>pixel_center_integer</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>By default, <em>gl_FragCoord</em> assumes a lower-left origin for window
+coordinates and assumes pixel centers are located at half-pixel coordinates.
+For example, the (<em>x, y</em>) location (0.5, 0.5) is returned for the
+lower-left-most pixel in a window.
+The origin can be changed by redeclaring <em>gl_FragCoord</em> with the
+<strong>origin_upper_left</strong> qualifier, moving the origin of <em>gl_FragCoord</em> to the
+upper left of the window, with <em>y</em> increasing in value toward the bottom of
+the window.
+The values returned can also be shifted by half a pixel in both <em>x</em> and <em>y</em>
+by <strong>pixel_center_integer</strong> so it appears the pixels are centered at whole
+number pixel offsets.
+This moves the (<em>x</em>, <em>y</em>) value returned by <em>gl_FragCoord</em> of (0.5, 0.5) by
+default, to (0.0, 0.0) with <strong>pixel_center_integer</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Redeclarations are done as follows</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 gl_FragCoord; <span class="comment">// redeclaration that changes nothing is allowed</span>
+
+<span class="comment">// All the following are allowed redeclaration that change behavior</span>
+layout(origin_upper_left) in vec4 gl_FragCoord;
+layout(pixel_center_integer) in vec4 gl_FragCoord;
+layout(origin_upper_left, pixel_center_integer) in vec4 gl_FragCoord;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If <em>gl_FragCoord</em> is redeclared in any fragment shader in a program, it must
+be redeclared in all the fragment shaders in that program that have a static
+use <em>gl_FragCoord</em>.
+All redeclarations of <em>gl_FragCoord in all fragment shaders in a single
+program must have the same set of qualifiers.
+Within any shader, the first redeclarations of _glFragCoord</em> must appear
+before any use of <em>gl_FragCoord</em>.
+The built-in <em>gl_FragCoord</em> is only predeclared in fragment shaders, so
+redeclaring it in any other shader language results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>Redeclaring <em>glFragCoord</em> with <strong>origin_upper_left</strong> and/or
+<strong>pixel_center_integer</strong> qualifiers only affects <em>gl_FragCoord.x</em> and
+<em>gl_FragCoord.y</em>.
+It has no effect on rasterization, transformation, or any other part of the
+OpenGL pipeline or language features.</p>
+</div>
+<div class="paragraph">
+<p>Fragment shaders allow the following layout qualifier on <strong>in</strong> only (not with
+variable declarations):</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>early_fragment_tests</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>to request that fragment tests be performed before fragment shader
+execution, as described in section 15.2.4 &#8220;Early Fragment Tests&#8221; of the
+<a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(early_fragment_tests) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Specifying this will make per-fragment tests be performed before fragment
+shader execution.
+If this is not declared, per-fragment tests will be performed after fragment
+shader execution.
+Only one fragment shader (compilation unit) need declare this, though more
+than one can.
+If at least one declares this, then it is enabled.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="compute-shader-inputs">Compute Shader Inputs</h5>
+<div class="paragraph">
+<p>There are no layout location qualifiers for compute shader inputs.</p>
+</div>
+<div class="paragraph">
+<p>Layout qualifier identifiers for compute shader inputs are the workgroup
+size qualifiers:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>local_size_x</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>local_size_y</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>local_size_z</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>local_size_x</strong>, <strong>local_size_y</strong>, and <strong>local_size_z</strong> qualifiers are used
+to declare a fixed workgroup size by the compute shader in the first,
+second, and third dimension, respectively.
+If a shader does not specify a size for one of the dimensions, that
+dimension will have a size of 1.</p>
+</div>
+<div class="paragraph">
+<p>For example, the following declaration in a compute shader</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(local_size_x = <span class="integer">32</span>, local_size_y = <span class="integer">32</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is used to declare a two-dimensional compute shader with a workgroup size of 32
+X 32 elements, which is equivalent to a three-dimensional compute shader
+where the third dimension has size one.</p>
+</div>
+<div class="paragraph">
+<p>As another example, the declaration</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(local_size_x = <span class="integer">8</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>effectively specifies that a one-dimensional compute shader is being
+compiled, and its size is 8 elements.</p>
+</div>
+<div class="paragraph">
+<p>If the fixed workgroup size of the shader in any dimension is less than
+or equal to zero or greater than the maximum size supported by the
+implementation for that dimension, a compile-time error results.
+Also, if such a layout qualifier is declared more than once in the same
+shader, all those declarations must set the same set of workgroup
+sizes and set them to the same values; otherwise a compile-time error
+results.
+If multiple compute shaders attached to a single program object declare a
+fixed workgroup size, the declarations must be identical; otherwise a
+link-time error results.</p>
+</div>
+<div class="paragraph">
+<p>Furthermore, if a program object contains any compute shaders, at least one
+must contain an input layout qualifier specifying a fixed workgroup size
+for the program, or a link-time error will occur.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="output-layout-qualifiers">4.4.2. Output Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Some output layout qualifiers apply to all shader stages and some apply only
+to specific stages.
+The latter are discussed in separate sections below.</p>
+</div>
+<div class="paragraph">
+<p>As with input layout qualifiers, all shaders except compute shaders allow
+<strong>location</strong> layout qualifiers on output variable declarations, output block
+declarations, and output block member declarations.
+Of these, variables and block members (but not blocks) additionally allow
+the <strong>component</strong> layout qualifier.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>location</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>component</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The usage and rules for applying the <strong>location</strong> qualifier
+and the <strong>component</strong> qualifier
+to blocks and structures are exactly as described in
+&#8220;<a href="#input-layout-qualifiers">Input Layout Qualifiers</a>&#8221;.
+Additionally, for fragment shader outputs, if two variables are placed
+within the same location, they must have the same underlying type
+(floating-point or integer).
+No component aliasing of output variables or members is allowed.</p>
+</div>
+<div class="paragraph">
+<p>Fragment shaders allow an additional <strong>index</strong> output layout qualifier:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>index</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Each of these qualifiers may appear at most once.
+If <strong>index</strong> is specified, <strong>location</strong> must also be specified.
+If <strong>index</strong> is not specified, the value 0 is used.
+For example, in a fragment shader,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>) out vec4 color;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the fragment shader output <em>color</em> is assigned to
+fragment color 3 as the first (index zero) input to the blend equation.
+And,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">3</span>, index = <span class="integer">1</span>) out vec4 factor;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the fragment shader output <em>factor</em> is assigned to
+fragment color 3 as the second (index one) input to the blend equation.</p>
+</div>
+<div class="paragraph">
+<p>For fragment shader outputs, the location
+and index specify
+the color output number
+and index
+receiving the values of the output.
+For outputs of all other shader stages, the location specifies a vector
+number that can be used to match against inputs in a subsequent shader
+stage, even if that shader is in a different program object.</p>
+</div>
+<div class="paragraph">
+<p>If a declared output is a scalar or vector type other than <strong>dvec3</strong> or
+<strong>dvec4</strong>, it will consume a single location.
+Outputs of type <strong>dvec3</strong> or <strong>dvec4</strong> will consume two consecutive locations.
+Outputs of type <strong>double</strong> and <strong>dvec2</strong> will consume only a single location, in
+all stages.</p>
+</div>
+<div class="paragraph">
+<p>If the declared output is an array, it will be assigned consecutive
+locations starting with the location specified.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(location = <span class="integer">2</span>) out vec4 colors[<span class="integer">3</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that <em>colors</em> is assigned to vector location numbers 2, 3,
+and 4.</p>
+</div>
+<div class="paragraph">
+<p>If the declared output is an <em>n</em> × <em>m</em>
+matrix, it will be assigned multiple locations starting with the location
+specified.
+The number of locations assigned will be the same as for an <em>n</em>-element
+array of <em>m</em>-component vectors.</p>
+</div>
+<div class="paragraph">
+<p>If the declared output is a structure, its members will be assigned
+consecutive locations in the order of declaration, with the first member
+assigned the location specified for the structure.
+The number of locations consumed by a structure member is determined by
+applying the rules above recursively as though the structure member were
+declared as an output variable of the same type.</p>
+</div>
+<div class="paragraph">
+<p><strong>location</strong> layout qualifiers may be used on output variables declared as
+structures.
+However, it is a compile-time error to use a <strong>location</strong> qualifier on a
+structure member.
+Location layout qualifiers may be used on output blocks and output block
+members.</p>
+</div>
+<div class="paragraph">
+<p>The number of output locations available to a shader is limited.
+For fragment shaders, the limit is the advertised number of draw buffers.</p>
+</div>
+<div class="paragraph">
+<p>For all other shaders, the limit is implementation-dependent and must be no
+less than one fourth of the advertised maximum output component count
+(compute shaders have no outputs).
+A program will fail to link if any attached shader uses a location greater
+than or equal to the number of supported locations, unless device-dependent
+optimizations are able to make the program fit within available hardware
+resources.</p>
+</div>
+<div class="paragraph">
+<p>Compile-time errors may also be given if at compile time it is known the
+link will fail.
+A negative output location will result in a compile-time error.
+It is also a compile-time error if a fragment shader sets a layout index to
+less than 0 or greater than 1.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time or link-time error if any of the following occur:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>any two fragment shader output variables are assigned to the same
+location and index.</p>
+</li>
+<li>
+<p>if any two output variables from the same vertex, tessellation or
+geometry shader stage are assigned to the same location.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>For fragment shader outputs, locations can be assigned using either a
+<strong>layout</strong> qualifier or via the OpenGL API.</p>
+</div>
+<div class="paragraph">
+<p>For all shader types, a program will fail to link if explicit location
+assignments leave the linker unable to find space for other variables
+without explicit assignments.</p>
+</div>
+<div class="paragraph">
+<p>If an output variable with no location or index assigned in the shader text
+has a location specified through the OpenGL API, the API-assigned
+location will be used.
+Otherwise, such variables will be assigned a location by the linker.
+All such assignments will have a color index of zero.
+See section 15.2 &#8220;Shader Execution&#8221; of the <a href="#references">OpenGL Specification</a> for
+more details.
+A link-time error will occur if an output variable is declared in multiple
+shaders of the same language with conflicting location or index values.</p>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if a non-fragment output matches an input
+from a subsequent shader stage, the <strong>location</strong> layout qualifier (if any)
+must match.</p>
+</div>
+<div class="sect4">
+<h5 id="transform-feedback-layout-qualifiers">Transform Feedback Layout Qualifiers</h5>
+<div class="paragraph">
+<p>The vertex, tessellation, and geometry stages allow shaders to control
+transform feedback.
+When doing this, shaders will dictate which transform feedback buffers are
+in use, which output variables will be written to which buffers, and how
+each buffer is laid out.
+To accomplish this, shaders allow the following layout qualifier identifiers
+on output declarations:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>xfb_buffer</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>xfb_offset</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>xfb_stride</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Any shader making any static use (after preprocessing) of any of these
+<strong>xfb_</strong> qualifiers will cause the shader to be in a transform feedback
+capturing mode and hence responsible for describing the transform feedback
+setup.
+This mode will capture any output selected by <strong>xfb_offset</strong>, directly or
+indirectly, to a transform feedback buffer.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>xfb_buffer</strong> qualifier specifies which transform feedback buffer will
+capture outputs selected with <strong>xfb_offset</strong>.
+The <strong>xfb_buffer</strong> qualifier can be applied to the qualifier <strong>out</strong>, to output
+variables, to output blocks, and to output block members.
+Shaders in the transform feedback capturing mode have an initial global
+default of</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(xfb_buffer = <span class="integer">0</span>) out;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This default can be changed by declaring a different buffer with
+<strong>xfb_buffer</strong> on the interface qualifier <strong>out</strong>.
+This is the only way the global default can be changed.
+When a variable or output block is declared without an <strong>xfb_buffer</strong>
+qualifier, it inherits the global default buffer.
+When a variable or output block is declared with an <strong>xfb_buffer</strong> qualifier,
+it has that declared buffer.
+All members of a block inherit the block&#8217;s buffer.
+A member is allowed to declare an <strong>xfb_buffer</strong>, but it must match the buffer
+inherited from its block, or a compile-time error results.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(xfb_buffer=<span class="integer">2</span>, xfb_offset=<span class="integer">0</span>) out block { <span class="comment">// block's buffer is 2</span>
+    layout(xfb_buffer = <span class="integer">2</span>) vec4 v; <span class="comment">// okay, matches the inherited 2</span>
+    layout(xfb_buffer = <span class="integer">3</span>) vec4 u; <span class="comment">// ERROR, mismatched buffer</span>
+    vec4 w; <span class="comment">// inherited</span>
+};
+layout(xfb_offset=<span class="integer">16</span>) out vec4 t;  <span class="comment">// initial default is buffer 0</span>
+layout(xfb_buffer=<span class="integer">1</span>) out;          <span class="comment">// new global default of 1</span>
+out block {                        <span class="comment">// block has buffer 1</span>
+    vec4 x;                        <span class="comment">// x has buffer 1 (not captured)</span>
+    layout(xfb_buffer = <span class="integer">1</span>) vec4 y; <span class="comment">// okay (not captured)</span>
+    layout(xfb_buffer = <span class="integer">0</span>) vec4 z; <span class="comment">// ERROR, mismatched buffer</span>
+};
+layout(xfb_offset=<span class="integer">0</span>) out vec4 g;   <span class="comment">// g has buffer 1</span>
+layout(xfb_buffer=<span class="integer">2</span>) out vec4 h;   <span class="comment">// does not change global default</span>
+layout(xfb_offset=<span class="integer">16</span>) out vec4 j;  <span class="comment">// j has buffer 1</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Note this means all members of a block that go to a transform feedback
+buffer will go to the same buffer.</p>
+</div>
+<div class="paragraph">
+<p>When a block is declared as an array, all members of block array-element 0
+are captured, as previously described, by the declared or inherited
+<strong>xfb_buffer</strong>.
+Generally, an array of size <em>N</em> of blocks is captured by <em>N</em> consecutive
+buffers, with all members of block array-element <em>E</em> captured by buffer <em>B</em>,
+where <em>B</em> equals the declared or inherited <strong>xfb_buffer</strong> plus <em>E</em>.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time or link-time error to specify an <strong>xfb_buffer</strong>,
+including any additional buffers needed to capture an arrays of blocks, that
+is less than zero or greater than or equal to the implementation-dependent
+constant <em>gl_MaxTransformFeedbackBuffers</em>.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>xfb_offset</strong> qualifier assigns a byte offset within a transform feedback
+buffer.
+Only variables, block members, or blocks can be qualified with <strong>xfb_offset</strong>.
+If a block is qualified with <strong>xfb_offset</strong>, all its members are assigned
+transform feedback buffer offsets.
+If a block is not qualified with <strong>xfb_offset</strong>, any members of that block not
+qualified with an <strong>xfb_offset</strong> will not be assigned transform feedback
+buffer offsets.
+Only variables and block members that are assigned offsets will be captured
+(thus, a proper subset of a block can be captured).
+Each time such a variable or block member is written in a shader, the
+written value is captured at the assigned offset.
+If such a block member or variable is not written during a shader
+invocation, the buffer contents at the assigned offset will be undefined.
+Even if there are no static writes to a variable or member that is assigned
+a transform feedback offset, the space is still allocated in the buffer and
+still affects the stride.</p>
+</div>
+<div class="paragraph">
+<p>Variables and block members qualified with <strong>xfb_offset</strong> can be scalars,
+vectors, matrices, structures, and (sized) arrays of these.
+The offset must be a multiple of the size of the first component of the
+first qualified variable or block member, or a compile-time error results.
+Further, if applied to an aggregate containing a <strong>double</strong>, the offset must
+also be a multiple of 8, and the space taken in the buffer will be a
+multiple of 8.
+The given offset applies to the first component of the first member of the
+qualified entity.
+Then, within the qualified entity, subsequent components are each assigned,
+in order, to the next available offset aligned to a multiple of that
+component&#8217;s size.
+Aggregate types are flattened down to the component level to get this
+sequence of components.
+It is a compile-time error to apply <strong>xfb_offset</strong> to the declaration of an
+unsized array.</p>
+</div>
+<div class="paragraph">
+<p>No aliasing in output buffers is allowed: It is a compile-time or link-time
+error to specify variables with overlapping transform feedback offsets.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>xfb_stride</strong> qualifier specifies how many bytes are consumed by each
+captured vertex.
+It applies to the transform feedback buffer for that declaration, whether it
+is inherited or explicitly declared.
+It can be applied to variables, blocks, block members, or just the qualifier
+<strong>out</strong>.
+If the buffer is capturing any outputs with double-precision components, the
+stride must be a multiple of 8, otherwise it must be a multiple of 4, or a
+compile-time or link-time error results.
+It is a compile-time or link-time error to have any <strong>xfb_offset</strong> that
+overflows <strong>xfb_stride</strong>, whether stated on declarations before or after the
+<strong>xfb_stride</strong>, or in different compilation units.
+While <strong>xfb_stride</strong> can be declared multiple times for the same buffer, it is
+a compile-time or link-time error to have different values specified for the
+stride for the same buffer.</p>
+</div>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// buffer 1 has 32-byte stride</span>
+layout(xfb_buffer = <span class="integer">1</span>, xfb_stride = <span class="integer">32</span>) out;
+
+<span class="comment">// same as previous example; order within layout does not matter</span>
+layout(xfb_stride = <span class="integer">32</span>, xfb_buffer = <span class="integer">1</span>) out;
+
+<span class="comment">// everything in this block goes to buffer 0</span>
+layout(xfb_buffer = <span class="integer">0</span>, xfb_stride = <span class="integer">32</span>) out block1 {
+    layout(xfb_offset = <span class="integer">0</span>) vec4 a;  <span class="comment">// a goes to byte offset 0 of buffer 0</span>
+    layout(xfb_offset = <span class="integer">16</span>) vec4 b; <span class="comment">// b goes to offset 16 of buffer 0</span>
+};
+
+layout(xfb_buffer = <span class="integer">3</span>, xfb_offset = <span class="integer">12</span>) out block2 {
+    vec4 v;  <span class="comment">// v will be written to byte offsets 12 through 27 of buffer</span>
+    <span class="predefined-type">float</span> u; <span class="comment">// u will be written to offset 28</span>
+    layout(xfb_offset = <span class="integer">40</span>) vec4 w;
+    vec4 x;  <span class="comment">// x will be written to offset 56, the next available offset</span>
+};
+
+layout(xfb_buffer = <span class="integer">2</span>, xfb_stride = <span class="integer">32</span>) out block3 {
+    layout(xfb_offset = <span class="integer">12</span>) vec3 c;
+    layout(xfb_offset = <span class="integer">24</span>) vec3 d; <span class="comment">// ERROR, requires stride of 36</span>
+    layout(xfb_offset = <span class="integer">0</span>) vec3 g;  <span class="comment">// okay, increasing order not required</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When no <strong>xfb_stride</strong> is specified for a buffer, the stride of the buffer
+will be the smallest needed to hold the variable placed at the highest
+offset, including any required padding.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// if there no other declarations for buffer 3, it has stride 32</span>
+layout(xfb_buffer = <span class="integer">3</span>) out block4 {
+    layout(xfb_offset = <span class="integer">0</span>) vec4 e;
+    layout(xfb_offset = <span class="integer">16</span>) vec4 f;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The resulting stride (implicit or explicit), when divided by 4, must be less
+than or equal to the implementation-dependent constant
+<em>gl_MaxTransformFeedbackInterleavedComponents</em>.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-control-outputs">Tessellation Control Outputs</h5>
+<div class="paragraph">
+<p>Other than for the transform feedback layout qualifiers, tessellation
+control shaders allow output layout qualifiers only on the interface
+qualifier <strong>out</strong>, not on an output block, block member, or variable
+declaration.
+The output layout qualifier identifiers allowed for tessellation control
+shaders are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>vertices</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>vertices</strong> specifies the number of vertices in the output
+patch produced by the tessellation control shader, which also specifies the
+number of times the tessellation control shader is invoked.
+It is a compile- or link-time error for the output vertex count to be less
+than or equal to zero, or greater than the implementation-dependent maximum
+patch size.</p>
+</div>
+<div class="paragraph">
+<p>The intrinsically declared tessellation control output array <em>gl_out[]</em> will
+also be sized by any output layout declaration.
+Hence, the expression</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_out.length()</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will return the output patch vertex count specified in a previous output
+layout qualifier.
+For outputs declared without an array size, including intrinsically declared
+outputs (i.e., <em>gl_out</em>), a layout must be declared before any use of the
+method <strong>length</strong>() or other array use that requires its size to be known.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error if the output patch vertex count specified in an
+output layout qualifier does not match the array size specified in any
+output variable declaration in the same shader.</p>
+</div>
+<div class="paragraph">
+<p>All tessellation control shader layout declarations in a program must
+specify the same output patch vertex count.
+There must be at least one layout qualifier specifying an output patch
+vertex count in any program containing tessellation control shaders;
+however, such a declaration is not required in all tessellation control
+shaders.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-outputs">Geometry Outputs</h5>
+<div class="paragraph">
+<p>Geometry shaders can have three additional types of output layout
+identifiers: an output <em>primitive type</em>, a maximum output <em>vertex count</em>,
+and per-output <em>stream</em> numbers.
+The primitive type and vertex count identifiers are allowed only on the
+interface qualifier <strong>out</strong>, not on an output block, block member, or variable
+declaration.
+The stream identifier is allowed on the interface qualifier <strong>out</strong>, on output
+blocks, and on variable declarations.</p>
+</div>
+<div class="paragraph">
+<p>The layout qualifier identifiers for geometry shader outputs are</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>points</strong><br>
+<strong>line_strip</strong><br>
+<strong>triangle_strip</strong><br>
+<strong>max_vertices</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>stream</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The primitive type identifiers <strong>points</strong>, <strong>line_strip</strong>, and <strong>triangle_strip</strong>
+are used to specify the type of output primitive produced by the geometry
+shader, and only one of these is accepted.
+At least one geometry shader (compilation unit) in a program must declare an
+output primitive type, and all geometry shader output primitive type
+declarations in a program must declare the same primitive type.
+It is not required that all geometry shaders in a program declare an output
+primitive type.</p>
+</div>
+<div class="paragraph">
+<p>The vertex count identifier <strong>max_vertices</strong> is used to specify the maximum
+number of vertices the shader will ever emit in a single invocation.
+At least one geometry shader (compilation unit) in a program must declare a
+maximum output vertex count, and all geometry shader output vertex count
+declarations in a program must declare the same count.
+It is not required that all geometry shaders in a program declare a count.</p>
+</div>
+<div class="paragraph">
+<p>In this example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(triangle_strip, max_vertices = <span class="integer">60</span>) out; <span class="comment">// order does not matter</span>
+layout(max_vertices = <span class="integer">60</span>) out;  <span class="comment">// redeclaration okay</span>
+layout(triangle_strip) out;     <span class="comment">// redeclaration okay</span>
+layout(points) out;             <span class="comment">// error, contradicts triangle_strip</span>
+layout(max_vertices = <span class="integer">30</span>) out;  <span class="comment">// error, contradicts 60</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>all outputs from the geometry shader are triangles and at most 60 vertices
+will be emitted by the shader.
+It is an error for the maximum number of vertices to be greater than
+<em>gl_MaxGeometryOutputVertices</em>.</p>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>stream</strong> is used to specify that a geometry shader output
+variable or block is associated with a particular vertex stream (numbered
+beginning with zero).
+A default stream number may be declared at global scope by qualifying
+interface qualifier <strong>out</strong> as in this example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(stream = <span class="integer">1</span>) out;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The stream number specified in such a declaration replaces any previous
+default and applies to all subsequent block and variable declarations until
+a new default is established.
+The initial default stream number is zero.</p>
+</div>
+<div class="paragraph">
+<p>Each output block or non-block output variable is associated with a vertex
+stream.
+If the block or variable is declared with the stream identifier, it is
+associated with the specified stream; otherwise, it is associated with the
+current default stream.
+A block member may be declared with a stream identifier, but the specified
+stream must match the stream associated with the containing block.
+One example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(stream=<span class="integer">1</span>) out;           <span class="comment">// default is now stream 1</span>
+out vec4 var1;                  <span class="comment">// var1 gets default stream (1)</span>
+layout(stream=<span class="integer">2</span>) out Block1 {   <span class="comment">// &quot;Block1&quot; belongs to stream 2</span>
+    layout(stream=<span class="integer">2</span>) vec4 var2; <span class="comment">// redundant block member stream decl</span>
+    layout(stream=<span class="integer">3</span>) vec2 var3; <span class="comment">// ILLEGAL (must match block stream)</span>
+    vec3 var4;                  <span class="comment">// belongs to stream 2</span>
+};
+layout(stream=<span class="integer">0</span>) out;           <span class="comment">// default is now stream 0</span>
+out vec4 var5;                  <span class="comment">// var5 gets default stream (0)</span>
+out Block2 {                    <span class="comment">// &quot;Block2&quot; gets default stream (0)</span>
+    vec4 var6;
+};
+layout(stream=<span class="integer">3</span>) out vec4 var7; <span class="comment">// var7 belongs to stream 3</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Each vertex emitted by the geometry shader is assigned to a specific stream,
+and the attributes of the emitted vertex are taken from the set of output
+blocks and variables assigned to the targeted stream.
+After each vertex is emitted, the values of all output variables become
+undefined.
+Additionally, the output variables associated with each vertex stream may
+share storage.
+Writing to an output variable associated with one stream may overwrite
+output variables associated with any other stream.
+When emitting each vertex, a geometry shader should write to all outputs
+associated with the stream to which the vertex will be emitted and to no
+outputs associated with any other stream.</p>
+</div>
+<div class="paragraph">
+<p>If a geometry shader output block or variable is declared more than once,
+all such declarations must associate the variable with the same vertex
+stream.
+If any stream declaration specifies a non-existent stream number, the shader
+will fail to compile.</p>
+</div>
+<div class="paragraph">
+<p>Built-in geometry shader outputs are always associated with vertex stream
+zero.</p>
+</div>
+<div class="paragraph">
+<p>All geometry shader output layout declarations in a program must declare the
+same layout and same value for <strong>max_vertices</strong>.
+If geometry shaders are in a program, there must be at least one geometry
+output layout declaration somewhere in that
+program, but not all geometry
+shaders (compilation units) are required to declare it.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="fragment-outputs">Fragment Outputs</h5>
+<div class="paragraph">
+<p>The built-in fragment shader variable <em>gl_FragDepth</em> may be redeclared using
+one of the following layout qualifiers.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>depth_any</strong><br>
+<strong>depth_greater</strong><br>
+<strong>depth_less</strong><br>
+<strong>depth_unchanged</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The layout qualifier for <em>gl_FragDepth</em> constrains intentions of the final
+value of <em>gl_FragDepth</em> written by any shader invocation.
+GL implementations are allowed to perform optimizations assuming that the
+depth test fails (or passes) for a given fragment if all values of
+<em>gl_FragDepth</em> consistent with the layout qualifier would fail (or pass).
+This potentially includes skipping shader execution if the fragment is
+discarded because it is occluded and the shader has no side effects.
+If the final value of <em>gl_FragDepth</em> is inconsistent with its layout
+qualifier, the result of the depth test for the corresponding fragment is
+undefined.
+However, no error will be generated in this case.
+If the depth test passes and depth writes are enabled, the value written to
+the depth buffer is always the value of <em>gl_FragDepth</em>, whether or not it is
+consistent with the layout qualifier.</p>
+</div>
+<div class="paragraph">
+<p>By default, <em>gl_FragDepth</em> is qualified as <em>depth_any</em>.
+When the layout qualifier for <em>gl_FragDepth</em> is <em>depth_any</em>, the shader
+compiler will note any assignment to <em>gl_FragDepth</em> modifying it in an
+unknown way, and depth testing will always be performed after the shader has
+executed.
+When the layout qualifier is <em>depth_greater</em>, the GL can assume that the
+final value of <em>gl_FragDepth</em> is greater than or equal to the fragment&#8217;s
+interpolated depth value, as given by the <em>z</em> component of <em>gl_FragCoord</em>.
+When the layout qualifier is <em>depth_less</em>, the GL can assume that any
+modification of <em>gl_FragDepth</em> will only decrease its value.
+When the layout qualifier is <em>depth_unchanged</em>, the shader compiler will
+honor any modification to <em>gl_FragDepth</em>, but the rest of the GL can assume
+that <em>gl_FragDepth</em> is not assigned a new value.</p>
+</div>
+<div class="paragraph">
+<p>Redeclarations of <em>gl_FragDepth</em> are performed as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// redeclaration that changes nothing is allowed +</span>
+out <span class="predefined-type">float</span> gl_FragDepth;
+
+<span class="comment">// assume it may be modified in any way</span>
+layout(depth_any) out <span class="predefined-type">float</span> gl_FragDepth;
+
+<span class="comment">// assume it may be modified such that its value will only increase</span>
+layout(depth_greater) out <span class="predefined-type">float</span> gl_FragDepth;
+
+<span class="comment">// assume it may be modified such that its value will only decrease</span>
+layout(depth_less) out <span class="predefined-type">float</span> gl_FragDepth;
+
+<span class="comment">// assume it will not be modified</span>
+layout(depth_unchanged) out <span class="predefined-type">float</span> gl_FragDepth;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If <em>gl_FragDepth</em> is redeclared in any fragment shader in a program, it must
+be redeclared in all fragment shaders in that program that have static
+assignments to <em>gl_FragDepth</em>.
+All redeclarations of <em>gl_FragDepth</em> in all fragment shaders in a single
+program must have the same set of qualifiers.
+Within any shader, the first redeclarations of <em>gl_FragDepth</em> must appear
+before any use of <em>gl_FragDepth</em>.
+The built-in <em>gl_FragDepth</em> is only predeclared in fragment shaders, so
+redeclaring it in any other shader language results in a compile-time error.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-variable-layout-qualifiers">4.4.3. Uniform Variable Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Layout qualifiers can be used for uniform variables and subroutine uniforms.
+The layout qualifier identifiers for uniform variables and subroutine
+uniforms are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>location</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The location identifier can be used with default-block uniform variables and
+subroutine uniforms.
+The location specifies the location by which the OpenGL API can reference
+the uniform and update its value.
+Individual elements of a uniform array are assigned consecutive locations
+with the first element taking location <strong>location</strong>.
+No two default-block uniform variables in the program can have the same
+location, even if they are unused, otherwise a compile-time or link-time
+error will be generated.
+No two subroutine uniform variables can have the same location in the same
+shader stage, otherwise a compile-time or link-time error will be generated.
+Valid locations for default-block uniform variable locations are in the
+range of 0 to the implementation-defined maximum number of uniform locations
+minus one.
+Valid locations for subroutine uniforms are in the range of 0 to the
+implementation-defined per-stage maximum number of subroutine uniform
+locations minus one.</p>
+</div>
+<div class="paragraph">
+<p>Locations can be assigned to default-block uniform arrays and structures.
+The first inner-most scalar, vector or matrix member or element takes the
+specified <strong>location</strong> and the compiler assigns the next inner-most member or
+element the next incremental location value.
+Each subsequent inner-most member or element gets incremental locations for
+the entire structure or array.
+This rule applies to nested structures and arrays and gives each inner-most
+scalar, vector, or matrix member a unique location.
+For arrays without an explicit size, the size is calculated based on its
+static usage.
+When the linker generates locations for uniforms without an explicit
+location, it assumes for all uniforms with an explicit location all their
+array elements and structure members are used and the linker will not
+generate a conflicting location, even if that element or member is deemed
+unused.</p>
+</div>
+<div class="paragraph">
+<p>When generating SPIR-V for OpenGL, it is a compile-time error to not
+include a location for individual (default block) non-opaque uniform
+variables.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="subroutine-function-layout-qualifiers">4.4.4. Subroutine Function Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Layout qualifiers can be used for subroutine functions.
+The layout qualifier identifiers for subroutine functions are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>index</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Each subroutine with an index qualifier in the shader must be given a unique
+index, otherwise a compile- or link-time error will be generated.
+The indices must be in the range of 0 to the implementation defined maximum
+number of subroutines minus one.
+It is recommended, but not required, that the shader assigns a range of
+tightly packed <em>index</em> values starting from zero so that the OpenGL
+subroutine function enumeration API returns a non-empty name for all active
+indices.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="uniform-and-shader-storage-block-layout-qualifiers">4.4.5. Uniform and Shader Storage Block Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Layout qualifiers can be used for uniform and shader storage blocks, but not
+for non-block uniform declarations.
+The layout qualifier identifiers (and <strong>shared</strong> keyword) for uniform and
+shader storage blocks are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>shared</strong><br>
+<strong>packed</strong><br>
+<strong>std140</strong><br>
+<strong>std430</strong><br>
+<strong>row_major</strong><br>
+<strong>column_major</strong><br>
+<strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>offset</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>align</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>None of these have any semantic effect at all on the usage of the variables
+being declared; they only describe how data is laid out in memory.
+For example, matrix semantics are always column-based, as described in the
+rest of this specification, no matter what layout qualifiers are being used.</p>
+</div>
+<div class="paragraph">
+<p>Uniform and shader storage block layout qualifiers can be declared for
+global scope, on a single uniform or shader storage block, or on a single
+block member declaration.</p>
+</div>
+<div class="paragraph">
+<p>Default layouts are established at global scope for uniform blocks as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(layout-qualifier-id-list) uniform;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and for shader storage blocks as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(layout-qualifier-id-list) buffer;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When this is done, the previous default qualification is first inherited and
+then overridden as per the override rules listed below for each qualifier
+listed in the declaration.
+The result becomes the new default qualification scoped to subsequent
+uniform or shader storage block definitions.</p>
+</div>
+<div class="paragraph">
+<p>The initial state of compilation
+when generating SPIR-V
+is as if the following were declared:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(std140, column_major) uniform;
+layout(std430, column_major) buffer;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The initial state of compilation when not generating SPIR-V is as if the
+following were declared:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(shared, column_major) uniform;
+layout(shared, column_major) buffer;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Uniform and shader storage blocks can be declared with optional layout
+qualifiers, and so can their individual member declarations.
+Such block layout qualification is scoped only to the content of the block.
+As with global layout declarations, block layout qualification first
+inherits from the current default qualification and then overrides it.
+Similarly, individual member layout qualification is scoped just to the
+member declaration, and inherits from and overrides the block&#8217;s
+qualification.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>shared</strong> qualifier overrides only the <strong>std140</strong>, <strong>std430</strong>, and <strong>packed</strong>
+qualifiers; other qualifiers are inherited.
+The compiler/linker will ensure that multiple programs and programmable
+stages containing this definition will share the same memory layout for this
+block, as long as all arrays are declared with explicit sizes and all
+matrices have matching <strong>row_major</strong> and/or <strong>column_major</strong> qualifications
+(which may come from a declaration outside the block definition).
+This allows use of the same buffer to back the same block definition across
+different programs.
+It is a compile-time error to use the <strong>shared</strong> qualifier when generating
+SPIR-V.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>packed</strong> qualifier overrides only <strong>std140</strong>, <strong>std430</strong>, and <strong>shared</strong>;
+other qualifiers are inherited.
+When <strong>packed</strong> is used, no shareable layout is guaranteed.
+The compiler and linker can optimize memory use based on what variables
+actively get used and on other criteria.
+Offsets must be queried, as there is no other way of guaranteeing where (and
+which) variables reside within the block.</p>
+</div>
+<div class="paragraph">
+<p>It is a link-time error to access the same packed uniform or shader storage
+block in multiple stages within a program.
+Attempts to access the same packed uniform or shader storage block across
+programs can result in conflicting member offsets and in undefined values
+being read.
+However, implementations may aid application management of packed blocks by
+using canonical layouts for packed blocks.
+It is a compile-time error to use the <strong>packed</strong> qualifier when generating
+SPIR-V.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>std140</strong> and <strong>std430</strong> qualifiers override only the <strong>packed</strong>, <strong>shared</strong>,
+<strong>std140</strong>, and <strong>std430</strong> qualifiers; other qualifiers are inherited.
+The <strong>std430</strong> qualifier is supported only for shader storage blocks; a shader
+using the <strong>std430</strong> qualifier on a uniform block will fail to compile.</p>
+</div>
+<div class="paragraph">
+<p>The layout is explicitly determined by this, as described in section 7.6.2.2
+&#8220;Standard Uniform Block Layout&#8221; of the <a href="#references">OpenGL Specification</a>.
+Hence, as in <strong>shared</strong> above, the resulting layout is shareable across
+programs.</p>
+</div>
+<div class="paragraph">
+<p>Layout qualifiers on member declarations cannot use the <strong>shared</strong>, <strong>packed</strong>,
+<strong>std140</strong>, or <strong>std430</strong> qualifiers.
+These can only be used at global scope (without an object) or on a block
+declaration, or a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>row_major</strong> and <strong>column_major</strong> qualifiers only affect the layout of
+matrices, including all matrices contained in structures and arrays they are
+applied to, to all depths of nesting.
+These qualifiers can be applied to other types, but will have no effect.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>row_major</strong> qualifier overrides only the <strong>column_major</strong> qualifier; other
+qualifiers are inherited.
+Elements within a matrix row will be contiguous in memory.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>column_major</strong> qualifier overrides only the <strong>row_major</strong> qualifier; other
+qualifiers are inherited.
+Elements within a matrix column will be contiguous in memory.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>binding</strong> qualifier specifies the uniform buffer binding point
+corresponding to the uniform or shader storage block, which will be used to
+obtain the values of the member variables of the block.
+It is a compile-time error to specify the <strong>binding</strong> qualifier for the global
+scope or for block member declarations.
+Any uniform or shader storage block declared without a <strong>binding</strong> qualifier
+is initially assigned to block binding point zero.
+After a program is linked, the binding points used for uniform
+and shader storage blocks
+declared with or without a <strong>binding</strong> qualifier can be updated
+by the OpenGL API.</p>
+</div>
+<div class="paragraph">
+<p>If the <strong>binding</strong> qualifier is used with a uniform block or shader storage
+block instanced as an array, the first element of the array takes the
+specified block binding and each subsequent element takes the next
+consecutive binding point.
+For an array of arrays, each element (e.g. 6 elements for a[2][3]) gets a
+binding point, and they are ordered per the array of array ordering
+described in &#8220;<a href="#arrays.">Arrays.</a>&#8221;</p>
+</div>
+<div class="paragraph">
+<p>If the binding point for any uniform or shader storage block instance is
+less than zero, or greater than or equal to the corresponding
+implementation-dependent maximum number of buffer bindings, a compile-time
+error will occur.
+When the <strong>binding</strong> qualifier is used with a uniform or shader storage block
+instanced as an array of size <em>N</em>, all elements of the array from <strong>binding</strong>
+through <em>binding + N - 1</em> must be within this range.
+It is a compile-time or link-time error to use the same binding number for
+more than one uniform block or for more than one buffer block.</p>
+</div>
+<div class="paragraph">
+<p>When multiple arguments are listed in a <strong>layout</strong> declaration, the effect
+will be the same as if they were declared one at a time, in order from left
+to right, each in turn inheriting from and overriding the result from the
+previous qualification.</p>
+</div>
+<div class="paragraph">
+<p>For example</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(row_major, column_major)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>results in the qualification being <strong>column_major</strong>.
+Other examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(shared, row_major) uniform; <span class="comment">// default is now shared and row_major</span>
+
+layout(std140) uniform Transform { <span class="comment">// layout of this block is std140</span>
+    mat4 M1;                       <span class="comment">// row major</span>
+    layout(column_major) mat4 M2;  <span class="comment">// column major</span>
+    mat3 N1;                       <span class="comment">// row major</span>
+};
+
+uniform T2 {                       <span class="comment">// layout of this block is shared</span>
+    ...
+};
+
+layout(column_major) uniform T3 {  <span class="comment">// shared and column major</span>
+    mat4 M3;                       <span class="comment">// column major</span>
+    layout(row_major) mat4 m4;     <span class="comment">// row major</span>
+    mat3 N2;                       <span class="comment">// column major</span>
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>offset</strong> qualifier can only be used on block members of blocks declared
+with <strong>std140</strong> or <strong>std430</strong> layouts.
+The <strong>offset</strong> qualifier forces the qualified member to start at or after the
+specified <em>layout-qualifier-value</em>, which will be its byte offset from
+the beginning of the buffer.
+It is a compile-time error to have any offset, explicit or assigned, that
+lies within another member of the block.
+When not generating SPIR-V, it is a compile-time error to specify an offset
+that is smaller than the offset of the previous member in the block.
+Two blocks linked together in the same program with the same block name must
+have the exact same set of members qualified with <strong>offset</strong> and their
+<em>layout-qualifier-value</em> values must be the same, or a link-time error
+results.
+The specified offset must be a multiple of the base alignment of the type of
+the block member it qualifies, or a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>align</strong> qualifier can only be used on blocks or block members, and only
+for blocks declared with <strong>std140</strong> or <strong>std430</strong> layouts.
+The <strong>align</strong> qualifier makes the start of each block member have a minimum
+byte alignment.
+It does not affect the internal layout within each member, which will still
+follow the <strong>std140</strong> or <strong>std430</strong> rules.
+The specified alignment must be greater than 0 and a power of 2, or a
+compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>The <em>actual alignment</em> of a member will be the greater of the specified
+<strong>align</strong> alignment and the standard (e.g. <strong>std140</strong>) base alignment for the
+member&#8217;s type.
+The <em>actual offset</em> of a member is computed as follows: If <strong>offset</strong> was
+declared, start with that offset, otherwise start with the next available
+offset.
+If the resulting offset is not a multiple of the <em>actual alignment</em>,
+increase it to the first offset that is a multiple of the <em>actual
+alignment</em>.
+This results in the <em>actual offset</em> the member will have.</p>
+</div>
+<div class="paragraph">
+<p>When <strong>align</strong> is applied to an array, it affects only the start of the array,
+not the array&#8217;s internal stride.
+Both an <strong>offset</strong> and an <strong>align</strong> qualifier can be specified on a declaration.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>align</strong> qualifier, when used on a block, has the same effect as
+qualifying each member with the same <strong>align</strong> value as declared on the block,
+and gets the same compile-time results and errors as if this had been done.
+As described in general earlier, an individual member can specify its own
+<strong>align</strong>, which overrides the block-level <strong>align</strong>, but just for that member.</p>
+</div>
+<div class="paragraph">
+<p>Examples:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(std140) uniform block {
+ vec4 a;                         <span class="comment">// a takes offsets 0-15</span>
+ layout(offset = <span class="integer">32</span>) vec3 b;     <span class="comment">// b takes offsets 32-43</span>
+ layout(offset = <span class="integer">40</span>) vec2 c;     <span class="comment">// ERROR, lies within previous member</span>
+ layout(offset = <span class="integer">48</span>) vec2 d;     <span class="comment">// d takes offsets 48-55</span>
+ layout(align = <span class="integer">16</span>) <span class="predefined-type">float</span> e;     <span class="comment">// e takes offsets 64-67</span>
+ layout(align = <span class="integer">2</span>) <span class="predefined-type">double</span> f;     <span class="comment">// f takes offsets 72-79</span>
+ layout(align = <span class="integer">6</span>) <span class="predefined-type">double</span> g;     <span class="comment">// ERROR, 6 is not a power of 2</span>
+ layout(offset = <span class="integer">80</span>) <span class="predefined-type">float</span> h;    <span class="comment">// h takes offsets 80-83</span>
+ layout(align = <span class="integer">64</span>) dvec3 i;     <span class="comment">// i takes offsets 128-151</span>
+ layout(offset = <span class="integer">164</span>, align = <span class="integer">8</span>)
+ <span class="predefined-type">float</span> j;                        <span class="comment">// j takes offsets 168-171</span>
+};</code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="opaque-uniform-layout-qualifiers">4.4.6. Opaque Uniform Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Uniform layout qualifiers can be used to bind opaque uniform variables to
+specific buffers or units.
+Samplers can be bound to texture image units, images can be bound to image
+units, and atomic counters can be bound to buffers.</p>
+</div>
+<div class="paragraph">
+<p>Sampler, image and atomic counter types take the uniform layout qualifier
+identifier for binding:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The identifier <strong>binding</strong> specifies which unit will be bound.
+Any uniform sampler or image
+variable declared without a binding qualifier
+is initially bound to unit zero.
+After a program is linked, the unit referenced by a sampler
+or image
+uniform variable declared with or without a <strong>binding</strong> qualifier can be
+updated by the OpenGL API.</p>
+</div>
+<div class="paragraph">
+<p>If the <strong>binding</strong> qualifier is used with an array, the first element of the
+array takes the specified unit and each subsequent element takes the next
+consecutive unit.
+For an array of arrays, each element (e.g. 6 elements for a[2][3]) gets a
+binding point, and they are ordered per the array of array ordering
+described in &#8220;<a href="#arrays.">Arrays.</a>&#8221;</p>
+</div>
+<div class="paragraph">
+<p>If the <strong>binding</strong> is less than zero, or greater than or equal to the
+implementation-dependent maximum supported number of units, a compile-time
+error will occur.
+When the <strong>binding</strong> qualifier is used with an array of size <em>N</em>, all elements
+of the array from <strong>binding</strong> through <em>binding + N - 1</em> must be within this
+range.
+It is a compile-time or link-time error to use the same <strong>binding</strong> number for
+more than one atomic counter, unless the <em>offset</em> for the atomic counters
+sharing the same binding are all different.</p>
+</div>
+<div class="paragraph">
+<p>A link-time error will result if two shaders in a program specify different
+<em>layout-qualifier-value</em> bindings for the same opaque-uniform name.
+However, it is not an error to specify a binding on some but not all
+declarations for the same name, as shown in the examples below.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// in one shader...</span>
+layout(binding=<span class="integer">3</span>) uniform sampler2D s; <span class="comment">// s bound to unit 3</span>
+
+<span class="comment">// in another shader...</span>
+uniform sampler2D s;                   <span class="comment">// okay, s still bound at 3</span>
+
+<span class="comment">// in another shader...</span>
+layout(binding=<span class="integer">4</span>) uniform sampler2D s; <span class="comment">// ERROR: contradictory bindings</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="atomic-counter-layout-qualifiers">4.4.7. Atomic Counter Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Atomic counter layout qualifiers can be used on atomic counter declarations.
+The atomic counter qualifiers are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em><br>
+<strong>offset</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>, offset = <span class="integer">4</span>) uniform atomic_uint a;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the opaque handle to the atomic counter <em>a</em> will be
+bound to atomic counter buffer binding point 2 at an offset of 4 basic
+machine units into that buffer.
+The default <em>offset</em> for binding point 2 will be post incremented by 4 (the
+size of an atomic counter).</p>
+</div>
+<div class="paragraph">
+<p>A subsequent atomic counter declaration will inherit the previous (post
+incremented) offset.
+For example, a subsequent declaration of</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>) uniform atomic_uint bar;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will establish that the atomic counter <em>bar</em> has a binding to buffer binding
+point 2 at an offset of 8 basic machine units into that buffer.
+The offset for binding point 2 will again be post-incremented by 4 (the size
+of an atomic counter).</p>
+</div>
+<div class="paragraph">
+<p>When multiple variables are listed in a layout declaration, the effect will
+be the same as if they were declared one at a time, in order from left to
+right.</p>
+</div>
+<div class="paragraph">
+<p>Binding points are not inherited, only offsets.
+Each binding point tracks its own current default <em>offset</em> for inheritance
+of subsequent variables using the same <strong>binding</strong>.
+The initial state of compilation is that all <strong>binding</strong> points have an
+<em>offset</em> of 0.
+The <em>offset</em> can be set per binding point at global scope (without declaring
+a variable).
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>, offset = <span class="integer">4</span>) uniform atomic_uint;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Establishes that the next <strong>atomic_uint</strong> declaration for binding point 2 will
+inherit <em>offset</em> 4 (but does not establish a default <strong>binding</strong>):</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding = <span class="integer">2</span>) uniform atomic_uint bar; <span class="comment">// offset is 4</span>
+layout(offset = <span class="integer">8</span>) uniform atomic_uint bar;  <span class="comment">// error, no default binding</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Atomic counters may share the same binding point, but if a binding is
+shared, their offsets must be either explicitly or implicitly (from
+inheritance) unique and non overlapping.</p>
+</div>
+<div class="paragraph">
+<p>Example valid uniform declarations, assuming top of shader:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(binding=<span class="integer">3</span>, offset=<span class="integer">4</span>) uniform atomic_uint a; <span class="comment">// offset = 4</span>
+layout(binding=<span class="integer">2</span>) uniform atomic_uint b;           <span class="comment">// offset = 0</span>
+layout(binding=<span class="integer">3</span>) uniform atomic_uint c;           <span class="comment">// offset = 8</span>
+layout(binding=<span class="integer">2</span>) uniform atomic_uint d;           <span class="comment">// offset = 4</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Example of an invalid uniform declaration:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(offset=<span class="integer">4</span>) ...               <span class="comment">// error, must include binding</span>
+layout(binding=<span class="integer">1</span>, offset=<span class="integer">0</span>) ... a; <span class="comment">// okay</span>
+layout(binding=<span class="integer">2</span>, offset=<span class="integer">0</span>) ... b; <span class="comment">// okay</span>
+layout(binding=<span class="integer">1</span>, offset=<span class="integer">0</span>) ... c; <span class="comment">// error, offsets must not be shared</span>
+                                   <span class="comment">// between a and c</span>
+layout(binding=<span class="integer">1</span>, offset=<span class="integer">2</span>) ... d; <span class="comment">// error, overlaps offset 0 of a</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to bind an atomic counter with a binding value
+greater than or equal to <em>gl_MaxAtomicCounterBindings</em>.
+It is a compile-time error to declare an unsized array of <strong>atomic_uint</strong>.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="format-layout-qualifiers">4.4.8. Format Layout Qualifiers</h4>
+<div class="paragraph">
+<p>Format layout qualifiers can be used on image variable declarations (those
+declared with a basic type having &#8220;<strong>image</strong>&#8221; in its keyword).
+The format layout qualifier identifiers for image variable declarations are:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>layout-qualifier-id</em> : </dt>
+<dd>
+<p><em>float-image-format-qualifier</em><br>
+<em>int-image-format-qualifier</em><br>
+<em>uint-image-format-qualifier</em><br>
+<strong>binding</strong> <strong>=</strong> <em>layout-qualifier-value</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>float-image-format-qualifier</em> : </dt>
+<dd>
+<p><strong>rgba32f</strong><br>
+<strong>rgba16f</strong><br>
+<strong>rg32f</strong><br>
+<strong>rg16f</strong><br>
+<strong>r11f_g11f_b10f</strong><br>
+<strong>r32f</strong><br>
+<strong>r16f</strong><br>
+<strong>rgba16</strong><br>
+<strong>rgb10_a2</strong><br>
+<strong>rgba8</strong><br>
+<strong>rg16</strong><br>
+<strong>rg8</strong><br>
+<strong>r16</strong><br>
+<strong>r8</strong><br>
+<strong>rgba16_snorm</strong><br>
+<strong>rgba8_snorm</strong><br>
+<strong>rg16_snorm</strong><br>
+<strong>rg8_snorm</strong><br>
+<strong>r16_snorm</strong><br>
+<strong>r8_snorm</strong></p>
+</dd>
+<dt class="hdlist1"><em>int-image-format-qualifier</em> : </dt>
+<dd>
+<p><strong>rgba32i</strong><br>
+<strong>rgba16i</strong><br>
+<strong>rgba8i</strong><br>
+<strong>rg32i</strong><br>
+<strong>rg16i</strong><br>
+<strong>rg8i</strong><br>
+<strong>r32i</strong><br>
+<strong>r16i</strong><br>
+<strong>r8i</strong></p>
+</dd>
+<dt class="hdlist1"><em>uint-image-format-qualifier</em> : </dt>
+<dd>
+<p><strong>rgba32ui</strong><br>
+<strong>rgba16ui</strong><br>
+<strong>rgb10_a2ui</strong><br>
+<strong>rgba8ui</strong><br>
+<strong>rg32ui</strong><br>
+<strong>rg16ui</strong><br>
+<strong>rg8ui</strong><br>
+<strong>r32ui</strong><br>
+<strong>r16ui</strong><br>
+<strong>r8ui</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>A format layout qualifier specifies the image format associated with a
+declared image variable.
+Only one format qualifier may be specified for any image variable
+declaration.
+For image variables with floating-point component types (keywords starting
+with &#8220;<strong>image</strong>&#8221;), signed integer component types (keywords starting with
+&#8220;<strong>iimage</strong>&#8221;), or unsigned integer component types (keywords starting with
+&#8220;<strong>uimage</strong>&#8221;), the format qualifier used must match the
+<em>float-image-format-qualifier</em>, <em>int-image-format-qualifier</em>, or
+<em>uint-image-format-qualifier</em> grammar rules, respectively.
+It is a compile-time error to declare an image variable where the format
+qualifier does not match the image variable type.</p>
+</div>
+<div class="paragraph">
+<p>Any image variable used for image loads or atomic operations must specify a
+format layout qualifier; it is a compile-time error to pass an image uniform
+variable or function parameter declared without a format layout qualifier to
+an image load or atomic function.</p>
+</div>
+<div class="paragraph">
+<p>Uniforms not qualified with <strong>writeonly</strong> must have a format layout qualifier.
+Note that an image variable passed to a function for read access cannot be
+declared as <strong>writeonly</strong> and hence must have been declared with a format
+layout qualifier.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>binding</strong> qualifier was described in
+&#8220;<a href="#opaque-uniform-layout-qualifiers">Opaque Uniform Layout Qualifiers</a>&#8221;.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="interpolation-qualifiers">4.5. Interpolation Qualifiers</h3>
+<div class="paragraph">
+<p>Inputs and outputs that could be interpolated can be further qualified by at
+most one of the following interpolation qualifiers:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>smooth</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">perspective correct interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>flat</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">no interpolation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>noperspective</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">linear interpolation</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The presence of and type of interpolation is controlled by the above
+interpolation qualifiers as well as the auxiliary storage qualifiers
+<strong>centroid</strong> and <strong>sample</strong>.
+When no interpolation qualifier is present, smooth interpolation is used.
+It is a compile-time error to use more than one interpolation qualifier.
+The auxiliary storage qualifier <strong>patch</strong> is not used for interpolation; it is
+a compile-time error to use interpolation qualifiers with <strong>patch</strong>.</p>
+</div>
+<div class="paragraph">
+<p>A variable qualified as <strong>flat</strong> will not be interpolated.
+Instead, it will have the same value for every fragment within a primitive.
+This value will come from a single provoking vertex, as described by the
+<a href="#references">OpenGL Specification</a>.
+A variable qualified as <strong>flat</strong> may also be qualified as <strong>centroid</strong> or
+<strong>sample</strong>, which will mean the same thing as qualifying it only as <strong>flat</strong>.</p>
+</div>
+<div class="paragraph">
+<p>A variable qualified as <strong>smooth</strong> will be interpolated in a
+perspective-correct manner over the primitive being rendered.
+Interpolation in a perspective correct manner is specified in equation 14.7
+of the <a href="#references">OpenGL Specification</a>, section 14.5 &#8220;Line Segments&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>A variable qualified as <strong>noperspective</strong> must be interpolated linearly in
+screen space, as described in equation 3.7 of the <a href="#references">OpenGL Specification</a>,
+section 3.5 &#8220;Line Segments&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>When multisample rasterization is disabled, or for fragment shader input
+variables qualified with neither <strong>centroid</strong> nor <strong>sample</strong>, the value of the
+assigned variable may be interpolated anywhere within the pixel and a single
+value may be assigned to each sample within the pixel, to the extent
+permitted by the <a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>When multisample rasterization is enabled, <strong>centroid</strong> and <strong>sample</strong> may be
+used to control the location and frequency of the sampling of the qualified
+fragment shader input.
+If a fragment shader input is qualified with <strong>centroid</strong>, a single value may
+be assigned to that variable for all samples in the pixel, but that value
+must be interpolated at a location that lies in both the pixel and in the
+primitive being rendered, including any of the pixel&#8217;s samples covered by
+the primitive.
+Because the location at which the variable is interpolated may be different
+in neighboring pixels, and derivatives may be computed by computing
+differences between neighboring pixels, derivatives of centroid-sampled
+inputs may be less accurate than those for non-centroid interpolated
+variables.
+If a fragment shader input is qualified with <strong>sample</strong>, a separate value must
+be assigned to that variable for each covered sample in the pixel, and that
+value must be sampled at the location of the individual sample.</p>
+</div>
+<div class="paragraph">
+<p>It is a link-time error if, within the same stage, the interpolation
+qualifiers of variables of the same name do not match.</p>
+</div>
+<div class="sect3">
+<h4 id="redeclaring-built-in-interpolation-variables-in-the-compatibility-profile">4.5.1. Redeclaring Built-In Interpolation Variables in the Compatibility Profile</h4>
+<div class="paragraph">
+<p>The following predeclared variables can be redeclared with an interpolation
+qualifier when using the compatibility profile:</p>
+</div>
+<div class="paragraph">
+<p>Vertex, tessellation control, tessellation evaluation, and geometry
+languages:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_FrontColor
+gl_BackColor
+gl_FrontSecondaryColor
+gl_BackSecondaryColor</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Fragment language:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_Color
+gl_SecondaryColor</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 gl_Color;            <span class="comment">// predeclared by the fragment language</span>
+flat in vec4 gl_Color;       <span class="comment">// redeclared by user to be flat</span>
+flat in vec4 gl_FrontColor;  <span class="comment">// input to geometry shader, no &quot;gl_in[]&quot;</span>
+flat out vec4 gl_FrontColor; <span class="comment">// output from geometry shader</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Ideally, these are redeclared as part of the redeclaration of an interface
+block, as described in
+&#8220;<a href="#compatibility-profile-built-in-language-variables">Compatibility Profile
+Built-In Language Variables</a>&#8221;.
+However, for the above purpose, they can be redeclared as individual
+variables at global scope, outside an interface block.
+Such redeclarations also allow adding the transform-feedback qualifiers
+<strong>xfb_buffer</strong>, <strong>xfb_stride</strong>, and <strong>xfb_offset</strong> to output variables.
+(Using <strong>xfb_buffer</strong> on a variable does not change the global default
+buffer.) A compile-time error will result if a shader has both an interface
+block redeclaration and a separate redeclaration of a member of that
+interface block outside the interface block redeclaration.</p>
+</div>
+<div class="paragraph">
+<p>If <em>gl_Color</em> is redeclared with an interpolation qualifier, then
+<em>gl_FrontColor</em> and <em>gl_BackColor</em> (if they are written to) must also be
+redeclared with the same interpolation qualifier, and vice versa.
+If <em>gl_SecondaryColor</em> is redeclared with an interpolation qualifier, then
+<em>gl_FrontSecondaryColor</em> and _gl_BackSecondaryColor _(if they are written
+to) must also be redeclared with the same interpolation qualifier, and vice
+versa.
+This qualifier matching on predeclared variables is only required for
+variables that are statically used within the shaders in a program.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="parameter-qualifiers">4.6. Parameter Qualifiers</h3>
+<div class="paragraph">
+<p>In addition to precision qualifiers and memory qualifiers, parameters can
+have these parameter qualifiers.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;none: default&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">same as <strong>in</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>const</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters that cannot be written to</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>in</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters passed into a function</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>out</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters passed back out of a function,
+                   but not initialized for use when passed in</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>inout</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">for function parameters passed both into and out of a
+                   function</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Parameter qualifiers are discussed in more detail in
+&#8220;<a href="#function-calling-conventions">Function Calling Conventions</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="precision-and-precision-qualifiers">4.7. Precision and Precision Qualifiers</h3>
+<div class="paragraph">
+<p>Precision qualifiers are added for code portability with OpenGL ES, not for
+functionality.
+They have the same syntax as in OpenGL ES, as described below, but they have
+no semantic meaning, which includes no effect on the precision used to store
+or operate on variables.</p>
+</div>
+<div class="paragraph">
+<p>If an extension adds in the same semantics and functionality in the OpenGL
+ES 2.0 specification for precision qualifiers, then the extension is allowed
+to reuse the keywords below for that purpose.</p>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if an output from one shader stage matches
+an input of the next stage, the precision qualifier need not match.</p>
+</div>
+<div class="sect3">
+<h4 id="range-and-precision">4.7.1. Range and Precision</h4>
+<div class="paragraph">
+<p>The precision of stored single- and double-precision floating-point
+variables is defined by the IEEE 754 standard for 32-bit and 64-bit
+floating-point numbers.
+This includes support for NaNs (Not a Number) and Infs (positive or negative
+infinities) and positive and negative zeros.</p>
+</div>
+<div class="paragraph">
+<p>The following rules apply to
+both single and double-precision
+operations:
+Signed infinities and zeros are generated as dictated by IEEE, but subject
+to the precisions allowed in the following table.
+Any subnormal (denormalized) value input into a shader or potentially
+generated by any operation in a shader can be flushed to 0.
+The rounding mode cannot be set and is undefined but must not affect the
+result by more than 1 ULP.
+NaNs are not required to be generated.
+Support for signaling NaNs is not required and exceptions are never raised.
+Operations including built-in functions that operate on a NaN are not
+required to return a NaN as the result.
+However if NaNs are generated, <strong>isnan</strong>() must return the correct value.</p>
+</div>
+<div class="paragraph">
+<p>Precisions are expressed in terms of maximum relative error in units of ULP
+(units in the last place), unless otherwise noted.</p>
+</div>
+<div class="paragraph">
+<p>For single precision operations, precisions are required as follows:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Operation</th>
+<th class="tableblock halign-left valign-top">Precision</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>a</em> + <em>b</em>, <em>a</em> - <em>b</em>, <em>a</em> * <em>b</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correctly rounded.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;, &lt;=, ==, &gt;, &gt;=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correct result.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>a</em> / <em>b</em>, 1.0 / <em>b</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2.5 ULP for <span class="eq">|b|</span> in the range <span class="eq">[2<sup>-126</sup>, 2<sup>126</sup>]</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>a</em> * <em>b</em> + <em>c</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correctly rounded single operation or
+                                    sequence of two correctly rounded operations.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>fma</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inherited from <em>a</em> * <em>b</em> + <em>c</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>pow</strong>(<em>x</em>, <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inherited from <strong>exp2</strong>(<em>y</em> * <strong>log2</strong>(<em>x</em>)).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>exp</strong>(<em>x</em>), <strong>exp2</strong>(<em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><span class="eq">(3 + 2 · |x|)</span> ULP.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>log</strong>(), <strong>log2</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3 ULP outside the range <span class="eq">[0.5,2.0]</span>.<br>
+                                    Absolute error &lt; 2<sup>-21</sup> inside the range
+                                    <span class="eq">[0.5,2.0]</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>sqrt</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inherited from 1.0 / <strong>inversesqrt</strong>().</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>inversesqrt</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2 ULP.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">implicit and explicit
+  conversions between types</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Correctly rounded.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Built-in functions defined in the specification with an equation built from
+the above operations inherit the above errors.
+These include, for example, the geometric functions, the common functions,
+and many of the matrix functions.
+Built-in functions not listed above and not defined as equations of the
+above have undefined precision.
+These include, for example, the trigonometric functions and determinant.</p>
+</div>
+<div class="paragraph">
+<p>The precision of double-precision operations is at least that of single
+precision.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="precision-qualifiers">4.7.2. Precision Qualifiers</h4>
+<div class="paragraph">
+<p>Any
+single-precision
+floating-point, integer, or opaque-type declaration can have the type
+preceded by one of these precision qualifiers:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>highp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">None.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mediump</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">None.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>lowp</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">None.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">lowp <span class="predefined-type">float</span> color;
+out mediump vec2 P;
+lowp ivec2 foo(lowp mat3);
+highp mat4 m;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Literal constants do not have precision qualifiers.
+Neither do Boolean variables.
+Neither do constructors.</p>
+</div>
+<div class="paragraph">
+<p>Precision qualifiers, as with other qualifiers, do not affect the basic type
+of the variable.
+In particular, there are no constructors for precision conversions;
+constructors only convert types.
+Similarly, precision qualifiers, as with other qualifiers, do not contribute
+to function overloading based on parameter types.
+As discussed in &#8220;<a href="#function-calling-conventions">Function Calling
+Conventions</a>&#8221;, function input and output is done through copies, and
+therefore qualifiers do not have to match.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="default-precision-qualifiers">4.7.3. Default Precision Qualifiers</h4>
+<div class="paragraph">
+<p>The precision statement</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision precision-qualifier type;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>can be used to establish a default precision qualifier.
+The <em>type</em> field can be either <strong>int</strong>, <strong>float</strong>, or any of the opaque types,
+and the <em>precision-qualifier</em> can be <strong>lowp</strong>, <strong>mediump</strong>, or <strong>highp</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Any other types or qualifiers will result in a compile-time error.
+If <em>type</em> is <strong>float</strong>, the directive applies to non-precision-qualified
+single-precision
+floating-point type (scalar, vector, and matrix) declarations.
+If <em>type</em> is <strong>int</strong>, the directive applies to all non-precision-qualified
+integer type (scalar, vector, signed, and unsigned) declarations.
+This includes global variable declarations, function return declarations,
+function parameter declarations, and local variable declarations.</p>
+</div>
+<div class="paragraph">
+<p>Non-precision qualified declarations will use the precision qualifier
+specified in the most recent <strong>precision</strong> statement that is still in scope.
+The <strong>precision</strong> statement has the same scoping rules as variable
+declarations.
+If it is declared inside a compound statement, its effect stops at the end
+of the inner-most statement it was declared in.
+Precision statements in nested scopes override precision statements in outer
+scopes.
+Multiple precision statements for the same basic type can appear inside the
+same scope, with later statements overriding earlier statements within that
+scope.</p>
+</div>
+<div class="paragraph">
+<p>All languages except for the fragment language have the following
+predeclared globally scoped default precision statements:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision highp <span class="predefined-type">float</span>;
+precision highp <span class="predefined-type">int</span>;
+precision highp atomic_uint;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The fragment language has the following predeclared globally scoped default
+precision statements:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precision mediump <span class="predefined-type">int</span>;
+precision highp <span class="predefined-type">float</span>;
+precision highp atomic_uint;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There are no errors for omission of a precision qualifier; so the above is
+just for reference of what may happen in OpenGL ES versions of the shading
+languages.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="available-precision-qualifiers">4.7.4. Available Precision Qualifiers</h4>
+<div class="paragraph">
+<p>The built-in macro GL_FRAGMENT_PRECISION_HIGH is defined to one:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#define</span> GL_FRAGMENT_PRECISION_HIGH <span class="integer">1</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This macro is available in all languages except compute.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="variance-and-the-invariant-qualifier">4.8. Variance and the Invariant Qualifier</h3>
+<div class="paragraph">
+<p>In this section, <em>variance</em> refers to the possibility of getting different
+values from the same expression in different programs.
+For example, consider the situation where two vertex shaders, in different
+programs, each set <em>gl_Position</em> with the same expression, and the input
+values into that expression are the same when both shaders run.
+It is possible, due to independent compilation of the two shaders, that the
+values assigned to <em>gl_Position</em> are not exactly the same when the two
+shaders run.
+In this example, this can cause problems with alignment of geometry in a
+multi-pass algorithm.</p>
+</div>
+<div class="paragraph">
+<p>In general, such variance between shaders is allowed.
+When such variance does not exist for a particular output variable, that
+variable is said to be <em>invariant</em>.</p>
+</div>
+<div class="sect3">
+<h4 id="the-invariant-qualifier">4.8.1. The Invariant Qualifier</h4>
+<div class="paragraph">
+<p>To ensure that a particular output variable is invariant, it is necessary to
+use the <strong>invariant</strong> qualifier.
+It can either be used to qualify a previously declared variable as being
+invariant:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">invariant gl_Position; <span class="comment">// make existing gl_Position be invariant</span>
+out vec3 Color;
+invariant Color;       <span class="comment">// make existing Color be invariant</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>or as part of a declaration when a variable is declared:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">invariant centroid out vec3 Color;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Only variables output from a shader can be candidates for invariance.
+This includes user-defined output variables and the built-in output
+variables.
+As only outputs can be declared as invariant, an output from one shader
+stage will still match an input of a subsequent stage without the input
+being declared as invariant.</p>
+</div>
+<div class="paragraph">
+<p>Input or output instance names on blocks are not used when redeclaring
+built-in variables.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>invariant</strong> keyword can be followed by a comma separated list of
+previously declared identifiers.
+All uses of <strong>invariant</strong> must be at global scope or on block
+members, and before any use of the variables being declared as invariant.</p>
+</div>
+<div class="paragraph">
+<p>To guarantee invariance of a particular output variable across two programs,
+the following must also be true:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The output variable is declared as invariant in both programs.</p>
+</li>
+<li>
+<p>The same values must be input to all shader input variables consumed by
+expressions and control flow contributing to the value assigned to the
+output variable.</p>
+</li>
+<li>
+<p>The texture formats, texel values, and texture filtering are set the
+same way for any texture function calls contributing to the value of the
+output variable.</p>
+</li>
+<li>
+<p>All input values are all operated on in the same way.
+    All operations in the consuming expressions and any intermediate
+    expressions must be the same, with the same order of operands and same
+    associativity, to give the same order of evaluation.
+    Intermediate variables and functions must be declared as the same type
+    with the same explicit or implicit precision
+qualifiers.
+    Any control flow affecting the output value must be the same, and any
+    expressions consumed to determine this control flow must also follow
+    these invariance rules.</p>
+</li>
+<li>
+<p>All the data flow and control flow leading to setting the invariant
+output variable reside in a single compilation unit.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Essentially, all the data flow and control flow leading to an invariant
+output must match.</p>
+</div>
+<div class="paragraph">
+<p>Initially, by default, all output variables are allowed to be variant.
+To force all output variables to be invariant, use the pragma</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="preprocessor">#pragma</span> STDGL invariant(all)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>before all declarations in a shader.
+If this pragma is used after the declaration of any variables or functions,
+then the set of outputs that behave as invariant is undefined.</p>
+</div>
+<div class="paragraph">
+<p>Generally, invariance is ensured at the cost of flexibility in optimization,
+so performance can be degraded by use of invariance.
+Hence, use of this pragma is intended as a debug aid, to avoid individually
+declaring all output variables as invariant.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="invariance-of-constant-expressions">4.8.2. Invariance of Constant Expressions</h4>
+<div class="paragraph">
+<p>Invariance must be guaranteed for constant expressions.
+A particular constant expression must evaluate to the same result if it
+appears again in the same shader or a different shader.
+This includes the same expression appearing in two shaders of the same
+language or shaders of two different languages.</p>
+</div>
+<div class="paragraph">
+<p>Constant expressions must evaluate to the same result when operated on as
+already described above for invariant variables.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="the-precise-qualifier">4.9. The Precise Qualifier</h3>
+<div class="paragraph">
+<p>Some algorithms require floating-point computations to exactly follow the
+order of operations specified in the source code and to treat all operations
+consistently, even if the implementation supports optimizations that could
+produce nearly equivalent results with higher performance.
+For example, many GL implementations support a &#8220;multiply-add&#8221; instruction
+that can compute a floating-point expression such as</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">result = (a * b) + (c * d);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>in two operations instead of three operations; one multiply and one
+multiply-add instead of two multiplies and one add.
+The result of a floating-point multiply-add might not always be identical to
+first doing a multiply yielding a floating-point result and then doing a
+floating-point add.
+Hence, in this example, the two multiply operations would not be treated
+consistently; the two multiplies could effectively appear to have differing
+precisions.</p>
+</div>
+<div class="paragraph">
+<p>The key computation that needs to be made consistent appears when
+tessellating, where intermediate points for subdivision are synthesized in
+different directions, yet need to yield the same result, as shown in the
+diagram below.</p>
+</div>
+<div id="img-precise" class="imageblock">
+<div class="content">
+<img src="data:image/svg+xml;base64,<?xml version="1.0" encoding="UTF-8"?>

<svg version="1.2" baseProfile="tiny" width="210mm" height="297mm" viewBox="0 0 21000 29700" preserveAspectRatio="xMidYMid" fill-rule="evenodd" clip-path="url(#presentation_clip_path)" stroke-width="28.222" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" xmlns:ooo="http://xml.openoffice.org/svg/export" xmlns:xlink="http://www.w3.org/1999/xlink" xml:space="preserve">
 <defs class="ClipPathGroup">
  <clipPath id="presentation_clip_path" clipPathUnits="userSpaceOnUse">
   <rect x="0" y="0" width="21000" height="29700"/>
  </clipPath>
 </defs>
 <defs>
  <font id="EmbeddedFont_1" horiz-adv-x="2048">
   <font-face font-family="Liberation Sans embedded" units-per-em="2048" font-weight="normal" font-style="normal" ascent="1852" descent="423"/>
   <missing-glyph horiz-adv-x="2048" d="M 0,0 L 2047,0 2047,2047 0,2047 0,0 Z"/>
   <glyph unicode="w" horiz-adv-x="1509" d="M 1174,0 L 965,0 792,698 C 787,716 781,738 776,765 770,792 764,818 759,843 752,872 746,903 740,934 734,904 728,874 721,845 716,820 710,793 704,766 697,739 691,715 686,694 L 508,0 300,0 -3,1082 175,1082 358,347 C 363,332 367,313 372,291 377,268 381,246 386,225 391,200 396,175 401,149 406,174 412,199 418,223 423,244 429,265 434,286 439,307 444,325 448,339 L 644,1082 837,1082 1026,339 C 1031,322 1036,302 1041,280 1046,258 1051,237 1056,218 1061,195 1067,172 1072,149 1077,174 1083,199 1088,223 1093,244 1098,265 1103,288 1108,310 1112,330 1117,347 L 1308,1082 1484,1082 1174,0 Z"/>
   <glyph unicode="v" horiz-adv-x="1033" d="M 613,0 L 400,0 7,1082 199,1082 437,378 C 442,363 447,346 454,325 460,304 466,282 473,259 480,236 486,215 492,194 497,173 502,155 506,141 510,155 515,173 522,194 528,215 534,236 541,258 548,280 555,302 562,323 569,344 575,361 580,376 L 826,1082 1017,1082 613,0 Z"/>
   <glyph unicode="u" horiz-adv-x="874" d="M 314,1082 L 314,396 C 314,343 318,299 326,264 333,229 346,200 363,179 380,157 403,142 432,133 460,124 495,119 537,119 580,119 618,127 653,142 687,157 716,178 741,207 765,235 784,270 797,312 810,353 817,401 817,455 L 817,1082 997,1082 997,231 C 997,208 997,185 998,160 998,135 998,111 999,89 1000,66 1000,47 1001,31 1002,15 1002,5 1003,0 L 833,0 C 832,3 832,12 831,27 830,42 830,59 829,78 828,97 827,116 826,136 825,155 825,172 825,185 L 822,185 C 805,154 786,125 765,100 744,75 720,53 693,36 666,18 634,4 599,-6 564,-15 523,-20 476,-20 416,-20 364,-13 321,2 278,17 242,39 214,70 186,101 166,140 153,188 140,236 133,294 133,361 L 133,1082 314,1082 Z"/>
   <glyph unicode="t" horiz-adv-x="531" d="M 554,8 C 527,1 499,-5 471,-10 442,-14 409,-16 372,-16 228,-16 156,66 156,229 L 156,951 31,951 31,1082 163,1082 216,1324 336,1324 336,1082 536,1082 536,951 336,951 336,268 C 336,216 345,180 362,159 379,138 408,127 450,127 467,127 484,128 501,131 517,134 535,137 554,141 L 554,8 Z"/>
   <glyph unicode="s" horiz-adv-x="901" d="M 950,299 C 950,248 940,203 921,164 901,124 872,91 835,64 798,37 752,16 698,2 643,-13 581,-20 511,-20 448,-20 392,-15 342,-6 291,4 247,20 209,41 171,62 139,91 114,126 88,161 69,203 57,254 L 216,285 C 231,227 263,185 311,158 359,131 426,117 511,117 550,117 585,120 618,125 650,130 678,140 701,153 724,166 743,183 756,205 769,226 775,253 775,285 775,318 767,345 752,366 737,387 715,404 688,418 661,432 628,444 589,455 550,465 507,476 460,489 417,500 374,513 331,527 288,541 250,560 216,583 181,606 153,634 132,668 111,702 100,745 100,796 100,895 135,970 206,1022 276,1073 378,1099 513,1099 632,1099 727,1078 798,1036 868,994 912,927 931,834 L 769,814 C 763,842 752,866 736,885 720,904 701,919 678,931 655,942 630,951 602,956 573,961 544,963 513,963 432,963 372,951 333,926 294,901 275,864 275,814 275,785 282,761 297,742 311,723 331,707 357,694 382,681 413,669 449,660 485,650 525,640 568,629 597,622 626,614 656,606 686,597 715,587 744,576 772,564 799,550 824,535 849,519 870,500 889,478 908,456 923,430 934,401 945,372 950,338 950,299 Z"/>
   <glyph unicode="r" horiz-adv-x="530" d="M 142,0 L 142,830 C 142,853 142,876 142,900 141,923 141,946 140,968 139,990 139,1011 138,1030 137,1049 137,1067 136,1082 L 306,1082 C 307,1067 308,1049 309,1030 310,1010 311,990 312,969 313,948 313,929 314,910 314,891 314,874 314,861 L 318,861 C 331,902 344,938 359,969 373,999 390,1024 409,1044 428,1063 451,1078 478,1088 505,1097 537,1102 575,1102 590,1102 604,1101 617,1099 630,1096 641,1094 648,1092 L 648,927 C 636,930 622,933 606,935 590,936 572,937 552,937 511,937 476,928 447,909 418,890 394,865 376,832 357,799 344,759 335,714 326,668 322,618 322,564 L 322,0 142,0 Z"/>
   <glyph unicode="p" horiz-adv-x="953" d="M 1053,546 C 1053,464 1046,388 1033,319 1020,250 998,190 967,140 936,90 895,51 844,23 793,-6 730,-20 655,-20 578,-20 510,-5 452,24 394,53 350,101 319,168 L 314,168 C 315,167 315,161 316,150 316,139 316,126 317,110 317,94 317,76 318,57 318,37 318,17 318,-2 L 318,-425 138,-425 138,861 C 138,887 138,912 138,936 137,960 137,982 136,1002 135,1021 135,1038 134,1052 133,1066 133,1076 132,1082 L 306,1082 C 307,1080 308,1073 309,1061 310,1049 311,1035 312,1018 313,1001 314,982 315,963 316,944 316,925 316,908 L 320,908 C 337,943 356,972 377,997 398,1021 423,1041 450,1057 477,1072 508,1084 542,1091 575,1098 613,1101 655,1101 730,1101 793,1088 844,1061 895,1034 936,997 967,949 998,900 1020,842 1033,774 1046,705 1053,629 1053,546 Z M 864,542 C 864,609 860,668 852,720 844,772 830,816 811,852 791,888 765,915 732,934 699,953 658,962 609,962 569,962 531,956 496,945 461,934 430,912 404,880 377,848 356,804 341,748 326,691 318,618 318,528 318,451 324,387 337,334 350,281 368,238 393,205 417,172 447,149 483,135 519,120 560,113 607,113 657,113 699,123 732,142 765,161 791,189 811,226 830,263 844,308 852,361 860,414 864,474 864,542 Z"/>
   <glyph unicode="o" horiz-adv-x="980" d="M 1053,542 C 1053,353 1011,212 928,119 845,26 724,-20 565,-20 490,-20 422,-9 363,14 304,37 254,71 213,118 172,165 140,223 119,294 97,364 86,447 86,542 86,915 248,1102 571,1102 655,1102 728,1090 789,1067 850,1044 900,1009 939,962 978,915 1006,857 1025,787 1044,717 1053,635 1053,542 Z M 864,542 C 864,626 858,695 845,750 832,805 813,848 788,881 763,914 732,937 696,950 660,963 619,969 574,969 528,969 487,962 450,949 413,935 381,912 355,879 329,846 309,802 296,747 282,692 275,624 275,542 275,458 282,389 297,334 312,279 332,235 358,202 383,169 414,146 449,133 484,120 522,113 563,113 609,113 651,120 688,133 725,146 757,168 783,201 809,234 829,278 843,333 857,388 864,458 864,542 Z"/>
   <glyph unicode="n" horiz-adv-x="874" d="M 825,0 L 825,686 C 825,739 821,783 814,818 806,853 793,882 776,904 759,925 736,941 708,950 679,959 644,963 602,963 559,963 521,956 487,941 452,926 423,904 399,876 374,847 355,812 342,771 329,729 322,681 322,627 L 322,0 142,0 142,851 C 142,874 142,898 142,923 141,948 141,971 140,994 139,1016 139,1035 138,1051 137,1067 137,1077 136,1082 L 306,1082 C 307,1079 307,1070 308,1055 309,1040 310,1024 311,1005 312,986 312,966 313,947 314,927 314,910 314,897 L 317,897 C 334,928 353,957 374,982 395,1007 419,1029 446,1047 473,1064 505,1078 540,1088 575,1097 616,1102 663,1102 723,1102 775,1095 818,1080 861,1065 897,1043 925,1012 953,981 974,942 987,894 1000,845 1006,788 1006,721 L 1006,0 825,0 Z"/>
   <glyph unicode="m" horiz-adv-x="1457" d="M 768,0 L 768,686 C 768,739 765,783 758,818 751,853 740,882 725,904 709,925 688,941 663,950 638,959 607,963 570,963 532,963 498,956 467,941 436,926 410,904 389,876 367,847 350,812 339,771 327,729 321,681 321,627 L 321,0 142,0 142,851 C 142,874 142,898 142,923 141,948 141,971 140,994 139,1016 139,1035 138,1051 137,1067 137,1077 136,1082 L 306,1082 C 307,1079 307,1070 308,1055 309,1040 310,1024 311,1005 312,986 312,966 313,947 314,927 314,910 314,897 L 317,897 C 333,928 350,957 369,982 388,1007 410,1029 435,1047 460,1064 488,1078 521,1088 553,1097 590,1102 633,1102 715,1102 780,1086 828,1053 875,1020 908,968 927,897 L 930,897 C 946,928 964,957 984,982 1004,1007 1027,1029 1054,1047 1081,1064 1111,1078 1144,1088 1177,1097 1215,1102 1258,1102 1313,1102 1360,1095 1400,1080 1439,1065 1472,1043 1497,1012 1522,981 1541,942 1553,894 1565,845 1571,788 1571,721 L 1571,0 1393,0 1393,686 C 1393,739 1390,783 1383,818 1376,853 1365,882 1350,904 1334,925 1313,941 1288,950 1263,959 1232,963 1195,963 1157,963 1123,956 1092,942 1061,927 1035,906 1014,878 992,850 975,815 964,773 952,731 946,682 946,627 L 946,0 768,0 Z"/>
   <glyph unicode="l" horiz-adv-x="187" d="M 138,0 L 138,1484 318,1484 318,0 138,0 Z"/>
   <glyph unicode="k" horiz-adv-x="901" d="M 816,0 L 450,494 318,385 318,0 138,0 138,1484 318,1484 318,557 793,1082 1004,1082 565,617 1027,0 816,0 Z"/>
   <glyph unicode="i" horiz-adv-x="187" d="M 137,1312 L 137,1484 317,1484 317,1312 137,1312 Z M 137,0 L 137,1082 317,1082 317,0 137,0 Z"/>
   <glyph unicode="h" horiz-adv-x="874" d="M 317,897 C 337,934 359,965 382,991 405,1016 431,1037 459,1054 487,1071 518,1083 551,1091 584,1098 622,1102 663,1102 732,1102 789,1093 834,1074 878,1055 913,1029 939,996 964,962 982,922 992,875 1001,828 1006,777 1006,721 L 1006,0 825,0 825,686 C 825,732 822,772 817,807 811,842 800,871 784,894 768,917 745,934 716,946 687,957 649,963 602,963 559,963 521,955 487,940 452,925 423,903 399,875 374,847 355,813 342,773 329,733 322,688 322,638 L 322,0 142,0 142,1484 322,1484 322,1098 C 322,1076 322,1054 321,1032 320,1010 320,990 319,971 318,952 317,937 316,924 315,911 315,902 314,897 L 317,897 Z"/>
   <glyph unicode="g" horiz-adv-x="927" d="M 548,-425 C 486,-425 431,-419 383,-406 335,-393 294,-375 260,-352 226,-328 198,-300 177,-267 156,-234 140,-198 131,-158 L 312,-132 C 324,-182 351,-220 392,-248 433,-274 486,-288 553,-288 594,-288 631,-282 664,-271 697,-260 726,-241 749,-217 772,-191 790,-159 803,-119 816,-79 822,-30 822,27 L 822,201 820,201 C 807,174 790,148 771,123 751,98 727,75 699,56 670,37 637,21 600,10 563,-2 520,-8 472,-8 403,-8 345,4 296,27 247,50 207,84 176,130 145,176 122,233 108,302 93,370 86,449 86,539 86,626 93,704 108,773 122,842 145,901 178,950 210,998 252,1035 304,1061 355,1086 418,1099 492,1099 569,1099 635,1082 692,1047 748,1012 791,962 822,897 L 824,897 C 824,914 825,932 826,953 827,974 828,993 829,1012 830,1030 831,1046 832,1059 833,1072 835,1080 836,1082 L 1007,1082 C 1006,1076 1006,1066 1005,1052 1004,1037 1004,1020 1003,1000 1002,980 1002,958 1002,934 1001,909 1001,884 1001,858 L 1001,31 C 1001,-120 964,-234 890,-311 815,-387 701,-425 548,-425 Z M 822,541 C 822,616 814,681 798,735 781,788 760,832 733,866 706,900 676,925 642,941 607,957 572,965 536,965 490,965 451,957 418,941 385,925 357,900 336,866 314,831 298,787 288,734 277,680 272,616 272,541 272,463 277,398 288,345 298,292 314,249 335,216 356,183 383,160 416,146 449,132 488,125 533,125 569,125 604,133 639,148 673,163 704,188 731,221 758,254 780,297 797,350 814,403 822,466 822,541 Z"/>
   <glyph unicode="f" horiz-adv-x="557" d="M 361,951 L 361,0 181,0 181,951 29,951 29,1082 181,1082 181,1204 C 181,1243 185,1280 192,1314 199,1347 213,1377 233,1402 252,1427 279,1446 313,1461 347,1475 391,1482 445,1482 466,1482 489,1481 512,1479 535,1477 555,1474 572,1470 L 572,1333 C 561,1335 548,1337 533,1339 518,1340 504,1341 492,1341 465,1341 444,1337 427,1330 410,1323 396,1312 387,1299 377,1285 370,1268 367,1248 363,1228 361,1205 361,1179 L 361,1082 572,1082 572,951 361,951 Z"/>
   <glyph unicode="e" horiz-adv-x="980" d="M 276,503 C 276,446 282,394 294,347 305,299 323,258 348,224 372,189 403,163 441,144 479,125 525,115 578,115 656,115 719,131 766,162 813,193 844,233 861,281 L 1019,236 C 1008,206 992,176 972,146 951,115 924,88 890,64 856,39 814,19 763,4 712,-12 650,-20 578,-20 418,-20 296,28 213,123 129,218 87,360 87,548 87,649 100,735 125,806 150,876 185,933 229,977 273,1021 324,1053 383,1073 442,1092 504,1102 571,1102 662,1102 738,1087 799,1058 860,1029 909,988 946,937 983,885 1009,824 1025,754 1040,684 1048,608 1048,527 L 1048,503 276,503 Z M 862,641 C 852,755 823,838 775,891 727,943 658,969 568,969 538,969 507,964 474,955 441,945 410,928 382,903 354,878 330,845 311,803 292,760 281,706 278,641 L 862,641 Z"/>
   <glyph unicode="d" horiz-adv-x="927" d="M 821,174 C 788,105 744,55 689,25 634,-5 565,-20 484,-20 347,-20 247,26 183,118 118,210 86,349 86,536 86,913 219,1102 484,1102 566,1102 634,1087 689,1057 744,1027 788,979 821,914 L 823,914 C 823,921 823,931 823,946 822,960 822,975 822,991 821,1006 821,1021 821,1035 821,1049 821,1059 821,1065 L 821,1484 1001,1484 1001,223 C 1001,197 1001,172 1002,148 1002,124 1002,102 1003,82 1004,62 1004,45 1005,31 1006,16 1006,6 1007,0 L 835,0 C 834,7 833,16 832,29 831,41 830,55 829,71 828,87 827,104 826,122 825,139 825,157 825,174 L 821,174 Z M 275,542 C 275,467 280,403 289,350 298,297 313,253 334,219 355,184 381,159 413,143 445,127 484,119 530,119 577,119 619,127 656,142 692,157 722,182 747,217 771,251 789,296 802,351 815,406 821,474 821,554 821,631 815,696 802,749 789,802 771,844 746,877 721,910 691,933 656,948 620,962 579,969 532,969 488,969 450,961 418,946 386,931 359,906 338,872 317,838 301,794 291,740 280,685 275,619 275,542 Z"/>
   <glyph unicode="c" horiz-adv-x="901" d="M 275,546 C 275,484 280,427 289,375 298,323 313,278 334,241 355,203 384,174 419,153 454,132 497,122 548,122 612,122 666,139 709,173 752,206 778,258 788,328 L 970,328 C 964,283 951,239 931,197 911,155 884,118 850,86 815,54 773,28 724,9 675,-10 618,-20 553,-20 468,-20 396,-6 337,23 278,52 230,91 193,142 156,192 129,251 112,320 95,388 87,462 87,542 87,615 93,679 105,735 117,790 134,839 156,881 177,922 203,957 232,986 261,1014 293,1037 328,1054 362,1071 398,1083 436,1091 474,1098 512,1102 551,1102 612,1102 666,1094 713,1077 760,1060 801,1038 836,1009 870,980 898,945 919,906 940,867 955,824 964,779 L 779,765 C 770,825 746,873 708,908 670,943 616,961 546,961 495,961 452,953 418,936 383,919 355,893 334,859 313,824 298,781 289,729 280,677 275,616 275,546 Z"/>
   <glyph unicode="b" horiz-adv-x="953" d="M 1053,546 C 1053,169 920,-20 655,-20 573,-20 505,-5 451,25 396,54 352,102 318,168 L 316,168 C 316,151 316,133 315,114 314,95 313,78 312,62 311,46 310,32 309,21 308,10 307,3 306,0 L 132,0 C 133,6 133,16 134,31 135,45 135,62 136,82 137,102 137,124 138,148 138,172 138,197 138,223 L 138,1484 318,1484 318,1061 C 318,1041 318,1022 318,1004 317,985 317,969 316,955 315,938 315,923 314,908 L 318,908 C 351,977 396,1027 451,1057 506,1087 574,1102 655,1102 792,1102 892,1056 957,964 1021,872 1053,733 1053,546 Z M 864,540 C 864,615 859,679 850,732 841,785 826,829 805,864 784,898 758,923 726,939 694,955 655,963 609,963 562,963 520,955 484,940 447,925 417,900 393,866 368,832 350,787 337,732 324,677 318,609 318,529 318,452 324,387 337,334 350,281 368,239 393,206 417,173 447,149 483,135 519,120 560,113 607,113 651,113 689,121 721,136 753,151 780,176 801,210 822,244 838,288 849,343 859,397 864,463 864,540 Z"/>
   <glyph unicode="a" horiz-adv-x="1060" d="M 414,-20 C 305,-20 224,9 169,66 114,124 87,203 87,303 87,375 101,434 128,480 155,526 190,562 234,588 277,614 327,632 383,642 439,652 496,657 554,657 L 797,657 797,717 C 797,762 792,800 783,832 774,863 759,889 740,908 721,928 697,942 668,951 639,960 604,965 565,965 530,965 499,963 471,958 443,953 419,944 398,931 377,918 361,900 348,878 335,855 327,827 323,793 L 135,810 C 142,853 154,892 173,928 192,963 218,994 253,1020 287,1046 330,1066 382,1081 433,1095 496,1102 569,1102 705,1102 807,1071 876,1009 945,946 979,856 979,738 L 979,272 C 979,219 986,179 1000,152 1014,125 1041,111 1080,111 1090,111 1100,112 1110,113 1120,114 1130,116 1139,118 L 1139,6 C 1116,1 1094,-3 1072,-6 1049,-9 1025,-10 1000,-10 966,-10 937,-5 913,4 888,13 868,26 853,45 838,63 826,86 818,113 810,140 805,171 803,207 L 797,207 C 778,172 757,141 734,113 711,85 684,61 653,42 622,22 588,7 549,-4 510,-15 465,-20 414,-20 Z M 455,115 C 512,115 563,125 606,146 649,167 684,194 713,226 741,259 762,294 776,332 790,371 797,408 797,443 L 797,531 600,531 C 556,531 514,528 475,522 435,517 400,506 370,489 340,472 316,449 299,418 281,388 272,349 272,300 272,241 288,195 320,163 351,131 396,115 455,115 Z"/>
   <glyph unicode="S" horiz-adv-x="1192" d="M 1272,389 C 1272,330 1261,275 1238,225 1215,175 1179,132 1131,96 1083,59 1023,31 950,11 877,-10 790,-20 690,-20 515,-20 378,11 280,72 182,133 120,222 93,338 L 278,375 C 287,338 302,305 321,275 340,245 367,219 400,198 433,176 473,159 522,147 571,135 629,129 697,129 754,129 806,134 853,144 900,153 941,168 975,188 1009,208 1036,234 1055,266 1074,297 1083,335 1083,379 1083,425 1073,462 1052,491 1031,520 1001,543 963,562 925,581 880,596 827,609 774,622 716,635 652,650 613,659 573,668 534,679 494,689 456,701 420,716 383,730 349,747 317,766 285,785 257,809 234,836 211,863 192,894 179,930 166,965 159,1006 159,1053 159,1120 173,1177 200,1225 227,1272 264,1311 312,1342 360,1373 417,1395 482,1409 547,1423 618,1430 694,1430 781,1430 856,1423 918,1410 980,1396 1032,1375 1075,1348 1118,1321 1152,1287 1178,1247 1203,1206 1224,1159 1239,1106 L 1051,1073 C 1042,1107 1028,1137 1011,1164 993,1191 970,1213 941,1231 912,1249 878,1263 837,1272 796,1281 747,1286 692,1286 627,1286 572,1280 528,1269 483,1257 448,1241 421,1221 394,1201 374,1178 363,1151 351,1124 345,1094 345,1063 345,1021 356,987 377,960 398,933 426,910 462,892 498,874 540,859 587,847 634,835 685,823 738,811 781,801 825,791 868,781 911,770 952,758 991,744 1030,729 1067,712 1102,693 1136,674 1166,650 1191,622 1216,594 1236,561 1251,523 1265,485 1272,440 1272,389 Z"/>
   <glyph unicode="O" horiz-adv-x="1430" d="M 1495,711 C 1495,601 1479,501 1448,411 1416,321 1370,244 1310,180 1250,116 1177,67 1090,32 1003,-3 905,-20 795,-20 679,-20 577,-2 490,35 403,71 330,122 272,187 214,252 170,329 141,418 112,507 97,605 97,711 97,821 112,920 143,1009 174,1098 219,1173 278,1236 337,1298 411,1346 498,1380 585,1413 684,1430 797,1430 909,1430 1009,1413 1096,1379 1183,1345 1256,1297 1315,1234 1374,1171 1418,1096 1449,1007 1480,918 1495,820 1495,711 Z M 1300,711 C 1300,796 1289,873 1268,942 1246,1011 1214,1071 1172,1120 1129,1169 1077,1207 1014,1234 951,1261 879,1274 797,1274 713,1274 639,1261 576,1234 513,1207 460,1169 418,1120 375,1071 344,1011 323,942 302,873 291,796 291,711 291,626 302,549 324,479 345,408 377,348 420,297 462,246 515,206 578,178 641,149 713,135 795,135 883,135 959,149 1023,178 1086,207 1139,247 1180,298 1221,349 1251,409 1271,480 1290,551 1300,628 1300,711 Z"/>
   <glyph unicode="C" horiz-adv-x="1324" d="M 792,1274 C 712,1274 641,1261 580,1234 518,1207 466,1169 425,1120 383,1071 351,1011 330,942 309,873 298,796 298,711 298,626 310,549 333,479 356,408 389,348 432,297 475,246 527,207 590,179 652,151 722,137 800,137 855,137 905,144 950,159 995,173 1035,193 1072,219 1108,245 1140,276 1169,312 1198,347 1223,387 1245,430 L 1401,352 C 1376,299 1344,250 1307,205 1270,160 1226,120 1176,87 1125,54 1068,28 1005,9 941,-10 870,-20 791,-20 677,-20 577,-2 492,35 406,71 334,122 277,187 219,252 176,329 147,418 118,507 104,605 104,711 104,821 119,920 150,1009 180,1098 224,1173 283,1236 341,1298 413,1346 498,1380 583,1413 681,1430 790,1430 940,1430 1065,1401 1166,1342 1267,1283 1341,1196 1388,1081 L 1207,1021 C 1194,1054 1176,1086 1153,1117 1130,1147 1102,1174 1068,1197 1034,1220 994,1239 949,1253 903,1267 851,1274 792,1274 Z"/>
   <glyph unicode=" " horiz-adv-x="556"/>
  </font>
 </defs>
 <defs class="TextShapeIndex">
  <g ooo:slide="id1" ooo:id-list="id3 id4 id5 id6 id7 id8 id9 id10 id11 id12 id13 id14 id15 id16 id17 id18 id19"/>
 </defs>
 <defs class="EmbeddedBulletChars">
  <g id="bullet-char-template(57356)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 580,1141 L 1163,571 580,0 -4,571 580,1141 Z"/>
  </g>
  <g id="bullet-char-template(57354)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 8,1128 L 1137,1128 1137,0 8,0 8,1128 Z"/>
  </g>
  <g id="bullet-char-template(10146)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 174,0 L 602,739 174,1481 1456,739 174,0 Z M 1358,739 L 309,1346 659,739 1358,739 Z"/>
  </g>
  <g id="bullet-char-template(10132)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 2015,739 L 1276,0 717,0 1260,543 174,543 174,936 1260,936 717,1481 1274,1481 2015,739 Z"/>
  </g>
  <g id="bullet-char-template(10007)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 0,-2 C -7,14 -16,27 -25,37 L 356,567 C 262,823 215,952 215,954 215,979 228,992 255,992 264,992 276,990 289,987 310,991 331,999 354,1012 L 381,999 492,748 772,1049 836,1024 860,1049 C 881,1039 901,1025 922,1006 886,937 835,863 770,784 769,783 710,716 594,584 L 774,223 C 774,196 753,168 711,139 L 727,119 C 717,90 699,76 672,76 641,76 570,178 457,381 L 164,-76 C 142,-110 111,-127 72,-127 30,-127 9,-110 8,-76 1,-67 -2,-52 -2,-32 -2,-23 -1,-13 0,-2 Z"/>
  </g>
  <g id="bullet-char-template(10004)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 285,-33 C 182,-33 111,30 74,156 52,228 41,333 41,471 41,549 55,616 82,672 116,743 169,778 240,778 293,778 328,747 346,684 L 369,508 C 377,444 397,411 428,410 L 1163,1116 C 1174,1127 1196,1133 1229,1133 1271,1133 1292,1118 1292,1087 L 1292,965 C 1292,929 1282,901 1262,881 L 442,47 C 390,-6 338,-33 285,-33 Z"/>
  </g>
  <g id="bullet-char-template(9679)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 813,0 C 632,0 489,54 383,161 276,268 223,411 223,592 223,773 276,916 383,1023 489,1130 632,1184 813,1184 992,1184 1136,1130 1245,1023 1353,916 1407,772 1407,592 1407,412 1353,268 1245,161 1136,54 992,0 813,0 Z"/>
  </g>
  <g id="bullet-char-template(8226)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M 346,457 C 273,457 209,483 155,535 101,586 74,649 74,723 74,796 101,859 155,911 209,963 273,989 346,989 419,989 480,963 531,910 582,859 608,796 608,723 608,648 583,586 532,535 482,483 420,457 346,457 Z"/>
  </g>
  <g id="bullet-char-template(8211)" transform="scale(0.00048828125,-0.00048828125)">
   <path d="M -4,459 L 1135,459 1135,606 -4,606 -4,459 Z"/>
  </g>
 </defs>
 <defs class="TextEmbeddedBitmaps"/>
 <g>
  <g id="id2" class="Master_Slide">
   <g id="bg-id2" class="Background"/>
   <g id="bo-id2" class="BackgroundObjects"/>
  </g>
 </g>
 <g class="SlideGroup">
  <g>
   <g id="id1" class="Slide" clip-path="url(#presentation_clip_path)">
    <g class="Page">
     <g class="com.sun.star.drawing.RectangleShape">
      <g id="id3">
       <path fill="none" stroke="rgb(0,0,0)" d="M 8450,7000 L 7000,7000 7000,3000 9900,3000 9900,7000 8450,7000 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.RectangleShape">
      <g id="id4">
       <path fill="none" stroke="rgb(0,0,0)" d="M 12050,7000 L 10100,7000 10100,3000 14000,3000 14000,7000 12050,7000 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.EllipseShape">
      <g id="id5">
       <path fill="none" stroke="rgb(0,0,0)" d="M 8999,3300 C 9105,3312 9195,3383 9288,3531 9387,3690 9459,3889 9516,4165 9574,4441 9600,4712 9600,5031 9600,5350 9574,5621 9516,5897 9459,6173 9402,6328 9319,6478"/>
       <path fill="rgb(0,0,0)" stroke="none" d="M 9141,6701 L 9405,6526 9248,6403 9141,6701 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.EllipseShape">
      <g id="id6">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10794,6710 C 10748,6669 10710,6618 10668,6540 10583,6380 10521,6181 10472,5905 10422,5628 10400,5356 10400,5036 10400,4716 10422,4444 10472,4168 10521,3891 10583,3692 10668,3532 10748,3383 10690,3492 10701,3474"/>
       <path fill="rgb(0,0,0)" stroke="none" d="M 10916,3300 L 10622,3416 10750,3569 10916,3300 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id7">
       <path fill="none" stroke="rgb(0,0,0)" d="M 9899,6900 C 9955,6900 9999,6943 9999,6999 9999,7055 9955,7099 9899,7099 9843,7099 9800,7055 9800,6999 9800,6943 9843,6900 9899,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9800,6900 L 9800,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10001,7101 L 10001,7101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id8">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10099,2900 C 10155,2900 10199,2943 10199,2999 10199,3055 10155,3099 10099,3099 10043,3099 10000,3055 10000,2999 10000,2943 10043,2900 10099,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10000,2900 L 10000,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10201,3101 L 10201,3101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id9">
       <path fill="none" stroke="rgb(0,0,0)" d="M 9899,2900 C 9955,2900 9999,2943 9999,2999 9999,3055 9955,3099 9899,3099 9843,3099 9800,3055 9800,2999 9800,2943 9843,2900 9899,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9800,2900 L 9800,2900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10001,3101 L 10001,3101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id10">
       <path fill="none" stroke="rgb(0,0,0)" d="M 9899,4900 C 9955,4900 9999,4943 9999,4999 9999,5055 9955,5099 9899,5099 9843,5099 9800,5055 9800,4999 9800,4943 9843,4900 9899,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9800,4900 L 9800,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10001,5101 L 10001,5101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id11">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10099,4900 C 10155,4900 10199,4943 10199,4999 10199,5055 10155,5099 10099,5099 10043,5099 10000,5055 10000,4999 10000,4943 10043,4900 10099,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10000,4900 L 10000,4900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10201,5101 L 10201,5101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id12">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10099,6900 C 10155,6900 10199,6943 10199,6999 10199,7055 10155,7099 10099,7099 10043,7099 10000,7055 10000,6999 10000,6943 10043,6900 10099,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10000,6900 L 10000,6900 Z"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10201,7101 L 10201,7101 Z"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id13">
       <path fill="rgb(255,255,255)" stroke="none" d="M 5100,5200 L 3500,5200 3500,3000 6700,3000 6700,5200 5100,5200 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="3750" y="3433"><tspan fill="rgb(0,0,0)" stroke="none">Subdivision </tspan></tspan><tspan class="TextPosition" x="3750" y="3827"><tspan fill="rgb(0,0,0)" stroke="none">points need to </tspan></tspan><tspan class="TextPosition" x="3750" y="4221"><tspan fill="rgb(0,0,0)" stroke="none">land on the same </tspan></tspan><tspan class="TextPosition" x="3750" y="4615"><tspan fill="rgb(0,0,0)" stroke="none">location to </tspan></tspan><tspan class="TextPosition" x="3750" y="5009"><tspan fill="rgb(0,0,0)" stroke="none">prevent cracking</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.LineShape">
      <g id="id14">
       <path fill="none" stroke="rgb(0,0,0)" d="M 6600,4200 L 6651,4213"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 6703,4227 L 6754,4240"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 6806,4253 L 6857,4266"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 6908,4280 L 6960,4293"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7011,4306 L 7063,4319"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7114,4333 L 7165,4346"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7217,4359 L 7268,4372"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7320,4386 L 7371,4399"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7423,4412 L 7474,4426"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7525,4439 L 7577,4452"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7628,4465 L 7680,4479"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7731,4492 L 7782,4505"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7834,4518 L 7885,4532"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 7937,4545 L 7988,4558"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8039,4571 L 8091,4585"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8142,4598 L 8194,4611"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8245,4625 L 8296,4638"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8348,4651 L 8399,4664"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8451,4678 L 8502,4691"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8553,4704 L 8605,4717"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8656,4731 L 8708,4744"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8759,4757 L 8811,4770"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8862,4784 L 8913,4797"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 8965,4810 L 9016,4824"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9068,4837 L 9119,4850"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9170,4863 L 9222,4877"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9273,4890 L 9325,4903"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9376,4916 L 9427,4930"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9479,4943 L 9530,4956"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9582,4969 L 9633,4983"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 9684,4996 L 9700,5000"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id15">
       <path fill="rgb(255,255,255)" stroke="none" d="M 12650,2700 L 10700,2700 10700,1500 14600,1500 14600,2700 12650,2700 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="10950" y="2024"><tspan fill="rgb(0,0,0)" stroke="none">Corner points start </tspan></tspan><tspan class="TextPosition" x="10950" y="2418"><tspan fill="rgb(0,0,0)" stroke="none">with the same values</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id16">
       <path fill="rgb(255,255,255)" stroke="none" d="M 12850,8500 L 10900,8500 10900,7300 14800,7300 14800,8500 12850,8500 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="11150" y="7824"><tspan fill="rgb(0,0,0)" stroke="none">Corner points start </tspan></tspan><tspan class="TextPosition" x="11150" y="8218"><tspan fill="rgb(0,0,0)" stroke="none">with the same values</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.CustomShape">
      <g id="id17">
       <path fill="rgb(255,255,255)" stroke="none" d="M 12400,5200 L 10900,5200 10900,3300 13900,3300 13900,5200 12400,5200 Z"/>
       <text class="TextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="353px" font-weight="400"><tspan class="TextPosition" x="11150" y="3780"><tspan fill="rgb(0,0,0)" stroke="none">Opposing </tspan></tspan><tspan class="TextPosition" x="11150" y="4174"><tspan fill="rgb(0,0,0)" stroke="none">directions of </tspan></tspan><tspan class="TextPosition" x="11150" y="4568"><tspan fill="rgb(0,0,0)" stroke="none">edge walking </tspan></tspan><tspan class="TextPosition" x="11150" y="4962"><tspan fill="rgb(0,0,0)" stroke="none">for subdivision</tspan></tspan></tspan></text>
      </g>
     </g>
     <g class="com.sun.star.drawing.LineShape">
      <g id="id18">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10300,2900 L 10341,2867"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10383,2834 L 10424,2801"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10466,2767 L 10507,2734"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10549,2701 L 10590,2668"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10632,2635 L 10673,2602"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10715,2568 L 10756,2535"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10797,2502 L 10800,2500"/>
      </g>
     </g>
     <g class="com.sun.star.drawing.LineShape">
      <g id="id19">
       <path fill="none" stroke="rgb(0,0,0)" d="M 10200,7100 L 10243,7131"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10286,7162 L 10330,7193"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10373,7223 L 10416,7254"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10459,7285 L 10502,7316"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10546,7347 L 10589,7378"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10632,7409 L 10675,7439"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10718,7470 L 10762,7501"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10805,7532 L 10848,7563"/>
       <path fill="none" stroke="rgb(0,0,0)" d="M 10891,7594 L 10900,7600"/>
      </g>
     </g>
    </g>
   </g>
  </g>
 </g>
</svg>" alt="precise">
+</div>
+</div>
+<div class="paragraph">
+<p>Without any qualifiers, implementations are permitted to perform
+optimizations that effectively modify the order or number of operations used
+to evaluate an expression, even if those optimizations may produce slightly
+different results relative to unoptimized code.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>precise</strong> qualifier ensures that operations contributing to a
+variable&#8217;s value are done in their stated order and with operator consistency.
+The order is determined by operator precedence and parenthesis, as described in
+&#8220;<a href="#operators">Operators</a>&#8221;.
+Operator consistency means for each particular operator, for example the
+multiply operator (<strong>*</strong>), its operation is always computed with the same
+precision.
+Specifically, values computed by compiler-generated code must adhere to the
+following identities:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>a + b = b + a</p>
+</li>
+<li>
+<p>a * b = b * a</p>
+</li>
+<li>
+<p>a * b + c * d = b * a + c* d = d * c + b * a = &lt;any other mathematically
+valid combination&gt;</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>While the following are prevented:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>a + (b + c) is not allowed to become (a + b) + c</p>
+</li>
+<li>
+<p>a * (b * c) is not allowed to become (a * b) * c</p>
+</li>
+<li>
+<p>a * b + c is not allowed to become a single operation <strong>fma</strong>(a, b, c)</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>Where <em>a</em>, <em>b</em>, <em>c</em>, and <em>d</em>, are scalars or vectors, not matrices.
+(Matrix multiplication generally does not commute.) It is the shader
+writer&#8217;s responsibility to express the computation in terms of these rules
+and the compiler&#8217;s responsibility to follow these rules.
+See the description of <em>gl_TessCoord</em> for the rules the tessellation stages
+are responsible for following, which in conjunction with the above allow
+avoiding cracking when subdividing.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">precise out vec4 position;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>declares that operations used to produce the value of <em>position</em> must be
+performed in exactly the order specified in the source code and with all
+operators being treated consistently.
+As with the <strong>invariant</strong> qualifier (see &#8220;<a href="#the-invariant-qualifier">The
+Invariant Qualifier</a>&#8221;), the <strong>precise</strong> qualifier may be used to qualify a
+built-in or previously declared user-defined variable as being precise:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec3 Color;
+precise Color; <span class="comment">// make existing Color be precise</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When applied to a block, a structure type, or a variable of structure type,
+<strong>precise</strong> applies to each contained member, recursively.</p>
+</div>
+<div class="paragraph">
+<p>This qualifier will affect the evaluation of an r-value in a particular
+function if and only if the result is eventually consumed in the same
+function by an l-value qualified as <strong>precise</strong>.
+Any other expressions within a function are not affected, including return
+values and output parameters not declared as <strong>precise</strong> but that are
+eventually consumed outside the function by a variable qualified as
+<strong>precise</strong>. Unaffected expressions also include the controlling expressions
+in selection and iteration statements and the condition in ternary
+operators (<strong>?:</strong>).</p>
+</div>
+<div class="paragraph">
+<p>Some examples of the use of <strong>precise</strong>:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 a, b, c, d;
+precise out vec4 v;
+
+<span class="predefined-type">float</span> func(<span class="predefined-type">float</span> e, <span class="predefined-type">float</span> f, <span class="predefined-type">float</span> g, <span class="predefined-type">float</span> h)
+{
+    <span class="keyword">return</span> (e*f) + (g*h); <span class="comment">// no constraint on order or operator consistency</span>
+}
+
+<span class="predefined-type">float</span> func2(<span class="predefined-type">float</span> e, <span class="predefined-type">float</span> f, <span class="predefined-type">float</span> g, <span class="predefined-type">float</span> h)
+{
+    precise <span class="predefined-type">float</span> result = (e*f) + (g*h); <span class="comment">// ensures same precision for the two multiplies</span>
+    <span class="keyword">return</span> result;
+}
+
+<span class="predefined-type">float</span> func3(<span class="predefined-type">float</span> i, <span class="predefined-type">float</span> j, precise out <span class="predefined-type">float</span> k)
+{
+    k = i * i + j;        <span class="comment">// precise, due to &lt;k&gt; declaration</span>
+}
+
+<span class="directive">void</span> main()
+{
+    vec3 r = vec3(a * b);             <span class="comment">// precise, used to compute v.xyz</span>
+    vec3 s = vec3(c * d);             <span class="comment">// precise, used to compute v.xyz</span>
+    v.xyz = r + s;                    <span class="comment">// precise</span>
+    v.w = (a.w * b.w) + (c.w * d.w);  <span class="comment">// precise</span>
+    v.x = func(a.x, b.x, c.x, d.x);   <span class="comment">// values computed in func() are NOT precise</span>
+    v.x = func2(a.x, b.x, c.x, d.x);  <span class="comment">// precise!</span>
+    func3(a.x * b.x, c.x * d.x, v.x); <span class="comment">// precise!</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>For the purposes of determining if an output from one shader stage matches
+an input of the next stage, the <strong>precise</strong> qualifier need not match between
+the input and the output.</p>
+</div>
+<div class="paragraph">
+<p>All constant expressions are evaluated as if <strong>precise</strong> was present, whether
+or not it is present.
+However, as described in &#8220;<a href="#constant-expressions">Constant Expressions</a>&#8221;,
+there is no requirement that a compile-time constant expression evaluates to
+the same value as a corresponding non-constant expression.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="memory-qualifiers">4.10. Memory Qualifiers</h3>
+<div class="paragraph">
+<p>Shader storage blocks, variables declared within shader storage blocks and
+variables declared as image types (the basic opaque types with &#8220;<strong>image</strong>&#8221;
+in their keyword), can be further qualified with one or more of the
+following memory qualifiers:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Qualifier</th>
+<th class="tableblock halign-left valign-top">Meaning</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>coherent</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable where reads and writes are coherent with
+                reads and writes from other shader invocations</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>volatile</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable whose underlying value may be changed at any
+                point during shader execution by some source other than the
+                current shader invocation</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>restrict</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable where use of that variable is the only way
+                to read and write the underlying memory in the relevant
+                shader stage</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>readonly</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable that can be used to read the underlying
+                memory, but cannot be used to write the underlying memory</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>writeonly</strong></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">memory variable that can be used to write the underlying
+                memory, but cannot be used to read the underlying memory</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>coherent</strong> qualifier
+are performed coherently with accesses to the same location from other
+shader invocations.
+In particular, when reading a variable declared as <strong>coherent</strong>, the values
+returned will reflect the results of previously completed writes performed
+by other shader invocations.
+When writing a variable declared as <strong>coherent</strong>, the values written will be
+reflected in subsequent coherent reads performed by other shader
+invocations.</p>
+</div>
+<div class="paragraph">
+<p>As described in section
+7.12
+&#8220;Shader Memory Access&#8221; of the
+<a href="#references">OpenGL Specification</a>, shader memory reads and writes complete in a
+largely undefined order.
+The built-in function <strong>memoryBarrier</strong>() can be used if needed to guarantee
+the completion and relative ordering of memory accesses performed by a
+single shader invocation.</p>
+</div>
+<div class="paragraph">
+<p>When accessing memory using variables not declared as <strong>coherent</strong>, the memory
+accessed by a shader may be cached by the implementation to service future
+accesses to the same address.
+Memory stores may be cached in such a way that the values written may not be
+visible to other shader invocations accessing the same memory.
+The implementation may cache the values fetched by memory reads and return
+the same values to any shader invocation accessing the same memory, even if
+the underlying memory has been modified since the first memory read.
+While variables not declared as <strong>coherent</strong> may not be useful for
+communicating between shader invocations, using non-coherent accesses may
+result in higher performance.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>volatile</strong> qualifier
+must treat the underlying memory as though it could be read or written at
+any point during shader execution by some source other than the executing
+shader invocation.
+When a volatile variable is read, its value must be re-fetched from the
+underlying memory, even if the shader invocation performing the read had
+previously fetched its value from the same memory.
+When a volatile variable is written, its value must be written to the
+underlying memory, even if the compiler can conclusively determine that its
+value will be overwritten by a subsequent write.
+Since the external source reading or writing a <strong>volatile</strong> variable may be
+another shader invocation, variables declared as <strong>volatile</strong> are
+automatically treated as coherent.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>restrict</strong> qualifier
+may be compiled assuming that the variable used to perform the memory access
+is the only way to access the underlying memory using the shader stage in
+question.
+This allows the compiler to coalesce or reorder loads and stores using
+<strong>restrict</strong>-qualified image variables in ways that wouldn&#8217;t be permitted
+for image variables not so qualified, because the compiler can assume that
+the underlying image won&#8217;t be read or written by other code.
+Applications are responsible for ensuring that image memory referenced by
+variables qualified with <strong>restrict</strong> will not be referenced using other
+variables in the same scope; otherwise, accesses to <strong>restrict</strong>-qualified
+variables will have undefined results.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>readonly</strong> qualifier
+may only read the underlying memory, which is treated as read-only memory
+and cannot be written to.
+It is a compile-time error to pass an image variable qualified with
+<strong>readonly</strong> to <strong>imageStore</strong>() or other built-in functions that modify image
+memory.</p>
+</div>
+<div class="paragraph">
+<p>Memory accesses to image variables declared using the <strong>writeonly</strong> qualifier
+may only write the underlying memory; the underlying memory cannot be read.
+It is a compile-time error to pass an image variable qualified with
+<strong>writeonly</strong> to <strong>imageLoad</strong>() or other built-in functions that read image
+memory.</p>
+</div>
+<div class="paragraph">
+<p>A variable could be qualified as both <strong>readonly</strong> and <strong>writeonly</strong>, disallowing
+both read and write. Such variables can still be used with some queries, for
+example <strong>imageSize</strong>() and <strong>.length</strong>().</p>
+</div>
+<div class="paragraph">
+<p>The memory qualifiers <strong>coherent</strong>, <strong>volatile</strong>, <strong>restrict</strong>, <strong>readonly</strong>, and
+<strong>writeonly</strong> may be used in the declaration of buffer variables (i.e.,
+members of shader storage blocks).
+When a buffer variable is declared with a memory qualifier, the behavior
+specified for memory accesses involving image variables described above
+applies identically to memory accesses involving that buffer variable.
+It is a compile-time error to assign to a buffer variable qualified with
+<strong>readonly</strong> or to read from a buffer variable qualified with <strong>writeonly</strong>.
+The combination <strong>readonly</strong> <strong>writeonly</strong> is allowed.</p>
+</div>
+<div class="paragraph">
+<p>Additionally, memory qualifiers may be used at the block-level declaration
+of a shader storage block, including the combination <strong>readonly</strong> <strong>writeonly</strong>.
+When a block declaration is qualified with a memory qualifier, it is as if
+all of its members were declared with the same memory qualifier.
+For example, the block declaration</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">coherent buffer Block {
+    readonly vec4 member1;
+    vec4 member2;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">buffer Block {
+    coherent readonly vec4 member1;
+    coherent vec4 member2;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Memory qualifiers are only supported in the declarations of image variables,
+buffer variables, and shader storage blocks; it is an error to use such
+qualifiers in any other declarations.</p>
+</div>
+<div class="paragraph">
+<p>When calling user-defined functions, variables qualified with <strong>coherent</strong>,
+<strong>volatile</strong>, <strong>readonly</strong>, or <strong>writeonly</strong> may not be passed to functions whose
+formal parameters lack such qualifiers.
+(See &#8220;<a href="#function-definitions">Function Definitions</a>&#8221; for more detail on
+function calling.) It is legal to have any additional memory qualifiers on a
+formal parameter, but only <strong>restrict</strong> can be taken away from a calling
+argument, by a formal parameter that lacks the <strong>restrict</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>When a built-in function is called, the code generated is to be based on the
+actual qualification of the calling argument, not on the list of memory
+qualifiers specified on the formal parameter in the prototype.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 funcA(restrict image2D a) { ... }
+vec4 funcB(image2D a) { ... }
+layout(rgba32f) uniform image2D img1;
+layout(rgba32f) coherent uniform image2D img2;
+
+funcA(img1);        <span class="comment">// OK, adding &quot;restrict&quot; is allowed</span>
+funcB(img2);        <span class="comment">// illegal, stripping &quot;coherent&quot; is not</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Layout qualifiers cannot be used on formal function parameters, and layout
+qualification is not included in parameter matching.</p>
+</div>
+<div class="paragraph">
+<p>Note that the use of <strong>const</strong> in an image variable declaration is qualifying
+the const-ness of the variable being declared, not the image it refers to.
+The qualifier <strong>readonly</strong> qualifies the image memory (as accessed through
+that variable) while <strong>const</strong> qualifies the variable itself.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="specialization-constant-qualifier">4.11. Specialization-Constant Qualifier</h3>
+<div class="paragraph">
+<p>Specialization constants are used only for SPIR-V and declared using the
+<strong>constant_id</strong> layout qualifier.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(constant_id = <span class="integer">17</span>) <span class="directive">const</span> <span class="predefined-type">int</span> arraySize = <span class="integer">12</span>;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The above makes a specialization constant with a default value of 12.
+The number 17 is an example author-chosen id by which the API or other tools
+can later refer to this specific specialization constant.
+If it is never changed before final lowering, it will retain the value of
+12.
+It is a compile-time error to use the <strong>constant_id</strong> qualifier on anything
+but SPIR-V generation of a scalar <strong>bool</strong>, <strong>int</strong>, <strong>uint</strong>, <strong>float</strong>, or
+<strong>double</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Built-in constants can be declared to be specialization constants.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(constant_id = <span class="integer">31</span>) gl_MaxClipDistances; <span class="comment">// add specialization_id</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The declaration uses just the name of the previously declared built-in
+variable, with a <strong>constant_id</strong> layout-qualifier declaration.
+It is a compile-time error to do this after the constant has been used:
+Constants are strictly either non-specialization constants or specialization
+constants, not both.</p>
+</div>
+<div class="paragraph">
+<p>The built-in constant vector <em>gl_WorkGroupSize</em> can be specialized using the
+<strong>local_size_{xyz}_id</strong> qualifiers, to individually give the components an id.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(local_size_x_id = <span class="integer">18</span>, local_size_z_id = <span class="integer">19</span>) in;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This leaves <em>gl_WorkGroupSize.y</em> as a non-specialization constant, with
+<em>gl_WorkGroupSize</em> being a partially specialized vector.
+Its <em>x</em> and <em>z</em> components can be later specialized, after generating
+SPIR-V, using the ids 18 and 19.
+These ids are declared independently from declaring the workgroup size:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(local_size_x = <span class="integer">32</span>, local_size_y = <span class="integer">32</span>) in;   <span class="comment">// size is (32,32,1)</span>
+layout(local_size_x_id = <span class="integer">18</span>) in;                   <span class="comment">// constant_id for x</span>
+layout(local_size_z_id = <span class="integer">19</span>) in;                   <span class="comment">// constant_id for z</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Existing rules for declaring <strong>local_size_x</strong>, <strong>local_size_y</strong>, and
+<strong>local_size_z</strong> are not changed.
+For the local-size ids, it is a compile-time error to provide different id
+values for the same local-size id, or to provide them after any use.
+Otherwise, order, placement, number of statements, and replication do not
+cause errors.</p>
+</div>
+<div class="paragraph">
+<p>Two arrays sized with specialization constants are the same type only if
+sized with the same symbol, and involving no operations.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">layout(constant_id = <span class="integer">51</span>) <span class="directive">const</span> <span class="predefined-type">int</span> aSize = <span class="integer">20</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> pad = <span class="integer">2</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> total = aSize + pad; <span class="comment">// specialization constant</span>
+<span class="predefined-type">int</span> a[total], b[total];        <span class="comment">// a and b have the same type</span>
+<span class="predefined-type">int</span> c[<span class="integer">22</span>];                     <span class="comment">// different type than a or b</span>
+<span class="predefined-type">int</span> d[aSize + pad];            <span class="comment">// different type than a, b, or c</span>
+<span class="predefined-type">int</span> e[aSize + <span class="integer">2</span>];              <span class="comment">// different type than a, b, c, or d</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Types containing arrays sized with a specialization constant cannot be
+compared, assigned as aggregates, declared with an initializer, or used as
+an initializer.
+They can, however, be passed as arguments to functions having formal
+parameters of the same type.
+Only the outer-most dimension of a variable declared as an array of arrays
+can be a specialization constant, otherwise a compile-time error results.</p>
+</div>
+<div class="paragraph">
+<p>Arrays inside a block may be sized with a specialization constant, but the
+block will have a static layout.
+Changing the specialized size will not re-layout the block.
+In the absence of explicit offsets, the layout will be based on the default
+size of the array.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="order-of-qualification">4.12. Order and Repetition of Qualification</h3>
+<div class="paragraph">
+<p>When multiple qualifiers are present in a declaration, they may appear in
+any order, but they must all appear before the type.
+The <strong>layout</strong> qualifier is the only qualifier that can appear more than once.
+Further, a declaration can have at most one storage qualifier, at most one
+auxiliary storage qualifier, and at most one interpolation qualifier.
+If <strong>inout</strong> is used, neither <strong>in</strong> nor <strong>out</strong> may be used.
+Multiple memory qualifiers can be used.
+Any violation of these rules will cause a compile-time error.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="empty-declarations">4.13. Empty Declarations</h3>
+<div class="paragraph">
+<p><em>Empty declarations</em> are declarations without a variable name, meaning no
+object is instantiated by the declaration.
+Generally, empty declarations are allowed.
+Some are useful when declaring structures, while many others have no effect.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span>;               <span class="comment">// No effect</span>
+<span class="keyword">struct</span> S {<span class="predefined-type">int</span> x;}; <span class="comment">// Defines a struct S</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The combinations of qualifiers that cause compile-time or link-time errors
+are the same whether or not the declaration is empty, for example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">invariant in <span class="predefined-type">float</span> x; <span class="comment">// Error. An input cannot be invariant.</span>
+invariant in <span class="predefined-type">float</span>;   <span class="comment">// Error even though no variable is declared.</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="operators-and-expressions">5. Operators and Expressions</h2>
+<div class="sectionbody">
+<div class="sect2">
+<h3 id="operators">5.1. Operators</h3>
+<div class="paragraph">
+<p>The OpenGL Shading Language has the following operators.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Precedence</th>
+<th class="tableblock halign-left valign-top">Operator Class</th>
+<th class="tableblock halign-left valign-top">Operators</th>
+<th class="tableblock halign-left valign-top">Associativity</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1 (highest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">parenthetical grouping</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">( )</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">NA</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">array subscript<br>
+                 function call and constructor structure<br>
+                 field or method selector, swizzle<br>
+                 post fix increment and decrement</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">[ ]<br>
+                                                  ( )<br>
+                                                  .<br>
+                                                  ++ --</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">prefix increment and decrement<br>
+                 unary</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">++ --<br>
+                                                  + - ~ !</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">multiplicative</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">* / %</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">additive</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">+ -</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">6</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise shift</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt;&lt; &gt;&gt;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">7</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">relational</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&lt; &gt; &lt;= &gt;=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">8</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">equality</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">== !=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">9</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">10</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise exclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">^</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">11</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bit-wise inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">|</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">12</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical and</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">&amp;&amp;</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">13</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical exclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">^^</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">14</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">logical inclusive or</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">||</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">15</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">selection</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">? :</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">16</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Assignment<br>
+                 arithmetic assignments</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">=<br>
+                                                  += -=<br>
+                                                  *= /=<br>
+                                                  %= &lt;&lt;= &gt;&gt;=<br>
+                                                  &amp;= ^= |=</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Right to Left</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">17 (lowest)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">sequence</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">,</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Left to Right</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>There is no address-of operator nor a dereference operator.
+There is no typecast operator; constructors are used instead.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="array-operations">5.2. Array Operations</h3>
+<div class="paragraph">
+<p>These are now described in &#8220;<a href="#structure-and-array-operations">Structure and
+Array Operations</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="function-calls">5.3. Function Calls</h3>
+<div class="paragraph">
+<p>If a function returns a value, then a call to that function may be used as
+an expression, whose type will be the type that was used to declare or
+define the function.</p>
+</div>
+<div class="paragraph">
+<p>Function definitions and calling conventions are discussed in
+&#8220;<a href="#function-definitions">Function Definitions</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="constructors">5.4. Constructors</h3>
+<div class="paragraph">
+<p>Constructors use the function call syntax, where the function name is a
+type, and the call makes an object of that type.
+Constructors are used the same way in both initializers and expressions.
+(See &#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; for details.)
+The parameters are used to initialize the constructed value.
+Constructors can be used to request a data type conversion to change from
+one scalar type to another scalar type, or to build larger types out of
+smaller types, or to reduce a larger type to a smaller type.</p>
+</div>
+<div class="paragraph">
+<p>In general, constructors are not built-in functions with predetermined
+prototypes.
+For arrays and structures, there must be exactly one argument in the
+constructor for each element or member.
+For the other types, the arguments must provide a sufficient number of
+components to perform the initialization, and it is a compile-time error to
+include so many arguments that they cannot all be used.
+Detailed rules follow.
+The prototypes actually listed below are merely a subset of examples.</p>
+</div>
+<div class="sect3">
+<h4 id="conversion-and-scalar-constructors">5.4.1. Conversion and Scalar Constructors</h4>
+<div class="paragraph">
+<p>Converting between scalar types is done as the following prototypes
+indicate:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">int</span>(uint)     <span class="comment">// converts an unsigned integer to a signed integer</span>
+<span class="predefined-type">int</span>(<span class="predefined-type">bool</span>)     <span class="comment">// converts a Boolean value to an int</span>
+<span class="predefined-type">int</span>(<span class="predefined-type">float</span>)    <span class="comment">// converts a float value to an int</span>
+<span class="predefined-type">int</span>(<span class="predefined-type">double</span>)   <span class="comment">// converts a double value to a signed integer</span>
+uint(<span class="predefined-type">int</span>)     <span class="comment">// converts a signed integer value to an unsigned integer</span>
+uint(<span class="predefined-type">bool</span>)    <span class="comment">// converts a Boolean value to an unsigned integer</span>
+uint(<span class="predefined-type">float</span>)   <span class="comment">// converts a float value to an unsigned integer</span>
+uint(<span class="predefined-type">double</span>)  <span class="comment">// converts a double value to an unsigned integer</span>
+<span class="predefined-type">bool</span>(<span class="predefined-type">int</span>)     <span class="comment">// converts a signed integer value to a Boolean</span>
+<span class="predefined-type">bool</span>(uint)    <span class="comment">// converts an unsigned integer value to a Boolean value</span>
+<span class="predefined-type">bool</span>(<span class="predefined-type">float</span>)   <span class="comment">// converts a float value to a Boolean</span>
+<span class="predefined-type">bool</span>(<span class="predefined-type">double</span>)  <span class="comment">// converts a double value to a Boolean</span>
+<span class="predefined-type">float</span>(<span class="predefined-type">int</span>)    <span class="comment">// converts a signed integer value to a float</span>
+<span class="predefined-type">float</span>(uint)   <span class="comment">// converts an unsigned integer value to a float value</span>
+<span class="predefined-type">float</span>(<span class="predefined-type">bool</span>)   <span class="comment">// converts a Boolean value to a float</span>
+<span class="predefined-type">float</span>(<span class="predefined-type">double</span>) <span class="comment">// converts a double value to a float</span>
+<span class="predefined-type">double</span>(<span class="predefined-type">int</span>)   <span class="comment">// converts a signed integer value to a double</span>
+<span class="predefined-type">double</span>(uint)  <span class="comment">// converts an unsigned integer value to a double</span>
+<span class="predefined-type">double</span>(<span class="predefined-type">bool</span>)  <span class="comment">// converts a Boolean value to a double</span>
+<span class="predefined-type">double</span>(<span class="predefined-type">float</span>) <span class="comment">// converts a float value to a double</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When constructors are used to convert a floating-point type to an integer
+type, the fractional part of the floating-point value is dropped.
+It is undefined to convert a negative floating-point value to an <strong>uint</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Integer values having more bits of precision than a single-precision
+floating-point mantissa will lose precision when converted to <strong>float</strong>.</p>
+</div>
+<div class="paragraph">
+<p>When a constructor is used to convert any integer or floating-point type to
+a <strong>bool</strong>, 0 and 0.0 are converted to <strong>false</strong>, and non-zero values are
+converted to <strong>true</strong>.
+When a constructor is used to convert a <strong>bool</strong> to any integer or
+floating-point type, <strong>false</strong> is converted to 0 or 0.0, and <strong>true</strong> is
+converted to 1 or 1.0.</p>
+</div>
+<div class="paragraph">
+<p>The constructor <strong>int</strong>(<strong>uint</strong>) preserves the bit pattern in the argument,
+which will change the argument&#8217;s value if its sign bit is set.
+The constructor <strong>uint</strong>(<strong>int</strong>) preserves the bit pattern in the argument,
+which will change its value if it is negative.</p>
+</div>
+<div class="paragraph">
+<p>Identity constructors, like <strong>float</strong>(<strong>float</strong>) are also legal, but of little
+use.</p>
+</div>
+<div class="paragraph">
+<p>Scalar constructors with non-scalar parameters can be used to take the first
+element from a non-scalar.
+For example, the constructor <strong>float</strong>(<strong>vec3</strong>) will select the first component
+of the <strong>vec3</strong> parameter.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="vector-and-matrix-constructors">5.4.2. Vector and Matrix Constructors</h4>
+<div class="paragraph">
+<p>Constructors can be used to create vectors or matrices from a set of
+scalars, vectors, or matrices.
+This includes the ability to shorten vectors.</p>
+</div>
+<div class="paragraph">
+<p>If there is a single scalar parameter to a vector constructor, it is used to
+initialize all components of the constructed vector to that scalar&#8217;s value.
+If there is a single scalar parameter to a matrix constructor, it is used to
+initialize all the components on the matrix&#8217;s diagonal, with the remaining
+components initialized to 0.0.</p>
+</div>
+<div class="paragraph">
+<p>If a vector is constructed from multiple scalars, one or more vectors, or
+one or more matrices, or a mixture of these, the vector&#8217;s components will be
+constructed in order from the components of the arguments.
+The arguments will be consumed left to right, and each argument will have
+all its components consumed, in order, before any components from the next
+argument are consumed.
+Similarly for constructing a matrix from multiple scalars or vectors, or a
+mixture of these.
+Matrix components will be constructed and consumed in column major order.
+In these cases, there must be enough components provided in the arguments to
+provide an initializer for every component in the constructed value.
+It is a compile-time error to provide extra arguments beyond this last used
+argument.</p>
+</div>
+<div class="paragraph">
+<p>If a matrix is constructed from a matrix, then each component (column <em>i</em>,
+row <em>j</em>) in the result that has a corresponding component (column <em>i</em>, row
+<em>j</em>) in the argument will be initialized from there.
+All other components will be initialized to the identity matrix.
+If a matrix argument is given to a matrix constructor, it is
+a compile-time error to have any other arguments.</p>
+</div>
+<div class="paragraph">
+<p>If the basic type (<strong>bool</strong>, <strong>int</strong>,
+<strong>float</strong>, or <strong>double</strong>)
+of a parameter to a
+constructor does not match the basic type of the object being constructed,
+the scalar construction rules (above) are used to convert the parameters.</p>
+</div>
+<div class="paragraph">
+<p>Some useful vector constructors are as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3(<span class="predefined-type">float</span>)          <span class="comment">// initializes each component of the vec3 with the float</span>
+vec4(ivec4)          <span class="comment">// makes a vec4 with component-wise conversion</span>
+vec4(mat2)           <span class="comment">// the vec4 is column 0 followed by column 1</span>
+vec2(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>)   <span class="comment">// initializes a vec2 with 2 floats</span>
+ivec3(<span class="predefined-type">int</span>, <span class="predefined-type">int</span>, <span class="predefined-type">int</span>) <span class="comment">// initializes an ivec3 with 3 ints</span>
+bvec4(<span class="predefined-type">int</span>, <span class="predefined-type">int</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>) <span class="comment">// uses 4 Boolean conversions</span>
+vec2(vec3)           <span class="comment">// drops the third component of a vec3</span>
+vec3(vec4)           <span class="comment">// drops the fourth component of a vec4</span>
+vec3(vec2, <span class="predefined-type">float</span>)    <span class="comment">// vec3.x = vec2.x, vec3.y = vec2.y, vec3.z = float</span>
+vec3(<span class="predefined-type">float</span>, vec2)    <span class="comment">// vec3.x = float, vec3.y = vec2.x, vec3.z = vec2.y</span>
+vec4(vec3, <span class="predefined-type">float</span>)
+vec4(<span class="predefined-type">float</span>, vec3)
+vec4(vec2, vec2)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Some examples of these are:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 color = vec4(<span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span>, <span class="float">0</span><span class="float">.0</span>, <span class="float">1</span><span class="float">.0</span>);
+vec4 rgba = vec4(<span class="float">1</span><span class="float">.0</span>);      <span class="comment">// sets each component to 1.0</span>
+vec3 rgb = vec3(color);     <span class="comment">// drop the 4th component</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>To initialize the diagonal of a matrix with all other elements set to zero:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2(<span class="predefined-type">float</span>)
+mat3(<span class="predefined-type">float</span>)
+mat4(<span class="predefined-type">float</span>)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>That is, <em>result[i][j]</em> is set to the <em>float</em> argument for all \(i
+= j\) and set to 0 for all \(i \neq j\).</p>
+</div>
+<div class="paragraph">
+<p>To initialize a matrix by specifying vectors or scalars, the components are
+assigned to the matrix elements in column-major order.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat2(vec2, vec2);                 <span class="comment">// one column per argument</span>
+mat3(vec3, vec3, vec3);           <span class="comment">// one column per argument</span>
+mat4(vec4, vec4, vec4, vec4);     <span class="comment">// one column per argument</span>
+mat3x2(vec2, vec2, vec2);         <span class="comment">// one column per argument</span>
+dmat2(dvec2, dvec2);
+dmat3(dvec3, dvec3, dvec3);
+dmat4(dvec4, dvec4, dvec4, dvec4);
+mat2(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>,                <span class="comment">// first column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>);               <span class="comment">// second column</span>
+mat3(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,         <span class="comment">// first column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,         <span class="comment">// second column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>);        <span class="comment">// third column</span>
+mat4(<span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,  <span class="comment">// first column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,  <span class="comment">// second column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>,  <span class="comment">// third column</span>
+     <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>, <span class="predefined-type">float</span>); <span class="comment">// fourth column</span>
+mat2x3(vec2, <span class="predefined-type">float</span>,               <span class="comment">// first column</span>
+       vec2, <span class="predefined-type">float</span>);              <span class="comment">// second column</span>
+dmat2x4(dvec3, <span class="predefined-type">double</span>,            <span class="comment">// first column</span>
+        <span class="predefined-type">double</span>, dvec3);           <span class="comment">// second column</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A wide range of other possibilities exist, to construct a matrix from
+vectors and scalars, as long as enough components are present to initialize
+the matrix.
+To construct a matrix from a matrix:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat3x3(mat4x4); <span class="comment">// takes the upper-left 3x3 of the mat4x4</span>
+mat2x3(mat4x2); <span class="comment">// takes the upper-left 2x2 of the mat4x4, last row is 0,0</span>
+mat4x4(mat3x3); <span class="comment">// puts the mat3x3 in the upper-left, sets the lower right</span>
+                <span class="comment">// component to 1, and the rest to 0</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="structure-constructors">5.4.3. Structure Constructors</h4>
+<div class="paragraph">
+<p>Once a structure is defined, and its type is given a name, a constructor is
+available with the same name to construct instances of that structure.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">struct</span> light {
+    <span class="predefined-type">float</span> intensity;
+    vec3 position;
+};
+
+light lightVar = light(<span class="float">3</span><span class="float">.0</span>, vec3(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>));</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The arguments to the constructor will be used to set the structure&#8217;s
+members, in order, using one argument per member.
+Each argument must be the same type as the member it
+sets, or be a type that can be converted to the member&#8217;s type according to
+section &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Structure constructors can be used as initializers or in expressions.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="array-constructors">5.4.4. Array Constructors</h4>
+<div class="paragraph">
+<p>Array types can also be used as constructor names, which can then be used in
+expressions or initializers.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> <span class="predefined-type">float</span> c[<span class="integer">3</span>] = <span class="predefined-type">float</span>[<span class="integer">3</span>](<span class="float">5</span><span class="float">.0</span>, <span class="float">7</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+<span class="directive">const</span> <span class="predefined-type">float</span> d[<span class="integer">3</span>] = <span class="predefined-type">float</span>[](<span class="float">5</span><span class="float">.0</span>, <span class="float">7</span><span class="float">.2</span>, <span class="float">1</span><span class="float">.1</span>);
+
+<span class="predefined-type">float</span> g;
+...
+<span class="predefined-type">float</span> a[<span class="integer">5</span>] = <span class="predefined-type">float</span>[<span class="integer">5</span>](g, <span class="integer">1</span>, g, <span class="float">2</span><span class="float">.3</span>, g);
+<span class="predefined-type">float</span> b[<span class="integer">3</span>];
+
+b = <span class="predefined-type">float</span>[<span class="integer">3</span>](g, g + <span class="float">1</span><span class="float">.0</span>, g + <span class="float">2</span><span class="float">.0</span>);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>There must be exactly the same number of arguments as the size of the array
+being constructed.
+If no size is present in the constructor, then the array is explicitly sized
+to the number of arguments provided.
+The arguments are assigned in order, starting at element 0, to the elements
+of the constructed array.
+Each argument must be the same type as the element type of the
+array, or be
+a type that can be converted to the element type of the array according to
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>Arrays of arrays are similarly constructed, and the size for any dimension
+is <strong class="purple">optional</strong></p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 b[<span class="integer">2</span>] = ...;
+vec4[<span class="integer">3</span>][<span class="integer">2</span>](b, b, b);    <span class="comment">// constructor</span>
+vec4[][<span class="integer">2</span>](b, b, b);     <span class="comment">// constructor, valid, size deduced</span>
+vec4[<span class="integer">3</span>][](b, b, b);     <span class="comment">// constructor, valid, size deduced</span>
+vec4[][](b, b, b);      <span class="comment">// constructor, valid, both sizes deduced</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="vector-components">5.5. Vector and Scalar Components and Length</h3>
+<div class="paragraph">
+<p>The names of the components of a vector
+or scalar
+are denoted by a single letter.
+As a notational convenience, several letters are associated with each
+component based on common usage of position, color or texture coordinate
+vectors.
+The individual components can be selected by following the variable name
+with period (<strong>.</strong>) and then the component name.</p>
+</div>
+<div class="paragraph">
+<p>The component names supported are:</p>
+</div>
+<table class="tableblock frame-all grid-all fit-content">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>{ x, y, z, w }</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Useful when accessing vectors that represent points or normals</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>{ r, g, b, a }</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Useful when accessing vectors that represent colors</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><em>{ s, t, p, q }</em></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Useful when accessing vectors that represent texture coordinates</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The component names <em>x</em>, <em>r</em>, and <em>s</em> are, for example, synonyms for the
+same (first) component in a vector.
+They are also the names of the only component in a scalar.</p>
+</div>
+<div class="paragraph">
+<p>Note that the third component of the texture coordinate set, <em>r</em> in
+OpenGL, has been renamed <em>p</em> so as to avoid the confusion with <em>r</em> (for
+red) in a color.</p>
+</div>
+<div class="paragraph">
+<p>Accessing components beyond those declared for the type is
+a compile-time error so, for example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec2 pos;
+<span class="predefined-type">float</span> height;
+pos.x       <span class="comment">// is legal</span>
+pos.z       <span class="comment">// is illegal</span>
+height.x    <span class="comment">// is legal</span>
+height.y    <span class="comment">// is illegal</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The component selection syntax allows multiple components to be selected by
+appending their names (from the same name set) after the period (<strong>.</strong>).</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 v4;
+v4.rgba;    <span class="comment">// is a vec4 and the same as just using v4,</span>
+v4.rgb;     <span class="comment">// is a vec3,</span>
+v4.b;       <span class="comment">// is a float,</span>
+v4.xy;      <span class="comment">// is a vec2,</span>
+v4.xgba;    <span class="comment">// is illegal - the component names do not come from the same set</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>No more than 4 components can be selected.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 v4;
+v4.xyzwxy;      <span class="comment">// is illegal since it has 6 components</span>
+(v4.xyzwxy).xy; <span class="comment">// is illegal since the intermediate value has 6</span>
+components</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The order of the components can be different to swizzle them, or replicated:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 pos = vec4(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>, <span class="float">4</span><span class="float">.0</span>);
+vec4 swiz = pos.wzyx;   <span class="comment">// swiz = (4.0, 3.0, 2.0, 1.0)</span>
+vec4 dup = pos.xxyy;    <span class="comment">// dup = (1.0, 1.0, 2.0, 2.0)</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This notation is more concise than the constructor syntax.
+To form an r-value, it can be applied to any expression that results in a
+vector or scalar r-value.</p>
+</div>
+<div class="paragraph">
+<p>The component group notation can occur on the left hand side of an
+expression.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 pos = vec4(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>, <span class="float">4</span><span class="float">.0</span>);
+pos.xw = vec2(<span class="float">5</span><span class="float">.0</span>, <span class="float">6</span><span class="float">.0</span>);        <span class="comment">// pos = (5.0, 2.0, 3.0, 6.0)</span>
+pos.wx = vec2(<span class="float">7</span><span class="float">.0</span>, <span class="float">8</span><span class="float">.0</span>);        <span class="comment">// pos = (8.0, 2.0, 3.0, 7.0)</span>
+pos.xx = vec2(<span class="float">3</span><span class="float">.0</span>, <span class="float">4</span><span class="float">.0</span>);        <span class="comment">// illegal - 'x' used twice</span>
+pos.xy = vec3(<span class="float">1</span><span class="float">.0</span>, <span class="float">2</span><span class="float">.0</span>, <span class="float">3</span><span class="float">.0</span>);   <span class="comment">// illegal - mismatch between vec2 and vec3</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>To form an l-value, swizzling must further be applied to an l-value and
+contain no duplicate components. It results in an l-value of scalar or
+vector type, depending on number of components specified.</p>
+</div>
+<div class="paragraph">
+<p>Array subscripting syntax can also be applied to vectors (but not to
+scalars) to provide numeric indexing.
+So in</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 pos;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p><em>pos[2]</em> refers to the third element of <em>pos</em> and is equivalent to <em>pos.z</em>.
+This allows variable indexing into a vector, as well as a generic way of
+accessing components.
+Any integer expression can be used as the subscript.
+The first component is at index zero.
+Reading from or writing to a vector using a constant integral expression
+with a value that is negative or greater than or equal to the size of the
+vector results in a compile-time error.
+When indexing with non-constant expressions, behavior is undefined if the
+index is negative, or greater than or equal to the size of the vector.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>length</strong>() method may be applied to vectors (but not scalars).
+The result is the number of components in the vector.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v;
+<span class="directive">const</span> <span class="predefined-type">int</span> L = v.length();</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>sets the constant <em>L</em> to 3.
+The type returned by <strong>.length</strong>() on a vector is <strong>int</strong>, and the value
+returned is a constant expression.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="matrix-components">5.6. Matrix Components</h3>
+<div class="paragraph">
+<p>The components of a matrix can be accessed using array subscripting syntax.
+Applying a single subscript to a matrix treats the matrix as an array of
+column vectors, and selects a single column, whose type is a vector of the
+same size as the (column size of the) matrix.
+The leftmost column is column 0.
+A second subscript would then operate on the resulting vector, as defined
+earlier for vectors.
+Hence, two subscripts select a column and then a row.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat4 m;
+m[<span class="integer">1</span>] = vec4(<span class="float">2</span><span class="float">.0</span>);   <span class="comment">// sets the second column to all 2.0</span>
+m[<span class="integer">0</span>][<span class="integer">0</span>] = <span class="float">1</span><span class="float">.0</span>;      <span class="comment">// sets the upper left element to 1.0</span>
+m[<span class="integer">2</span>][<span class="integer">3</span>] = <span class="float">2</span><span class="float">.0</span>;      <span class="comment">// sets the 4th element of the third column to 2.0</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Behavior is undefined when accessing a component outside the bounds of a
+matrix with a non-constant expression.
+It is a compile-time error to access a matrix with a constant expression
+that is outside the bounds of the matrix.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>length</strong>() method may be applied to matrices.
+The result is the number of columns of the matrix.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat3x4 v;
+<span class="directive">const</span> <span class="predefined-type">int</span> L = v.length();</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>sets the constant <em>L</em> to 3.
+The type returned by <strong>.length</strong>() on a matrix is <strong>int</strong>, and the value
+returned is a constant expression.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="structure-and-array-operations">5.7. Structure and Array Operations</h3>
+<div class="paragraph">
+<p>The members of a structure and the <strong>length</strong>() method of an array are
+selected using the period (<strong>.</strong>).</p>
+</div>
+<div class="paragraph">
+<p>In total, only the following operators are allowed to operate on arrays and
+structures as whole entities:</p>
+</div>
+<table class="tableblock frame-all grid-all fit-content">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">field selector</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>.</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">equality</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>==</strong> <strong>!=</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">assignment</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>=</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Ternary operator</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>?:</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Sequence operator</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>,</strong></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">indexing (arrays only)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>[</strong> <strong>]</strong></p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The equality operators and assignment operator are only allowed if the two
+operands are same size and type.
+The operands cannot contain any opaque types.
+Structure types must be of the same declared structure.
+Both array operands must be
+explicitly
+sized.
+When using the equality operators, two structures are equal if and only if
+all the members are component-wise equal, and two arrays are equal if and
+only if all the elements are element-wise equal.</p>
+</div>
+<div class="paragraph">
+<p>Array elements are accessed using the array subscript operator (<strong>[ ]</strong>).
+An example of accessing an array element is</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">diffuseColor += lightIntensity[<span class="integer">3</span>] * NdotL;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Array indices start at zero.
+Array elements are accessed using an expression whose type is <strong>int</strong> or
+<strong>uint</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Behavior is undefined if a shader subscripts an array with an index less
+than 0 or greater than or equal to the size the array was declared with.</p>
+</div>
+<div class="paragraph">
+<p>Arrays can also be accessed with the method operator (<strong>.</strong>) and the <strong>length</strong>
+method to query the size of the array:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">lightIntensity.length() <span class="comment">// return the size of the array</span></code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="assignments">5.8. Assignments</h3>
+<div class="paragraph">
+<p>Assignments of values to variable names are done with the assignment
+operator (<strong>=</strong>):</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>lvalue-expression</em> = <em>rvalue-expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>The <em>lvalue-expression</em> evaluates to an l-value.
+The assignment operator stores the value of <em>rvalue-expression</em> into the
+l-value and returns an r-value with the type and precision of
+<em>lvalue-expression</em>.
+The <em>lvalue-expression</em> and <em>rvalue-expression</em> must have the same
+type, or the expression must have a type in the table in section
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; that converts to the type
+of <em>lvalue-expression</em>, in which case an implicit conversion will be done on
+the <em>rvalue-expression</em> before the assignment is done.
+Any other desired type-conversions must be specified explicitly via a
+constructor.
+It is a compile-time error if the l-value is not writable.
+Variables that are built-in types, entire structures or arrays, structure
+members, l-values with the field selector (<strong>.</strong>) applied to select components
+or swizzles without repeated fields, l-values within parentheses, and
+l-values dereferenced with the array subscript operator (<strong>[ ]</strong>) are all
+l-values.
+Other binary or unary expressions, function names, swizzles with repeated
+fields, and constants cannot be l-values.
+The ternary operator (<strong>?:</strong>) is also not allowed as an l-value.
+Using an incorrect expression as an l-value results in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>Expressions on the left of an assignment are evaluated before expressions on
+the right of the assignment.</p>
+</div>
+<div class="paragraph">
+<p>The other assignment operators are</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>add into (<strong>+=</strong>)</p>
+</li>
+<li>
+<p>subtract from (<strong>-=</strong>)</p>
+</li>
+<li>
+<p>multiply into (<strong>*=</strong>)</p>
+</li>
+<li>
+<p>divide into (<strong>/=</strong>)</p>
+</li>
+<li>
+<p>modulus into (<strong>%=</strong>)</p>
+</li>
+<li>
+<p>left shift by (<strong>&lt;&lt;=</strong>)</p>
+</li>
+<li>
+<p>right shift by (<strong>&gt;&gt;=</strong>)</p>
+</li>
+<li>
+<p>and into (<strong>&amp;=</strong>)</p>
+</li>
+<li>
+<p>inclusive-or into (<strong>|=</strong>)</p>
+</li>
+<li>
+<p>exclusive-or into (<strong>^=</strong>)</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>where the general expression</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>lvalue</em> <em>op</em>= <em>expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>lvalue</em> = <em>lvalue</em> <em>op</em> <em>expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>where <em>lvalue</em> is the value returned by <em>lvalue-expression</em>, <em>op</em> is as
+described below, and the <em>lvalue-expression</em> and <em>expression</em> must satisfy
+the semantic requirements of both <em>op</em> and equals (<strong>=</strong>).</p>
+</div>
+<div class="paragraph">
+<p>Reading a variable before writing (or initializing) it is legal, however the
+value is undefined.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="expressions">5.9. Expressions</h3>
+<div class="paragraph">
+<p>Expressions in the shading language are built from the following:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Constants of type <strong>bool</strong>, all integral types, all floating-point types,
+all vector types, and all matrix types.</p>
+</li>
+<li>
+<p>Constructors of all types.</p>
+</li>
+<li>
+<p>Variable names of all types.</p>
+</li>
+<li>
+<p>An array, vector, or matrix expression with the <strong>length</strong>() method
+applied.</p>
+</li>
+<li>
+<p>Subscripted arrays.</p>
+</li>
+<li>
+<p>Function calls that return values.
+In some cases, function calls returning <strong>void</strong> are also allowed in
+expressions as specified below.</p>
+</li>
+<li>
+<p>Component field selectors and array subscript results.</p>
+</li>
+<li>
+<p>Parenthesized expressions.
+Any expression, including expressions with void type can be
+parenthesized.
+Parentheses can be used to group operations.
+Operations within parentheses are done before operations across
+parentheses.</p>
+</li>
+<li>
+<p>The arithmetic binary operators add (<strong>+</strong>), subtract (<strong>-</strong>), multiply
+(<strong>*</strong>), and divide (<strong>/</strong>) operate on integer and floating-point scalars,
+vectors, and matrices.
+If the fundamental types in the operands do not match, then the
+conversions from &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; are
+applied to create matching types.
+All arithmetic binary operators result in the same fundamental type
+(signed integer, unsigned integer, single-precision floating-point, or
+double-precision floating-point) as the operands they operate on, after
+operand type conversion.
+After conversion, the following cases are valid</p>
+<div class="ulist">
+<ul>
+<li>
+<p>The two operands are scalars.
+In this case the operation is applied, resulting in a scalar.</p>
+</li>
+<li>
+<p>One operand is a scalar, and the other is a vector or matrix.
+In this case, the scalar operation is applied independently to each
+component of the vector or matrix, resulting in the same size vector or
+matrix.</p>
+</li>
+<li>
+<p>The two operands are vectors of the same size.
+In this case, the operation is done component-wise resulting in the
+same size vector.</p>
+</li>
+<li>
+<p>The operator is add (<strong>+</strong>), subtract (<strong>-</strong>), or divide (<strong>/</strong>), and the
+operands are matrices with the same number of rows and the same number
+of columns.
+In this case, the operation is done component-wise resulting in the
+same size matrix.</p>
+</li>
+<li>
+<p>The operator is multiply (<strong>*</strong>), where both operands are matrices or one
+operand is a vector and the other a matrix.
+A right vector operand is treated as a column vector and a left vector
+operand as a row vector.
+In all these cases, it is required that the number of columns of the
+left operand is equal to the number of rows of the right operand.
+Then, the multiply (<strong>*</strong>) operation does a linear algebraic multiply,
+yielding an object that has the same number of rows as the left operand
+and the same number of columns as the right operand.
+&#8220;<a href="#vector-and-matrix-operations">Vector and Matrix Operations</a>&#8221;
+explains in more detail how vectors and matrices are operated on.</p>
+<div class="openblock">
+<div class="content">
+<div class="paragraph">
+<p>All other cases result in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>Use the built-in functions <strong>dot</strong>, <strong>cross</strong>, <strong>matrixCompMult</strong>, and
+<strong>outerProduct</strong>, to get, respectively, vector dot product, vector cross
+product, matrix component-wise multiplication, and the matrix product of a
+column vector times a row vector.</p>
+</div>
+</div>
+</div>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>The operator modulus (<strong>%</strong>) operates on signed or unsigned integers or
+integer vectors.
+If the fundamental types in the operands do not match, then the
+conversions from &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; are
+applied to create matching types.
+The operands cannot be vectors of differing size; this is
+a compile-time error.
+If one operand is a scalar and the other vector, then the scalar is
+applied component-wise to the vector, resulting in the same type as the
+vector.
+If both are vectors of the same size, the result is computed
+component-wise.
+The resulting value is undefined for any component computed with a
+second operand that is zero, while results for other components with
+non-zero second operands remain defined.
+If both operands are non-negative, then the remainder is non-negative.
+Results are undefined if one or both operands are negative.
+The operator modulus (<strong>%</strong>) is not defined for any other data types
+(non-integer types).</p>
+</li>
+<li>
+<p>The arithmetic unary operators negate (<strong>-</strong>), post- and pre-increment and
+decrement (<strong>--</strong> and <strong>++</strong>) operate on integer or floating-point values
+(including vectors and matrices).
+All unary operators work component-wise on their operands.
+These result with the same type they operated on.
+For post- and pre-increment and decrement, the expression must be a writable
+l-value.
+Pre-increment and pre-decrement add or subtract 1 or 1.0 to the contents
+of the expression they operate on, and the value of the pre-increment or
+pre-decrement expression is the resulting value of that modification.
+Post-increment and post-decrement expressions add or subtract 1 or 1.0
+to the contents of the expression they operate on, but the resulting
+expression has the expression&#8217;s value before the post-increment or
+post-decrement was executed.</p>
+</li>
+<li>
+<p>The relational operators greater than (<strong>&gt;</strong>), less than (<strong>&lt;</strong>), greater
+than or equal (<strong>&gt;=</strong>), and less than or equal (<strong>&lt;=</strong>) operate only on
+scalar integer and scalar floating-point expressions.
+The result is scalar Boolean.
+Either the operands' types must match, or the conversions from section
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; will be applied to
+obtain matching types.
+To do component-wise relational comparisons on vectors, use the built-in
+functions <strong>lessThan</strong>, <strong>lessThanEqual</strong>, <strong>greaterThan</strong>, and
+<strong>greaterThanEqual.</strong></p>
+</li>
+<li>
+<p>The equality operators <strong>equal</strong> (<strong>==</strong>), and not equal (<strong>!=</strong>) operate on
+all types except opaque types, aggregates that contain opaque types,
+subroutine uniforms, and aggregates that contain subroutine uniforms.
+They result in a scalar Boolean.
+If the operand types do not match, then there must be a conversion from
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; applied to one operand
+that can make them match, in which case this conversion is done.
+For vectors, matrices, structures, and arrays, all components, members,
+or elements of one operand must equal the corresponding components,
+members, or elements in the other operand for the operands to be
+considered equal.
+To get a vector of component-wise equality results for vectors, use the
+built-in functions <strong>equal</strong> and <strong>notEqual</strong>.</p>
+</li>
+<li>
+<p>The logical binary operators and (<strong>&amp;&amp;</strong>), or (<strong>||</strong>), and exclusive or
+(<strong>^^</strong>) operate only on two Boolean expressions and result in a Boolean
+expression.
+And (<strong>&amp;&amp;</strong>) will only evaluate the right hand operand if the left hand
+operand evaluated to <strong>true</strong>.
+Or (<strong>||</strong>) will only evaluate the right hand operand if the left hand
+operand evaluated to <strong>false</strong>.
+Exclusive or (<strong>^^</strong>) will always evaluate both operands.</p>
+</li>
+<li>
+<p>The logical unary operator not (<strong>!</strong>).
+It operates only on a Boolean expression and results in a Boolean
+expression.
+To operate on a vector, use the built-in function <strong>not</strong>.</p>
+</li>
+<li>
+<p>The sequence (<strong>,</strong>) operator that operates on expressions by returning
+the type and value of the right-most expression in a comma separated
+list of expressions.
+All expressions are evaluated, in order, from left to right.
+The operands to the sequence operator may have <strong>void</strong> type.</p>
+</li>
+<li>
+<p>The ternary selection operator (<strong>?:</strong>).
+It operates on three expressions (<em>exp1</em> <strong>?</strong> <em>exp2</em> <strong>:</strong> <em>exp3</em>).
+This operator evaluates the first expression, which must result in a
+scalar Boolean.
+If the result is true, it selects to evaluate the second expression,
+otherwise it selects to evaluate the third expression.
+Only one of the second and third expressions is evaluated.
+The second and third expressions can be any type, including <strong>void</strong>, as
+long their types match, or there is a conversion in section
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; that can be applied to
+one of the expressions to make their types match.
+This resulting matching type is the type of the entire expression.</p>
+</li>
+<li>
+<p>The one&#8217;s complement operator (<strong>~</strong>).
+The operand must be of type signed or unsigned integer or integer
+vector, and the result is the one&#8217;s complement of its operand; each bit
+of each component is complemented, including any sign bits.</p>
+</li>
+<li>
+<p>The shift operators (<strong>&lt;&lt;</strong>) and (<strong>&gt;&gt;</strong>).
+For both operators, the operands must be signed or unsigned integers or
+integer vectors.
+One operand can be signed while the other is unsigned.
+In all cases, the resulting type will be the same type as the left
+operand.
+If the first operand is a scalar, the second operand has to be a scalar
+as well.
+If the first operand is a vector, the second operand must be a scalar or
+a vector with the same size as the first operand, and the result is
+computed component-wise.
+The result is undefined if the right operand is negative, or greater
+than or equal to the number of bits in the left expression&#8217;s base type.
+The value of E1 &lt;&lt; E2 is E1 (interpreted as a bit pattern) left-shifted
+by E2 bits.
+The value of E1 &gt;&gt; E2 is E1 right-shifted by E2 bit positions.
+If E1 is a signed integer, the right-shift will extend the sign bit.
+If E1 is an unsigned integer, the right-shift will zero-extend.</p>
+</li>
+<li>
+<p>The bitwise operators and (<strong>&amp;</strong>), exclusive-or (<strong>^</strong>), and inclusive-or
+(<strong>|</strong>).
+The operands must be of type signed or unsigned integers or integer
+vectors.
+The operands cannot be vectors of differing size; this is a compile-time error.
+If one operand is a scalar and the other a vector, the scalar is applied
+component-wise to the vector, resulting in the same type as the vector.
+If the fundamental types in the operands do not match, then the
+conversions from &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; are
+applied to create matching types, and this will be the resulting
+fundamental type.
+For and (<strong>&amp;</strong>), the result is the bitwise-and function of the operands.
+For exclusive-or (<strong>^</strong>), the result is the bitwise exclusive-or function
+of the operands.
+For inclusive-or (<strong>|</strong>), the result is the bitwise inclusive-or function
+of the operands.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>For a complete specification of the syntax of expressions, see
+&#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221;.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="vector-and-matrix-operations">5.10. Vector and Matrix Operations</h3>
+<div class="paragraph">
+<p>With a few exceptions, operations are component-wise.
+Usually, when an operator operates on a vector or matrix, it is operating
+independently on each component of the vector or matrix, in a component-wise
+fashion.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v, u;
+<span class="predefined-type">float</span> f;
+v = u + f;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will be equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">v.x = u.x + f;
+v.y = u.y + f;
+v.z = u.z + f;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>And</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v, u, w;
+w = v + u;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>will be equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">w.x = v.x + u.x;
+w.y = v.y + u.y;
+w.z = v.z + u.z;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and likewise for most operators and all integer and floating-point vector
+and matrix types.
+The exceptions are matrix multiplied by vector, vector multiplied by matrix,
+and matrix multiplied by matrix.
+These do not operate component-wise, but rather perform the correct linear
+algebraic multiply.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec3 v, u;
+mat3 m;
+u = v * m;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">u.x = dot(v, m[<span class="integer">0</span>]); <span class="comment">// m[0] is the left column of m</span>
+u.y = dot(v, m[<span class="integer">1</span>]); <span class="comment">// dot(a,b) is the inner (dot) product of a and b</span>
+u.z = dot(v, m[<span class="integer">2</span>]);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>And</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">u = m * v;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">u.x = m[<span class="integer">0</span>].x * v.x + m[<span class="integer">1</span>].x * v.y + m[<span class="integer">2</span>].x * v.z;
+u.y = m[<span class="integer">0</span>].y * v.x + m[<span class="integer">1</span>].y * v.y + m[<span class="integer">2</span>].y * v.z;
+u.z = m[<span class="integer">0</span>].z * v.x + m[<span class="integer">1</span>].z * v.y + m[<span class="integer">2</span>].z * v.z;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>And</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">mat3 m, n, r;
+r = m * n;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>is equivalent to</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">r[<span class="integer">0</span>].x = m[<span class="integer">0</span>].x * n[<span class="integer">0</span>].x + m[<span class="integer">1</span>].x * n[<span class="integer">0</span>].y + m[<span class="integer">2</span>].x * n[<span class="integer">0</span>].z;
+r[<span class="integer">1</span>].x = m[<span class="integer">0</span>].x * n[<span class="integer">1</span>].x + m[<span class="integer">1</span>].x * n[<span class="integer">1</span>].y + m[<span class="integer">2</span>].x * n[<span class="integer">1</span>].z;
+r[<span class="integer">2</span>].x = m[<span class="integer">0</span>].x * n[<span class="integer">2</span>].x + m[<span class="integer">1</span>].x * n[<span class="integer">2</span>].y + m[<span class="integer">2</span>].x * n[<span class="integer">2</span>].z;
+r[<span class="integer">0</span>].y = m[<span class="integer">0</span>].y * n[<span class="integer">0</span>].x + m[<span class="integer">1</span>].y * n[<span class="integer">0</span>].y + m[<span class="integer">2</span>].y * n[<span class="integer">0</span>].z;
+r[<span class="integer">1</span>].y = m[<span class="integer">0</span>].y * n[<span class="integer">1</span>].x + m[<span class="integer">1</span>].y * n[<span class="integer">1</span>].y + m[<span class="integer">2</span>].y * n[<span class="integer">1</span>].z;
+r[<span class="integer">2</span>].y = m[<span class="integer">0</span>].y * n[<span class="integer">2</span>].x + m[<span class="integer">1</span>].y * n[<span class="integer">2</span>].y + m[<span class="integer">2</span>].y * n[<span class="integer">2</span>].z;
+r[<span class="integer">0</span>].z = m[<span class="integer">0</span>].z * n[<span class="integer">0</span>].x + m[<span class="integer">1</span>].z * n[<span class="integer">0</span>].y + m[<span class="integer">2</span>].z * n[<span class="integer">0</span>].z;
+r[<span class="integer">1</span>].z = m[<span class="integer">0</span>].z * n[<span class="integer">1</span>].x + m[<span class="integer">1</span>].z * n[<span class="integer">1</span>].y + m[<span class="integer">2</span>].z * n[<span class="integer">1</span>].z;
+r[<span class="integer">2</span>].z = m[<span class="integer">0</span>].z * n[<span class="integer">2</span>].x + m[<span class="integer">1</span>].z * n[<span class="integer">2</span>].y + m[<span class="integer">2</span>].z * n[<span class="integer">2</span>].z;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and similarly for other sizes of vectors and matrices.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="out-of-bounds-accesses">5.11. Out-of-Bounds Accesses</h3>
+<div class="paragraph">
+<p>In the subsections described above for array, vector, matrix and structure
+accesses, any out-of-bounds access produced undefined behavior.
+However, if robust buffer access is enabled via the OpenGL API, such
+accesses will be bound within the memory extent of the active program.
+It will not be possible to access memory from other programs, and accesses
+will not result in abnormal program termination.
+Out-of-bounds reads return undefined values, which include values from other
+variables of the active program or zero.
+Out-of-bounds writes may be discarded or overwrite other variables of the
+active program, depending on the value of the computed index and how this
+relates to the extent of the active program&#8217;s memory.
+Applications that require defined behavior for out-of-bounds accesses should
+range check all computed indices before dereferencing an array.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="specialization-constant-operations">5.12. Specialization Constant Operations</h3>
+<div class="paragraph">
+<p>Only some operations discussed in this section may be applied to a
+specialization constant and still yield a result that is a specialization
+constant.
+The operations that do so are listed below.
+When a specialization constant is operated on with one of these operators
+and with another constant or specialization constant, the result is
+implicitly a specialization constant.</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>int</strong>(), <strong>uint</strong>(), and <strong>bool</strong>() constructors for type conversions from
+any of the following types to any of the following types:</p>
+<div class="ulist">
+<ul>
+<li>
+<p><strong>int</strong></p>
+</li>
+<li>
+<p><strong>uint</strong></p>
+</li>
+<li>
+<p><strong>bool</strong></p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>vector versions of the above conversion constructors</p>
+</li>
+<li>
+<p>allowed implicit conversions of the above</p>
+</li>
+<li>
+<p>swizzles (e.g. <code>foo.yx</code>)</p>
+</li>
+<li>
+<p>the following when applied to integer or unsigned integer types:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>unary negative (<strong>-</strong>)</p>
+</li>
+<li>
+<p>binary operations (<strong>+</strong>, <strong>-</strong>, <strong>*</strong>, <strong>/</strong>, <strong>%</strong>)</p>
+</li>
+<li>
+<p>shift (<strong>&lt;&lt;</strong>, <strong>&gt;&gt;</strong>)</p>
+</li>
+<li>
+<p>bitwise operations (<strong>&amp;</strong>, <strong>|</strong>, <strong>^</strong>)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>the following when applied to integer or unsigned integer scalar types:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>comparison (<strong>==</strong>, <strong>!=</strong>, <strong>&gt;</strong>, <strong>&gt;=</strong>, <strong>&lt;</strong>, <strong>&#8656;</strong>)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>The following when applied to the Boolean scalar type:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>not (<strong>!</strong>)</p>
+</li>
+<li>
+<p>logical operations (<strong>&amp;&amp;</strong>, <strong>||</strong>, <strong>^^</strong>)</p>
+</li>
+<li>
+<p>comparison (<strong>==</strong>, <strong>!=</strong>)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>the ternary operator (<strong>?:</strong>)</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="statements-and-structure">6. Statements and Structure</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The fundamental building blocks of the OpenGL Shading Language are:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>statements and declarations</p>
+</li>
+<li>
+<p>function definitions</p>
+</li>
+<li>
+<p>selection (<strong>if</strong>-<strong>else</strong> and <strong>switch</strong>-<strong>case</strong>-<strong>default</strong>)</p>
+</li>
+<li>
+<p>iteration (<strong>for</strong>, <strong>while</strong>, and <strong>do</strong>-<strong>while</strong>)</p>
+</li>
+<li>
+<p>jumps (<strong>discard</strong>, <strong>return</strong>, <strong>break</strong>, and <strong>continue</strong>)</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>The overall structure of a shader is as follows</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>translation-unit</em> : </dt>
+<dd>
+<p><em>global-declaration</em><br>
+<em>translation-unit</em> <em>global-declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>global-declaration</em> : </dt>
+<dd>
+<p><em>function-definition</em><br>
+<em>declaration</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>That is, a shader is a sequence of declarations and function bodies.
+Function bodies are defined as</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>function-definition</em> : </dt>
+<dd>
+<p><em>function-prototype</em> <strong>{</strong> <em>statement-list</em> <strong>}</strong></p>
+</dd>
+<dt class="hdlist1"><em>statement-list</em> : </dt>
+<dd>
+<p><em>statement</em><br>
+<em>statement-list</em> <em>statement</em></p>
+</dd>
+<dt class="hdlist1"><em>statement</em> : </dt>
+<dd>
+<p><em>compound-statement</em><br>
+<em>simple-statement</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Curly braces are used to group sequences of statements into compound
+statements.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>compound-statement</em> : </dt>
+<dd>
+<p><strong>{</strong> <em>statement-list</em> <strong>}</strong></p>
+</dd>
+<dt class="hdlist1"><em>simple-statement</em> : </dt>
+<dd>
+<p><em>declaration-statement</em><br>
+<em>expression-statement</em><br>
+<em>selection-statement</em><br>
+<em>iteration-statement</em><br>
+<em>jump-statement</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Simple declaration, expression, and jump statements end in a semi-colon.</p>
+</div>
+<div class="paragraph">
+<p>This above is slightly simplified, and the complete grammar specified in
+&#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; should be used as
+the definitive specification.</p>
+</div>
+<div class="paragraph">
+<p>Declarations and expressions have already been discussed.</p>
+</div>
+<div class="sect2">
+<h3 id="function-definitions">6.1. Function Definitions</h3>
+<div class="paragraph">
+<p>As indicated by the grammar above, a valid shader is a sequence of global
+declarations and function definitions.
+A function is declared as the following example shows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// prototype</span>
+returnType functionName (type0 arg0, type1 arg1, ..., typen argn);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>and a function is defined like</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// definition</span>
+returnType functionName (type0 arg0, type1 arg1, ..., typen argn)
+{
+    <span class="comment">// do some computation</span>
+    <span class="keyword">return</span> returnValue;
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>where <em>returnType</em> must be present and cannot be void, or:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> functionName (type0 arg0, type1 arg1, ..., typen argn)
+{
+    <span class="comment">// do some computation</span>
+    <span class="keyword">return</span>; <span class="comment">// optional</span>
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If the type of <em>returnValue</em> does not match <em>returnType</em>, there must be an
+implicit conversion in &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221;
+that converts the type of <em>returnValue</em> to <em>returnType</em>, or a compile-time
+error will result.</p>
+</div>
+<div class="paragraph">
+<p>Each of the <em>typeN</em> must include a type and can optionally include parameter
+qualifiers.
+The formal argument names (<em>args</em> above) in the declarations are optional
+for both the declaration and definition forms.</p>
+</div>
+<div class="paragraph">
+<p>A function is called by using its name followed by a list of arguments in
+parentheses.</p>
+</div>
+<div class="paragraph">
+<p>Arrays are allowed as arguments and as the return type.
+In both cases, the array must be
+explicitly
+sized.
+An array is passed or returned by using just its name, without brackets, and
+the size of the array must match the size specified in the function&#8217;s
+declaration.</p>
+</div>
+<div class="paragraph">
+<p>Structures are also allowed as argument types.
+The return type can also be a structure.</p>
+</div>
+<div class="paragraph">
+<p>See &#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; for the
+definitive reference on the syntax to declare and define functions.</p>
+</div>
+<div class="paragraph">
+<p>All functions must be either declared with a prototype or defined with a
+body before they are called.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> myfunc (<span class="predefined-type">float</span> f,      <span class="comment">// f is an input parameter</span>
+              out <span class="predefined-type">float</span> g); <span class="comment">// g is an output parameter</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Functions that return no value must be declared as <strong>void</strong>.
+A <strong>void</strong> function can only use <strong>return</strong> without a return argument, even if
+the return argument has <strong>void</strong> type.
+Return statements only accept values:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> func1() { }
+<span class="directive">void</span> func2() { <span class="keyword">return</span> func1(); } <span class="comment">// illegal return statement</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Only a precision qualifier is allowed on the return type of a function.
+Formal parameters can have parameter, precision, and memory qualifiers, but
+no other qualifiers.</p>
+</div>
+<div class="paragraph">
+<p>Functions that accept no input arguments need not use <strong>void</strong> in the argument
+list because prototypes (or definitions) are required and therefore there is
+no ambiguity when an empty argument list &#8220;( )&#8221; is declared.
+The idiom &#8220;(<strong>void</strong>)&#8221; as a parameter list is provided for convenience.</p>
+</div>
+<div class="paragraph">
+<p>Function names can be overloaded.
+The same function name can be used for multiple functions, as long as the
+parameter types differ.
+If a function name is declared twice with the same parameter types, then the
+return types and all qualifiers must also match, and it is the same function
+being declared.</p>
+</div>
+<div class="paragraph">
+<p>For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4 f(in vec4 x, out vec4 y);       <span class="comment">// (A)</span>
+vec4 f(in vec4 x, out uvec4 y);      <span class="comment">// (B) okay, different argument type</span>
+vec4 f(in ivec4 x, out dvec4 y);     <span class="comment">// (C) okay, different argument type</span>
+<span class="predefined-type">int</span> f(in vec4 x, out vec4 y);        <span class="comment">// error, only return type differs</span>
+vec4 f(in vec4 x, in vec4 y);        <span class="comment">// error, only qualifier differs</span>
+vec4 f(<span class="directive">const</span> in vec4 x, out vec4 y); <span class="comment">// error, only qualifier differs</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>When function calls are resolved, an exact type match for all the arguments
+is sought.
+If an exact match is found, all other functions are ignored, and the exact
+match is used.
+If no exact match is found, then the implicit conversions in section
+&#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221; will be applied to find a
+match.
+Mismatched types on input parameters (<strong>in</strong> or <strong>inout</strong> or default) <strong>must</strong>
+have a conversion from the calling argument type to the formal parameter
+type.
+Mismatched types on output parameters (<strong>out</strong> or <strong>inout</strong>) must have a
+conversion from the formal parameter type to the calling argument type.</p>
+</div>
+<div class="paragraph">
+<p>If implicit conversions can be used to find more than one matching function,
+a single best-matching function is sought.
+To determine a best match, the conversions between calling argument and
+formal parameter types are compared for each function argument and pair of
+matching functions.
+After these comparisons are performed, each pair of matching functions are
+compared.
+A function declaration <em>A</em> is considered a better match than function
+declaration <em>B</em> if</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>for at least one function argument, the conversion for that argument in
+<em>A</em> is better than the corresponding conversion in <em>B</em>; and</p>
+</li>
+<li>
+<p>there is no function argument for which the conversion in <em>B</em> is better
+than the corresponding conversion in <em>A</em>.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>If a single function declaration is considered a better match than every
+other matching function declaration, it will be used.
+Otherwise, a compile-time semantic error for an ambiguous overloaded
+function call occurs.</p>
+</div>
+<div class="paragraph">
+<p>To determine whether the conversion for a single argument in one match is
+better than that for another match, the following rules are applied, in
+order:</p>
+</div>
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>An exact match is better than a match involving any implicit conversion.</p>
+</li>
+<li>
+<p>A match involving an implicit conversion from <strong>float</strong> to <strong>double</strong> is
+better than a match involving any other implicit conversion.</p>
+</li>
+<li>
+<p>A match involving an implicit conversion from either <strong>int</strong> or <strong>uint</strong> to
+<strong>float</strong> is better than a match involving an implicit conversion from
+either <strong>int</strong> or <strong>uint</strong> to <strong>double</strong>.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>If none of the rules above apply to a particular pair of conversions,
+neither conversion is considered better than the other.</p>
+</div>
+<div class="paragraph">
+<p>For the example function prototypes (A), (B), and &#169; above, the following
+examples show how the rules apply to different sets of calling argument
+types:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">f(vec4, vec4)   <span class="comment">// exact match of vec4 f(in vec4 x, out vec4 y)</span>
+f(vec4, uvec4)  <span class="comment">// exact match of vec4 f(in vec4 x, out uvec4 y)</span>
+f(vec4, ivec4)  <span class="comment">// matched to vec4 f(in vec4 x, out vec4 y)</span>
+                <span class="comment">// (C) not relevant, can't convert vec4 to</span>
+                <span class="comment">// ivec4. (A) better than (B) for 2nd</span>
+                <span class="comment">// argument (rule 3), same on first argument.</span>
+f(ivec4, vec4); <span class="comment">// NOT matched. All three match by implicit</span>
+                <span class="comment">// conversion. (C) is better than (A) and (B)</span>
+                <span class="comment">// on the first argument. (A) is better than</span>
+                <span class="comment">// (B) and (C).</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>User-defined functions can have multiple declarations, but only one
+definition.</p>
+</div>
+<div class="paragraph">
+<p>A shader can redefine built-in functions.
+If a built-in function is redeclared in a shader (i.e., a prototype is
+visible) before a call to it, then the linker will only attempt to resolve
+that call within the set of shaders that are linked with it.</p>
+</div>
+<div class="paragraph">
+<p>The function <em>main</em> is used as the entry point to a shader executable.
+A shader need not contain a function named <em>main</em>, but one shader in a set
+of shaders linked together to form a single shader executable must, or a
+link-time error results.
+This function takes no arguments, returns no value, and must be declared as
+type <strong>void</strong>:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">void</span> main()
+{
+    ...
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The function <em>main</em> can contain uses of <strong>return</strong>.
+See &#8220;<a href="#jumps">Jumps</a>&#8221; for more details.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time or link-time error to declare or define a function
+<strong>main</strong> with any other parameters or return type.</p>
+</div>
+<div class="sect3">
+<h4 id="function-calling-conventions">6.1.1. Function Calling Conventions</h4>
+<div class="paragraph">
+<p>Functions are called by value-return.
+This means input arguments are copied into the function at call time, and
+output arguments are copied back to the caller before function exit.
+Because the function works with local copies of parameters, there are no
+issues regarding aliasing of variables within a function.
+To control what parameters are copied in and/or out through a function
+definition or declaration:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>The keyword <strong>in</strong> is used as a qualifier to denote a parameter is to be
+copied in, but not copied out.</p>
+</li>
+<li>
+<p>The keyword <strong>out</strong> is used as a qualifier to denote a parameter is to be
+copied out, but not copied in.
+This should be used whenever possible to avoid unnecessarily copying
+parameters in.</p>
+</li>
+<li>
+<p>The keyword <strong>inout</strong> is used as a qualifier to denote the parameter is to
+be both copied in and copied out.
+It means the same thing as specifying both <strong>in</strong> and <strong>out</strong>.</p>
+</li>
+<li>
+<p>A function parameter declared with no such qualifier means the same
+thing as specifying <strong>in</strong>.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>All arguments are evaluated at call time, exactly once, in order, from left
+to right.
+Evaluation of an <strong>in</strong> parameter results in a value that is copied to the
+formal parameter.
+Evaluation of an <strong>out</strong> parameter results in an l-value that is used to copy
+out a value when the function returns.
+Evaluation of an <strong>inout</strong> parameter results in both a value and an l-value;
+the value is copied to the formal parameter at call time and the l-value is
+used to copy out a value when the function returns.</p>
+</div>
+<div class="paragraph">
+<p>The order in which output parameters are copied back to the caller is
+undefined.</p>
+</div>
+<div class="paragraph">
+<p>If the function matching described in the previous section required argument
+type conversions, these conversions are applied at copy-in and copy-out
+times.</p>
+</div>
+<div class="paragraph">
+<p>In a function, writing to an input-only parameter is allowed.
+Only the function&#8217;s copy is modified.
+This can be prevented by declaring a parameter with the <strong>const</strong> qualifier.</p>
+</div>
+<div class="paragraph">
+<p>When calling a function, expressions that do not evaluate to l-values cannot
+be passed to parameters declared as <strong>out</strong> or <strong>inout</strong>, or a compile-time error
+results.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>function-prototype</em> : </dt>
+<dd>
+<p><em>precision-qualifier</em> <em>type</em> <em>function-name</em> <strong>(</strong> <em>parameter-qualifiers</em>
+<em>precision-qualifier</em> <em>type</em> <em>name</em> <em>array-specifier</em> <strong>,</strong> &#8230;&#8203;
+<strong>)</strong></p>
+</dd>
+<dt class="hdlist1"><em>type</em> : </dt>
+<dd>
+<p>any basic type, array type, structure name, or structure definition</p>
+</dd>
+<dt class="hdlist1"><em>parameter-qualifiers</em> : </dt>
+<dd>
+<p><em>empty</em><br>
+list of <em>parameter-qualifier</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter-qualifier</em> : </dt>
+<dd>
+<p><strong>const</strong><br>
+<strong>in</strong><br>
+<strong>out</strong><br>
+<strong>inout</strong><br>
+<strong>precise</strong><br>
+<em>memory-qualifier</em><br>
+<em>precision-qualifier</em></p>
+</dd>
+<dt class="hdlist1"><em>name</em> : </dt>
+<dd>
+<p>empty<br>
+identifier</p>
+</dd>
+<dt class="hdlist1"><em>array-specifier</em> : </dt>
+<dd>
+<p>empty<br>
+<strong>[</strong> <em>integral-constant-expression</em> <strong>]</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>The <strong>const</strong> qualifier cannot be used with <strong>out</strong> or <strong>inout</strong>, or
+a compile-time error results.
+The above is used both for function declarations (i.e., prototypes) and for
+function definitions.
+Hence, function definitions can have unnamed arguments.</p>
+</div>
+<div class="paragraph">
+<p>Recursion is not allowed, not even statically.
+Static recursion is present if the static function-call graph of a program
+contains cycles.
+This includes all potential function calls through variables declared as
+<strong>subroutine</strong> <strong>uniform</strong> (described below).
+It is a compile-time or link-time error if a single compilation unit
+(shader) contains either static recursion or the potential for recursion
+through subroutine variables.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="subroutines">6.1.2. Subroutines</h4>
+<div class="paragraph">
+<p>Subroutines provide a mechanism allowing shaders to be compiled in a manner
+where the target of one or more function calls can be changed at run-time
+without requiring any shader recompilation.
+For example, a single shader may be compiled with support for multiple
+illumination algorithms to handle different kinds of lights or surface
+materials.
+An application using such a shader may switch illumination algorithms by
+changing the value of its subroutine uniforms.
+To use subroutines, a subroutine type is declared, one or more functions are
+associated with that subroutine type, and a subroutine variable of that type
+is declared.
+The function currently assigned to the variable function is then called by
+using function calling syntax replacing a function name with the name of the
+subroutine variable.
+Subroutine variables are uniforms, and are assigned to specific functions
+only through commands (<strong>UniformSubroutinesuiv</strong>) in the OpenGL API.</p>
+</div>
+<div class="paragraph">
+<p>Subroutine functionality is not available when generating SPIR-V.</p>
+</div>
+<div class="paragraph">
+<p>Subroutine types are declared using a statement similar to a function
+declaration, with the <strong>subroutine</strong> keyword, as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">subroutine returnType subroutineTypeName(type0 arg0, type1 arg1,
+                                         ..., typen argn);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>As with function declarations, the formal argument names (<em>args</em> above) are
+optional.
+Functions are associated with subroutine types of matching declarations by
+defining the function with the <strong>subroutine</strong> keyword and a list of subroutine
+types the function matches:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">subroutine(subroutineTypeName0, ..., subroutineTypeNameN)
+returnType functionName(type0 arg0, type1 arg1, ..., typen argn)
+{ ... } <span class="comment">// function body</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error if arguments and return type don&#8217;t match between
+the function and each associated subroutine type.</p>
+</div>
+<div class="paragraph">
+<p>Functions declared with <strong>subroutine</strong> must include a body.
+An overloaded function cannot be declared with <strong>subroutine</strong>; a program will
+fail to compile or link if any shader or stage contains two or more
+functions with the same name if the name is associated with a subroutine
+type.</p>
+</div>
+<div class="paragraph">
+<p>A function declared with <strong>subroutine</strong> can also be called directly with a
+static use of <em>functionName</em>, as is done with non-subroutine function
+declarations and calls.</p>
+</div>
+<div class="paragraph">
+<p>Subroutine type variables are required to be <em>subroutine uniforms</em>, and are
+declared with a specific subroutine type in a subroutine uniform variable
+declaration:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">subroutine uniform subroutineTypeName subroutineVarName;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Subroutine uniform variables are called the same way functions are called.
+When a subroutine variable (or an element of a subroutine variable array) is
+associated with a particular function, all function calls through that
+variable will call that particular function.</p>
+</div>
+<div class="paragraph">
+<p>Unlike other uniform variables, subroutine uniform variables are scoped to
+the shader execution stage the variable is declared in.</p>
+</div>
+<div class="paragraph">
+<p>Subroutine variables may be declared as explicitly-sized arrays, which can
+be indexed only with dynamically uniform expressions.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time error to use the <strong>subroutine</strong> keyword in any places
+other than (as shown above) to</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>declare a subroutine type at global scope,</p>
+</li>
+<li>
+<p>declare a function as a subroutine, or</p>
+</li>
+<li>
+<p>declare a subroutine variable at global scope.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="selection">6.2. Selection</h3>
+<div class="paragraph">
+<p>Conditional control flow in the shading language is done by either <strong>if</strong>,
+<strong>if</strong>-<strong>else</strong>, or <strong>switch</strong> statements:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>selection-statement</em> : </dt>
+<dd>
+<p><strong>if</strong> <strong>(</strong> <em>bool-expression</em> <strong>)</strong> <em>statement</em><br>
+<strong>if</strong> <strong>(</strong> <em>bool-expression</em> <strong>)</strong> <em>statement</em> <strong>else</strong> <em>statement</em><br>
+<strong>switch</strong> <strong>(</strong> <em>init-expression</em> <strong>)</strong> <strong>{</strong> <em>switch-statement-list<sub>opt</sub></em> <strong>}</strong></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Where <em>switch-statement-list</em> is a nested scope containing a list of zero or
+more <em>switch-statement</em> and other statements defined by the language, where
+<em>switch-statement</em> adds some forms of labels.
+That is</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>switch-statement-list</em> : </dt>
+<dd>
+<p><em>switch-statement</em><br>
+<em>switch-statement-list</em> <em>switch-statement</em></p>
+</dd>
+<dt class="hdlist1"><em>switch-statement</em> : </dt>
+<dd>
+<p><strong>case</strong> <em>constant-expression</em> <strong>:</strong><br>
+<strong>default</strong> <strong>:</strong> <em>statement</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>Note the above grammar&#8217;s purpose is to aid discussion in this section; the
+normative grammar is in &#8220;<a href="#shading-language-grammar">Shading Language
+Grammar</a>&#8221;.</p>
+</div>
+<div class="paragraph">
+<p>If an <strong>if</strong>-expression evaluates to <strong>true</strong>, then the first <em>statement</em> is
+executed.
+If it evaluates to <strong>false</strong> and there is an <strong>else</strong> part then the second
+<em>statement</em> is executed.</p>
+</div>
+<div class="paragraph">
+<p>Any expression whose type evaluates to a Boolean can be used as the
+conditional expression <em>bool-expression</em>.
+Vector types are not accepted as the expression to <strong>if</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Conditionals can be nested.</p>
+</div>
+<div class="paragraph">
+<p>The type of <em>init-expression</em> in a <strong>switch</strong> statement must be a scalar
+integer.
+The type of the <em>constant-expression</em> value in a case label also must be a
+scalar integer.
+When any pair of these values is tested for &#8220;equal value&#8221; and the types do
+not match, an implicit conversion will be done to convert the <strong>int</strong> to a
+<strong>uint</strong> (see &#8220;<a href="#implicit-conversions">Implicit Conversions</a>&#8221;) before the
+compare is done.
+If a <strong>case</strong> label has a <em>constant-expression</em> of equal value to
+<em>init-expression</em>, execution will continue after that label.
+Otherwise, if there is a <strong>default</strong> label, execution will continue after that
+label.
+Otherwise, execution skips the rest of the switch statement.
+It is a compile-time error to have more than one <strong>default</strong> or a replicated
+<em>constant-expression</em>.
+A <strong>break</strong> statement not nested in a loop or other switch statement (either
+not nested or nested only in <strong>if</strong> or <strong>if</strong>-<strong>else</strong> statements) will also skip
+the rest of the switch statement.
+Fall through labels are allowed, but it is a compile-time error to have no
+statement between a label and the end of the switch statement.
+No statements are allowed in a switch statement before the first <strong>case</strong>
+statement.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>case</strong> and <strong>default</strong> labels can only appear within a <strong>switch</strong> statement.
+No <strong>case</strong> or <strong>default</strong> labels can be nested inside other statements or
+compound statements within their corresponding <strong>switch</strong>.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="iteration">6.3. Iteration</h3>
+<div class="paragraph">
+<p>For, while, and do loops are allowed as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">for</span> (init-expression; condition-expression; loop-expression)
+    sub-statement
+<span class="keyword">while</span> (condition-expression)
+    sub-statement
+<span class="keyword">do</span>
+    statement
+<span class="keyword">while</span> (condition-expression)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>See &#8220;<a href="#shading-language-grammar">Shading Language Grammar</a>&#8221; for the
+definitive specification of loops.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>for</strong> loop first evaluates the <em>init-expression</em>, then the
+<em>condition-expression</em>.
+If the <em>condition-expression</em> evaluates to <strong>true</strong>, then the body of the loop
+is executed.
+After the body is executed, a <strong>for</strong> loop will then evaluate the
+<em>loop-expression</em>, and then loop back to evaluate the
+<em>condition-expression</em>, repeating until the <em>condition-expression</em> evaluates
+to <strong>false</strong>.
+The loop is then exited, skipping its body and skipping its
+<em>loop-expression</em>.
+Variables modified by the <em>loop-expression</em> maintain their value after the
+loop is exited, provided they are still in scope.
+Variables declared in <em>init-expression</em> or <em>condition-expression</em> are only
+in scope until the end of the sub-statement of the <strong>for</strong> loop.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>while</strong> loop first evaluates the <em>condition-expression</em>.
+If <strong>true</strong>, then the body is executed.
+This is then repeated, until the <em>condition-expression</em> evaluates to
+<strong>false</strong>, exiting the loop and skipping its body.
+Variables declared in the <em>condition-expression</em> are only in scope until the
+end of the sub-statement of the <strong>while</strong> loop.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>do</strong>-<strong>while</strong> loop first executes the body, then executes the
+<em>condition-expression</em>.
+This is repeated until <em>condition-expression</em> evaluates to <strong>false</strong>, and then
+the loop is exited.</p>
+</div>
+<div class="paragraph">
+<p>Expressions for <em>condition-expression</em> must evaluate to a Boolean.</p>
+</div>
+<div class="paragraph">
+<p>Both the <em>condition-expression</em> and the <em>init-expression</em> can declare and
+initialize a variable, except in the <strong>do</strong>-<strong>while</strong> loop, which cannot declare
+a variable in its <em>condition-expression</em>.
+The variable&#8217;s scope lasts only until the end of the sub-statement that
+forms the body of the loop.</p>
+</div>
+<div class="paragraph">
+<p>Loops can be nested.</p>
+</div>
+<div class="paragraph">
+<p>Non-terminating loops are allowed.
+The consequences of very long or non-terminating loops are platform
+dependent.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="jumps">6.4. Jumps</h3>
+<div class="paragraph">
+<p>These are the jumps:</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>jump_statement</em> : </dt>
+<dd>
+<p><strong>continue</strong> <strong>;</strong><br>
+<strong>break</strong> <strong>;</strong><br>
+<strong>return</strong> <strong>;</strong><br>
+<strong>return</strong> <em>expression</em> <strong>;</strong><br>
+<strong>discard</strong> <strong>;</strong> // in the fragment shader language only</p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>There is no &#8220;goto&#8221; or other non-structured flow of control.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>continue</strong> jump is used only in loops.
+It skips the remainder of the body of the inner-most loop of which it is
+inside.
+For <strong>while</strong> and <strong>do</strong>-<strong>while</strong> loops, this jump is to the next evaluation of
+the loop <em>condition-expression</em> from which the loop continues as previously
+defined.
+For <strong>for</strong> loops, the jump is to the <em>loop-expression</em>, followed by the
+<em>condition-expression</em>.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>break</strong> jump can also be used only in loops and <strong>switch</strong> statements.
+It is simply an immediate exit of the inner-most loop or <strong>switch</strong> statements
+containing the <strong>break</strong>.
+No further execution of <em>condition-expression</em>, <em>loop-expression</em>, or
+<em>switch-statement</em> is done.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>discard</strong> keyword is only allowed within fragment shaders.
+It can be used within a fragment shader to abandon the operation on the
+current fragment.
+This keyword causes the fragment to be discarded and no updates to any
+buffers will occur.
+Any prior writes to other buffers such as shader storage buffers are
+unaffected.
+Control flow exits the shader, and subsequent implicit or explicit
+derivatives are undefined when this control flow is non-uniform (meaning
+different fragments within the primitive take different control paths).
+It would typically be used within a conditional statement, for example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="keyword">if</span> (intensity &lt; <span class="float">0</span><span class="float">.0</span>)
+    discard;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>A fragment shader may test a fragment&#8217;s alpha value and discard the fragment
+based on that test.
+However, it should be noted that coverage testing occurs after the fragment
+shader runs, and the coverage test can change the alpha value.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>return</strong> jump causes immediate exit of the current function.
+If it has <em>expression</em> then that is the return value for the function.</p>
+</div>
+<div class="paragraph">
+<p>The function <em>main</em> can use <strong>return</strong>.
+This simply causes <em>main</em> to exit in the same way as when the end of the
+function had been reached.
+It does not imply a use of <strong>discard</strong> in a fragment shader.
+Using <strong>return</strong> in <em>main</em> before defining outputs will have the same behavior
+as reaching the end of <em>main</em> before defining outputs.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="built-in-variables">7. Built-In Variables</h2>
+<div class="sectionbody">
+<div class="sect2">
+<h3 id="built-in-language-variables">7.1. Built-In Language Variables</h3>
+<div class="paragraph">
+<p>Some OpenGL operations occur in fixed functionality and need to provide
+values to or receive values from shader executables.
+Shaders communicate with fixed-function OpenGL pipeline stages, and
+optionally with other shader executables, through the use of built-in input
+and output variables.</p>
+</div>
+<div class="sect3">
+<h4 id="vertex-shader-special-variables">7.1.1. Vertex Shader Special Variables</h4>
+<div class="paragraph">
+<p>The built-in vertex shader variables are intrinsically declared as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in <span class="predefined-type">int</span> gl_VertexID;
+in <span class="predefined-type">int</span> gl_InstanceID;
+in <span class="predefined-type">int</span> gl_DrawID;
+in <span class="predefined-type">int</span> gl_BaseVertex;
+in <span class="predefined-type">int</span> gl_BaseInstance;
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_Position</em> is intended for writing the homogeneous vertex
+position.
+It can be written at any time during shader execution.
+This value will be used by primitive assembly, clipping, culling, and other
+fixed functionality operations, if present, that operate on primitives after
+vertex processing has occurred.
+Its value is undefined after the vertex processing stage if the vertex
+shader executable does not write <em>gl_Position</em>.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_PointSize</em> is intended for a shader to write the size of
+the point to be rasterized.
+It is measured in pixels.
+If <em>gl_PointSize</em> is not written to, its value is undefined in subsequent
+pipe stages.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_ClipDistance</em> is intended for writing clip distances, and
+provides the forward compatible mechanism for controlling user clipping.
+The element <em>gl_ClipDistance[i]</em> specifies a clip distance for each plane
+<em>i</em>.
+A distance of 0 means the vertex is on the plane, a positive distance means
+the vertex is inside the clip plane, and a negative distance means the point
+is outside the clip plane.
+The clip distances will be linearly interpolated across the primitive and
+the portion of the primitive with interpolated distances less than 0 will be
+clipped.</p>
+</div>
+<div class="paragraph">
+<p>The <em>gl_ClipDistance</em> array is predeclared as unsized and must be explicitly
+sized by the shader either redeclaring it with a size or implicitly sized by
+indexing it only with constant integral expressions.
+This needs to size the array to include all the clip planes that are enabled
+via the OpenGL API; if the size does not include all enabled planes,
+results are undefined.
+The size can be at most <em>gl_MaxClipDistances</em>.
+The number of varying components (see <em>gl_MaxVaryingComponents)</em> consumed by
+<em>gl_ClipDistance</em> will match the size of the array, no matter how many
+planes are enabled.
+The shader must also set all values in <em>gl_ClipDistance</em> that have been
+enabled via the OpenGL API, or results are undefined.
+Values written into <em>gl_ClipDistance</em> for planes that are not enabled have
+no effect.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_CullDistance</em> provides a mechanism for controlling user
+culling.
+The element <em>gl_CullDistance[i]</em> specifies a cull distance for plane <em>i</em>.
+A distance of 0 means the vertex is on the plane, a positive distance means
+the vertex is inside the cull volume, and a negative distance means the
+point is outside the cull volume.
+Primitives whose vertices all have a negative cull distance for plane <em>i</em>
+will be discarded.</p>
+</div>
+<div class="paragraph">
+<p>The <em>gl_CullDistance</em> array is predeclared as unsized and must be sized by
+the shader either redeclaring it with a size or indexing it only with
+constant integral expressions.
+The size determines the number and set of enabled cull distances and can be
+at most <em>gl_MaxCullDistances</em>.
+The number of varying components (see <em>gl_MaxVaryingComponents</em>) consumed by
+<em>gl_CullDistance</em> will match the size of the array.
+Shaders writing <em>gl_CullDistance</em> must write all enabled distances, or
+culling results are undefined.</p>
+</div>
+<div class="paragraph">
+<p>As an output variable, <em>gl_CullDistance</em> provides the place for the shader
+to write these distances.
+As an input in all but the fragment language, it reads the values written in
+the previous shader stage.
+In the fragment language, <em>gl_CullDistance</em> array contains linearly
+interpolated values for the vertex values written by a shader to the
+<em>gl_CullDistance</em> vertex output variable.</p>
+</div>
+<div class="paragraph">
+<p>It is a compile-time or link-time error for the set of shaders forming a
+program to have the sum of the sizes of the <em>gl_ClipDistance</em> and
+<em>gl_CullDistance</em> arrays to be larger than
+<em>gl_MaxCombinedClipAndCullDistances</em>.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_VertexID</em> is a vertex shader input variable that holds an
+integer index for the vertex, as defined under &#8220;Shader Inputs&#8221; in section
+11.1.3.9 &#8220;Shader Inputs&#8221; of the <a href="#references">OpenGL Specification</a>.
+While the variable <em>gl_VertexID</em> is always present, its value is not always
+defined.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_InstanceID</em> is a vertex shader input variable that holds
+the instance number of the current primitive in an instanced draw call (see
+&#8220;Shader Inputs&#8221; in section 11.1.3.9 &#8220;Shader Inputs&#8221; of the
+<a href="#references">OpenGL Specification</a>).
+If the current primitive does not come from an instanced draw call, the
+value of <em>gl_InstanceID</em> is zero.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_DrawID</em> is a vertex shader input variable that holds the
+integer index of the drawing command to which the current vertex belongs
+(see &#8220;Shader Inputs&#8221; in section 11.1.3.9 of the <a href="#references">OpenGL Specification</a>).
+If the vertex is not invoked by a <strong>Multi</strong>* form of a draw command, then the
+value of <em>gl_DrawID</em> is zero.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_BaseVertex</em> is a vertex shader input variable that holds
+the integer value passed to the baseVertex parameter of the command that
+resulted in the current shader invocation (see &#8220;Shader Inputs&#8221; in section
+11.1.3.9 of the <a href="#references">OpenGL Specification</a>).</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_BaseInstance</em> is a vertex shader input variable that holds
+the integer value passed to the baseInstance parameter of the command that
+resulted in the current shader invocation (see &#8220;Shader Inputs&#8221; in section
+11.1.3.9 of the <a href="#references">OpenGL Specification</a>).</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="tessellation-control-shader-special-variables">7.1.2. Tessellation Control Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the tessellation control shader, built-in variables are intrinsically
+declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+} gl_in[gl_MaxPatchVertices];
+
+in <span class="predefined-type">int</span> gl_PatchVerticesIn;
+in <span class="predefined-type">int</span> gl_PrimitiveID;
+in <span class="predefined-type">int</span> gl_InvocationID;
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+} gl_out[];
+
+patch out <span class="predefined-type">float</span> gl_TessLevelOuter[<span class="integer">4</span>];
+patch out <span class="predefined-type">float</span> gl_TessLevelInner[<span class="integer">2</span>];</code></pre>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-control-input-variables">Tessellation Control Input Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em>, <em>gl_PointSize</em>, <em>gl_ClipDistance</em>, and <em>gl_CullDistance</em>
+contain the values written in the previous shader stage to the corresponding
+outputs.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PatchVerticesIn</em> contains the number of vertices in the input patch
+being processed by the shader.
+A single shader can read patches of differing sizes, so the value of
+<em>gl_PatchVerticesIn</em> may differ between patches.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PrimitiveID</em> contains the number of primitives processed by the shader
+since the current set of rendering primitives was started.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_InvocationID</em> contains the number of the output patch vertex assigned to
+the tessellation control shader invocation.
+It is assigned integer values in the range [0, N-1], where N is the number
+of output patch vertices per primitive.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-control-output-variables">Tessellation Control Output Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em>, <em>gl_PointSize</em>, <em>gl_ClipDistance</em>, and <em>gl_CullDistance</em> are
+used in the same fashion as the corresponding output variables in the vertex
+shader.</p>
+</div>
+<div class="paragraph">
+<p>The values written to <em>gl_TessLevelOuter</em> and <em>gl_TessLevelInner</em> are
+assigned to the corresponding outer and inner tessellation levels of the
+output patch.
+They are used by the tessellation primitive generator to control primitive
+tessellation and may be read by tessellation evaluation shaders.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="tessellation-evaluation-shader-special-variables">7.1.3. Tessellation Evaluation Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the tessellation evaluation shader, built-in variables are intrinsically
+declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+} gl_in[gl_MaxPatchVertices];
+
+in <span class="predefined-type">int</span> gl_PatchVerticesIn;
+in <span class="predefined-type">int</span> gl_PrimitiveID;
+in vec3 gl_TessCoord;
+patch in <span class="predefined-type">float</span> gl_TessLevelOuter[<span class="integer">4</span>];
+patch in <span class="predefined-type">float</span> gl_TessLevelInner[<span class="integer">2</span>];
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+};</code></pre>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-evaluation-input-variables">Tessellation Evaluation Input Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em>, <em>gl_PointSize</em>, <em>gl_ClipDistance</em>, and <em>gl_CullDistance</em>
+contain the values written in the previous shader stage to the corresponding
+outputs.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PatchVerticesIn</em> and <em>gl_PrimitiveID</em> are defined in the same fashion as
+the corresponding input variables in the tessellation control shader.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_TessCoord</em> specifies a three-component <em>(u,v,w)</em> vector identifying the
+position of the vertex being processed by the shader relative to the
+primitive being tessellated.
+Its values will obey the properties</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_TessCoord.x == <span class="float">1</span><span class="float">.0</span> - (<span class="float">1</span><span class="float">.0</span> - gl_TessCoord.x) <span class="comment">// two operations performed</span>
+gl_TessCoord.y == <span class="float">1</span><span class="float">.0</span> - (<span class="float">1</span><span class="float">.0</span> - gl_TessCoord.y) <span class="comment">// two operations performed</span>
+gl_TessCoord.z == <span class="float">1</span><span class="float">.0</span> - (<span class="float">1</span><span class="float">.0</span> - gl_TessCoord.z) <span class="comment">// two operations performed</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>to aid in replicating subdivision computations.</p>
+</div>
+<div class="paragraph">
+<p>If a tessellation control shader is active, the input variables
+<em>gl_TessLevelOuter</em> and <em>gl_TessLevelInner</em> are filled with the
+corresponding outputs written by the tessellation control shader.
+Otherwise, they are assigned with default tessellation levels specified in
+section 11.2.3.3 &#8220;Tessellation Evaluation Shader Inputs&#8221; of the
+<a href="#references">OpenGL Specification</a>.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="tessellation-evaluation-output-variables">Tessellation Evaluation Output Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em>, <em>gl_PointSize</em>, <em>gl_ClipDistance</em>, and <em>gl_CullDistance</em> are
+used in the same fashion as the corresponding output variables in the vertex
+shader.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="geometry-shader-special-variables">7.1.4. Geometry Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the geometry shader, built-in variables are intrinsically declared as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+} gl_in[];
+
+in <span class="predefined-type">int</span> gl_PrimitiveIDIn;
+in <span class="predefined-type">int</span> gl_InvocationID;
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    <span class="predefined-type">float</span> gl_PointSize;
+    <span class="predefined-type">float</span> gl_ClipDistance[];
+    <span class="predefined-type">float</span> gl_CullDistance[];
+};
+
+out <span class="predefined-type">int</span> gl_PrimitiveID;
+out <span class="predefined-type">int</span> gl_Layer;
+out <span class="predefined-type">int</span> gl_ViewportIndex;</code></pre>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-shader-input-variables">Geometry Shader Input Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em>, <em>gl_PointSize</em>, <em>gl_ClipDistance</em>, and <em>gl_CullDistance</em>
+contain the values written in the previous shader stage to the corresponding
+outputs.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PrimitiveIDIn</em> contains the number of primitives processed by the shader
+since the current set of rendering primitives was started.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_InvocationID</em> contains the invocation number assigned to the geometry
+shader invocation.
+It is assigned integer values in the range [0, N-1], where N is the number
+of geometry shader invocations per primitive.</p>
+</div>
+</div>
+<div class="sect4">
+<h5 id="geometry-shader-output-variables">Geometry Shader Output Variables</h5>
+<div class="paragraph">
+<p><em>gl_Position</em>, <em>gl_PointSize</em>, <em>gl_ClipDistance</em>, and <em>gl_CullDistance</em> are
+used in the same fashion as the corresponding output variables in the vertex
+shader.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_PrimitiveID</em> is filled with a single integer that serves as a primitive
+identifier to the fragment shader.
+This is then available to fragment shaders, which will select the written
+primitive ID from the provoking vertex of the primitive being shaded.
+If a fragment shader using <em>gl_PrimitiveID</em> is active and a geometry shader
+is also active, the geometry shader must write to <em>gl_PrimitiveID</em> or the
+fragment shader input <em>gl_PrimitiveID</em> is undefined.
+See section 11.3.4.5 &#8220;Geometry Shader Outputs&#8221; of the
+<a href="#references">OpenGL Specification</a> for more information.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_Layer</em> is used to select a specific layer (or face and layer of a cube
+map) of a multi-layer framebuffer attachment.
+The actual layer used will come from one of the vertices in the primitive
+being shaded.
+Which vertex the layer comes from is determined as discussed in section
+11.3.4.6 &#8220;Layer and Viewport Selection&#8221; of the <a href="#references">OpenGL Specification</a>
+but may be undefined, so it is best to write the same layer value for all
+vertices of a primitive.
+If a shader statically assigns a value to <em>gl_Layer</em>, layered rendering mode
+is enabled.
+See section 11.3.4.5 &#8220;Geometry Shader Outputs&#8221; and section 9.4.9 &#8220;Layered
+Framebuffers&#8221; of the <a href="#references">OpenGL Specification</a> for more information.
+If a shader statically assigns a value to <em>gl_Layer</em>, and there is an
+execution path through the shader that does not set <em>gl_Layer</em>, then the
+value of <em>gl_Layer</em> is undefined for executions of the shader that take that
+path.</p>
+</div>
+<div class="paragraph">
+<p>The output variable <em>gl_Layer</em> takes on a special value when used with an
+array of cube map textures.
+Instead of only referring to the layer, it is used to select a cube map face
+and a layer.
+Setting <em>gl_Layer</em> to the value <em>layer*6+face</em> will render to face <em>face</em> of
+the cube defined in layer <em>layer</em>.
+The face values are defined in table 9.3 of section 9.4.9 &#8220;Layered
+Framebuffers&#8221; of the <a href="#references">OpenGL Specification</a>,
+but repeated below for clarity.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Face Value</th>
+<th class="tableblock halign-left valign-top">Resulting Target</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">0</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_POSITIVE_X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">1</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_NEGATIVE_X</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">2</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_POSITIVE_Y</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">3</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_NEGATIVE_Y</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">4</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_POSITIVE_Z</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">5</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">TEXTURE_CUBE_MAP_NEGATIVE_Z</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>For example, to render to the positive <em>y</em> cube map face located in the 5th
+layer of the cube map array, <em>gl_Layer</em> should be set to <em>5 * 6 + 2</em>.</p>
+</div>
+<div class="paragraph">
+<p>The output variable <em>gl_ViewportIndex</em> provides the index of the viewport to
+which the next primitive emitted from the geometry shader should be drawn.
+Primitives generated by the geometry shader will undergo viewport
+transformation and scissor testing using the viewport transformation and
+scissor rectangle selected by the value of <em>gl_ViewportIndex</em>.
+The viewport index used will come from one of the vertices in the primitive
+being shaded.
+However, which vertex the viewport index comes from is
+implementation-dependent, so it is best to use the same viewport index for
+all vertices of the primitive.
+If a geometry shader does not assign a value to <em>gl_ViewportIndex</em>, viewport
+transform and scissor rectangle zero will be used.
+If a geometry shader statically assigns a value to <em>gl_ViewportIndex</em> and
+there is a path through the shader that does not assign a value to
+<em>gl_ViewportIndex</em>, the value of <em>gl_ViewportIndex</em> is undefined for
+executions of the shader that take that path.
+See section 11.3.4.6 &#8220;Layer and Viewport Selection&#8221; of the
+<a href="#references">OpenGL Specification</a> for more information.</p>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="fragment-shader-special-variables">7.1.5. Fragment Shader Special Variables</h4>
+<div class="paragraph">
+<p>The built-in special variables that are accessible from a fragment shader
+are intrinsically declared as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 gl_FragCoord;
+in <span class="predefined-type">bool</span> gl_FrontFacing;
+in <span class="predefined-type">float</span> gl_ClipDistance[];
+in <span class="predefined-type">float</span> gl_CullDistance[];
+in vec2 gl_PointCoord;
+in <span class="predefined-type">int</span> gl_PrimitiveID;
+in <span class="predefined-type">int</span> gl_SampleID;
+in vec2 gl_SamplePosition;
+in <span class="predefined-type">int</span> gl_SampleMaskIn[];
+in <span class="predefined-type">int</span> gl_Layer;
+in <span class="predefined-type">int</span> gl_ViewportIndex;
+in <span class="predefined-type">bool</span> gl_HelperInvocation;
+
+out <span class="predefined-type">float</span> gl_FragDepth;
+out <span class="predefined-type">int</span> gl_SampleMask[];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The output of the fragment shader executable is processed by the fixed
+function operations at the back end of the OpenGL pipeline.</p>
+</div>
+<div class="paragraph">
+<p>The fixed functionality computed depth for a fragment may be obtained by
+reading <em>gl_FragCoord.z</em>, described below.</p>
+</div>
+<div class="paragraph">
+<p>Writing to <em>gl_FragDepth</em> will establish the depth value for the fragment
+being processed.
+If depth buffering is enabled, and no shader writes <em>gl_FragDepth</em>, then the
+fixed function value for depth will be used as the fragment&#8217;s depth value.
+If a shader statically assigns a value to <em>gl_FragDepth</em>, and there is an
+execution path through the shader that does not set <em>gl_FragDepth</em>, then the
+value of the fragment&#8217;s depth may be undefined for executions of the shader
+that take that path.
+That is, if the set of linked fragment shaders statically contain a write to
+<em>gl_FragDepth</em>, then it is responsible for always writing it.</p>
+</div>
+<div class="paragraph">
+<p>If a shader executes the <strong>discard</strong> keyword, the fragment is discarded, and
+the values of any user-defined fragment outputs, <em>gl_FragDepth</em>, and
+<em>gl_SampleMask</em> become irrelevant.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_FragCoord</em> is available as an input variable from within
+fragment shaders and it holds the window relative coordinates (<em>x</em>, <em>y</em>,
+<em>z</em>, <em>1/w</em>) values for the fragment.
+If multi-sampling, this value can be for any location within the pixel, or
+one of the fragment samples.
+The use of <strong>centroid</strong> does not further restrict this value to be inside the
+current primitive.
+This value is the result of the fixed functionality that interpolates
+primitives after vertex processing to generate fragments.
+The <em>z</em> component is the depth value that would be used for the fragment&#8217;s
+depth if no shader contained any writes to <em>gl_FragDepth</em>.
+This is useful for invariance if a shader conditionally computes
+<em>gl_FragDepth</em> but otherwise wants the fixed functionality fragment depth.</p>
+</div>
+<div class="paragraph">
+<p>Fragment shaders have access to the input built-in variable
+<em>gl_FrontFacing</em>, whose value is <strong>true</strong> if the fragment belongs to a
+front-facing primitive.
+One use of this is to emulate two-sided lighting by selecting one of two
+colors calculated by a vertex or geometry shader.</p>
+</div>
+<div class="paragraph">
+<p>The values in <em>gl_PointCoord</em> are two-dimensional coordinates indicating
+where within a point primitive the current fragment is located, when point
+sprites are enabled.
+They range from 0.0 to 1.0 across the point.
+If the current primitive is not a point, or if point sprites are not
+enabled, then the values read from <em>gl_PointCoord</em> are undefined.</p>
+</div>
+<div class="paragraph">
+<p>For both the input array <em>gl_SampleMaskIn[]</em> and the output array
+<em>gl_SampleMask[]</em>, bit <em>B</em> of mask <em>M</em> (<em>gl_SampleMaskIn[M]</em> or
+<em>gl_SampleMask[M]</em>) corresponds to sample <em>32*M+B</em>.
+These arrays have <strong>ceil</strong>(<em>s</em>/32) elements, where <em>s</em> is the maximum number
+of color samples supported by the implementation.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_SampleMaskIn</em> indicates the set of samples covered by
+the primitive generating the fragment during multisample rasterization.
+It has a sample bit set if and only if the sample is considered covered for
+this fragment shader invocation.</p>
+</div>
+<div class="paragraph">
+<p>The output array <em>gl_SampleMask[]</em> sets the sample mask for the fragment
+being processed.
+Coverage for the current fragment will become the logical AND of the
+coverage mask and the output <em>gl_SampleMask</em>.
+This array must be sized in the fragment shader either implicitly or
+explicitly, to be no larger than the implementation-dependent maximum
+sample-mask (as an array of 32bit elements), determined by the maximum
+number of samples..
+If the fragment shader statically assigns a value to <em>gl_SampleMask</em>, the
+sample mask will be undefined for any array elements of any fragment shader
+invocations that fail to assign a value.
+If a shader does not statically assign a value to <em>gl_SampleMask</em>, the
+sample mask has no effect on the processing of a fragment.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_SampleID</em> is filled with the sample number of the
+sample currently being processed.
+This variable is in the range <em>0</em> to <em>gl_NumSamples-1</em>, where
+<em>gl_NumSamples</em> is the total number of samples in the framebuffer, or 1 if
+rendering to a non-multisample framebuffer.
+Any static use of this variable in a fragment shader causes the entire
+shader to be evaluated per-sample.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_SamplePosition</em> contains the position of the current
+sample within the multisample draw buffer.
+The <em>x</em> and <em>y</em> components of <em>gl_SamplePosition</em> contain the sub-pixel
+coordinate of the current sample and will have values in the range 0.0 to
+1.0.
+Any static use of this variable in a fragment shader causes the entire
+shader to be evaluated per sample.</p>
+</div>
+<div class="paragraph">
+<p>The value <em>gl_HelperInvocation</em> is <strong>true</strong> if the fragment shader invocation
+is considered a <em>helper invocation</em> and is <strong>false</strong> otherwise.
+A helper invocation is a fragment shader invocation that is created solely
+for the purposes of evaluating derivatives for use in non-helper fragment
+shader invocations.
+Such derivatives are computed implicitly in the built-in function
+<strong>texture</strong>() (see &#8220;<a href="#texture-functions">Texture Functions</a>&#8221;), and
+explicitly in the derivative functions in
+&#8220;<a href="#derivative-functions">Derivative Functions</a>&#8221;, for example <strong>dFdx</strong>() and
+<strong>dFdy</strong>().</p>
+</div>
+<div class="paragraph">
+<p>Fragment shader helper invocations execute the same shader code as
+non-helper invocations, but will not have side effects that modify the
+framebuffer or other shader-accessible memory.
+In particular:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Fragments corresponding to helper invocations are discarded when shader
+execution is complete, without updating the framebuffer.</p>
+</li>
+<li>
+<p>Stores to image and buffer variables performed by helper invocations
+have no effect on the underlying image or buffer memory.</p>
+</li>
+<li>
+<p>Atomic operations to image, buffer, or atomic counter variables
+performed by helper invocations have no effect on the underlying image
+or buffer memory.
+The values returned by such atomic operations are undefined.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Helper invocations may be generated for pixels not covered by a primitive
+being rendered.
+While fragment shader inputs qualified with <strong>centroid</strong> are normally required
+to be sampled in the intersection of the pixel and the primitive, the
+requirement is ignored for such pixels since there is no intersection
+between the pixel and primitive.</p>
+</div>
+<div class="paragraph">
+<p>Helper invocations may also be generated for fragments that are covered by a
+primitive being rendered when the fragment is killed by early fragment tests
+(using the <strong>early_fragment_tests</strong> qualifier) or where the implementation is
+able to determine that executing the fragment shader would have no effect
+other than assisting in computing derivatives for other fragment shader
+invocations.</p>
+</div>
+<div class="paragraph">
+<p>The set of helper invocations generated when processing any set of
+primitives is implementation-dependent.</p>
+</div>
+<div class="paragraph">
+<p><em>gl_ClipDistance</em> contains linearly interpolated values for the vertex-
+pipeline values written by a shader to the <em>gl_ClipDistance</em> output
+variable. Only elements in this array that have clipping enabled will
+have defined values.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_PrimitiveID</em> is filled with the value written to the
+<em>gl_PrimitiveID</em> geometry shader output, if a geometry shader is present.
+Otherwise, it is filled with the number of primitives processed by the
+shader since the current set of rendering primitives was started.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_Layer</em> is filled with the value written to the
+<em>gl_Layer</em> geometry shader output, if a geometry shader is present.
+If the geometry stage does not dynamically assign a value to <em>gl_Layer</em>, the
+value of <em>gl_Layer</em> in the fragment stage will be undefined.
+If the geometry stage makes no static assignment to <em>gl_Layer</em>, the input
+value in the fragment stage will be zero.
+Otherwise, the fragment stage will read the same value written by the
+geometry stage, even if that value is out of range.
+If a fragment shader contains a static access to <em>gl_Layer</em>, it will count
+against the implementation defined limit for the maximum number of inputs to
+the fragment stage.</p>
+</div>
+<div class="paragraph">
+<p>The input variable <em>gl_ViewportIndex</em> is filled with the value written to
+the output variable <em>gl_ViewportIndex</em> in the geometry stage, if a geometry
+shader is present.
+If the geometry stage does not dynamically assign a value to
+<em>gl_ViewportIndex</em>, the value of <em>gl_ViewportIndex</em> in the fragment shader
+will be undefined.
+If the geometry stage makes no static assignment to <em>gl_ViewportIndex</em>, the
+fragment stage will read zero.
+Otherwise, the fragment stage will read the same value written by the
+geometry stage, even if that value is out of range.
+If a fragment shader contains a static access to <em>gl_ViewportIndex</em>, it will
+count against the implementation defined limit for the maximum number of
+inputs to the fragment stage.</p>
+</div>
+</div>
+<div class="sect3">
+<h4 id="compute-shader-special-variables">7.1.6. Compute Shader Special Variables</h4>
+<div class="paragraph">
+<p>In the compute shader, built-in variables are declared as follows:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">// workgroup dimensions</span>
+in uvec3 gl_NumWorkGroups;
+<span class="directive">const</span> uvec3 gl_WorkGroupSize;
+
+<span class="comment">// workgroup and invocation IDs</span>
+in uvec3 gl_WorkGroupID;
+in uvec3 gl_LocalInvocationID;
+
+<span class="comment">// derived variables</span>
+in uvec3 gl_GlobalInvocationID;
+in uint gl_LocalInvocationIndex;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_NumWorkGroups</em> is a compute-shader input variable
+containing the number of workgroups in each dimension of the dispatch that
+will execute the compute shader.
+Its content is equal to the values specified in the <em>num_groups_x</em>,
+<em>num_groups_y</em>, and <em>num_groups_z</em> parameters passed to the
+<em>DispatchCompute</em> API entry point.</p>
+</div>
+<div class="paragraph">
+<p>The built-in constant <em>gl_WorkGroupSize</em> is a compute-shader constant
+containing the workgroup size of the shader.
+The size of the workgroup in the <em>X</em>, <em>Y</em>, and <em>Z</em> dimensions is stored in
+the <em>x</em>, <em>y</em>, and <em>z</em> components.
+The constants values in <em>gl_WorkGroupSize</em> will match those specified in the
+required <strong>local_size_x</strong>, <strong>local_size_y</strong>, and <strong>local_size_z</strong> layout
+qualifiers for the current shader.
+This is a constant so that it can be used to size arrays of memory that can
+be shared within the workgroup.
+It is a compile-time error to use <em>gl_WorkGroupSize</em> in a shader that does
+not declare a fixed workgroup size, or before that shader has declared a
+fixed workgroup size, using <strong>local_size_x</strong>, <strong>local_size_y</strong>, and
+<strong>local_size_z</strong>.</p>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_WorkGroupID</em> is a compute-shader input variable
+containing the three-dimensional index of the workgroup that the
+current invocation is executing in.
+The possible values range across the parameters passed into
+<em>DispatchCompute</em>, i.e., from (0, 0, 0) to (<em>gl_NumWorkGroups.x</em> - 1,
+<em>gl_NumWorkGroups.y</em> - 1, <em>gl_NumWorkGroups.z</em> -1).</p>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_LocalInvocationID</em> is a compute-shader input
+variable containing the three-dimensional index of the current work item
+within the workgroup.
+The possible values for this variable range across the workgroup
+size, i.e., (0,0,0) to (<em>gl_WorkGroupSize.x</em> - 1, <em>gl_WorkGroupSize.y</em> - 1,
+<em>gl_WorkGroupSize.z</em> - 1).</p>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_GlobalInvocationID</em> is a compute shader input
+variable containing the global index of the current work item.
+This value uniquely identifies this invocation from all other invocations
+across all workgroups initiated by the current <em>DispatchCompute</em> call.
+This is computed as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_GlobalInvocationID =
+    gl_WorkGroupID * gl_WorkGroupSize + gl_LocalInvocationID;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The built-in variable <em>gl_LocalInvocationIndex</em> is a compute shader input
+variable that contains the one-dimensional representation of the
+<em>gl_LocalInvocationID</em>.
+This is computed as:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">gl_LocalInvocationIndex =
+    gl_LocalInvocationID.z * gl_WorkGroupSize.x * gl_WorkGroupSize.y +
+    gl_LocalInvocationID.y * gl_WorkGroupSize.x +
+    gl_LocalInvocationID.x;</code></pre>
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="compatibility-profile-built-in-language-variables">7.1.7. Compatibility Profile Built-In Language Variables</h4>
+<div class="paragraph">
+<p>When using the compatibility profile, the GL can provide fixed functionality
+behavior for the vertex and fragment programmable pipeline stages.
+For example, mixing a fixed functionality vertex stage with a programmable
+fragment stage.</p>
+</div>
+<div class="paragraph">
+<p>The following built-in vertex, tessellation control, tessellation
+evaluation, and geometry output variables are available to specify inputs
+for the subsequent programmable shader stage or the fixed functionality
+fragment stage.
+A particular one should be written to if any functionality in a
+corresponding fragment shader or fixed pipeline uses it or state derived
+from it.
+Otherwise, behavior is undefined.
+The following members are added to the output <em>gl_PerVertex</em> block in these
+languages:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out gl_PerVertex { <span class="comment">// part of the gl_PerVertex block described in 7.1</span>
+    <span class="comment">// in addition to other gl_PerVertex members...</span>
+    vec4  gl_ClipVertex;
+    vec4  gl_FrontColor;
+    vec4  gl_BackColor;
+    vec4  gl_FrontSecondaryColor;
+    vec4  gl_BackSecondaryColor;
+    vec4  gl_TexCoord[];
+    <span class="predefined-type">float</span> gl_FogFragCoord;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The output variable <em>gl_ClipVertex</em> provides a place for vertex and geometry
+shaders to write the coordinate to be used with the user clipping planes.
+Writing to <em>gl_ClipDistance</em> is the preferred method for user clipping.
+It is a compile-time or link-time error for the set of shaders forming a
+program to statically read or write both <em>gl_ClipVertex</em> and either
+<em>gl_ClipDistance</em> or <em>gl_CullDistance</em>.
+If neither <em>gl_ClipVertex</em> nor <em>gl_ClipDistance</em> is written, their values
+are undefined and any clipping against user clip planes is also undefined.</p>
+</div>
+<div class="paragraph">
+<p>Similarly to what was previously described for the core profile, the
+<em>gl_PerVertex</em> block can be redeclared in a shader to explicitly include
+these additional members.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out gl_PerVertex {
+    vec4 gl_Position;    <span class="comment">// will use gl_Position</span>
+    vec4 gl_FrontColor;  <span class="comment">// will consume gl_color in the fragment shader</span>
+    vec4 gl_BackColor;
+    vec4 gl_TexCoord[<span class="integer">3</span>]; <span class="comment">// 3 elements of gl_TexCoord will be used</span>
+}; <span class="comment">// no other aspects of the fixed interface will be used</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The user must ensure the clip vertex and user clipping planes are defined in
+the same coordinate space.
+User clip planes work properly only under linear transform.
+It is undefined what happens under non-linear transform.</p>
+</div>
+<div class="paragraph">
+<p>The output variables <em>gl_FrontColor</em>, <em>glFrontSecondaryColor</em>,
+<em>gl_BackColor</em>, and <em>glBackSecondaryColor</em> assign primary and secondary
+colors for front and back faces of primitives containing the vertex being
+processed.
+The output variable <em>gl_TexCoord</em> assigns texture coordinates for the vertex
+being processed.</p>
+</div>
+<div class="paragraph">
+<p>For <em>gl_FogFragCoord</em>, the value written will be used as the &#8220;c&#8221; value in
+section 16.4 &#8220;Fog&#8221; of the Compatibility profile of the
+<a href="#references">OpenGL Specification</a>, by the fixed functionality pipeline.
+For example, if the z-coordinate of the fragment in eye space is desired as
+&#8220;c&#8221;, then that&#8217;s what the vertex shader executable should write into
+<em>gl_FogFragCoord</em>.</p>
+</div>
+<div class="paragraph">
+<p>As with all arrays, indices used to subscript <em>gl_TexCoord</em> must either be a
+constant integral expressions, or this array must be redeclared by the
+shader with a size.
+The size can be at most <em>gl_MaxTextureCoords</em>.
+Using indexes close to 0 may aid the implementation in preserving varying
+resources.
+The redeclaration of <em>gl_TexCoord</em> can also be done at global scope as, for
+example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 gl_TexCoord[<span class="integer">3</span>];
+out vec4 gl_TexCoord[<span class="integer">4</span>];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>(This treatment is a special case for <em>gl_TexCoord[]</em>, not a general method
+for redeclaring members of blocks.) It is a compile-time error to redeclare
+<em>gl_TexCoord[]</em> at global scope if there is a redeclaration of the
+corresponding built-in block; only one form of redeclaration is allowed
+within a shader (and hence within a stage, as block redeclarations must
+match across all shaders using it).</p>
+</div>
+<div class="paragraph">
+<p>In the tessellation control, evaluation, and geometry shaders, the outputs
+of the previous stage described above are also available in the input
+<em>gl_PerVertex</em> block in these languages.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex { <span class="comment">// part of the gl_PerVertex block described in 7.1</span>
+    <span class="comment">// in addition to other gl_PerVertex members...</span>
+    vec4  gl_ClipVertex;
+    vec4  gl_FrontColor;
+    vec4  gl_BackColor;
+    vec4  gl_FrontSecondaryColor;
+    vec4  gl_BackSecondaryColor;
+    vec4  gl_TexCoord[];
+    <span class="predefined-type">float</span> gl_FogFragCoord;
+} gl_in[];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>These can be redeclared to establish an explicit pipeline interface, the
+same way as described above for the output block <em>gl_PerVertex</em>, and the
+input redeclaration must match the output redeclaration of the previous
+stage.
+However, when a built-in interface block with an instance name is redeclared
+(e.g. <em>gl_in</em>), the instance name must be included in the redeclaration.
+It is a compile-time error to not include the built-in instance name or to
+change its name.
+For example,</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerVertex {
+    vec4 gl_ClipVertex;
+    vec4 gl_FrontColor;
+} gl_in[]; <span class="comment">// must be present and must be &quot;gl_in[]&quot;</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Built-in block arrays predeclared with a size can be redeclared with unsized syntax.
+This keeps their size equal to the original predeclared size.</p>
+</div>
+<div class="paragraph">
+<p>Treatment of <em>gl_TexCoord[]</em> redeclaration is also identical to that
+described for the output block <em>gl_TexCoord[]</em> redeclaration.</p>
+</div>
+<div class="paragraph">
+<p>The following fragment input block is also available in a fragment shader
+when using the compatibility profile:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in gl_PerFragment {
+    in <span class="predefined-type">float</span> gl_FogFragCoord;
+    in vec4  gl_TexCoord[];
+    in vec4  gl_Color;
+    in vec4  gl_SecondaryColor;
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The values in <em>gl_Color</em> and <em>gl_SecondaryColor</em> will be derived
+automatically by the system from <em>gl_FrontColor</em>, <em>gl_BackColor</em>,
+<em>gl_FrontSecondaryColor</em>, and <em>gl_BackSecondaryColor</em> based on which face is
+visible in the primitive producing the fragment.
+If fixed functionality is used for vertex processing, then <em>gl_FogFragCoord</em>
+will either be the z-coordinate of the fragment in eye space, or the
+interpolation of the fog coordinate, as described in section 16.4 &#8220;Fog&#8221; of
+the Compatibility profile of the <a href="#references">OpenGL Specification</a>.
+The <em>gl_TexCoord[]</em> values are the interpolated <em>gl_TexCoord[]</em> values from
+a vertex shader or the texture coordinates of any fixed pipeline based
+vertex functionality.</p>
+</div>
+<div class="paragraph">
+<p>Indices to the fragment shader <em>gl_TexCoord</em> array are as described above in
+the vertex shader text.</p>
+</div>
+<div class="paragraph">
+<p>As described above for the input and output <em>gl_PerVertex</em> blocks, the
+<em>gl_PerFragment</em> block can be redeclared to create an explicit interface to
+another program.
+When matching these interfaces between separate programs, members in the
+<em>gl_PerVertex</em> output block must be declared if and only if the
+corresponding fragment shader members generated from them are present in the
+<em>gl_PerFragment</em> input block.
+These matches are described in detail in section 7.4.1 &#8220;Shader Interface
+Matching&#8221; of the <a href="#references">OpenGL Specification</a>.
+If they don&#8217;t match within a program, a link-time error will result.
+If the mismatch is between two programs, values passed between programs are
+undefined.
+Unlike with all other block matching, the order of declaration within
+<em>gl_PerFragment</em> does not have to match across shaders and does not have to
+correspond with order of declaration in a matching <em>gl_PerVertex</em>
+redeclaration.</p>
+</div>
+<div class="paragraph">
+<p>The following fragment output variables are available in a fragment shader
+when using the compatibility profile:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out vec4 gl_FragColor;
+out vec4 gl_FragData[gl_MaxDrawBuffers];</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Writing to <em>gl_FragColor</em> specifies the fragment color that will be used by
+the subsequent fixed functionality pipeline.
+If subsequent fixed functionality consumes fragment color and an execution
+of the fragment shader executable does not write a value to <em>gl_FragColor</em>
+then the fragment color consumed is undefined.</p>
+</div>
+<div class="paragraph">
+<p>The variable <em>gl_FragData</em> is an array.
+Writing to <em>gl_FragData[n]</em> specifies the fragment data that will be used by
+the subsequent fixed functionality pipeline for data <em>n</em>.
+If subsequent fixed functionality consumes fragment data and an execution of
+a fragment shader executable does not write a value to it, then the fragment
+data consumed is undefined.</p>
+</div>
+<div class="paragraph">
+<p>If a shader statically assigns a value to <em>gl_FragColor</em>, it may not assign
+a value to any element of <em>gl_FragData</em>.
+If a shader statically writes a value to any element of <em>gl_FragData</em>, it
+may not assign a value to <em>gl_FragColor</em>.
+That is, a shader may assign values to either <em>gl_FragColor</em> or
+<em>gl_FragData</em>, but not both.
+Multiple shaders linked together must also consistently write just one of
+these variables.
+Similarly, if user-declared output variables are in use (statically assigned
+to), then the built-in variables <em>gl_FragColor</em> and <em>gl_FragData</em> may not be
+assigned to.
+These incorrect usages all generate compile-time or link-time errors.</p>
+</div>
+<div class="paragraph">
+<p>If a shader executes the <strong>discard</strong> keyword, the fragment is discarded, and
+the values of <em>gl_FragDepth</em> and <em>gl_FragColor</em> become irrelevant.</p>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="compatibility-profile-vertex-shader-built-in-inputs">7.2. Compatibility Profile Vertex Shader Built-In Inputs</h3>
+<div class="paragraph">
+<p>The following predeclared input names can be used from within a vertex
+shader to access the current values of OpenGL state when using the
+compatibility profile.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">in vec4 gl_Color;
+in vec4 gl_SecondaryColor;
+in vec3 gl_Normal;
+in vec4 gl_Vertex;
+in vec4 gl_MultiTexCoord0;
+in vec4 gl_MultiTexCoord1;
+in vec4 gl_MultiTexCoord2;
+in vec4 gl_MultiTexCoord3;
+in vec4 gl_MultiTexCoord4;
+in vec4 gl_MultiTexCoord5;
+in vec4 gl_MultiTexCoord6;
+in vec4 gl_MultiTexCoord7;
+in <span class="predefined-type">float</span> gl_FogCoord;</code></pre>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="built-in-constants">7.3. Built-In Constants</h3>
+<div class="paragraph">
+<p>The following built-in constants are provided to all shaders.
+The actual values used are implementation-dependent, but must be at least
+the value shown.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">//</span>
+<span class="comment">// Implementation-dependent constants. The example values below</span>
+<span class="comment">// are the minimum values allowed for these maximums.</span>
+<span class="comment">//</span></code></pre>
+</div>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexAttribs = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexUniformVectors = <span class="integer">256</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexOutputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVaryingComponents = <span class="integer">60</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVaryingVectors = <span class="integer">15</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVertexAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessPatchComponents = <span class="integer">120</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxPatchVertices = <span class="integer">32</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessGenLevel = <span class="integer">64</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlInputComponents = <span class="integer">128</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlOutputComponents = <span class="integer">128</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlTotalOutputComponents = <span class="integer">4096</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessControlAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationInputComponents = <span class="integer">128</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationOutputComponents = <span class="integer">128</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTessEvaluationAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryInputComponents = <span class="integer">64</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryOutputComponents = <span class="integer">128</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryImageUniforms = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryOutputVertices = <span class="integer">256</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryTotalOutputComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryVaryingComponents = <span class="integer">64</span>;            <span class="comment">// deprecated</span>
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryAtomicCounters = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxGeometryAtomicCounterBuffers = <span class="integer">0</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxFragmentImageUniforms = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxFragmentInputComponents = <span class="integer">128</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxFragmentUniformVectors = <span class="integer">256</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxFragmentUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxFragmentAtomicCounters = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxFragmentAtomicCounterBuffers = <span class="integer">1</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxDrawBuffers = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MinProgramTexelOffset = -<span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxProgramTexelOffset = <span class="integer">7</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxImageUnits = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxSamples = <span class="integer">4</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxImageSamples = <span class="integer">0</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxClipDistances = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCullDistances = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxViewports = <span class="integer">16</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxComputeImageUniforms = <span class="integer">8</span>;
+<span class="directive">const</span> ivec3 gl_MaxComputeWorkGroupCount = { <span class="integer">65535</span>, <span class="integer">65535</span>, <span class="integer">65535</span> };
+<span class="directive">const</span> ivec3 gl_MaxComputeWorkGroupSize = { <span class="integer">1024</span>, <span class="integer">1024</span>, <span class="integer">64</span> };
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxComputeUniformComponents = <span class="integer">1024</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxComputeTextureImageUnits = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxComputeAtomicCounters = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxComputeAtomicCounterBuffers = <span class="integer">8</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedTextureImageUnits = <span class="integer">96</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedImageUniforms = <span class="integer">48</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedImageUnitsAndFragmentOutputs = <span class="integer">8</span>;  <span class="comment">// deprecated</span>
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedShaderOutputResources = <span class="integer">16</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedAtomicCounters = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedAtomicCounterBuffers = <span class="integer">1</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxCombinedClipAndCullDistances = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxAtomicCounterBindings = <span class="integer">1</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxAtomicCounterBufferSize = <span class="integer">32</span>;
+
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTransformFeedbackBuffers = <span class="integer">4</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTransformFeedbackInterleavedComponents = <span class="integer">64</span>;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The constant <em>gl_MaxVaryingFloats</em> is removed in the core profile, use
+<em>gl_MaxVaryingComponents</em> instead.</p>
+</div>
+<div class="sect3">
+<h4 id="compatibility-profile-built-in-constants">7.3.1. Compatibility Profile Built-In Constants</h4>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTextureUnits = <span class="integer">2</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxTextureCoords = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxClipPlanes = <span class="integer">8</span>;
+<span class="directive">const</span> <span class="predefined-type">int</span> gl_MaxVaryingFloats = <span class="integer">60</span>;</code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="built-in-uniform-state">7.4. Built-In Uniform State</h3>
+<div class="paragraph">
+<p>Built-in uniform state is not available when generating SPIR-V.</p>
+</div>
+<div class="paragraph">
+<p>Otherwise, as an aid to accessing OpenGL processing state, the following
+uniform variables are built into the OpenGL Shading Language.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">//</span>
+<span class="comment">// Depth range in window coordinates,</span>
+<span class="comment">// section 13.6.1 &quot;Controlling the Viewport&quot; in the</span>
+<span class="comment">// OpenGL Specification.</span>
+<span class="comment">//</span>
+<span class="comment">// Note: Depth-range state is only for viewport 0.</span>
+<span class="comment">//</span>
+<span class="keyword">struct</span> gl_DepthRangeParameters {
+    <span class="predefined-type">float</span> near; <span class="comment">// n</span>
+    <span class="predefined-type">float</span> far;  <span class="comment">// f</span>
+    <span class="predefined-type">float</span> diff; <span class="comment">// f - n</span>
+};
+uniform gl_DepthRangeParameters gl_DepthRange;
+uniform <span class="predefined-type">int</span> gl_NumSamples;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>These variables are only guaranteed to be available in the fragment stage.
+In other stages, their presence and function is implementation-defined.</p>
+</div>
+<div class="sect3">
+<h4 id="compatibility-profile-state">7.4.1. Compatibility Profile State</h4>
+<div class="paragraph">
+<p>These variables are present only in the compatibility profile.
+They are not available to compute shaders, but are available to all other
+shaders.</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+uniform mat4 gl_ModelViewMatrix;
+uniform mat4 gl_ProjectionMatrix;
+uniform mat4 gl_ModelViewProjectionMatrix;
+uniform mat4 gl_TextureMatrix[gl_MaxTextureCoords];
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+uniform mat3 gl_NormalMatrix; <span class="comment">// transpose of the inverse of the</span>
+                              <span class="comment">// upper leftmost 3x3 of gl_ModelViewMatrix</span>
+
+uniform mat4 gl_ModelViewMatrixInverse;
+uniform mat4 gl_ProjectionMatrixInverse;
+uniform mat4 gl_ModelViewProjectionMatrixInverse;
+uniform mat4 gl_TextureMatrixInverse[gl_MaxTextureCoords];
+
+uniform mat4 gl_ModelViewMatrixTranspose;
+uniform mat4 gl_ProjectionMatrixTranspose;
+uniform mat4 gl_ModelViewProjectionMatrixTranspose;
+uniform mat4 gl_TextureMatrixTranspose[gl_MaxTextureCoords];
+
+uniform mat4 gl_ModelViewMatrixInverseTranspose;
+uniform mat4 gl_ProjectionMatrixInverseTranspose;
+uniform mat4 gl_ModelViewProjectionMatrixInverseTranspose;
+uniform mat4 gl_TextureMatrixInverseTranspose[gl_MaxTextureCoords];
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+uniform <span class="predefined-type">float</span> gl_NormalScale;
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+uniform vec4 gl_ClipPlane[gl_MaxClipPlanes];
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+<span class="keyword">struct</span> gl_PointParameters {
+    <span class="predefined-type">float</span> size;
+    <span class="predefined-type">float</span> sizeMin;
+    <span class="predefined-type">float</span> sizeMax;
+    <span class="predefined-type">float</span> fadeThresholdSize;
+    <span class="predefined-type">float</span> distanceConstantAttenuation;
+    <span class="predefined-type">float</span> distanceLinearAttenuation;
+    <span class="predefined-type">float</span> distanceQuadraticAttenuation;
+};
+
+uniform gl_PointParameters gl_Point;
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+<span class="keyword">struct</span> gl_MaterialParameters {
+ vec4 emission;   <span class="comment">// Ecm</span>
+ vec4 ambient;    <span class="comment">// Acm</span>
+ vec4 diffuse;    <span class="comment">// Dcm</span>
+ vec4 specular;   <span class="comment">// Scm</span>
+ <span class="predefined-type">float</span> shininess; <span class="comment">// Srm</span>
+};
+uniform gl_MaterialParameters gl_FrontMaterial;
+uniform gl_MaterialParameters gl_BackMaterial;
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+<span class="keyword">struct</span> gl_LightSourceParameters {
+    vec4 ambient;               <span class="comment">// Acli</span>
+    vec4 diffuse;               <span class="comment">// Dcli</span>
+    vec4 specular;              <span class="comment">// Scli</span>
+    vec4 position;              <span class="comment">// Ppli</span>
+    vec4 halfVector;            <span class="comment">// Derived: Hi</span>
+    vec3 spotDirection;         <span class="comment">// Sdli</span>
+    <span class="predefined-type">float</span> spotExponent;         <span class="comment">// Srli</span>
+    <span class="predefined-type">float</span> spotCutoff;           <span class="comment">// Crli</span>
+                                <span class="comment">// (range: [0.0,90.0], 180.0)</span>
+    <span class="predefined-type">float</span> spotCosCutoff;        <span class="comment">// Derived: cos(Crli)</span>
+                                <span class="comment">// (range: [1.0,0.0],-1.0)</span>
+    <span class="predefined-type">float</span> constantAttenuation;  <span class="comment">// K0</span>
+    <span class="predefined-type">float</span> linearAttenuation;    <span class="comment">// K1</span>
+    <span class="predefined-type">float</span> quadraticAttenuation; <span class="comment">// K2</span>
+};
+
+uniform gl_LightSourceParameters gl_LightSource[gl_MaxLights];
+
+<span class="keyword">struct</span> gl_LightModelParameters {
+    vec4 ambient;                  <span class="comment">// Acs</span>
+};
+
+uniform gl_LightModelParameters gl_LightModel;
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+<span class="comment">// Derived state from products of light and material.</span>
+<span class="comment">//</span>
+
+<span class="keyword">struct</span> gl_LightModelProducts {
+    vec4 sceneColor; <span class="comment">// Derived. Ecm + Acm * Acs</span>
+};
+
+uniform gl_LightModelProducts gl_FrontLightModelProduct;
+uniform gl_LightModelProducts gl_BackLightModelProduct;
+
+<span class="keyword">struct</span> gl_LightProducts {
+    vec4 ambient; <span class="comment">// Acm * Acli</span>
+    vec4 diffuse; <span class="comment">// Dcm * Dcli</span>
+    vec4 specular; <span class="comment">// Scm * Scli</span>
+};
+
+uniform gl_LightProducts gl_FrontLightProduct[gl_MaxLights];
+uniform gl_LightProducts gl_BackLightProduct[gl_MaxLights];
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+uniform vec4 gl_TextureEnvColor[gl_MaxTextureUnits];
+uniform vec4 gl_EyePlaneS[gl_MaxTextureCoords];
+uniform vec4 gl_EyePlaneT[gl_MaxTextureCoords];
+uniform vec4 gl_EyePlaneR[gl_MaxTextureCoords];
+uniform vec4 gl_EyePlaneQ[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneS[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneT[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneR[gl_MaxTextureCoords];
+uniform vec4 gl_ObjectPlaneQ[gl_MaxTextureCoords];
+
+<span class="comment">//</span>
+<span class="comment">// compatibility profile only</span>
+<span class="comment">//</span>
+<span class="keyword">struct</span> gl_FogParameters {
+    vec4 color;
+    <span class="predefined-type">float</span> density;
+    <span class="predefined-type">float</span> start;
+    <span class="predefined-type">float</span> end;
+    <span class="predefined-type">float</span> scale; <span class="comment">// Derived: 1.0 / (end - start)</span>
+};
+
+uniform gl_FogParameters gl_Fog;</code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="redeclaring-built-in-blocks">7.5. Redeclaring Built-In Blocks</h3>
+<div class="paragraph">
+<p>The <em>gl_PerVertex</em> block can be redeclared in a shader to explicitly
+indicate what subset of the fixed pipeline interface will be used.
+This is necessary to establish the interface between multiple programs.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out gl_PerVertex {
+    vec4 gl_Position;   <span class="comment">// will use gl_Position</span>
+    <span class="predefined-type">float</span> gl_PointSize; <span class="comment">// will use gl_PointSize</span>
+    vec4 t;             <span class="comment">// error, only gl_PerVertex members allowed</span>
+}; <span class="comment">// no other members of gl_PerVertex will be used</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This establishes the output interface the shader will use with the
+subsequent pipeline stage.
+It must be a subset of the built-in members of <em>gl_PerVertex</em>.
+Such a redeclaration can also add the <strong>invariant</strong> qualifier, interpolation
+qualifiers, and the layout qualifiers <strong>xfb_offset</strong>, <strong>xfb_buffer</strong>, and
+<strong>xfb_stride</strong>.
+It can also add an array size for unsized arrays.
+For example:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">out layout(xfb_buffer = <span class="integer">1</span>, xfb_stride = <span class="integer">16</span>) gl_PerVertex {
+    vec4 gl_Position;
+    layout(xfb_offset = <span class="integer">0</span>) <span class="predefined-type">float</span> gl_ClipDistance[<span class="integer">4</span>];
+};</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Other layout qualifiers, like <strong>location</strong>, cannot be added to such a
+redeclaration, unless specifically stated.</p>
+</div>
+<div class="paragraph">
+<p>If a built-in interface block is redeclared, it must appear in the shader
+before any use of any member included in the built-in declaration, or a
+compile-time error will result.
+It is also a compile-time error to redeclare the block more than once or to
+redeclare a built-in block and then use a member from that built-in block
+that was not included in the redeclaration.
+Also, if a built-in interface block is redeclared, no member of the built-in
+declaration can be redeclared outside the block redeclaration.
+If multiple shaders using members of a built-in block belonging to the same
+interface are linked together in the same program, they must all redeclare
+the built-in block in the same way, as described in
+&#8220;<a href="#interface-blocks">Interface Blocks</a>&#8221; for interface block matching, or a
+link-time error will result.
+It will also be a link-time error if some shaders in a program redeclare a
+specific built-in interface block while another shader in that program does
+not redeclare that interface block yet still uses a member of that interface
+block.
+If a built-in block interface is formed across shaders in different
+programs, the shaders must all redeclare the built-in block in the same way
+(as described for a single program), or the values passed along the
+interface are undefined.</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="built-in-functions">8. Built-In Functions</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The OpenGL Shading Language defines an assortment of built-in convenience functions for
+scalar and vector operations.
+Many of these built-in functions can be used in more than one type of
+shader, but some are intended to provide a direct mapping to hardware and so
+are available only for a specific type of shader.</p>
+</div>
+<div class="paragraph">
+<p>The built-in functions basically fall into three categories:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>They expose some necessary hardware functionality in a convenient way
+such as accessing a texture map.
+There is no way in the language for these functions to be emulated by a
+shader.</p>
+</li>
+<li>
+<p>They represent a trivial operation (clamp, mix, etc.) that is very
+simple for the user to write, but they are very common and may have
+direct hardware support.
+It is a very hard problem for the compiler to map expressions to complex
+assembler instructions.</p>
+</li>
+<li>
+<p>They represent an operation graphics hardware is likely to accelerate at
+some point.
+The trigonometry functions fall into this category.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Many of the functions are similar to the same named ones in common C
+libraries, but they support vector input as well as the more traditional
+scalar input.</p>
+</div>
+<div class="paragraph">
+<p>Applications should be encouraged to use the built-in functions rather than
+do the equivalent computations in their own shader code since the built-in
+functions are assumed to be optimal (e.g. perhaps supported directly in
+hardware).</p>
+</div>
+<div class="paragraph">
+<p>User code can replace built-in functions with their own if they choose, by
+simply redeclaring and defining the same name and argument list.
+Because built-in functions are in a more outer scope than user built-in
+functions, doing this will hide all built-in functions with the same name as
+the redeclared function.</p>
+</div>
+<div class="paragraph">
+<p>When the built-in functions are specified below, where the input arguments
+(and corresponding output) can be <strong>float</strong>, <strong>vec2</strong>, <strong>vec3</strong>, or <strong>vec4</strong>,
+<em>genFType</em> is used as the argument.
+Where the input arguments (and corresponding output) can be <strong>int</strong>, <strong>ivec2</strong>,
+<strong>ivec3</strong>, or <strong>ivec4</strong>, <em>genIType</em> is used as the argument.
+Where the input arguments (and corresponding output) can be <strong>uint</strong>, <strong>uvec2</strong>,
+<strong>uvec3</strong>, or <strong>uvec4</strong>, <em>genUType</em> is used as the argument.
+Where the input arguments (or corresponding output) can be <strong>bool</strong>, <strong>bvec2</strong>,
+<strong>bvec3</strong>, or <strong>bvec4</strong>, <em>genBType</em> is used as the argument.
+Where the input arguments (and corresponding output) can be <strong>double</strong>,
+<strong>dvec2</strong>, <strong>dvec3</strong>, <strong>dvec4</strong>, <em>genDType</em> is used as the argument.
+For any specific use of a function, the actual types substituted for
+<em>genFType</em>, <em>genIType</em>, <em>genUType</em>, or <em>genBType</em> have to have the same
+number of components for all arguments and for the return type.
+Similarly, <em>mat</em> is used for any matrix basic
+type with single-precision
+components and <em>dmat</em> is used for any matrix basic type with
+double-precision components.</p>
+</div>
+<div class="sect2">
+<h3 id="angle-and-trigonometry-functions">8.1. Angle and Trigonometry Functions</h3>
+<div class="paragraph">
+<p>Function parameters specified as <em>angle</em> are assumed to be in units of
+radians.
+In no case will any of these functions result in a divide by zero error.
+If the divisor of a ratio is 0, then results will be undefined.</p>
+</div>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>radians</strong>(genFType <em>degrees</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Converts <em>degrees</em> to radians, i.e.,
+      <span class="eq">(π / 180) · degrees</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>degrees</strong>(genFType <em>radians</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Converts <em>radians</em> to degrees, i.e.,
+      <span class="eq">(180 / π) · radians</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sin</strong>(genFType <em>angle</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The standard trigonometric sine function.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>cos</strong>(genFType <em>angle</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The standard trigonometric cosine function.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>tan</strong>(genFType <em>angle</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">The standard trigonometric tangent.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>asin</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc sine.
+      Returns an angle whose sine is <em>x</em>.
+      The range of values returned by this function is
+      <span class="eq">[-π / 2, π / 2]</span>.
+      Results are undefined if <span class="eq">|x| &gt; 1</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>acos</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc cosine.
+      Returns an angle whose cosine is <em>x</em>.
+      The range of values returned by this function is <span class="eq">[0,π]</span>.
+      Results are undefined if <span class="eq">|x| &gt; 1</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>atan</strong>(genFType <em>y</em>, genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc tangent.
+      Returns an angle whose tangent is <span class="eq">y / x</span>.
+      The signs of <em>x</em> and <em>y</em> are used to determine what quadrant the angle
+      is in.
+      The range of values returned by this function is <span class="eq">[-π, π</span>.
+      Results are undefined if <em>x</em> and <em>y</em> are both 0.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>atan</strong>(genFType <em>y_over_x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc tangent.
+      Returns an angle whose tangent is <em>y_over_x</em>.
+      The range of values returned by this function is
+      <span class="eq">[-π / 2, π / 2]</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sinh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the hyperbolic sine function <span class="eq">(e<sup>x</sup> - e<sup>-x</sup>) / 2</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>cosh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the hyperbolic cosine function <span class="eq">(e<sup>x</sup> + e<sup>-x</sup>) / 2</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>tanh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the hyperbolic tangent function <span class="eq">sinh(x) / cosh(x)</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>asinh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc hyperbolic sine; returns the inverse of <strong>sinh</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>acosh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc hyperbolic cosine; returns the non-negative inverse of <strong>cosh</strong>.
+      Results are undefined if <span class="eq">x &lt; 1</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>atanh</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Arc hyperbolic tangent; returns the inverse of <strong>tanh</strong>.
+      Results are undefined if <span class="eq">x ≥ 1</span>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="exponential-functions">8.2. Exponential Functions</h3>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>pow</strong>(genFType <em>x</em>, genFType <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> raised to the <em>y</em> power, i.e., <span class="eq">x<sup>y</sup></span>.
+      Results are undefined if <span class="eq">x &lt; 0</span>.
+      Results are undefined if <span class="eq">x = 0</span> and <span class="eq">y ≤ 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>exp</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the natural exponentiation of <em>x</em>, i.e., <span class="eq">e<sup>x</sup></span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>log</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the natural logarithm of <em>x</em>, i.e., returns the value <em>y</em>
+      which satisfies the equation <span class="eq">x = e<sup>y</sup></span>.
+      Results are undefined if <span class="eq">x ≤ 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>exp2</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 2 raised to the <em>x</em> power, i.e., <span class="eq">2<sup>x</sup></span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>log2</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the base 2 logarithm of <em>x</em>, i.e., returns the value <em>y</em> which
+      satisfies the equation <span class="eq">x = 2<sup>y</sup></span>.
+      Results are undefined if <span class="eq">x ≤ 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sqrt</strong>(genFType <em>x</em>)<br>
+  genDType <strong>sqrt</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <span class="eq">sqrt(x)</span>.
+      Results are undefined if <span class="eq">x &lt; 0</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>inversesqrt</strong>(genFType <em>x</em>)<br>
+  genDType <strong>inversesqrt</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <span class="eq">1 / sqrt(x)</span>.
+      Results are undefined if <span class="eq">x ≤ 0</span>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="common-functions">8.3. Common Functions</h3>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>abs</strong>(genFType <em>x</em>)<br>
+  genIType <strong>abs</strong>(genIType <em>x</em>)<br>
+  genDType <strong>abs</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> if <span class="eq">x ≥ 0</span>; otherwise it returns -<em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>sign</strong>(genFType <em>x</em>)<br>
+  genIType <strong>sign</strong>(genIType <em>x</em>)<br>
+  genDType <strong>sign</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 1.0 if <em>x</em> &gt; 0, 0.0 if <em>x</em> = 0, or -1.0 if <em>x</em> &lt; 0.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>floor</strong>(genFType <em>x</em>)<br>
+  genDType <strong>floor</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer that is less than or
+      equal to <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>trunc</strong>(genFType <em>x</em>)<br>
+  genDType <strong>trunc</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer to <em>x</em> whose absolute
+      value is not larger than the absolute value of <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>round</strong>(genFType <em>x</em>)<br>
+  genDType <strong>round</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer to <em>x</em>.
+      The fraction 0.5 will round in a direction chosen by the
+      implementation, presumably the direction that is fastest.
+      This includes the possibility that <strong>round</strong>(<em>x</em>) returns the same value
+      as <strong>roundEven</strong>(<em>x</em>) for all values of <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>roundEven</strong>(genFType <em>x</em>)<br>
+  genDType <strong>roundEven</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer to <em>x</em>.
+      A fractional part of 0.5 will round toward the nearest even integer.
+      (Both 3.5 and 4.5 for x will return 4.0.)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>ceil</strong>(genFType <em>x</em>)<br>
+  genDType <strong>ceil</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a value equal to the nearest integer that is greater than or
+      equal to <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fract</strong>(genFType <em>x</em>)<br>
+  genDType <strong>fract</strong>(genDType <em>x</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> - <strong>floor</strong>(<em>x</em>).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>mod</strong>(genFType <em>x</em>, float <em>y</em>)<br>
+  genFType <strong>mod</strong>(genFType <em>x</em>, genFType <em>y</em>)<br>
+  genDType <strong>mod</strong>(genDType <em>x</em>, double <em>y</em>)<br>
+  genDType <strong>mod</strong>(genDType <em>x</em>, genDType <em>y</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Modulus.
+      Returns <span class="eq">x - y · <strong>floor</strong>(x / y)</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>modf</strong>(genFType <em>x</em>, out genFType <em>i</em>)<br>
+  genDType <strong>modf</strong>(genDType <em>x</em>, out genDType <em>i</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the fractional part of <em>x</em> and sets <em>i</em> to the integer part (as
+      a whole number floating-point value).
+      Both the return value and the output parameter will have the same sign
+      as <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>min</strong>(genFType <em>x</em>, genFType <em>y</em>)<br>
+  genFType <strong>min</strong>(genFType <em>x</em>, float <em>y</em>)<br>
+  genDType <strong>min</strong>(genDType <em>x</em>, genDType <em>y</em>)<br>
+  genDType <strong>min</strong>(genDType <em>x</em>, double <em>y</em>)<br>
+  genIType <strong>min</strong>(genIType <em>x</em>, genIType <em>y</em>)<br>
+  genIType <strong>min</strong>(genIType <em>x</em>, int <em>y</em>)<br>
+  genUType <strong>min</strong>(genUType <em>x</em>, genUType <em>y</em>)<br>
+  genUType <strong>min</strong>(genUType <em>x</em>, uint <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>y</em> if <em>y</em> &lt; <em>x;</em> otherwise it returns <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>max</strong>(genFType <em>x</em>, genFType <em>y</em>)<br>
+  genFType <strong>max</strong>(genFType <em>x</em>, float <em>y</em>)<br>
+  genDType <strong>max</strong>(genDType <em>x</em>, genDType <em>y</em>)<br>
+  genDType <strong>max</strong>(genDType <em>x</em>, double <em>y</em>)<br>
+  genIType <strong>max</strong>(genIType <em>x</em>, genIType <em>y</em>)<br>
+  genIType <strong>max</strong>(genIType <em>x</em>, int <em>y</em>)<br>
+  genUType <strong>max</strong>(genUType <em>x</em>, genUType <em>y</em>)<br>
+  genUType <strong>max</strong>(genUType <em>x</em>, uint <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>y</em> if <em>x</em> &lt; <em>y;</em> otherwise it returns <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>clamp</strong>(genFType <em>x</em>, genFType <em>minVal</em>, genFType <em>maxVal</em>)<br>
+  genFType <strong>clamp</strong>(genFType <em>x</em>, float <em>minVal</em>, float <em>maxVal</em>)<br>
+  genDType <strong>clamp</strong>(genDType <em>x</em>, genDType <em>minVal</em>, genDType <em>maxVal</em>)<br>
+  genDType <strong>clamp</strong>(genDType <em>x</em>, double <em>minVal</em>, double <em>maxVal</em>)<br>
+  genIType <strong>clamp</strong>(genIType <em>x</em>, genIType <em>minVal</em>, genIType <em>maxVal</em>)<br>
+  genIType <strong>clamp</strong>(genIType <em>x</em>, int <em>minVal</em>, int <em>maxVal</em>)<br>
+  genUType <strong>clamp</strong>(genUType <em>x</em>, genUType <em>minVal</em>, genUType <em>maxVal</em>)<br>
+  genUType <strong>clamp</strong>(genUType <em>x</em>, uint <em>minVal</em>, uint <em>maxVal</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>min</strong>(<strong>max</strong>(<em>x</em>, <em>minVal</em>), <em>maxVal</em>).
+      Results are undefined if <em>minVal</em> &gt; <em>maxVal</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>, genFType <em>a</em>)<br>
+  genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>, float <em>a</em>)<br>
+  genDType <strong>mix</strong>(genDType <em>x</em>, genDType <em>y</em>, genDType <em>a</em>)<br>
+  genDType <strong>mix</strong>(genDType <em>x</em>, genDType <em>y</em>, double <em>a</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the linear blend of <em>x</em> and <em>y</em>, i.e.,
+      <span class="eq">x · (1 - a) + y · a</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>,  genBType <em>a</em>)<br>
+  genDType <strong>mix</strong>(genDType <em>x</em>, genDType <em>y</em>, genBType <em>a</em>)<br>
+  genIType <strong>mix</strong>(genIType <em>x</em>, genIType <em>y</em>, genBType <em>a</em>)<br>
+  genUType <strong>mix</strong>(genUType <em>x</em>, genUType <em>y</em>, genBType <em>a</em>)<br>
+  genBType <strong>mix</strong>(genBType <em>x</em>, genBType <em>y</em>, genBType <em>a</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Selects which vector each returned component comes from.
+      For a component of <em>a</em> that is <strong>false</strong>, the corresponding component of
+      <em>x</em> is returned.
+      For a component of <em>a</em> that is <strong>true</strong>, the corresponding component of
+      <em>y</em> is returned.
+      Components of <em>x</em> and <em>y</em> that are not selected are allowed to be
+      invalid floating-point values and will have no effect on the results.
+      Thus, this provides different functionality than, for example,<br>
+      genFType <strong>mix</strong>(genFType <em>x</em>, genFType <em>y</em>, genFType(<em>a</em>))<br>
+      where <em>a</em> is a Boolean vector.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>step</strong>(genFType <em>edge</em>, genFType <em>x</em>)<br>
+  genFType <strong>step</strong>(float <em>edge</em>, genFType <em>x</em>)<br>
+  genDType <strong>step</strong>(genDType <em>edge</em>, genDType <em>x</em>)<br>
+  genDType <strong>step</strong>(double <em>edge</em>, genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 0.0 if <em>x</em> &lt; <em>edge;</em> otherwise it returns 1.0.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>smoothstep</strong>(genFType <em>edge0</em>, genFType <em>edge1</em>, genFType <em>x</em>)<br>
+  genFType <strong>smoothstep</strong>(float <em>edge0</em>, float <em>edge1</em>, genFType <em>x</em>)<br>
+  genDType <strong>smoothstep</strong>(genDType <em>edge0</em>, genDType <em>edge1</em>, genDType <em>x</em>)<br>
+  genDType <strong>smoothstep</strong>(double <em>edge0</em>, double <em>edge1</em>, genDType <em>x</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns 0.0 if <span class="eq">x ≤ edge0</span> and 1.0 if <span class="eq">x ≥ edge1</span>, and
+      performs smooth Hermite interpolation between 0 and 1 when <span class="eq">edge0
+      &lt; x &lt; edge1</span>.
+      This is useful in cases where you would want a threshold function with
+      a smooth transition.
+      This is equivalent to:</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">genFType t;
+t = clamp ((x - edge0) / (edge1 - edge0), <span class="integer">0</span>, <span class="integer">1</span>);
+<span class="keyword">return</span> t * t * (<span class="integer">3</span> - <span class="integer">2</span> * t);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>(And similarly for doubles.) Results are undefined if <span class="eq">edge0 ≥
+edge1</span>.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genBType <strong>isnan</strong>(genFType <em>x</em>)<br>
+  genBType <strong>isnan</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if <em>x</em> holds a NaN.
+      Returns <strong>false</strong> otherwise.
+      Always returns <strong>false</strong> if NaNs are not implemented.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genBType <strong>isinf</strong>(genFType <em>x</em>)<br>
+  genBType <strong>isinf</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if <em>x</em> holds a positive infinity or negative infinity.
+      Returns <strong>false</strong> otherwise.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>floatBitsToInt</strong>( genFType <em>value</em>)<br>
+  genUType <strong>floatBitsToUint</strong>( genFType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a signed or unsigned integer value representing the encoding
+      of a floating-point value.
+      The <strong>float</strong> value&#8217;s bit-level representation is preserved.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>intBitsToFloat</strong>( genIType <em>value</em>)<br>
+  genFType <strong>uintBitsToFloat</strong>( genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a floating-point value corresponding to a signed or unsigned
+      integer encoding of a floating-point value.
+      If a NaN is passed in, it will not signal, and the resulting value is
+      unspecified.
+      If an Inf is passed in, the resulting value is the corresponding Inf.
+      Otherwise, the bit-level representation is preserved.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fma</strong>(genFType <em>a</em>, genFType <em>b</em>, genFType <em>c</em>)<br>
+  genDType <strong>fma</strong>(genDType <em>a</em>, genDType <em>b</em>, genDType <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Computes and returns <span class="eq">a * b + c</span>.
+      In uses where the return value is eventually consumed by a variable
+      declared as <strong>precise</strong>:</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="ulist">
+<ul>
+<li>
+<p><strong>fma</strong>() is considered a single operation, whereas the expression &#8220;a * b
++ c&#8221; consumed by a variable declared <strong>precise</strong> is considered two
+operations.</p>
+</li>
+<li>
+<p>The precision of <strong>fma</strong>() can differ from the precision of the expression
+&#8220;a * b + c&#8221;.</p>
+</li>
+<li>
+<p><strong>fma</strong>() will be computed with the same precision as any other <strong>fma</strong>()
+consumed by a precise variable, giving invariant results for the same
+input values of <em>a</em>, <em>b</em>, and <em>c</em>.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Otherwise, in the absence of <strong>precise</strong> consumption, there are no special
+constraints on the number of operations or difference in precision between
+<strong>fma</strong>() and the expression &#8220;_a_ * <em>b</em> + <em>c</em>&#8221;.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>frexp</strong>( genFType <em>x</em>, out  genIType <em>exp</em>)
+  genDType <strong>frexp</strong>(genDType <em>x</em>, out genIType <em>exp</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Splits <em>x</em> into a floating-point significand in the range
+      <span class="eq">[0.5,1.0]</span>, and an integral exponent of two, such that</p>
+<p class="tableblock">      <span class="eq">x = significant · 2<sup>exponent</sup></span></p>
+<p class="tableblock">      The significand is returned by the function and the exponent is
+      returned in the parameter <em>exp</em>.
+      For a floating-point value of zero, the significand and exponent are
+      both zero.</p>
+<p class="tableblock">      If an implementation supports signed zero, an input value of minus
+      zero should return a significand of minus zero.
+      For a floating-point value that is an infinity or is not a number, the
+      results are undefined.</p>
+<p class="tableblock">      If the input <em>x</em> is a vector, this operation is performed in a
+      component-wise manner; the value returned by the function and the
+      value written to <em>exp</em> are vectors with the same number of components
+      as <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>ldexp</strong>( genFType <em>x</em>,  genIType <em>exp</em>)<br>
+  genDType <strong>ldexp</strong>(genDType <em>x</em>, genIType <em>exp</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Builds a floating-point number from <em>x</em> and the corresponding integral
+      exponent of two in <em>exp</em>, returning:</p>
+<p class="tableblock">      <span class="eq">significand · 2<sup>exponent</sup></span></p>
+<p class="tableblock">      If this product is too large to be represented in the floating-point
+      type, the result is undefined.</p>
+<p class="tableblock">      If <em>exp</em> is greater than +128 (single-precision) or +1024
+      (double-precision), the value returned is undefined.
+      If <em>exp</em> is less than -126 (single-precision) or -1022
+      (double-precision), the value returned may be flushed to zero.
+      Additionally, splitting the value into a significand and exponent
+      using <strong>frexp</strong>() and then reconstructing a floating-point value using
+      <strong>ldexp</strong>() should yield the original input for zero and all finite
+      non-denormalized values.<br>
+      If the input <em>x</em> is a vector, this operation is performed in a
+      component-wise manner; the value passed in <em>exp</em> and returned by the
+      function are vectors with the same number of components as <em>x</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="floating-point-pack-and-unpack-functions">8.4. Floating-Point Pack and Unpack Functions</h3>
+<div class="paragraph">
+<p>These functions do not operate component-wise, rather, as described in each
+case.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>packUnorm2x16</strong>(vec2 <em>v</em>)<br>
+   uint <strong>packSnorm2x16</strong>(vec2 <em>v</em>)<br>
+   uint <strong>packUnorm4x8</strong>(vec4 <em>v</em>)<br>
+   uint <strong>packSnorm4x8</strong>(vec4 <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">First, converts each component of the normalized floating-point value
+      <em>v</em> into 16-bit (<strong>2x16</strong>) or 8-bit (<strong>4x8</strong>) integer values.
+      Then, the results are packed into the returned 32-bit unsigned
+      integer.</p>
+<p class="tableblock">      The conversion for component <em>c</em> of <em>v</em> to fixed point is done as
+      follows:</p>
+<p class="tableblock">      <strong>packUnorm2x16</strong>: <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, 0, +1) * 65535.0)<br>
+      <strong>packSnorm2x16:</strong> <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, -1, +1) * 32767.0)<br>
+      <strong>packUnorm4x8</strong>: <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, 0, +1) * 255.0)<br>
+      <strong>packSnorm4x8</strong>: <strong>round</strong>(<strong>clamp</strong>(<em>c</em>, -1, +1) * 127.0)</p>
+<p class="tableblock">      The first component of the vector will be written to the least
+      significant bits of the output; the last component will be written to
+      the most significant bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> vec2 <strong>unpackUnorm2x16</strong>( uint <em>p</em>)<br>
+   vec2 <strong>unpackSnorm2x16</strong>( uint <em>p</em>)<br>
+   vec4 <strong>unpackUnorm4x8</strong>( uint <em>p</em>)<br>
+   vec4 <strong>unpackSnorm4x8</strong>( uint <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">First, unpacks a single 32-bit unsigned integer <em>p</em> into a pair of
+      16-bit unsigned integers, a pair of 16-bit signed integers, four 8-bit
+      unsigned integers, or four 8-bit signed integers, respectively.
+      Then, each component is converted to a normalized floating-point value
+      to generate the returned two- or four-component vector.</p>
+<p class="tableblock">      The conversion for unpacked fixed-point value <em>f</em> to floating-point is
+      done as follows:</p>
+<p class="tableblock">      <strong>unpackUnorm2x16</strong>: <em>f</em> / 65535.0<br>
+      <strong>unpackSnorm2x16</strong>: <strong>clamp</strong>(<em>f</em> / 32767.0, -1, +1)<br>
+      <strong>unpackUnorm4x8</strong>: <em>f</em> / 255.0<br>
+      <strong>unpackSnorm4x8</strong>: <strong>clamp</strong>(<em>f</em> / 127.0, -1, +1)</p>
+<p class="tableblock">      The first component of the returned vector will be extracted from the
+      least significant bits of the input; the last component will be
+      extracted from the most significant bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>packHalf2x16</strong>(vec2 <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns an unsigned integer obtained by converting the components of a
+      two-component floating-point vector to the 16-bit floating-point
+      representation found in the <a href="#references">OpenGL Specification</a>, and
+      then packing these two 16-bit integers into a 32-bit unsigned integer.</p>
+<p class="tableblock">      The first vector component specifies the 16 least-significant bits of
+      the result; the second component specifies the 16 most-significant
+      bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> vec2 <strong>unpackHalf2x16</strong>( uint <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a two-component floating-point vector with components obtained
+      by unpacking a 32-bit unsigned integer into a pair of 16-bit values,
+      interpreting those values as 16-bit floating-point numbers according
+      to the <a href="#references">OpenGL Specification</a>, and converting them to
+      32-bit floating-point values.</p>
+<p class="tableblock">      The first component of the vector is obtained from the 16
+      least-significant bits of <em>v</em>; the second component is obtained from
+      the 16 most-significant bits of <em>v</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">double <strong>packDouble2x32</strong>(uvec2 <em>v</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a double-precision value obtained by packing the components of
+      <em>v</em> into a 64-bit value.
+      If an IEEE 754 Inf or NaN is created, it will not signal, and the
+      resulting floating-point value is unspecified.
+      Otherwise, the bit-level representation of <em>v</em> is preserved.
+      The first vector component specifies the 32 least significant bits;
+      the second component specifies the 32 most significant bits.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uvec2 <strong>unpackDouble2x32</strong>(double <em>v</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a two-component unsigned integer vector representation of <em>v</em>.
+      The bit-level representation of <em>v</em> is preserved.
+      The first component of the vector contains the 32 least significant
+      bits of the double; the second component consists of the 32 most
+      significant bits.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="geometric-functions">8.5. Geometric Functions</h3>
+<div class="paragraph">
+<p>These operate on vectors as vectors, not component-wise.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>length</strong>(genFType <em>x</em>)<br>
+  double <strong>length</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns the length of vector <em>x</em>, i.e.,
+      <span class="eq">sqrt( x<sub>0</sub><sup>2</sup> + x<sub>1</sub><sup>2</sup> + &#8230;&#8203; )</span>.</p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>distance</strong>(genFType <em>p0</em>, genFType <em>p1</em>)<br>
+  double <strong>distance</strong>(genDType <em>p0</em>, genDType <em>p1</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the distance between <em>p0</em> and <em>p1</em>, i.e.,
+      <strong>length</strong>(<em>p0</em> - <em>p1</em>)</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>dot</strong>(genFType <em>x</em>, genFType <em>y</em>)<br>
+  double <strong>dot</strong>(genDType <em>x</em>, genDType <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the dot product of <em>x</em> and <em>y</em>, i.e.,
+      <span class="eq">x<sub>0</sub> · y<sub>0</sub> + x<sub>1</sub> · y<sub>1</sub> + &#8230;&#8203;</span></p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec3 <strong>cross</strong>(vec3 <em>x</em>, vec3 <em>y</em>)<br>
+  dvec3 <strong>cross</strong>(dvec3 <em>x</em>, dvec3 <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns the cross product of <em>x</em> and <em>y</em>, i.e.,
+      <span class="eq">(x<sub>1</sub> · y<sub>2</sub> - y<sub>1</sub> · x<sub>2</sub>,
+            x<sub>2</sub> · y<sub>0</sub> - y<sub>2</sub> · x<sub>0</sub>,
+            x<sub>0</sub> · y<sub>1</sub> - y<sub>0</sub> · x<sub>1</sub>)</span>.</p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>normalize</strong>(genFType <em>x</em>)<br>
+  genDType <strong>normalize</strong>(genDType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a vector in the same direction as <em>x</em> but with a length of 1,
+      i.e. <em>x</em> / <strong>length</strong>(x).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">compatibility profile only<br>
+  vec4 <strong>ftransform</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Available only when using the compatibility profile.
+      For core OpenGL, use <strong>invariant</strong>.<br>
+      For vertex shaders only.
+      This function will ensure that the incoming vertex value will be
+      transformed in a way that produces exactly the same result as would be
+      produced by OpenGL&#8217;s fixed functionality transform.
+      It is intended to be used to compute <em>gl_Position</em>, e.g.</p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p><em>gl_Position</em> = <strong>ftransform</strong>()</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>This function should be used, for example, when an application is rendering
+the same geometry in separate passes, and one pass uses the fixed
+functionality path to render and another pass uses programmable shaders.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>faceforward</strong>(genFType <em>N</em>, genFType <em>I</em>, genFType <em>Nref</em>)<br>
+  genDType <strong>faceforward</strong>(genDType <em>N</em>, genDType <em>I</em>, genDType <em>Nref</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">If <strong>dot</strong>(<em>Nref</em>, <em>I</em>) &lt; 0 return <em>N</em>, otherwise return -<em>N</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>reflect</strong>(genFType <em>I</em>, genFType <em>N</em>)<br>
+  genDType <strong>reflect</strong>(genDType <em>I</em>, genDType <em>N</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">For the incident vector <em>I</em> and surface orientation <em>N</em>, returns the
+      reflection direction: <span class="eq">I - 2 · <strong>dot</strong>(N, I) · N</span>.
+      <em>N</em> must already be normalized in order to achieve the desired result.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>refract</strong>(genFType <em>I</em>, genFType <em>N</em>, float <em>eta</em>)<br>
+  genDType <strong>refract</strong>(genDType <em>I</em>, genDType <em>N</em>, double <em>eta</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>For the incident vector <em>I</em> and surface normal <em>N</em>, and the ratio of
+      indices of refraction <em>eta</em>, return the refraction vector.
+      The result is computed by the <a href="#refraction-equation">refraction
+      equation</a> shown below.</p>
+</div>
+<div class="literalblock">
+<div class="content">
+<pre>The input parameters for the incident vector _I_ and the surface
+normal _N_ must already be normalized to get the desired results.</pre>
+</div>
+</div></div></td>
+</tr>
+</tbody>
+</table>
+<div class="sect3">
+<h4 id="refraction-equation">8.5.1. Refraction Equation</h4>
+<div class="stemblock">
+<div class="content">
+\[k = 1.0 - eta * eta * (1.0 - \textbf{dot}(N,I) \cdot \textbf{dot}(N,I))\]
+</div>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\begin{aligned}
+result &amp;=
+  \begin{cases}
+    genFType(0.0), &amp; k &lt; 0.0 \\
+    eta * I - (eta * \textbf{dot}(N,I) + \sqrt { k }) * N, &amp; \textbf{otherwise}
+  \end{cases}
+\end{aligned}\]
+</div>
+</div>
+</div>
+</div>
+<div class="sect2">
+<h3 id="matrix-functions">8.6. Matrix Functions</h3>
+<div class="paragraph">
+<p>For each of the following built-in matrix functions, there is both a
+single-precision floating-point version, where all arguments and return
+values are single precision, and a double-precision floating-point version,
+where all arguments and return values are double precision.
+Only the single-precision floating-point version is shown.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat <strong>matrixCompMult</strong>(mat <em>x</em>, mat <em>y</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Multiply matrix <em>x</em> by matrix <em>y</em> component-wise, i.e., result[i][j]
+      is the scalar product of <em>x</em>[i][j] and <em>y</em>[i][j].<br></p>
+<p class="tableblock">      Note: to get linear algebraic matrix multiplication, use the multiply
+      operator (<strong>*</strong>).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat2 <strong>outerProduct</strong>(vec2 <em>c</em>, vec2 <em>r</em>)<br>
+  mat3 <strong>outerProduct</strong>(vec3 <em>c</em>, vec3 <em>r</em>)<br>
+  mat4 <strong>outerProduct</strong>(vec4 <em>c</em>, vec4 <em>r</em>)<br>
+  mat2x3 <strong>outerProduct</strong>(vec3 <em>c</em>, vec2 <em>r</em>)<br>
+  mat3x2 <strong>outerProduct</strong>(vec2 <em>c</em>, vec3 <em>r</em>)<br>
+  mat2x4 <strong>outerProduct</strong>(vec4 <em>c</em>, vec2 <em>r</em>)<br>
+  mat4x2 <strong>outerProduct</strong>(vec2 <em>c</em>, vec4 <em>r</em>)<br>
+  mat3x4 <strong>outerProduct</strong>(vec4 <em>c</em>, vec3 <em>r</em>)<br>
+  mat4x3 <strong>outerProduct</strong>(vec3 <em>c</em>, vec4 <em>r</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Treats the first parameter <em>c</em> as a column vector (matrix with one
+      column) and the second parameter <em>r</em> as a row vector (matrix with one
+      row) and does a linear algebraic matrix multiply <em>c</em> * <em>r</em>, yielding a
+      matrix whose number of rows is the number of components in <em>c</em> and
+      whose number of columns is the number of components in <em>r</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat2 <strong>transpose</strong>(mat2 <em>m</em>)<br>
+  mat3 <strong>transpose</strong>(mat3 <em>m</em>)<br>
+  mat4 <strong>transpose</strong>(mat4 <em>m</em>)<br>
+  mat2x3 <strong>transpose</strong>(mat3x2 <em>m</em>)<br>
+  mat3x2 <strong>transpose</strong>(mat2x3 <em>m</em>)<br>
+  mat2x4 <strong>transpose</strong>(mat4x2 <em>m</em>)<br>
+  mat4x2 <strong>transpose</strong>(mat2x4 <em>m</em>)<br>
+  mat3x4 <strong>transpose</strong>(mat4x3 <em>m</em>)<br>
+  mat4x3 <strong>transpose</strong>(mat3x4 <em>m</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a matrix that is the transpose of <em>m</em>.
+      The input matrix <em>m</em> is not modified.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>determinant</strong>(mat2 <em>m</em>)<br>
+  float <strong>determinant</strong>(mat3 <em>m</em>)<br>
+  float <strong>determinant</strong>(mat4 <em>m</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the determinant of <em>m</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">mat2 <strong>inverse</strong>(mat2 <em>m</em>)<br>
+  mat3 <strong>inverse</strong>(mat3 <em>m</em>)<br>
+  mat4 <strong>inverse</strong>(mat4 <em>m</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a matrix that is the inverse of <em>m</em>.
+      The input matrix <em>m</em> is not modified.
+      The values in the returned matrix are undefined if <em>m</em> is singular or
+      poorly-conditioned (nearly singular).</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="vector-relational-functions">8.7. Vector Relational Functions</h3>
+<div class="paragraph">
+<p>Relational and equality operators (<strong>&lt;</strong>, <strong>&lt;=</strong>, <strong>&gt;</strong>, <strong>&gt;=</strong>, <strong>==</strong>, <strong>!=</strong>) are
+defined to operate on scalars and produce scalar Boolean results.
+For vector results, use the following built-in functions.
+Below, the following placeholders are used for the listed specific types:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Placeholder</th>
+<th class="tableblock halign-left valign-top">Specific Types Allowed</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec2, bvec3, bvec4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">ivec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">ivec2, ivec3, ivec4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uvec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uvec2, uvec3, uvec4</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec2, vec3, vec4, dvec2, dvec3, dvec4</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>In all cases, the sizes of all the input and return vectors for any
+particular call must match.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>lessThan</strong>(vec x, vec y)<br>
+  bvec <strong>lessThan</strong>(ivec x, ivec y)<br>
+  bvec <strong>lessThan</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x &lt; y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>lessThanEqual</strong>(vec x, vec y)<br>
+  bvec <strong>lessThanEqual</strong>(ivec x, ivec y)<br>
+  bvec <strong>lessThanEqual</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x ≤ y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>greaterThan</strong>(vec x, vec y)<br>
+  bvec <strong>greaterThan</strong>(ivec x, ivec y)<br>
+  bvec <strong>greaterThan</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x &gt; y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>greaterThanEqual</strong>(vec x, vec y)<br>
+  bvec <strong>greaterThanEqual</strong>(ivec x, ivec y)<br>
+  bvec <strong>greaterThanEqual</strong>(uvec x, uvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x ≥ y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>equal</strong>(vec x, vec y)<br>
+  bvec <strong>equal</strong>(ivec x, ivec y)<br>
+  bvec <strong>equal</strong>(uvec x, uvec y)<br>
+  bvec <strong>equal</strong>(bvec x, bvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x == y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>notEqual</strong>(vec x, vec y)<br>
+  bvec <strong>notEqual</strong>(ivec x, ivec y)<br>
+  bvec <strong>notEqual</strong>(uvec x, uvec y)<br>
+  bvec <strong>notEqual</strong>(bvec x, bvec y)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise compare of <span class="eq">x ≠ y</span>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>any</strong>(bvec x)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if any component of <em>x</em> is <strong>true</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>all</strong>(bvec x)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> only if all components of <em>x</em> are <strong>true</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bvec <strong>not</strong>(bvec x)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the component-wise logical complement of <em>x</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="integer-functions">8.8. Integer Functions</h3>
+<div class="paragraph">
+<p>These all operate component-wise.
+The description is per component.
+The notation [<em>a</em>, <em>b</em>] means the set of bits from bit-number <em>a</em> through
+bit-number <em>b</em>, inclusive.
+The lowest-order bit is bit 0.
+&#8220;Bit number&#8221; will always refer to counting up from the lowest-order bit as
+bit 0.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genUType <strong>uaddCarry</strong>( genUType <em>x</em>,  genUType <em>y</em>, out  genUType <em>carry</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Adds 32-bit unsigned integers <em>x</em> and <em>y</em>, returning the sum modulo
+      2<sup>32</sup>.
+      The value <em>carry</em> is set to zero if the sum was less than 2<sup>32</sup>, or
+      one otherwise.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genUType <strong>usubBorrow</strong>( genUType <em>x</em>,  genUType <em>y</em>, out  genUType <em>borrow</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Subtracts the 32-bit unsigned integer <em>y</em> from <em>x</em>, returning the
+      difference if non-negative, or 2<sup>32</sup> plus the difference otherwise.
+      The value <em>borrow</em> is set to zero if <span class="eq">x ≥ y</span>, or one
+      otherwise.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>umulExtended</strong>( genUType <em>x</em>,  genUType <em>y</em>, out  genUType <em>msb</em>, out  genUType <em>lsb</em>)<br>
+  void <strong>imulExtended</strong>( genIType <em>x</em>,  genIType <em>y</em>, out  genIType <em>msb</em>, out  genIType <em>lsb</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Multiplies 32-bit unsigned or signed integers <em>x</em> and <em>y</em>, producing a
+      64-bit result.
+      The 32 least-significant bits are returned in <em>lsb</em>.
+      The 32 most-significant bits are returned in <em>msb</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>bitfieldExtract</strong>(genIType <em>value</em>, int <em>offset</em>, int <em>bits</em>)<br>
+  genUType <strong>bitfieldExtract</strong>(genUType <em>value</em>, int <em>offset</em>, int <em>bits</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Extracts bits <span class="eq">[offset, offset + bits - 1]</span> from <em>value</em>,
+      returning them in the least significant bits of the result.<br></p>
+<p class="tableblock">      For unsigned data types, the most significant bits of the result will
+      be set to zero.
+      For signed data types, the most significant bits will be set to the
+      value of bit <span class="eq">offset + bits - 1</span>.<br></p>
+<p class="tableblock">      If <em>bits</em> is zero, the result will be zero.
+      The result will be undefined if <em>offset</em> or <em>bits</em> is negative, or if
+      the sum of <em>offset</em> and <em>bits</em> is greater than the number of bits used
+      to store the operand.
+      Note that for vector versions of <strong>bitfieldExtract</strong>(), a single pair of
+      <em>offset</em> and <em>bits</em> values is shared for all components.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>bitfieldInsert</strong>(genIType <em>base</em>, genIType <em>insert</em>, int <em>offset</em>, int <em>bits</em>)<br>
+  genUType <strong>bitfieldInsert</strong>(genUType <em>base</em>, genUType <em>insert</em>, int <em>offset</em>, int <em>bits</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Inserts the <em>bits</em> least significant bits of <em>insert</em> into <em>base</em>.</p>
+<p class="tableblock">      The result will have bits <span class="eq">[offset, offset + bits - 1]</span> taken from
+      bits <span class="eq">[0, bits - 1]</span> of <em>insert</em>, and all other bits taken
+      directly from the corresponding bits of <em>base</em>.
+      If <em>bits</em> is zero, the result will simply be <em>base</em>.
+      The result will be undefined if <em>offset</em> or <em>bits</em> is negative, or if
+      the sum of <em>offset</em> and <em>bits</em> is greater than the number of bits used
+      to store the operand.<br>
+      Note that for vector versions of <strong>bitfieldInsert</strong>(), a single pair of
+      <em>offset</em> and <em>bits</em> values is shared for all components.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genIType <strong>bitfieldReverse</strong>( genIType <em>value</em>)<br>
+  genUType <strong>bitfieldReverse</strong>( genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Reverses the bits of <em>value</em>.
+      The bit numbered <em>n</em> of the result will be taken from bit <span class="eq">(bits -
+      1) - n</span> of <em>value</em>, where <em>bits</em> is the total number of bits used to
+      represent <em>value</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> genIType <strong>bitCount</strong>(genIType <em>value</em>)<br>
+   genIType <strong>bitCount</strong>(genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the number of one bits in the binary representation of
+      <em>value</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> genIType <strong>findLSB</strong>(genIType <em>value</em>)<br>
+   genIType <strong>findLSB</strong>(genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the bit number of the least significant one bit in the binary
+      representation of <em>value</em>.
+      If <em>value</em> is zero, -1 will be returned.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> genIType <strong>findMSB</strong>( genIType <em>value</em>)<br>
+   genIType <strong>findMSB</strong>( genUType <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the bit number of the most significant bit in the binary
+      representation of <em>value</em>.</p>
+<p class="tableblock">      For positive integers, the result will be the bit number of the most
+      significant one bit.
+      For negative integers, the result will be the bit number of the most
+      significant zero bit.
+      For a <em>value</em> of zero or negative one, -1 will be returned.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="texture-functions">8.9. Texture Functions</h3>
+<div class="paragraph">
+<p>Texture lookup functions are available in all shading stages.
+However, level-of-detail is implicitly computed only for fragment shaders.
+Other shaders operate as though the base level-of-detail were computed as
+zero.
+The functions in the table below provide access to textures through
+samplers, as set up through the OpenGL API.
+Texture properties such as size, pixel format, number of dimensions,
+filtering method, number of mipmap levels, depth comparison, and so on are
+also defined by OpenGL API calls.
+Such properties are taken into account as the texture is accessed via the
+built-in functions defined below.</p>
+</div>
+<div class="paragraph">
+<p>Texture data can be stored by the GL as single-precision floating-point,
+unsigned normalized integer, unsigned integer or signed integer data.
+This is determined by the type of the internal format of the texture.</p>
+</div>
+<div class="paragraph">
+<p>Texture lookup functions are provided that can return their result as
+floating-point, unsigned integer or signed integer, depending on the sampler
+type passed to the lookup function.
+Care must be taken to use the right sampler type for texture access.
+The following table lists the supported combinations of sampler types and
+texture internal formats.
+Blank entries are unsupported.
+Doing a texture lookup will return undefined values for unsupported
+combinations.</p>
+</div>
+<div class="paragraph">
+<p>For depth/stencil textures, the internal texture format is determined by the
+component being accessed as set through the OpenGL API.
+When the depth/stencil texture mode is set to DEPTH_COMPONENT, the internal
+format of the depth component should be used.
+When the depth/stencil texture mode is set to STENCIL_INDEX, the internal format
+of the stencil component should be used.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+<col style="width: 25%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Internal Texture Format</th>
+<th class="tableblock halign-left valign-top">Floating-Point Sampler Types</th>
+<th class="tableblock halign-left valign-top">Signed Integer Sampler Types</th>
+<th class="tableblock halign-left valign-top">Unsigned Integer Sampler Types</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Floating-point</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Normalized Integer</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Signed Integer</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+<td class="tableblock halign-left valign-top"></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Unsigned Integer</p></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Supported</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>If an integer sampler type is used, the result of a texture lookup is an
+<strong>ivec4</strong>.
+If an unsigned integer sampler type is used, the result of a texture lookup
+is a <strong>uvec4</strong>.
+If a floating-point sampler type is used, the result of a texture lookup is
+a <strong>vec4</strong>.</p>
+</div>
+<div class="paragraph">
+<p>In the prototypes below, the &#8220;_g_&#8221; in the return type &#8220;_gvec4_&#8221; is used
+as a placeholder for nothing, &#8220;_i_&#8221;, or &#8220;_u_&#8221; making a return type of
+<strong>vec4</strong>, <strong>ivec4</strong>, or <strong>uvec4</strong>.
+In these cases, the sampler argument type also starts with &#8220;_g_&#8221;,
+indicating the same substitution done on the return type; it is either a
+single-precision
+floating-point, signed integer, or unsigned integer sampler, matching the
+basic type of the return type, as described above.</p>
+</div>
+<div class="paragraph">
+<p>For shadow forms (the sampler parameter is a shadow-type), a depth
+comparison lookup on the depth texture bound to <em>sampler</em> is done as
+described in section
+8.23
+&#8220;Texture Comparison Modes&#8221; of the
+<a href="#references">OpenGL Specification</a>.
+See the table below for which component specifies <em>D<sub>ref</sub></em>.
+The texture bound to <em>sampler</em> must be a depth texture, or results are
+undefined.
+If a non-shadow texture call is made to a sampler that represents a depth
+texture with depth comparisons turned on, then results are undefined.
+If a shadow texture call is made to a sampler that represents a depth
+texture with depth comparisons turned off, then results are undefined.
+If a shadow texture call is made to a sampler that does not represent a
+depth texture, then results are undefined.</p>
+</div>
+<div class="paragraph">
+<p>In all functions below, the <em>bias</em> parameter is optional for fragment
+shaders.
+The <em>bias</em> parameter is not accepted in any other shader stage.
+For a fragment shader, if <em>bias</em> is present, it is added to the implicit
+level-of-detail prior to performing the texture access operation.
+No <em>bias</em> or <em>lod</em> parameters for
+rectangle textures,
+multisample textures, or texture buffers
+are supported because mipmaps are not allowed for these types of textures.</p>
+</div>
+<div class="paragraph">
+<p>The implicit level-of-detail is selected as follows: For a texture that is
+not mipmapped, the texture is used directly.
+If it is mipmapped and running in a fragment shader, the level-of-detail
+computed by the implementation is used to do the texture lookup.
+If it is mipmapped and running in a non-fragment shader, then the base
+texture is used.</p>
+</div>
+<div class="paragraph">
+<p>Some texture functions (non-&#8220;<strong>Lod</strong>&#8221; and non-&#8220;<strong>Grad</strong>&#8221; versions) may
+require implicit derivatives.
+Implicit derivatives are undefined within non-uniform control flow and for
+non-fragment shader texture fetches.</p>
+</div>
+<div class="paragraph">
+<p>For <strong>Cube</strong> forms, the direction of <em>P</em> is used to select which face to do a
+2-dimensional texture lookup in, as described in section 8.13 &#8220;Cube Map
+Texture Selection&#8221; of the <a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>For <strong>Array</strong> forms, the array layer used will be</p>
+</div>
+<div class="paragraph">
+<p>\(\max(0,\min(d-1,\left\lfloor layer + 0.5\right\rfloor))\)</p>
+</div>
+<div class="paragraph">
+<p>where <em>d</em> is the depth of the texture array and <em>layer</em> comes from the
+component indicated in the tables below.</p>
+</div>
+<div class="sect3">
+<h4 id="texture-query-functions">8.9.1. Texture Query Functions</h4>
+<div class="paragraph">
+<p>The <strong>textureSize</strong> functions query the dimensions of a specific texture level
+for a sampler.</p>
+</div>
+<div class="paragraph">
+<p>The <strong>textureQueryLod</strong> functions are available only in a fragment shader.
+They take the components of <em>P</em> and compute the level-of-detail information
+that the texture pipe would use to access that texture through a normal
+texture lookup.
+The level-of-detail \(\lambda^{'}\) (equation 3.18 of the
+<a href="#references">OpenGL Specification</a>) is obtained after any level-of-detail bias, but
+prior to clamping to [TEXTURE_MIN_LOD, TEXTURE_MAX_LOD].
+The mipmap array(s) that would be accessed are also computed.
+If a single level-of-detail would be accessed, the level-of-detail number
+relative to the base level is returned.
+If multiple levels-of-detail would be accessed, a floating-point number
+between the two levels is returned, with the fractional part equal to the
+fractional part of the computed and clamped level-of-detail.</p>
+</div>
+<div class="paragraph">
+<p>The algorithm used is given by the following pseudo-code:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++"><span class="predefined-type">float</span> ComputeAccessedLod(<span class="predefined-type">float</span> computedLod)
+{
+    <span class="comment">// Clamp the computed LOD according to the texture LOD clamps.</span>
+    <span class="keyword">if</span> (computedLod &lt; TEXTURE_MIN_LOD) computedLod = TEXTURE_MIN_LOD;
+    <span class="keyword">if</span> (computedLod &gt; TEXTURE_MAX_LOD) computedLod = TEXTURE_MAX_LOD;
+
+    <span class="comment">// Clamp the computed LOD to the range of accessible levels.</span>
+    <span class="keyword">if</span> (computedLod &lt; <span class="float">0</span><span class="float">.0</span>)
+        computedLod = <span class="float">0</span><span class="float">.0</span>;
+    <span class="keyword">if</span> (computedLod &gt; (<span class="predefined-type">float</span>) maxAccessibleLevel)
+        computedLod = (<span class="predefined-type">float</span>) maxAccessibleLevel;
+
+    <span class="comment">// Return a value according to the min filter.</span>
+    <span class="keyword">if</span> (TEXTURE_MIN_FILTER is LINEAR <span class="keyword">or</span> NEAREST) {
+        <span class="keyword">return</span> <span class="float">0</span><span class="float">.0</span>;
+    } <span class="keyword">else</span> <span class="keyword">if</span> (TEXTURE_MIN_FILTER is NEAREST_MIPMAP_NEAREST
+               <span class="keyword">or</span> LINEAR_MIPMAP_NEAREST) {
+        <span class="keyword">return</span> ceil(computedLod + <span class="float">0</span><span class="float">.5</span>) - <span class="float">1</span><span class="float">.0</span>;
+    } <span class="keyword">else</span> {
+        <span class="keyword">return</span> computedLod;
+    }
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The value <em>maxAccessibleLevel</em> is the level number of the smallest
+accessible level of the mipmap array (the value <em>q</em> in section 8.14.3
+&#8220;Mipmapping&#8221; of the <a href="#references">OpenGL Specification</a>) minus the base level.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> int <strong>textureSize</strong>(gsampler1D <em>sampler</em>, int <em>lod</em>)<br>
+   ivec2 <strong>textureSize</strong>(gsampler2D <em>sampler</em>, int <em>lod</em>)<br>
+   ivec3 <strong>textureSize</strong>(gsampler3D <em>sampler</em>, int <em>lod</em>)<br>
+   ivec2 <strong>textureSize</strong>(gsamplerCube <em>sampler</em>, int <em>lod</em>)<br>
+   int <strong>textureSize</strong>(sampler1DShadow <em>sampler</em>, int <em>lod</em>)<br>
+   ivec2 <strong>textureSize</strong>(sampler2DShadow <em>sampler</em>, int <em>lod</em>)<br>
+   ivec2 <strong>textureSize</strong>(samplerCubeShadow <em>sampler</em>, int <em>lod</em>)
+   ivec3 <strong>textureSize</strong>(gsamplerCubeArray <em>sampler</em>, int <em>lod</em>)<br>
+   ivec3 <strong>textureSize</strong>(samplerCubeArrayShadow <em>sampler</em>, int <em>lod</em>)<br>
+   ivec2 <strong>textureSize</strong>(gsampler2DRect <em>sampler</em>)<br>
+   ivec2 <strong>textureSize</strong>(sampler2DRectShadow <em>sampler</em>)<br>
+   ivec2 <strong>textureSize</strong>(gsampler1DArray <em>sampler</em>, int <em>lod</em>)<br>
+   ivec2 <strong>textureSize</strong>(sampler1DArrayShadow <em>sampler</em>, int <em>lod</em>)<br>
+   ivec3 <strong>textureSize</strong>(gsampler2DArray <em>sampler</em>, int <em>lod</em>)<br>
+   ivec3 <strong>textureSize</strong>(sampler2DArrayShadow <em>sampler</em>, int <em>lod</em>)<br>
+   int <strong>textureSize</strong>(gsamplerBuffer <em>sampler</em>)<br>
+   ivec2 <strong>textureSize</strong>(gsampler2DMS <em>sampler</em>)<br>
+   ivec3 <strong>textureSize</strong>(gsampler2DMSArray <em>sampler</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the dimensions of level <em>lod</em> (if present) for the texture
+      bound to <em>sampler</em>, as described in section
+      8.11 &#8220;Texture Queries&#8221; of the <a href="#references">OpenGL Specification</a>.<br>
+      The components in the return value are filled in, in order, with the
+      width, height, and depth of the texture.</p>
+<p class="tableblock">      For the array forms, the last component of the return value is the
+      number of layers in the texture array, or the number of cubes in the
+      texture cube map array.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec2 <strong>textureQueryLod</strong>(gsampler1D <em>sampler</em>, float <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(gsampler1DArray <em>sampler</em>, float <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(gsampler2DArray <em>sampler</em>, vec2 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(gsamplerCubeArray <em>sampler</em>, vec3 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(sampler1DShadow <em>sampler</em>, float <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(samplerCubeShadow <em>sampler</em>, vec3 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(sampler1DArrayShadow <em>sampler</em>, float <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(sampler2DArrayShadow <em>sampler</em>, vec2 <em>P</em>)<br>
+  vec2 <strong>textureQueryLod</strong>(samplerCubeArrayShadow <em>sampler</em>, vec3 <em>P</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the mipmap array(s) that would be accessed in the <em>x</em>
+      component of the return value.</p>
+<p class="tableblock">      Returns the computed level-of-detail relative to the base level in the
+      <em>y</em> component of the return value.</p>
+<p class="tableblock">      If called on an incomplete texture, the results are undefined.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">int <strong>textureQueryLevels</strong>(gsampler1D <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(gsampler2D <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(gsampler3D <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(gsamplerCube <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(gsampler1DArray <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(gsampler2DArray <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(gsamplerCubeArray <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(sampler1DShadow <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(sampler2DShadow <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(samplerCubeShadow <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(sampler1DArrayShadow <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(sampler2DArrayShadow <em>sampler</em>)<br>
+  int <strong>textureQueryLevels</strong>(samplerCubeArrayShadow <em>sampler</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the number of mipmap levels accessible in the texture
+      associated with <em>sampler</em>, as defined in the <a href="#references">OpenGL Specification.</a></p>
+<p class="tableblock">      The value zero will be returned if no texture or an incomplete texture
+      is associated with <em>sampler</em>.</p>
+<p class="tableblock">      Available in all shader stages.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">int <strong>textureSamples</strong>(gsampler2DMS <em>sampler</em>)<br>
+  int <strong>textureSamples</strong>(gsampler2DMSArray <em>sampler</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the number of samples of the texture or textures bound to
+      <em>sampler</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="texel-lookup-functions">8.9.2. Texel Lookup Functions</h4>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>texture</strong>(gsampler1D <em>sampler</em>, float <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>[, float <em>bias</em>] )<br>
+  float <strong>texture</strong>(sampler1DShadow <em>sampler</em>, <em>vec3 _P</em> [, float <em>bias</em>])<br>
+  float <strong>texture</strong>(sampler2DShadow <em>sampler</em>, <em>vec3 _P</em> [, float <em>bias</em>])<br>
+  float <strong>texture</strong>(samplerCubeShadow <em>sampler</em>, <em>vec4 _P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>texture</strong>(gsampler1DArray <em>sampler</em>, <em>vec2 _P</em> [, float <em>bias</em>] )<br>
+  float <strong>texture</strong>(sampler1DArrayShadow <em>sampler</em>,  <em>P</em> [, float <em>bias</em>] )<br>
+  float <strong>texture</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 <em>P</em>)<br>
+  gvec4 <strong>texture</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>)<br>
+  float <strong>texture</strong>(sampler2DRectShadow <em>sampler</em>, vec3 <em>P</em>)<br>
+  float <strong>texture</strong>(samplerCubeArrayShadow <em>sampler</em>, vec4 <em>P</em>, float <em>compare</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Use the texture coordinate <em>P</em> to do a texture lookup in the texture
+      currently bound to <em>sampler</em>.</p>
+<p class="tableblock">      For shadow forms: When <em>compare</em> is present, it is used as <em>D<sub>ref</sub></em>
+      and the array layer comes from the last component of <em>P</em>.
+      When <em>compare</em> is not present, the last component of <em>P</em> is used as
+      <em>D<sub>ref</sub></em> and the array layer comes from the second to last component
+      of <em>P</em>.
+      (The second component of <em>P</em> is unused for <strong>1D</strong> shadow lookups.)</p>
+<p class="tableblock">      For non-shadow forms: the array layer comes from the last component of
+      <em>P</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProj</strong>(gsampler1D <em>sampler</em>, vec2 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler1D <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  float <strong>textureProj</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  float <strong>textureProj</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProj</strong>(gsampler2DRect <em>sampler</em>, vec3 <em>P</em>)<br>
+  gvec4 <strong>textureProj</strong>(gsampler2DRect <em>sampler</em>, vec4 <em>P</em>)<br>
+  float <strong>textureProj</strong>(sampler2DRectShadow <em>sampler</em>, vec4 <em>P</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup with projection.
+      The texture coordinates consumed from <em>P</em>, not including the last
+      component of <em>P</em>, are divided by the last component of <em>P</em> to
+      form projected coordinates <em>P'</em>.
+      The resulting third component of <em>P</em> in the shadow forms is used as
+      <em>D<sub>ref</sub></em>.
+      The third component of <em>P</em> is ignored when <em>sampler</em> has type
+      <strong>gsampler2D</strong> and <em>P</em> has type <strong>vec4</strong>.
+      After these values are computed, texture lookup proceeds as in
+      <strong>texture</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureLod</strong>(gsampler1D <em>sampler</em>, float <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureLod</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureLod</strong>(sampler1DShadow <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsampler1DArray <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureLod</strong>(sampler1DArrayShadow <em>sampler</em>,  <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureLod</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Do a texture lookup as in <strong>texture</strong> but with explicit level-of-detail;
+      <em>lod</em> specifies <span class="eq">λ<sub>base</sub>]</span> and sets the partial derivatives
+      as follows:<br>
+      (See section 8.14 &#8220;Texture Minification&#8221; and equations 8.4-8.6 of
+      the <a href="#references">OpenGL Specification</a>.)<br>
+     <br>
+      <span class="eq">∂u / ∂x =
+           ∂v / ∂x =
+           ∂w / ∂x = 0</span>
+     <br>
+      <span class="eq">∂u / ∂y =
+           ∂v / ∂y =
+           ∂w / ∂y = 0</span></p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureOffset</strong>(gsampler1D <em>sampler</em>, float <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, ivec3 <em>offset</em> [, float <em>bias</em>] )<br>
+  float <strong>textureOffset</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureOffset</strong>(sampler2DRectShadow <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureOffset</strong>(sampler1DShadow <em>sampler</em>, vec3 <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler1DArray <em>sampler</em>, vec2 <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  float <strong>textureOffset</strong>(sampler1DArrayShadow <em>sampler</em>, vec3 <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  float <strong>textureOffset</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 P, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup as in <strong>texture</strong> but with <em>offset</em> added to the
+      <span class="eq">(u,v,w)</span> texel coordinates before looking up each texel.
+      The offset value must be a constant expression.
+      A limited range of offset values are supported; the minimum and
+      maximum offset values are implementation-dependent and given by
+      <em>gl_MinProgramTexelOffset</em> and <em>gl_MaxProgramTexelOffset</em>,
+      respectively.</p>
+<p class="tableblock">      Note that <em>offset</em> does not apply to the layer coordinate for texture
+      arrays.
+      This is explained in detail in section 8.14.2 &#8220;Coordinate Wrapping
+      and Texel Selection&#8221; of the <a href="#references">OpenGL Specification</a>, where <em>offset</em>
+      is <span class="eq">(δ<sub>u</sub>, δ<sub>v</sub>, δ<sub>w</sub>)</span>.<br>
+      Note that texel offsets are also not supported for cube maps.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>texelFetch</strong>(gsampler1D <em>sampler</em>, int <em>P</em>, int <em>lod</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler2D <em>sampler</em>, ivec2 <em>P</em>, int <em>lod</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler3D <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>)
+  gvec4 <strong>texelFetch</strong>(gsampler2DRect <em>sampler</em>, ivec2 <em>P</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler1DArray <em>sampler</em>, ivec2 <em>P</em>, int <em>lod</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler2DArray <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsamplerBuffer <em>sampler</em>, int <em>P</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler2DMS <em>sampler</em>, ivec2 <em>P</em>, int <em>sample</em>)<br>
+  gvec4 <strong>texelFetch</strong>(gsampler2DMSArray <em>sampler</em>, ivec3 <em>P</em>, int <em>sample</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Use integer texture coordinate <em>P</em> to lookup a single texel from
+      <em>sampler</em>.
+      The array layer comes from the last component of <em>P</em> for the array
+      forms.
+      The level-of-detail <em>lod</em> (if present) is as described in sections
+      11.1.3.2 &#8220;Texel Fetches&#8221; and 8.14.1 &#8220;Scale Factor and Level of
+      Detail&#8221; of the <a href="#references">OpenGL Specification</a>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>texelFetchOffset</strong>(gsampler1D <em>sampler</em>, int <em>P</em>, int <em>lod</em>, int <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler2D <em>sampler</em>, ivec2 <em>P</em>, int <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler3D <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>, ivec3 <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler2DRect <em>sampler</em>, ivec2 <em>P</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler1DArray <em>sampler</em>, ivec2 <em>P</em>, int <em>lod</em>, int <em>offset</em>)<br>
+  gvec4 <strong>texelFetchOffset</strong>(gsampler2DArray <em>sampler</em>, ivec3 <em>P</em>, int <em>lod</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Fetch a single texel as in <strong>texelFetch</strong>, offset by <em>offset</em> as
+      described in <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjOffset</strong>(gsampler1D <em>sampler</em>, vec2 <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler1D <em>sampler</em>, vec4 <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, ivec3 <em>offset</em> [, float <em>bias</em>] )<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler2DRect <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjOffset</strong>(gsampler2DRect <em>sampler</em>, vec4 <em>P</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureProjOffset</strong>(sampler2DRectShadow <em>sampler</em>, vec4 <em>P</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureProjOffset</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>P</em>, int <em>offset</em> [, float <em>bias</em>] )<br>
+  float <strong>textureProjOffset</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, ivec2 <em>offset</em> [, float <em>bias</em>] )</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a projective texture lookup as described in <strong>textureProj</strong>, offset
+      by <em>offset</em> as described in <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureLodOffset</strong>(gsampler1D <em>sampler</em>, float <em>P</em>, float <em>lod</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureLodOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureLodOffset</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>, ivec3 <em>offset</em>)<br>
+  float <strong>textureLodOffset</strong>(sampler1DShadow <em>sampler</em>,  <em>P</em>, float <em>lod</em>, int <em>offset</em>)<br>
+  float <strong>textureLodOffset</strong>(sampler2DShadow <em>sampler</em>,  <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureLodOffset</strong>(gsampler1DArray <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureLodOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureLodOffset</strong>(sampler1DArrayShadow <em>sampler</em>,  <em>P</em>, float <em>lod</em>, int <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do an offset texture lookup with explicit level-of-detail.
+      See <strong>textureLod</strong> and <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjLod</strong>(gsampler1D <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureProjLod</strong>(gsampler1D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureProjLod</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureProjLod</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)<br>
+  gvec4 <strong>textureProjLod</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureProjLod</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)<br>
+  float <strong>textureProjLod</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a projective texture lookup with explicit level-of-detail.
+      See <strong>textureProj</strong> and <strong>textureLod</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjLodOffset</strong>(gsampler1D <em>sampler</em>, vec2 <em>P</em>, float <em>lod</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureProjLodOffset</strong>(gsampler1D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureProjLodOffset</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjLodOffset</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjLodOffset</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, ivec3 <em>offset</em>)<br>
+  float <strong>textureProjLodOffset</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, int <em>offset</em>)<br>
+  float <strong>textureProjLodOffset</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>lod</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do an offset projective texture lookup with explicit level-of-detail.
+      See <strong>textureProj</strong>, <strong>textureLod</strong>, and <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGrad</strong>(gsampler1D <em>sampler</em>, <em>float _P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsampler3D <em>sampler</em>,  <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler2DRectShadow <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler1DShadow <em>sampler</em>, vec3 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsampler1DArray <em>sampler</em>, vec2 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsampler2DArray <em>sampler</em>,  <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler1DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(samplerCubeShadow <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  float <strong>textureGrad</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureGrad</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Do a texture lookup as in <strong>texture</strong> but with <a href="#explicit-gradients">explicit gradients</a> as shown below.
+      The partial derivatives of <em>P</em> are with respect to window <em>x</em> and
+      window <em>y</em>.
+      For the cube version, the partial derivatives of <em>P</em> are assumed to be
+      in the coordinate system used before texture coordinates are projected
+      onto the appropriate cube face.</p>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGradOffset</strong>(gsampler1D <em>sampler</em>, float <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler3D <em>sampler</em>, vec3 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>, ivec3 <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler2DRectShadow <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler1DShadow <em>sampler</em>, vec3 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureGradOffset</strong>(gsampler1DArray <em>sampler</em>, vec2 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler1DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  float <strong>textureGradOffset</strong>(sampler2DArrayShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup with both explicit gradient and offset, as
+      described in <strong>textureGrad</strong> and <strong>textureOffset</strong>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjGrad</strong>(gsampler1D <em>sampler</em>, vec2 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler1D <em>sampler</em>, vec4 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler2DRect <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  gvec4 <strong>textureProjGrad</strong>(gsampler2DRect <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureProjGrad</strong>(sampler2DRectShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)<br>
+  float <strong>textureProjGrad</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>)<br>
+  float <strong>textureProjGrad</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup both projectively, as described in <strong>textureProj</strong>,
+      and with explicit gradient as described in <strong>textureGrad</strong>.
+      The partial derivatives <em>dPdx</em> and <em>dPdy</em> are assumed to be already
+      projected.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureProjGradOffset</strong>(gsampler1D <em>sampler</em>, vec2 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler1D <em>sampler</em>, vec4 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler2D <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler2D <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler3D <em>sampler</em>, vec4 <em>P</em>, vec3 <em>dPdx</em>, vec3 <em>dPdy</em>, ivec3 <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler2DRect <em>sampler</em>, vec3 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureProjGradOffset</strong>(gsampler2DRect <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureProjGradOffset</strong>(sampler2DRectShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)<br>
+  float <strong>textureProjGradOffset</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>P</em>, float <em>dPdx</em>, float <em>dPdy</em>, int <em>offset</em>)<br>
+  float <strong>textureProjGradOffset</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>P</em>, vec2 <em>dPdx</em>, vec2 <em>dPdy</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Do a texture lookup projectively and with explicit gradient as
+      described in <strong>textureProjGrad</strong>, as well as with offset, as described in
+      <strong>textureOffset</strong>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="explicit-gradients">8.9.3. Explicit Gradients</h4>
+<div class="paragraph">
+<p>In the <strong>textureGrad</strong> functions described above, explicit gradients control
+texture lookups as follows:</p>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\begin{aligned}
+  \frac{\partial{s}}{\partial{x}} &amp; =
+    \begin{cases}
+      \frac{\partial{P}}{\partial{x}}, &amp; \text{for a 1D texture} \\[0.8em]
+      \frac{\partial{P.s}}{\partial{x}}, &amp; \text{otherwise}
+    \end{cases} \\[2.5em]
+  \frac{\partial{s}}{\partial{y}} &amp; =
+    \begin{cases}
+      \frac{\partial{P}}{\partial{y}}, &amp; \text{for a 1D texture} \\[0.8em]
+      \frac{\partial{P.s}}{\partial{y}}, &amp; \text{otherwise}
+    \end{cases} \\[2.5em]
+  \frac{\partial{t}}{\partial{x}} &amp; =
+    \begin{cases}
+      0.0,                               &amp; \text{for a 1D texture} \\[0.8em]
+      \frac{\partial{P.t}}{\partial{x}}, &amp; \text{otherwise}
+    \end{cases} \\[2.5em]
+  \frac{\partial{t}}{\partial{y}} &amp; =
+    \begin{cases}
+      0.0,                               &amp; \text{for a 1D texture} \\[0.8em]
+      \frac{\partial{P.t}}{\partial{y}}, &amp; \text{otherwise}
+    \end{cases} \\[2.5em]
+  \frac{\partial{r}}{\partial{x}} &amp; =
+    \begin{cases}
+      0.0,                               &amp; \text{for 1D or 2D} \\[0.8em]
+      \frac{\partial{P.p}}{\partial{x}}, &amp; \text{cube, other}
+    \end{cases} \\[2.5em]
+  \frac{\partial{r}}{\partial{y}} &amp; =
+    \begin{cases}
+      0.0,                               &amp; \text{for 1D or 2D} \\[0.8em]
+      \frac{\partial{P.p}}{\partial{y}}, &amp; \text{cube, other}
+    \end{cases}
+\end{aligned}\]
+</div>
+</div>
+</div>
+<div class="sect3">
+<h4 id="texture-gather-functions">8.9.4. Texture Gather Functions</h4>
+<div class="paragraph">
+<p>The texture gather functions take components of a single floating-point
+vector operand as a texture coordinate, determine a set of four texels to
+sample from the base level-of-detail of the specified texture image, and
+return one component from each texel in a four-component result vector.</p>
+</div>
+<div class="paragraph">
+<p>When performing a texture gather operation, the minification and
+magnification filters are ignored, and the rules for LINEAR filtering in the
+<a href="#references">OpenGL Specification</a> are applied to the base level of the texture image
+to identify the four texels <em>i<sub>0</sub> j<sub>1</sub></em>, <em>i<sub>1</sub> j<sub>1</sub></em>, <em>i<sub>1</sub> j<sub>0</sub></em>, and <em>i<sub>0</sub>
+j<sub>0</sub></em>.
+The texels are then converted to texture base colors (<em>R<sub>s</sub></em>, <em>G<sub>s</sub></em>,
+<em>B<sub>s</sub></em>, <em>A<sub>s</sub></em>) according to table 15.1, followed by application of the
+texture swizzle as described in section 15.2.1 &#8220;Texture Access&#8221; of the
+<a href="#references">OpenGL Specification</a>.
+A four-component vector is assembled by taking the selected component from
+each of the post-swizzled texture source colors in the order (<em>i<sub>0</sub> j<sub>1</sub></em>,
+<em>i<sub>1</sub> j<sub>1</sub></em>, <em>i<sub>1</sub> j<sub>0</sub></em>, <em>i<sub>0</sub> j<sub>0</sub></em>).</p>
+</div>
+<div class="paragraph">
+<p>For texture gather functions using a shadow sampler type, each of the four
+texel lookups perform a depth comparison against the depth reference value
+passed in (<em>refZ</em>), and returns the result of that comparison in the
+appropriate component of the result vector.</p>
+</div>
+<div class="paragraph">
+<p>As with other texture lookup functions, the results of a texture gather are
+undefined for shadow samplers if the texture referenced is not a depth
+texture or has depth comparisons disabled; or for non-shadow samplers if the
+texture referenced is a depth texture with depth comparisons enabled.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGather</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em> [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em> [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsamplerCube <em>sampler</em>, vec3 <em>P</em> [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsamplerCubeArray <em>sampler</em>, vec4 <em>P</em>[, int <em>comp</em>])<br>
+  gvec4 <strong>textureGather</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>[, int <em>comp</em>])<br>
+  vec4 <strong>textureGather</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(sampler2DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(samplerCubeShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(samplerCubeArrayShadow <em>sampler</em>, vec4 <em>P</em>, float <em>refZ</em>)<br>
+  vec4 <strong>textureGather</strong>(sampler2DRectShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Returns the value<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">vec4(Sample_i0_j1(P, base).comp,
+     Sample_i1_j1(P, base).comp,
+     Sample_i1_j0(P, base).comp,
+     Sample_i0_j0(P, base).comp)</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>If specified, the value of <em>comp</em> must be a constant integer expression with
+a value of 0, 1, 2, or 3, identifying the <em>x</em>, <em>y</em>, <em>z</em>, or <em>w</em>
+post-swizzled component of the four-component vector lookup result for each
+texel, respectively.
+If <em>comp</em> is not specified, it is treated as 0, selecting the <em>x</em> component
+of each texel to generate the result.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGatherOffset</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offset</em>, [ int <em>comp</em>])<br>
+  gvec4 <strong>textureGatherOffset</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offset</em> [ int <em>comp</em>])<br>
+  vec4 <strong>textureGatherOffset</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>, ivec2 <em>offset</em>)<br>
+  vec4 <strong>textureGatherOffset</strong>(sampler2DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>, ivec2 <em>offset</em>)<br>
+  gvec4 <strong>textureGatherOffset</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offset</em> [ int <em>comp</em>])<br>
+  vec4 <strong>textureGatherOffset</strong>(sampler2DRectShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>, ivec2 <em>offset</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Perform a texture gather operation as in <strong>textureGather</strong> by <em>offset</em>
+      as described in <strong>textureOffset</strong> except that the <em>offset</em> can be
+      variable (non constant) and the implementation-dependent minimum and
+      maximum offset values are given by MIN_PROGRAM_TEXTURE_GATHER_OFFSET
+      and MAX_PROGRAM_TEXTURE_GATHER_OFFSET, respectively.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">gvec4 <strong>textureGatherOffsets</strong>(gsampler2D <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offsets</em>[4] [, int <em>comp</em>])<br>
+  gvec4 <strong>textureGatherOffsets</strong>(gsampler2DArray <em>sampler</em>, vec3 <em>P</em>, ivec2 <em>offsets</em>[4]   [, int <em>comp</em>])<br>
+  vec4 <strong>textureGatherOffsets</strong>(sampler2DShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>, ivec2 <em>offsets</em>[4])<br>
+  vec4 <strong>textureGatherOffsets</strong>(sampler2DArrayShadow <em>sampler</em>, vec3 <em>P</em>, float <em>refZ</em>, ivec2 <em>offsets</em>[4])<br>
+  gvec4 <strong>textureGatherOffsets</strong>(gsampler2DRect <em>sampler</em>, vec2 <em>P</em>, ivec2 <em>offsets</em>[4] [, int <em>comp</em>])<br>
+  vec4 <strong>textureGatherOffsets</strong>(sampler2DRectShadow <em>sampler</em>, vec2 <em>P</em>, float <em>refZ</em>, ivec2 <em>offsets</em>[4])</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Operate identically to <strong>textureGatherOffset</strong> except that <em>offsets</em> is
+      used to determine the location of the four texels to sample.
+      Each of the four texels is obtained by applying the corresponding
+      offset in <em>offsets</em> as a (<em>u</em>, <em>v</em>) coordinate offset to <em>P</em>,
+      identifying the four-texel LINEAR footprint, and then selecting the
+      texel <em>i<sub>0</sub> j<sub>0</sub></em> of that footprint.
+      The specified values in <em>offsets</em> must be constant integral
+      expressions.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="compatibility-profile-texture-functions">8.9.5. Compatibility Profile Texture Functions</h4>
+<div class="paragraph">
+<p>The following texture functions are only in the compatibility profile.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec4 <strong>texture1D</strong>(sampler1D <em>sampler</em>, float <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture1DProj</strong>(sampler1D <em>sampler</em>, vec2 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture1DProj</strong>(sampler1D <em>sampler</em>, vec4 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture1DLod</strong>(sampler1D <em>sampler</em>, float <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>texture1DProjLod</strong>(sampler1D <em>sampler</em>, vec2 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>texture1DProjLod</strong>(sampler1D <em>sampler</em>, vec4 <em>coord</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">See corresponding signature above without &#8220;1D&#8221; in the name.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec4 <strong>texture2D</strong>(sampler2D <em>sampler</em>, vec2 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture2DProj</strong>(sampler2D <em>sampler</em>, vec3 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture2DProj</strong>(sampler2D <em>sampler</em>, vec4 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture2DLod</strong>(sampler2D <em>sampler</em>, vec2 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>texture2DProjLod</strong>(sampler2D <em>sampler</em>, vec3 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>texture2DProjLod</strong>(sampler2D <em>sampler</em>, vec4 <em>coord</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">See corresponding signature above without &#8220;2D&#8221; in the name.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec4 <strong>texture3D</strong>(sampler3D <em>sampler</em>, vec3 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture3DProj</strong>(sampler3D <em>sampler</em>, vec4 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>texture3DLod</strong>(sampler3D <em>sampler</em>, vec3 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>texture3DProjLod</strong>(sampler3D <em>sampler</em>, vec4 <em>coord</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">See corresponding signature above without &#8220;3D&#8221; in the name.<br>
+      Use the texture coordinate <em>coord</em> to do a texture lookup in the 3D
+      texture currently bound to <em>sampler</em>.
+      For the projective (&#8220;<strong>Proj</strong>&#8221;) versions, the texture coordinate is
+      divided by <em>coord.q</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec4 <strong>textureCube</strong>(samplerCube <em>sampler</em>, vec3 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>textureCubeLod</strong>(samplerCube <em>sampler</em>, vec3 <em>coord</em>, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">See corresponding signature above without &#8220;Cube&#8221; in the name.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec4 <strong>shadow1D</strong>(sampler1DShadow <em>sampler</em>, vec3 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>shadow2D</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>shadow1DProj</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>shadow2DProj</strong>(sampler2DShadow <em>sampler</em>, vec4 <em>coord</em> [, float <em>bias</em>] )<br>
+  vec4 <strong>shadow1DLod</strong>(sampler1DShadow <em>sampler</em>, vec3 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>shadow2DLod</strong>(sampler2DShadow <em>sampler</em>, vec3 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>shadow1DProjLod</strong>(sampler1DShadow <em>sampler</em>, vec4 <em>coord</em>, float <em>lod</em>)<br>
+  vec4 <strong>shadow2DProjLod</strong>(sampler2DShadow <em>sampler</em>, vec4 coord, float <em>lod</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Same functionality as the &#8220;<strong>texture</strong>&#8221; based names above with the
+      same signature.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect2">
+<h3 id="atomic-counter-functions">8.10. Atomic Counter Functions</h3>
+<div class="paragraph">
+<p>The atomic-counter operations in this section operate atomically with
+respect to each other.
+They are atomic for any single counter, meaning any of these operations on a
+specific counter in one shader instantiation will be indivisible by any of
+these operations on the same counter from another shader instantiation.
+There is no guarantee that these operations are atomic with respect to other
+forms of access to the counter or that they are serialized when applied to
+separate counters.
+Such cases would require additional use of fences, barriers, or other forms
+of synchronization, if atomicity or serialization is desired.</p>
+</div>
+<div class="paragraph">
+<p>The underlying counter is a 32-bit unsigned integer.
+The result of operations will wrap to [0, 2<sup>32</sup>-1].</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterIncrement</strong>(atomic_uint <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>increments the counter for <em>c</em>, and</p>
+</li>
+<li>
+<p>returns its value prior to the increment operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterDecrement</strong>(atomic_uint <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>decrements the counter for <em>c</em>, and</p>
+</li>
+<li>
+<p>returns the value resulting from the decrement operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounter</strong>(atomic_uint <em>c</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the counter value for <em>c</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterAdd</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>adds the value of <em>data</em> to the counter for <em>c</em>, and</p>
+</li>
+<li>
+<p>returns its value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterSubtract</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>subtracts the value of <em>data</em> from the counter for <em>c</em>, and</p>
+</li>
+<li>
+<p>returns its value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterMin</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>sets the counter for <em>c</em> to the minimum of the value of the counter and
+the value of <em>data</em>, and</p>
+</li>
+<li>
+<p>returns the value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterMax</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>sets the counter for <em>c</em> to the maximum of the value of the counter and
+the value of <em>data</em>, and</p>
+</li>
+<li>
+<p>returns the value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterAnd</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>sets the counter for <em>c</em> to the bitwise AND of the value of the counter
+and the value of <em>data</em>, and</p>
+</li>
+<li>
+<p>returns the value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterOr</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>sets the counter for <em>c</em> to the bitwise OR of the value of the counter
+and the value of <em>data</em>, and</p>
+</li>
+<li>
+<p>returns the value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterXor</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>sets the counter for <em>c</em> to the bitwise XOR of the value of the counter
+and the value of <em>data</em>, and</p>
+</li>
+<li>
+<p>returns the value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterExchange</strong>(atomic_uint <em>c</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>sets the counter value for <em>c</em> to the value of <em>data</em>, and</p>
+</li>
+<li>
+<p>returns its value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These two steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCounterCompSwap</strong>(atomic_uint <em>c</em>, uint <em>compare</em>, uint <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><div class="content"><div class="paragraph">
+<p>Atomically<br></p>
+</div>
+<div class="openblock">
+<div class="content">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>compares the value of <em>compare</em> and the counter value for <em>c</em></p>
+</li>
+<li>
+<p>if the values are equal, sets the counter value for <em>c</em> to the value of
+<em>data</em>, and</p>
+</li>
+<li>
+<p>returns its value prior to the operation.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>These three steps are done atomically with respect to the atomic counter
+functions in this table.</p>
+</div>
+</div>
+</div></div></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="atomic-memory-functions">8.11. Atomic Memory Functions</h3>
+<div class="paragraph">
+<p>Atomic memory functions perform atomic operations on an individual signed or
+unsigned integer stored in buffer object or shared variable storage.
+All of the atomic memory operations read a value from memory, compute a new
+value using one of the operations described below, write the new value to
+memory, and return the original value read.
+The contents of the memory being updated by the atomic operation are
+guaranteed not to be modified by any other assignment or atomic memory
+function in any shader invocation between the time the original value is
+read and the time the new value is written.</p>
+</div>
+<div class="paragraph">
+<p>Atomic memory functions are supported only for a limited set of variables.
+A shader will fail to compile if the value passed to the <em>mem</em> argument of
+an atomic memory function does not correspond to a buffer or shared
+variable.
+It is acceptable to pass an element of an array or a single component of a
+vector to the <em>mem</em> argument of an atomic memory function, as long as the
+underlying array or vector is a buffer or shared variable.</p>
+</div>
+<div class="paragraph">
+<p>All the built-in functions in this section accept arguments with
+combinations of <strong>restrict</strong>, <strong>coherent</strong>, and <strong>volatile</strong> memory qualification,
+despite not having them listed in the prototypes.
+The atomic operation will operate as required by the calling argument&#8217;s
+memory qualification, not by the built-in function&#8217;s formal parameter memory
+qualification.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicAdd</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicAdd</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by adding the value of <em>data</em> to the contents
+      <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicMin</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicMin</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the minimum of the value of <em>data</em> and
+      the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicMax</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicMax</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the maximum of the value of <em>data</em> and
+      the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicAnd</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicAnd</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise AND of the value of
+      <em>data</em> and the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicOr</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicOr</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise OR of the value of
+      <em>data</em> and the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicXor</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicXor</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise EXCLUSIVE OR of the
+      value of <em>data</em> and the contents of <em>mem</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicExchange</strong>(inout uint <em>mem</em>, uint <em>data</em>)<br>
+  int <strong>atomicExchange</strong>(inout int <em>mem</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by simply copying the value of <em>data</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">uint <strong>atomicCompSwap</strong>(inout uint <em>mem</em>, uint <em>compare</em>, uint <em>data</em>)<br>
+  int <strong>atomicCompSwap</strong>(inout int <em>mem</em>, int <em>compare</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Compares the value of <em>compare</em> and the contents of <em>mem</em>.
+      If the values are equal, the new value is given by <em>data</em>; otherwise,
+      it is taken from the original contents of <em>mem</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="image-functions">8.12. Image Functions</h3>
+<div class="paragraph">
+<p>Variables using one of the image basic types may be used by the built-in
+shader image memory functions defined in this section to read and write
+individual texels of a texture.
+Each image variable references an image unit, which has a texture image
+attached.</p>
+</div>
+<div class="paragraph">
+<p>When image memory functions below access memory, an individual texel in the
+image is identified using an (<em>i</em>), (<em>i, j</em>), or (<em>i, j, k</em>) coordinate
+corresponding to the values of <em>P</em>.
+For <strong>image2DMS</strong> and <strong>image2DMSArray</strong> variables (and the corresponding
+int/unsigned int types) corresponding to multisample textures, each texel
+may have multiple samples and an individual sample is identified using the
+integer <em>sample</em> parameter.
+The coordinates
+and sample number
+are used to select an individual texel in the manner described in section
+8.26
+&#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>Loads and stores support float, integer, and unsigned integer types.
+The data types below starting &#8220;_gimage_&#8221; serve as placeholders meaning
+types starting either &#8220;<strong>image</strong>&#8221;, &#8220;<strong>iimage</strong>&#8221;, or &#8220;<strong>uimage</strong>&#8221; in the same
+way as <em>gvec</em> or <em>gsampler</em> in earlier sections.</p>
+</div>
+<div class="paragraph">
+<p>The <em>IMAGE_PARAMS</em> in the prototypes below is a placeholder representing
+33
+separate functions, each for a different type of image variable.
+The <em>IMAGE_PARAMS</em> placeholder is replaced by one of the following parameter
+lists:</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2D <em>image</em>, ivec2 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage3D <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimageCube <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimageBuffer <em>image</em>, int <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2DArray <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimageCubeArray <em>image</em>, ivec3 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage1D <em>image</em>, int <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage1DArray <em>image</em>, ivec2 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2DRect <em>image</em>, ivec2 <em>P</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2DMS <em>image</em>, ivec2 <em>P</em>, int <em>sample</em></p>
+</dd>
+<dt class="hdlist1"></dt>
+<dd>
+<p>gimage2DMSArray <em>image</em>, ivec3 <em>P</em>, int <em>sample</em></p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>where each of the lines represents one of three different image variable
+types, and <em>image</em>,
+<em>P</em>, and <em>sample</em>
+specify the individual texel to operate on.
+The method for identifying the individual texel operated on from <em>image</em>,
+<em>P</em>,
+and <em>sample</em>,
+and the method for reading and writing the texel are specified in section
+8.26
+&#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL Specification</a>.</p>
+</div>
+<div class="paragraph">
+<p>The atomic functions perform operations on individual texels or samples of
+an image variable.
+Atomic memory operations read a value from the selected texel, compute a new
+value using one of the operations described below, write the new value to
+the selected texel, and return the original value read.
+The contents of the texel being updated by the atomic operation are
+guaranteed not to be modified by any other image store or atomic function
+between the time the original value is read and the time the new value is
+written.</p>
+</div>
+<div class="paragraph">
+<p>Atomic memory operations are supported on only a subset of all image
+variable types; <em>image</em> must be either:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>a signed integer image variable (type starts &#8220;<strong>iimage</strong>&#8221;) and a format
+qualifier of <strong>r32i</strong>, used with a <em>data</em> argument of type <strong>int</strong>, or</p>
+</li>
+<li>
+<p>an unsigned integer image variable (type starts &#8220;<strong>uimage</strong>&#8221;) and a
+format qualifier of <strong>r32ui</strong>, used with a <em>data</em> argument of type <strong>uint</strong>,
+or</p>
+</li>
+<li>
+<p>a float image variable (type starts &#8220;<strong>image</strong>&#8221;) and a format qualifier
+of <strong>r32f</strong>, used with a <em>data</em> argument of type <strong>float</strong>
+(<strong>imageAtomicExchange</strong> only).</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>All the built-in functions in this section accept arguments with
+combinations of <strong>restrict</strong>, <strong>coherent</strong>, and <strong>volatile</strong> memory qualification,
+despite not having them listed in the prototypes.
+The image operation will operate as required by the calling argument&#8217;s
+memory qualification, not by the built-in function&#8217;s formal parameter memory
+qualification.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">   int <strong>imageSize</strong>(readonly writeonly gimage1D <em>image</em>)<br>
+   ivec2 <strong>imageSize</strong>(readonly writeonly gimage2D <em>image</em>)<br>
+   ivec3 <strong>imageSize</strong>(readonly writeonly gimage3D <em>image</em>)<br>
+   ivec2 <strong>imageSize</strong>(readonly writeonly gimageCube <em>image</em>)<br>
+   ivec3 <strong>imageSize</strong>(readonly writeonly gimageCubeArray <em>image</em>)<br>
+   ivec3 <strong>imageSize</strong>(readonly writeonly gimage2DArray <em>image</em>)<br>
+   ivec2 <strong>imageSize</strong>(readonly writeonly gimageRect <em>image</em>)<br>
+   ivec2 <strong>imageSize</strong>(readonly writeonly gimage1DArray <em>image</em>)<br>
+   ivec2 <strong>imageSize</strong>(readonly writeonly gimage2DMS <em>image</em>)<br>
+   ivec3 <strong>imageSize</strong>(readonly writeonly gimage2DMSArray <em>image</em>)<br>
+     int <strong>imageSize</strong>(readonly writeonly gimageBuffer <em>image</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the dimensions of the image or images bound to <em>image</em>.
+      For arrayed images, the last component of the return value will hold
+      the size of the array.
+      Cube images only return the dimensions of one face, and the number of
+      cubes in the cube map array, if arrayed.<br>
+      Note: The qualification <strong>readonly writeonly</strong> accepts a variable
+      qualified with <strong>readonly</strong>, <strong>writeonly</strong>, both, or neither.
+      It means the formal argument will be used for neither reading nor
+      writing to the underlying memory.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">int <strong>imageSamples</strong>(readonly writeonly gimage2DMS <em>image</em>)<br>
+  int <strong>imageSamples</strong>(readonly writeonly gimage2DMSArray <em>image</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the number of samples of the image or images bound to <em>image</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> gvec4 <strong>imageLoad</strong>(readonly <em>IMAGE_PARAMS</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Loads the texel at the coordinate <em>P</em> from the image unit <em>image</em> (in
+      <em>IMAGE_PARAMS</em>).
+      For multisample loads, the sample number is given by <em>sample</em>.
+      When <em>image</em>, <em>P</em>, and <em>sample</em>
+      identify a valid texel, the bits used to represent the selected texel in
+      memory are converted to a <strong>vec4</strong>, <strong>ivec4</strong>, or <strong>uvec4</strong> in the manner
+      described in section
+8.26
+      &#8220;Texture Image Loads and Stores&#8221; of the
+      <a href="#references">OpenGL Specification</a> and returned.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>imageStore</strong>(writeonly <em>IMAGE_PARAMS</em>, gvec4 <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Stores <em>data</em> into the texel at the coordinate <em>P</em> from the image
+      specified by <em>image</em>.
+      For multisample stores, the sample number is given by <em>sample</em>.
+      When <em>image</em>, <em>P</em>, and <em>sample</em>
+      identify a valid texel, the bits used to represent <em>data</em> are converted
+      to the format of the image unit in the manner described in section
+8.26
+      &#8220;Texture Image Loads and Stores&#8221; of the <a href="#references">OpenGL Specification</a>
+      and stored to the specified texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicAdd</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicAdd</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by adding the value of <em>data</em> to the contents of
+      the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicMin</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicMin</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the minimum of the value of <em>data</em> and
+      the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicMax</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicMax</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by taking the maximum of the value <em>data</em> and the
+      contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicAnd</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicAnd</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise AND of the value of
+      <em>data</em> and the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicOr</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicOr</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise OR of the value of
+      <em>data</em> and the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicXor</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicXor</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by performing a bit-wise EXCLUSIVE OR of the
+      value of <em>data</em> and the contents of the selected texel.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicExchange</strong>(<em>IMAGE_PARAMS</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicExchange</strong>(<em>IMAGE_PARAMS</em>, int <em>data</em>)<br>
+   float <strong>imageAtomicExchange</strong>(<em>IMAGE_PARAMS</em>, float <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Computes a new value by simply copying the value of <em>data</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock"> uint <strong>imageAtomicCompSwap</strong>(<em>IMAGE_PARAMS</em>, uint <em>compare</em>, uint <em>data</em>)<br>
+   int <strong>imageAtomicCompSwap</strong>(<em>IMAGE_PARAMS</em>, int <em>compare</em>, int <em>data</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Compares the value of <em>compare</em> and the contents of the selected
+      texel.
+      If the values are equal, the new value is given by <em>data</em>; otherwise,
+      it is taken from the original value loaded from the texel.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="geometry-shader-functions">8.13. Geometry Shader Functions</h3>
+<div class="paragraph">
+<p>These functions are only available in geometry shaders.
+They are described in more depth following the table.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>EmitStreamVertex</strong>(int <em>stream</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Emits the current values of output variables to the current output
+      primitive on stream <em>stream</em>.
+      The argument to <em>stream</em> must be a constant integral expression.
+      On return from this call, the values of all output variables are
+      undefined.<br>
+      Can only be used if multiple output streams are supported.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>EndStreamPrimitive</strong>(int <em>stream</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Completes the current output primitive on stream <em>stream</em> and starts a
+      new one.
+      The argument to <em>stream</em> must be a constant integral expression.
+      No vertex is emitted.<br>
+      Can only be used if multiple output streams are supported.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>EmitVertex</strong>()<br></p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Emits the current values of output variables to the current output
+      primitive.
+      When multiple output streams are supported, this is equivalent to
+      calling <strong>EmitStreamVertex</strong>(0).<br>
+      On return from this call, the values of output variables are
+      undefined.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>EndPrimitive</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Completes the current output primitive and starts a new one.
+      When multiple output streams are supported, this is equivalent to
+      calling <strong>EndStreamPrimitive</strong>(0).<br>
+      No vertex is emitted.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The function <strong>EmitStreamVertex</strong>() specifies that a vertex is completed.
+A vertex is added to the current output primitive in vertex stream <em>stream</em>
+using the current values of all built-in and user-defined output variables
+associated with <em>stream</em>.
+The values of all output variables for all output streams are undefined
+after a call to <strong>EmitStreamVertex</strong>().
+If a geometry shader invocation has emitted more vertices than permitted by
+the output layout qualifier <strong>max_vertices</strong>, the results of calling
+<strong>EmitStreamVertex</strong>() are undefined.</p>
+</div>
+<div class="paragraph">
+<p>The function <strong>EndStreamPrimitive</strong>() specifies that the current output
+primitive for vertex stream <em>stream</em> is completed and a new output primitive
+(of the same type) will be started by any subsequent <strong>EmitStreamVertex</strong>().
+This function does not emit a vertex.
+If the output layout is declared to be <strong>points</strong>, calling
+<strong>EndStreamPrimitive</strong>() is optional.</p>
+</div>
+<div class="paragraph">
+<p>A geometry shader starts with an output primitive containing no vertices for
+each stream.
+When a geometry shader terminates, the current output primitive for each
+stream is automatically completed.
+It is not necessary to call <strong>EndStreamPrimitive</strong>() if the geometry shader
+writes only a single primitive.</p>
+</div>
+<div class="paragraph">
+<p>Multiple output streams are supported only if the output primitive type is
+declared to be <strong>points</strong>.
+It is a compile-time or link-time error if a program contains a geometry
+shader calling <strong>EmitStreamVertex</strong>() or <strong>EndStreamPrimitive</strong>() if its output
+primitive type is not <strong>points</strong>.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="fragment-processing-functions">8.14. Fragment Processing Functions</h3>
+<div class="paragraph">
+<p>Fragment processing functions are only available in fragment shaders.</p>
+</div>
+<div class="sect3">
+<h4 id="derivative-functions">8.14.1. Derivative Functions</h4>
+<div class="paragraph">
+<p>Derivatives may be computationally expensive and/or numerically unstable.
+Therefore, an OpenGL implementation may approximate the true derivatives
+by using a fast but not entirely accurate derivative computation.
+Derivatives are undefined within non-uniform control flow.</p>
+</div>
+<div class="paragraph">
+<p>The expected behavior of a derivative is specified using forward/backward
+differencing.</p>
+</div>
+<div class="paragraph">
+<p>Forward differencing:</p>
+</div>
+<div class="paragraph">
+<p>\(F(x+dx) - F(x) \sim dFdx(x) \cdot dx (1a)\)</p>
+</div>
+<div class="paragraph">
+<p>\(dFdx(x) \sim \frac{F(x+dx) - F(x)}{dx} (1b)\)</p>
+</div>
+<div class="paragraph">
+<p>Backward differencing:</p>
+</div>
+<div class="paragraph">
+<p>\(F(x-dx) - F(x) \sim -dFdx(x) \cdot dx (2a)\)</p>
+</div>
+<div class="paragraph">
+<p>\(dFdx(x) \sim \frac{F(x) - F(x-dx)}{dx} (2b)\)</p>
+</div>
+<div class="paragraph">
+<p>With single-sample rasterization, \(dx \leq 1.0\) in equations 1b
+and 2b.
+For multisample rasterization, \(dx &lt; 2.0\) in equations 1b and 2b.</p>
+</div>
+<div class="paragraph">
+<p>\(dFdy\) is approximated similarly, with <em>y</em> replacing <em>x</em>.</p>
+</div>
+<div class="paragraph">
+<p>With multisample rasterization, for any given fragment or sample, either
+neighboring fragments or samples may be considered.</p>
+</div>
+<div class="paragraph">
+<p>It is typical to consider a 2x2 square of fragments or samples, and compute
+independent <strong>dFdxFine</strong> per row and independent <strong>dFdyFine</strong> per column, while
+computing only a single <strong>dFdxCoarse</strong> and a single <strong>dFdyCoarse</strong> for the
+entire 2x2 square.
+Thus, all second-order coarse derivatives, e.g.
+<strong>dFdxCoarse</strong>(<strong>dFdxCoarse</strong>(<em>x</em>)), may be 0, even for non-linear arguments.
+However, second-order fine derivatives, e.g. <strong>dFdxFine</strong>(<strong>dFdyFine</strong>(<em>x</em>))
+will properly reflect the difference between the independent fine
+derivatives computed within the 2x2 square.</p>
+</div>
+<div class="paragraph">
+<p>The method may differ per fragment, subject to the constraint that the
+method may vary by window coordinates, not screen coordinates.
+The invariance requirement described in section 14.2 &#8220;Invariance&#8221; of the
+<a href="#references">OpenGL Specification</a>, is relaxed for derivative calculations, because
+the method may be a function of fragment location.</p>
+</div>
+<div class="paragraph">
+<p>In some implementations, varying degrees of derivative accuracy for <strong>dFdx</strong>
+and <strong>dFdy</strong> may be obtained by providing GL hints (see section 21.4 &#8220;Hints&#8221;
+of the <a href="#references">OpenGL Specification</a>), allowing a user to make an image quality
+versus speed trade off.
+These hints have no effect on <strong>dFdxCoarse</strong>, <strong>dFdyCoarse</strong>, <strong>dFdxFine</strong> and
+<strong>dFdyFine</strong>.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdx</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns either <strong>dFdxFine</strong>(<em>p</em>) or <strong>dFdxCoarse</strong>(<em>p</em>), based on
+      implementation choice, presumably whichever is the faster, or by whichever
+      is selected in the API through quality-versus-speed hints.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdy</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns either <strong>dFdyFine</strong>(<em>p</em>) or <strong>dFdyCoarse</strong>(<em>p</em>), based on
+      implementation choice, presumably whichever is the faster, or by
+      whichever is selected in the API through quality-versus-speed hints.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdxFine</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the partial derivative of <em>p</em> with respect to the window x
+      coordinate.
+      Will use local differencing based on the value of <em>p</em> for the current
+      fragment and its immediate neighbor(s).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdyFine</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the partial derivative of <em>p</em> with respect to the window y
+      coordinate.
+      Will use local differencing based on the value of <em>p</em> for the current
+      fragment and its immediate neighbor(s).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdxCoarse</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the partial derivative of <em>p</em> with respect to the window x
+      coordinate.
+      Will use local differencing based on the value of <em>p</em> for the current
+      fragment&#8217;s neighbors, and will possibly, but not necessarily, include
+      the value of <em>p</em> for the current fragment.
+      That is, over a given area, the implementation can x compute
+      derivatives in fewer unique locations than would be allowed for
+      <strong>dFdxFine</strong>(<em>p</em>).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>dFdyCoarse</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the partial derivative of <em>p</em> with respect to the window y
+      coordinate.
+      Will use local differencing based on the value of <em>p</em> for the current
+      fragment&#8217;s neighbors, and will possibly, but not necessarily, include
+      the value of <em>p</em> for the current fragment.
+      That is, over a given area, the implementation can compute y
+      derivatives in fewer unique locations than would be allowed for
+      <strong>dFdyFine</strong>(<em>p</em>).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fwidth</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>abs</strong>(<strong>dFdx</strong>(<em>p</em>)) + <strong>abs</strong>(<strong>dFdy</strong>(<em>p</em>)).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fwidthFine</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>abs</strong>(<strong>dFdxFine</strong>(<em>p</em>)) + <strong>abs</strong>(<strong>dFdyFine</strong>(<em>p</em>)).</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">genFType <strong>fwidthCoarse</strong>(genFType <em>p</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>abs</strong>(<strong>dFdxCoarse</strong>(<em>p</em>)) + <strong>abs</strong>(<strong>dFdyCoarse</strong>(<em>p</em>)).</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect3">
+<h4 id="interpolation-functions">8.14.2. Interpolation Functions</h4>
+<div class="paragraph">
+<p>Built-in interpolation functions are available to compute an interpolated
+value of a fragment shader input variable at a shader-specified (<em>x</em>, <em>y</em>)
+location.
+A separate (<em>x</em>, <em>y</em>) location may be used for each invocation of the
+built-in function, and those locations may differ from the default (<em>x</em>,
+<em>y</em>) location used to produce the default value of the input.</p>
+</div>
+<div class="paragraph">
+<p>For all of the interpolation functions, <em>interpolant</em> must be an l-value
+from an <strong>in</strong> declaration;
+this can include a variable, a block or structure member, an array element, or
+some combination of these.
+Additionally, component selection operators (e.g. <strong>.xy</strong>, <strong>.xxz</strong>) may be applied
+to <em>interpolant</em>, in which case the interpolation function will return the
+result of applying the component selection operator to the interpolated value
+of <em>interpolant</em> (for example, interpolateAt(v.xxz) is defined to return
+interpolateAt(v).xxz).
+Arrayed inputs can be indexed with general (nonuniform) integer expressions.</p>
+</div>
+<div class="paragraph">
+<p>If <em>interpolant</em> is declared with the <strong>flat</strong> qualifier, the interpolated
+value will have the same value everywhere for a single primitive, so the
+location used for interpolation has no effect and the functions just return
+that same value.
+If <em>interpolant</em> is declared with the <strong>centroid</strong> qualifier, the value
+returned by <strong>interpolateAtSample</strong>() and <strong>interpolateAtOffset</strong>() will be
+evaluated at the specified location, ignoring the location normally used
+with the <strong>centroid</strong> qualifier.
+If <em>interpolant</em> is declared with the <strong>noperspective</strong> qualifier, the
+interpolated value will be computed without perspective correction.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>interpolateAtCentroid</strong>(float <em>interpolant</em>)<br>
+  vec2 <strong>interpolateAtCentroid</strong>(vec2 <em>interpolant</em>)<br>
+  vec3 <strong>interpolateAtCentroid</strong>(vec3 <em>interpolant</em>)<br>
+  vec4 <strong>interpolateAtCentroid</strong>(vec4 <em>interpolant</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the value of the input <em>interpolant</em> sampled at a location
+      inside both the pixel and the primitive being processed.
+      The value obtained would be the same value assigned to the input
+      variable if declared with the <strong>centroid</strong> qualifier.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>interpolateAtSample</strong>(float <em>interpolant</em>, int <em>sample</em>)<br>
+  vec2 <strong>interpolateAtSample</strong>(vec2 <em>interpolant</em>, int <em>sample</em>)<br>
+  vec3 <strong>interpolateAtSample</strong>(vec3 <em>interpolant</em>, int <em>sample</em>)<br>
+  vec4 <strong>interpolateAtSample</strong>(vec4 <em>interpolant</em>, int <em>sample</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the value of the input <em>interpolant</em> variable at the location
+      of sample number <em>sample</em>.
+      If multisample buffers are not available, the input variable will be
+      evaluated at the center of the pixel.
+      If sample <em>sample</em> does not exist, the position used to interpolate
+      the input variable is undefined.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>interpolateAtOffset</strong>(float <em>interpolant</em>, vec2 offset)<br>
+  vec2 <strong>interpolateAtOffset</strong>(vec2 <em>interpolant</em>, vec2 offset)<br>
+  vec3 <strong>interpolateAtOffset</strong>(vec3 <em>interpolant</em>, vec2 offset)<br>
+  vec4 <strong>interpolateAtOffset</strong>(vec4 <em>interpolant</em>, vec2 offset)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the value of the input <em>interpolant</em> variable sampled at an
+      offset from the center of the pixel specified by <em>offset</em>.
+      The two floating-point components of <em>offset</em>, give the offset in
+      pixels in the <em>x</em> and <em>y</em> directions, respectively.<br>
+      An offset of (0, 0) identifies the center of the pixel.
+      The range and granularity of offsets supported by this function is
+      implementation-dependent.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect2">
+<h3 id="noise-functions">8.15. Noise Functions</h3>
+<div class="paragraph">
+<p>The noise functions <strong>noise1</strong>, <strong>noise2</strong>, <strong>noise3</strong>, and <strong>noise4</strong> have been
+deprecated starting with version 4.4 of GLSL.
+When not generating SPIR-V they are defined to return the value 0.0 or a vector
+whose components are all 0.0. When generating SPIR-V the noise functions are
+not declared and may not be used.</p>
+</div>
+<div class="paragraph">
+<p>As in previous releases, the noise functions are not semantically considered to
+be compile-time constant expressions.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax (deprecated)</th>
+<th class="tableblock halign-left valign-top">Description (deprecated)</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">float <strong>noise1</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a 1D noise value based on the input value <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec2 <strong>noise2</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a 2D noise value based on the input value <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec3 <strong>noise3</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a 3D noise value based on the input value <em>x</em>.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">vec4 <strong>noise4</strong>(genFType <em>x</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a 4D noise value based on the input value <em>x</em>.</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="sect2">
+<h3 id="shader-invocation-control-functions">8.16. Shader Invocation Control Functions</h3>
+<div class="paragraph">
+<p>The shader invocation control function is only available in tessellation
+control and compute shaders.
+It is used to control the relative execution order of multiple shader
+invocations used to process a patch (in the case of tessellation control
+shaders) or a workgroup (in the case of compute shaders), which are
+otherwise executed with an undefined relative order.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>barrier</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">For any given static instance of <strong>barrier</strong>(), all tessellation control
+      shader invocations for a single input patch must enter it before any
+      will be allowed to continue beyond it, or all compute shader
+      invocations for a single workgroup must enter it before any will
+      continue beyond it.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The function <strong>barrier</strong>() provides a partially defined order of execution
+between shader invocations.
+The ensures that, for some types of memory accesses, values written by one
+invocation prior to a given static instance of <strong>barrier</strong>() can be safely read
+by other invocations after their call to the same static instance <strong>barrier</strong>().
+Because invocations may execute in an undefined order between these barrier
+calls, the values of a per-vertex or per-patch output variable for tessellation
+control shaders, or the values of <strong>shared</strong> variables for compute shaders will be
+undefined in a number of cases enumerated in
+&#8220;<a href="#output-variables">Output Variables</a>&#8221; (for tessellation control shaders)
+and &#8220;<a href="#shared-variables">Shared Variables</a>&#8221; (for compute shaders).</p>
+</div>
+<div class="paragraph">
+<p>For tessellation control shaders, the <strong>barrier</strong>() function may only be
+placed inside the function <strong>main</strong>() of the shader and may not be called
+within any control flow.
+Barriers are also disallowed after a return statement in the function
+<strong>main</strong>().
+Any such misplaced barriers result in a compile-time error.</p>
+</div>
+<div class="paragraph">
+<p>A <strong>barrier</strong>() affects control flow but only synchronizes memory accesses
+to <strong>shared</strong> variables and tessellation control output variables.
+For other memory accesses, it does not ensure that values written by one invocation
+prior to a given static instance of <strong>barrier</strong>() can be safely read by other
+invocations after their call to the same static instance of <strong>barrier</strong>().
+To achieve this requires the use of both <strong>barrier</strong>() and a memory barrier.</p>
+</div>
+<div class="paragraph">
+<p>For compute shaders, the <strong>barrier</strong>() function may be placed within control
+flow, but that control flow must be uniform control flow.
+That is, all the controlling expressions that lead to execution of the
+barrier must be dynamically uniform expressions.
+This ensures that if any shader invocation enters a conditional statement,
+then all invocations will enter it.
+While compilers are encouraged to give warnings if they can detect this
+might not happen, compilers cannot completely determine this.
+Hence, it is the author&#8217;s responsibility to ensure <strong>barrier</strong>() only exists
+inside uniform control flow.
+Otherwise, some shader invocations will stall indefinitely, waiting for a
+barrier that is never reached by other invocations.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="shader-memory-control-functions">8.17. Shader Memory Control Functions</h3>
+<div class="paragraph">
+<p>Within a single shader invocation, the visibility and order of writes made
+by that invocation are well-defined.
+However, the relative order of reads and writes to a single shared memory
+address from multiple separate shader invocations is largely undefined.
+Additionally, the order of accesses to multiple memory addresses performed
+by a single shader invocation, as observed by other shader invocations, is
+also undefined.</p>
+</div>
+<div class="paragraph">
+<p>The following built-in functions can be used to control the ordering of
+reads and writes:</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrier</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions issued by a single shader
+      invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierAtomicCounter</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of accesses to atomic-counter variables issued by
+      a single shader invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierBuffer</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions to buffer variables issued
+      within a single shader invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierShared</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions to shared variables issued
+      within a single shader invocation, as viewed by other invocations in
+      the same workgroup.<br>
+      Only available in compute shaders.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>memoryBarrierImage</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of memory transactions to images issued within a
+      single shader invocation.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">void <strong>groupMemoryBarrier</strong>()</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Control the ordering of all memory transactions issued within a single
+      shader invocation, as viewed by other invocations in the same workgroup.<br>
+      Only available in compute shaders.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>The memory barrier built-in functions can be used to order reads and writes
+to variables stored in memory accessible to other shader invocations.
+When called, these functions will wait for the completion of all reads and
+writes previously performed by the caller that access selected variable
+types, and then return with no other effect.
+The built-in functions <strong>memoryBarrierAtomicCounter</strong>(),
+<strong>memoryBarrierBuffer</strong>(), <strong>memoryBarrierImage</strong>(), and <strong>memoryBarrierShared</strong>()
+wait for the completion of accesses to atomic counter, buffer, image, and
+shared variables, respectively.
+The built-in functions <strong>memoryBarrier</strong>() and <strong>groupMemoryBarrier</strong>() wait for
+the completion of accesses to all of the above variable types.
+The functions <strong>memoryBarrierShared</strong>() and <strong>groupMemoryBarrier</strong>() are
+available only in compute shaders; the other functions are available in all
+shader types.</p>
+</div>
+<div class="paragraph">
+<p>When these functions return, the effects of any memory stores performed
+using coherent variables prior to the call will be visible to any
+future<sup>1</sup> coherent access to the same memory performed by any other shader
+invocation.
+In particular, the values written this way in one shader stage are
+guaranteed to be visible to coherent memory accesses performed by shader
+invocations in subsequent stages when those invocations were triggered by
+the execution of the original shader invocation (e.g. fragment shader
+invocations for a primitive resulting from a particular geometry
+shader invocation).</p>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1">1</dt>
+<dd>
+<p>An access is only a <em>future</em> access if a <em>happens-before</em> relation can
+be established between the store and the load.</p>
+</dd>
+</dl>
+</div>
+<div class="paragraph">
+<p>Additionally, memory barrier functions order stores performed by the calling
+invocation, as observed by other shader invocations.
+Without memory barriers, if one shader invocation performs two stores to
+coherent variables, a second shader invocation might see the values written
+by the second store prior to seeing those written by the first.
+However, if the first shader invocation calls a memory barrier function
+between the two stores, selected other shader invocations will never see the
+results of the second store before seeing those of the first.
+When using the functions <strong>groupMemoryBarrier</strong>() or <strong>memoryBarrierShared</strong>(),
+this ordering guarantee applies only to other shader invocations in the same
+compute shader workgroup; all other memory barrier functions provide the
+guarantee to all other shader invocations.
+No memory barrier is required to guarantee the order of memory stores as
+observed by the invocation performing the stores; an invocation reading from
+a variable that it previously wrote will always see the most recently
+written value unless another shader invocation also wrote to the same
+memory.</p>
+</div>
+</div>
+<div class="sect2">
+<h3 id="shader-invocation-group-functions">8.18. Shader Invocation Group Functions</h3>
+<div class="paragraph">
+<p>Implementations of the OpenGL Shading Language may optionally group multiple shader
+invocations for a single shader stage into a single SIMD invocation group,
+where invocations are assigned to groups in an undefined,
+implementation-dependent manner.
+Shader algorithms on such implementations may benefit from being able to
+evaluate a composite of Boolean values over all active invocations in a
+group.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">Syntax</th>
+<th class="tableblock halign-left valign-top">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>anyInvocation</strong>(bool <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if and only if <em>value</em> is <strong>true</strong> for at least one
+      active invocation in the group.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>allInvocations</strong>(bool <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if and only if <em>value</em> is <strong>true</strong> for all active
+      invocations in the group.</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">bool <strong>allInvocationsEqual</strong>(bool <em>value</em>)</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>true</strong> if <em>value</em> is the same for all active invocations in
+      the group.</p></td>
+</tr>
+</tbody>
+</table>
+<div class="paragraph">
+<p>For all of these functions, the same result is returned to all active
+invocations in the group.</p>
+</div>
+<div class="paragraph">
+<p>These functions may be called within conditionally executed code.
+In groups where some invocations do not execute the function call, the value
+returned by the function is not affected by any invocation not calling the
+function, even when value is well-defined for that invocation.</p>
+</div>
+<div class="paragraph">
+<p>Because these functions depend on the values of <em>value</em> in an undefined
+group of invocations, the value returned by these functions is largely
+undefined.
+However, <strong>anyInvocation</strong>() is guaranteed to return <strong>true</strong> if <em>value</em> is
+<strong>true</strong>, and <strong>allInvocations</strong>() is guaranteed to return <strong>false</strong> if <em>value</em> is
+<strong>false</strong>.</p>
+</div>
+<div class="paragraph">
+<p>Because implementations are not required to combine invocations into groups,
+simply returning <em>value</em> for <strong>anyInvocation</strong>() and <strong>allInvocations</strong>() and
+returning true for <strong>allInvocationsEqual</strong>() is a legal implementation of
+these functions.</p>
+</div>
+<div class="paragraph">
+<p>For fragment shaders, invocations in a SIMD invocation group may include
+invocations corresponding to pixels that are covered by a primitive being
+rasterized, as well as invocations corresponding to neighboring pixels not
+covered by the primitive.
+<em>Helper invocations</em> (see &#8220;<a href="#built-in-language-variables">Built-In Language
+Variables</a>&#8221;) may be created and the value of <em>value</em> for such
+helper-invocation pixels may affect the value returned by <strong>anyInvocation</strong>(),
+<strong>allInvocations</strong>(), and <strong>allInvocationsEqual</strong>().</p>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="shading-language-grammar">9. Shading Language Grammar</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>The grammar is fed from the output of lexical analysis.
+The tokens returned from lexical analysis are</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="CodeRay highlight"><code data-lang="c++">CONST BOOL FLOAT INT UINT
+DOUBLE
+
+BVEC2 BVEC3 BVEC4 IVEC2 IVEC3 IVEC4 UVEC2 UVEC3 UVEC4 VEC2 VEC3 VEC4
+
+MAT2 MAT3 MAT4 CENTROID IN OUT INOUT
+
+UNIFORM PATCH SAMPLE BUFFER SHARED
+
+COHERENT VOLATILE RESTRICT READONLY WRITEONLY
+
+NOPERSPECTIVE
+FLAT SMOOTH LAYOUT
+
+MAT2X2 MAT2X3 MAT2X4
+
+MAT3X2 MAT3X3 MAT3X4
+
+MAT4X2 MAT4X3 MAT4X4
+
+DVEC2 DVEC3 DVEC4 DMAT2 DMAT3 DMAT4
+
+DMAT2X2 DMAT2X3 DMAT2X4
+
+DMAT3X2 DMAT3X3 DMAT3X4
+
+DMAT4X2 DMAT4X3 DMAT4X4
+
+ATOMIC_UINT
+
+SAMPLER2D SAMPLER3D SAMPLERCUBE SAMPLER2DSHADOW
+
+SAMPLERCUBESHADOW SAMPLER2DARRAY SAMPLER2DARRAYSHADOW
+
+ISAMPLER2D ISAMPLER3D ISAMPLERCUBE ISAMPLER2DARRAY
+
+USAMPLER2D USAMPLER3D USAMPLERCUBE USAMPLER2DARRAY
+
+SAMPLER1D SAMPLER1DSHADOW
+
+SAMPLER1DARRAY SAMPLER1DARRAYSHADOW
+
+ISAMPLER1D ISAMPLER1DARRAY
+
+USAMPLER1D USAMPLER1DARRAY
+
+SAMPLER2DRECT SAMPLER2DRECTSHADOW ISAMPLER2DRECT USAMPLER2DRECT
+
+SAMPLERBUFFER ISAMPLERBUFFER USAMPLERBUFFER
+
+SAMPLERCUBEARRAY SAMPLERCUBEARRAYSHADOW
+
+ISAMPLERCUBEARRAY USAMPLERCUBEARRAY
+
+SAMPLER2DMS ISAMPLER2DMS USAMPLER2DMS
+
+SAMPLER2DMSARRAY ISAMPLER2DMSARRAY USAMPLER2DMSARRAY
+
+IMAGE2D IIMAGE2D UIMAGE2D
+
+IMAGE3D IIMAGE3D UIMAGE3D
+
+IMAGECUBE IIMAGECUBE UIMAGECUBE
+
+IMAGEBUFFER IIMAGEBUFFER UIMAGEBUFFER
+
+IMAGE2DARRAY IIMAGE2DARRAY UIMAGE2DARRAY
+
+IMAGECUBEARRAY IIMAGECUBEARRAY UIMAGECUBEARRAY
+
+IMAGE1D IIMAGE1D UIMAGE1D
+
+IMAGE1DARRAY IIMAGE1DARRAY UIMAGE1DARRAY
+
+IMAGE2DRECT IIMAGE2DRECT UIMAGE2DRECT
+
+IMAGE2DMS IIMAGE2DMS UIMAGE2DMS
+
+IMAGE2DMSARRAY IIMAGE2DMSARRAY UIMAGE2DMSARRAY
+
+STRUCT VOID
+
+WHILE BREAK CONTINUE DO ELSE FOR IF DISCARD RETURN SWITCH CASE DEFAULT
+SUBROUTINE
+
+IDENTIFIER TYPE_NAME
+
+FLOATCONSTANT INTCONSTANT UINTCONSTANT BOOLCONSTANT
+DOUBLECONSTANT
+
+FIELD_SELECTION
+
+LEFT_OP RIGHT_OP
+
+INC_OP DEC_OP LE_OP GE_OP EQ_OP NE_OP
+
+AND_OP OR_OP XOR_OP MUL_ASSIGN DIV_ASSIGN ADD_ASSIGN
+
+MOD_ASSIGN LEFT_ASSIGN RIGHT_ASSIGN AND_ASSIGN XOR_ASSIGN OR_ASSIGN
+
+SUB_ASSIGN
+
+LEFT_PAREN RIGHT_PAREN LEFT_BRACKET RIGHT_BRACKET LEFT_BRACE RIGHT_BRACE DOT
+
+COMMA COLON EQUAL SEMICOLON BANG DASH TILDE PLUS STAR SLASH PERCENT
+
+LEFT_ANGLE RIGHT_ANGLE VERTICAL_BAR CARET AMPERSAND QUESTION
+
+INVARIANT PRECISE
+
+HIGH_PRECISION MEDIUM_PRECISION LOW_PRECISION PRECISION</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>The following describes the grammar for the OpenGL Shading Language in terms of the above
+tokens.
+The starting rule is <em>translation_unit</em>.
+An empty shader (one having no tokens to parse, after pre-processing) is
+valid, resulting in no compile-time errors, even though the grammar below
+does not have a rule to accept an empty token stream.</p>
+</div>
+<div class="openblock bnf">
+<div class="content">
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>variable_identifier</em> : </dt>
+<dd>
+<p><em>IDENTIFIER</em></p>
+</dd>
+<dt class="hdlist1"><em>primary_expression</em> : </dt>
+<dd>
+<p><em>variable_identifier</em><br>
+<em>INTCONSTANT</em><br>
+<em>UINTCONSTANT</em><br>
+<em>FLOATCONSTANT</em><br>
+<em>BOOLCONSTANT</em><br>
+<em>DOUBLECONSTANT</em><br>
+<em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>postfix_expression</em> : </dt>
+<dd>
+<p><em>primary_expression</em><br>
+<em>postfix_expression</em> <em>LEFT_BRACKET</em> <em>integer_expression</em> <em>RIGHT_BRACKET</em><br>
+<em>function_call</em><br>
+<em>postfix_expression</em> <em>DOT</em> <em>FIELD_SELECTION</em><br>
+<em>postfix_expression</em> <em>INC_OP</em><br>
+<em>postfix_expression</em> <em>DEC_OP</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>FIELD_SELECTION includes members in structures, component selection for
+vectors and the 'length' identifier for the length() method</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>integer_expression</em> : </dt>
+<dd>
+<p><em>expression</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call</em> : </dt>
+<dd>
+<p><em>function_call_or_method</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_or_method</em> : </dt>
+<dd>
+<p><em>function_call_generic</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_generic</em> : </dt>
+<dd>
+<p><em>function_call_header_with_parameters</em> <em>RIGHT_PAREN</em><br>
+<em>function_call_header_no_parameters</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_header_no_parameters</em> : </dt>
+<dd>
+<p><em>function_call_header</em> <em>VOID</em><br>
+<em>function_call_header</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_header_with_parameters</em> : </dt>
+<dd>
+<p><em>function_call_header</em> <em>assignment_expression</em><br>
+<em>function_call_header_with_parameters</em> <em>COMMA</em> <em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>function_call_header</em> : </dt>
+<dd>
+<p><em>function_identifier</em> <em>LEFT_PAREN</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: Constructors look like functions, but lexical analysis
+recognized most of them as keywords.
+They are now recognized through <em>type_specifier</em>.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Methods (<strong>.length</strong>), subroutine array calls, and identifiers are recognized
+through <em>postfix_expression</em>.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>function_identifier</em> : </dt>
+<dd>
+<p><em>type_specifier</em><br>
+<em>postfix_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>unary_expression</em> : </dt>
+<dd>
+<p><em>postfix_expression</em><br>
+<em>INC_OP</em> <em>unary_expression</em><br>
+<em>DEC_OP</em> <em>unary_expression</em><br>
+<em>unary_operator</em> <em>unary_expression</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No traditional style type casts.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>unary_operator</em> : </dt>
+<dd>
+<p><em>PLUS</em><br>
+<em>DASH</em><br>
+<em>BANG</em><br>
+<em>TILDE</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No '*' or '&amp;' unary ops.
+Pointers are not supported.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>multiplicative_expression</em> : </dt>
+<dd>
+<p><em>unary_expression</em><br>
+<em>multiplicative_expression</em> <em>STAR</em> <em>unary_expression</em><br>
+<em>multiplicative_expression</em> <em>SLASH</em> <em>unary_expression</em><br>
+<em>multiplicative_expression</em> <em>PERCENT</em> <em>unary_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>additive_expression</em> : </dt>
+<dd>
+<p><em>multiplicative_expression</em><br>
+<em>additive_expression</em> <em>PLUS</em> <em>multiplicative_expression</em><br>
+<em>additive_expression</em> <em>DASH</em> <em>multiplicative_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>shift_expression</em> : </dt>
+<dd>
+<p><em>additive_expression</em><br>
+<em>shift_expression</em> <em>LEFT_OP</em> <em>additive_expression</em><br>
+<em>shift_expression</em> <em>RIGHT_OP</em> <em>additive_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>relational_expression</em> : </dt>
+<dd>
+<p><em>shift_expression</em><br>
+<em>relational_expression</em> <em>LEFT_ANGLE</em> <em>shift_expression</em><br>
+<em>relational_expression</em> <em>RIGHT_ANGLE</em> <em>shift_expression</em><br>
+<em>relational_expression</em> <em>LE_OP</em> <em>shift_expression</em><br>
+<em>relational_expression</em> <em>GE_OP</em> <em>shift_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>equality_expression</em> : </dt>
+<dd>
+<p><em>relational_expression</em><br>
+<em>equality_expression</em> <em>EQ_OP</em> <em>relational_expression</em><br>
+<em>equality_expression</em> <em>NE_OP</em> <em>relational_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>and_expression</em> : </dt>
+<dd>
+<p><em>equality_expression</em><br>
+<em>and_expression</em> <em>AMPERSAND</em> <em>equality_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>exclusive_or_expression</em> : </dt>
+<dd>
+<p><em>and_expression</em><br>
+<em>exclusive_or_expression</em> <em>CARET</em> <em>and_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>inclusive_or_expression</em> : </dt>
+<dd>
+<p><em>exclusive_or_expression</em><br>
+<em>inclusive_or_expression</em> <em>VERTICAL_BAR</em> <em>exclusive_or_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>logical_and_expression</em> : </dt>
+<dd>
+<p><em>inclusive_or_expression</em><br>
+<em>logical_and_expression</em> <em>AND_OP</em> <em>inclusive_or_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>logical_xor_expression</em> : </dt>
+<dd>
+<p><em>logical_and_expression</em><br>
+<em>logical_xor_expression</em> <em>XOR_OP</em> <em>logical_and_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>logical_or_expression</em> : </dt>
+<dd>
+<p><em>logical_xor_expression</em><br>
+<em>logical_or_expression</em> <em>OR_OP</em> <em>logical_xor_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>conditional_expression</em> : </dt>
+<dd>
+<p><em>logical_or_expression</em><br>
+<em>logical_or_expression</em> <em>QUESTION</em> <em>expression</em> <em>COLON</em>
+<em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>assignment_expression</em> : </dt>
+<dd>
+<p><em>conditional_expression</em><br>
+<em>unary_expression</em> <em>assignment_operator</em> <em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>assignment_operator</em> : </dt>
+<dd>
+<p><em>EQUAL</em><br>
+<em>MUL_ASSIGN</em><br>
+<em>DIV_ASSIGN</em><br>
+<em>MOD_ASSIGN</em><br>
+<em>ADD_ASSIGN</em><br>
+<em>SUB_ASSIGN</em><br>
+<em>LEFT_ASSIGN</em><br>
+<em>RIGHT_ASSIGN</em><br>
+<em>AND_ASSIGN</em><br>
+<em>XOR_ASSIGN</em><br>
+<em>OR_ASSIGN</em></p>
+</dd>
+<dt class="hdlist1"><em>expression</em> : </dt>
+<dd>
+<p><em>assignment_expression</em><br>
+<em>expression</em> <em>COMMA</em> <em>assignment_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>constant_expression</em> : </dt>
+<dd>
+<p><em>conditional_expression</em></p>
+</dd>
+<dt class="hdlist1"><em>declaration</em> : </dt>
+<dd>
+<p><em>function_prototype</em> <em>SEMICOLON</em><br>
+<em>init_declarator_list</em> <em>SEMICOLON</em><br>
+<em>PRECISION</em> <em>precision_qualifier</em> <em>type_specifier</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em> <em>IDENTIFIER</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em> <em>IDENTIFIER</em> <em>array_specifier</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>IDENTIFIER</em> <em>identifier_list</em> <em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>identifier_list</em> : </dt>
+<dd>
+<p><em>COMMA</em> <em>IDENTIFIER</em><br>
+<em>identifier_list</em> <em>COMMA</em> <em>IDENTIFIER</em></p>
+</dd>
+<dt class="hdlist1"><em>function_prototype</em> : </dt>
+<dd>
+<p><em>function_declarator</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>function_declarator</em> : </dt>
+<dd>
+<p><em>function_header</em><br>
+<em>function_header_with_parameters</em></p>
+</dd>
+<dt class="hdlist1"><em>function_header_with_parameters</em> : </dt>
+<dd>
+<p><em>function_header</em> <em>parameter_declaration</em><br>
+<em>function_header_with_parameters</em> <em>COMMA</em> <em>parameter_declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>function_header</em> : </dt>
+<dd>
+<p><em>fully_specified_type</em> <em>IDENTIFIER</em> <em>LEFT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_declarator</em> : </dt>
+<dd>
+<p><em>type_specifier</em> <em>IDENTIFIER</em><br>
+<em>type_specifier</em> <em>IDENTIFIER</em> <em>array_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_declaration</em> : </dt>
+<dd>
+<p><em>type_qualifier</em> <em>parameter_declarator</em><br>
+<em>parameter_declarator</em><br>
+<em>type_qualifier</em> <em>parameter_type_specifier</em><br>
+<em>parameter_type_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>parameter_type_specifier</em> : </dt>
+<dd>
+<p><em>type_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>init_declarator_list</em> : </dt>
+<dd>
+<p><em>single_declaration</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em> <em>array_specifier</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em> <em>array_specifier</em> <em>EQUAL</em>
+<em>initializer</em><br>
+<em>init_declarator_list</em> <em>COMMA</em> <em>IDENTIFIER</em> <em>EQUAL</em> <em>initializer</em></p>
+</dd>
+<dt class="hdlist1"><em>single_declaration</em> : </dt>
+<dd>
+<p><em>fully_specified_type</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>array_specifier</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>array_specifier</em> <em>EQUAL</em>
+<em>initializer</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>EQUAL</em> <em>initializer</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No 'enum', or 'typedef'.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>fully_specified_type</em> : </dt>
+<dd>
+<p><em>type_specifier</em><br>
+<em>type_qualifier</em> <em>type_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>invariant_qualifier</em> : </dt>
+<dd>
+<p><em>INVARIANT</em></p>
+</dd>
+<dt class="hdlist1"><em>interpolation_qualifier</em> : </dt>
+<dd>
+<p><em>SMOOTH</em><br>
+<em>FLAT</em><br>
+<em>NOPERSPECTIVE</em></p>
+</dd>
+<dt class="hdlist1"><em>layout_qualifier</em> : </dt>
+<dd>
+<p><em>LAYOUT</em> <em>LEFT_PAREN</em> <em>layout_qualifier_id_list</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>layout_qualifier_id_list</em> : </dt>
+<dd>
+<p><em>layout_qualifier_id</em><br>
+<em>layout_qualifier_id_list</em> <em>COMMA</em> <em>layout_qualifier_id</em></p>
+</dd>
+<dt class="hdlist1"><em>layout_qualifier_id</em> : </dt>
+<dd>
+<p><em>IDENTIFIER</em><br>
+<em>IDENTIFIER</em> <em>EQUAL</em> <em>constant_expression</em><br>
+<em>SHARED</em></p>
+</dd>
+<dt class="hdlist1"><em>precise_qualifier</em> : </dt>
+<dd>
+<p><em>PRECISE</em></p>
+</dd>
+<dt class="hdlist1"><em>type_qualifier</em> : </dt>
+<dd>
+<p><em>single_type_qualifier</em><br>
+<em>type_qualifier</em> <em>single_type_qualifier</em></p>
+</dd>
+<dt class="hdlist1"><em>single_type_qualifier</em> : </dt>
+<dd>
+<p><em>storage_qualifier</em><br>
+<em>layout_qualifier</em><br>
+<em>precision_qualifier</em><br>
+<em>interpolation_qualifier</em><br>
+<em>invariant_qualifier</em><br>
+<em>precise_qualifier</em></p>
+</dd>
+<dt class="hdlist1"><em>storage_qualifier</em> : </dt>
+<dd>
+<p><em>CONST</em><br>
+<em>IN</em><br>
+<em>OUT</em><br>
+<em>INOUT</em><br>
+<em>CENTROID</em><br>
+<em>PATCH</em><br>
+<em>SAMPLE</em><br>
+<em>UNIFORM</em><br>
+<em>BUFFER</em><br>
+<em>SHARED</em><br>
+<em>COHERENT</em><br>
+<em>VOLATILE</em><br>
+<em>RESTRICT</em><br>
+<em>READONLY</em><br>
+<em>WRITEONLY</em><br>
+<em>SUBROUTINE</em><br>
+<em>SUBROUTINE</em> <em>LEFT_PAREN</em> <em>type_name_list</em> <em>RIGHT_PAREN</em></p>
+</dd>
+<dt class="hdlist1"><em>type_name_list</em> : </dt>
+<dd>
+<p><em>TYPE_NAME</em><br>
+<em>type_name_list</em> <em>COMMA</em> <em>TYPE_NAME</em></p>
+</dd>
+<dt class="hdlist1"><em>type_specifier</em> : </dt>
+<dd>
+<p><em>type_specifier_nonarray</em><br>
+<em>type_specifier_nonarray</em> <em>array_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>array_specifier</em> : </dt>
+<dd>
+<p><em>LEFT_BRACKET</em> <em>RIGHT_BRACKET</em><br>
+<em>LEFT_BRACKET</em> <em>constant_expression</em> <em>RIGHT_BRACKET</em><br>
+<em>array_specifier</em> <em>LEFT_BRACKET</em> <em>RIGHT_BRACKET</em><br>
+<em>array_specifier</em> <em>LEFT_BRACKET</em> <em>constant_expression</em> <em>RIGHT_BRACKET</em></p>
+</dd>
+<dt class="hdlist1"><em>type_specifier_nonarray</em> : </dt>
+<dd>
+<p><em>VOID</em><br>
+<em>FLOAT</em><br>
+<em>DOUBLE</em><br>
+<em>INT</em><br>
+<em>UINT</em><br>
+<em>BOOL</em><br>
+<em>VEC2</em><br>
+<em>VEC3</em><br>
+<em>VEC4</em><br>
+<em>DVEC2</em><br>
+<em>DVEC3</em><br>
+<em>DVEC4</em><br>
+<em>BVEC2</em><br>
+<em>BVEC3</em><br>
+<em>BVEC4</em><br>
+<em>IVEC2</em><br>
+<em>IVEC3</em><br>
+<em>IVEC4</em><br>
+<em>UVEC2</em><br>
+<em>UVEC3</em><br>
+<em>UVEC4</em><br>
+<em>MAT2</em><br>
+<em>MAT3</em><br>
+<em>MAT4</em><br>
+<em>MAT2X2</em><br>
+<em>MAT2X3</em><br>
+<em>MAT2X4</em><br>
+<em>MAT3X2</em><br>
+<em>MAT3X3</em><br>
+<em>MAT3X4</em><br>
+<em>MAT4X2</em><br>
+<em>MAT4X3</em><br>
+<em>MAT4X4</em><br>
+<em>DMAT2</em><br>
+<em>DMAT3</em><br>
+<em>DMAT4</em><br>
+<em>DMAT2X2</em><br>
+<em>DMAT2X3</em><br>
+<em>DMAT2X4</em><br>
+<em>DMAT3X2</em><br>
+<em>DMAT3X3</em><br>
+<em>DMAT3X4</em><br>
+<em>DMAT4X2</em><br>
+<em>DMAT4X3</em><br>
+<em>DMAT4X4</em><br>
+<em>ATOMIC_UINT</em><br>
+<em>SAMPLER2D</em><br>
+<em>SAMPLER3D</em><br>
+<em>SAMPLERCUBE</em><br>
+<em>SAMPLER2DSHADOW</em><br>
+<em>SAMPLERCUBESHADOW</em><br>
+<em>SAMPLER2DARRAY</em><br>
+<em>SAMPLER2DARRAYSHADOW</em><br>
+<em>SAMPLERCUBEARRAY</em><br>
+<em>SAMPLERCUBEARRAYSHADOW</em><br>
+<em>ISAMPLER2D</em><br>
+<em>ISAMPLER3D</em><br>
+<em>ISAMPLERCUBE</em><br>
+<em>ISAMPLER2DARRAY</em><br>
+<em>ISAMPLERCUBEARRAY</em><br>
+<em>USAMPLER2D</em><br>
+<em>USAMPLER3D</em><br>
+<em>USAMPLERCUBE</em><br>
+<em>USAMPLER2DARRAY</em><br>
+<em>USAMPLERCUBEARRAY</em><br>
+<em>SAMPLER1D</em><br>
+<em>SAMPLER1DSHADOW</em><br>
+<em>SAMPLER1DARRAY</em><br>
+<em>SAMPLER1DARRAYSHADOW</em><br>
+<em>ISAMPLER1D</em><br>
+<em>ISAMPLER1DARRAY</em><br>
+<em>USAMPLER1D</em><br>
+<em>USAMPLER1DARRAY</em><br>
+<em>SAMPLER2DRECT</em><br>
+<em>SAMPLER2DRECTSHADOW</em><br>
+<em>ISAMPLER2DRECT</em><br>
+<em>USAMPLER2DRECT</em><br>
+<em>SAMPLERBUFFER</em><br>
+<em>ISAMPLERBUFFER</em><br>
+<em>USAMPLERBUFFER</em><br>
+<em>SAMPLER2DMS</em><br>
+<em>ISAMPLER2DMS</em><br>
+<em>USAMPLER2DMS</em><br>
+<em>SAMPLER2DMSARRAY</em><br>
+<em>ISAMPLER2DMSARRAY</em><br>
+<em>USAMPLER2DMSARRAY</em><br>
+<em>IMAGE2D</em><br>
+<em>IIMAGE2D</em><br>
+<em>UIMAGE2D</em><br>
+<em>IMAGE3D</em><br>
+<em>IIMAGE3D</em><br>
+<em>UIMAGE3D</em><br>
+<em>IMAGECUBE</em><br>
+<em>IIMAGECUBE</em><br>
+<em>UIMAGECUBE</em><br>
+<em>IMAGEBUFFER</em><br>
+<em>IIMAGEBUFFER</em><br>
+<em>UIMAGEBUFFER</em><br>
+<em>IMAGE1D</em><br>
+<em>IIMAGE1D</em><br>
+<em>UIMAGE1D</em><br>
+<em>IMAGE1DARRAY</em><br>
+<em>IIMAGE1DARRAY</em><br>
+<em>UIMAGE1DARRAY</em><br>
+<em>IMAGE2DRECT</em><br>
+<em>IIMAGE2DRECT</em><br>
+<em>UIMAGE2DRECT</em><br>
+<em>IMAGE2DARRAY</em><br>
+<em>IIMAGE2DARRAY</em><br>
+<em>UIMAGE2DARRAY</em><br>
+<em>IMAGECUBEARRAY</em><br>
+<em>IIMAGECUBEARRAY</em><br>
+<em>UIMAGECUBEARRAY</em><br>
+<em>IMAGE2DMS</em><br>
+<em>IIMAGE2DMS</em><br>
+<em>UIMAGE2DMS</em><br>
+<em>IMAGE2DMSARRAY</em><br>
+<em>IIMAGE2DMSARRAY</em><br>
+<em>UIMAGE2DMSARRAY</em><br>
+<em>struct_specifier</em><br>
+<em>TYPE_NAME</em></p>
+</dd>
+<dt class="hdlist1"><em>precision_qualifier</em> : </dt>
+<dd>
+<p><em>HIGH_PRECISION</em><br>
+<em>MEDIUM_PRECISION</em><br>
+<em>LOW_PRECISION</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_specifier</em> : </dt>
+<dd>
+<p><em>STRUCT</em> <em>IDENTIFIER</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em>
+<em>RIGHT_BRACE</em><br>
+<em>STRUCT</em> <em>LEFT_BRACE</em> <em>struct_declaration_list</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declaration_list</em> : </dt>
+<dd>
+<p><em>struct_declaration</em><br>
+<em>struct_declaration_list</em> <em>struct_declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declaration</em> : </dt>
+<dd>
+<p><em>type_specifier</em> <em>struct_declarator_list</em> <em>SEMICOLON</em><br>
+<em>type_qualifier</em> <em>type_specifier</em> <em>struct_declarator_list</em> <em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declarator_list</em> : </dt>
+<dd>
+<p><em>struct_declarator</em><br>
+<em>struct_declarator_list</em> <em>COMMA</em> <em>struct_declarator</em></p>
+</dd>
+<dt class="hdlist1"><em>struct_declarator</em> : </dt>
+<dd>
+<p><em>IDENTIFIER</em><br>
+<em>IDENTIFIER</em> <em>array_specifier</em></p>
+</dd>
+<dt class="hdlist1"><em>initializer</em> : </dt>
+<dd>
+<p><em>assignment_expression</em><br>
+<em>LEFT_BRACE</em> <em>initializer_list</em> <em>RIGHT_BRACE</em><br>
+<em>LEFT_BRACE</em> <em>initializer_list</em> <em>COMMA</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>initializer_list</em> : </dt>
+<dd>
+<p><em>initializer</em><br>
+<em>initializer_list</em> <em>COMMA</em> <em>initializer</em></p>
+</dd>
+<dt class="hdlist1"><em>declaration_statement</em> : </dt>
+<dd>
+<p><em>declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>statement</em> : </dt>
+<dd>
+<p><em>compound_statement</em><br>
+<em>simple_statement</em></p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: labeled statements for SWITCH only; 'goto' is not supported.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>simple_statement</em> : </dt>
+<dd>
+<p><em>declaration_statement</em><br>
+<em>expression_statement</em><br>
+<em>selection_statement</em><br>
+<em>switch_statement</em><br>
+<em>case_label</em><br>
+<em>iteration_statement</em><br>
+<em>jump_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>compound_statement</em> : </dt>
+<dd>
+<p><em>LEFT_BRACE</em> <em>RIGHT_BRACE</em><br>
+<em>LEFT_BRACE</em> <em>statement_list</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>statement_no_new_scope</em> : </dt>
+<dd>
+<p><em>compound_statement_no_new_scope</em><br>
+<em>simple_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>compound_statement_no_new_scope</em> : </dt>
+<dd>
+<p><em>LEFT_BRACE</em> <em>RIGHT_BRACE</em><br>
+<em>LEFT_BRACE</em> <em>statement_list</em> <em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>statement_list</em> : </dt>
+<dd>
+<p><em>statement</em><br>
+<em>statement_list</em> <em>statement</em></p>
+</dd>
+<dt class="hdlist1"><em>expression_statement</em> : </dt>
+<dd>
+<p><em>SEMICOLON</em><br>
+<em>expression</em> <em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>selection_statement</em> : </dt>
+<dd>
+<p><em>IF</em> <em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em> <em>selection_rest_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>selection_rest_statement</em> : </dt>
+<dd>
+<p><em>statement</em> <em>ELSE</em> <em>statement</em><br>
+<em>statement</em></p>
+</dd>
+<dt class="hdlist1"><em>condition</em> : </dt>
+<dd>
+<p><em>expression</em><br>
+<em>fully_specified_type</em> <em>IDENTIFIER</em> <em>EQUAL</em> <em>initializer</em></p>
+</dd>
+<dt class="hdlist1"><em>switch_statement</em> : </dt>
+<dd>
+<p><em>SWITCH</em> <em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em> <em>LEFT_BRACE</em>
+<em>switch_statement_list</em><br>
+<em>RIGHT_BRACE</em></p>
+</dd>
+<dt class="hdlist1"><em>switch_statement_list</em> : </dt>
+<dd>
+<p>/* <em>nothing</em> */<br>
+<em>statement_list</em></p>
+</dd>
+<dt class="hdlist1"><em>case_label</em> : </dt>
+<dd>
+<p><em>CASE</em> <em>expression</em> <em>COLON</em><br>
+<em>DEFAULT</em> <em>COLON</em></p>
+</dd>
+<dt class="hdlist1"><em>iteration_statement</em> : </dt>
+<dd>
+<p><em>WHILE</em> <em>LEFT_PAREN</em> <em>condition</em> <em>RIGHT_PAREN</em> <em>statement_no_new_scope</em><br>
+<em>DO</em> <em>statement</em> <em>WHILE</em> <em>LEFT_PAREN</em> <em>expression</em> <em>RIGHT_PAREN</em>
+<em>SEMICOLON</em><br>
+<em>FOR</em> <em>LEFT_PAREN</em> <em>for_init_statement</em> <em>for_rest_statement</em>
+<em>RIGHT_PAREN</em> <em>statement_no_new_scope</em></p>
+</dd>
+<dt class="hdlist1"><em>for_init_statement</em> : </dt>
+<dd>
+<p><em>expression_statement</em><br>
+<em>declaration_statement</em></p>
+</dd>
+<dt class="hdlist1"><em>conditionopt</em> : </dt>
+<dd>
+<p><em>condition</em><br>
+/* <em>empty</em> */</p>
+</dd>
+<dt class="hdlist1"><em>for_rest_statement</em> : </dt>
+<dd>
+<p><em>conditionopt</em> <em>SEMICOLON</em><br>
+<em>conditionopt</em> <em>SEMICOLON</em> <em>expression</em></p>
+</dd>
+<dt class="hdlist1"><em>jump_statement</em> : </dt>
+<dd>
+<p><em>CONTINUE</em> <em>SEMICOLON</em><br>
+<em>BREAK</em> <em>SEMICOLON</em><br>
+<em>RETURN</em> <em>SEMICOLON</em><br>
+<em>RETURN</em> <em>expression</em> <em>SEMICOLON</em><br>
+<em>DISCARD</em> <em>SEMICOLON</em> // Fragment shader only.</p>
+</dd>
+</dl>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<i class="fa icon-note" title="Note"></i>
+</td>
+<td class="content">
+<div class="paragraph">
+<p>Grammar Note: No 'goto'.
+Gotos are not supported.</p>
+</div>
+</td>
+</tr>
+</table>
+</div>
+<div class="dlist">
+<dl>
+<dt class="hdlist1"><em>translation_unit</em> : </dt>
+<dd>
+<p><em>external_declaration</em><br>
+<em>translation_unit</em> <em>external_declaration</em></p>
+</dd>
+<dt class="hdlist1"><em>external_declaration</em> : </dt>
+<dd>
+<p><em>function_definition</em><br>
+<em>declaration</em><br>
+<em>SEMICOLON</em></p>
+</dd>
+<dt class="hdlist1"><em>function_definition</em> : </dt>
+<dd>
+<p><em>function_prototype</em> <em>compound_statement_no_new_scope</em></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="paragraph">
+<p>In general the above grammar describes a super set of the OpenGL Shading Language.
+Certain constructs that are valid purely in terms of the grammar are
+disallowed by statements elsewhere in this specification.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="acknowledgments">10. Acknowledgments</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>This specification is based on the work of those who contributed to past
+versions of the Open GL and Open GL ES Language Specifications and the
+following contributors to this version:</p>
+</div>
+<div class="paragraph">
+<p>Pat Brown, NVIDIA<br>
+Jeff Bolz, NVIDIA<br>
+Frank Chen<br>
+Pierre Boudier, AMD<br>
+Piers Daniell, NVIDIA<br>
+Chris Dodd, NVIDIA<br>
+Nick Haemel, NVIDIA<br>
+Jason Green, Transgaming<br>
+Brent Insko, Intel<br>
+Jon Leech<br>
+Bill Licea-Kane, Qualcomm<br>
+Daniel Koch, NVIDIA<br>
+Graeme Leese, Broadcom<br>
+Barthold Lichtenbelt, NVIDIA<br>
+Bruce Merry, ARM<br>
+Robert Ohannessian<br>
+Tom Olson, ARM<br>
+Brian Paul, VMware<br>
+Acorn Pooley, NVIDIA<br>
+Daniel Rakos, AMD<br>
+Christophe Riccio, AMD<br>
+Kevin Rogovin<br>
+Ian Romanick, Intel<br>
+Greg Roth, NVIDIA<br>
+Graham Sellers, AMD<br>
+Dave Shreiner, ARM<br>
+Jeremy Sandmel, Apple<br>
+Robert Simpson, Qualcomm<br>
+Eric Werness, NVIDIA<br>
+Mark Young, AMD</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="references">11. Normative References</h2>
+<div class="sectionbody">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p>International Standard ISO/IEC 14882:1998(E).
+Programming Languages - C++. Referenced for preprocessor only</p>
+</li>
+<li>
+<p>IEEE 754-2008.
+<em>IEEE Standard for Floating-Point Arithmetic</em></p>
+</li>
+</ol>
+</div>
+</div>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Version 4.60.6<br>
+Last updated 2018-12-12 16:37:44 MST
+</div>
+</div>
+
+<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_HTMLorMML"></script>
+</body>
+</html>
\ No newline at end of file
diff --git a/specs/gl/GLSLangSpec.4.60.pdf b/specs/gl/GLSLangSpec.4.60.pdf
index bfdb80a..86aded6 100644
--- a/specs/gl/GLSLangSpec.4.60.pdf
+++ b/specs/gl/GLSLangSpec.4.60.pdf
Binary files differ
diff --git a/specs/gl/glspec46.compatibility.pdf b/specs/gl/glspec46.compatibility.pdf
index 9f09b25..467fd68 100644
--- a/specs/gl/glspec46.compatibility.pdf
+++ b/specs/gl/glspec46.compatibility.pdf
Binary files differ
diff --git a/specs/gl/glspec46.compatibility.withchanges.pdf b/specs/gl/glspec46.compatibility.withchanges.pdf
index 5344bbc..b682eab 100644
--- a/specs/gl/glspec46.compatibility.withchanges.pdf
+++ b/specs/gl/glspec46.compatibility.withchanges.pdf
Binary files differ
diff --git a/specs/gl/glspec46.core.pdf b/specs/gl/glspec46.core.pdf
index 65dba25..159d77e 100644
--- a/specs/gl/glspec46.core.pdf
+++ b/specs/gl/glspec46.core.pdf
Binary files differ
diff --git a/specs/gl/glspec46.core.withchanges.pdf b/specs/gl/glspec46.core.withchanges.pdf
index b92ea3a..a58e958 100644
--- a/specs/gl/glspec46.core.withchanges.pdf
+++ b/specs/gl/glspec46.core.withchanges.pdf
Binary files differ
diff --git a/specs/gl/katex/README.md b/specs/gl/katex/README.md
new file mode 100644
index 0000000..5f8caa8
--- /dev/null
+++ b/specs/gl/katex/README.md
@@ -0,0 +1,68 @@
+# [<img src="https://khan.github.io/KaTeX/katex-logo.svg" width="130" alt="KaTeX">](https://khan.github.io/KaTeX/) [![Build Status](https://travis-ci.org/Khan/KaTeX.svg?branch=master)](https://travis-ci.org/Khan/KaTeX)
+
+[![Join the chat at https://gitter.im/Khan/KaTeX](https://badges.gitter.im/Join%20Chat.svg)](https://gitter.im/Khan/KaTeX?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
+
+KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web.
+
+ * **Fast:** KaTeX renders its math synchronously and doesn't need to reflow the page. See how it compares to a competitor in [this speed test](http://jsperf.com/katex-vs-mathjax/).
+ * **Print quality:** KaTeX’s layout is based on Donald Knuth’s TeX, the gold standard for math typesetting.
+ * **Self contained:** KaTeX has no dependencies and can easily be bundled with your website resources.
+ * **Server side rendering:** KaTeX produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML.
+
+KaTeX supports all major browsers, including Chrome, Safari, Firefox, Opera, and IE 8 - IE 11.  A list of supported  commands can be on the [wiki](https://github.com/Khan/KaTeX/wiki/Function-Support-in-KaTeX).
+
+## Usage
+
+You can [download KaTeX](https://github.com/khan/katex/releases) and host it on your server or include the `katex.min.js` and `katex.min.css` files on your page directly from a CDN:
+
+```html
+<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.6.0/katex.min.css">
+<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.6.0/katex.min.js"></script>
+```
+
+#### In-browser rendering
+
+Call `katex.render` with a TeX expression and a DOM element to render into:
+
+```js
+katex.render("c = \\pm\\sqrt{a^2 + b^2}", element);
+```
+
+If KaTeX can't parse the expression, it throws a `katex.ParseError` error.
+
+#### Server side rendering or rendering to a string
+
+To generate HTML on the server or to generate an HTML string of the rendered math, you can use `katex.renderToString`:
+
+```js
+var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}");
+// '<span class="katex">...</span>'
+```
+
+Make sure to include the CSS and font files, but there is no need to include the JavaScript. Like `render`, `renderToString` throws if it can't parse the expression.
+
+#### Rendering options
+
+You can provide an object of options as the last argument to `katex.render` and `katex.renderToString`. Available options are:
+
+- `displayMode`: `boolean`. If `true` the math will be rendered in display mode, which will put the math in display style (so `\int` and `\sum` are large, for example), and will center the math on the page on its own line. If `false` the math will be rendered in inline mode. (default: `false`)
+- `throwOnError`: `boolean`. If `true`, KaTeX will throw a `ParseError` when it encounters an unsupported command. If `false`, KaTeX will render the unsupported command as text in the color given by `errorColor`. (default: `true`)
+- `errorColor`: `string`. A color string given in the format `"#XXX"` or `"#XXXXXX"`. This option determines the color which unsupported commands are rendered in. (default: `#cc0000`)
+
+For example:
+
+```js
+katex.render("c = \\pm\\sqrt{a^2 + b^2}", element, { displayMode: true });
+```
+
+#### Automatic rendering of math on a page
+
+Math on the page can be automatically rendered using the auto-render extension. See [the Auto-render README](contrib/auto-render/README.md) for more information.
+
+## Contributing
+
+See [CONTRIBUTING.md](CONTRIBUTING.md)
+
+## License
+
+KaTeX is licensed under the [MIT License](http://opensource.org/licenses/MIT).
diff --git a/specs/gl/katex/contrib/auto-render.min.js b/specs/gl/katex/contrib/auto-render.min.js
new file mode 100644
index 0000000..30cc312
--- /dev/null
+++ b/specs/gl/katex/contrib/auto-render.min.js
@@ -0,0 +1 @@
+(function(e){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=e()}else if(typeof define==="function"&&define.amd){define([],e)}else{var t;if(typeof window!=="undefined"){t=window}else if(typeof global!=="undefined"){t=global}else if(typeof self!=="undefined"){t=self}else{t=this}t.renderMathInElement=e()}})(function(){var e,t,r;return function n(e,t,r){function a(o,l){if(!t[o]){if(!e[o]){var f=typeof require=="function"&&require;if(!l&&f)return f(o,!0);if(i)return i(o,!0);var d=new Error("Cannot find module '"+o+"'");throw d.code="MODULE_NOT_FOUND",d}var s=t[o]={exports:{}};e[o][0].call(s.exports,function(t){var r=e[o][1][t];return a(r?r:t)},s,s.exports,n,e,t,r)}return t[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)a(r[o]);return a}({1:[function(e,t,r){var n=e("./splitAtDelimiters");var a=function(e,t){var r=[{type:"text",data:e}];for(var a=0;a<t.length;a++){var i=t[a];r=n(r,i.left,i.right,i.display||false)}return r};var i=function(e,t){var r=a(e,t);var n=document.createDocumentFragment();for(var i=0;i<r.length;i++){if(r[i].type==="text"){n.appendChild(document.createTextNode(r[i].data))}else{var o=document.createElement("span");var l=r[i].data;try{katex.render(l,o,{displayMode:r[i].display})}catch(f){if(!(f instanceof katex.ParseError)){throw f}console.error("KaTeX auto-render: Failed to parse `"+r[i].data+"` with ",f);n.appendChild(document.createTextNode(r[i].rawData));continue}n.appendChild(o)}}return n};var o=function(e,t,r){for(var n=0;n<e.childNodes.length;n++){var a=e.childNodes[n];if(a.nodeType===3){var l=i(a.textContent,t);n+=l.childNodes.length-1;e.replaceChild(l,a)}else if(a.nodeType===1){var f=r.indexOf(a.nodeName.toLowerCase())===-1;if(f){o(a,t,r)}}}};var l={delimiters:[{left:"$$",right:"$$",display:true},{left:"\\[",right:"\\]",display:true},{left:"\\(",right:"\\)",display:false}],ignoredTags:["script","noscript","style","textarea","pre","code"]};var f=function(e){var t;var r;for(var n=1,a=arguments.length;n<a;n++){t=arguments[n];for(r in t){if(Object.prototype.hasOwnProperty.call(t,r)){e[r]=t[r]}}}return e};var d=function(e,t){if(!e){throw new Error("No element provided to render")}t=f({},l,t);o(e,t.delimiters,t.ignoredTags)};t.exports=d},{"./splitAtDelimiters":2}],2:[function(e,t,r){var n=function(e,t,r){var n=r;var a=0;var i=e.length;while(n<t.length){var o=t[n];if(a<=0&&t.slice(n,n+i)===e){return n}else if(o==="\\"){n++}else if(o==="{"){a++}else if(o==="}"){a--}n++}return-1};var a=function(e,t,r,a){var i=[];for(var o=0;o<e.length;o++){if(e[o].type==="text"){var l=e[o].data;var f=true;var d=0;var s;s=l.indexOf(t);if(s!==-1){d=s;i.push({type:"text",data:l.slice(0,d)});f=false}while(true){if(f){s=l.indexOf(t,d);if(s===-1){break}i.push({type:"text",data:l.slice(d,s)});d=s}else{s=n(r,l,d+t.length);if(s===-1){break}i.push({type:"math",data:l.slice(d+t.length,s),rawData:l.slice(d,s+r.length),display:a});d=s+r.length}f=!f}i.push({type:"text",data:l.slice(d)})}else{i.push(e[o])}}return i};t.exports=a},{}]},{},[1])(1)});
diff --git a/specs/gl/katex/fonts/KaTeX_AMS-Regular.eot b/specs/gl/katex/fonts/KaTeX_AMS-Regular.eot
new file mode 100644
index 0000000..784276a
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_AMS-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_AMS-Regular.ttf b/specs/gl/katex/fonts/KaTeX_AMS-Regular.ttf
new file mode 100644
index 0000000..6f1e0be
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_AMS-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_AMS-Regular.woff b/specs/gl/katex/fonts/KaTeX_AMS-Regular.woff
new file mode 100644
index 0000000..4dded47
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_AMS-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_AMS-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_AMS-Regular.woff2
new file mode 100644
index 0000000..ea81079
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_AMS-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.eot b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.eot
new file mode 100644
index 0000000..1a0db0c
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.ttf b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.ttf
new file mode 100644
index 0000000..b94907d
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.woff b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.woff
new file mode 100644
index 0000000..799fa81
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.woff2 b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.woff2
new file mode 100644
index 0000000..73bb542
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Bold.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.eot b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.eot
new file mode 100644
index 0000000..6cc83d0
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.ttf
new file mode 100644
index 0000000..cf51e20
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.woff b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.woff
new file mode 100644
index 0000000..f5e5c62
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.woff2
new file mode 100644
index 0000000..dd76d34
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Caligraphic-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.eot b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.eot
new file mode 100644
index 0000000..1960b10
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.ttf b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.ttf
new file mode 100644
index 0000000..7b0790f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.woff b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.woff
new file mode 100644
index 0000000..dc32571
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.woff2 b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.woff2
new file mode 100644
index 0000000..fdc4292
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Bold.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.eot b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.eot
new file mode 100644
index 0000000..e4e7379
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.ttf
new file mode 100644
index 0000000..063bc02
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.woff b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.woff
new file mode 100644
index 0000000..c4b18d8
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.woff2
new file mode 100644
index 0000000..4318d93
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Fraktur-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Bold.eot b/specs/gl/katex/fonts/KaTeX_Main-Bold.eot
new file mode 100644
index 0000000..80fbd02
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Bold.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Bold.ttf b/specs/gl/katex/fonts/KaTeX_Main-Bold.ttf
new file mode 100644
index 0000000..8e10722
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Bold.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Bold.woff b/specs/gl/katex/fonts/KaTeX_Main-Bold.woff
new file mode 100644
index 0000000..43b361a
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Bold.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Bold.woff2 b/specs/gl/katex/fonts/KaTeX_Main-Bold.woff2
new file mode 100644
index 0000000..af57a96
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Bold.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Italic.eot b/specs/gl/katex/fonts/KaTeX_Main-Italic.eot
new file mode 100644
index 0000000..fc77016
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Italic.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Italic.ttf b/specs/gl/katex/fonts/KaTeX_Main-Italic.ttf
new file mode 100644
index 0000000..d124495
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Italic.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Italic.woff b/specs/gl/katex/fonts/KaTeX_Main-Italic.woff
new file mode 100644
index 0000000..e623236
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Italic.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Italic.woff2 b/specs/gl/katex/fonts/KaTeX_Main-Italic.woff2
new file mode 100644
index 0000000..944e974
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Italic.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Regular.eot b/specs/gl/katex/fonts/KaTeX_Main-Regular.eot
new file mode 100644
index 0000000..dc60c09
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Main-Regular.ttf
new file mode 100644
index 0000000..da5797f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Regular.woff b/specs/gl/katex/fonts/KaTeX_Main-Regular.woff
new file mode 100644
index 0000000..37db672
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Main-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Main-Regular.woff2
new file mode 100644
index 0000000..4882042
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Main-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.eot b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.eot
new file mode 100644
index 0000000..52c8b8c
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.ttf b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.ttf
new file mode 100644
index 0000000..a8b527c
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.woff b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.woff
new file mode 100644
index 0000000..8940e0b
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.woff2 b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.woff2
new file mode 100644
index 0000000..15cf56d
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-BoldItalic.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Italic.eot b/specs/gl/katex/fonts/KaTeX_Math-Italic.eot
new file mode 100644
index 0000000..64c8992
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Italic.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Italic.ttf b/specs/gl/katex/fonts/KaTeX_Math-Italic.ttf
new file mode 100644
index 0000000..06f39d3
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Italic.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Italic.woff b/specs/gl/katex/fonts/KaTeX_Math-Italic.woff
new file mode 100644
index 0000000..cf3b4b7
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Italic.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Italic.woff2 b/specs/gl/katex/fonts/KaTeX_Math-Italic.woff2
new file mode 100644
index 0000000..5f8c4bf
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Italic.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Regular.eot b/specs/gl/katex/fonts/KaTeX_Math-Regular.eot
new file mode 100644
index 0000000..5521e6a
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Math-Regular.ttf
new file mode 100644
index 0000000..7312708
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Regular.woff b/specs/gl/katex/fonts/KaTeX_Math-Regular.woff
new file mode 100644
index 0000000..0e2ebdf
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Math-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Math-Regular.woff2
new file mode 100644
index 0000000..ebe3d02
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Math-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.eot b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.eot
new file mode 100644
index 0000000..1660e76
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.ttf b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.ttf
new file mode 100644
index 0000000..dbeb7b9
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.woff b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.woff
new file mode 100644
index 0000000..8f144a8
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.woff2 b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.woff2
new file mode 100644
index 0000000..329e855
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Bold.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.eot b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.eot
new file mode 100644
index 0000000..289ae3f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.ttf b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.ttf
new file mode 100644
index 0000000..b3a2f38
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.woff b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.woff
new file mode 100644
index 0000000..bddf7ea
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.woff2 b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.woff2
new file mode 100644
index 0000000..5fa767b
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Italic.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.eot b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.eot
new file mode 100644
index 0000000..1b38b98
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.ttf b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.ttf
new file mode 100644
index 0000000..e4712f8
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.woff b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.woff
new file mode 100644
index 0000000..33be368
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.woff2
new file mode 100644
index 0000000..4fcb2e2
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_SansSerif-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Script-Regular.eot b/specs/gl/katex/fonts/KaTeX_Script-Regular.eot
new file mode 100644
index 0000000..7870d7f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Script-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Script-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Script-Regular.ttf
new file mode 100644
index 0000000..da4d113
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Script-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Script-Regular.woff b/specs/gl/katex/fonts/KaTeX_Script-Regular.woff
new file mode 100644
index 0000000..d6ae79f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Script-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Script-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Script-Regular.woff2
new file mode 100644
index 0000000..1b43deb
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Script-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size1-Regular.eot b/specs/gl/katex/fonts/KaTeX_Size1-Regular.eot
new file mode 100644
index 0000000..29950f9
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size1-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size1-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Size1-Regular.ttf
new file mode 100644
index 0000000..194466a
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size1-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size1-Regular.woff b/specs/gl/katex/fonts/KaTeX_Size1-Regular.woff
new file mode 100644
index 0000000..237f271
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size1-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size1-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Size1-Regular.woff2
new file mode 100644
index 0000000..39b6f8f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size1-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size2-Regular.eot b/specs/gl/katex/fonts/KaTeX_Size2-Regular.eot
new file mode 100644
index 0000000..b8b0536
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size2-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size2-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Size2-Regular.ttf
new file mode 100644
index 0000000..b41b66a
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size2-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size2-Regular.woff b/specs/gl/katex/fonts/KaTeX_Size2-Regular.woff
new file mode 100644
index 0000000..4a30558
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size2-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size2-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Size2-Regular.woff2
new file mode 100644
index 0000000..3facec1
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size2-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size3-Regular.eot b/specs/gl/katex/fonts/KaTeX_Size3-Regular.eot
new file mode 100644
index 0000000..576b864
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size3-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size3-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Size3-Regular.ttf
new file mode 100644
index 0000000..790ddbb
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size3-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size3-Regular.woff b/specs/gl/katex/fonts/KaTeX_Size3-Regular.woff
new file mode 100644
index 0000000..3a6d062
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size3-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size3-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Size3-Regular.woff2
new file mode 100644
index 0000000..2cffafe
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size3-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size4-Regular.eot b/specs/gl/katex/fonts/KaTeX_Size4-Regular.eot
new file mode 100644
index 0000000..c2b045f
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size4-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size4-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Size4-Regular.ttf
new file mode 100644
index 0000000..ce660aa
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size4-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size4-Regular.woff b/specs/gl/katex/fonts/KaTeX_Size4-Regular.woff
new file mode 100644
index 0000000..7826c6c
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size4-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Size4-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Size4-Regular.woff2
new file mode 100644
index 0000000..c921898
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Size4-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.eot b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.eot
new file mode 100644
index 0000000..4c178f4
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.eot
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.ttf b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.ttf
new file mode 100644
index 0000000..b0427ad
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.ttf
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.woff b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.woff
new file mode 100644
index 0000000..78e9904
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.woff
Binary files differ
diff --git a/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.woff2 b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.woff2
new file mode 100644
index 0000000..618de99
--- /dev/null
+++ b/specs/gl/katex/fonts/KaTeX_Typewriter-Regular.woff2
Binary files differ
diff --git a/specs/gl/katex/katex.css b/specs/gl/katex/katex.css
new file mode 100644
index 0000000..ef0aa62
--- /dev/null
+++ b/specs/gl/katex/katex.css
@@ -0,0 +1,976 @@
+@font-face {
+  font-family: 'KaTeX_AMS';
+  src: url('fonts/KaTeX_AMS-Regular.eot');
+  src: url('fonts/KaTeX_AMS-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_AMS-Regular.woff2') format('woff2'), url('fonts/KaTeX_AMS-Regular.woff') format('woff'), url('fonts/KaTeX_AMS-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Caligraphic';
+  src: url('fonts/KaTeX_Caligraphic-Bold.eot');
+  src: url('fonts/KaTeX_Caligraphic-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Caligraphic-Bold.woff2') format('woff2'), url('fonts/KaTeX_Caligraphic-Bold.woff') format('woff'), url('fonts/KaTeX_Caligraphic-Bold.ttf') format('truetype');
+  font-weight: bold;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Caligraphic';
+  src: url('fonts/KaTeX_Caligraphic-Regular.eot');
+  src: url('fonts/KaTeX_Caligraphic-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Caligraphic-Regular.woff2') format('woff2'), url('fonts/KaTeX_Caligraphic-Regular.woff') format('woff'), url('fonts/KaTeX_Caligraphic-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Fraktur';
+  src: url('fonts/KaTeX_Fraktur-Bold.eot');
+  src: url('fonts/KaTeX_Fraktur-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Fraktur-Bold.woff2') format('woff2'), url('fonts/KaTeX_Fraktur-Bold.woff') format('woff'), url('fonts/KaTeX_Fraktur-Bold.ttf') format('truetype');
+  font-weight: bold;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Fraktur';
+  src: url('fonts/KaTeX_Fraktur-Regular.eot');
+  src: url('fonts/KaTeX_Fraktur-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Fraktur-Regular.woff2') format('woff2'), url('fonts/KaTeX_Fraktur-Regular.woff') format('woff'), url('fonts/KaTeX_Fraktur-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Main';
+  src: url('fonts/KaTeX_Main-Bold.eot');
+  src: url('fonts/KaTeX_Main-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Bold.woff2') format('woff2'), url('fonts/KaTeX_Main-Bold.woff') format('woff'), url('fonts/KaTeX_Main-Bold.ttf') format('truetype');
+  font-weight: bold;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Main';
+  src: url('fonts/KaTeX_Main-Italic.eot');
+  src: url('fonts/KaTeX_Main-Italic.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Italic.woff2') format('woff2'), url('fonts/KaTeX_Main-Italic.woff') format('woff'), url('fonts/KaTeX_Main-Italic.ttf') format('truetype');
+  font-weight: normal;
+  font-style: italic;
+}
+@font-face {
+  font-family: 'KaTeX_Main';
+  src: url('fonts/KaTeX_Main-Regular.eot');
+  src: url('fonts/KaTeX_Main-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Regular.woff2') format('woff2'), url('fonts/KaTeX_Main-Regular.woff') format('woff'), url('fonts/KaTeX_Main-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Math';
+  src: url('fonts/KaTeX_Math-Italic.eot');
+  src: url('fonts/KaTeX_Math-Italic.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Math-Italic.woff2') format('woff2'), url('fonts/KaTeX_Math-Italic.woff') format('woff'), url('fonts/KaTeX_Math-Italic.ttf') format('truetype');
+  font-weight: normal;
+  font-style: italic;
+}
+@font-face {
+  font-family: 'KaTeX_SansSerif';
+  src: url('fonts/KaTeX_SansSerif-Regular.eot');
+  src: url('fonts/KaTeX_SansSerif-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_SansSerif-Regular.woff2') format('woff2'), url('fonts/KaTeX_SansSerif-Regular.woff') format('woff'), url('fonts/KaTeX_SansSerif-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Script';
+  src: url('fonts/KaTeX_Script-Regular.eot');
+  src: url('fonts/KaTeX_Script-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Script-Regular.woff2') format('woff2'), url('fonts/KaTeX_Script-Regular.woff') format('woff'), url('fonts/KaTeX_Script-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size1';
+  src: url('fonts/KaTeX_Size1-Regular.eot');
+  src: url('fonts/KaTeX_Size1-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size1-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size1-Regular.woff') format('woff'), url('fonts/KaTeX_Size1-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size2';
+  src: url('fonts/KaTeX_Size2-Regular.eot');
+  src: url('fonts/KaTeX_Size2-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size2-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size2-Regular.woff') format('woff'), url('fonts/KaTeX_Size2-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size3';
+  src: url('fonts/KaTeX_Size3-Regular.eot');
+  src: url('fonts/KaTeX_Size3-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size3-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size3-Regular.woff') format('woff'), url('fonts/KaTeX_Size3-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Size4';
+  src: url('fonts/KaTeX_Size4-Regular.eot');
+  src: url('fonts/KaTeX_Size4-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size4-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size4-Regular.woff') format('woff'), url('fonts/KaTeX_Size4-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+@font-face {
+  font-family: 'KaTeX_Typewriter';
+  src: url('fonts/KaTeX_Typewriter-Regular.eot');
+  src: url('fonts/KaTeX_Typewriter-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Typewriter-Regular.woff2') format('woff2'), url('fonts/KaTeX_Typewriter-Regular.woff') format('woff'), url('fonts/KaTeX_Typewriter-Regular.ttf') format('truetype');
+  font-weight: normal;
+  font-style: normal;
+}
+.katex-display {
+  display: block;
+  margin: 1em 0;
+  text-align: center;
+}
+.katex-display > .katex {
+  display: inline-block;
+  text-align: initial;
+}
+.katex {
+  font: normal 1.21em KaTeX_Main, Times New Roman, serif;
+  line-height: 1.2;
+  white-space: nowrap;
+  text-indent: 0;
+}
+.katex .katex-html {
+  display: inline-block;
+}
+.katex .katex-mathml {
+  position: absolute;
+  clip: rect(1px, 1px, 1px, 1px);
+  padding: 0;
+  border: 0;
+  height: 1px;
+  width: 1px;
+  overflow: hidden;
+}
+.katex .base {
+  display: inline-block;
+}
+.katex .strut {
+  display: inline-block;
+}
+.katex .mathrm {
+  font-style: normal;
+}
+.katex .textit {
+  font-style: italic;
+}
+.katex .mathit {
+  font-family: KaTeX_Math;
+  font-style: italic;
+}
+.katex .mathbf {
+  font-family: KaTeX_Main;
+  font-weight: bold;
+}
+.katex .amsrm {
+  font-family: KaTeX_AMS;
+}
+.katex .mathbb {
+  font-family: KaTeX_AMS;
+}
+.katex .mathcal {
+  font-family: KaTeX_Caligraphic;
+}
+.katex .mathfrak {
+  font-family: KaTeX_Fraktur;
+}
+.katex .mathtt {
+  font-family: KaTeX_Typewriter;
+}
+.katex .mathscr {
+  font-family: KaTeX_Script;
+}
+.katex .mathsf {
+  font-family: KaTeX_SansSerif;
+}
+.katex .mainit {
+  font-family: KaTeX_Main;
+  font-style: italic;
+}
+.katex .mord + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mord + .mbin {
+  margin-left: 0.22222em;
+}
+.katex .mord + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .mord + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mord {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .mop + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mbin + .mord {
+  margin-left: 0.22222em;
+}
+.katex .mbin + .mop {
+  margin-left: 0.22222em;
+}
+.katex .mbin + .mopen {
+  margin-left: 0.22222em;
+}
+.katex .mbin + .minner {
+  margin-left: 0.22222em;
+}
+.katex .mrel + .mord {
+  margin-left: 0.27778em;
+}
+.katex .mrel + .mop {
+  margin-left: 0.27778em;
+}
+.katex .mrel + .mopen {
+  margin-left: 0.27778em;
+}
+.katex .mrel + .minner {
+  margin-left: 0.27778em;
+}
+.katex .mclose + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mclose + .mbin {
+  margin-left: 0.22222em;
+}
+.katex .mclose + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .mclose + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mord {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mop {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mrel {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mopen {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mclose {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .mpunct {
+  margin-left: 0.16667em;
+}
+.katex .mpunct + .minner {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mord {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mop {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mbin {
+  margin-left: 0.22222em;
+}
+.katex .minner + .mrel {
+  margin-left: 0.27778em;
+}
+.katex .minner + .mopen {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mpunct {
+  margin-left: 0.16667em;
+}
+.katex .minner + .minner {
+  margin-left: 0.16667em;
+}
+.katex .mord.mtight {
+  margin-left: 0;
+}
+.katex .mop.mtight {
+  margin-left: 0;
+}
+.katex .mbin.mtight {
+  margin-left: 0;
+}
+.katex .mrel.mtight {
+  margin-left: 0;
+}
+.katex .mopen.mtight {
+  margin-left: 0;
+}
+.katex .mclose.mtight {
+  margin-left: 0;
+}
+.katex .mpunct.mtight {
+  margin-left: 0;
+}
+.katex .minner.mtight {
+  margin-left: 0;
+}
+.katex .mord + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mord.mtight {
+  margin-left: 0.16667em;
+}
+.katex .mop + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .mclose + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .minner + .mop.mtight {
+  margin-left: 0.16667em;
+}
+.katex .reset-textstyle.textstyle {
+  font-size: 1em;
+}
+.katex .reset-textstyle.scriptstyle {
+  font-size: 0.7em;
+}
+.katex .reset-textstyle.scriptscriptstyle {
+  font-size: 0.5em;
+}
+.katex .reset-scriptstyle.textstyle {
+  font-size: 1.42857em;
+}
+.katex .reset-scriptstyle.scriptstyle {
+  font-size: 1em;
+}
+.katex .reset-scriptstyle.scriptscriptstyle {
+  font-size: 0.71429em;
+}
+.katex .reset-scriptscriptstyle.textstyle {
+  font-size: 2em;
+}
+.katex .reset-scriptscriptstyle.scriptstyle {
+  font-size: 1.4em;
+}
+.katex .reset-scriptscriptstyle.scriptscriptstyle {
+  font-size: 1em;
+}
+.katex .style-wrap {
+  position: relative;
+}
+.katex .vlist {
+  display: inline-block;
+}
+.katex .vlist > span {
+  display: block;
+  height: 0;
+  position: relative;
+}
+.katex .vlist > span > span {
+  display: inline-block;
+}
+.katex .vlist .baseline-fix {
+  display: inline-table;
+  table-layout: fixed;
+}
+.katex .msupsub {
+  text-align: left;
+}
+.katex .mfrac > span > span {
+  text-align: center;
+}
+.katex .mfrac .frac-line {
+  width: 100%;
+}
+.katex .mfrac .frac-line:before {
+  border-bottom-style: solid;
+  border-bottom-width: 1px;
+  content: "";
+  display: block;
+}
+.katex .mfrac .frac-line:after {
+  border-bottom-style: solid;
+  border-bottom-width: 0.04em;
+  content: "";
+  display: block;
+  margin-top: -1px;
+}
+.katex .mspace {
+  display: inline-block;
+}
+.katex .mspace.negativethinspace {
+  margin-left: -0.16667em;
+}
+.katex .mspace.thinspace {
+  width: 0.16667em;
+}
+.katex .mspace.negativemediumspace {
+  margin-left: -0.22222em;
+}
+.katex .mspace.mediumspace {
+  width: 0.22222em;
+}
+.katex .mspace.thickspace {
+  width: 0.27778em;
+}
+.katex .mspace.sixmuspace {
+  width: 0.333333em;
+}
+.katex .mspace.eightmuspace {
+  width: 0.444444em;
+}
+.katex .mspace.enspace {
+  width: 0.5em;
+}
+.katex .mspace.twelvemuspace {
+  width: 0.666667em;
+}
+.katex .mspace.quad {
+  width: 1em;
+}
+.katex .mspace.qquad {
+  width: 2em;
+}
+.katex .llap,
+.katex .rlap {
+  width: 0;
+  position: relative;
+}
+.katex .llap > .inner,
+.katex .rlap > .inner {
+  position: absolute;
+}
+.katex .llap > .fix,
+.katex .rlap > .fix {
+  display: inline-block;
+}
+.katex .llap > .inner {
+  right: 0;
+}
+.katex .rlap > .inner {
+  left: 0;
+}
+.katex .katex-logo .a {
+  font-size: 0.75em;
+  margin-left: -0.32em;
+  position: relative;
+  top: -0.2em;
+}
+.katex .katex-logo .t {
+  margin-left: -0.23em;
+}
+.katex .katex-logo .e {
+  margin-left: -0.1667em;
+  position: relative;
+  top: 0.2155em;
+}
+.katex .katex-logo .x {
+  margin-left: -0.125em;
+}
+.katex .rule {
+  display: inline-block;
+  border: solid 0;
+  position: relative;
+}
+.katex .overline .overline-line,
+.katex .underline .underline-line {
+  width: 100%;
+}
+.katex .overline .overline-line:before,
+.katex .underline .underline-line:before {
+  border-bottom-style: solid;
+  border-bottom-width: 1px;
+  content: "";
+  display: block;
+}
+.katex .overline .overline-line:after,
+.katex .underline .underline-line:after {
+  border-bottom-style: solid;
+  border-bottom-width: 0.04em;
+  content: "";
+  display: block;
+  margin-top: -1px;
+}
+.katex .sqrt > .sqrt-sign {
+  position: relative;
+}
+.katex .sqrt .sqrt-line {
+  width: 100%;
+}
+.katex .sqrt .sqrt-line:before {
+  border-bottom-style: solid;
+  border-bottom-width: 1px;
+  content: "";
+  display: block;
+}
+.katex .sqrt .sqrt-line:after {
+  border-bottom-style: solid;
+  border-bottom-width: 0.04em;
+  content: "";
+  display: block;
+  margin-top: -1px;
+}
+.katex .sqrt > .root {
+  margin-left: 0.27777778em;
+  margin-right: -0.55555556em;
+}
+.katex .sizing,
+.katex .fontsize-ensurer {
+  display: inline-block;
+}
+.katex .sizing.reset-size1.size1,
+.katex .fontsize-ensurer.reset-size1.size1 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size1.size2,
+.katex .fontsize-ensurer.reset-size1.size2 {
+  font-size: 1.4em;
+}
+.katex .sizing.reset-size1.size3,
+.katex .fontsize-ensurer.reset-size1.size3 {
+  font-size: 1.6em;
+}
+.katex .sizing.reset-size1.size4,
+.katex .fontsize-ensurer.reset-size1.size4 {
+  font-size: 1.8em;
+}
+.katex .sizing.reset-size1.size5,
+.katex .fontsize-ensurer.reset-size1.size5 {
+  font-size: 2em;
+}
+.katex .sizing.reset-size1.size6,
+.katex .fontsize-ensurer.reset-size1.size6 {
+  font-size: 2.4em;
+}
+.katex .sizing.reset-size1.size7,
+.katex .fontsize-ensurer.reset-size1.size7 {
+  font-size: 2.88em;
+}
+.katex .sizing.reset-size1.size8,
+.katex .fontsize-ensurer.reset-size1.size8 {
+  font-size: 3.46em;
+}
+.katex .sizing.reset-size1.size9,
+.katex .fontsize-ensurer.reset-size1.size9 {
+  font-size: 4.14em;
+}
+.katex .sizing.reset-size1.size10,
+.katex .fontsize-ensurer.reset-size1.size10 {
+  font-size: 4.98em;
+}
+.katex .sizing.reset-size2.size1,
+.katex .fontsize-ensurer.reset-size2.size1 {
+  font-size: 0.71428571em;
+}
+.katex .sizing.reset-size2.size2,
+.katex .fontsize-ensurer.reset-size2.size2 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size2.size3,
+.katex .fontsize-ensurer.reset-size2.size3 {
+  font-size: 1.14285714em;
+}
+.katex .sizing.reset-size2.size4,
+.katex .fontsize-ensurer.reset-size2.size4 {
+  font-size: 1.28571429em;
+}
+.katex .sizing.reset-size2.size5,
+.katex .fontsize-ensurer.reset-size2.size5 {
+  font-size: 1.42857143em;
+}
+.katex .sizing.reset-size2.size6,
+.katex .fontsize-ensurer.reset-size2.size6 {
+  font-size: 1.71428571em;
+}
+.katex .sizing.reset-size2.size7,
+.katex .fontsize-ensurer.reset-size2.size7 {
+  font-size: 2.05714286em;
+}
+.katex .sizing.reset-size2.size8,
+.katex .fontsize-ensurer.reset-size2.size8 {
+  font-size: 2.47142857em;
+}
+.katex .sizing.reset-size2.size9,
+.katex .fontsize-ensurer.reset-size2.size9 {
+  font-size: 2.95714286em;
+}
+.katex .sizing.reset-size2.size10,
+.katex .fontsize-ensurer.reset-size2.size10 {
+  font-size: 3.55714286em;
+}
+.katex .sizing.reset-size3.size1,
+.katex .fontsize-ensurer.reset-size3.size1 {
+  font-size: 0.625em;
+}
+.katex .sizing.reset-size3.size2,
+.katex .fontsize-ensurer.reset-size3.size2 {
+  font-size: 0.875em;
+}
+.katex .sizing.reset-size3.size3,
+.katex .fontsize-ensurer.reset-size3.size3 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size3.size4,
+.katex .fontsize-ensurer.reset-size3.size4 {
+  font-size: 1.125em;
+}
+.katex .sizing.reset-size3.size5,
+.katex .fontsize-ensurer.reset-size3.size5 {
+  font-size: 1.25em;
+}
+.katex .sizing.reset-size3.size6,
+.katex .fontsize-ensurer.reset-size3.size6 {
+  font-size: 1.5em;
+}
+.katex .sizing.reset-size3.size7,
+.katex .fontsize-ensurer.reset-size3.size7 {
+  font-size: 1.8em;
+}
+.katex .sizing.reset-size3.size8,
+.katex .fontsize-ensurer.reset-size3.size8 {
+  font-size: 2.1625em;
+}
+.katex .sizing.reset-size3.size9,
+.katex .fontsize-ensurer.reset-size3.size9 {
+  font-size: 2.5875em;
+}
+.katex .sizing.reset-size3.size10,
+.katex .fontsize-ensurer.reset-size3.size10 {
+  font-size: 3.1125em;
+}
+.katex .sizing.reset-size4.size1,
+.katex .fontsize-ensurer.reset-size4.size1 {
+  font-size: 0.55555556em;
+}
+.katex .sizing.reset-size4.size2,
+.katex .fontsize-ensurer.reset-size4.size2 {
+  font-size: 0.77777778em;
+}
+.katex .sizing.reset-size4.size3,
+.katex .fontsize-ensurer.reset-size4.size3 {
+  font-size: 0.88888889em;
+}
+.katex .sizing.reset-size4.size4,
+.katex .fontsize-ensurer.reset-size4.size4 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size4.size5,
+.katex .fontsize-ensurer.reset-size4.size5 {
+  font-size: 1.11111111em;
+}
+.katex .sizing.reset-size4.size6,
+.katex .fontsize-ensurer.reset-size4.size6 {
+  font-size: 1.33333333em;
+}
+.katex .sizing.reset-size4.size7,
+.katex .fontsize-ensurer.reset-size4.size7 {
+  font-size: 1.6em;
+}
+.katex .sizing.reset-size4.size8,
+.katex .fontsize-ensurer.reset-size4.size8 {
+  font-size: 1.92222222em;
+}
+.katex .sizing.reset-size4.size9,
+.katex .fontsize-ensurer.reset-size4.size9 {
+  font-size: 2.3em;
+}
+.katex .sizing.reset-size4.size10,
+.katex .fontsize-ensurer.reset-size4.size10 {
+  font-size: 2.76666667em;
+}
+.katex .sizing.reset-size5.size1,
+.katex .fontsize-ensurer.reset-size5.size1 {
+  font-size: 0.5em;
+}
+.katex .sizing.reset-size5.size2,
+.katex .fontsize-ensurer.reset-size5.size2 {
+  font-size: 0.7em;
+}
+.katex .sizing.reset-size5.size3,
+.katex .fontsize-ensurer.reset-size5.size3 {
+  font-size: 0.8em;
+}
+.katex .sizing.reset-size5.size4,
+.katex .fontsize-ensurer.reset-size5.size4 {
+  font-size: 0.9em;
+}
+.katex .sizing.reset-size5.size5,
+.katex .fontsize-ensurer.reset-size5.size5 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size5.size6,
+.katex .fontsize-ensurer.reset-size5.size6 {
+  font-size: 1.2em;
+}
+.katex .sizing.reset-size5.size7,
+.katex .fontsize-ensurer.reset-size5.size7 {
+  font-size: 1.44em;
+}
+.katex .sizing.reset-size5.size8,
+.katex .fontsize-ensurer.reset-size5.size8 {
+  font-size: 1.73em;
+}
+.katex .sizing.reset-size5.size9,
+.katex .fontsize-ensurer.reset-size5.size9 {
+  font-size: 2.07em;
+}
+.katex .sizing.reset-size5.size10,
+.katex .fontsize-ensurer.reset-size5.size10 {
+  font-size: 2.49em;
+}
+.katex .sizing.reset-size6.size1,
+.katex .fontsize-ensurer.reset-size6.size1 {
+  font-size: 0.41666667em;
+}
+.katex .sizing.reset-size6.size2,
+.katex .fontsize-ensurer.reset-size6.size2 {
+  font-size: 0.58333333em;
+}
+.katex .sizing.reset-size6.size3,
+.katex .fontsize-ensurer.reset-size6.size3 {
+  font-size: 0.66666667em;
+}
+.katex .sizing.reset-size6.size4,
+.katex .fontsize-ensurer.reset-size6.size4 {
+  font-size: 0.75em;
+}
+.katex .sizing.reset-size6.size5,
+.katex .fontsize-ensurer.reset-size6.size5 {
+  font-size: 0.83333333em;
+}
+.katex .sizing.reset-size6.size6,
+.katex .fontsize-ensurer.reset-size6.size6 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size6.size7,
+.katex .fontsize-ensurer.reset-size6.size7 {
+  font-size: 1.2em;
+}
+.katex .sizing.reset-size6.size8,
+.katex .fontsize-ensurer.reset-size6.size8 {
+  font-size: 1.44166667em;
+}
+.katex .sizing.reset-size6.size9,
+.katex .fontsize-ensurer.reset-size6.size9 {
+  font-size: 1.725em;
+}
+.katex .sizing.reset-size6.size10,
+.katex .fontsize-ensurer.reset-size6.size10 {
+  font-size: 2.075em;
+}
+.katex .sizing.reset-size7.size1,
+.katex .fontsize-ensurer.reset-size7.size1 {
+  font-size: 0.34722222em;
+}
+.katex .sizing.reset-size7.size2,
+.katex .fontsize-ensurer.reset-size7.size2 {
+  font-size: 0.48611111em;
+}
+.katex .sizing.reset-size7.size3,
+.katex .fontsize-ensurer.reset-size7.size3 {
+  font-size: 0.55555556em;
+}
+.katex .sizing.reset-size7.size4,
+.katex .fontsize-ensurer.reset-size7.size4 {
+  font-size: 0.625em;
+}
+.katex .sizing.reset-size7.size5,
+.katex .fontsize-ensurer.reset-size7.size5 {
+  font-size: 0.69444444em;
+}
+.katex .sizing.reset-size7.size6,
+.katex .fontsize-ensurer.reset-size7.size6 {
+  font-size: 0.83333333em;
+}
+.katex .sizing.reset-size7.size7,
+.katex .fontsize-ensurer.reset-size7.size7 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size7.size8,
+.katex .fontsize-ensurer.reset-size7.size8 {
+  font-size: 1.20138889em;
+}
+.katex .sizing.reset-size7.size9,
+.katex .fontsize-ensurer.reset-size7.size9 {
+  font-size: 1.4375em;
+}
+.katex .sizing.reset-size7.size10,
+.katex .fontsize-ensurer.reset-size7.size10 {
+  font-size: 1.72916667em;
+}
+.katex .sizing.reset-size8.size1,
+.katex .fontsize-ensurer.reset-size8.size1 {
+  font-size: 0.28901734em;
+}
+.katex .sizing.reset-size8.size2,
+.katex .fontsize-ensurer.reset-size8.size2 {
+  font-size: 0.40462428em;
+}
+.katex .sizing.reset-size8.size3,
+.katex .fontsize-ensurer.reset-size8.size3 {
+  font-size: 0.46242775em;
+}
+.katex .sizing.reset-size8.size4,
+.katex .fontsize-ensurer.reset-size8.size4 {
+  font-size: 0.52023121em;
+}
+.katex .sizing.reset-size8.size5,
+.katex .fontsize-ensurer.reset-size8.size5 {
+  font-size: 0.57803468em;
+}
+.katex .sizing.reset-size8.size6,
+.katex .fontsize-ensurer.reset-size8.size6 {
+  font-size: 0.69364162em;
+}
+.katex .sizing.reset-size8.size7,
+.katex .fontsize-ensurer.reset-size8.size7 {
+  font-size: 0.83236994em;
+}
+.katex .sizing.reset-size8.size8,
+.katex .fontsize-ensurer.reset-size8.size8 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size8.size9,
+.katex .fontsize-ensurer.reset-size8.size9 {
+  font-size: 1.19653179em;
+}
+.katex .sizing.reset-size8.size10,
+.katex .fontsize-ensurer.reset-size8.size10 {
+  font-size: 1.43930636em;
+}
+.katex .sizing.reset-size9.size1,
+.katex .fontsize-ensurer.reset-size9.size1 {
+  font-size: 0.24154589em;
+}
+.katex .sizing.reset-size9.size2,
+.katex .fontsize-ensurer.reset-size9.size2 {
+  font-size: 0.33816425em;
+}
+.katex .sizing.reset-size9.size3,
+.katex .fontsize-ensurer.reset-size9.size3 {
+  font-size: 0.38647343em;
+}
+.katex .sizing.reset-size9.size4,
+.katex .fontsize-ensurer.reset-size9.size4 {
+  font-size: 0.43478261em;
+}
+.katex .sizing.reset-size9.size5,
+.katex .fontsize-ensurer.reset-size9.size5 {
+  font-size: 0.48309179em;
+}
+.katex .sizing.reset-size9.size6,
+.katex .fontsize-ensurer.reset-size9.size6 {
+  font-size: 0.57971014em;
+}
+.katex .sizing.reset-size9.size7,
+.katex .fontsize-ensurer.reset-size9.size7 {
+  font-size: 0.69565217em;
+}
+.katex .sizing.reset-size9.size8,
+.katex .fontsize-ensurer.reset-size9.size8 {
+  font-size: 0.83574879em;
+}
+.katex .sizing.reset-size9.size9,
+.katex .fontsize-ensurer.reset-size9.size9 {
+  font-size: 1em;
+}
+.katex .sizing.reset-size9.size10,
+.katex .fontsize-ensurer.reset-size9.size10 {
+  font-size: 1.20289855em;
+}
+.katex .sizing.reset-size10.size1,
+.katex .fontsize-ensurer.reset-size10.size1 {
+  font-size: 0.20080321em;
+}
+.katex .sizing.reset-size10.size2,
+.katex .fontsize-ensurer.reset-size10.size2 {
+  font-size: 0.2811245em;
+}
+.katex .sizing.reset-size10.size3,
+.katex .fontsize-ensurer.reset-size10.size3 {
+  font-size: 0.32128514em;
+}
+.katex .sizing.reset-size10.size4,
+.katex .fontsize-ensurer.reset-size10.size4 {
+  font-size: 0.36144578em;
+}
+.katex .sizing.reset-size10.size5,
+.katex .fontsize-ensurer.reset-size10.size5 {
+  font-size: 0.40160643em;
+}
+.katex .sizing.reset-size10.size6,
+.katex .fontsize-ensurer.reset-size10.size6 {
+  font-size: 0.48192771em;
+}
+.katex .sizing.reset-size10.size7,
+.katex .fontsize-ensurer.reset-size10.size7 {
+  font-size: 0.57831325em;
+}
+.katex .sizing.reset-size10.size8,
+.katex .fontsize-ensurer.reset-size10.size8 {
+  font-size: 0.69477912em;
+}
+.katex .sizing.reset-size10.size9,
+.katex .fontsize-ensurer.reset-size10.size9 {
+  font-size: 0.8313253em;
+}
+.katex .sizing.reset-size10.size10,
+.katex .fontsize-ensurer.reset-size10.size10 {
+  font-size: 1em;
+}
+.katex .delimsizing.size1 {
+  font-family: KaTeX_Size1;
+}
+.katex .delimsizing.size2 {
+  font-family: KaTeX_Size2;
+}
+.katex .delimsizing.size3 {
+  font-family: KaTeX_Size3;
+}
+.katex .delimsizing.size4 {
+  font-family: KaTeX_Size4;
+}
+.katex .delimsizing.mult .delim-size1 > span {
+  font-family: KaTeX_Size1;
+}
+.katex .delimsizing.mult .delim-size4 > span {
+  font-family: KaTeX_Size4;
+}
+.katex .nulldelimiter {
+  display: inline-block;
+  width: 0.12em;
+}
+.katex .op-symbol {
+  position: relative;
+}
+.katex .op-symbol.small-op {
+  font-family: KaTeX_Size1;
+}
+.katex .op-symbol.large-op {
+  font-family: KaTeX_Size2;
+}
+.katex .op-limits > .vlist > span {
+  text-align: center;
+}
+.katex .accent > .vlist > span {
+  text-align: center;
+}
+.katex .accent .accent-body > span {
+  width: 0;
+}
+.katex .accent .accent-body.accent-vec > span {
+  position: relative;
+  left: 0.326em;
+}
+.katex .mtable .vertical-separator {
+  display: inline-block;
+  margin: 0 -0.025em;
+  border-right: 0.05em solid black;
+}
+.katex .mtable .arraycolsep {
+  display: inline-block;
+}
+.katex .mtable .col-align-c > .vlist {
+  text-align: center;
+}
+.katex .mtable .col-align-l > .vlist {
+  text-align: left;
+}
+.katex .mtable .col-align-r > .vlist {
+  text-align: right;
+}
diff --git a/specs/gl/katex/katex.js b/specs/gl/katex/katex.js
new file mode 100644
index 0000000..e104be9
--- /dev/null
+++ b/specs/gl/katex/katex.js
@@ -0,0 +1,9075 @@
+(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.katex = f()}})(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
+/* eslint no-console:0 */
+/**
+ * This is the main entry point for KaTeX. Here, we expose functions for
+ * rendering expressions either to DOM nodes or to markup strings.
+ *
+ * We also expose the ParseError class to check if errors thrown from KaTeX are
+ * errors in the expression, or errors in javascript handling.
+ */
+
+var ParseError = require("./src/ParseError");
+var Settings = require("./src/Settings");
+
+var buildTree = require("./src/buildTree");
+var parseTree = require("./src/parseTree");
+var utils = require("./src/utils");
+
+/**
+ * Parse and build an expression, and place that expression in the DOM node
+ * given.
+ */
+var render = function(expression, baseNode, options) {
+    utils.clearNode(baseNode);
+
+    var settings = new Settings(options);
+
+    var tree = parseTree(expression, settings);
+    var node = buildTree(tree, expression, settings).toNode();
+
+    baseNode.appendChild(node);
+};
+
+// KaTeX's styles don't work properly in quirks mode. Print out an error, and
+// disable rendering.
+if (typeof document !== "undefined") {
+    if (document.compatMode !== "CSS1Compat") {
+        typeof console !== "undefined" && console.warn(
+            "Warning: KaTeX doesn't work in quirks mode. Make sure your " +
+                "website has a suitable doctype.");
+
+        render = function() {
+            throw new ParseError("KaTeX doesn't work in quirks mode.");
+        };
+    }
+}
+
+/**
+ * Parse and build an expression, and return the markup for that.
+ */
+var renderToString = function(expression, options) {
+    var settings = new Settings(options);
+
+    var tree = parseTree(expression, settings);
+    return buildTree(tree, expression, settings).toMarkup();
+};
+
+/**
+ * Parse an expression and return the parse tree.
+ */
+var generateParseTree = function(expression, options) {
+    var settings = new Settings(options);
+    return parseTree(expression, settings);
+};
+
+module.exports = {
+    render: render,
+    renderToString: renderToString,
+    /**
+     * NOTE: This method is not currently recommended for public use.
+     * The internal tree representation is unstable and is very likely
+     * to change. Use at your own risk.
+     */
+    __parse: generateParseTree,
+    ParseError: ParseError
+};
+
+},{"./src/ParseError":6,"./src/Settings":8,"./src/buildTree":13,"./src/parseTree":22,"./src/utils":25}],2:[function(require,module,exports){
+/** @flow */
+
+"use strict";
+
+function getRelocatable(re) {
+  // In the future, this could use a WeakMap instead of an expando.
+  if (!re.__matchAtRelocatable) {
+    // Disjunctions are the lowest-precedence operator, so we can make any
+    // pattern match the empty string by appending `|()` to it:
+    // https://people.mozilla.org/~jorendorff/es6-draft.html#sec-patterns
+    var source = re.source + "|()";
+
+    // We always make the new regex global.
+    var flags = "g" + (re.ignoreCase ? "i" : "") + (re.multiline ? "m" : "") + (re.unicode ? "u" : "")
+    // sticky (/.../y) doesn't make sense in conjunction with our relocation
+    // logic, so we ignore it here.
+    ;
+
+    re.__matchAtRelocatable = new RegExp(source, flags);
+  }
+  return re.__matchAtRelocatable;
+}
+
+function matchAt(re, str, pos) {
+  if (re.global || re.sticky) {
+    throw new Error("matchAt(...): Only non-global regexes are supported");
+  }
+  var reloc = getRelocatable(re);
+  reloc.lastIndex = pos;
+  var match = reloc.exec(str);
+  // Last capturing group is our sentinel that indicates whether the regex
+  // matched at the given location.
+  if (match[match.length - 1] == null) {
+    // Original regex matched.
+    match.length = match.length - 1;
+    return match;
+  } else {
+    return null;
+  }
+}
+
+module.exports = matchAt;
+},{}],3:[function(require,module,exports){
+/**
+ * The Lexer class handles tokenizing the input in various ways. Since our
+ * parser expects us to be able to backtrack, the lexer allows lexing from any
+ * given starting point.
+ *
+ * Its main exposed function is the `lex` function, which takes a position to
+ * lex from and a type of token to lex. It defers to the appropriate `_innerLex`
+ * function.
+ *
+ * The various `_innerLex` functions perform the actual lexing of different
+ * kinds.
+ */
+
+var matchAt = require("match-at");
+
+var ParseError = require("./ParseError");
+
+// The main lexer class
+function Lexer(input) {
+    this.input = input;
+    this.pos = 0;
+}
+
+/**
+ * The resulting token returned from `lex`.
+ *
+ * It consists of the token text plus some position information.
+ * The position information is essentially a range in an input string,
+ * but instead of referencing the bare input string, we refer to the lexer.
+ * That way it is possible to attach extra metadata to the input string,
+ * like for example a file name or similar.
+ *
+ * The position information (all three parameters) is optional,
+ * so it is OK to construct synthetic tokens if appropriate.
+ * Not providing available position information may lead to
+ * degraded error reporting, though.
+ *
+ * @param {string}  text   the text of this token
+ * @param {number=} start  the start offset, zero-based inclusive
+ * @param {number=} end    the end offset, zero-based exclusive
+ * @param {Lexer=}  lexer  the lexer which in turn holds the input string
+ */
+function Token(text, start, end, lexer) {
+    this.text = text;
+    this.start = start;
+    this.end = end;
+    this.lexer = lexer;
+}
+
+/**
+ * Given a pair of tokens (this and endToken), compute a “Token” encompassing
+ * the whole input range enclosed by these two.
+ *
+ * @param {Token}  endToken  last token of the range, inclusive
+ * @param {string} text      the text of the newly constructed token
+ */
+Token.prototype.range = function(endToken, text) {
+    if (endToken.lexer !== this.lexer) {
+        return new Token(text); // sorry, no position information available
+    }
+    return new Token(text, this.start, endToken.end, this.lexer);
+};
+
+/* The following tokenRegex
+ * - matches typical whitespace (but not NBSP etc.) using its first group
+ * - does not match any control character \x00-\x1f except whitespace
+ * - does not match a bare backslash
+ * - matches any ASCII character except those just mentioned
+ * - does not match the BMP private use area \uE000-\uF8FF
+ * - does not match bare surrogate code units
+ * - matches any BMP character except for those just described
+ * - matches any valid Unicode surrogate pair
+ * - matches a backslash followed by one or more letters
+ * - matches a backslash followed by any BMP character, including newline
+ * Just because the Lexer matches something doesn't mean it's valid input:
+ * If there is no matching function or symbol definition, the Parser will
+ * still reject the input.
+ */
+var tokenRegex = new RegExp(
+    "([ \r\n\t]+)|" +                                 // whitespace
+    "([!-\\[\\]-\u2027\u202A-\uD7FF\uF900-\uFFFF]" +  // single codepoint
+    "|[\uD800-\uDBFF][\uDC00-\uDFFF]" +               // surrogate pair
+    "|\\\\(?:[a-zA-Z]+|[^\uD800-\uDFFF])" +           // function name
+    ")"
+);
+
+/**
+ * This function lexes a single token.
+ */
+Lexer.prototype.lex = function() {
+    var input = this.input;
+    var pos = this.pos;
+    if (pos === input.length) {
+        return new Token("EOF", pos, pos, this);
+    }
+    var match = matchAt(tokenRegex, input, pos);
+    if (match === null) {
+        throw new ParseError(
+            "Unexpected character: '" + input[pos] + "'",
+            new Token(input[pos], pos, pos + 1, this));
+    }
+    var text = match[2] || " ";
+    var start = this.pos;
+    this.pos += match[0].length;
+    var end = this.pos;
+    return new Token(text, start, end, this);
+};
+
+module.exports = Lexer;
+
+},{"./ParseError":6,"match-at":2}],4:[function(require,module,exports){
+/**
+ * This file contains the “gullet” where macros are expanded
+ * until only non-macro tokens remain.
+ */
+
+var Lexer = require("./Lexer");
+
+function MacroExpander(input, macros) {
+    this.lexer = new Lexer(input);
+    this.macros = macros;
+    this.stack = []; // contains tokens in REVERSE order
+    this.discardedWhiteSpace = [];
+}
+
+/**
+ * Recursively expand first token, then return first non-expandable token.
+ */
+MacroExpander.prototype.nextToken = function() {
+    for (;;) {
+        if (this.stack.length === 0) {
+            this.stack.push(this.lexer.lex());
+        }
+        var topToken = this.stack.pop();
+        var name = topToken.text;
+        if (!(name.charAt(0) === "\\" && this.macros.hasOwnProperty(name))) {
+            return topToken;
+        }
+        var expansion = this.macros[name];
+        if (typeof expansion === "string") {
+            var bodyLexer = new Lexer(expansion);
+            expansion = [];
+            var tok = bodyLexer.lex();
+            while (tok.text !== "EOF") {
+                expansion.push(tok);
+                tok = bodyLexer.lex();
+            }
+            expansion.reverse(); // to fit in with stack using push and pop
+            this.macros[name] = expansion;
+        }
+        this.stack = this.stack.concat(expansion);
+    }
+};
+
+MacroExpander.prototype.get = function(ignoreSpace) {
+    this.discardedWhiteSpace = [];
+    var token = this.nextToken();
+    if (ignoreSpace) {
+        while (token.text === " ") {
+            this.discardedWhiteSpace.push(token);
+            token = this.nextToken();
+        }
+    }
+    return token;
+};
+
+/**
+ * Undo the effect of the preceding call to the get method.
+ * A call to this method MUST be immediately preceded and immediately followed
+ * by a call to get.  Only used during mode switching, i.e. after one token
+ * was got in the old mode but should get got again in a new mode
+ * with possibly different whitespace handling.
+ */
+MacroExpander.prototype.unget = function(token) {
+    this.stack.push(token);
+    while (this.discardedWhiteSpace.length !== 0) {
+        this.stack.push(this.discardedWhiteSpace.pop());
+    }
+};
+
+module.exports = MacroExpander;
+
+},{"./Lexer":3}],5:[function(require,module,exports){
+/**
+ * This file contains information about the options that the Parser carries
+ * around with it while parsing. Data is held in an `Options` object, and when
+ * recursing, a new `Options` object can be created with the `.with*` and
+ * `.reset` functions.
+ */
+
+/**
+ * This is the main options class. It contains the style, size, color, and font
+ * of the current parse level. It also contains the style and size of the parent
+ * parse level, so size changes can be handled efficiently.
+ *
+ * Each of the `.with*` and `.reset` functions passes its current style and size
+ * as the parentStyle and parentSize of the new options class, so parent
+ * handling is taken care of automatically.
+ */
+function Options(data) {
+    this.style = data.style;
+    this.color = data.color;
+    this.size = data.size;
+    this.phantom = data.phantom;
+    this.font = data.font;
+
+    if (data.parentStyle === undefined) {
+        this.parentStyle = data.style;
+    } else {
+        this.parentStyle = data.parentStyle;
+    }
+
+    if (data.parentSize === undefined) {
+        this.parentSize = data.size;
+    } else {
+        this.parentSize = data.parentSize;
+    }
+}
+
+/**
+ * Returns a new options object with the same properties as "this".  Properties
+ * from "extension" will be copied to the new options object.
+ */
+Options.prototype.extend = function(extension) {
+    var data = {
+        style: this.style,
+        size: this.size,
+        color: this.color,
+        parentStyle: this.style,
+        parentSize: this.size,
+        phantom: this.phantom,
+        font: this.font
+    };
+
+    for (var key in extension) {
+        if (extension.hasOwnProperty(key)) {
+            data[key] = extension[key];
+        }
+    }
+
+    return new Options(data);
+};
+
+/**
+ * Create a new options object with the given style.
+ */
+Options.prototype.withStyle = function(style) {
+    return this.extend({
+        style: style
+    });
+};
+
+/**
+ * Create a new options object with the given size.
+ */
+Options.prototype.withSize = function(size) {
+    return this.extend({
+        size: size
+    });
+};
+
+/**
+ * Create a new options object with the given color.
+ */
+Options.prototype.withColor = function(color) {
+    return this.extend({
+        color: color
+    });
+};
+
+/**
+ * Create a new options object with "phantom" set to true.
+ */
+Options.prototype.withPhantom = function() {
+    return this.extend({
+        phantom: true
+    });
+};
+
+/**
+ * Create a new options objects with the give font.
+ */
+Options.prototype.withFont = function(font) {
+    return this.extend({
+        font: font || this.font
+    });
+};
+
+/**
+ * Create a new options object with the same style, size, and color. This is
+ * used so that parent style and size changes are handled correctly.
+ */
+Options.prototype.reset = function() {
+    return this.extend({});
+};
+
+/**
+ * A map of color names to CSS colors.
+ * TODO(emily): Remove this when we have real macros
+ */
+var colorMap = {
+    "katex-blue": "#6495ed",
+    "katex-orange": "#ffa500",
+    "katex-pink": "#ff00af",
+    "katex-red": "#df0030",
+    "katex-green": "#28ae7b",
+    "katex-gray": "gray",
+    "katex-purple": "#9d38bd",
+    "katex-blueA": "#ccfaff",
+    "katex-blueB": "#80f6ff",
+    "katex-blueC": "#63d9ea",
+    "katex-blueD": "#11accd",
+    "katex-blueE": "#0c7f99",
+    "katex-tealA": "#94fff5",
+    "katex-tealB": "#26edd5",
+    "katex-tealC": "#01d1c1",
+    "katex-tealD": "#01a995",
+    "katex-tealE": "#208170",
+    "katex-greenA": "#b6ffb0",
+    "katex-greenB": "#8af281",
+    "katex-greenC": "#74cf70",
+    "katex-greenD": "#1fab54",
+    "katex-greenE": "#0d923f",
+    "katex-goldA": "#ffd0a9",
+    "katex-goldB": "#ffbb71",
+    "katex-goldC": "#ff9c39",
+    "katex-goldD": "#e07d10",
+    "katex-goldE": "#a75a05",
+    "katex-redA": "#fca9a9",
+    "katex-redB": "#ff8482",
+    "katex-redC": "#f9685d",
+    "katex-redD": "#e84d39",
+    "katex-redE": "#bc2612",
+    "katex-maroonA": "#ffbde0",
+    "katex-maroonB": "#ff92c6",
+    "katex-maroonC": "#ed5fa6",
+    "katex-maroonD": "#ca337c",
+    "katex-maroonE": "#9e034e",
+    "katex-purpleA": "#ddd7ff",
+    "katex-purpleB": "#c6b9fc",
+    "katex-purpleC": "#aa87ff",
+    "katex-purpleD": "#7854ab",
+    "katex-purpleE": "#543b78",
+    "katex-mintA": "#f5f9e8",
+    "katex-mintB": "#edf2df",
+    "katex-mintC": "#e0e5cc",
+    "katex-grayA": "#f6f7f7",
+    "katex-grayB": "#f0f1f2",
+    "katex-grayC": "#e3e5e6",
+    "katex-grayD": "#d6d8da",
+    "katex-grayE": "#babec2",
+    "katex-grayF": "#888d93",
+    "katex-grayG": "#626569",
+    "katex-grayH": "#3b3e40",
+    "katex-grayI": "#21242c",
+    "katex-kaBlue": "#314453",
+    "katex-kaGreen": "#71B307"
+};
+
+/**
+ * Gets the CSS color of the current options object, accounting for the
+ * `colorMap`.
+ */
+Options.prototype.getColor = function() {
+    if (this.phantom) {
+        return "transparent";
+    } else {
+        return colorMap[this.color] || this.color;
+    }
+};
+
+module.exports = Options;
+
+},{}],6:[function(require,module,exports){
+/**
+ * This is the ParseError class, which is the main error thrown by KaTeX
+ * functions when something has gone wrong. This is used to distinguish internal
+ * errors from errors in the expression that the user provided.
+ *
+ * If possible, a caller should provide a Token or ParseNode with information
+ * about where in the source string the problem occurred.
+ *
+ * @param {string} message  The error message
+ * @param {(Token|ParseNode)=} token  An object providing position information
+ */
+function ParseError(message, token) {
+    var error = "KaTeX parse error: " + message;
+    var start;
+    var end;
+
+    if (token && token.lexer && token.start <= token.end) {
+        // If we have the input and a position, make the error a bit fancier
+
+        // Get the input
+        var input = token.lexer.input;
+
+        // Prepend some information
+        start = token.start;
+        end = token.end;
+        if (start === input.length) {
+            error += " at end of input: ";
+        } else {
+            error += " at position " + (start + 1) + ": ";
+        }
+
+        // Underline token in question using combining underscores
+        var underlined = input.slice(start, end).replace(/[^]/g, "$&\u0332");
+
+        // Extract some context from the input and add it to the error
+        var left;
+        if (start > 15) {
+            left = "…" + input.slice(start - 15, start);
+        } else {
+            left = input.slice(0, start);
+        }
+        var right;
+        if (end + 15 < input.length) {
+            right = input.slice(end, end + 15) + "…";
+        } else {
+            right = input.slice(end);
+        }
+        error += left + underlined + right;
+    }
+
+    // Some hackery to make ParseError a prototype of Error
+    // See http://stackoverflow.com/a/8460753
+    var self = new Error(error);
+    self.name = "ParseError";
+    self.__proto__ = ParseError.prototype;
+
+    self.position = start;
+    return self;
+}
+
+// More hackery
+ParseError.prototype.__proto__ = Error.prototype;
+
+module.exports = ParseError;
+
+},{}],7:[function(require,module,exports){
+/* eslint no-constant-condition:0 */
+var functions = require("./functions");
+var environments = require("./environments");
+var MacroExpander = require("./MacroExpander");
+var symbols = require("./symbols");
+var utils = require("./utils");
+var cjkRegex = require("./unicodeRegexes").cjkRegex;
+
+var parseData = require("./parseData");
+var ParseError = require("./ParseError");
+
+/**
+ * This file contains the parser used to parse out a TeX expression from the
+ * input. Since TeX isn't context-free, standard parsers don't work particularly
+ * well.
+ *
+ * The strategy of this parser is as such:
+ *
+ * The main functions (the `.parse...` ones) take a position in the current
+ * parse string to parse tokens from. The lexer (found in Lexer.js, stored at
+ * this.lexer) also supports pulling out tokens at arbitrary places. When
+ * individual tokens are needed at a position, the lexer is called to pull out a
+ * token, which is then used.
+ *
+ * The parser has a property called "mode" indicating the mode that
+ * the parser is currently in. Currently it has to be one of "math" or
+ * "text", which denotes whether the current environment is a math-y
+ * one or a text-y one (e.g. inside \text). Currently, this serves to
+ * limit the functions which can be used in text mode.
+ *
+ * The main functions then return an object which contains the useful data that
+ * was parsed at its given point, and a new position at the end of the parsed
+ * data. The main functions can call each other and continue the parsing by
+ * using the returned position as a new starting point.
+ *
+ * There are also extra `.handle...` functions, which pull out some reused
+ * functionality into self-contained functions.
+ *
+ * The earlier functions return ParseNodes.
+ * The later functions (which are called deeper in the parse) sometimes return
+ * ParseFuncOrArgument, which contain a ParseNode as well as some data about
+ * whether the parsed object is a function which is missing some arguments, or a
+ * standalone object which can be used as an argument to another function.
+ */
+
+/**
+ * Main Parser class
+ */
+function Parser(input, settings) {
+    // Create a new macro expander (gullet) and (indirectly via that) also a
+    // new lexer (mouth) for this parser (stomach, in the language of TeX)
+    this.gullet = new MacroExpander(input, settings.macros);
+    // Store the settings for use in parsing
+    this.settings = settings;
+    // Count leftright depth (for \middle errors)
+    this.leftrightDepth = 0;
+}
+
+var ParseNode = parseData.ParseNode;
+
+/**
+ * An initial function (without its arguments), or an argument to a function.
+ * The `result` argument should be a ParseNode.
+ */
+function ParseFuncOrArgument(result, isFunction, token) {
+    this.result = result;
+    // Is this a function (i.e. is it something defined in functions.js)?
+    this.isFunction = isFunction;
+    this.token = token;
+}
+
+/**
+ * Checks a result to make sure it has the right type, and throws an
+ * appropriate error otherwise.
+ *
+ * @param {boolean=} consume whether to consume the expected token,
+ *                           defaults to true
+ */
+Parser.prototype.expect = function(text, consume) {
+    if (this.nextToken.text !== text) {
+        throw new ParseError(
+            "Expected '" + text + "', got '" + this.nextToken.text + "'",
+            this.nextToken
+        );
+    }
+    if (consume !== false) {
+        this.consume();
+    }
+};
+
+/**
+ * Considers the current look ahead token as consumed,
+ * and fetches the one after that as the new look ahead.
+ */
+Parser.prototype.consume = function() {
+    this.nextToken = this.gullet.get(this.mode === "math");
+};
+
+Parser.prototype.switchMode = function(newMode) {
+    this.gullet.unget(this.nextToken);
+    this.mode = newMode;
+    this.consume();
+};
+
+/**
+ * Main parsing function, which parses an entire input.
+ *
+ * @return {?Array.<ParseNode>}
+ */
+Parser.prototype.parse = function() {
+    // Try to parse the input
+    this.mode = "math";
+    this.consume();
+    var parse = this.parseInput();
+    return parse;
+};
+
+/**
+ * Parses an entire input tree.
+ */
+Parser.prototype.parseInput = function() {
+    // Parse an expression
+    var expression = this.parseExpression(false);
+    // If we succeeded, make sure there's an EOF at the end
+    this.expect("EOF", false);
+    return expression;
+};
+
+var endOfExpression = ["}", "\\end", "\\right", "&", "\\\\", "\\cr"];
+
+/**
+ * Parses an "expression", which is a list of atoms.
+ *
+ * @param {boolean} breakOnInfix  Should the parsing stop when we hit infix
+ *                  nodes? This happens when functions have higher precendence
+ *                  than infix nodes in implicit parses.
+ *
+ * @param {?string} breakOnTokenText  The text of the token that the expression
+ *                  should end with, or `null` if something else should end the
+ *                  expression.
+ *
+ * @return {ParseNode}
+ */
+Parser.prototype.parseExpression = function(breakOnInfix, breakOnTokenText) {
+    var body = [];
+    // Keep adding atoms to the body until we can't parse any more atoms (either
+    // we reached the end, a }, or a \right)
+    while (true) {
+        var lex = this.nextToken;
+        if (endOfExpression.indexOf(lex.text) !== -1) {
+            break;
+        }
+        if (breakOnTokenText && lex.text === breakOnTokenText) {
+            break;
+        }
+        if (breakOnInfix && functions[lex.text] && functions[lex.text].infix) {
+            break;
+        }
+        var atom = this.parseAtom();
+        if (!atom) {
+            if (!this.settings.throwOnError && lex.text[0] === "\\") {
+                var errorNode = this.handleUnsupportedCmd();
+                body.push(errorNode);
+                continue;
+            }
+
+            break;
+        }
+        body.push(atom);
+    }
+    return this.handleInfixNodes(body);
+};
+
+/**
+ * Rewrites infix operators such as \over with corresponding commands such
+ * as \frac.
+ *
+ * There can only be one infix operator per group.  If there's more than one
+ * then the expression is ambiguous.  This can be resolved by adding {}.
+ *
+ * @returns {Array}
+ */
+Parser.prototype.handleInfixNodes = function(body) {
+    var overIndex = -1;
+    var funcName;
+
+    for (var i = 0; i < body.length; i++) {
+        var node = body[i];
+        if (node.type === "infix") {
+            if (overIndex !== -1) {
+                throw new ParseError(
+                    "only one infix operator per group",
+                    node.value.token);
+            }
+            overIndex = i;
+            funcName = node.value.replaceWith;
+        }
+    }
+
+    if (overIndex !== -1) {
+        var numerNode;
+        var denomNode;
+
+        var numerBody = body.slice(0, overIndex);
+        var denomBody = body.slice(overIndex + 1);
+
+        if (numerBody.length === 1 && numerBody[0].type === "ordgroup") {
+            numerNode = numerBody[0];
+        } else {
+            numerNode = new ParseNode("ordgroup", numerBody, this.mode);
+        }
+
+        if (denomBody.length === 1 && denomBody[0].type === "ordgroup") {
+            denomNode = denomBody[0];
+        } else {
+            denomNode = new ParseNode("ordgroup", denomBody, this.mode);
+        }
+
+        var value = this.callFunction(
+            funcName, [numerNode, denomNode], null);
+        return [new ParseNode(value.type, value, this.mode)];
+    } else {
+        return body;
+    }
+};
+
+// The greediness of a superscript or subscript
+var SUPSUB_GREEDINESS = 1;
+
+/**
+ * Handle a subscript or superscript with nice errors.
+ */
+Parser.prototype.handleSupSubscript = function(name) {
+    var symbolToken = this.nextToken;
+    var symbol = symbolToken.text;
+    this.consume();
+    var group = this.parseGroup();
+
+    if (!group) {
+        if (!this.settings.throwOnError && this.nextToken.text[0] === "\\") {
+            return this.handleUnsupportedCmd();
+        } else {
+            throw new ParseError(
+                "Expected group after '" + symbol + "'",
+                symbolToken
+            );
+        }
+    } else if (group.isFunction) {
+        // ^ and _ have a greediness, so handle interactions with functions'
+        // greediness
+        var funcGreediness = functions[group.result].greediness;
+        if (funcGreediness > SUPSUB_GREEDINESS) {
+            return this.parseFunction(group);
+        } else {
+            throw new ParseError(
+                "Got function '" + group.result + "' with no arguments " +
+                    "as " + name, symbolToken);
+        }
+    } else {
+        return group.result;
+    }
+};
+
+/**
+ * Converts the textual input of an unsupported command into a text node
+ * contained within a color node whose color is determined by errorColor
+ */
+Parser.prototype.handleUnsupportedCmd = function() {
+    var text = this.nextToken.text;
+    var textordArray = [];
+
+    for (var i = 0; i < text.length; i++) {
+        textordArray.push(new ParseNode("textord", text[i], "text"));
+    }
+
+    var textNode = new ParseNode(
+        "text",
+        {
+            body: textordArray,
+            type: "text"
+        },
+        this.mode);
+
+    var colorNode = new ParseNode(
+        "color",
+        {
+            color: this.settings.errorColor,
+            value: [textNode],
+            type: "color"
+        },
+        this.mode);
+
+    this.consume();
+    return colorNode;
+};
+
+/**
+ * Parses a group with optional super/subscripts.
+ *
+ * @return {?ParseNode}
+ */
+Parser.prototype.parseAtom = function() {
+    // The body of an atom is an implicit group, so that things like
+    // \left(x\right)^2 work correctly.
+    var base = this.parseImplicitGroup();
+
+    // In text mode, we don't have superscripts or subscripts
+    if (this.mode === "text") {
+        return base;
+    }
+
+    // Note that base may be empty (i.e. null) at this point.
+
+    var superscript;
+    var subscript;
+    while (true) {
+        // Lex the first token
+        var lex = this.nextToken;
+
+        if (lex.text === "\\limits" || lex.text === "\\nolimits") {
+            // We got a limit control
+            if (!base || base.type !== "op") {
+                throw new ParseError(
+                    "Limit controls must follow a math operator",
+                    lex);
+            } else {
+                var limits = lex.text === "\\limits";
+                base.value.limits = limits;
+                base.value.alwaysHandleSupSub = true;
+            }
+            this.consume();
+        } else if (lex.text === "^") {
+            // We got a superscript start
+            if (superscript) {
+                throw new ParseError("Double superscript", lex);
+            }
+            superscript = this.handleSupSubscript("superscript");
+        } else if (lex.text === "_") {
+            // We got a subscript start
+            if (subscript) {
+                throw new ParseError("Double subscript", lex);
+            }
+            subscript = this.handleSupSubscript("subscript");
+        } else if (lex.text === "'") {
+            // We got a prime
+            var prime = new ParseNode("textord", "\\prime", this.mode);
+
+            // Many primes can be grouped together, so we handle this here
+            var primes = [prime];
+            this.consume();
+            // Keep lexing tokens until we get something that's not a prime
+            while (this.nextToken.text === "'") {
+                // For each one, add another prime to the list
+                primes.push(prime);
+                this.consume();
+            }
+            // Put them into an ordgroup as the superscript
+            superscript = new ParseNode("ordgroup", primes, this.mode);
+        } else {
+            // If it wasn't ^, _, or ', stop parsing super/subscripts
+            break;
+        }
+    }
+
+    if (superscript || subscript) {
+        // If we got either a superscript or subscript, create a supsub
+        return new ParseNode("supsub", {
+            base: base,
+            sup: superscript,
+            sub: subscript
+        }, this.mode);
+    } else {
+        // Otherwise return the original body
+        return base;
+    }
+};
+
+// A list of the size-changing functions, for use in parseImplicitGroup
+var sizeFuncs = [
+    "\\tiny", "\\scriptsize", "\\footnotesize", "\\small", "\\normalsize",
+    "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"
+];
+
+// A list of the style-changing functions, for use in parseImplicitGroup
+var styleFuncs = [
+    "\\displaystyle", "\\textstyle", "\\scriptstyle", "\\scriptscriptstyle"
+];
+
+/**
+ * Parses an implicit group, which is a group that starts at the end of a
+ * specified, and ends right before a higher explicit group ends, or at EOL. It
+ * is used for functions that appear to affect the current style, like \Large or
+ * \textrm, where instead of keeping a style we just pretend that there is an
+ * implicit grouping after it until the end of the group. E.g.
+ *   small text {\Large large text} small text again
+ * It is also used for \left and \right to get the correct grouping.
+ *
+ * @return {?ParseNode}
+ */
+Parser.prototype.parseImplicitGroup = function() {
+    var start = this.parseSymbol();
+
+    if (start == null) {
+        // If we didn't get anything we handle, fall back to parseFunction
+        return this.parseFunction();
+    }
+
+    var func = start.result;
+    var body;
+
+    if (func === "\\left") {
+        // If we see a left:
+        // Parse the entire left function (including the delimiter)
+        var left = this.parseFunction(start);
+        // Parse out the implicit body
+        ++this.leftrightDepth;
+        body = this.parseExpression(false);
+        --this.leftrightDepth;
+        // Check the next token
+        this.expect("\\right", false);
+        var right = this.parseFunction();
+        return new ParseNode("leftright", {
+            body: body,
+            left: left.value.value,
+            right: right.value.value
+        }, this.mode);
+    } else if (func === "\\begin") {
+        // begin...end is similar to left...right
+        var begin = this.parseFunction(start);
+        var envName = begin.value.name;
+        if (!environments.hasOwnProperty(envName)) {
+            throw new ParseError(
+                "No such environment: " + envName, begin.value.nameGroup);
+        }
+        // Build the environment object. Arguments and other information will
+        // be made available to the begin and end methods using properties.
+        var env = environments[envName];
+        var args = this.parseArguments("\\begin{" + envName + "}", env);
+        var context = {
+            mode: this.mode,
+            envName: envName,
+            parser: this,
+            positions: args.pop()
+        };
+        var result = env.handler(context, args);
+        this.expect("\\end", false);
+        var endNameToken = this.nextToken;
+        var end = this.parseFunction();
+        if (end.value.name !== envName) {
+            throw new ParseError(
+                "Mismatch: \\begin{" + envName + "} matched " +
+                "by \\end{" + end.value.name + "}",
+                endNameToken);
+        }
+        result.position = end.position;
+        return result;
+    } else if (utils.contains(sizeFuncs, func)) {
+        // If we see a sizing function, parse out the implict body
+        body = this.parseExpression(false);
+        return new ParseNode("sizing", {
+            // Figure out what size to use based on the list of functions above
+            size: "size" + (utils.indexOf(sizeFuncs, func) + 1),
+            value: body
+        }, this.mode);
+    } else if (utils.contains(styleFuncs, func)) {
+        // If we see a styling function, parse out the implict body
+        body = this.parseExpression(true);
+        return new ParseNode("styling", {
+            // Figure out what style to use by pulling out the style from
+            // the function name
+            style: func.slice(1, func.length - 5),
+            value: body
+        }, this.mode);
+    } else {
+        // Defer to parseFunction if it's not a function we handle
+        return this.parseFunction(start);
+    }
+};
+
+/**
+ * Parses an entire function, including its base and all of its arguments.
+ * The base might either have been parsed already, in which case
+ * it is provided as an argument, or it's the next group in the input.
+ *
+ * @param {ParseFuncOrArgument=} baseGroup optional as described above
+ * @return {?ParseNode}
+ */
+Parser.prototype.parseFunction = function(baseGroup) {
+    if (!baseGroup) {
+        baseGroup = this.parseGroup();
+    }
+
+    if (baseGroup) {
+        if (baseGroup.isFunction) {
+            var func = baseGroup.result;
+            var funcData = functions[func];
+            if (this.mode === "text" && !funcData.allowedInText) {
+                throw new ParseError(
+                    "Can't use function '" + func + "' in text mode",
+                    baseGroup.token);
+            }
+
+            var args = this.parseArguments(func, funcData);
+            var token = baseGroup.token;
+            var result = this.callFunction(func, args, args.pop(), token);
+            return new ParseNode(result.type, result, this.mode);
+        } else {
+            return baseGroup.result;
+        }
+    } else {
+        return null;
+    }
+};
+
+/**
+ * Call a function handler with a suitable context and arguments.
+ */
+Parser.prototype.callFunction = function(name, args, positions, token) {
+    var context = {
+        funcName: name,
+        parser: this,
+        positions: positions,
+        token: token
+    };
+    return functions[name].handler(context, args);
+};
+
+/**
+ * Parses the arguments of a function or environment
+ *
+ * @param {string} func  "\name" or "\begin{name}"
+ * @param {{numArgs:number,numOptionalArgs:number|undefined}} funcData
+ * @return the array of arguments, with the list of positions as last element
+ */
+Parser.prototype.parseArguments = function(func, funcData) {
+    var totalArgs = funcData.numArgs + funcData.numOptionalArgs;
+    if (totalArgs === 0) {
+        return [[this.pos]];
+    }
+
+    var baseGreediness = funcData.greediness;
+    var positions = [this.pos];
+    var args = [];
+
+    for (var i = 0; i < totalArgs; i++) {
+        var nextToken = this.nextToken;
+        var argType = funcData.argTypes && funcData.argTypes[i];
+        var arg;
+        if (i < funcData.numOptionalArgs) {
+            if (argType) {
+                arg = this.parseGroupOfType(argType, true);
+            } else {
+                arg = this.parseGroup(true);
+            }
+            if (!arg) {
+                args.push(null);
+                positions.push(this.pos);
+                continue;
+            }
+        } else {
+            if (argType) {
+                arg = this.parseGroupOfType(argType);
+            } else {
+                arg = this.parseGroup();
+            }
+            if (!arg) {
+                if (!this.settings.throwOnError &&
+                    this.nextToken.text[0] === "\\") {
+                    arg = new ParseFuncOrArgument(
+                        this.handleUnsupportedCmd(this.nextToken.text),
+                        false);
+                } else {
+                    throw new ParseError(
+                        "Expected group after '" + func + "'", nextToken);
+                }
+            }
+        }
+        var argNode;
+        if (arg.isFunction) {
+            var argGreediness =
+                functions[arg.result].greediness;
+            if (argGreediness > baseGreediness) {
+                argNode = this.parseFunction(arg);
+            } else {
+                throw new ParseError(
+                    "Got function '" + arg.result + "' as " +
+                    "argument to '" + func + "'", nextToken);
+            }
+        } else {
+            argNode = arg.result;
+        }
+        args.push(argNode);
+        positions.push(this.pos);
+    }
+
+    args.push(positions);
+
+    return args;
+};
+
+
+/**
+ * Parses a group when the mode is changing.
+ *
+ * @return {?ParseFuncOrArgument}
+ */
+Parser.prototype.parseGroupOfType = function(innerMode, optional) {
+    var outerMode = this.mode;
+    // Handle `original` argTypes
+    if (innerMode === "original") {
+        innerMode = outerMode;
+    }
+
+    if (innerMode === "color") {
+        return this.parseColorGroup(optional);
+    }
+    if (innerMode === "size") {
+        return this.parseSizeGroup(optional);
+    }
+
+    this.switchMode(innerMode);
+    if (innerMode === "text") {
+        // text mode is special because it should ignore the whitespace before
+        // it
+        while (this.nextToken.text === " ") {
+            this.consume();
+        }
+    }
+    // By the time we get here, innerMode is one of "text" or "math".
+    // We switch the mode of the parser, recurse, then restore the old mode.
+    var res = this.parseGroup(optional);
+    this.switchMode(outerMode);
+    return res;
+};
+
+/**
+ * Parses a group, essentially returning the string formed by the
+ * brace-enclosed tokens plus some position information.
+ *
+ * @param {string} modeName  Used to describe the mode in error messages
+ * @param {boolean=} optional  Whether the group is optional or required
+ */
+Parser.prototype.parseStringGroup = function(modeName, optional) {
+    if (optional && this.nextToken.text !== "[") {
+        return null;
+    }
+    var outerMode = this.mode;
+    this.mode = "text";
+    this.expect(optional ? "[" : "{");
+    var str = "";
+    var firstToken = this.nextToken;
+    var lastToken = firstToken;
+    while (this.nextToken.text !== (optional ? "]" : "}")) {
+        if (this.nextToken.text === "EOF") {
+            throw new ParseError(
+                "Unexpected end of input in " + modeName,
+                firstToken.range(this.nextToken, str));
+        }
+        lastToken = this.nextToken;
+        str += lastToken.text;
+        this.consume();
+    }
+    this.mode = outerMode;
+    this.expect(optional ? "]" : "}");
+    return firstToken.range(lastToken, str);
+};
+
+/**
+ * Parses a regex-delimited group: the largest sequence of tokens
+ * whose concatenated strings match `regex`. Returns the string
+ * formed by the tokens plus some position information.
+ *
+ * @param {RegExp} regex
+ * @param {string} modeName  Used to describe the mode in error messages
+ */
+Parser.prototype.parseRegexGroup = function(regex, modeName) {
+    var outerMode = this.mode;
+    this.mode = "text";
+    var firstToken = this.nextToken;
+    var lastToken = firstToken;
+    var str = "";
+    while (this.nextToken.text !== "EOF"
+           && regex.test(str + this.nextToken.text)) {
+        lastToken = this.nextToken;
+        str += lastToken.text;
+        this.consume();
+    }
+    if (str === "") {
+        throw new ParseError(
+            "Invalid " + modeName + ": '" + firstToken.text + "'",
+            firstToken);
+    }
+    this.mode = outerMode;
+    return firstToken.range(lastToken, str);
+};
+
+/**
+ * Parses a color description.
+ */
+Parser.prototype.parseColorGroup = function(optional) {
+    var res = this.parseStringGroup("color", optional);
+    if (!res) {
+        return null;
+    }
+    var match = (/^(#[a-z0-9]+|[a-z]+)$/i).exec(res.text);
+    if (!match) {
+        throw new ParseError("Invalid color: '" + res.text + "'", res);
+    }
+    return new ParseFuncOrArgument(
+        new ParseNode("color", match[0], this.mode),
+        false);
+};
+
+/**
+ * Parses a size specification, consisting of magnitude and unit.
+ */
+Parser.prototype.parseSizeGroup = function(optional) {
+    var res;
+    if (!optional && this.nextToken.text !== "{") {
+        res = this.parseRegexGroup(
+            /^[-+]? *(?:$|\d+|\d+\.\d*|\.\d*) *[a-z]{0,2}$/, "size");
+    } else {
+        res = this.parseStringGroup("size", optional);
+    }
+    if (!res) {
+        return null;
+    }
+    var match = (/([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/).exec(res.text);
+    if (!match) {
+        throw new ParseError("Invalid size: '" + res.text + "'", res);
+    }
+    var data = {
+        number: +(match[1] + match[2]), // sign + magnitude, cast to number
+        unit: match[3]
+    };
+    if (data.unit !== "em" && data.unit !== "ex" && data.unit !== "mu") {
+        throw new ParseError("Invalid unit: '" + data.unit + "'", res);
+    }
+    return new ParseFuncOrArgument(
+        new ParseNode("color", data, this.mode),
+        false);
+};
+
+/**
+ * If the argument is false or absent, this parses an ordinary group,
+ * which is either a single nucleus (like "x") or an expression
+ * in braces (like "{x+y}").
+ * If the argument is true, it parses either a bracket-delimited expression
+ * (like "[x+y]") or returns null to indicate the absence of a
+ * bracket-enclosed group.
+ *
+ * @param {boolean=} optional  Whether the group is optional or required
+ * @return {?ParseFuncOrArgument}
+ */
+Parser.prototype.parseGroup = function(optional) {
+    var firstToken = this.nextToken;
+    // Try to parse an open brace
+    if (this.nextToken.text === (optional ? "[" : "{")) {
+        // If we get a brace, parse an expression
+        this.consume();
+        var expression = this.parseExpression(false, optional ? "]" : null);
+        var lastToken = this.nextToken;
+        // Make sure we get a close brace
+        this.expect(optional ? "]" : "}");
+        if (this.mode === "text") {
+            this.formLigatures(expression);
+        }
+        return new ParseFuncOrArgument(
+            new ParseNode("ordgroup", expression, this.mode,
+                          firstToken, lastToken),
+            false);
+    } else {
+        // Otherwise, just return a nucleus, or nothing for an optional group
+        return optional ? null : this.parseSymbol();
+    }
+};
+
+/**
+ * Form ligature-like combinations of characters for text mode.
+ * This includes inputs like "--", "---", "``" and "''".
+ * The result will simply replace multiple textord nodes with a single
+ * character in each value by a single textord node having multiple
+ * characters in its value.  The representation is still ASCII source.
+ *
+ * @param {Array.<ParseNode>} group  the nodes of this group,
+ *                                   list will be moified in place
+ */
+Parser.prototype.formLigatures = function(group) {
+    var i;
+    var n = group.length - 1;
+    for (i = 0; i < n; ++i) {
+        var a = group[i];
+        var v = a.value;
+        if (v === "-" && group[i + 1].value === "-") {
+            if (i + 1 < n && group[i + 2].value === "-") {
+                group.splice(i, 3, new ParseNode(
+                    "textord", "---", "text", a, group[i + 2]));
+                n -= 2;
+            } else {
+                group.splice(i, 2, new ParseNode(
+                    "textord", "--", "text", a, group[i + 1]));
+                n -= 1;
+            }
+        }
+        if ((v === "'" || v === "`") && group[i + 1].value === v) {
+            group.splice(i, 2, new ParseNode(
+                "textord", v + v, "text", a, group[i + 1]));
+            n -= 1;
+        }
+    }
+};
+
+/**
+ * Parse a single symbol out of the string. Here, we handle both the functions
+ * we have defined, as well as the single character symbols
+ *
+ * @return {?ParseFuncOrArgument}
+ */
+Parser.prototype.parseSymbol = function() {
+    var nucleus = this.nextToken;
+
+    if (functions[nucleus.text]) {
+        this.consume();
+        // If there exists a function with this name, we return the function and
+        // say that it is a function.
+        return new ParseFuncOrArgument(
+            nucleus.text,
+            true, nucleus);
+    } else if (symbols[this.mode][nucleus.text]) {
+        this.consume();
+        // Otherwise if this is a no-argument function, find the type it
+        // corresponds to in the symbols map
+        return new ParseFuncOrArgument(
+            new ParseNode(symbols[this.mode][nucleus.text].group,
+                          nucleus.text, this.mode, nucleus),
+            false, nucleus);
+    } else if (this.mode === "text" && cjkRegex.test(nucleus.text)) {
+        this.consume();
+        return new ParseFuncOrArgument(
+            new ParseNode("textord", nucleus.text, this.mode, nucleus),
+            false, nucleus);
+    } else {
+        return null;
+    }
+};
+
+Parser.prototype.ParseNode = ParseNode;
+
+module.exports = Parser;
+
+},{"./MacroExpander":4,"./ParseError":6,"./environments":16,"./functions":19,"./parseData":21,"./symbols":23,"./unicodeRegexes":24,"./utils":25}],8:[function(require,module,exports){
+/**
+ * This is a module for storing settings passed into KaTeX. It correctly handles
+ * default settings.
+ */
+
+/**
+ * Helper function for getting a default value if the value is undefined
+ */
+function get(option, defaultValue) {
+    return option === undefined ? defaultValue : option;
+}
+
+/**
+ * The main Settings object
+ *
+ * The current options stored are:
+ *  - displayMode: Whether the expression should be typeset by default in
+ *                 textstyle or displaystyle (default false)
+ */
+function Settings(options) {
+    // allow null options
+    options = options || {};
+    this.displayMode = get(options.displayMode, false);
+    this.throwOnError = get(options.throwOnError, true);
+    this.errorColor = get(options.errorColor, "#cc0000");
+    this.macros = options.macros || {};
+}
+
+module.exports = Settings;
+
+},{}],9:[function(require,module,exports){
+/**
+ * This file contains information and classes for the various kinds of styles
+ * used in TeX. It provides a generic `Style` class, which holds information
+ * about a specific style. It then provides instances of all the different kinds
+ * of styles possible, and provides functions to move between them and get
+ * information about them.
+ */
+
+var sigmas = require("./fontMetrics.js").sigmas;
+
+var metrics = [{}, {}, {}];
+var i;
+for (var key in sigmas) {
+    if (sigmas.hasOwnProperty(key)) {
+        for (i = 0; i < 3; i++) {
+            metrics[i][key] = sigmas[key][i];
+        }
+    }
+}
+for (i = 0; i < 3; i++) {
+    metrics[i].emPerEx = sigmas.xHeight[i] / sigmas.quad[i];
+}
+
+/**
+ * The main style class. Contains a unique id for the style, a size (which is
+ * the same for cramped and uncramped version of a style), a cramped flag, and a
+ * size multiplier, which gives the size difference between a style and
+ * textstyle.
+ */
+function Style(id, size, multiplier, cramped) {
+    this.id = id;
+    this.size = size;
+    this.cramped = cramped;
+    this.sizeMultiplier = multiplier;
+    this.metrics = metrics[size > 0 ? size - 1 : 0];
+}
+
+/**
+ * Get the style of a superscript given a base in the current style.
+ */
+Style.prototype.sup = function() {
+    return styles[sup[this.id]];
+};
+
+/**
+ * Get the style of a subscript given a base in the current style.
+ */
+Style.prototype.sub = function() {
+    return styles[sub[this.id]];
+};
+
+/**
+ * Get the style of a fraction numerator given the fraction in the current
+ * style.
+ */
+Style.prototype.fracNum = function() {
+    return styles[fracNum[this.id]];
+};
+
+/**
+ * Get the style of a fraction denominator given the fraction in the current
+ * style.
+ */
+Style.prototype.fracDen = function() {
+    return styles[fracDen[this.id]];
+};
+
+/**
+ * Get the cramped version of a style (in particular, cramping a cramped style
+ * doesn't change the style).
+ */
+Style.prototype.cramp = function() {
+    return styles[cramp[this.id]];
+};
+
+/**
+ * HTML class name, like "displaystyle cramped"
+ */
+Style.prototype.cls = function() {
+    return sizeNames[this.size] + (this.cramped ? " cramped" : " uncramped");
+};
+
+/**
+ * HTML Reset class name, like "reset-textstyle"
+ */
+Style.prototype.reset = function() {
+    return resetNames[this.size];
+};
+
+/**
+ * Return if this style is tightly spaced (scriptstyle/scriptscriptstyle)
+ */
+Style.prototype.isTight = function() {
+    return this.size >= 2;
+};
+
+// IDs of the different styles
+var D = 0;
+var Dc = 1;
+var T = 2;
+var Tc = 3;
+var S = 4;
+var Sc = 5;
+var SS = 6;
+var SSc = 7;
+
+// String names for the different sizes
+var sizeNames = [
+    "displaystyle textstyle",
+    "textstyle",
+    "scriptstyle",
+    "scriptscriptstyle"
+];
+
+// Reset names for the different sizes
+var resetNames = [
+    "reset-textstyle",
+    "reset-textstyle",
+    "reset-scriptstyle",
+    "reset-scriptscriptstyle"
+];
+
+// Instances of the different styles
+var styles = [
+    new Style(D, 0, 1.0, false),
+    new Style(Dc, 0, 1.0, true),
+    new Style(T, 1, 1.0, false),
+    new Style(Tc, 1, 1.0, true),
+    new Style(S, 2, 0.7, false),
+    new Style(Sc, 2, 0.7, true),
+    new Style(SS, 3, 0.5, false),
+    new Style(SSc, 3, 0.5, true)
+];
+
+// Lookup tables for switching from one style to another
+var sup = [S, Sc, S, Sc, SS, SSc, SS, SSc];
+var sub = [Sc, Sc, Sc, Sc, SSc, SSc, SSc, SSc];
+var fracNum = [T, Tc, S, Sc, SS, SSc, SS, SSc];
+var fracDen = [Tc, Tc, Sc, Sc, SSc, SSc, SSc, SSc];
+var cramp = [Dc, Dc, Tc, Tc, Sc, Sc, SSc, SSc];
+
+// We only export some of the styles. Also, we don't export the `Style` class so
+// no more styles can be generated.
+module.exports = {
+    DISPLAY: styles[D],
+    TEXT: styles[T],
+    SCRIPT: styles[S],
+    SCRIPTSCRIPT: styles[SS]
+};
+
+},{"./fontMetrics.js":17}],10:[function(require,module,exports){
+/* eslint no-console:0 */
+/**
+ * This module contains general functions that can be used for building
+ * different kinds of domTree nodes in a consistent manner.
+ */
+
+var domTree = require("./domTree");
+var fontMetrics = require("./fontMetrics");
+var symbols = require("./symbols");
+var utils = require("./utils");
+
+var greekCapitals = [
+    "\\Gamma",
+    "\\Delta",
+    "\\Theta",
+    "\\Lambda",
+    "\\Xi",
+    "\\Pi",
+    "\\Sigma",
+    "\\Upsilon",
+    "\\Phi",
+    "\\Psi",
+    "\\Omega"
+];
+
+// The following have to be loaded from Main-Italic font, using class mainit
+var mainitLetters = [
+    "\u0131",   // dotless i, \imath
+    "\u0237",   // dotless j, \jmath
+    "\u00a3"   // \pounds
+];
+
+/**
+ * Makes a symbolNode after translation via the list of symbols in symbols.js.
+ * Correctly pulls out metrics for the character, and optionally takes a list of
+ * classes to be attached to the node.
+ *
+ * TODO: make argument order closer to makeSpan
+ * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which
+ * should if present come first in `classes`.
+ */
+var makeSymbol = function(value, fontFamily, mode, options, classes) {
+    // Replace the value with its replaced value from symbol.js
+    if (symbols[mode][value] && symbols[mode][value].replace) {
+        value = symbols[mode][value].replace;
+    }
+
+    var metrics = fontMetrics.getCharacterMetrics(value, fontFamily);
+
+    var symbolNode;
+    if (metrics) {
+        var italic = metrics.italic;
+        if (mode === "text") {
+            italic = 0;
+        }
+        symbolNode = new domTree.symbolNode(
+            value, metrics.height, metrics.depth, italic, metrics.skew,
+            classes);
+    } else {
+        // TODO(emily): Figure out a good way to only print this in development
+        typeof console !== "undefined" && console.warn(
+            "No character metrics for '" + value + "' in style '" +
+                fontFamily + "'");
+        symbolNode = new domTree.symbolNode(value, 0, 0, 0, 0, classes);
+    }
+
+    if (options) {
+        if (options.style.isTight()) {
+            symbolNode.classes.push("mtight");
+        }
+        if (options.getColor()) {
+            symbolNode.style.color = options.getColor();
+        }
+    }
+
+    return symbolNode;
+};
+
+/**
+ * Makes a symbol in Main-Regular or AMS-Regular.
+ * Used for rel, bin, open, close, inner, and punct.
+ */
+var mathsym = function(value, mode, options, classes) {
+    // Decide what font to render the symbol in by its entry in the symbols
+    // table.
+    // Have a special case for when the value = \ because the \ is used as a
+    // textord in unsupported command errors but cannot be parsed as a regular
+    // text ordinal and is therefore not present as a symbol in the symbols
+    // table for text
+    if (value === "\\" || symbols[mode][value].font === "main") {
+        return makeSymbol(value, "Main-Regular", mode, options, classes);
+    } else {
+        return makeSymbol(
+            value, "AMS-Regular", mode, options, classes.concat(["amsrm"]));
+    }
+};
+
+/**
+ * Makes a symbol in the default font for mathords and textords.
+ */
+var mathDefault = function(value, mode, options, classes, type) {
+    if (type === "mathord") {
+        return mathit(value, mode, options, classes);
+    } else if (type === "textord") {
+        return makeSymbol(
+            value, "Main-Regular", mode, options, classes.concat(["mathrm"]));
+    } else {
+        throw new Error("unexpected type: " + type + " in mathDefault");
+    }
+};
+
+/**
+ * Makes a symbol in the italic math font.
+ */
+var mathit = function(value, mode, options, classes) {
+    if (/[0-9]/.test(value.charAt(0)) ||
+            // glyphs for \imath and \jmath do not exist in Math-Italic so we
+            // need to use Main-Italic instead
+            utils.contains(mainitLetters, value) ||
+            utils.contains(greekCapitals, value)) {
+        return makeSymbol(
+            value, "Main-Italic", mode, options, classes.concat(["mainit"]));
+    } else {
+        return makeSymbol(
+            value, "Math-Italic", mode, options, classes.concat(["mathit"]));
+    }
+};
+
+/**
+ * Makes either a mathord or textord in the correct font and color.
+ */
+var makeOrd = function(group, options, type) {
+    var mode = group.mode;
+    var value = group.value;
+    if (symbols[mode][value] && symbols[mode][value].replace) {
+        value = symbols[mode][value].replace;
+    }
+
+    var classes = ["mord"];
+
+    var font = options.font;
+    if (font) {
+        if (font === "mathit" || utils.contains(mainitLetters, value)) {
+            return mathit(value, mode, options, classes);
+        } else {
+            var fontName = fontMap[font].fontName;
+            if (fontMetrics.getCharacterMetrics(value, fontName)) {
+                return makeSymbol(
+                    value, fontName, mode, options, classes.concat([font]));
+            } else {
+                return mathDefault(value, mode, options, classes, type);
+            }
+        }
+    } else {
+        return mathDefault(value, mode, options, classes, type);
+    }
+};
+
+/**
+ * Calculate the height, depth, and maxFontSize of an element based on its
+ * children.
+ */
+var sizeElementFromChildren = function(elem) {
+    var height = 0;
+    var depth = 0;
+    var maxFontSize = 0;
+
+    if (elem.children) {
+        for (var i = 0; i < elem.children.length; i++) {
+            if (elem.children[i].height > height) {
+                height = elem.children[i].height;
+            }
+            if (elem.children[i].depth > depth) {
+                depth = elem.children[i].depth;
+            }
+            if (elem.children[i].maxFontSize > maxFontSize) {
+                maxFontSize = elem.children[i].maxFontSize;
+            }
+        }
+    }
+
+    elem.height = height;
+    elem.depth = depth;
+    elem.maxFontSize = maxFontSize;
+};
+
+/**
+ * Makes a span with the given list of classes, list of children, and options.
+ *
+ * TODO: Ensure that `options` is always provided (currently some call sites
+ * don't pass it).
+ * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which
+ * should if present come first in `classes`.
+ */
+var makeSpan = function(classes, children, options) {
+    var span = new domTree.span(classes, children, options);
+
+    sizeElementFromChildren(span);
+
+    return span;
+};
+
+/**
+ * Prepends the given children to the given span, updating height, depth, and
+ * maxFontSize.
+ */
+var prependChildren = function(span, children) {
+    span.children = children.concat(span.children);
+
+    sizeElementFromChildren(span);
+};
+
+/**
+ * Makes a document fragment with the given list of children.
+ */
+var makeFragment = function(children) {
+    var fragment = new domTree.documentFragment(children);
+
+    sizeElementFromChildren(fragment);
+
+    return fragment;
+};
+
+/**
+ * Makes an element placed in each of the vlist elements to ensure that each
+ * element has the same max font size. To do this, we create a zero-width space
+ * with the correct font size.
+ */
+var makeFontSizer = function(options, fontSize) {
+    var fontSizeInner = makeSpan([], [new domTree.symbolNode("\u200b")]);
+    fontSizeInner.style.fontSize =
+        (fontSize / options.style.sizeMultiplier) + "em";
+
+    var fontSizer = makeSpan(
+        ["fontsize-ensurer", "reset-" + options.size, "size5"],
+        [fontSizeInner]);
+
+    return fontSizer;
+};
+
+/**
+ * Makes a vertical list by stacking elements and kerns on top of each other.
+ * Allows for many different ways of specifying the positioning method.
+ *
+ * Arguments:
+ *  - children: A list of child or kern nodes to be stacked on top of each other
+ *              (i.e. the first element will be at the bottom, and the last at
+ *              the top). Element nodes are specified as
+ *                {type: "elem", elem: node}
+ *              while kern nodes are specified as
+ *                {type: "kern", size: size}
+ *  - positionType: The method by which the vlist should be positioned. Valid
+ *                  values are:
+ *                   - "individualShift": The children list only contains elem
+ *                                        nodes, and each node contains an extra
+ *                                        "shift" value of how much it should be
+ *                                        shifted (note that shifting is always
+ *                                        moving downwards). positionData is
+ *                                        ignored.
+ *                   - "top": The positionData specifies the topmost point of
+ *                            the vlist (note this is expected to be a height,
+ *                            so positive values move up)
+ *                   - "bottom": The positionData specifies the bottommost point
+ *                               of the vlist (note this is expected to be a
+ *                               depth, so positive values move down
+ *                   - "shift": The vlist will be positioned such that its
+ *                              baseline is positionData away from the baseline
+ *                              of the first child. Positive values move
+ *                              downwards.
+ *                   - "firstBaseline": The vlist will be positioned such that
+ *                                      its baseline is aligned with the
+ *                                      baseline of the first child.
+ *                                      positionData is ignored. (this is
+ *                                      equivalent to "shift" with
+ *                                      positionData=0)
+ *  - positionData: Data used in different ways depending on positionType
+ *  - options: An Options object
+ *
+ */
+var makeVList = function(children, positionType, positionData, options) {
+    var depth;
+    var currPos;
+    var i;
+    if (positionType === "individualShift") {
+        var oldChildren = children;
+        children = [oldChildren[0]];
+
+        // Add in kerns to the list of children to get each element to be
+        // shifted to the correct specified shift
+        depth = -oldChildren[0].shift - oldChildren[0].elem.depth;
+        currPos = depth;
+        for (i = 1; i < oldChildren.length; i++) {
+            var diff = -oldChildren[i].shift - currPos -
+                oldChildren[i].elem.depth;
+            var size = diff -
+                (oldChildren[i - 1].elem.height +
+                 oldChildren[i - 1].elem.depth);
+
+            currPos = currPos + diff;
+
+            children.push({type: "kern", size: size});
+            children.push(oldChildren[i]);
+        }
+    } else if (positionType === "top") {
+        // We always start at the bottom, so calculate the bottom by adding up
+        // all the sizes
+        var bottom = positionData;
+        for (i = 0; i < children.length; i++) {
+            if (children[i].type === "kern") {
+                bottom -= children[i].size;
+            } else {
+                bottom -= children[i].elem.height + children[i].elem.depth;
+            }
+        }
+        depth = bottom;
+    } else if (positionType === "bottom") {
+        depth = -positionData;
+    } else if (positionType === "shift") {
+        depth = -children[0].elem.depth - positionData;
+    } else if (positionType === "firstBaseline") {
+        depth = -children[0].elem.depth;
+    } else {
+        depth = 0;
+    }
+
+    // Make the fontSizer
+    var maxFontSize = 0;
+    for (i = 0; i < children.length; i++) {
+        if (children[i].type === "elem") {
+            maxFontSize = Math.max(maxFontSize, children[i].elem.maxFontSize);
+        }
+    }
+    var fontSizer = makeFontSizer(options, maxFontSize);
+
+    // Create a new list of actual children at the correct offsets
+    var realChildren = [];
+    currPos = depth;
+    for (i = 0; i < children.length; i++) {
+        if (children[i].type === "kern") {
+            currPos += children[i].size;
+        } else {
+            var child = children[i].elem;
+
+            var shift = -child.depth - currPos;
+            currPos += child.height + child.depth;
+
+            var childWrap = makeSpan([], [fontSizer, child]);
+            childWrap.height -= shift;
+            childWrap.depth += shift;
+            childWrap.style.top = shift + "em";
+
+            realChildren.push(childWrap);
+        }
+    }
+
+    // Add in an element at the end with no offset to fix the calculation of
+    // baselines in some browsers (namely IE, sometimes safari)
+    var baselineFix = makeSpan(
+        ["baseline-fix"], [fontSizer, new domTree.symbolNode("\u200b")]);
+    realChildren.push(baselineFix);
+
+    var vlist = makeSpan(["vlist"], realChildren);
+    // Fix the final height and depth, in case there were kerns at the ends
+    // since the makeSpan calculation won't take that in to account.
+    vlist.height = Math.max(currPos, vlist.height);
+    vlist.depth = Math.max(-depth, vlist.depth);
+    return vlist;
+};
+
+// A table of size -> font size for the different sizing functions
+var sizingMultiplier = {
+    size1: 0.5,
+    size2: 0.7,
+    size3: 0.8,
+    size4: 0.9,
+    size5: 1.0,
+    size6: 1.2,
+    size7: 1.44,
+    size8: 1.73,
+    size9: 2.07,
+    size10: 2.49
+};
+
+// A map of spacing functions to their attributes, like size and corresponding
+// CSS class
+var spacingFunctions = {
+    "\\qquad": {
+        size: "2em",
+        className: "qquad"
+    },
+    "\\quad": {
+        size: "1em",
+        className: "quad"
+    },
+    "\\enspace": {
+        size: "0.5em",
+        className: "enspace"
+    },
+    "\\;": {
+        size: "0.277778em",
+        className: "thickspace"
+    },
+    "\\:": {
+        size: "0.22222em",
+        className: "mediumspace"
+    },
+    "\\,": {
+        size: "0.16667em",
+        className: "thinspace"
+    },
+    "\\!": {
+        size: "-0.16667em",
+        className: "negativethinspace"
+    }
+};
+
+/**
+ * Maps TeX font commands to objects containing:
+ * - variant: string used for "mathvariant" attribute in buildMathML.js
+ * - fontName: the "style" parameter to fontMetrics.getCharacterMetrics
+ */
+// A map between tex font commands an MathML mathvariant attribute values
+var fontMap = {
+    // styles
+    "mathbf": {
+        variant: "bold",
+        fontName: "Main-Bold"
+    },
+    "mathrm": {
+        variant: "normal",
+        fontName: "Main-Regular"
+    },
+    "textit": {
+        variant: "italic",
+        fontName: "Main-Italic"
+    },
+
+    // "mathit" is missing because it requires the use of two fonts: Main-Italic
+    // and Math-Italic.  This is handled by a special case in makeOrd which ends
+    // up calling mathit.
+
+    // families
+    "mathbb": {
+        variant: "double-struck",
+        fontName: "AMS-Regular"
+    },
+    "mathcal": {
+        variant: "script",
+        fontName: "Caligraphic-Regular"
+    },
+    "mathfrak": {
+        variant: "fraktur",
+        fontName: "Fraktur-Regular"
+    },
+    "mathscr": {
+        variant: "script",
+        fontName: "Script-Regular"
+    },
+    "mathsf": {
+        variant: "sans-serif",
+        fontName: "SansSerif-Regular"
+    },
+    "mathtt": {
+        variant: "monospace",
+        fontName: "Typewriter-Regular"
+    }
+};
+
+module.exports = {
+    fontMap: fontMap,
+    makeSymbol: makeSymbol,
+    mathsym: mathsym,
+    makeSpan: makeSpan,
+    makeFragment: makeFragment,
+    makeVList: makeVList,
+    makeOrd: makeOrd,
+    prependChildren: prependChildren,
+    sizingMultiplier: sizingMultiplier,
+    spacingFunctions: spacingFunctions
+};
+
+},{"./domTree":15,"./fontMetrics":17,"./symbols":23,"./utils":25}],11:[function(require,module,exports){
+/* eslint no-console:0 */
+/**
+ * This file does the main work of building a domTree structure from a parse
+ * tree. The entry point is the `buildHTML` function, which takes a parse tree.
+ * Then, the buildExpression, buildGroup, and various groupTypes functions are
+ * called, to produce a final HTML tree.
+ */
+
+var ParseError = require("./ParseError");
+var Style = require("./Style");
+
+var buildCommon = require("./buildCommon");
+var delimiter = require("./delimiter");
+var domTree = require("./domTree");
+var fontMetrics = require("./fontMetrics");
+var utils = require("./utils");
+
+var makeSpan = buildCommon.makeSpan;
+
+var isSpace = function(node) {
+    return node instanceof domTree.span && node.classes[0] === "mspace";
+};
+
+// Binary atoms (first class `mbin`) change into ordinary atoms (`mord`)
+// depending on their surroundings. See TeXbook pg. 442-446, Rules 5 and 6,
+// and the text before Rule 19.
+
+var isBin = function(node) {
+    return node && node.classes[0] === "mbin";
+};
+
+var isBinLeftCanceller = function(node, isRealGroup) {
+    // TODO: This code assumes that a node's math class is the first element
+    // of its `classes` array. A later cleanup should ensure this, for
+    // instance by changing the signature of `makeSpan`.
+    if (node) {
+        return utils.contains(["mbin", "mopen", "mrel", "mop", "mpunct"],
+                              node.classes[0]);
+    } else {
+        return isRealGroup;
+    }
+};
+
+var isBinRightCanceller = function(node, isRealGroup) {
+    if (node) {
+        return utils.contains(["mrel", "mclose", "mpunct"], node.classes[0]);
+    } else {
+        return isRealGroup;
+    }
+};
+
+/**
+ * Take a list of nodes, build them in order, and return a list of the built
+ * nodes. documentFragments are flattened into their contents, so the
+ * returned list contains no fragments. `isRealGroup` is true if `expression`
+ * is a real group (no atoms will be added on either side), as opposed to
+ * a partial group (e.g. one created by \color).
+ */
+var buildExpression = function(expression, options, isRealGroup) {
+    // Parse expressions into `groups`.
+    var groups = [];
+    for (var i = 0; i < expression.length; i++) {
+        var group = expression[i];
+        var output = buildGroup(group, options);
+        if (output instanceof domTree.documentFragment) {
+            Array.prototype.push.apply(groups, output.children);
+        } else {
+            groups.push(output);
+        }
+    }
+    // At this point `groups` consists entirely of `symbolNode`s and `span`s.
+
+    // Explicit spaces (e.g., \;, \,) should be ignored with respect to atom
+    // spacing (e.g., "add thick space between mord and mrel"). Since CSS
+    // adjacency rules implement atom spacing, spaces should be invisible to
+    // CSS. So we splice them out of `groups` and into the atoms themselves.
+    var spaces = null;
+    for (i = 0; i < groups.length; i++) {
+        if (isSpace(groups[i])) {
+            spaces = spaces || [];
+            spaces.push(groups[i]);
+            groups.splice(i, 1);
+            i--;
+        } else if (spaces) {
+            if (groups[i] instanceof domTree.symbolNode) {
+                groups[i] = makeSpan([].concat(groups[i].classes), [groups[i]]);
+            }
+            buildCommon.prependChildren(groups[i], spaces);
+            spaces = null;
+        }
+    }
+    if (spaces) {
+        Array.prototype.push.apply(groups, spaces);
+    }
+
+    // Binary operators change to ordinary symbols in some contexts.
+    for (i = 0; i < groups.length; i++) {
+        if (isBin(groups[i])
+            && (isBinLeftCanceller(groups[i - 1], isRealGroup)
+                || isBinRightCanceller(groups[i + 1], isRealGroup))) {
+            groups[i].classes[0] = "mord";
+        }
+    }
+
+    return groups;
+};
+
+// Return math atom class (mclass) of a domTree.
+var getTypeOfDomTree = function(node) {
+    if (node instanceof domTree.documentFragment) {
+        if (node.children.length) {
+            return getTypeOfDomTree(
+                node.children[node.children.length - 1]);
+        }
+    } else {
+        if (utils.contains(["mord", "mop", "mbin", "mrel", "mopen", "mclose",
+            "mpunct", "minner"], node.classes[0])) {
+            return node.classes[0];
+        }
+    }
+    return null;
+};
+
+/**
+ * Sometimes, groups perform special rules when they have superscripts or
+ * subscripts attached to them. This function lets the `supsub` group know that
+ * its inner element should handle the superscripts and subscripts instead of
+ * handling them itself.
+ */
+var shouldHandleSupSub = function(group, options) {
+    if (!group) {
+        return false;
+    } else if (group.type === "op") {
+        // Operators handle supsubs differently when they have limits
+        // (e.g. `\displaystyle\sum_2^3`)
+        return group.value.limits &&
+            (options.style.size === Style.DISPLAY.size ||
+            group.value.alwaysHandleSupSub);
+    } else if (group.type === "accent") {
+        return isCharacterBox(group.value.base);
+    } else {
+        return null;
+    }
+};
+
+/**
+ * Sometimes we want to pull out the innermost element of a group. In most
+ * cases, this will just be the group itself, but when ordgroups and colors have
+ * a single element, we want to pull that out.
+ */
+var getBaseElem = function(group) {
+    if (!group) {
+        return false;
+    } else if (group.type === "ordgroup") {
+        if (group.value.length === 1) {
+            return getBaseElem(group.value[0]);
+        } else {
+            return group;
+        }
+    } else if (group.type === "color") {
+        if (group.value.value.length === 1) {
+            return getBaseElem(group.value.value[0]);
+        } else {
+            return group;
+        }
+    } else if (group.type === "font") {
+        return getBaseElem(group.value.body);
+    } else {
+        return group;
+    }
+};
+
+/**
+ * TeXbook algorithms often reference "character boxes", which are simply groups
+ * with a single character in them. To decide if something is a character box,
+ * we find its innermost group, and see if it is a single character.
+ */
+var isCharacterBox = function(group) {
+    var baseElem = getBaseElem(group);
+
+    // These are all they types of groups which hold single characters
+    return baseElem.type === "mathord" ||
+        baseElem.type === "textord" ||
+        baseElem.type === "bin" ||
+        baseElem.type === "rel" ||
+        baseElem.type === "inner" ||
+        baseElem.type === "open" ||
+        baseElem.type === "close" ||
+        baseElem.type === "punct";
+};
+
+var makeNullDelimiter = function(options, classes) {
+    return makeSpan(classes.concat([
+        "sizing", "reset-" + options.size, "size5",
+        options.style.reset(), Style.TEXT.cls(),
+        "nulldelimiter"]));
+};
+
+/**
+ * This is a map of group types to the function used to handle that type.
+ * Simpler types come at the beginning, while complicated types come afterwards.
+ */
+var groupTypes = {};
+
+groupTypes.mathord = function(group, options) {
+    return buildCommon.makeOrd(group, options, "mathord");
+};
+
+groupTypes.textord = function(group, options) {
+    return buildCommon.makeOrd(group, options, "textord");
+};
+
+groupTypes.bin = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mbin"]);
+};
+
+groupTypes.rel = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mrel"]);
+};
+
+groupTypes.open = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mopen"]);
+};
+
+groupTypes.close = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mclose"]);
+};
+
+groupTypes.inner = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["minner"]);
+};
+
+groupTypes.punct = function(group, options) {
+    return buildCommon.mathsym(
+        group.value, group.mode, options, ["mpunct"]);
+};
+
+groupTypes.ordgroup = function(group, options) {
+    return makeSpan(
+        ["mord", options.style.cls()],
+        buildExpression(group.value, options.reset(), true),
+        options
+    );
+};
+
+groupTypes.text = function(group, options) {
+    var newOptions = options.withFont(group.value.style);
+    var inner = buildExpression(group.value.body, newOptions, true);
+    for (var i = 0; i < inner.length - 1; i++) {
+        if (inner[i].tryCombine(inner[i + 1])) {
+            inner.splice(i + 1, 1);
+            i--;
+        }
+    }
+    return makeSpan(["mord", "text", newOptions.style.cls()],
+        inner, newOptions);
+};
+
+groupTypes.color = function(group, options) {
+    var elements = buildExpression(
+        group.value.value,
+        options.withColor(group.value.color),
+        false
+    );
+
+    // \color isn't supposed to affect the type of the elements it contains.
+    // To accomplish this, we wrap the results in a fragment, so the inner
+    // elements will be able to directly interact with their neighbors. For
+    // example, `\color{red}{2 +} 3` has the same spacing as `2 + 3`
+    return new buildCommon.makeFragment(elements);
+};
+
+groupTypes.supsub = function(group, options) {
+    // Superscript and subscripts are handled in the TeXbook on page
+    // 445-446, rules 18(a-f).
+
+    // Here is where we defer to the inner group if it should handle
+    // superscripts and subscripts itself.
+    if (shouldHandleSupSub(group.value.base, options)) {
+        return groupTypes[group.value.base.type](group, options);
+    }
+
+    var base = buildGroup(group.value.base, options.reset());
+    var supmid;
+    var submid;
+    var sup;
+    var sub;
+
+    var style = options.style;
+    var newOptions;
+
+    if (group.value.sup) {
+        newOptions = options.withStyle(style.sup());
+        sup = buildGroup(group.value.sup, newOptions);
+        supmid = makeSpan([style.reset(), style.sup().cls()],
+            [sup], newOptions);
+    }
+
+    if (group.value.sub) {
+        newOptions = options.withStyle(style.sub());
+        sub = buildGroup(group.value.sub, newOptions);
+        submid = makeSpan([style.reset(), style.sub().cls()],
+            [sub], newOptions);
+    }
+
+    // Rule 18a
+    var supShift;
+    var subShift;
+    if (isCharacterBox(group.value.base)) {
+        supShift = 0;
+        subShift = 0;
+    } else {
+        supShift = base.height - style.metrics.supDrop;
+        subShift = base.depth + style.metrics.subDrop;
+    }
+
+    // Rule 18c
+    var minSupShift;
+    if (style === Style.DISPLAY) {
+        minSupShift = style.metrics.sup1;
+    } else if (style.cramped) {
+        minSupShift = style.metrics.sup3;
+    } else {
+        minSupShift = style.metrics.sup2;
+    }
+
+    // scriptspace is a font-size-independent size, so scale it
+    // appropriately
+    var multiplier = Style.TEXT.sizeMultiplier *
+            style.sizeMultiplier;
+    var scriptspace =
+        (0.5 / fontMetrics.metrics.ptPerEm) / multiplier + "em";
+
+    var supsub;
+    if (!group.value.sup) {
+        // Rule 18b
+        subShift = Math.max(
+            subShift, style.metrics.sub1,
+            sub.height - 0.8 * style.metrics.xHeight);
+
+        supsub = buildCommon.makeVList([
+            {type: "elem", elem: submid}
+        ], "shift", subShift, options);
+
+        supsub.children[0].style.marginRight = scriptspace;
+
+        // Subscripts shouldn't be shifted by the base's italic correction.
+        // Account for that by shifting the subscript back the appropriate
+        // amount. Note we only do this when the base is a single symbol.
+        if (base instanceof domTree.symbolNode) {
+            supsub.children[0].style.marginLeft = -base.italic + "em";
+        }
+    } else if (!group.value.sub) {
+        // Rule 18c, d
+        supShift = Math.max(supShift, minSupShift,
+            sup.depth + 0.25 * style.metrics.xHeight);
+
+        supsub = buildCommon.makeVList([
+            {type: "elem", elem: supmid}
+        ], "shift", -supShift, options);
+
+        supsub.children[0].style.marginRight = scriptspace;
+    } else {
+        supShift = Math.max(
+            supShift, minSupShift, sup.depth + 0.25 * style.metrics.xHeight);
+        subShift = Math.max(subShift, style.metrics.sub2);
+
+        var ruleWidth = fontMetrics.metrics.defaultRuleThickness;
+
+        // Rule 18e
+        if ((supShift - sup.depth) - (sub.height - subShift) <
+                4 * ruleWidth) {
+            subShift = 4 * ruleWidth - (supShift - sup.depth) + sub.height;
+            var psi = 0.8 * style.metrics.xHeight - (supShift - sup.depth);
+            if (psi > 0) {
+                supShift += psi;
+                subShift -= psi;
+            }
+        }
+
+        supsub = buildCommon.makeVList([
+            {type: "elem", elem: submid, shift: subShift},
+            {type: "elem", elem: supmid, shift: -supShift}
+        ], "individualShift", null, options);
+
+        // See comment above about subscripts not being shifted
+        if (base instanceof domTree.symbolNode) {
+            supsub.children[0].style.marginLeft = -base.italic + "em";
+        }
+
+        supsub.children[0].style.marginRight = scriptspace;
+        supsub.children[1].style.marginRight = scriptspace;
+    }
+
+    // We ensure to wrap the supsub vlist in a span.msupsub to reset text-align
+    var mclass = getTypeOfDomTree(base) || "mord";
+    return makeSpan([mclass],
+        [base, makeSpan(["msupsub"], [supsub])],
+        options);
+};
+
+groupTypes.genfrac = function(group, options) {
+    // Fractions are handled in the TeXbook on pages 444-445, rules 15(a-e).
+    // Figure out what style this fraction should be in based on the
+    // function used
+    var style = options.style;
+    if (group.value.size === "display") {
+        style = Style.DISPLAY;
+    } else if (group.value.size === "text") {
+        style = Style.TEXT;
+    }
+
+    var nstyle = style.fracNum();
+    var dstyle = style.fracDen();
+    var newOptions;
+
+    newOptions = options.withStyle(nstyle);
+    var numer = buildGroup(group.value.numer, newOptions);
+    var numerreset = makeSpan([style.reset(), nstyle.cls()],
+        [numer], newOptions);
+
+    newOptions = options.withStyle(dstyle);
+    var denom = buildGroup(group.value.denom, newOptions);
+    var denomreset = makeSpan([style.reset(), dstyle.cls()],
+        [denom], newOptions);
+
+    var ruleWidth;
+    if (group.value.hasBarLine) {
+        ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+            options.style.sizeMultiplier;
+    } else {
+        ruleWidth = 0;
+    }
+
+    // Rule 15b
+    var numShift;
+    var clearance;
+    var denomShift;
+    if (style.size === Style.DISPLAY.size) {
+        numShift = style.metrics.num1;
+        if (ruleWidth > 0) {
+            clearance = 3 * ruleWidth;
+        } else {
+            clearance = 7 * fontMetrics.metrics.defaultRuleThickness;
+        }
+        denomShift = style.metrics.denom1;
+    } else {
+        if (ruleWidth > 0) {
+            numShift = style.metrics.num2;
+            clearance = ruleWidth;
+        } else {
+            numShift = style.metrics.num3;
+            clearance = 3 * fontMetrics.metrics.defaultRuleThickness;
+        }
+        denomShift = style.metrics.denom2;
+    }
+
+    var frac;
+    if (ruleWidth === 0) {
+        // Rule 15c
+        var candidateClearance =
+            (numShift - numer.depth) - (denom.height - denomShift);
+        if (candidateClearance < clearance) {
+            numShift += 0.5 * (clearance - candidateClearance);
+            denomShift += 0.5 * (clearance - candidateClearance);
+        }
+
+        frac = buildCommon.makeVList([
+            {type: "elem", elem: denomreset, shift: denomShift},
+            {type: "elem", elem: numerreset, shift: -numShift}
+        ], "individualShift", null, options);
+    } else {
+        // Rule 15d
+        var axisHeight = style.metrics.axisHeight;
+
+        if ((numShift - numer.depth) - (axisHeight + 0.5 * ruleWidth) <
+                clearance) {
+            numShift +=
+                clearance - ((numShift - numer.depth) -
+                             (axisHeight + 0.5 * ruleWidth));
+        }
+
+        if ((axisHeight - 0.5 * ruleWidth) - (denom.height - denomShift) <
+                clearance) {
+            denomShift +=
+                clearance - ((axisHeight - 0.5 * ruleWidth) -
+                             (denom.height - denomShift));
+        }
+
+        var mid = makeSpan(
+            [options.style.reset(), Style.TEXT.cls(), "frac-line"]);
+        // Manually set the height of the line because its height is
+        // created in CSS
+        mid.height = ruleWidth;
+
+        var midShift = -(axisHeight - 0.5 * ruleWidth);
+
+        frac = buildCommon.makeVList([
+            {type: "elem", elem: denomreset, shift: denomShift},
+            {type: "elem", elem: mid,        shift: midShift},
+            {type: "elem", elem: numerreset, shift: -numShift}
+        ], "individualShift", null, options);
+    }
+
+    // Since we manually change the style sometimes (with \dfrac or \tfrac),
+    // account for the possible size change here.
+    frac.height *= style.sizeMultiplier / options.style.sizeMultiplier;
+    frac.depth *= style.sizeMultiplier / options.style.sizeMultiplier;
+
+    // Rule 15e
+    var delimSize;
+    if (style.size === Style.DISPLAY.size) {
+        delimSize = style.metrics.delim1;
+    } else {
+        delimSize = style.metrics.delim2;
+    }
+
+    var leftDelim;
+    var rightDelim;
+    if (group.value.leftDelim == null) {
+        leftDelim = makeNullDelimiter(options, ["mopen"]);
+    } else {
+        leftDelim = delimiter.customSizedDelim(
+            group.value.leftDelim, delimSize, true,
+            options.withStyle(style), group.mode, ["mopen"]);
+    }
+    if (group.value.rightDelim == null) {
+        rightDelim = makeNullDelimiter(options, ["mclose"]);
+    } else {
+        rightDelim = delimiter.customSizedDelim(
+            group.value.rightDelim, delimSize, true,
+            options.withStyle(style), group.mode, ["mclose"]);
+    }
+
+    return makeSpan(
+        ["mord", options.style.reset(), style.cls()],
+        [leftDelim, makeSpan(["mfrac"], [frac]), rightDelim],
+        options);
+};
+
+var calculateSize = function(sizeValue, style) {
+    var x = sizeValue.number;
+    if (sizeValue.unit === "ex") {
+        x *= style.metrics.emPerEx;
+    } else if (sizeValue.unit === "mu") {
+        x /= 18;
+    }
+    return x;
+};
+
+groupTypes.array = function(group, options) {
+    var r;
+    var c;
+    var nr = group.value.body.length;
+    var nc = 0;
+    var body = new Array(nr);
+
+    var style = options.style;
+
+    // Horizontal spacing
+    var pt = 1 / fontMetrics.metrics.ptPerEm;
+    var arraycolsep = 5 * pt; // \arraycolsep in article.cls
+
+    // Vertical spacing
+    var baselineskip = 12 * pt; // see size10.clo
+    // Default \arraystretch from lttab.dtx
+    // TODO(gagern): may get redefined once we have user-defined macros
+    var arraystretch = utils.deflt(group.value.arraystretch, 1);
+    var arrayskip = arraystretch * baselineskip;
+    var arstrutHeight = 0.7 * arrayskip; // \strutbox in ltfsstrc.dtx and
+    var arstrutDepth = 0.3 * arrayskip;  // \@arstrutbox in lttab.dtx
+
+    var totalHeight = 0;
+    for (r = 0; r < group.value.body.length; ++r) {
+        var inrow = group.value.body[r];
+        var height = arstrutHeight; // \@array adds an \@arstrut
+        var depth = arstrutDepth;   // to each tow (via the template)
+
+        if (nc < inrow.length) {
+            nc = inrow.length;
+        }
+
+        var outrow = new Array(inrow.length);
+        for (c = 0; c < inrow.length; ++c) {
+            var elt = buildGroup(inrow[c], options);
+            if (depth < elt.depth) {
+                depth = elt.depth;
+            }
+            if (height < elt.height) {
+                height = elt.height;
+            }
+            outrow[c] = elt;
+        }
+
+        var gap = 0;
+        if (group.value.rowGaps[r]) {
+            gap = calculateSize(group.value.rowGaps[r].value, style);
+            if (gap > 0) { // \@argarraycr
+                gap += arstrutDepth;
+                if (depth < gap) {
+                    depth = gap; // \@xargarraycr
+                }
+                gap = 0;
+            }
+        }
+
+        outrow.height = height;
+        outrow.depth = depth;
+        totalHeight += height;
+        outrow.pos = totalHeight;
+        totalHeight += depth + gap; // \@yargarraycr
+        body[r] = outrow;
+    }
+
+    var offset = totalHeight / 2 + style.metrics.axisHeight;
+    var colDescriptions = group.value.cols || [];
+    var cols = [];
+    var colSep;
+    var colDescrNum;
+    for (c = 0, colDescrNum = 0;
+         // Continue while either there are more columns or more column
+         // descriptions, so trailing separators don't get lost.
+         c < nc || colDescrNum < colDescriptions.length;
+         ++c, ++colDescrNum) {
+
+        var colDescr = colDescriptions[colDescrNum] || {};
+
+        var firstSeparator = true;
+        while (colDescr.type === "separator") {
+            // If there is more than one separator in a row, add a space
+            // between them.
+            if (!firstSeparator) {
+                colSep = makeSpan(["arraycolsep"], []);
+                colSep.style.width =
+                    fontMetrics.metrics.doubleRuleSep + "em";
+                cols.push(colSep);
+            }
+
+            if (colDescr.separator === "|") {
+                var separator = makeSpan(
+                    ["vertical-separator"],
+                    []);
+                separator.style.height = totalHeight + "em";
+                separator.style.verticalAlign =
+                    -(totalHeight - offset) + "em";
+
+                cols.push(separator);
+            } else {
+                throw new ParseError(
+                    "Invalid separator type: " + colDescr.separator);
+            }
+
+            colDescrNum++;
+            colDescr = colDescriptions[colDescrNum] || {};
+            firstSeparator = false;
+        }
+
+        if (c >= nc) {
+            continue;
+        }
+
+        var sepwidth;
+        if (c > 0 || group.value.hskipBeforeAndAfter) {
+            sepwidth = utils.deflt(colDescr.pregap, arraycolsep);
+            if (sepwidth !== 0) {
+                colSep = makeSpan(["arraycolsep"], []);
+                colSep.style.width = sepwidth + "em";
+                cols.push(colSep);
+            }
+        }
+
+        var col = [];
+        for (r = 0; r < nr; ++r) {
+            var row = body[r];
+            var elem = row[c];
+            if (!elem) {
+                continue;
+            }
+            var shift = row.pos - offset;
+            elem.depth = row.depth;
+            elem.height = row.height;
+            col.push({type: "elem", elem: elem, shift: shift});
+        }
+
+        col = buildCommon.makeVList(col, "individualShift", null, options);
+        col = makeSpan(
+            ["col-align-" + (colDescr.align || "c")],
+            [col]);
+        cols.push(col);
+
+        if (c < nc - 1 || group.value.hskipBeforeAndAfter) {
+            sepwidth = utils.deflt(colDescr.postgap, arraycolsep);
+            if (sepwidth !== 0) {
+                colSep = makeSpan(["arraycolsep"], []);
+                colSep.style.width = sepwidth + "em";
+                cols.push(colSep);
+            }
+        }
+    }
+    body = makeSpan(["mtable"], cols);
+    return makeSpan(["mord"], [body], options);
+};
+
+groupTypes.spacing = function(group, options) {
+    if (group.value === "\\ " || group.value === "\\space" ||
+        group.value === " " || group.value === "~") {
+        // Spaces are generated by adding an actual space. Each of these
+        // things has an entry in the symbols table, so these will be turned
+        // into appropriate outputs.
+        if (group.mode === "text") {
+            return buildCommon.makeOrd(group, options, "textord");
+        } else {
+            return makeSpan(["mspace"],
+                [buildCommon.mathsym(group.value, group.mode, options)],
+                options);
+        }
+    } else {
+        // Other kinds of spaces are of arbitrary width. We use CSS to
+        // generate these.
+        return makeSpan(
+            ["mspace",
+                buildCommon.spacingFunctions[group.value].className],
+            [], options);
+    }
+};
+
+groupTypes.llap = function(group, options) {
+    var inner = makeSpan(
+        ["inner"], [buildGroup(group.value.body, options.reset())]);
+    var fix = makeSpan(["fix"], []);
+    return makeSpan(
+        ["mord", "llap", options.style.cls()], [inner, fix], options);
+};
+
+groupTypes.rlap = function(group, options) {
+    var inner = makeSpan(
+        ["inner"], [buildGroup(group.value.body, options.reset())]);
+    var fix = makeSpan(["fix"], []);
+    return makeSpan(
+        ["mord", "rlap", options.style.cls()], [inner, fix], options);
+};
+
+groupTypes.op = function(group, options) {
+    // Operators are handled in the TeXbook pg. 443-444, rule 13(a).
+    var supGroup;
+    var subGroup;
+    var hasLimits = false;
+    if (group.type === "supsub") {
+        // If we have limits, supsub will pass us its group to handle. Pull
+        // out the superscript and subscript and set the group to the op in
+        // its base.
+        supGroup = group.value.sup;
+        subGroup = group.value.sub;
+        group = group.value.base;
+        hasLimits = true;
+    }
+
+    var style = options.style;
+
+    // Most operators have a large successor symbol, but these don't.
+    var noSuccessor = [
+        "\\smallint"
+    ];
+
+    var large = false;
+    if (style.size === Style.DISPLAY.size &&
+        group.value.symbol &&
+        !utils.contains(noSuccessor, group.value.body)) {
+
+        // Most symbol operators get larger in displaystyle (rule 13)
+        large = true;
+    }
+
+    var base;
+    var baseShift = 0;
+    var slant = 0;
+    if (group.value.symbol) {
+        // If this is a symbol, create the symbol.
+        var fontName = large ? "Size2-Regular" : "Size1-Regular";
+        base = buildCommon.makeSymbol(
+            group.value.body, fontName, "math", options,
+            ["mop", "op-symbol", large ? "large-op" : "small-op"]);
+
+        // Shift the symbol so its center lies on the axis (rule 13). It
+        // appears that our fonts have the centers of the symbols already
+        // almost on the axis, so these numbers are very small. Note we
+        // don't actually apply this here, but instead it is used either in
+        // the vlist creation or separately when there are no limits.
+        baseShift = (base.height - base.depth) / 2 -
+            style.metrics.axisHeight * style.sizeMultiplier;
+
+        // The slant of the symbol is just its italic correction.
+        slant = base.italic;
+    } else if (group.value.value) {
+        // If this is a list, compose that list.
+        var inner = buildExpression(group.value.value, options, true);
+
+        base = makeSpan(["mop"], inner, options);
+    } else {
+        // Otherwise, this is a text operator. Build the text from the
+        // operator's name.
+        // TODO(emily): Add a space in the middle of some of these
+        // operators, like \limsup
+        var output = [];
+        for (var i = 1; i < group.value.body.length; i++) {
+            output.push(buildCommon.mathsym(group.value.body[i], group.mode));
+        }
+        base = makeSpan(["mop"], output, options);
+    }
+
+    if (hasLimits) {
+        // IE 8 clips \int if it is in a display: inline-block. We wrap it
+        // in a new span so it is an inline, and works.
+        base = makeSpan([], [base]);
+
+        var supmid;
+        var supKern;
+        var submid;
+        var subKern;
+        var newOptions;
+        // We manually have to handle the superscripts and subscripts. This,
+        // aside from the kern calculations, is copied from supsub.
+        if (supGroup) {
+            newOptions = options.withStyle(style.sup());
+            var sup = buildGroup(supGroup, newOptions);
+            supmid = makeSpan([style.reset(), style.sup().cls()],
+                [sup], newOptions);
+
+            supKern = Math.max(
+                fontMetrics.metrics.bigOpSpacing1,
+                fontMetrics.metrics.bigOpSpacing3 - sup.depth);
+        }
+
+        if (subGroup) {
+            newOptions = options.withStyle(style.sub());
+            var sub = buildGroup(subGroup, newOptions);
+            submid = makeSpan([style.reset(), style.sub().cls()],
+                [sub], newOptions);
+
+            subKern = Math.max(
+                fontMetrics.metrics.bigOpSpacing2,
+                fontMetrics.metrics.bigOpSpacing4 - sub.height);
+        }
+
+        // Build the final group as a vlist of the possible subscript, base,
+        // and possible superscript.
+        var finalGroup;
+        var top;
+        var bottom;
+        if (!supGroup) {
+            top = base.height - baseShift;
+
+            finalGroup = buildCommon.makeVList([
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5},
+                {type: "elem", elem: submid},
+                {type: "kern", size: subKern},
+                {type: "elem", elem: base}
+            ], "top", top, options);
+
+            // Here, we shift the limits by the slant of the symbol. Note
+            // that we are supposed to shift the limits by 1/2 of the slant,
+            // but since we are centering the limits adding a full slant of
+            // margin will shift by 1/2 that.
+            finalGroup.children[0].style.marginLeft = -slant + "em";
+        } else if (!subGroup) {
+            bottom = base.depth + baseShift;
+
+            finalGroup = buildCommon.makeVList([
+                {type: "elem", elem: base},
+                {type: "kern", size: supKern},
+                {type: "elem", elem: supmid},
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5}
+            ], "bottom", bottom, options);
+
+            // See comment above about slants
+            finalGroup.children[1].style.marginLeft = slant + "em";
+        } else if (!supGroup && !subGroup) {
+            // This case probably shouldn't occur (this would mean the
+            // supsub was sending us a group with no superscript or
+            // subscript) but be safe.
+            return base;
+        } else {
+            bottom = fontMetrics.metrics.bigOpSpacing5 +
+                submid.height + submid.depth +
+                subKern +
+                base.depth + baseShift;
+
+            finalGroup = buildCommon.makeVList([
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5},
+                {type: "elem", elem: submid},
+                {type: "kern", size: subKern},
+                {type: "elem", elem: base},
+                {type: "kern", size: supKern},
+                {type: "elem", elem: supmid},
+                {type: "kern", size: fontMetrics.metrics.bigOpSpacing5}
+            ], "bottom", bottom, options);
+
+            // See comment above about slants
+            finalGroup.children[0].style.marginLeft = -slant + "em";
+            finalGroup.children[2].style.marginLeft = slant + "em";
+        }
+
+        return makeSpan(["mop", "op-limits"], [finalGroup], options);
+    } else {
+        if (group.value.symbol) {
+            base.style.top = baseShift + "em";
+        }
+
+        return base;
+    }
+};
+
+groupTypes.mod = function(group, options) {
+    var inner = [];
+
+    if (group.value.modType === "bmod") {
+        // “\nonscript\mskip-\medmuskip\mkern5mu”
+        if (!options.style.isTight()) {
+            inner.push(makeSpan(
+                ["mspace", "negativemediumspace"], [], options));
+        }
+        inner.push(makeSpan(["mspace", "thickspace"], [], options));
+    } else if (options.style.size === Style.DISPLAY.size) {
+        inner.push(makeSpan(["mspace", "quad"], [], options));
+    } else if (group.value.modType === "mod") {
+        inner.push(makeSpan(["mspace", "twelvemuspace"], [], options));
+    } else {
+        inner.push(makeSpan(["mspace", "eightmuspace"], [], options));
+    }
+
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(buildCommon.mathsym("(", group.mode));
+    }
+
+    if (group.value.modType !== "pod") {
+        var modInner = [
+            buildCommon.mathsym("m", group.mode),
+            buildCommon.mathsym("o", group.mode),
+            buildCommon.mathsym("d", group.mode)];
+        if (group.value.modType === "bmod") {
+            inner.push(makeSpan(["mbin"], modInner, options));
+            // “\mkern5mu\nonscript\mskip-\medmuskip”
+            inner.push(makeSpan(["mspace", "thickspace"], [], options));
+            if (!options.style.isTight()) {
+                inner.push(makeSpan(
+                    ["mspace", "negativemediumspace"], [], options));
+            }
+        } else {
+            Array.prototype.push.apply(inner, modInner);
+            inner.push(makeSpan(["mspace", "sixmuspace"], [], options));
+        }
+    }
+
+    if (group.value.value) {
+        Array.prototype.push.apply(inner,
+            buildExpression(group.value.value, options, false));
+    }
+
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(buildCommon.mathsym(")", group.mode));
+    }
+
+    return buildCommon.makeFragment(inner);
+};
+
+groupTypes.katex = function(group, options) {
+    // The KaTeX logo. The offsets for the K and a were chosen to look
+    // good, but the offsets for the T, E, and X were taken from the
+    // definition of \TeX in TeX (see TeXbook pg. 356)
+    var k = makeSpan(
+        ["k"], [buildCommon.mathsym("K", group.mode)], options);
+    var a = makeSpan(
+        ["a"], [buildCommon.mathsym("A", group.mode)], options);
+
+    a.height = (a.height + 0.2) * 0.75;
+    a.depth = (a.height - 0.2) * 0.75;
+
+    var t = makeSpan(
+        ["t"], [buildCommon.mathsym("T", group.mode)], options);
+    var e = makeSpan(
+        ["e"], [buildCommon.mathsym("E", group.mode)], options);
+
+    e.height = (e.height - 0.2155);
+    e.depth = (e.depth + 0.2155);
+
+    var x = makeSpan(
+        ["x"], [buildCommon.mathsym("X", group.mode)], options);
+
+    return makeSpan(
+        ["mord", "katex-logo"], [k, a, t, e, x], options);
+};
+
+groupTypes.overline = function(group, options) {
+    // Overlines are handled in the TeXbook pg 443, Rule 9.
+    var style = options.style;
+
+    // Build the inner group in the cramped style.
+    var innerGroup = buildGroup(group.value.body,
+            options.withStyle(style.cramp()));
+
+    var ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+        style.sizeMultiplier;
+
+    // Create the line above the body
+    var line = makeSpan(
+        [style.reset(), Style.TEXT.cls(), "overline-line"]);
+    line.height = ruleWidth;
+    line.maxFontSize = 1.0;
+
+    // Generate the vlist, with the appropriate kerns
+    var vlist = buildCommon.makeVList([
+        {type: "elem", elem: innerGroup},
+        {type: "kern", size: 3 * ruleWidth},
+        {type: "elem", elem: line},
+        {type: "kern", size: ruleWidth}
+    ], "firstBaseline", null, options);
+
+    return makeSpan(["mord", "overline"], [vlist], options);
+};
+
+groupTypes.underline = function(group, options) {
+    // Underlines are handled in the TeXbook pg 443, Rule 10.
+    var style = options.style;
+
+    // Build the inner group.
+    var innerGroup = buildGroup(group.value.body, options);
+
+    var ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+        style.sizeMultiplier;
+
+    // Create the line above the body
+    var line = makeSpan([style.reset(), Style.TEXT.cls(), "underline-line"]);
+    line.height = ruleWidth;
+    line.maxFontSize = 1.0;
+
+    // Generate the vlist, with the appropriate kerns
+    var vlist = buildCommon.makeVList([
+        {type: "kern", size: ruleWidth},
+        {type: "elem", elem: line},
+        {type: "kern", size: 3 * ruleWidth},
+        {type: "elem", elem: innerGroup}
+    ], "top", innerGroup.height, options);
+
+    return makeSpan(["mord", "underline"], [vlist], options);
+};
+
+groupTypes.sqrt = function(group, options) {
+    // Square roots are handled in the TeXbook pg. 443, Rule 11.
+    var style = options.style;
+
+    // First, we do the same steps as in overline to build the inner group
+    // and line
+    var inner = buildGroup(group.value.body, options.withStyle(style.cramp()));
+
+    var ruleWidth = fontMetrics.metrics.defaultRuleThickness /
+        style.sizeMultiplier;
+
+    var line = makeSpan(
+        [style.reset(), Style.TEXT.cls(), "sqrt-line"], [],
+        options);
+    line.height = ruleWidth;
+    line.maxFontSize = 1.0;
+
+    var phi = ruleWidth;
+    if (style.id < Style.TEXT.id) {
+        phi = style.metrics.xHeight;
+    }
+
+    // Calculate the clearance between the body and line
+    var lineClearance = ruleWidth + phi / 4;
+
+    var innerHeight = (inner.height + inner.depth) * style.sizeMultiplier;
+    var minDelimiterHeight = innerHeight + lineClearance + ruleWidth;
+
+    // Create a \surd delimiter of the required minimum size
+    var delim = makeSpan(["sqrt-sign"], [
+        delimiter.customSizedDelim("\\surd", minDelimiterHeight,
+                                   false, options, group.mode)],
+                         options);
+
+    var delimDepth = (delim.height + delim.depth) - ruleWidth;
+
+    // Adjust the clearance based on the delimiter size
+    if (delimDepth > inner.height + inner.depth + lineClearance) {
+        lineClearance =
+            (lineClearance + delimDepth - inner.height - inner.depth) / 2;
+    }
+
+    // Shift the delimiter so that its top lines up with the top of the line
+    var delimShift = -(inner.height + lineClearance + ruleWidth) + delim.height;
+    delim.style.top = delimShift + "em";
+    delim.height -= delimShift;
+    delim.depth += delimShift;
+
+    // We add a special case here, because even when `inner` is empty, we
+    // still get a line. So, we use a simple heuristic to decide if we
+    // should omit the body entirely. (note this doesn't work for something
+    // like `\sqrt{\rlap{x}}`, but if someone is doing that they deserve for
+    // it not to work.
+    var body;
+    if (inner.height === 0 && inner.depth === 0) {
+        body = makeSpan();
+    } else {
+        body = buildCommon.makeVList([
+            {type: "elem", elem: inner},
+            {type: "kern", size: lineClearance},
+            {type: "elem", elem: line},
+            {type: "kern", size: ruleWidth}
+        ], "firstBaseline", null, options);
+    }
+
+    if (!group.value.index) {
+        return makeSpan(["mord", "sqrt"], [delim, body], options);
+    } else {
+        // Handle the optional root index
+
+        // The index is always in scriptscript style
+        var newOptions = options.withStyle(Style.SCRIPTSCRIPT);
+        var root = buildGroup(group.value.index, newOptions);
+        var rootWrap = makeSpan(
+            [style.reset(), Style.SCRIPTSCRIPT.cls()],
+            [root],
+            newOptions);
+
+        // Figure out the height and depth of the inner part
+        var innerRootHeight = Math.max(delim.height, body.height);
+        var innerRootDepth = Math.max(delim.depth, body.depth);
+
+        // The amount the index is shifted by. This is taken from the TeX
+        // source, in the definition of `\r@@t`.
+        var toShift = 0.6 * (innerRootHeight - innerRootDepth);
+
+        // Build a VList with the superscript shifted up correctly
+        var rootVList = buildCommon.makeVList(
+            [{type: "elem", elem: rootWrap}],
+            "shift", -toShift, options);
+        // Add a class surrounding it so we can add on the appropriate
+        // kerning
+        var rootVListWrap = makeSpan(["root"], [rootVList]);
+
+        return makeSpan(["mord", "sqrt"],
+            [rootVListWrap, delim, body], options);
+    }
+};
+
+groupTypes.sizing = function(group, options) {
+    // Handle sizing operators like \Huge. Real TeX doesn't actually allow
+    // these functions inside of math expressions, so we do some special
+    // handling.
+    var inner = buildExpression(group.value.value,
+            options.withSize(group.value.size), false);
+
+    // Compute the correct maxFontSize.
+    var style = options.style;
+    var fontSize = buildCommon.sizingMultiplier[group.value.size];
+    fontSize = fontSize * style.sizeMultiplier;
+
+    // Add size-resetting classes to the inner list and set maxFontSize
+    // manually. Handle nested size changes.
+    for (var i = 0; i < inner.length; i++) {
+        var pos = utils.indexOf(inner[i].classes, "sizing");
+        if (pos < 0) {
+            inner[i].classes.push("sizing", "reset-" + options.size,
+                                  group.value.size, style.cls());
+            inner[i].maxFontSize = fontSize;
+        } else if (inner[i].classes[pos + 1] === "reset-" + group.value.size) {
+            // This is a nested size change: e.g., inner[i] is the "b" in
+            // `\Huge a \small b`. Override the old size (the `reset-` class)
+            // but not the new size.
+            inner[i].classes[pos + 1] = "reset-" + options.size;
+        }
+    }
+
+    return buildCommon.makeFragment(inner);
+};
+
+groupTypes.styling = function(group, options) {
+    // Style changes are handled in the TeXbook on pg. 442, Rule 3.
+
+    // Figure out what style we're changing to.
+    var styleMap = {
+        "display": Style.DISPLAY,
+        "text": Style.TEXT,
+        "script": Style.SCRIPT,
+        "scriptscript": Style.SCRIPTSCRIPT
+    };
+
+    var newStyle = styleMap[group.value.style];
+    var newOptions = options.withStyle(newStyle);
+
+    // Build the inner expression in the new style.
+    var inner = buildExpression(
+        group.value.value, newOptions, false);
+
+    // Add style-resetting classes to the inner list. Handle nested changes.
+    for (var i = 0; i < inner.length; i++) {
+        var pos = utils.indexOf(inner[i].classes, newStyle.reset());
+        if (pos < 0) {
+            inner[i].classes.push(options.style.reset(), newStyle.cls());
+        } else {
+            // This is a nested style change, as `\textstyle a\scriptstyle b`.
+            // Only override the old style (the reset class).
+            inner[i].classes[pos] = options.style.reset();
+        }
+    }
+
+    return new buildCommon.makeFragment(inner);
+};
+
+groupTypes.font = function(group, options) {
+    var font = group.value.font;
+    return buildGroup(group.value.body, options.withFont(font));
+};
+
+groupTypes.delimsizing = function(group, options) {
+    var delim = group.value.value;
+
+    if (delim === ".") {
+        // Empty delimiters still count as elements, even though they don't
+        // show anything.
+        return makeSpan([group.value.mclass]);
+    }
+
+    // Use delimiter.sizedDelim to generate the delimiter.
+    return delimiter.sizedDelim(
+            delim, group.value.size, options, group.mode,
+            [group.value.mclass]);
+};
+
+groupTypes.leftright = function(group, options) {
+    // Build the inner expression
+    var inner = buildExpression(group.value.body, options.reset(), true);
+
+    var innerHeight = 0;
+    var innerDepth = 0;
+    var hadMiddle = false;
+
+    // Calculate its height and depth
+    for (var i = 0; i < inner.length; i++) {
+        if (inner[i].isMiddle) {
+            hadMiddle = true;
+        } else {
+            innerHeight = Math.max(inner[i].height, innerHeight);
+            innerDepth = Math.max(inner[i].depth, innerDepth);
+        }
+    }
+
+    var style = options.style;
+
+    // The size of delimiters is the same, regardless of what style we are
+    // in. Thus, to correctly calculate the size of delimiter we need around
+    // a group, we scale down the inner size based on the size.
+    innerHeight *= style.sizeMultiplier;
+    innerDepth *= style.sizeMultiplier;
+
+    var leftDelim;
+    if (group.value.left === ".") {
+        // Empty delimiters in \left and \right make null delimiter spaces.
+        leftDelim = makeNullDelimiter(options, ["mopen"]);
+    } else {
+        // Otherwise, use leftRightDelim to generate the correct sized
+        // delimiter.
+        leftDelim = delimiter.leftRightDelim(
+            group.value.left, innerHeight, innerDepth, options,
+            group.mode, ["mopen"]);
+    }
+    // Add it to the beginning of the expression
+    inner.unshift(leftDelim);
+
+    // Handle middle delimiters
+    if (hadMiddle) {
+        for (i = 1; i < inner.length; i++) {
+            if (inner[i].isMiddle) {
+                // Apply the options that were active when \middle was called
+                inner[i] = delimiter.leftRightDelim(
+                    inner[i].isMiddle.value, innerHeight, innerDepth,
+                    inner[i].isMiddle.options, group.mode, []);
+            }
+        }
+    }
+
+    var rightDelim;
+    // Same for the right delimiter
+    if (group.value.right === ".") {
+        rightDelim = makeNullDelimiter(options, ["mclose"]);
+    } else {
+        rightDelim = delimiter.leftRightDelim(
+            group.value.right, innerHeight, innerDepth, options,
+            group.mode, ["mclose"]);
+    }
+    // Add it to the end of the expression.
+    inner.push(rightDelim);
+
+    return makeSpan(
+        ["minner", style.cls()], inner, options);
+};
+
+groupTypes.middle = function(group, options) {
+    var middleDelim;
+    if (group.value.value === ".") {
+        middleDelim = makeNullDelimiter(options, []);
+    } else {
+        middleDelim = delimiter.sizedDelim(
+            group.value.value, 1, options,
+            group.mode, []);
+        middleDelim.isMiddle = {value: group.value.value, options: options};
+    }
+    return middleDelim;
+};
+
+groupTypes.rule = function(group, options) {
+    // Make an empty span for the rule
+    var rule = makeSpan(["mord", "rule"], [], options);
+    var style = options.style;
+
+    // Calculate the shift, width, and height of the rule, and account for units
+    var shift = 0;
+    if (group.value.shift) {
+        shift = calculateSize(group.value.shift, style);
+    }
+
+    var width = calculateSize(group.value.width, style);
+    var height = calculateSize(group.value.height, style);
+
+    // The sizes of rules are absolute, so make it larger if we are in a
+    // smaller style.
+    shift /= style.sizeMultiplier;
+    width /= style.sizeMultiplier;
+    height /= style.sizeMultiplier;
+
+    // Style the rule to the right size
+    rule.style.borderRightWidth = width + "em";
+    rule.style.borderTopWidth = height + "em";
+    rule.style.bottom = shift + "em";
+
+    // Record the height and width
+    rule.width = width;
+    rule.height = height + shift;
+    rule.depth = -shift;
+
+    return rule;
+};
+
+groupTypes.kern = function(group, options) {
+    // Make an empty span for the rule
+    var rule = makeSpan(["mord", "rule"], [], options);
+    var style = options.style;
+
+    var dimension = 0;
+    if (group.value.dimension) {
+        dimension = calculateSize(group.value.dimension, style);
+    }
+
+    dimension /= style.sizeMultiplier;
+
+    rule.style.marginLeft = dimension + "em";
+
+    return rule;
+};
+
+groupTypes.accent = function(group, options) {
+    // Accents are handled in the TeXbook pg. 443, rule 12.
+    var base = group.value.base;
+    var style = options.style;
+
+    var supsubGroup;
+    if (group.type === "supsub") {
+        // If our base is a character box, and we have superscripts and
+        // subscripts, the supsub will defer to us. In particular, we want
+        // to attach the superscripts and subscripts to the inner body (so
+        // that the position of the superscripts and subscripts won't be
+        // affected by the height of the accent). We accomplish this by
+        // sticking the base of the accent into the base of the supsub, and
+        // rendering that, while keeping track of where the accent is.
+
+        // The supsub group is the group that was passed in
+        var supsub = group;
+        // The real accent group is the base of the supsub group
+        group = supsub.value.base;
+        // The character box is the base of the accent group
+        base = group.value.base;
+        // Stick the character box into the base of the supsub group
+        supsub.value.base = base;
+
+        // Rerender the supsub group with its new base, and store that
+        // result.
+        supsubGroup = buildGroup(
+            supsub, options.reset());
+    }
+
+    // Build the base group
+    var body = buildGroup(
+        base, options.withStyle(style.cramp()));
+
+    // Calculate the skew of the accent. This is based on the line "If the
+    // nucleus is not a single character, let s = 0; otherwise set s to the
+    // kern amount for the nucleus followed by the \skewchar of its font."
+    // Note that our skew metrics are just the kern between each character
+    // and the skewchar.
+    var skew;
+    if (isCharacterBox(base)) {
+        // If the base is a character box, then we want the skew of the
+        // innermost character. To do that, we find the innermost character:
+        var baseChar = getBaseElem(base);
+        // Then, we render its group to get the symbol inside it
+        var baseGroup = buildGroup(
+            baseChar, options.withStyle(style.cramp()));
+        // Finally, we pull the skew off of the symbol.
+        skew = baseGroup.skew;
+        // Note that we now throw away baseGroup, because the layers we
+        // removed with getBaseElem might contain things like \color which
+        // we can't get rid of.
+        // TODO(emily): Find a better way to get the skew
+    } else {
+        skew = 0;
+    }
+
+    // calculate the amount of space between the body and the accent
+    var clearance = Math.min(
+        body.height,
+        style.metrics.xHeight);
+
+    // Build the accent
+    var accent = buildCommon.makeSymbol(
+        group.value.accent, "Main-Regular", "math", options);
+    // Remove the italic correction of the accent, because it only serves to
+    // shift the accent over to a place we don't want.
+    accent.italic = 0;
+
+    // The \vec character that the fonts use is a combining character, and
+    // thus shows up much too far to the left. To account for this, we add a
+    // specific class which shifts the accent over to where we want it.
+    // TODO(emily): Fix this in a better way, like by changing the font
+    var vecClass = group.value.accent === "\\vec" ? "accent-vec" : null;
+
+    var accentBody = makeSpan(["accent-body", vecClass], [
+        makeSpan([], [accent])]);
+
+    accentBody = buildCommon.makeVList([
+        {type: "elem", elem: body},
+        {type: "kern", size: -clearance},
+        {type: "elem", elem: accentBody}
+    ], "firstBaseline", null, options);
+
+    // Shift the accent over by the skew. Note we shift by twice the skew
+    // because we are centering the accent, so by adding 2*skew to the left,
+    // we shift it to the right by 1*skew.
+    accentBody.children[1].style.marginLeft = 2 * skew + "em";
+
+    var accentWrap = makeSpan(["mord", "accent"], [accentBody], options);
+
+    if (supsubGroup) {
+        // Here, we replace the "base" child of the supsub with our newly
+        // generated accent.
+        supsubGroup.children[0] = accentWrap;
+
+        // Since we don't rerun the height calculation after replacing the
+        // accent, we manually recalculate height.
+        supsubGroup.height = Math.max(accentWrap.height, supsubGroup.height);
+
+        // Accents should always be ords, even when their innards are not.
+        supsubGroup.classes[0] = "mord";
+
+        return supsubGroup;
+    } else {
+        return accentWrap;
+    }
+};
+
+groupTypes.phantom = function(group, options) {
+    var elements = buildExpression(
+        group.value.value,
+        options.withPhantom(),
+        false
+    );
+
+    // \phantom isn't supposed to affect the elements it contains.
+    // See "color" for more details.
+    return new buildCommon.makeFragment(elements);
+};
+
+groupTypes.mclass = function(group, options) {
+    var elements = buildExpression(group.value.value, options, true);
+
+    return makeSpan([group.value.mclass], elements, options);
+};
+
+/**
+ * buildGroup is the function that takes a group and calls the correct groupType
+ * function for it. It also handles the interaction of size and style changes
+ * between parents and children.
+ */
+var buildGroup = function(group, options) {
+    if (!group) {
+        return makeSpan();
+    }
+
+    if (groupTypes[group.type]) {
+        // Call the groupTypes function
+        var groupNode = groupTypes[group.type](group, options);
+        var multiplier;
+
+        // If the style changed between the parent and the current group,
+        // account for the size difference
+        if (options.style !== options.parentStyle) {
+            multiplier = options.style.sizeMultiplier /
+                    options.parentStyle.sizeMultiplier;
+
+            groupNode.height *= multiplier;
+            groupNode.depth *= multiplier;
+        }
+
+        // If the size changed between the parent and the current group, account
+        // for that size difference.
+        if (options.size !== options.parentSize) {
+            multiplier = buildCommon.sizingMultiplier[options.size] /
+                    buildCommon.sizingMultiplier[options.parentSize];
+
+            groupNode.height *= multiplier;
+            groupNode.depth *= multiplier;
+        }
+
+        return groupNode;
+    } else {
+        throw new ParseError(
+            "Got group of unknown type: '" + group.type + "'");
+    }
+};
+
+/**
+ * Take an entire parse tree, and build it into an appropriate set of HTML
+ * nodes.
+ */
+var buildHTML = function(tree, options) {
+    // buildExpression is destructive, so we need to make a clone
+    // of the incoming tree so that it isn't accidentally changed
+    tree = JSON.parse(JSON.stringify(tree));
+
+    // Build the expression contained in the tree
+    var expression = buildExpression(tree, options, true);
+    var body = makeSpan(["base", options.style.cls()], expression, options);
+
+    // Add struts, which ensure that the top of the HTML element falls at the
+    // height of the expression, and the bottom of the HTML element falls at the
+    // depth of the expression.
+    var topStrut = makeSpan(["strut"]);
+    var bottomStrut = makeSpan(["strut", "bottom"]);
+
+    topStrut.style.height = body.height + "em";
+    bottomStrut.style.height = (body.height + body.depth) + "em";
+    // We'd like to use `vertical-align: top` but in IE 9 this lowers the
+    // baseline of the box to the bottom of this strut (instead staying in the
+    // normal place) so we use an absolute value for vertical-align instead
+    bottomStrut.style.verticalAlign = -body.depth + "em";
+
+    // Wrap the struts and body together
+    var htmlNode = makeSpan(["katex-html"], [topStrut, bottomStrut, body]);
+
+    htmlNode.setAttribute("aria-hidden", "true");
+
+    return htmlNode;
+};
+
+module.exports = buildHTML;
+
+},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./delimiter":14,"./domTree":15,"./fontMetrics":17,"./utils":25}],12:[function(require,module,exports){
+/**
+ * This file converts a parse tree into a cooresponding MathML tree. The main
+ * entry point is the `buildMathML` function, which takes a parse tree from the
+ * parser.
+ */
+
+var buildCommon = require("./buildCommon");
+var fontMetrics = require("./fontMetrics");
+var mathMLTree = require("./mathMLTree");
+var ParseError = require("./ParseError");
+var symbols = require("./symbols");
+var utils = require("./utils");
+
+var makeSpan = buildCommon.makeSpan;
+var fontMap = buildCommon.fontMap;
+
+/**
+ * Takes a symbol and converts it into a MathML text node after performing
+ * optional replacement from symbols.js.
+ */
+var makeText = function(text, mode) {
+    if (symbols[mode][text] && symbols[mode][text].replace) {
+        text = symbols[mode][text].replace;
+    }
+
+    return new mathMLTree.TextNode(text);
+};
+
+/**
+ * Returns the math variant as a string or null if none is required.
+ */
+var getVariant = function(group, options) {
+    var font = options.font;
+    if (!font) {
+        return null;
+    }
+
+    var mode = group.mode;
+    if (font === "mathit") {
+        return "italic";
+    }
+
+    var value = group.value;
+    if (utils.contains(["\\imath", "\\jmath"], value)) {
+        return null;
+    }
+
+    if (symbols[mode][value] && symbols[mode][value].replace) {
+        value = symbols[mode][value].replace;
+    }
+
+    var fontName = fontMap[font].fontName;
+    if (fontMetrics.getCharacterMetrics(value, fontName)) {
+        return fontMap[options.font].variant;
+    }
+
+    return null;
+};
+
+/**
+ * Functions for handling the different types of groups found in the parse
+ * tree. Each function should take a parse group and return a MathML node.
+ */
+var groupTypes = {};
+
+groupTypes.mathord = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mi",
+        [makeText(group.value, group.mode)]);
+
+    var variant = getVariant(group, options);
+    if (variant) {
+        node.setAttribute("mathvariant", variant);
+    }
+    return node;
+};
+
+groupTypes.textord = function(group, options) {
+    var text = makeText(group.value, group.mode);
+
+    var variant = getVariant(group, options) || "normal";
+
+    var node;
+    if (/[0-9]/.test(group.value)) {
+        // TODO(kevinb) merge adjacent <mn> nodes
+        // do it as a post processing step
+        node = new mathMLTree.MathNode("mn", [text]);
+        if (options.font) {
+            node.setAttribute("mathvariant", variant);
+        }
+    } else {
+        node = new mathMLTree.MathNode("mi", [text]);
+        node.setAttribute("mathvariant", variant);
+    }
+
+    return node;
+};
+
+groupTypes.bin = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.rel = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.open = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.close = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.inner = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    return node;
+};
+
+groupTypes.punct = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mo", [makeText(group.value, group.mode)]);
+
+    node.setAttribute("separator", "true");
+
+    return node;
+};
+
+groupTypes.ordgroup = function(group, options) {
+    var inner = buildExpression(group.value, options);
+
+    var node = new mathMLTree.MathNode("mrow", inner);
+
+    return node;
+};
+
+groupTypes.text = function(group, options) {
+    var inner = buildExpression(group.value.body, options);
+
+    var node = new mathMLTree.MathNode("mtext", inner);
+
+    return node;
+};
+
+groupTypes.color = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+
+    var node = new mathMLTree.MathNode("mstyle", inner);
+
+    node.setAttribute("mathcolor", group.value.color);
+
+    return node;
+};
+
+groupTypes.supsub = function(group, options) {
+    var children = [buildGroup(group.value.base, options)];
+
+    if (group.value.sub) {
+        children.push(buildGroup(group.value.sub, options));
+    }
+
+    if (group.value.sup) {
+        children.push(buildGroup(group.value.sup, options));
+    }
+
+    var nodeType;
+    if (!group.value.sub) {
+        nodeType = "msup";
+    } else if (!group.value.sup) {
+        nodeType = "msub";
+    } else {
+        nodeType = "msubsup";
+    }
+
+    var node = new mathMLTree.MathNode(nodeType, children);
+
+    return node;
+};
+
+groupTypes.genfrac = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mfrac",
+        [buildGroup(group.value.numer, options),
+            buildGroup(group.value.denom, options)]);
+
+    if (!group.value.hasBarLine) {
+        node.setAttribute("linethickness", "0px");
+    }
+
+    if (group.value.leftDelim != null || group.value.rightDelim != null) {
+        var withDelims = [];
+
+        if (group.value.leftDelim != null) {
+            var leftOp = new mathMLTree.MathNode(
+                "mo", [new mathMLTree.TextNode(group.value.leftDelim)]);
+
+            leftOp.setAttribute("fence", "true");
+
+            withDelims.push(leftOp);
+        }
+
+        withDelims.push(node);
+
+        if (group.value.rightDelim != null) {
+            var rightOp = new mathMLTree.MathNode(
+                "mo", [new mathMLTree.TextNode(group.value.rightDelim)]);
+
+            rightOp.setAttribute("fence", "true");
+
+            withDelims.push(rightOp);
+        }
+
+        var outerNode = new mathMLTree.MathNode("mrow", withDelims);
+
+        return outerNode;
+    }
+
+    return node;
+};
+
+groupTypes.array = function(group, options) {
+    return new mathMLTree.MathNode(
+        "mtable", group.value.body.map(function(row) {
+            return new mathMLTree.MathNode(
+                "mtr", row.map(function(cell) {
+                    return new mathMLTree.MathNode(
+                        "mtd", [buildGroup(cell, options)]);
+                }));
+        }));
+};
+
+groupTypes.sqrt = function(group, options) {
+    var node;
+    if (group.value.index) {
+        node = new mathMLTree.MathNode(
+            "mroot", [
+                buildGroup(group.value.body, options),
+                buildGroup(group.value.index, options)
+            ]);
+    } else {
+        node = new mathMLTree.MathNode(
+            "msqrt", [buildGroup(group.value.body, options)]);
+    }
+
+    return node;
+};
+
+groupTypes.leftright = function(group, options) {
+    var inner = buildExpression(group.value.body, options);
+
+    if (group.value.left !== ".") {
+        var leftNode = new mathMLTree.MathNode(
+            "mo", [makeText(group.value.left, group.mode)]);
+
+        leftNode.setAttribute("fence", "true");
+
+        inner.unshift(leftNode);
+    }
+
+    if (group.value.right !== ".") {
+        var rightNode = new mathMLTree.MathNode(
+            "mo", [makeText(group.value.right, group.mode)]);
+
+        rightNode.setAttribute("fence", "true");
+
+        inner.push(rightNode);
+    }
+
+    var outerNode = new mathMLTree.MathNode("mrow", inner);
+
+    return outerNode;
+};
+
+groupTypes.middle = function(group, options) {
+    var middleNode = new mathMLTree.MathNode(
+        "mo", [makeText(group.value.middle, group.mode)]);
+    middleNode.setAttribute("fence", "true");
+    return middleNode;
+};
+
+groupTypes.accent = function(group, options) {
+    var accentNode = new mathMLTree.MathNode(
+        "mo", [makeText(group.value.accent, group.mode)]);
+
+    var node = new mathMLTree.MathNode(
+        "mover",
+        [buildGroup(group.value.base, options),
+            accentNode]);
+
+    node.setAttribute("accent", "true");
+
+    return node;
+};
+
+groupTypes.spacing = function(group) {
+    var node;
+
+    if (group.value === "\\ " || group.value === "\\space" ||
+        group.value === " " || group.value === "~") {
+        node = new mathMLTree.MathNode(
+            "mtext", [new mathMLTree.TextNode("\u00a0")]);
+    } else {
+        node = new mathMLTree.MathNode("mspace");
+
+        node.setAttribute(
+            "width", buildCommon.spacingFunctions[group.value].size);
+    }
+
+    return node;
+};
+
+groupTypes.op = function(group, options) {
+    var node;
+
+    // TODO(emily): handle big operators using the `largeop` attribute
+
+    if (group.value.symbol) {
+        // This is a symbol. Just add the symbol.
+        node = new mathMLTree.MathNode(
+            "mo", [makeText(group.value.body, group.mode)]);
+    } else if (group.value.value) {
+        // This is an operator with children. Add them.
+        node = new mathMLTree.MathNode(
+            "mo", buildExpression(group.value.value, options));
+    } else {
+        // This is a text operator. Add all of the characters from the
+        // operator's name.
+        // TODO(emily): Add a space in the middle of some of these
+        // operators, like \limsup.
+        node = new mathMLTree.MathNode(
+            "mi", [new mathMLTree.TextNode(group.value.body.slice(1))]);
+    }
+
+    return node;
+};
+
+groupTypes.mod = function(group, options) {
+    var inner = [];
+
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(new mathMLTree.MathNode(
+            "mo", [makeText("(", group.mode)]));
+    }
+    if (group.value.modType !== "pod") {
+        inner.push(new mathMLTree.MathNode(
+            "mo", [makeText("mod", group.mode)]));
+    }
+    if (group.value.value) {
+        var space = new mathMLTree.MathNode("mspace");
+        space.setAttribute("width", "0.333333em");
+        inner.push(space);
+        inner = inner.concat(buildExpression(group.value.value, options));
+    }
+    if (group.value.modType === "pod" || group.value.modType === "pmod") {
+        inner.push(new mathMLTree.MathNode(
+            "mo", [makeText(")", group.mode)]));
+    }
+
+    return new mathMLTree.MathNode("mo", inner);
+};
+
+groupTypes.katex = function(group) {
+    var node = new mathMLTree.MathNode(
+        "mtext", [new mathMLTree.TextNode("KaTeX")]);
+
+    return node;
+};
+
+groupTypes.font = function(group, options) {
+    var font = group.value.font;
+    return buildGroup(group.value.body, options.withFont(font));
+};
+
+groupTypes.delimsizing = function(group) {
+    var children = [];
+
+    if (group.value.value !== ".") {
+        children.push(makeText(group.value.value, group.mode));
+    }
+
+    var node = new mathMLTree.MathNode("mo", children);
+
+    if (group.value.mclass === "mopen" ||
+        group.value.mclass === "mclose") {
+        // Only some of the delimsizing functions act as fences, and they
+        // return "mopen" or "mclose" mclass.
+        node.setAttribute("fence", "true");
+    } else {
+        // Explicitly disable fencing if it's not a fence, to override the
+        // defaults.
+        node.setAttribute("fence", "false");
+    }
+
+    return node;
+};
+
+groupTypes.styling = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+
+    var node = new mathMLTree.MathNode("mstyle", inner);
+
+    var styleAttributes = {
+        "display": ["0", "true"],
+        "text": ["0", "false"],
+        "script": ["1", "false"],
+        "scriptscript": ["2", "false"]
+    };
+
+    var attr = styleAttributes[group.value.style];
+
+    node.setAttribute("scriptlevel", attr[0]);
+    node.setAttribute("displaystyle", attr[1]);
+
+    return node;
+};
+
+groupTypes.sizing = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+
+    var node = new mathMLTree.MathNode("mstyle", inner);
+
+    // TODO(emily): This doesn't produce the correct size for nested size
+    // changes, because we don't keep state of what style we're currently
+    // in, so we can't reset the size to normal before changing it.  Now
+    // that we're passing an options parameter we should be able to fix
+    // this.
+    node.setAttribute(
+        "mathsize", buildCommon.sizingMultiplier[group.value.size] + "em");
+
+    return node;
+};
+
+groupTypes.overline = function(group, options) {
+    var operator = new mathMLTree.MathNode(
+        "mo", [new mathMLTree.TextNode("\u203e")]);
+    operator.setAttribute("stretchy", "true");
+
+    var node = new mathMLTree.MathNode(
+        "mover",
+        [buildGroup(group.value.body, options),
+            operator]);
+    node.setAttribute("accent", "true");
+
+    return node;
+};
+
+groupTypes.underline = function(group, options) {
+    var operator = new mathMLTree.MathNode(
+        "mo", [new mathMLTree.TextNode("\u203e")]);
+    operator.setAttribute("stretchy", "true");
+
+    var node = new mathMLTree.MathNode(
+        "munder",
+        [buildGroup(group.value.body, options),
+            operator]);
+    node.setAttribute("accentunder", "true");
+
+    return node;
+};
+
+groupTypes.rule = function(group) {
+    // TODO(emily): Figure out if there's an actual way to draw black boxes
+    // in MathML.
+    var node = new mathMLTree.MathNode("mrow");
+
+    return node;
+};
+
+groupTypes.kern = function(group) {
+    // TODO(kevin): Figure out if there's a way to add space in MathML
+    var node = new mathMLTree.MathNode("mrow");
+
+    return node;
+};
+
+groupTypes.llap = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mpadded", [buildGroup(group.value.body, options)]);
+
+    node.setAttribute("lspace", "-1width");
+    node.setAttribute("width", "0px");
+
+    return node;
+};
+
+groupTypes.rlap = function(group, options) {
+    var node = new mathMLTree.MathNode(
+        "mpadded", [buildGroup(group.value.body, options)]);
+
+    node.setAttribute("width", "0px");
+
+    return node;
+};
+
+groupTypes.phantom = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+    return new mathMLTree.MathNode("mphantom", inner);
+};
+
+groupTypes.mclass = function(group, options) {
+    var inner = buildExpression(group.value.value, options);
+    return new mathMLTree.MathNode("mstyle", inner);
+};
+
+/**
+ * Takes a list of nodes, builds them, and returns a list of the generated
+ * MathML nodes. A little simpler than the HTML version because we don't do any
+ * previous-node handling.
+ */
+var buildExpression = function(expression, options) {
+    var groups = [];
+    for (var i = 0; i < expression.length; i++) {
+        var group = expression[i];
+        groups.push(buildGroup(group, options));
+    }
+    return groups;
+};
+
+/**
+ * Takes a group from the parser and calls the appropriate groupTypes function
+ * on it to produce a MathML node.
+ */
+var buildGroup = function(group, options) {
+    if (!group) {
+        return new mathMLTree.MathNode("mrow");
+    }
+
+    if (groupTypes[group.type]) {
+        // Call the groupTypes function
+        return groupTypes[group.type](group, options);
+    } else {
+        throw new ParseError(
+            "Got group of unknown type: '" + group.type + "'");
+    }
+};
+
+/**
+ * Takes a full parse tree and settings and builds a MathML representation of
+ * it. In particular, we put the elements from building the parse tree into a
+ * <semantics> tag so we can also include that TeX source as an annotation.
+ *
+ * Note that we actually return a domTree element with a `<math>` inside it so
+ * we can do appropriate styling.
+ */
+var buildMathML = function(tree, texExpression, options) {
+    var expression = buildExpression(tree, options);
+
+    // Wrap up the expression in an mrow so it is presented in the semantics
+    // tag correctly.
+    var wrapper = new mathMLTree.MathNode("mrow", expression);
+
+    // Build a TeX annotation of the source
+    var annotation = new mathMLTree.MathNode(
+        "annotation", [new mathMLTree.TextNode(texExpression)]);
+
+    annotation.setAttribute("encoding", "application/x-tex");
+
+    var semantics = new mathMLTree.MathNode(
+        "semantics", [wrapper, annotation]);
+
+    var math = new mathMLTree.MathNode("math", [semantics]);
+
+    // You can't style <math> nodes, so we wrap the node in a span.
+    return makeSpan(["katex-mathml"], [math]);
+};
+
+module.exports = buildMathML;
+
+},{"./ParseError":6,"./buildCommon":10,"./fontMetrics":17,"./mathMLTree":20,"./symbols":23,"./utils":25}],13:[function(require,module,exports){
+var buildHTML = require("./buildHTML");
+var buildMathML = require("./buildMathML");
+var buildCommon = require("./buildCommon");
+var Options = require("./Options");
+var Settings = require("./Settings");
+var Style = require("./Style");
+
+var makeSpan = buildCommon.makeSpan;
+
+var buildTree = function(tree, expression, settings) {
+    settings = settings || new Settings({});
+
+    var startStyle = Style.TEXT;
+    if (settings.displayMode) {
+        startStyle = Style.DISPLAY;
+    }
+
+    // Setup the default options
+    var options = new Options({
+        style: startStyle,
+        size: "size5"
+    });
+
+    // `buildHTML` sometimes messes with the parse tree (like turning bins ->
+    // ords), so we build the MathML version first.
+    var mathMLNode = buildMathML(tree, expression, options);
+    var htmlNode = buildHTML(tree, options);
+
+    var katexNode = makeSpan(["katex"], [
+        mathMLNode, htmlNode
+    ]);
+
+    if (settings.displayMode) {
+        return makeSpan(["katex-display"], [katexNode]);
+    } else {
+        return katexNode;
+    }
+};
+
+module.exports = buildTree;
+
+},{"./Options":5,"./Settings":8,"./Style":9,"./buildCommon":10,"./buildHTML":11,"./buildMathML":12}],14:[function(require,module,exports){
+/**
+ * This file deals with creating delimiters of various sizes. The TeXbook
+ * discusses these routines on page 441-442, in the "Another subroutine sets box
+ * x to a specified variable delimiter" paragraph.
+ *
+ * There are three main routines here. `makeSmallDelim` makes a delimiter in the
+ * normal font, but in either text, script, or scriptscript style.
+ * `makeLargeDelim` makes a delimiter in textstyle, but in one of the Size1,
+ * Size2, Size3, or Size4 fonts. `makeStackedDelim` makes a delimiter out of
+ * smaller pieces that are stacked on top of one another.
+ *
+ * The functions take a parameter `center`, which determines if the delimiter
+ * should be centered around the axis.
+ *
+ * Then, there are three exposed functions. `sizedDelim` makes a delimiter in
+ * one of the given sizes. This is used for things like `\bigl`.
+ * `customSizedDelim` makes a delimiter with a given total height+depth. It is
+ * called in places like `\sqrt`. `leftRightDelim` makes an appropriate
+ * delimiter which surrounds an expression of a given height an depth. It is
+ * used in `\left` and `\right`.
+ */
+
+var ParseError = require("./ParseError");
+var Style = require("./Style");
+
+var buildCommon = require("./buildCommon");
+var fontMetrics = require("./fontMetrics");
+var symbols = require("./symbols");
+var utils = require("./utils");
+
+var makeSpan = buildCommon.makeSpan;
+
+/**
+ * Get the metrics for a given symbol and font, after transformation (i.e.
+ * after following replacement from symbols.js)
+ */
+var getMetrics = function(symbol, font) {
+    if (symbols.math[symbol] && symbols.math[symbol].replace) {
+        return fontMetrics.getCharacterMetrics(
+            symbols.math[symbol].replace, font);
+    } else {
+        return fontMetrics.getCharacterMetrics(
+            symbol, font);
+    }
+};
+
+/**
+ * Builds a symbol in the given font size (note size is an integer)
+ */
+var mathrmSize = function(value, size, mode, options) {
+    return buildCommon.makeSymbol(value, "Size" + size + "-Regular",
+        mode, options);
+};
+
+/**
+ * Puts a delimiter span in a given style, and adds appropriate height, depth,
+ * and maxFontSizes.
+ */
+var styleWrap = function(delim, toStyle, options, classes) {
+    classes = classes || [];
+    var span = makeSpan(
+        classes.concat(["style-wrap", options.style.reset(), toStyle.cls()]),
+        [delim], options);
+
+    var multiplier = toStyle.sizeMultiplier / options.style.sizeMultiplier;
+
+    span.height *= multiplier;
+    span.depth *= multiplier;
+    span.maxFontSize = toStyle.sizeMultiplier;
+
+    return span;
+};
+
+/**
+ * Makes a small delimiter. This is a delimiter that comes in the Main-Regular
+ * font, but is restyled to either be in textstyle, scriptstyle, or
+ * scriptscriptstyle.
+ */
+var makeSmallDelim = function(delim, style, center, options, mode, classes) {
+    var text = buildCommon.makeSymbol(delim, "Main-Regular", mode, options);
+
+    var span = styleWrap(text, style, options, classes);
+
+    if (center) {
+        var shift =
+            (1 - options.style.sizeMultiplier / style.sizeMultiplier) *
+            options.style.metrics.axisHeight;
+
+        span.style.top = shift + "em";
+        span.height -= shift;
+        span.depth += shift;
+    }
+
+    return span;
+};
+
+/**
+ * Makes a large delimiter. This is a delimiter that comes in the Size1, Size2,
+ * Size3, or Size4 fonts. It is always rendered in textstyle.
+ */
+var makeLargeDelim = function(delim, size, center, options, mode, classes) {
+    var inner = mathrmSize(delim, size, mode, options);
+
+    var span = styleWrap(
+        makeSpan(["delimsizing", "size" + size], [inner], options),
+        Style.TEXT, options, classes);
+
+    if (center) {
+        var shift = (1 - options.style.sizeMultiplier) *
+            options.style.metrics.axisHeight;
+
+        span.style.top = shift + "em";
+        span.height -= shift;
+        span.depth += shift;
+    }
+
+    return span;
+};
+
+/**
+ * Make an inner span with the given offset and in the given font. This is used
+ * in `makeStackedDelim` to make the stacking pieces for the delimiter.
+ */
+var makeInner = function(symbol, font, mode) {
+    var sizeClass;
+    // Apply the correct CSS class to choose the right font.
+    if (font === "Size1-Regular") {
+        sizeClass = "delim-size1";
+    } else if (font === "Size4-Regular") {
+        sizeClass = "delim-size4";
+    }
+
+    var inner = makeSpan(
+        ["delimsizinginner", sizeClass],
+        [makeSpan([], [buildCommon.makeSymbol(symbol, font, mode)])]);
+
+    // Since this will be passed into `makeVList` in the end, wrap the element
+    // in the appropriate tag that VList uses.
+    return {type: "elem", elem: inner};
+};
+
+/**
+ * Make a stacked delimiter out of a given delimiter, with the total height at
+ * least `heightTotal`. This routine is mentioned on page 442 of the TeXbook.
+ */
+var makeStackedDelim = function(delim, heightTotal, center, options, mode,
+                                classes) {
+    // There are four parts, the top, an optional middle, a repeated part, and a
+    // bottom.
+    var top;
+    var middle;
+    var repeat;
+    var bottom;
+    top = repeat = bottom = delim;
+    middle = null;
+    // Also keep track of what font the delimiters are in
+    var font = "Size1-Regular";
+
+    // We set the parts and font based on the symbol. Note that we use
+    // '\u23d0' instead of '|' and '\u2016' instead of '\\|' for the
+    // repeats of the arrows
+    if (delim === "\\uparrow") {
+        repeat = bottom = "\u23d0";
+    } else if (delim === "\\Uparrow") {
+        repeat = bottom = "\u2016";
+    } else if (delim === "\\downarrow") {
+        top = repeat = "\u23d0";
+    } else if (delim === "\\Downarrow") {
+        top = repeat = "\u2016";
+    } else if (delim === "\\updownarrow") {
+        top = "\\uparrow";
+        repeat = "\u23d0";
+        bottom = "\\downarrow";
+    } else if (delim === "\\Updownarrow") {
+        top = "\\Uparrow";
+        repeat = "\u2016";
+        bottom = "\\Downarrow";
+    } else if (delim === "[" || delim === "\\lbrack") {
+        top = "\u23a1";
+        repeat = "\u23a2";
+        bottom = "\u23a3";
+        font = "Size4-Regular";
+    } else if (delim === "]" || delim === "\\rbrack") {
+        top = "\u23a4";
+        repeat = "\u23a5";
+        bottom = "\u23a6";
+        font = "Size4-Regular";
+    } else if (delim === "\\lfloor") {
+        repeat = top = "\u23a2";
+        bottom = "\u23a3";
+        font = "Size4-Regular";
+    } else if (delim === "\\lceil") {
+        top = "\u23a1";
+        repeat = bottom = "\u23a2";
+        font = "Size4-Regular";
+    } else if (delim === "\\rfloor") {
+        repeat = top = "\u23a5";
+        bottom = "\u23a6";
+        font = "Size4-Regular";
+    } else if (delim === "\\rceil") {
+        top = "\u23a4";
+        repeat = bottom = "\u23a5";
+        font = "Size4-Regular";
+    } else if (delim === "(") {
+        top = "\u239b";
+        repeat = "\u239c";
+        bottom = "\u239d";
+        font = "Size4-Regular";
+    } else if (delim === ")") {
+        top = "\u239e";
+        repeat = "\u239f";
+        bottom = "\u23a0";
+        font = "Size4-Regular";
+    } else if (delim === "\\{" || delim === "\\lbrace") {
+        top = "\u23a7";
+        middle = "\u23a8";
+        bottom = "\u23a9";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\}" || delim === "\\rbrace") {
+        top = "\u23ab";
+        middle = "\u23ac";
+        bottom = "\u23ad";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\lgroup") {
+        top = "\u23a7";
+        bottom = "\u23a9";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\rgroup") {
+        top = "\u23ab";
+        bottom = "\u23ad";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\lmoustache") {
+        top = "\u23a7";
+        bottom = "\u23ad";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\rmoustache") {
+        top = "\u23ab";
+        bottom = "\u23a9";
+        repeat = "\u23aa";
+        font = "Size4-Regular";
+    } else if (delim === "\\surd") {
+        top = "\ue001";
+        bottom = "\u23b7";
+        repeat = "\ue000";
+        font = "Size4-Regular";
+    }
+
+    // Get the metrics of the four sections
+    var topMetrics = getMetrics(top, font);
+    var topHeightTotal = topMetrics.height + topMetrics.depth;
+    var repeatMetrics = getMetrics(repeat, font);
+    var repeatHeightTotal = repeatMetrics.height + repeatMetrics.depth;
+    var bottomMetrics = getMetrics(bottom, font);
+    var bottomHeightTotal = bottomMetrics.height + bottomMetrics.depth;
+    var middleHeightTotal = 0;
+    var middleFactor = 1;
+    if (middle !== null) {
+        var middleMetrics = getMetrics(middle, font);
+        middleHeightTotal = middleMetrics.height + middleMetrics.depth;
+        middleFactor = 2; // repeat symmetrically above and below middle
+    }
+
+    // Calcuate the minimal height that the delimiter can have.
+    // It is at least the size of the top, bottom, and optional middle combined.
+    var minHeight = topHeightTotal + bottomHeightTotal + middleHeightTotal;
+
+    // Compute the number of copies of the repeat symbol we will need
+    var repeatCount = Math.ceil(
+        (heightTotal - minHeight) / (middleFactor * repeatHeightTotal));
+
+    // Compute the total height of the delimiter including all the symbols
+    var realHeightTotal =
+        minHeight + repeatCount * middleFactor * repeatHeightTotal;
+
+    // The center of the delimiter is placed at the center of the axis. Note
+    // that in this context, "center" means that the delimiter should be
+    // centered around the axis in the current style, while normally it is
+    // centered around the axis in textstyle.
+    var axisHeight = options.style.metrics.axisHeight;
+    if (center) {
+        axisHeight *= options.style.sizeMultiplier;
+    }
+    // Calculate the depth
+    var depth = realHeightTotal / 2 - axisHeight;
+
+    // Now, we start building the pieces that will go into the vlist
+
+    // Keep a list of the inner pieces
+    var inners = [];
+
+    // Add the bottom symbol
+    inners.push(makeInner(bottom, font, mode));
+
+    var i;
+    if (middle === null) {
+        // Add that many symbols
+        for (i = 0; i < repeatCount; i++) {
+            inners.push(makeInner(repeat, font, mode));
+        }
+    } else {
+        // When there is a middle bit, we need the middle part and two repeated
+        // sections
+        for (i = 0; i < repeatCount; i++) {
+            inners.push(makeInner(repeat, font, mode));
+        }
+        inners.push(makeInner(middle, font, mode));
+        for (i = 0; i < repeatCount; i++) {
+            inners.push(makeInner(repeat, font, mode));
+        }
+    }
+
+    // Add the top symbol
+    inners.push(makeInner(top, font, mode));
+
+    // Finally, build the vlist
+    var inner = buildCommon.makeVList(inners, "bottom", depth, options);
+
+    return styleWrap(
+        makeSpan(["delimsizing", "mult"], [inner], options),
+        Style.TEXT, options, classes);
+};
+
+// There are three kinds of delimiters, delimiters that stack when they become
+// too large
+var stackLargeDelimiters = [
+    "(", ")", "[", "\\lbrack", "]", "\\rbrack",
+    "\\{", "\\lbrace", "\\}", "\\rbrace",
+    "\\lfloor", "\\rfloor", "\\lceil", "\\rceil",
+    "\\surd"
+];
+
+// delimiters that always stack
+var stackAlwaysDelimiters = [
+    "\\uparrow", "\\downarrow", "\\updownarrow",
+    "\\Uparrow", "\\Downarrow", "\\Updownarrow",
+    "|", "\\|", "\\vert", "\\Vert",
+    "\\lvert", "\\rvert", "\\lVert", "\\rVert",
+    "\\lgroup", "\\rgroup", "\\lmoustache", "\\rmoustache"
+];
+
+// and delimiters that never stack
+var stackNeverDelimiters = [
+    "<", ">", "\\langle", "\\rangle", "/", "\\backslash", "\\lt", "\\gt"
+];
+
+// Metrics of the different sizes. Found by looking at TeX's output of
+// $\bigl| // \Bigl| \biggl| \Biggl| \showlists$
+// Used to create stacked delimiters of appropriate sizes in makeSizedDelim.
+var sizeToMaxHeight = [0, 1.2, 1.8, 2.4, 3.0];
+
+/**
+ * Used to create a delimiter of a specific size, where `size` is 1, 2, 3, or 4.
+ */
+var makeSizedDelim = function(delim, size, options, mode, classes) {
+    // < and > turn into \langle and \rangle in delimiters
+    if (delim === "<" || delim === "\\lt") {
+        delim = "\\langle";
+    } else if (delim === ">" || delim === "\\gt") {
+        delim = "\\rangle";
+    }
+
+    // Sized delimiters are never centered.
+    if (utils.contains(stackLargeDelimiters, delim) ||
+        utils.contains(stackNeverDelimiters, delim)) {
+        return makeLargeDelim(delim, size, false, options, mode, classes);
+    } else if (utils.contains(stackAlwaysDelimiters, delim)) {
+        return makeStackedDelim(
+            delim, sizeToMaxHeight[size], false, options, mode, classes);
+    } else {
+        throw new ParseError("Illegal delimiter: '" + delim + "'");
+    }
+};
+
+/**
+ * There are three different sequences of delimiter sizes that the delimiters
+ * follow depending on the kind of delimiter. This is used when creating custom
+ * sized delimiters to decide whether to create a small, large, or stacked
+ * delimiter.
+ *
+ * In real TeX, these sequences aren't explicitly defined, but are instead
+ * defined inside the font metrics. Since there are only three sequences that
+ * are possible for the delimiters that TeX defines, it is easier to just encode
+ * them explicitly here.
+ */
+
+// Delimiters that never stack try small delimiters and large delimiters only
+var stackNeverDelimiterSequence = [
+    {type: "small", style: Style.SCRIPTSCRIPT},
+    {type: "small", style: Style.SCRIPT},
+    {type: "small", style: Style.TEXT},
+    {type: "large", size: 1},
+    {type: "large", size: 2},
+    {type: "large", size: 3},
+    {type: "large", size: 4}
+];
+
+// Delimiters that always stack try the small delimiters first, then stack
+var stackAlwaysDelimiterSequence = [
+    {type: "small", style: Style.SCRIPTSCRIPT},
+    {type: "small", style: Style.SCRIPT},
+    {type: "small", style: Style.TEXT},
+    {type: "stack"}
+];
+
+// Delimiters that stack when large try the small and then large delimiters, and
+// stack afterwards
+var stackLargeDelimiterSequence = [
+    {type: "small", style: Style.SCRIPTSCRIPT},
+    {type: "small", style: Style.SCRIPT},
+    {type: "small", style: Style.TEXT},
+    {type: "large", size: 1},
+    {type: "large", size: 2},
+    {type: "large", size: 3},
+    {type: "large", size: 4},
+    {type: "stack"}
+];
+
+/**
+ * Get the font used in a delimiter based on what kind of delimiter it is.
+ */
+var delimTypeToFont = function(type) {
+    if (type.type === "small") {
+        return "Main-Regular";
+    } else if (type.type === "large") {
+        return "Size" + type.size + "-Regular";
+    } else if (type.type === "stack") {
+        return "Size4-Regular";
+    }
+};
+
+/**
+ * Traverse a sequence of types of delimiters to decide what kind of delimiter
+ * should be used to create a delimiter of the given height+depth.
+ */
+var traverseSequence = function(delim, height, sequence, options) {
+    // Here, we choose the index we should start at in the sequences. In smaller
+    // sizes (which correspond to larger numbers in style.size) we start earlier
+    // in the sequence. Thus, scriptscript starts at index 3-3=0, script starts
+    // at index 3-2=1, text starts at 3-1=2, and display starts at min(2,3-0)=2
+    var start = Math.min(2, 3 - options.style.size);
+    for (var i = start; i < sequence.length; i++) {
+        if (sequence[i].type === "stack") {
+            // This is always the last delimiter, so we just break the loop now.
+            break;
+        }
+
+        var metrics = getMetrics(delim, delimTypeToFont(sequence[i]));
+        var heightDepth = metrics.height + metrics.depth;
+
+        // Small delimiters are scaled down versions of the same font, so we
+        // account for the style change size.
+
+        if (sequence[i].type === "small") {
+            heightDepth *= sequence[i].style.sizeMultiplier;
+        }
+
+        // Check if the delimiter at this size works for the given height.
+        if (heightDepth > height) {
+            return sequence[i];
+        }
+    }
+
+    // If we reached the end of the sequence, return the last sequence element.
+    return sequence[sequence.length - 1];
+};
+
+/**
+ * Make a delimiter of a given height+depth, with optional centering. Here, we
+ * traverse the sequences, and create a delimiter that the sequence tells us to.
+ */
+var makeCustomSizedDelim = function(delim, height, center, options, mode,
+                                    classes) {
+    if (delim === "<" || delim === "\\lt") {
+        delim = "\\langle";
+    } else if (delim === ">" || delim === "\\gt") {
+        delim = "\\rangle";
+    }
+
+    // Decide what sequence to use
+    var sequence;
+    if (utils.contains(stackNeverDelimiters, delim)) {
+        sequence = stackNeverDelimiterSequence;
+    } else if (utils.contains(stackLargeDelimiters, delim)) {
+        sequence = stackLargeDelimiterSequence;
+    } else {
+        sequence = stackAlwaysDelimiterSequence;
+    }
+
+    // Look through the sequence
+    var delimType = traverseSequence(delim, height, sequence, options);
+
+    // Depending on the sequence element we decided on, call the appropriate
+    // function.
+    if (delimType.type === "small") {
+        return makeSmallDelim(delim, delimType.style, center, options, mode,
+                              classes);
+    } else if (delimType.type === "large") {
+        return makeLargeDelim(delim, delimType.size, center, options, mode,
+                              classes);
+    } else if (delimType.type === "stack") {
+        return makeStackedDelim(delim, height, center, options, mode, classes);
+    }
+};
+
+/**
+ * Make a delimiter for use with `\left` and `\right`, given a height and depth
+ * of an expression that the delimiters surround.
+ */
+var makeLeftRightDelim = function(delim, height, depth, options, mode,
+                                  classes) {
+    // We always center \left/\right delimiters, so the axis is always shifted
+    var axisHeight =
+        options.style.metrics.axisHeight * options.style.sizeMultiplier;
+
+    // Taken from TeX source, tex.web, function make_left_right
+    var delimiterFactor = 901;
+    var delimiterExtend = 5.0 / fontMetrics.metrics.ptPerEm;
+
+    var maxDistFromAxis = Math.max(
+        height - axisHeight, depth + axisHeight);
+
+    var totalHeight = Math.max(
+        // In real TeX, calculations are done using integral values which are
+        // 65536 per pt, or 655360 per em. So, the division here truncates in
+        // TeX but doesn't here, producing different results. If we wanted to
+        // exactly match TeX's calculation, we could do
+        //   Math.floor(655360 * maxDistFromAxis / 500) *
+        //    delimiterFactor / 655360
+        // (To see the difference, compare
+        //    x^{x^{\left(\rule{0.1em}{0.68em}\right)}}
+        // in TeX and KaTeX)
+        maxDistFromAxis / 500 * delimiterFactor,
+        2 * maxDistFromAxis - delimiterExtend);
+
+    // Finally, we defer to `makeCustomSizedDelim` with our calculated total
+    // height
+    return makeCustomSizedDelim(delim, totalHeight, true, options, mode,
+                                classes);
+};
+
+module.exports = {
+    sizedDelim: makeSizedDelim,
+    customSizedDelim: makeCustomSizedDelim,
+    leftRightDelim: makeLeftRightDelim
+};
+
+},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./fontMetrics":17,"./symbols":23,"./utils":25}],15:[function(require,module,exports){
+/**
+ * These objects store the data about the DOM nodes we create, as well as some
+ * extra data. They can then be transformed into real DOM nodes with the
+ * `toNode` function or HTML markup using `toMarkup`. They are useful for both
+ * storing extra properties on the nodes, as well as providing a way to easily
+ * work with the DOM.
+ *
+ * Similar functions for working with MathML nodes exist in mathMLTree.js.
+ */
+var unicodeRegexes = require("./unicodeRegexes");
+var utils = require("./utils");
+
+/**
+ * Create an HTML className based on a list of classes. In addition to joining
+ * with spaces, we also remove null or empty classes.
+ */
+var createClass = function(classes) {
+    classes = classes.slice();
+    for (var i = classes.length - 1; i >= 0; i--) {
+        if (!classes[i]) {
+            classes.splice(i, 1);
+        }
+    }
+
+    return classes.join(" ");
+};
+
+/**
+ * This node represents a span node, with a className, a list of children, and
+ * an inline style. It also contains information about its height, depth, and
+ * maxFontSize.
+ */
+function span(classes, children, options) {
+    this.classes = classes || [];
+    this.children = children || [];
+    this.height = 0;
+    this.depth = 0;
+    this.maxFontSize = 0;
+    this.style = {};
+    this.attributes = {};
+    if (options) {
+        if (options.style.isTight()) {
+            this.classes.push("mtight");
+        }
+        if (options.getColor()) {
+            this.style.color = options.getColor();
+        }
+    }
+}
+
+/**
+ * Sets an arbitrary attribute on the span. Warning: use this wisely. Not all
+ * browsers support attributes the same, and having too many custom attributes
+ * is probably bad.
+ */
+span.prototype.setAttribute = function(attribute, value) {
+    this.attributes[attribute] = value;
+};
+
+span.prototype.tryCombine = function(sibling) {
+    return false;
+};
+
+/**
+ * Convert the span into an HTML node
+ */
+span.prototype.toNode = function() {
+    var span = document.createElement("span");
+
+    // Apply the class
+    span.className = createClass(this.classes);
+
+    // Apply inline styles
+    for (var style in this.style) {
+        if (Object.prototype.hasOwnProperty.call(this.style, style)) {
+            span.style[style] = this.style[style];
+        }
+    }
+
+    // Apply attributes
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            span.setAttribute(attr, this.attributes[attr]);
+        }
+    }
+
+    // Append the children, also as HTML nodes
+    for (var i = 0; i < this.children.length; i++) {
+        span.appendChild(this.children[i].toNode());
+    }
+
+    return span;
+};
+
+/**
+ * Convert the span into an HTML markup string
+ */
+span.prototype.toMarkup = function() {
+    var markup = "<span";
+
+    // Add the class
+    if (this.classes.length) {
+        markup += " class=\"";
+        markup += utils.escape(createClass(this.classes));
+        markup += "\"";
+    }
+
+    var styles = "";
+
+    // Add the styles, after hyphenation
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)) {
+            styles += utils.hyphenate(style) + ":" + this.style[style] + ";";
+        }
+    }
+
+    if (styles) {
+        markup += " style=\"" + utils.escape(styles) + "\"";
+    }
+
+    // Add the attributes
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            markup += " " + attr + "=\"";
+            markup += utils.escape(this.attributes[attr]);
+            markup += "\"";
+        }
+    }
+
+    markup += ">";
+
+    // Add the markup of the children, also as markup
+    for (var i = 0; i < this.children.length; i++) {
+        markup += this.children[i].toMarkup();
+    }
+
+    markup += "</span>";
+
+    return markup;
+};
+
+/**
+ * This node represents a document fragment, which contains elements, but when
+ * placed into the DOM doesn't have any representation itself. Thus, it only
+ * contains children and doesn't have any HTML properties. It also keeps track
+ * of a height, depth, and maxFontSize.
+ */
+function documentFragment(children) {
+    this.children = children || [];
+    this.height = 0;
+    this.depth = 0;
+    this.maxFontSize = 0;
+}
+
+/**
+ * Convert the fragment into a node
+ */
+documentFragment.prototype.toNode = function() {
+    // Create a fragment
+    var frag = document.createDocumentFragment();
+
+    // Append the children
+    for (var i = 0; i < this.children.length; i++) {
+        frag.appendChild(this.children[i].toNode());
+    }
+
+    return frag;
+};
+
+/**
+ * Convert the fragment into HTML markup
+ */
+documentFragment.prototype.toMarkup = function() {
+    var markup = "";
+
+    // Simply concatenate the markup for the children together
+    for (var i = 0; i < this.children.length; i++) {
+        markup += this.children[i].toMarkup();
+    }
+
+    return markup;
+};
+
+var iCombinations = {
+    'î': '\u0131\u0302',
+    'ï': '\u0131\u0308',
+    'í': '\u0131\u0301',
+    // 'ī': '\u0131\u0304', // enable when we add Extended Latin
+    'ì': '\u0131\u0300'
+};
+
+/**
+ * A symbol node contains information about a single symbol. It either renders
+ * to a single text node, or a span with a single text node in it, depending on
+ * whether it has CSS classes, styles, or needs italic correction.
+ */
+function symbolNode(value, height, depth, italic, skew, classes, style) {
+    this.value = value || "";
+    this.height = height || 0;
+    this.depth = depth || 0;
+    this.italic = italic || 0;
+    this.skew = skew || 0;
+    this.classes = classes || [];
+    this.style = style || {};
+    this.maxFontSize = 0;
+
+    // Mark CJK characters with specific classes so that we can specify which
+    // fonts to use.  This allows us to render these characters with a serif
+    // font in situations where the browser would either default to a sans serif
+    // or render a placeholder character.
+    if (unicodeRegexes.cjkRegex.test(value)) {
+        // I couldn't find any fonts that contained Hangul as well as all of
+        // the other characters we wanted to test there for it gets its own
+        // CSS class.
+        if (unicodeRegexes.hangulRegex.test(value)) {
+            this.classes.push('hangul_fallback');
+        } else {
+            this.classes.push('cjk_fallback');
+        }
+    }
+
+    if (/[îïíì]/.test(this.value)) {    // add ī when we add Extended Latin
+        this.value = iCombinations[this.value];
+    }
+}
+
+symbolNode.prototype.tryCombine = function(sibling) {
+    if (!sibling
+        || !(sibling instanceof symbolNode)
+        || this.italic > 0
+        || createClass(this.classes) !== createClass(sibling.classes)
+        || this.skew !== sibling.skew
+        || this.maxFontSize !== sibling.maxFontSize) {
+        return false;
+    }
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)
+            && this.style[style] !== sibling.style[style]) {
+            return false;
+        }
+    }
+    for (style in sibling.style) {
+        if (sibling.style.hasOwnProperty(style)
+            && this.style[style] !== sibling.style[style]) {
+            return false;
+        }
+    }
+    this.value += sibling.value;
+    this.height = Math.max(this.height, sibling.height);
+    this.depth = Math.max(this.depth, sibling.depth);
+    this.italic = sibling.italic;
+    return true;
+};
+
+/**
+ * Creates a text node or span from a symbol node. Note that a span is only
+ * created if it is needed.
+ */
+symbolNode.prototype.toNode = function() {
+    var node = document.createTextNode(this.value);
+    var span = null;
+
+    if (this.italic > 0) {
+        span = document.createElement("span");
+        span.style.marginRight = this.italic + "em";
+    }
+
+    if (this.classes.length > 0) {
+        span = span || document.createElement("span");
+        span.className = createClass(this.classes);
+    }
+
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)) {
+            span = span || document.createElement("span");
+            span.style[style] = this.style[style];
+        }
+    }
+
+    if (span) {
+        span.appendChild(node);
+        return span;
+    } else {
+        return node;
+    }
+};
+
+/**
+ * Creates markup for a symbol node.
+ */
+symbolNode.prototype.toMarkup = function() {
+    // TODO(alpert): More duplication than I'd like from
+    // span.prototype.toMarkup and symbolNode.prototype.toNode...
+    var needsSpan = false;
+
+    var markup = "<span";
+
+    if (this.classes.length) {
+        needsSpan = true;
+        markup += " class=\"";
+        markup += utils.escape(createClass(this.classes));
+        markup += "\"";
+    }
+
+    var styles = "";
+
+    if (this.italic > 0) {
+        styles += "margin-right:" + this.italic + "em;";
+    }
+    for (var style in this.style) {
+        if (this.style.hasOwnProperty(style)) {
+            styles += utils.hyphenate(style) + ":" + this.style[style] + ";";
+        }
+    }
+
+    if (styles) {
+        needsSpan = true;
+        markup += " style=\"" + utils.escape(styles) + "\"";
+    }
+
+    var escaped = utils.escape(this.value);
+    if (needsSpan) {
+        markup += ">";
+        markup += escaped;
+        markup += "</span>";
+        return markup;
+    } else {
+        return escaped;
+    }
+};
+
+module.exports = {
+    span: span,
+    documentFragment: documentFragment,
+    symbolNode: symbolNode
+};
+
+},{"./unicodeRegexes":24,"./utils":25}],16:[function(require,module,exports){
+/* eslint no-constant-condition:0 */
+var parseData = require("./parseData");
+var ParseError = require("./ParseError");
+var Style = require("./Style");
+
+var ParseNode = parseData.ParseNode;
+
+/**
+ * Parse the body of the environment, with rows delimited by \\ and
+ * columns delimited by &, and create a nested list in row-major order
+ * with one group per cell.
+ */
+function parseArray(parser, result) {
+    var row = [];
+    var body = [row];
+    var rowGaps = [];
+    while (true) {
+        var cell = parser.parseExpression(false, null);
+        row.push(new ParseNode("ordgroup", cell, parser.mode));
+        var next = parser.nextToken.text;
+        if (next === "&") {
+            parser.consume();
+        } else if (next === "\\end") {
+            break;
+        } else if (next === "\\\\" || next === "\\cr") {
+            var cr = parser.parseFunction();
+            rowGaps.push(cr.value.size);
+            row = [];
+            body.push(row);
+        } else {
+            throw new ParseError("Expected & or \\\\ or \\end",
+                                 parser.nextToken);
+        }
+    }
+    result.body = body;
+    result.rowGaps = rowGaps;
+    return new ParseNode(result.type, result, parser.mode);
+}
+
+/*
+ * An environment definition is very similar to a function definition:
+ * it is declared with a name or a list of names, a set of properties
+ * and a handler containing the actual implementation.
+ *
+ * The properties include:
+ *  - numArgs: The number of arguments after the \begin{name} function.
+ *  - argTypes: (optional) Just like for a function
+ *  - allowedInText: (optional) Whether or not the environment is allowed inside
+ *                   text mode (default false) (not enforced yet)
+ *  - numOptionalArgs: (optional) Just like for a function
+ * A bare number instead of that object indicates the numArgs value.
+ *
+ * The handler function will receive two arguments
+ *  - context: information and references provided by the parser
+ *  - args: an array of arguments passed to \begin{name}
+ * The context contains the following properties:
+ *  - envName: the name of the environment, one of the listed names.
+ *  - parser: the parser object
+ *  - lexer: the lexer object
+ *  - positions: the positions associated with these arguments from args.
+ * The handler must return a ParseResult.
+ */
+
+function defineEnvironment(names, props, handler) {
+    if (typeof names === "string") {
+        names = [names];
+    }
+    if (typeof props === "number") {
+        props = { numArgs: props };
+    }
+    // Set default values of environments
+    var data = {
+        numArgs: props.numArgs || 0,
+        argTypes: props.argTypes,
+        greediness: 1,
+        allowedInText: !!props.allowedInText,
+        numOptionalArgs: props.numOptionalArgs || 0,
+        handler: handler
+    };
+    for (var i = 0; i < names.length; ++i) {
+        module.exports[names[i]] = data;
+    }
+}
+
+// Arrays are part of LaTeX, defined in lttab.dtx so its documentation
+// is part of the source2e.pdf file of LaTeX2e source documentation.
+defineEnvironment("array", {
+    numArgs: 1
+}, function(context, args) {
+    var colalign = args[0];
+    colalign = colalign.value.map ? colalign.value : [colalign];
+    var cols = colalign.map(function(node) {
+        var ca = node.value;
+        if ("lcr".indexOf(ca) !== -1) {
+            return {
+                type: "align",
+                align: ca
+            };
+        } else if (ca === "|") {
+            return {
+                type: "separator",
+                separator: "|"
+            };
+        }
+        throw new ParseError(
+            "Unknown column alignment: " + node.value,
+            node);
+    });
+    var res = {
+        type: "array",
+        cols: cols,
+        hskipBeforeAndAfter: true // \@preamble in lttab.dtx
+    };
+    res = parseArray(context.parser, res);
+    return res;
+});
+
+// The matrix environments of amsmath builds on the array environment
+// of LaTeX, which is discussed above.
+defineEnvironment([
+    "matrix",
+    "pmatrix",
+    "bmatrix",
+    "Bmatrix",
+    "vmatrix",
+    "Vmatrix"
+], {
+}, function(context) {
+    var delimiters = {
+        "matrix": null,
+        "pmatrix": ["(", ")"],
+        "bmatrix": ["[", "]"],
+        "Bmatrix": ["\\{", "\\}"],
+        "vmatrix": ["|", "|"],
+        "Vmatrix": ["\\Vert", "\\Vert"]
+    }[context.envName];
+    var res = {
+        type: "array",
+        hskipBeforeAndAfter: false // \hskip -\arraycolsep in amsmath
+    };
+    res = parseArray(context.parser, res);
+    if (delimiters) {
+        res = new ParseNode("leftright", {
+            body: [res],
+            left: delimiters[0],
+            right: delimiters[1]
+        }, context.mode);
+    }
+    return res;
+});
+
+// A cases environment (in amsmath.sty) is almost equivalent to
+// \def\arraystretch{1.2}%
+// \left\{\begin{array}{@{}l@{\quad}l@{}} … \end{array}\right.
+defineEnvironment("cases", {
+}, function(context) {
+    var res = {
+        type: "array",
+        arraystretch: 1.2,
+        cols: [{
+            type: "align",
+            align: "l",
+            pregap: 0,
+            // TODO(kevinb) get the current style.
+            // For now we use the metrics for TEXT style which is what we were
+            // doing before.  Before attempting to get the current style we
+            // should look at TeX's behavior especially for \over and matrices.
+            postgap: Style.TEXT.metrics.quad
+        }, {
+            type: "align",
+            align: "l",
+            pregap: 0,
+            postgap: 0
+        }]
+    };
+    res = parseArray(context.parser, res);
+    res = new ParseNode("leftright", {
+        body: [res],
+        left: "\\{",
+        right: "."
+    }, context.mode);
+    return res;
+});
+
+// An aligned environment is like the align* environment
+// except it operates within math mode.
+// Note that we assume \nomallineskiplimit to be zero,
+// so that \strut@ is the same as \strut.
+defineEnvironment("aligned", {
+}, function(context) {
+    var res = {
+        type: "array",
+        cols: []
+    };
+    res = parseArray(context.parser, res);
+    var emptyGroup = new ParseNode("ordgroup", [], context.mode);
+    var numCols = 0;
+    res.value.body.forEach(function(row) {
+        var i;
+        for (i = 1; i < row.length; i += 2) {
+            row[i].value.unshift(emptyGroup);
+        }
+        if (numCols < row.length) {
+            numCols = row.length;
+        }
+    });
+    for (var i = 0; i < numCols; ++i) {
+        var align = "r";
+        var pregap = 0;
+        if (i % 2 === 1) {
+            align = "l";
+        } else if (i > 0) {
+            pregap = 2; // one \qquad between columns
+        }
+        res.value.cols[i] = {
+            type: "align",
+            align: align,
+            pregap: pregap,
+            postgap: 0
+        };
+    }
+    return res;
+});
+
+},{"./ParseError":6,"./Style":9,"./parseData":21}],17:[function(require,module,exports){
+/* eslint no-unused-vars:0 */
+
+var Style = require("./Style");
+var cjkRegex = require("./unicodeRegexes").cjkRegex;
+
+/**
+ * This file contains metrics regarding fonts and individual symbols. The sigma
+ * and xi variables, as well as the metricMap map contain data extracted from
+ * TeX, TeX font metrics, and the TTF files. These data are then exposed via the
+ * `metrics` variable and the getCharacterMetrics function.
+ */
+
+// In TeX, there are actually three sets of dimensions, one for each of
+// textstyle, scriptstyle, and scriptscriptstyle.  These are provided in the
+// the arrays below, in that order.
+//
+// The font metrics are stored in fonts cmsy10, cmsy7, and cmsy5 respsectively.
+// This was determined by running the folllowing script:
+//
+//     latex -interaction=nonstopmode \
+//     '\documentclass{article}\usepackage{amsmath}\begin{document}' \
+//     '$a$ \expandafter\show\the\textfont2' \
+//     '\expandafter\show\the\scriptfont2' \
+//     '\expandafter\show\the\scriptscriptfont2' \
+//     '\stop'
+//
+// The metrics themselves were retreived using the following commands:
+//
+//     tftopl cmsy10
+//     tftopl cmsy7
+//     tftopl cmsy5
+//
+// The output of each of these commands is quite lengthy.  The only part we
+// care about is the FONTDIMEN section. Each value is measured in EMs.
+var sigmas = {
+    slant: [0.250, 0.250, 0.250],       // sigma1
+    space: [0.000, 0.000, 0.000],       // sigma2
+    stretch: [0.000, 0.000, 0.000],     // sigma3
+    shrink: [0.000, 0.000, 0.000],      // sigma4
+    xHeight: [0.431, 0.431, 0.431],     // sigma5
+    quad: [1.000, 1.171, 1.472],        // sigma6
+    extraSpace: [0.000, 0.000, 0.000],  // sigma7
+    num1: [0.677, 0.732, 0.925],        // sigma8
+    num2: [0.394, 0.384, 0.387],        // sigma9
+    num3: [0.444, 0.471, 0.504],        // sigma10
+    denom1: [0.686, 0.752, 1.025],      // sigma11
+    denom2: [0.345, 0.344, 0.532],      // sigma12
+    sup1: [0.413, 0.503, 0.504],        // sigma13
+    sup2: [0.363, 0.431, 0.404],        // sigma14
+    sup3: [0.289, 0.286, 0.294],        // sigma15
+    sub1: [0.150, 0.143, 0.200],        // sigma16
+    sub2: [0.247, 0.286, 0.400],        // sigma17
+    supDrop: [0.386, 0.353, 0.494],     // sigma18
+    subDrop: [0.050, 0.071, 0.100],     // sigma19
+    delim1: [2.390, 1.700, 1.980],      // sigma20
+    delim2: [1.010, 1.157, 1.420],      // sigma21
+    axisHeight: [0.250, 0.250, 0.250]  // sigma22
+};
+
+// These font metrics are extracted from TeX by using
+// \font\a=cmex10
+// \showthe\fontdimenX\a
+// where X is the corresponding variable number. These correspond to the font
+// parameters of the extension fonts (family 3). See the TeXbook, page 441.
+var xi1 = 0;
+var xi2 = 0;
+var xi3 = 0;
+var xi4 = 0;
+var xi5 = 0.431;
+var xi6 = 1;
+var xi7 = 0;
+var xi8 = 0.04;
+var xi9 = 0.111;
+var xi10 = 0.166;
+var xi11 = 0.2;
+var xi12 = 0.6;
+var xi13 = 0.1;
+
+// This value determines how large a pt is, for metrics which are defined in
+// terms of pts.
+// This value is also used in katex.less; if you change it make sure the values
+// match.
+var ptPerEm = 10.0;
+
+// The space between adjacent `|` columns in an array definition. From
+// `\showthe\doublerulesep` in LaTeX.
+var doubleRuleSep = 2.0 / ptPerEm;
+
+/**
+ * This is just a mapping from common names to real metrics
+ */
+var metrics = {
+    defaultRuleThickness: xi8,
+    bigOpSpacing1: xi9,
+    bigOpSpacing2: xi10,
+    bigOpSpacing3: xi11,
+    bigOpSpacing4: xi12,
+    bigOpSpacing5: xi13,
+    ptPerEm: ptPerEm,
+    doubleRuleSep: doubleRuleSep
+};
+
+// This map contains a mapping from font name and character code to character
+// metrics, including height, depth, italic correction, and skew (kern from the
+// character to the corresponding \skewchar)
+// This map is generated via `make metrics`. It should not be changed manually.
+var metricMap = require("./fontMetricsData");
+
+// These are very rough approximations.  We default to Times New Roman which
+// should have Latin-1 and Cyrillic characters, but may not depending on the
+// operating system.  The metrics do not account for extra height from the
+// accents.  In the case of Cyrillic characters which have both ascenders and
+// descenders we prefer approximations with ascenders, primarily to prevent
+// the fraction bar or root line from intersecting the glyph.
+// TODO(kevinb) allow union of multiple glyph metrics for better accuracy.
+var extraCharacterMap = {
+    // Latin-1
+    'À': 'A',
+    'Á': 'A',
+    'Â': 'A',
+    'Ã': 'A',
+    'Ä': 'A',
+    'Å': 'A',
+    'Æ': 'A',
+    'Ç': 'C',
+    'È': 'E',
+    'É': 'E',
+    'Ê': 'E',
+    'Ë': 'E',
+    'Ì': 'I',
+    'Í': 'I',
+    'Î': 'I',
+    'Ï': 'I',
+    'Ð': 'D',
+    'Ñ': 'N',
+    'Ò': 'O',
+    'Ó': 'O',
+    'Ô': 'O',
+    'Õ': 'O',
+    'Ö': 'O',
+    'Ø': 'O',
+    'Ù': 'U',
+    'Ú': 'U',
+    'Û': 'U',
+    'Ü': 'U',
+    'Ý': 'Y',
+    'Þ': 'o',
+    'ß': 'B',
+    'à': 'a',
+    'á': 'a',
+    'â': 'a',
+    'ã': 'a',
+    'ä': 'a',
+    'å': 'a',
+    'æ': 'a',
+    'ç': 'c',
+    'è': 'e',
+    'é': 'e',
+    'ê': 'e',
+    'ë': 'e',
+    'ì': 'i',
+    'í': 'i',
+    'î': 'i',
+    'ï': 'i',
+    'ð': 'd',
+    'ñ': 'n',
+    'ò': 'o',
+    'ó': 'o',
+    'ô': 'o',
+    'õ': 'o',
+    'ö': 'o',
+    'ø': 'o',
+    'ù': 'u',
+    'ú': 'u',
+    'û': 'u',
+    'ü': 'u',
+    'ý': 'y',
+    'þ': 'o',
+    'ÿ': 'y',
+
+    // Cyrillic
+    'А': 'A',
+    'Б': 'B',
+    'В': 'B',
+    'Г': 'F',
+    'Д': 'A',
+    'Е': 'E',
+    'Ж': 'K',
+    'З': '3',
+    'И': 'N',
+    'Й': 'N',
+    'К': 'K',
+    'Л': 'N',
+    'М': 'M',
+    'Н': 'H',
+    'О': 'O',
+    'П': 'N',
+    'Р': 'P',
+    'С': 'C',
+    'Т': 'T',
+    'У': 'y',
+    'Ф': 'O',
+    'Х': 'X',
+    'Ц': 'U',
+    'Ч': 'h',
+    'Ш': 'W',
+    'Щ': 'W',
+    'Ъ': 'B',
+    'Ы': 'X',
+    'Ь': 'B',
+    'Э': '3',
+    'Ю': 'X',
+    'Я': 'R',
+    'а': 'a',
+    'б': 'b',
+    'в': 'a',
+    'г': 'r',
+    'д': 'y',
+    'е': 'e',
+    'ж': 'm',
+    'з': 'e',
+    'и': 'n',
+    'й': 'n',
+    'к': 'n',
+    'л': 'n',
+    'м': 'm',
+    'н': 'n',
+    'о': 'o',
+    'п': 'n',
+    'р': 'p',
+    'с': 'c',
+    'т': 'o',
+    'у': 'y',
+    'ф': 'b',
+    'х': 'x',
+    'ц': 'n',
+    'ч': 'n',
+    'ш': 'w',
+    'щ': 'w',
+    'ъ': 'a',
+    'ы': 'm',
+    'ь': 'a',
+    'э': 'e',
+    'ю': 'm',
+    'я': 'r'
+};
+
+/**
+ * This function is a convenience function for looking up information in the
+ * metricMap table. It takes a character as a string, and a style.
+ *
+ * Note: the `width` property may be undefined if fontMetricsData.js wasn't
+ * built using `Make extended_metrics`.
+ */
+var getCharacterMetrics = function(character, style) {
+    var ch = character.charCodeAt(0);
+    if (character[0] in extraCharacterMap) {
+        ch = extraCharacterMap[character[0]].charCodeAt(0);
+    } else if (cjkRegex.test(character[0])) {
+        ch = 'M'.charCodeAt(0);
+    }
+    var metrics = metricMap[style][ch];
+    if (metrics) {
+        return {
+            depth: metrics[0],
+            height: metrics[1],
+            italic: metrics[2],
+            skew: metrics[3],
+            width: metrics[4]
+        };
+    }
+};
+
+module.exports = {
+    metrics: metrics,
+    sigmas: sigmas,
+    getCharacterMetrics: getCharacterMetrics
+};
+
+},{"./Style":9,"./fontMetricsData":18,"./unicodeRegexes":24}],18:[function(require,module,exports){
+module.exports = {
+    "AMS-Regular": {
+        "65": [0, 0.68889, 0, 0],
+        "66": [0, 0.68889, 0, 0],
+        "67": [0, 0.68889, 0, 0],
+        "68": [0, 0.68889, 0, 0],
+        "69": [0, 0.68889, 0, 0],
+        "70": [0, 0.68889, 0, 0],
+        "71": [0, 0.68889, 0, 0],
+        "72": [0, 0.68889, 0, 0],
+        "73": [0, 0.68889, 0, 0],
+        "74": [0.16667, 0.68889, 0, 0],
+        "75": [0, 0.68889, 0, 0],
+        "76": [0, 0.68889, 0, 0],
+        "77": [0, 0.68889, 0, 0],
+        "78": [0, 0.68889, 0, 0],
+        "79": [0.16667, 0.68889, 0, 0],
+        "80": [0, 0.68889, 0, 0],
+        "81": [0.16667, 0.68889, 0, 0],
+        "82": [0, 0.68889, 0, 0],
+        "83": [0, 0.68889, 0, 0],
+        "84": [0, 0.68889, 0, 0],
+        "85": [0, 0.68889, 0, 0],
+        "86": [0, 0.68889, 0, 0],
+        "87": [0, 0.68889, 0, 0],
+        "88": [0, 0.68889, 0, 0],
+        "89": [0, 0.68889, 0, 0],
+        "90": [0, 0.68889, 0, 0],
+        "107": [0, 0.68889, 0, 0],
+        "165": [0, 0.675, 0.025, 0],
+        "174": [0.15559, 0.69224, 0, 0],
+        "240": [0, 0.68889, 0, 0],
+        "295": [0, 0.68889, 0, 0],
+        "710": [0, 0.825, 0, 0],
+        "732": [0, 0.9, 0, 0],
+        "770": [0, 0.825, 0, 0],
+        "771": [0, 0.9, 0, 0],
+        "989": [0.08167, 0.58167, 0, 0],
+        "1008": [0, 0.43056, 0.04028, 0],
+        "8245": [0, 0.54986, 0, 0],
+        "8463": [0, 0.68889, 0, 0],
+        "8487": [0, 0.68889, 0, 0],
+        "8498": [0, 0.68889, 0, 0],
+        "8502": [0, 0.68889, 0, 0],
+        "8503": [0, 0.68889, 0, 0],
+        "8504": [0, 0.68889, 0, 0],
+        "8513": [0, 0.68889, 0, 0],
+        "8592": [-0.03598, 0.46402, 0, 0],
+        "8594": [-0.03598, 0.46402, 0, 0],
+        "8602": [-0.13313, 0.36687, 0, 0],
+        "8603": [-0.13313, 0.36687, 0, 0],
+        "8606": [0.01354, 0.52239, 0, 0],
+        "8608": [0.01354, 0.52239, 0, 0],
+        "8610": [0.01354, 0.52239, 0, 0],
+        "8611": [0.01354, 0.52239, 0, 0],
+        "8619": [0, 0.54986, 0, 0],
+        "8620": [0, 0.54986, 0, 0],
+        "8621": [-0.13313, 0.37788, 0, 0],
+        "8622": [-0.13313, 0.36687, 0, 0],
+        "8624": [0, 0.69224, 0, 0],
+        "8625": [0, 0.69224, 0, 0],
+        "8630": [0, 0.43056, 0, 0],
+        "8631": [0, 0.43056, 0, 0],
+        "8634": [0.08198, 0.58198, 0, 0],
+        "8635": [0.08198, 0.58198, 0, 0],
+        "8638": [0.19444, 0.69224, 0, 0],
+        "8639": [0.19444, 0.69224, 0, 0],
+        "8642": [0.19444, 0.69224, 0, 0],
+        "8643": [0.19444, 0.69224, 0, 0],
+        "8644": [0.1808, 0.675, 0, 0],
+        "8646": [0.1808, 0.675, 0, 0],
+        "8647": [0.1808, 0.675, 0, 0],
+        "8648": [0.19444, 0.69224, 0, 0],
+        "8649": [0.1808, 0.675, 0, 0],
+        "8650": [0.19444, 0.69224, 0, 0],
+        "8651": [0.01354, 0.52239, 0, 0],
+        "8652": [0.01354, 0.52239, 0, 0],
+        "8653": [-0.13313, 0.36687, 0, 0],
+        "8654": [-0.13313, 0.36687, 0, 0],
+        "8655": [-0.13313, 0.36687, 0, 0],
+        "8666": [0.13667, 0.63667, 0, 0],
+        "8667": [0.13667, 0.63667, 0, 0],
+        "8669": [-0.13313, 0.37788, 0, 0],
+        "8672": [-0.064, 0.437, 0, 0],
+        "8674": [-0.064, 0.437, 0, 0],
+        "8705": [0, 0.825, 0, 0],
+        "8708": [0, 0.68889, 0, 0],
+        "8709": [0.08167, 0.58167, 0, 0],
+        "8717": [0, 0.43056, 0, 0],
+        "8722": [-0.03598, 0.46402, 0, 0],
+        "8724": [0.08198, 0.69224, 0, 0],
+        "8726": [0.08167, 0.58167, 0, 0],
+        "8733": [0, 0.69224, 0, 0],
+        "8736": [0, 0.69224, 0, 0],
+        "8737": [0, 0.69224, 0, 0],
+        "8738": [0.03517, 0.52239, 0, 0],
+        "8739": [0.08167, 0.58167, 0, 0],
+        "8740": [0.25142, 0.74111, 0, 0],
+        "8741": [0.08167, 0.58167, 0, 0],
+        "8742": [0.25142, 0.74111, 0, 0],
+        "8756": [0, 0.69224, 0, 0],
+        "8757": [0, 0.69224, 0, 0],
+        "8764": [-0.13313, 0.36687, 0, 0],
+        "8765": [-0.13313, 0.37788, 0, 0],
+        "8769": [-0.13313, 0.36687, 0, 0],
+        "8770": [-0.03625, 0.46375, 0, 0],
+        "8774": [0.30274, 0.79383, 0, 0],
+        "8776": [-0.01688, 0.48312, 0, 0],
+        "8778": [0.08167, 0.58167, 0, 0],
+        "8782": [0.06062, 0.54986, 0, 0],
+        "8783": [0.06062, 0.54986, 0, 0],
+        "8785": [0.08198, 0.58198, 0, 0],
+        "8786": [0.08198, 0.58198, 0, 0],
+        "8787": [0.08198, 0.58198, 0, 0],
+        "8790": [0, 0.69224, 0, 0],
+        "8791": [0.22958, 0.72958, 0, 0],
+        "8796": [0.08198, 0.91667, 0, 0],
+        "8806": [0.25583, 0.75583, 0, 0],
+        "8807": [0.25583, 0.75583, 0, 0],
+        "8808": [0.25142, 0.75726, 0, 0],
+        "8809": [0.25142, 0.75726, 0, 0],
+        "8812": [0.25583, 0.75583, 0, 0],
+        "8814": [0.20576, 0.70576, 0, 0],
+        "8815": [0.20576, 0.70576, 0, 0],
+        "8816": [0.30274, 0.79383, 0, 0],
+        "8817": [0.30274, 0.79383, 0, 0],
+        "8818": [0.22958, 0.72958, 0, 0],
+        "8819": [0.22958, 0.72958, 0, 0],
+        "8822": [0.1808, 0.675, 0, 0],
+        "8823": [0.1808, 0.675, 0, 0],
+        "8828": [0.13667, 0.63667, 0, 0],
+        "8829": [0.13667, 0.63667, 0, 0],
+        "8830": [0.22958, 0.72958, 0, 0],
+        "8831": [0.22958, 0.72958, 0, 0],
+        "8832": [0.20576, 0.70576, 0, 0],
+        "8833": [0.20576, 0.70576, 0, 0],
+        "8840": [0.30274, 0.79383, 0, 0],
+        "8841": [0.30274, 0.79383, 0, 0],
+        "8842": [0.13597, 0.63597, 0, 0],
+        "8843": [0.13597, 0.63597, 0, 0],
+        "8847": [0.03517, 0.54986, 0, 0],
+        "8848": [0.03517, 0.54986, 0, 0],
+        "8858": [0.08198, 0.58198, 0, 0],
+        "8859": [0.08198, 0.58198, 0, 0],
+        "8861": [0.08198, 0.58198, 0, 0],
+        "8862": [0, 0.675, 0, 0],
+        "8863": [0, 0.675, 0, 0],
+        "8864": [0, 0.675, 0, 0],
+        "8865": [0, 0.675, 0, 0],
+        "8872": [0, 0.69224, 0, 0],
+        "8873": [0, 0.69224, 0, 0],
+        "8874": [0, 0.69224, 0, 0],
+        "8876": [0, 0.68889, 0, 0],
+        "8877": [0, 0.68889, 0, 0],
+        "8878": [0, 0.68889, 0, 0],
+        "8879": [0, 0.68889, 0, 0],
+        "8882": [0.03517, 0.54986, 0, 0],
+        "8883": [0.03517, 0.54986, 0, 0],
+        "8884": [0.13667, 0.63667, 0, 0],
+        "8885": [0.13667, 0.63667, 0, 0],
+        "8888": [0, 0.54986, 0, 0],
+        "8890": [0.19444, 0.43056, 0, 0],
+        "8891": [0.19444, 0.69224, 0, 0],
+        "8892": [0.19444, 0.69224, 0, 0],
+        "8901": [0, 0.54986, 0, 0],
+        "8903": [0.08167, 0.58167, 0, 0],
+        "8905": [0.08167, 0.58167, 0, 0],
+        "8906": [0.08167, 0.58167, 0, 0],
+        "8907": [0, 0.69224, 0, 0],
+        "8908": [0, 0.69224, 0, 0],
+        "8909": [-0.03598, 0.46402, 0, 0],
+        "8910": [0, 0.54986, 0, 0],
+        "8911": [0, 0.54986, 0, 0],
+        "8912": [0.03517, 0.54986, 0, 0],
+        "8913": [0.03517, 0.54986, 0, 0],
+        "8914": [0, 0.54986, 0, 0],
+        "8915": [0, 0.54986, 0, 0],
+        "8916": [0, 0.69224, 0, 0],
+        "8918": [0.0391, 0.5391, 0, 0],
+        "8919": [0.0391, 0.5391, 0, 0],
+        "8920": [0.03517, 0.54986, 0, 0],
+        "8921": [0.03517, 0.54986, 0, 0],
+        "8922": [0.38569, 0.88569, 0, 0],
+        "8923": [0.38569, 0.88569, 0, 0],
+        "8926": [0.13667, 0.63667, 0, 0],
+        "8927": [0.13667, 0.63667, 0, 0],
+        "8928": [0.30274, 0.79383, 0, 0],
+        "8929": [0.30274, 0.79383, 0, 0],
+        "8934": [0.23222, 0.74111, 0, 0],
+        "8935": [0.23222, 0.74111, 0, 0],
+        "8936": [0.23222, 0.74111, 0, 0],
+        "8937": [0.23222, 0.74111, 0, 0],
+        "8938": [0.20576, 0.70576, 0, 0],
+        "8939": [0.20576, 0.70576, 0, 0],
+        "8940": [0.30274, 0.79383, 0, 0],
+        "8941": [0.30274, 0.79383, 0, 0],
+        "8994": [0.19444, 0.69224, 0, 0],
+        "8995": [0.19444, 0.69224, 0, 0],
+        "9416": [0.15559, 0.69224, 0, 0],
+        "9484": [0, 0.69224, 0, 0],
+        "9488": [0, 0.69224, 0, 0],
+        "9492": [0, 0.37788, 0, 0],
+        "9496": [0, 0.37788, 0, 0],
+        "9585": [0.19444, 0.68889, 0, 0],
+        "9586": [0.19444, 0.74111, 0, 0],
+        "9632": [0, 0.675, 0, 0],
+        "9633": [0, 0.675, 0, 0],
+        "9650": [0, 0.54986, 0, 0],
+        "9651": [0, 0.54986, 0, 0],
+        "9654": [0.03517, 0.54986, 0, 0],
+        "9660": [0, 0.54986, 0, 0],
+        "9661": [0, 0.54986, 0, 0],
+        "9664": [0.03517, 0.54986, 0, 0],
+        "9674": [0.11111, 0.69224, 0, 0],
+        "9733": [0.19444, 0.69224, 0, 0],
+        "10003": [0, 0.69224, 0, 0],
+        "10016": [0, 0.69224, 0, 0],
+        "10731": [0.11111, 0.69224, 0, 0],
+        "10846": [0.19444, 0.75583, 0, 0],
+        "10877": [0.13667, 0.63667, 0, 0],
+        "10878": [0.13667, 0.63667, 0, 0],
+        "10885": [0.25583, 0.75583, 0, 0],
+        "10886": [0.25583, 0.75583, 0, 0],
+        "10887": [0.13597, 0.63597, 0, 0],
+        "10888": [0.13597, 0.63597, 0, 0],
+        "10889": [0.26167, 0.75726, 0, 0],
+        "10890": [0.26167, 0.75726, 0, 0],
+        "10891": [0.48256, 0.98256, 0, 0],
+        "10892": [0.48256, 0.98256, 0, 0],
+        "10901": [0.13667, 0.63667, 0, 0],
+        "10902": [0.13667, 0.63667, 0, 0],
+        "10933": [0.25142, 0.75726, 0, 0],
+        "10934": [0.25142, 0.75726, 0, 0],
+        "10935": [0.26167, 0.75726, 0, 0],
+        "10936": [0.26167, 0.75726, 0, 0],
+        "10937": [0.26167, 0.75726, 0, 0],
+        "10938": [0.26167, 0.75726, 0, 0],
+        "10949": [0.25583, 0.75583, 0, 0],
+        "10950": [0.25583, 0.75583, 0, 0],
+        "10955": [0.28481, 0.79383, 0, 0],
+        "10956": [0.28481, 0.79383, 0, 0],
+        "57350": [0.08167, 0.58167, 0, 0],
+        "57351": [0.08167, 0.58167, 0, 0],
+        "57352": [0.08167, 0.58167, 0, 0],
+        "57353": [0, 0.43056, 0.04028, 0],
+        "57356": [0.25142, 0.75726, 0, 0],
+        "57357": [0.25142, 0.75726, 0, 0],
+        "57358": [0.41951, 0.91951, 0, 0],
+        "57359": [0.30274, 0.79383, 0, 0],
+        "57360": [0.30274, 0.79383, 0, 0],
+        "57361": [0.41951, 0.91951, 0, 0],
+        "57366": [0.25142, 0.75726, 0, 0],
+        "57367": [0.25142, 0.75726, 0, 0],
+        "57368": [0.25142, 0.75726, 0, 0],
+        "57369": [0.25142, 0.75726, 0, 0],
+        "57370": [0.13597, 0.63597, 0, 0],
+        "57371": [0.13597, 0.63597, 0, 0]
+    },
+    "Caligraphic-Regular": {
+        "48": [0, 0.43056, 0, 0],
+        "49": [0, 0.43056, 0, 0],
+        "50": [0, 0.43056, 0, 0],
+        "51": [0.19444, 0.43056, 0, 0],
+        "52": [0.19444, 0.43056, 0, 0],
+        "53": [0.19444, 0.43056, 0, 0],
+        "54": [0, 0.64444, 0, 0],
+        "55": [0.19444, 0.43056, 0, 0],
+        "56": [0, 0.64444, 0, 0],
+        "57": [0.19444, 0.43056, 0, 0],
+        "65": [0, 0.68333, 0, 0.19445],
+        "66": [0, 0.68333, 0.03041, 0.13889],
+        "67": [0, 0.68333, 0.05834, 0.13889],
+        "68": [0, 0.68333, 0.02778, 0.08334],
+        "69": [0, 0.68333, 0.08944, 0.11111],
+        "70": [0, 0.68333, 0.09931, 0.11111],
+        "71": [0.09722, 0.68333, 0.0593, 0.11111],
+        "72": [0, 0.68333, 0.00965, 0.11111],
+        "73": [0, 0.68333, 0.07382, 0],
+        "74": [0.09722, 0.68333, 0.18472, 0.16667],
+        "75": [0, 0.68333, 0.01445, 0.05556],
+        "76": [0, 0.68333, 0, 0.13889],
+        "77": [0, 0.68333, 0, 0.13889],
+        "78": [0, 0.68333, 0.14736, 0.08334],
+        "79": [0, 0.68333, 0.02778, 0.11111],
+        "80": [0, 0.68333, 0.08222, 0.08334],
+        "81": [0.09722, 0.68333, 0, 0.11111],
+        "82": [0, 0.68333, 0, 0.08334],
+        "83": [0, 0.68333, 0.075, 0.13889],
+        "84": [0, 0.68333, 0.25417, 0],
+        "85": [0, 0.68333, 0.09931, 0.08334],
+        "86": [0, 0.68333, 0.08222, 0],
+        "87": [0, 0.68333, 0.08222, 0.08334],
+        "88": [0, 0.68333, 0.14643, 0.13889],
+        "89": [0.09722, 0.68333, 0.08222, 0.08334],
+        "90": [0, 0.68333, 0.07944, 0.13889]
+    },
+    "Fraktur-Regular": {
+        "33": [0, 0.69141, 0, 0],
+        "34": [0, 0.69141, 0, 0],
+        "38": [0, 0.69141, 0, 0],
+        "39": [0, 0.69141, 0, 0],
+        "40": [0.24982, 0.74947, 0, 0],
+        "41": [0.24982, 0.74947, 0, 0],
+        "42": [0, 0.62119, 0, 0],
+        "43": [0.08319, 0.58283, 0, 0],
+        "44": [0, 0.10803, 0, 0],
+        "45": [0.08319, 0.58283, 0, 0],
+        "46": [0, 0.10803, 0, 0],
+        "47": [0.24982, 0.74947, 0, 0],
+        "48": [0, 0.47534, 0, 0],
+        "49": [0, 0.47534, 0, 0],
+        "50": [0, 0.47534, 0, 0],
+        "51": [0.18906, 0.47534, 0, 0],
+        "52": [0.18906, 0.47534, 0, 0],
+        "53": [0.18906, 0.47534, 0, 0],
+        "54": [0, 0.69141, 0, 0],
+        "55": [0.18906, 0.47534, 0, 0],
+        "56": [0, 0.69141, 0, 0],
+        "57": [0.18906, 0.47534, 0, 0],
+        "58": [0, 0.47534, 0, 0],
+        "59": [0.12604, 0.47534, 0, 0],
+        "61": [-0.13099, 0.36866, 0, 0],
+        "63": [0, 0.69141, 0, 0],
+        "65": [0, 0.69141, 0, 0],
+        "66": [0, 0.69141, 0, 0],
+        "67": [0, 0.69141, 0, 0],
+        "68": [0, 0.69141, 0, 0],
+        "69": [0, 0.69141, 0, 0],
+        "70": [0.12604, 0.69141, 0, 0],
+        "71": [0, 0.69141, 0, 0],
+        "72": [0.06302, 0.69141, 0, 0],
+        "73": [0, 0.69141, 0, 0],
+        "74": [0.12604, 0.69141, 0, 0],
+        "75": [0, 0.69141, 0, 0],
+        "76": [0, 0.69141, 0, 0],
+        "77": [0, 0.69141, 0, 0],
+        "78": [0, 0.69141, 0, 0],
+        "79": [0, 0.69141, 0, 0],
+        "80": [0.18906, 0.69141, 0, 0],
+        "81": [0.03781, 0.69141, 0, 0],
+        "82": [0, 0.69141, 0, 0],
+        "83": [0, 0.69141, 0, 0],
+        "84": [0, 0.69141, 0, 0],
+        "85": [0, 0.69141, 0, 0],
+        "86": [0, 0.69141, 0, 0],
+        "87": [0, 0.69141, 0, 0],
+        "88": [0, 0.69141, 0, 0],
+        "89": [0.18906, 0.69141, 0, 0],
+        "90": [0.12604, 0.69141, 0, 0],
+        "91": [0.24982, 0.74947, 0, 0],
+        "93": [0.24982, 0.74947, 0, 0],
+        "94": [0, 0.69141, 0, 0],
+        "97": [0, 0.47534, 0, 0],
+        "98": [0, 0.69141, 0, 0],
+        "99": [0, 0.47534, 0, 0],
+        "100": [0, 0.62119, 0, 0],
+        "101": [0, 0.47534, 0, 0],
+        "102": [0.18906, 0.69141, 0, 0],
+        "103": [0.18906, 0.47534, 0, 0],
+        "104": [0.18906, 0.69141, 0, 0],
+        "105": [0, 0.69141, 0, 0],
+        "106": [0, 0.69141, 0, 0],
+        "107": [0, 0.69141, 0, 0],
+        "108": [0, 0.69141, 0, 0],
+        "109": [0, 0.47534, 0, 0],
+        "110": [0, 0.47534, 0, 0],
+        "111": [0, 0.47534, 0, 0],
+        "112": [0.18906, 0.52396, 0, 0],
+        "113": [0.18906, 0.47534, 0, 0],
+        "114": [0, 0.47534, 0, 0],
+        "115": [0, 0.47534, 0, 0],
+        "116": [0, 0.62119, 0, 0],
+        "117": [0, 0.47534, 0, 0],
+        "118": [0, 0.52396, 0, 0],
+        "119": [0, 0.52396, 0, 0],
+        "120": [0.18906, 0.47534, 0, 0],
+        "121": [0.18906, 0.47534, 0, 0],
+        "122": [0.18906, 0.47534, 0, 0],
+        "8216": [0, 0.69141, 0, 0],
+        "8217": [0, 0.69141, 0, 0],
+        "58112": [0, 0.62119, 0, 0],
+        "58113": [0, 0.62119, 0, 0],
+        "58114": [0.18906, 0.69141, 0, 0],
+        "58115": [0.18906, 0.69141, 0, 0],
+        "58116": [0.18906, 0.47534, 0, 0],
+        "58117": [0, 0.69141, 0, 0],
+        "58118": [0, 0.62119, 0, 0],
+        "58119": [0, 0.47534, 0, 0]
+    },
+    "Main-Bold": {
+        "33": [0, 0.69444, 0, 0],
+        "34": [0, 0.69444, 0, 0],
+        "35": [0.19444, 0.69444, 0, 0],
+        "36": [0.05556, 0.75, 0, 0],
+        "37": [0.05556, 0.75, 0, 0],
+        "38": [0, 0.69444, 0, 0],
+        "39": [0, 0.69444, 0, 0],
+        "40": [0.25, 0.75, 0, 0],
+        "41": [0.25, 0.75, 0, 0],
+        "42": [0, 0.75, 0, 0],
+        "43": [0.13333, 0.63333, 0, 0],
+        "44": [0.19444, 0.15556, 0, 0],
+        "45": [0, 0.44444, 0, 0],
+        "46": [0, 0.15556, 0, 0],
+        "47": [0.25, 0.75, 0, 0],
+        "48": [0, 0.64444, 0, 0],
+        "49": [0, 0.64444, 0, 0],
+        "50": [0, 0.64444, 0, 0],
+        "51": [0, 0.64444, 0, 0],
+        "52": [0, 0.64444, 0, 0],
+        "53": [0, 0.64444, 0, 0],
+        "54": [0, 0.64444, 0, 0],
+        "55": [0, 0.64444, 0, 0],
+        "56": [0, 0.64444, 0, 0],
+        "57": [0, 0.64444, 0, 0],
+        "58": [0, 0.44444, 0, 0],
+        "59": [0.19444, 0.44444, 0, 0],
+        "60": [0.08556, 0.58556, 0, 0],
+        "61": [-0.10889, 0.39111, 0, 0],
+        "62": [0.08556, 0.58556, 0, 0],
+        "63": [0, 0.69444, 0, 0],
+        "64": [0, 0.69444, 0, 0],
+        "65": [0, 0.68611, 0, 0],
+        "66": [0, 0.68611, 0, 0],
+        "67": [0, 0.68611, 0, 0],
+        "68": [0, 0.68611, 0, 0],
+        "69": [0, 0.68611, 0, 0],
+        "70": [0, 0.68611, 0, 0],
+        "71": [0, 0.68611, 0, 0],
+        "72": [0, 0.68611, 0, 0],
+        "73": [0, 0.68611, 0, 0],
+        "74": [0, 0.68611, 0, 0],
+        "75": [0, 0.68611, 0, 0],
+        "76": [0, 0.68611, 0, 0],
+        "77": [0, 0.68611, 0, 0],
+        "78": [0, 0.68611, 0, 0],
+        "79": [0, 0.68611, 0, 0],
+        "80": [0, 0.68611, 0, 0],
+        "81": [0.19444, 0.68611, 0, 0],
+        "82": [0, 0.68611, 0, 0],
+        "83": [0, 0.68611, 0, 0],
+        "84": [0, 0.68611, 0, 0],
+        "85": [0, 0.68611, 0, 0],
+        "86": [0, 0.68611, 0.01597, 0],
+        "87": [0, 0.68611, 0.01597, 0],
+        "88": [0, 0.68611, 0, 0],
+        "89": [0, 0.68611, 0.02875, 0],
+        "90": [0, 0.68611, 0, 0],
+        "91": [0.25, 0.75, 0, 0],
+        "92": [0.25, 0.75, 0, 0],
+        "93": [0.25, 0.75, 0, 0],
+        "94": [0, 0.69444, 0, 0],
+        "95": [0.31, 0.13444, 0.03194, 0],
+        "96": [0, 0.69444, 0, 0],
+        "97": [0, 0.44444, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.44444, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.44444, 0, 0],
+        "102": [0, 0.69444, 0.10903, 0],
+        "103": [0.19444, 0.44444, 0.01597, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.69444, 0, 0],
+        "106": [0.19444, 0.69444, 0, 0],
+        "107": [0, 0.69444, 0, 0],
+        "108": [0, 0.69444, 0, 0],
+        "109": [0, 0.44444, 0, 0],
+        "110": [0, 0.44444, 0, 0],
+        "111": [0, 0.44444, 0, 0],
+        "112": [0.19444, 0.44444, 0, 0],
+        "113": [0.19444, 0.44444, 0, 0],
+        "114": [0, 0.44444, 0, 0],
+        "115": [0, 0.44444, 0, 0],
+        "116": [0, 0.63492, 0, 0],
+        "117": [0, 0.44444, 0, 0],
+        "118": [0, 0.44444, 0.01597, 0],
+        "119": [0, 0.44444, 0.01597, 0],
+        "120": [0, 0.44444, 0, 0],
+        "121": [0.19444, 0.44444, 0.01597, 0],
+        "122": [0, 0.44444, 0, 0],
+        "123": [0.25, 0.75, 0, 0],
+        "124": [0.25, 0.75, 0, 0],
+        "125": [0.25, 0.75, 0, 0],
+        "126": [0.35, 0.34444, 0, 0],
+        "168": [0, 0.69444, 0, 0],
+        "172": [0, 0.44444, 0, 0],
+        "175": [0, 0.59611, 0, 0],
+        "176": [0, 0.69444, 0, 0],
+        "177": [0.13333, 0.63333, 0, 0],
+        "180": [0, 0.69444, 0, 0],
+        "215": [0.13333, 0.63333, 0, 0],
+        "247": [0.13333, 0.63333, 0, 0],
+        "305": [0, 0.44444, 0, 0],
+        "567": [0.19444, 0.44444, 0, 0],
+        "710": [0, 0.69444, 0, 0],
+        "711": [0, 0.63194, 0, 0],
+        "713": [0, 0.59611, 0, 0],
+        "714": [0, 0.69444, 0, 0],
+        "715": [0, 0.69444, 0, 0],
+        "728": [0, 0.69444, 0, 0],
+        "729": [0, 0.69444, 0, 0],
+        "730": [0, 0.69444, 0, 0],
+        "732": [0, 0.69444, 0, 0],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0, 0],
+        "770": [0, 0.69444, 0, 0],
+        "771": [0, 0.69444, 0, 0],
+        "772": [0, 0.59611, 0, 0],
+        "774": [0, 0.69444, 0, 0],
+        "775": [0, 0.69444, 0, 0],
+        "776": [0, 0.69444, 0, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0, 0],
+        "780": [0, 0.63194, 0, 0],
+        "824": [0.19444, 0.69444, 0, 0],
+        "915": [0, 0.68611, 0, 0],
+        "916": [0, 0.68611, 0, 0],
+        "920": [0, 0.68611, 0, 0],
+        "923": [0, 0.68611, 0, 0],
+        "926": [0, 0.68611, 0, 0],
+        "928": [0, 0.68611, 0, 0],
+        "931": [0, 0.68611, 0, 0],
+        "933": [0, 0.68611, 0, 0],
+        "934": [0, 0.68611, 0, 0],
+        "936": [0, 0.68611, 0, 0],
+        "937": [0, 0.68611, 0, 0],
+        "8211": [0, 0.44444, 0.03194, 0],
+        "8212": [0, 0.44444, 0.03194, 0],
+        "8216": [0, 0.69444, 0, 0],
+        "8217": [0, 0.69444, 0, 0],
+        "8220": [0, 0.69444, 0, 0],
+        "8221": [0, 0.69444, 0, 0],
+        "8224": [0.19444, 0.69444, 0, 0],
+        "8225": [0.19444, 0.69444, 0, 0],
+        "8242": [0, 0.55556, 0, 0],
+        "8407": [0, 0.72444, 0.15486, 0],
+        "8463": [0, 0.69444, 0, 0],
+        "8465": [0, 0.69444, 0, 0],
+        "8467": [0, 0.69444, 0, 0],
+        "8472": [0.19444, 0.44444, 0, 0],
+        "8476": [0, 0.69444, 0, 0],
+        "8501": [0, 0.69444, 0, 0],
+        "8592": [-0.10889, 0.39111, 0, 0],
+        "8593": [0.19444, 0.69444, 0, 0],
+        "8594": [-0.10889, 0.39111, 0, 0],
+        "8595": [0.19444, 0.69444, 0, 0],
+        "8596": [-0.10889, 0.39111, 0, 0],
+        "8597": [0.25, 0.75, 0, 0],
+        "8598": [0.19444, 0.69444, 0, 0],
+        "8599": [0.19444, 0.69444, 0, 0],
+        "8600": [0.19444, 0.69444, 0, 0],
+        "8601": [0.19444, 0.69444, 0, 0],
+        "8636": [-0.10889, 0.39111, 0, 0],
+        "8637": [-0.10889, 0.39111, 0, 0],
+        "8640": [-0.10889, 0.39111, 0, 0],
+        "8641": [-0.10889, 0.39111, 0, 0],
+        "8656": [-0.10889, 0.39111, 0, 0],
+        "8657": [0.19444, 0.69444, 0, 0],
+        "8658": [-0.10889, 0.39111, 0, 0],
+        "8659": [0.19444, 0.69444, 0, 0],
+        "8660": [-0.10889, 0.39111, 0, 0],
+        "8661": [0.25, 0.75, 0, 0],
+        "8704": [0, 0.69444, 0, 0],
+        "8706": [0, 0.69444, 0.06389, 0],
+        "8707": [0, 0.69444, 0, 0],
+        "8709": [0.05556, 0.75, 0, 0],
+        "8711": [0, 0.68611, 0, 0],
+        "8712": [0.08556, 0.58556, 0, 0],
+        "8715": [0.08556, 0.58556, 0, 0],
+        "8722": [0.13333, 0.63333, 0, 0],
+        "8723": [0.13333, 0.63333, 0, 0],
+        "8725": [0.25, 0.75, 0, 0],
+        "8726": [0.25, 0.75, 0, 0],
+        "8727": [-0.02778, 0.47222, 0, 0],
+        "8728": [-0.02639, 0.47361, 0, 0],
+        "8729": [-0.02639, 0.47361, 0, 0],
+        "8730": [0.18, 0.82, 0, 0],
+        "8733": [0, 0.44444, 0, 0],
+        "8734": [0, 0.44444, 0, 0],
+        "8736": [0, 0.69224, 0, 0],
+        "8739": [0.25, 0.75, 0, 0],
+        "8741": [0.25, 0.75, 0, 0],
+        "8743": [0, 0.55556, 0, 0],
+        "8744": [0, 0.55556, 0, 0],
+        "8745": [0, 0.55556, 0, 0],
+        "8746": [0, 0.55556, 0, 0],
+        "8747": [0.19444, 0.69444, 0.12778, 0],
+        "8764": [-0.10889, 0.39111, 0, 0],
+        "8768": [0.19444, 0.69444, 0, 0],
+        "8771": [0.00222, 0.50222, 0, 0],
+        "8776": [0.02444, 0.52444, 0, 0],
+        "8781": [0.00222, 0.50222, 0, 0],
+        "8801": [0.00222, 0.50222, 0, 0],
+        "8804": [0.19667, 0.69667, 0, 0],
+        "8805": [0.19667, 0.69667, 0, 0],
+        "8810": [0.08556, 0.58556, 0, 0],
+        "8811": [0.08556, 0.58556, 0, 0],
+        "8826": [0.08556, 0.58556, 0, 0],
+        "8827": [0.08556, 0.58556, 0, 0],
+        "8834": [0.08556, 0.58556, 0, 0],
+        "8835": [0.08556, 0.58556, 0, 0],
+        "8838": [0.19667, 0.69667, 0, 0],
+        "8839": [0.19667, 0.69667, 0, 0],
+        "8846": [0, 0.55556, 0, 0],
+        "8849": [0.19667, 0.69667, 0, 0],
+        "8850": [0.19667, 0.69667, 0, 0],
+        "8851": [0, 0.55556, 0, 0],
+        "8852": [0, 0.55556, 0, 0],
+        "8853": [0.13333, 0.63333, 0, 0],
+        "8854": [0.13333, 0.63333, 0, 0],
+        "8855": [0.13333, 0.63333, 0, 0],
+        "8856": [0.13333, 0.63333, 0, 0],
+        "8857": [0.13333, 0.63333, 0, 0],
+        "8866": [0, 0.69444, 0, 0],
+        "8867": [0, 0.69444, 0, 0],
+        "8868": [0, 0.69444, 0, 0],
+        "8869": [0, 0.69444, 0, 0],
+        "8900": [-0.02639, 0.47361, 0, 0],
+        "8901": [-0.02639, 0.47361, 0, 0],
+        "8902": [-0.02778, 0.47222, 0, 0],
+        "8968": [0.25, 0.75, 0, 0],
+        "8969": [0.25, 0.75, 0, 0],
+        "8970": [0.25, 0.75, 0, 0],
+        "8971": [0.25, 0.75, 0, 0],
+        "8994": [-0.13889, 0.36111, 0, 0],
+        "8995": [-0.13889, 0.36111, 0, 0],
+        "9651": [0.19444, 0.69444, 0, 0],
+        "9657": [-0.02778, 0.47222, 0, 0],
+        "9661": [0.19444, 0.69444, 0, 0],
+        "9667": [-0.02778, 0.47222, 0, 0],
+        "9711": [0.19444, 0.69444, 0, 0],
+        "9824": [0.12963, 0.69444, 0, 0],
+        "9825": [0.12963, 0.69444, 0, 0],
+        "9826": [0.12963, 0.69444, 0, 0],
+        "9827": [0.12963, 0.69444, 0, 0],
+        "9837": [0, 0.75, 0, 0],
+        "9838": [0.19444, 0.69444, 0, 0],
+        "9839": [0.19444, 0.69444, 0, 0],
+        "10216": [0.25, 0.75, 0, 0],
+        "10217": [0.25, 0.75, 0, 0],
+        "10815": [0, 0.68611, 0, 0],
+        "10927": [0.19667, 0.69667, 0, 0],
+        "10928": [0.19667, 0.69667, 0, 0]
+    },
+    "Main-Italic": {
+        "33": [0, 0.69444, 0.12417, 0],
+        "34": [0, 0.69444, 0.06961, 0],
+        "35": [0.19444, 0.69444, 0.06616, 0],
+        "37": [0.05556, 0.75, 0.13639, 0],
+        "38": [0, 0.69444, 0.09694, 0],
+        "39": [0, 0.69444, 0.12417, 0],
+        "40": [0.25, 0.75, 0.16194, 0],
+        "41": [0.25, 0.75, 0.03694, 0],
+        "42": [0, 0.75, 0.14917, 0],
+        "43": [0.05667, 0.56167, 0.03694, 0],
+        "44": [0.19444, 0.10556, 0, 0],
+        "45": [0, 0.43056, 0.02826, 0],
+        "46": [0, 0.10556, 0, 0],
+        "47": [0.25, 0.75, 0.16194, 0],
+        "48": [0, 0.64444, 0.13556, 0],
+        "49": [0, 0.64444, 0.13556, 0],
+        "50": [0, 0.64444, 0.13556, 0],
+        "51": [0, 0.64444, 0.13556, 0],
+        "52": [0.19444, 0.64444, 0.13556, 0],
+        "53": [0, 0.64444, 0.13556, 0],
+        "54": [0, 0.64444, 0.13556, 0],
+        "55": [0.19444, 0.64444, 0.13556, 0],
+        "56": [0, 0.64444, 0.13556, 0],
+        "57": [0, 0.64444, 0.13556, 0],
+        "58": [0, 0.43056, 0.0582, 0],
+        "59": [0.19444, 0.43056, 0.0582, 0],
+        "61": [-0.13313, 0.36687, 0.06616, 0],
+        "63": [0, 0.69444, 0.1225, 0],
+        "64": [0, 0.69444, 0.09597, 0],
+        "65": [0, 0.68333, 0, 0],
+        "66": [0, 0.68333, 0.10257, 0],
+        "67": [0, 0.68333, 0.14528, 0],
+        "68": [0, 0.68333, 0.09403, 0],
+        "69": [0, 0.68333, 0.12028, 0],
+        "70": [0, 0.68333, 0.13305, 0],
+        "71": [0, 0.68333, 0.08722, 0],
+        "72": [0, 0.68333, 0.16389, 0],
+        "73": [0, 0.68333, 0.15806, 0],
+        "74": [0, 0.68333, 0.14028, 0],
+        "75": [0, 0.68333, 0.14528, 0],
+        "76": [0, 0.68333, 0, 0],
+        "77": [0, 0.68333, 0.16389, 0],
+        "78": [0, 0.68333, 0.16389, 0],
+        "79": [0, 0.68333, 0.09403, 0],
+        "80": [0, 0.68333, 0.10257, 0],
+        "81": [0.19444, 0.68333, 0.09403, 0],
+        "82": [0, 0.68333, 0.03868, 0],
+        "83": [0, 0.68333, 0.11972, 0],
+        "84": [0, 0.68333, 0.13305, 0],
+        "85": [0, 0.68333, 0.16389, 0],
+        "86": [0, 0.68333, 0.18361, 0],
+        "87": [0, 0.68333, 0.18361, 0],
+        "88": [0, 0.68333, 0.15806, 0],
+        "89": [0, 0.68333, 0.19383, 0],
+        "90": [0, 0.68333, 0.14528, 0],
+        "91": [0.25, 0.75, 0.1875, 0],
+        "93": [0.25, 0.75, 0.10528, 0],
+        "94": [0, 0.69444, 0.06646, 0],
+        "95": [0.31, 0.12056, 0.09208, 0],
+        "97": [0, 0.43056, 0.07671, 0],
+        "98": [0, 0.69444, 0.06312, 0],
+        "99": [0, 0.43056, 0.05653, 0],
+        "100": [0, 0.69444, 0.10333, 0],
+        "101": [0, 0.43056, 0.07514, 0],
+        "102": [0.19444, 0.69444, 0.21194, 0],
+        "103": [0.19444, 0.43056, 0.08847, 0],
+        "104": [0, 0.69444, 0.07671, 0],
+        "105": [0, 0.65536, 0.1019, 0],
+        "106": [0.19444, 0.65536, 0.14467, 0],
+        "107": [0, 0.69444, 0.10764, 0],
+        "108": [0, 0.69444, 0.10333, 0],
+        "109": [0, 0.43056, 0.07671, 0],
+        "110": [0, 0.43056, 0.07671, 0],
+        "111": [0, 0.43056, 0.06312, 0],
+        "112": [0.19444, 0.43056, 0.06312, 0],
+        "113": [0.19444, 0.43056, 0.08847, 0],
+        "114": [0, 0.43056, 0.10764, 0],
+        "115": [0, 0.43056, 0.08208, 0],
+        "116": [0, 0.61508, 0.09486, 0],
+        "117": [0, 0.43056, 0.07671, 0],
+        "118": [0, 0.43056, 0.10764, 0],
+        "119": [0, 0.43056, 0.10764, 0],
+        "120": [0, 0.43056, 0.12042, 0],
+        "121": [0.19444, 0.43056, 0.08847, 0],
+        "122": [0, 0.43056, 0.12292, 0],
+        "126": [0.35, 0.31786, 0.11585, 0],
+        "163": [0, 0.69444, 0, 0],
+        "305": [0, 0.43056, 0, 0.02778],
+        "567": [0.19444, 0.43056, 0, 0.08334],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0.09694, 0],
+        "770": [0, 0.69444, 0.06646, 0],
+        "771": [0, 0.66786, 0.11585, 0],
+        "772": [0, 0.56167, 0.10333, 0],
+        "774": [0, 0.69444, 0.10806, 0],
+        "775": [0, 0.66786, 0.11752, 0],
+        "776": [0, 0.66786, 0.10474, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0.1225, 0],
+        "780": [0, 0.62847, 0.08295, 0],
+        "915": [0, 0.68333, 0.13305, 0],
+        "916": [0, 0.68333, 0, 0],
+        "920": [0, 0.68333, 0.09403, 0],
+        "923": [0, 0.68333, 0, 0],
+        "926": [0, 0.68333, 0.15294, 0],
+        "928": [0, 0.68333, 0.16389, 0],
+        "931": [0, 0.68333, 0.12028, 0],
+        "933": [0, 0.68333, 0.11111, 0],
+        "934": [0, 0.68333, 0.05986, 0],
+        "936": [0, 0.68333, 0.11111, 0],
+        "937": [0, 0.68333, 0.10257, 0],
+        "8211": [0, 0.43056, 0.09208, 0],
+        "8212": [0, 0.43056, 0.09208, 0],
+        "8216": [0, 0.69444, 0.12417, 0],
+        "8217": [0, 0.69444, 0.12417, 0],
+        "8220": [0, 0.69444, 0.1685, 0],
+        "8221": [0, 0.69444, 0.06961, 0],
+        "8463": [0, 0.68889, 0, 0]
+    },
+    "Main-Regular": {
+        "32": [0, 0, 0, 0],
+        "33": [0, 0.69444, 0, 0],
+        "34": [0, 0.69444, 0, 0],
+        "35": [0.19444, 0.69444, 0, 0],
+        "36": [0.05556, 0.75, 0, 0],
+        "37": [0.05556, 0.75, 0, 0],
+        "38": [0, 0.69444, 0, 0],
+        "39": [0, 0.69444, 0, 0],
+        "40": [0.25, 0.75, 0, 0],
+        "41": [0.25, 0.75, 0, 0],
+        "42": [0, 0.75, 0, 0],
+        "43": [0.08333, 0.58333, 0, 0],
+        "44": [0.19444, 0.10556, 0, 0],
+        "45": [0, 0.43056, 0, 0],
+        "46": [0, 0.10556, 0, 0],
+        "47": [0.25, 0.75, 0, 0],
+        "48": [0, 0.64444, 0, 0],
+        "49": [0, 0.64444, 0, 0],
+        "50": [0, 0.64444, 0, 0],
+        "51": [0, 0.64444, 0, 0],
+        "52": [0, 0.64444, 0, 0],
+        "53": [0, 0.64444, 0, 0],
+        "54": [0, 0.64444, 0, 0],
+        "55": [0, 0.64444, 0, 0],
+        "56": [0, 0.64444, 0, 0],
+        "57": [0, 0.64444, 0, 0],
+        "58": [0, 0.43056, 0, 0],
+        "59": [0.19444, 0.43056, 0, 0],
+        "60": [0.0391, 0.5391, 0, 0],
+        "61": [-0.13313, 0.36687, 0, 0],
+        "62": [0.0391, 0.5391, 0, 0],
+        "63": [0, 0.69444, 0, 0],
+        "64": [0, 0.69444, 0, 0],
+        "65": [0, 0.68333, 0, 0],
+        "66": [0, 0.68333, 0, 0],
+        "67": [0, 0.68333, 0, 0],
+        "68": [0, 0.68333, 0, 0],
+        "69": [0, 0.68333, 0, 0],
+        "70": [0, 0.68333, 0, 0],
+        "71": [0, 0.68333, 0, 0],
+        "72": [0, 0.68333, 0, 0],
+        "73": [0, 0.68333, 0, 0],
+        "74": [0, 0.68333, 0, 0],
+        "75": [0, 0.68333, 0, 0],
+        "76": [0, 0.68333, 0, 0],
+        "77": [0, 0.68333, 0, 0],
+        "78": [0, 0.68333, 0, 0],
+        "79": [0, 0.68333, 0, 0],
+        "80": [0, 0.68333, 0, 0],
+        "81": [0.19444, 0.68333, 0, 0],
+        "82": [0, 0.68333, 0, 0],
+        "83": [0, 0.68333, 0, 0],
+        "84": [0, 0.68333, 0, 0],
+        "85": [0, 0.68333, 0, 0],
+        "86": [0, 0.68333, 0.01389, 0],
+        "87": [0, 0.68333, 0.01389, 0],
+        "88": [0, 0.68333, 0, 0],
+        "89": [0, 0.68333, 0.025, 0],
+        "90": [0, 0.68333, 0, 0],
+        "91": [0.25, 0.75, 0, 0],
+        "92": [0.25, 0.75, 0, 0],
+        "93": [0.25, 0.75, 0, 0],
+        "94": [0, 0.69444, 0, 0],
+        "95": [0.31, 0.12056, 0.02778, 0],
+        "96": [0, 0.69444, 0, 0],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.43056, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.43056, 0, 0],
+        "102": [0, 0.69444, 0.07778, 0],
+        "103": [0.19444, 0.43056, 0.01389, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.66786, 0, 0],
+        "106": [0.19444, 0.66786, 0, 0],
+        "107": [0, 0.69444, 0, 0],
+        "108": [0, 0.69444, 0, 0],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0],
+        "112": [0.19444, 0.43056, 0, 0],
+        "113": [0.19444, 0.43056, 0, 0],
+        "114": [0, 0.43056, 0, 0],
+        "115": [0, 0.43056, 0, 0],
+        "116": [0, 0.61508, 0, 0],
+        "117": [0, 0.43056, 0, 0],
+        "118": [0, 0.43056, 0.01389, 0],
+        "119": [0, 0.43056, 0.01389, 0],
+        "120": [0, 0.43056, 0, 0],
+        "121": [0.19444, 0.43056, 0.01389, 0],
+        "122": [0, 0.43056, 0, 0],
+        "123": [0.25, 0.75, 0, 0],
+        "124": [0.25, 0.75, 0, 0],
+        "125": [0.25, 0.75, 0, 0],
+        "126": [0.35, 0.31786, 0, 0],
+        "160": [0, 0, 0, 0],
+        "168": [0, 0.66786, 0, 0],
+        "172": [0, 0.43056, 0, 0],
+        "175": [0, 0.56778, 0, 0],
+        "176": [0, 0.69444, 0, 0],
+        "177": [0.08333, 0.58333, 0, 0],
+        "180": [0, 0.69444, 0, 0],
+        "215": [0.08333, 0.58333, 0, 0],
+        "247": [0.08333, 0.58333, 0, 0],
+        "305": [0, 0.43056, 0, 0],
+        "567": [0.19444, 0.43056, 0, 0],
+        "710": [0, 0.69444, 0, 0],
+        "711": [0, 0.62847, 0, 0],
+        "713": [0, 0.56778, 0, 0],
+        "714": [0, 0.69444, 0, 0],
+        "715": [0, 0.69444, 0, 0],
+        "728": [0, 0.69444, 0, 0],
+        "729": [0, 0.66786, 0, 0],
+        "730": [0, 0.69444, 0, 0],
+        "732": [0, 0.66786, 0, 0],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0, 0],
+        "770": [0, 0.69444, 0, 0],
+        "771": [0, 0.66786, 0, 0],
+        "772": [0, 0.56778, 0, 0],
+        "774": [0, 0.69444, 0, 0],
+        "775": [0, 0.66786, 0, 0],
+        "776": [0, 0.66786, 0, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0, 0],
+        "780": [0, 0.62847, 0, 0],
+        "824": [0.19444, 0.69444, 0, 0],
+        "915": [0, 0.68333, 0, 0],
+        "916": [0, 0.68333, 0, 0],
+        "920": [0, 0.68333, 0, 0],
+        "923": [0, 0.68333, 0, 0],
+        "926": [0, 0.68333, 0, 0],
+        "928": [0, 0.68333, 0, 0],
+        "931": [0, 0.68333, 0, 0],
+        "933": [0, 0.68333, 0, 0],
+        "934": [0, 0.68333, 0, 0],
+        "936": [0, 0.68333, 0, 0],
+        "937": [0, 0.68333, 0, 0],
+        "8211": [0, 0.43056, 0.02778, 0],
+        "8212": [0, 0.43056, 0.02778, 0],
+        "8216": [0, 0.69444, 0, 0],
+        "8217": [0, 0.69444, 0, 0],
+        "8220": [0, 0.69444, 0, 0],
+        "8221": [0, 0.69444, 0, 0],
+        "8224": [0.19444, 0.69444, 0, 0],
+        "8225": [0.19444, 0.69444, 0, 0],
+        "8230": [0, 0.12, 0, 0],
+        "8242": [0, 0.55556, 0, 0],
+        "8407": [0, 0.71444, 0.15382, 0],
+        "8463": [0, 0.68889, 0, 0],
+        "8465": [0, 0.69444, 0, 0],
+        "8467": [0, 0.69444, 0, 0.11111],
+        "8472": [0.19444, 0.43056, 0, 0.11111],
+        "8476": [0, 0.69444, 0, 0],
+        "8501": [0, 0.69444, 0, 0],
+        "8592": [-0.13313, 0.36687, 0, 0],
+        "8593": [0.19444, 0.69444, 0, 0],
+        "8594": [-0.13313, 0.36687, 0, 0],
+        "8595": [0.19444, 0.69444, 0, 0],
+        "8596": [-0.13313, 0.36687, 0, 0],
+        "8597": [0.25, 0.75, 0, 0],
+        "8598": [0.19444, 0.69444, 0, 0],
+        "8599": [0.19444, 0.69444, 0, 0],
+        "8600": [0.19444, 0.69444, 0, 0],
+        "8601": [0.19444, 0.69444, 0, 0],
+        "8614": [0.011, 0.511, 0, 0],
+        "8617": [0.011, 0.511, 0, 0],
+        "8618": [0.011, 0.511, 0, 0],
+        "8636": [-0.13313, 0.36687, 0, 0],
+        "8637": [-0.13313, 0.36687, 0, 0],
+        "8640": [-0.13313, 0.36687, 0, 0],
+        "8641": [-0.13313, 0.36687, 0, 0],
+        "8652": [0.011, 0.671, 0, 0],
+        "8656": [-0.13313, 0.36687, 0, 0],
+        "8657": [0.19444, 0.69444, 0, 0],
+        "8658": [-0.13313, 0.36687, 0, 0],
+        "8659": [0.19444, 0.69444, 0, 0],
+        "8660": [-0.13313, 0.36687, 0, 0],
+        "8661": [0.25, 0.75, 0, 0],
+        "8704": [0, 0.69444, 0, 0],
+        "8706": [0, 0.69444, 0.05556, 0.08334],
+        "8707": [0, 0.69444, 0, 0],
+        "8709": [0.05556, 0.75, 0, 0],
+        "8711": [0, 0.68333, 0, 0],
+        "8712": [0.0391, 0.5391, 0, 0],
+        "8715": [0.0391, 0.5391, 0, 0],
+        "8722": [0.08333, 0.58333, 0, 0],
+        "8723": [0.08333, 0.58333, 0, 0],
+        "8725": [0.25, 0.75, 0, 0],
+        "8726": [0.25, 0.75, 0, 0],
+        "8727": [-0.03472, 0.46528, 0, 0],
+        "8728": [-0.05555, 0.44445, 0, 0],
+        "8729": [-0.05555, 0.44445, 0, 0],
+        "8730": [0.2, 0.8, 0, 0],
+        "8733": [0, 0.43056, 0, 0],
+        "8734": [0, 0.43056, 0, 0],
+        "8736": [0, 0.69224, 0, 0],
+        "8739": [0.25, 0.75, 0, 0],
+        "8741": [0.25, 0.75, 0, 0],
+        "8743": [0, 0.55556, 0, 0],
+        "8744": [0, 0.55556, 0, 0],
+        "8745": [0, 0.55556, 0, 0],
+        "8746": [0, 0.55556, 0, 0],
+        "8747": [0.19444, 0.69444, 0.11111, 0],
+        "8764": [-0.13313, 0.36687, 0, 0],
+        "8768": [0.19444, 0.69444, 0, 0],
+        "8771": [-0.03625, 0.46375, 0, 0],
+        "8773": [-0.022, 0.589, 0, 0],
+        "8776": [-0.01688, 0.48312, 0, 0],
+        "8781": [-0.03625, 0.46375, 0, 0],
+        "8784": [-0.133, 0.67, 0, 0],
+        "8800": [0.215, 0.716, 0, 0],
+        "8801": [-0.03625, 0.46375, 0, 0],
+        "8804": [0.13597, 0.63597, 0, 0],
+        "8805": [0.13597, 0.63597, 0, 0],
+        "8810": [0.0391, 0.5391, 0, 0],
+        "8811": [0.0391, 0.5391, 0, 0],
+        "8826": [0.0391, 0.5391, 0, 0],
+        "8827": [0.0391, 0.5391, 0, 0],
+        "8834": [0.0391, 0.5391, 0, 0],
+        "8835": [0.0391, 0.5391, 0, 0],
+        "8838": [0.13597, 0.63597, 0, 0],
+        "8839": [0.13597, 0.63597, 0, 0],
+        "8846": [0, 0.55556, 0, 0],
+        "8849": [0.13597, 0.63597, 0, 0],
+        "8850": [0.13597, 0.63597, 0, 0],
+        "8851": [0, 0.55556, 0, 0],
+        "8852": [0, 0.55556, 0, 0],
+        "8853": [0.08333, 0.58333, 0, 0],
+        "8854": [0.08333, 0.58333, 0, 0],
+        "8855": [0.08333, 0.58333, 0, 0],
+        "8856": [0.08333, 0.58333, 0, 0],
+        "8857": [0.08333, 0.58333, 0, 0],
+        "8866": [0, 0.69444, 0, 0],
+        "8867": [0, 0.69444, 0, 0],
+        "8868": [0, 0.69444, 0, 0],
+        "8869": [0, 0.69444, 0, 0],
+        "8872": [0.249, 0.75, 0, 0],
+        "8900": [-0.05555, 0.44445, 0, 0],
+        "8901": [-0.05555, 0.44445, 0, 0],
+        "8902": [-0.03472, 0.46528, 0, 0],
+        "8904": [0.005, 0.505, 0, 0],
+        "8942": [0.03, 0.9, 0, 0],
+        "8943": [-0.19, 0.31, 0, 0],
+        "8945": [-0.1, 0.82, 0, 0],
+        "8968": [0.25, 0.75, 0, 0],
+        "8969": [0.25, 0.75, 0, 0],
+        "8970": [0.25, 0.75, 0, 0],
+        "8971": [0.25, 0.75, 0, 0],
+        "8994": [-0.14236, 0.35764, 0, 0],
+        "8995": [-0.14236, 0.35764, 0, 0],
+        "9136": [0.244, 0.744, 0, 0],
+        "9137": [0.244, 0.744, 0, 0],
+        "9651": [0.19444, 0.69444, 0, 0],
+        "9657": [-0.03472, 0.46528, 0, 0],
+        "9661": [0.19444, 0.69444, 0, 0],
+        "9667": [-0.03472, 0.46528, 0, 0],
+        "9711": [0.19444, 0.69444, 0, 0],
+        "9824": [0.12963, 0.69444, 0, 0],
+        "9825": [0.12963, 0.69444, 0, 0],
+        "9826": [0.12963, 0.69444, 0, 0],
+        "9827": [0.12963, 0.69444, 0, 0],
+        "9837": [0, 0.75, 0, 0],
+        "9838": [0.19444, 0.69444, 0, 0],
+        "9839": [0.19444, 0.69444, 0, 0],
+        "10216": [0.25, 0.75, 0, 0],
+        "10217": [0.25, 0.75, 0, 0],
+        "10222": [0.244, 0.744, 0, 0],
+        "10223": [0.244, 0.744, 0, 0],
+        "10229": [0.011, 0.511, 0, 0],
+        "10230": [0.011, 0.511, 0, 0],
+        "10231": [0.011, 0.511, 0, 0],
+        "10232": [0.024, 0.525, 0, 0],
+        "10233": [0.024, 0.525, 0, 0],
+        "10234": [0.024, 0.525, 0, 0],
+        "10236": [0.011, 0.511, 0, 0],
+        "10815": [0, 0.68333, 0, 0],
+        "10927": [0.13597, 0.63597, 0, 0],
+        "10928": [0.13597, 0.63597, 0, 0]
+    },
+    "Math-BoldItalic": {
+        "47": [0.19444, 0.69444, 0, 0],
+        "65": [0, 0.68611, 0, 0],
+        "66": [0, 0.68611, 0.04835, 0],
+        "67": [0, 0.68611, 0.06979, 0],
+        "68": [0, 0.68611, 0.03194, 0],
+        "69": [0, 0.68611, 0.05451, 0],
+        "70": [0, 0.68611, 0.15972, 0],
+        "71": [0, 0.68611, 0, 0],
+        "72": [0, 0.68611, 0.08229, 0],
+        "73": [0, 0.68611, 0.07778, 0],
+        "74": [0, 0.68611, 0.10069, 0],
+        "75": [0, 0.68611, 0.06979, 0],
+        "76": [0, 0.68611, 0, 0],
+        "77": [0, 0.68611, 0.11424, 0],
+        "78": [0, 0.68611, 0.11424, 0],
+        "79": [0, 0.68611, 0.03194, 0],
+        "80": [0, 0.68611, 0.15972, 0],
+        "81": [0.19444, 0.68611, 0, 0],
+        "82": [0, 0.68611, 0.00421, 0],
+        "83": [0, 0.68611, 0.05382, 0],
+        "84": [0, 0.68611, 0.15972, 0],
+        "85": [0, 0.68611, 0.11424, 0],
+        "86": [0, 0.68611, 0.25555, 0],
+        "87": [0, 0.68611, 0.15972, 0],
+        "88": [0, 0.68611, 0.07778, 0],
+        "89": [0, 0.68611, 0.25555, 0],
+        "90": [0, 0.68611, 0.06979, 0],
+        "97": [0, 0.44444, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.44444, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.44444, 0, 0],
+        "102": [0.19444, 0.69444, 0.11042, 0],
+        "103": [0.19444, 0.44444, 0.03704, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.69326, 0, 0],
+        "106": [0.19444, 0.69326, 0.0622, 0],
+        "107": [0, 0.69444, 0.01852, 0],
+        "108": [0, 0.69444, 0.0088, 0],
+        "109": [0, 0.44444, 0, 0],
+        "110": [0, 0.44444, 0, 0],
+        "111": [0, 0.44444, 0, 0],
+        "112": [0.19444, 0.44444, 0, 0],
+        "113": [0.19444, 0.44444, 0.03704, 0],
+        "114": [0, 0.44444, 0.03194, 0],
+        "115": [0, 0.44444, 0, 0],
+        "116": [0, 0.63492, 0, 0],
+        "117": [0, 0.44444, 0, 0],
+        "118": [0, 0.44444, 0.03704, 0],
+        "119": [0, 0.44444, 0.02778, 0],
+        "120": [0, 0.44444, 0, 0],
+        "121": [0.19444, 0.44444, 0.03704, 0],
+        "122": [0, 0.44444, 0.04213, 0],
+        "915": [0, 0.68611, 0.15972, 0],
+        "916": [0, 0.68611, 0, 0],
+        "920": [0, 0.68611, 0.03194, 0],
+        "923": [0, 0.68611, 0, 0],
+        "926": [0, 0.68611, 0.07458, 0],
+        "928": [0, 0.68611, 0.08229, 0],
+        "931": [0, 0.68611, 0.05451, 0],
+        "933": [0, 0.68611, 0.15972, 0],
+        "934": [0, 0.68611, 0, 0],
+        "936": [0, 0.68611, 0.11653, 0],
+        "937": [0, 0.68611, 0.04835, 0],
+        "945": [0, 0.44444, 0, 0],
+        "946": [0.19444, 0.69444, 0.03403, 0],
+        "947": [0.19444, 0.44444, 0.06389, 0],
+        "948": [0, 0.69444, 0.03819, 0],
+        "949": [0, 0.44444, 0, 0],
+        "950": [0.19444, 0.69444, 0.06215, 0],
+        "951": [0.19444, 0.44444, 0.03704, 0],
+        "952": [0, 0.69444, 0.03194, 0],
+        "953": [0, 0.44444, 0, 0],
+        "954": [0, 0.44444, 0, 0],
+        "955": [0, 0.69444, 0, 0],
+        "956": [0.19444, 0.44444, 0, 0],
+        "957": [0, 0.44444, 0.06898, 0],
+        "958": [0.19444, 0.69444, 0.03021, 0],
+        "959": [0, 0.44444, 0, 0],
+        "960": [0, 0.44444, 0.03704, 0],
+        "961": [0.19444, 0.44444, 0, 0],
+        "962": [0.09722, 0.44444, 0.07917, 0],
+        "963": [0, 0.44444, 0.03704, 0],
+        "964": [0, 0.44444, 0.13472, 0],
+        "965": [0, 0.44444, 0.03704, 0],
+        "966": [0.19444, 0.44444, 0, 0],
+        "967": [0.19444, 0.44444, 0, 0],
+        "968": [0.19444, 0.69444, 0.03704, 0],
+        "969": [0, 0.44444, 0.03704, 0],
+        "977": [0, 0.69444, 0, 0],
+        "981": [0.19444, 0.69444, 0, 0],
+        "982": [0, 0.44444, 0.03194, 0],
+        "1009": [0.19444, 0.44444, 0, 0],
+        "1013": [0, 0.44444, 0, 0]
+    },
+    "Math-Italic": {
+        "47": [0.19444, 0.69444, 0, 0],
+        "65": [0, 0.68333, 0, 0.13889],
+        "66": [0, 0.68333, 0.05017, 0.08334],
+        "67": [0, 0.68333, 0.07153, 0.08334],
+        "68": [0, 0.68333, 0.02778, 0.05556],
+        "69": [0, 0.68333, 0.05764, 0.08334],
+        "70": [0, 0.68333, 0.13889, 0.08334],
+        "71": [0, 0.68333, 0, 0.08334],
+        "72": [0, 0.68333, 0.08125, 0.05556],
+        "73": [0, 0.68333, 0.07847, 0.11111],
+        "74": [0, 0.68333, 0.09618, 0.16667],
+        "75": [0, 0.68333, 0.07153, 0.05556],
+        "76": [0, 0.68333, 0, 0.02778],
+        "77": [0, 0.68333, 0.10903, 0.08334],
+        "78": [0, 0.68333, 0.10903, 0.08334],
+        "79": [0, 0.68333, 0.02778, 0.08334],
+        "80": [0, 0.68333, 0.13889, 0.08334],
+        "81": [0.19444, 0.68333, 0, 0.08334],
+        "82": [0, 0.68333, 0.00773, 0.08334],
+        "83": [0, 0.68333, 0.05764, 0.08334],
+        "84": [0, 0.68333, 0.13889, 0.08334],
+        "85": [0, 0.68333, 0.10903, 0.02778],
+        "86": [0, 0.68333, 0.22222, 0],
+        "87": [0, 0.68333, 0.13889, 0],
+        "88": [0, 0.68333, 0.07847, 0.08334],
+        "89": [0, 0.68333, 0.22222, 0],
+        "90": [0, 0.68333, 0.07153, 0.08334],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.43056, 0, 0.05556],
+        "100": [0, 0.69444, 0, 0.16667],
+        "101": [0, 0.43056, 0, 0.05556],
+        "102": [0.19444, 0.69444, 0.10764, 0.16667],
+        "103": [0.19444, 0.43056, 0.03588, 0.02778],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.65952, 0, 0],
+        "106": [0.19444, 0.65952, 0.05724, 0],
+        "107": [0, 0.69444, 0.03148, 0],
+        "108": [0, 0.69444, 0.01968, 0.08334],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0.05556],
+        "112": [0.19444, 0.43056, 0, 0.08334],
+        "113": [0.19444, 0.43056, 0.03588, 0.08334],
+        "114": [0, 0.43056, 0.02778, 0.05556],
+        "115": [0, 0.43056, 0, 0.05556],
+        "116": [0, 0.61508, 0, 0.08334],
+        "117": [0, 0.43056, 0, 0.02778],
+        "118": [0, 0.43056, 0.03588, 0.02778],
+        "119": [0, 0.43056, 0.02691, 0.08334],
+        "120": [0, 0.43056, 0, 0.02778],
+        "121": [0.19444, 0.43056, 0.03588, 0.05556],
+        "122": [0, 0.43056, 0.04398, 0.05556],
+        "915": [0, 0.68333, 0.13889, 0.08334],
+        "916": [0, 0.68333, 0, 0.16667],
+        "920": [0, 0.68333, 0.02778, 0.08334],
+        "923": [0, 0.68333, 0, 0.16667],
+        "926": [0, 0.68333, 0.07569, 0.08334],
+        "928": [0, 0.68333, 0.08125, 0.05556],
+        "931": [0, 0.68333, 0.05764, 0.08334],
+        "933": [0, 0.68333, 0.13889, 0.05556],
+        "934": [0, 0.68333, 0, 0.08334],
+        "936": [0, 0.68333, 0.11, 0.05556],
+        "937": [0, 0.68333, 0.05017, 0.08334],
+        "945": [0, 0.43056, 0.0037, 0.02778],
+        "946": [0.19444, 0.69444, 0.05278, 0.08334],
+        "947": [0.19444, 0.43056, 0.05556, 0],
+        "948": [0, 0.69444, 0.03785, 0.05556],
+        "949": [0, 0.43056, 0, 0.08334],
+        "950": [0.19444, 0.69444, 0.07378, 0.08334],
+        "951": [0.19444, 0.43056, 0.03588, 0.05556],
+        "952": [0, 0.69444, 0.02778, 0.08334],
+        "953": [0, 0.43056, 0, 0.05556],
+        "954": [0, 0.43056, 0, 0],
+        "955": [0, 0.69444, 0, 0],
+        "956": [0.19444, 0.43056, 0, 0.02778],
+        "957": [0, 0.43056, 0.06366, 0.02778],
+        "958": [0.19444, 0.69444, 0.04601, 0.11111],
+        "959": [0, 0.43056, 0, 0.05556],
+        "960": [0, 0.43056, 0.03588, 0],
+        "961": [0.19444, 0.43056, 0, 0.08334],
+        "962": [0.09722, 0.43056, 0.07986, 0.08334],
+        "963": [0, 0.43056, 0.03588, 0],
+        "964": [0, 0.43056, 0.1132, 0.02778],
+        "965": [0, 0.43056, 0.03588, 0.02778],
+        "966": [0.19444, 0.43056, 0, 0.08334],
+        "967": [0.19444, 0.43056, 0, 0.05556],
+        "968": [0.19444, 0.69444, 0.03588, 0.11111],
+        "969": [0, 0.43056, 0.03588, 0],
+        "977": [0, 0.69444, 0, 0.08334],
+        "981": [0.19444, 0.69444, 0, 0.08334],
+        "982": [0, 0.43056, 0.02778, 0],
+        "1009": [0.19444, 0.43056, 0, 0.08334],
+        "1013": [0, 0.43056, 0, 0.05556]
+    },
+    "Math-Regular": {
+        "65": [0, 0.68333, 0, 0.13889],
+        "66": [0, 0.68333, 0.05017, 0.08334],
+        "67": [0, 0.68333, 0.07153, 0.08334],
+        "68": [0, 0.68333, 0.02778, 0.05556],
+        "69": [0, 0.68333, 0.05764, 0.08334],
+        "70": [0, 0.68333, 0.13889, 0.08334],
+        "71": [0, 0.68333, 0, 0.08334],
+        "72": [0, 0.68333, 0.08125, 0.05556],
+        "73": [0, 0.68333, 0.07847, 0.11111],
+        "74": [0, 0.68333, 0.09618, 0.16667],
+        "75": [0, 0.68333, 0.07153, 0.05556],
+        "76": [0, 0.68333, 0, 0.02778],
+        "77": [0, 0.68333, 0.10903, 0.08334],
+        "78": [0, 0.68333, 0.10903, 0.08334],
+        "79": [0, 0.68333, 0.02778, 0.08334],
+        "80": [0, 0.68333, 0.13889, 0.08334],
+        "81": [0.19444, 0.68333, 0, 0.08334],
+        "82": [0, 0.68333, 0.00773, 0.08334],
+        "83": [0, 0.68333, 0.05764, 0.08334],
+        "84": [0, 0.68333, 0.13889, 0.08334],
+        "85": [0, 0.68333, 0.10903, 0.02778],
+        "86": [0, 0.68333, 0.22222, 0],
+        "87": [0, 0.68333, 0.13889, 0],
+        "88": [0, 0.68333, 0.07847, 0.08334],
+        "89": [0, 0.68333, 0.22222, 0],
+        "90": [0, 0.68333, 0.07153, 0.08334],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.43056, 0, 0.05556],
+        "100": [0, 0.69444, 0, 0.16667],
+        "101": [0, 0.43056, 0, 0.05556],
+        "102": [0.19444, 0.69444, 0.10764, 0.16667],
+        "103": [0.19444, 0.43056, 0.03588, 0.02778],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.65952, 0, 0],
+        "106": [0.19444, 0.65952, 0.05724, 0],
+        "107": [0, 0.69444, 0.03148, 0],
+        "108": [0, 0.69444, 0.01968, 0.08334],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0.05556],
+        "112": [0.19444, 0.43056, 0, 0.08334],
+        "113": [0.19444, 0.43056, 0.03588, 0.08334],
+        "114": [0, 0.43056, 0.02778, 0.05556],
+        "115": [0, 0.43056, 0, 0.05556],
+        "116": [0, 0.61508, 0, 0.08334],
+        "117": [0, 0.43056, 0, 0.02778],
+        "118": [0, 0.43056, 0.03588, 0.02778],
+        "119": [0, 0.43056, 0.02691, 0.08334],
+        "120": [0, 0.43056, 0, 0.02778],
+        "121": [0.19444, 0.43056, 0.03588, 0.05556],
+        "122": [0, 0.43056, 0.04398, 0.05556],
+        "915": [0, 0.68333, 0.13889, 0.08334],
+        "916": [0, 0.68333, 0, 0.16667],
+        "920": [0, 0.68333, 0.02778, 0.08334],
+        "923": [0, 0.68333, 0, 0.16667],
+        "926": [0, 0.68333, 0.07569, 0.08334],
+        "928": [0, 0.68333, 0.08125, 0.05556],
+        "931": [0, 0.68333, 0.05764, 0.08334],
+        "933": [0, 0.68333, 0.13889, 0.05556],
+        "934": [0, 0.68333, 0, 0.08334],
+        "936": [0, 0.68333, 0.11, 0.05556],
+        "937": [0, 0.68333, 0.05017, 0.08334],
+        "945": [0, 0.43056, 0.0037, 0.02778],
+        "946": [0.19444, 0.69444, 0.05278, 0.08334],
+        "947": [0.19444, 0.43056, 0.05556, 0],
+        "948": [0, 0.69444, 0.03785, 0.05556],
+        "949": [0, 0.43056, 0, 0.08334],
+        "950": [0.19444, 0.69444, 0.07378, 0.08334],
+        "951": [0.19444, 0.43056, 0.03588, 0.05556],
+        "952": [0, 0.69444, 0.02778, 0.08334],
+        "953": [0, 0.43056, 0, 0.05556],
+        "954": [0, 0.43056, 0, 0],
+        "955": [0, 0.69444, 0, 0],
+        "956": [0.19444, 0.43056, 0, 0.02778],
+        "957": [0, 0.43056, 0.06366, 0.02778],
+        "958": [0.19444, 0.69444, 0.04601, 0.11111],
+        "959": [0, 0.43056, 0, 0.05556],
+        "960": [0, 0.43056, 0.03588, 0],
+        "961": [0.19444, 0.43056, 0, 0.08334],
+        "962": [0.09722, 0.43056, 0.07986, 0.08334],
+        "963": [0, 0.43056, 0.03588, 0],
+        "964": [0, 0.43056, 0.1132, 0.02778],
+        "965": [0, 0.43056, 0.03588, 0.02778],
+        "966": [0.19444, 0.43056, 0, 0.08334],
+        "967": [0.19444, 0.43056, 0, 0.05556],
+        "968": [0.19444, 0.69444, 0.03588, 0.11111],
+        "969": [0, 0.43056, 0.03588, 0],
+        "977": [0, 0.69444, 0, 0.08334],
+        "981": [0.19444, 0.69444, 0, 0.08334],
+        "982": [0, 0.43056, 0.02778, 0],
+        "1009": [0.19444, 0.43056, 0, 0.08334],
+        "1013": [0, 0.43056, 0, 0.05556]
+    },
+    "SansSerif-Regular": {
+        "33": [0, 0.69444, 0, 0],
+        "34": [0, 0.69444, 0, 0],
+        "35": [0.19444, 0.69444, 0, 0],
+        "36": [0.05556, 0.75, 0, 0],
+        "37": [0.05556, 0.75, 0, 0],
+        "38": [0, 0.69444, 0, 0],
+        "39": [0, 0.69444, 0, 0],
+        "40": [0.25, 0.75, 0, 0],
+        "41": [0.25, 0.75, 0, 0],
+        "42": [0, 0.75, 0, 0],
+        "43": [0.08333, 0.58333, 0, 0],
+        "44": [0.125, 0.08333, 0, 0],
+        "45": [0, 0.44444, 0, 0],
+        "46": [0, 0.08333, 0, 0],
+        "47": [0.25, 0.75, 0, 0],
+        "48": [0, 0.65556, 0, 0],
+        "49": [0, 0.65556, 0, 0],
+        "50": [0, 0.65556, 0, 0],
+        "51": [0, 0.65556, 0, 0],
+        "52": [0, 0.65556, 0, 0],
+        "53": [0, 0.65556, 0, 0],
+        "54": [0, 0.65556, 0, 0],
+        "55": [0, 0.65556, 0, 0],
+        "56": [0, 0.65556, 0, 0],
+        "57": [0, 0.65556, 0, 0],
+        "58": [0, 0.44444, 0, 0],
+        "59": [0.125, 0.44444, 0, 0],
+        "61": [-0.13, 0.37, 0, 0],
+        "63": [0, 0.69444, 0, 0],
+        "64": [0, 0.69444, 0, 0],
+        "65": [0, 0.69444, 0, 0],
+        "66": [0, 0.69444, 0, 0],
+        "67": [0, 0.69444, 0, 0],
+        "68": [0, 0.69444, 0, 0],
+        "69": [0, 0.69444, 0, 0],
+        "70": [0, 0.69444, 0, 0],
+        "71": [0, 0.69444, 0, 0],
+        "72": [0, 0.69444, 0, 0],
+        "73": [0, 0.69444, 0, 0],
+        "74": [0, 0.69444, 0, 0],
+        "75": [0, 0.69444, 0, 0],
+        "76": [0, 0.69444, 0, 0],
+        "77": [0, 0.69444, 0, 0],
+        "78": [0, 0.69444, 0, 0],
+        "79": [0, 0.69444, 0, 0],
+        "80": [0, 0.69444, 0, 0],
+        "81": [0.125, 0.69444, 0, 0],
+        "82": [0, 0.69444, 0, 0],
+        "83": [0, 0.69444, 0, 0],
+        "84": [0, 0.69444, 0, 0],
+        "85": [0, 0.69444, 0, 0],
+        "86": [0, 0.69444, 0.01389, 0],
+        "87": [0, 0.69444, 0.01389, 0],
+        "88": [0, 0.69444, 0, 0],
+        "89": [0, 0.69444, 0.025, 0],
+        "90": [0, 0.69444, 0, 0],
+        "91": [0.25, 0.75, 0, 0],
+        "93": [0.25, 0.75, 0, 0],
+        "94": [0, 0.69444, 0, 0],
+        "95": [0.35, 0.09444, 0.02778, 0],
+        "97": [0, 0.44444, 0, 0],
+        "98": [0, 0.69444, 0, 0],
+        "99": [0, 0.44444, 0, 0],
+        "100": [0, 0.69444, 0, 0],
+        "101": [0, 0.44444, 0, 0],
+        "102": [0, 0.69444, 0.06944, 0],
+        "103": [0.19444, 0.44444, 0.01389, 0],
+        "104": [0, 0.69444, 0, 0],
+        "105": [0, 0.67937, 0, 0],
+        "106": [0.19444, 0.67937, 0, 0],
+        "107": [0, 0.69444, 0, 0],
+        "108": [0, 0.69444, 0, 0],
+        "109": [0, 0.44444, 0, 0],
+        "110": [0, 0.44444, 0, 0],
+        "111": [0, 0.44444, 0, 0],
+        "112": [0.19444, 0.44444, 0, 0],
+        "113": [0.19444, 0.44444, 0, 0],
+        "114": [0, 0.44444, 0.01389, 0],
+        "115": [0, 0.44444, 0, 0],
+        "116": [0, 0.57143, 0, 0],
+        "117": [0, 0.44444, 0, 0],
+        "118": [0, 0.44444, 0.01389, 0],
+        "119": [0, 0.44444, 0.01389, 0],
+        "120": [0, 0.44444, 0, 0],
+        "121": [0.19444, 0.44444, 0.01389, 0],
+        "122": [0, 0.44444, 0, 0],
+        "126": [0.35, 0.32659, 0, 0],
+        "305": [0, 0.44444, 0, 0],
+        "567": [0.19444, 0.44444, 0, 0],
+        "768": [0, 0.69444, 0, 0],
+        "769": [0, 0.69444, 0, 0],
+        "770": [0, 0.69444, 0, 0],
+        "771": [0, 0.67659, 0, 0],
+        "772": [0, 0.60889, 0, 0],
+        "774": [0, 0.69444, 0, 0],
+        "775": [0, 0.67937, 0, 0],
+        "776": [0, 0.67937, 0, 0],
+        "778": [0, 0.69444, 0, 0],
+        "779": [0, 0.69444, 0, 0],
+        "780": [0, 0.63194, 0, 0],
+        "915": [0, 0.69444, 0, 0],
+        "916": [0, 0.69444, 0, 0],
+        "920": [0, 0.69444, 0, 0],
+        "923": [0, 0.69444, 0, 0],
+        "926": [0, 0.69444, 0, 0],
+        "928": [0, 0.69444, 0, 0],
+        "931": [0, 0.69444, 0, 0],
+        "933": [0, 0.69444, 0, 0],
+        "934": [0, 0.69444, 0, 0],
+        "936": [0, 0.69444, 0, 0],
+        "937": [0, 0.69444, 0, 0],
+        "8211": [0, 0.44444, 0.02778, 0],
+        "8212": [0, 0.44444, 0.02778, 0],
+        "8216": [0, 0.69444, 0, 0],
+        "8217": [0, 0.69444, 0, 0],
+        "8220": [0, 0.69444, 0, 0],
+        "8221": [0, 0.69444, 0, 0]
+    },
+    "Script-Regular": {
+        "65": [0, 0.7, 0.22925, 0],
+        "66": [0, 0.7, 0.04087, 0],
+        "67": [0, 0.7, 0.1689, 0],
+        "68": [0, 0.7, 0.09371, 0],
+        "69": [0, 0.7, 0.18583, 0],
+        "70": [0, 0.7, 0.13634, 0],
+        "71": [0, 0.7, 0.17322, 0],
+        "72": [0, 0.7, 0.29694, 0],
+        "73": [0, 0.7, 0.19189, 0],
+        "74": [0.27778, 0.7, 0.19189, 0],
+        "75": [0, 0.7, 0.31259, 0],
+        "76": [0, 0.7, 0.19189, 0],
+        "77": [0, 0.7, 0.15981, 0],
+        "78": [0, 0.7, 0.3525, 0],
+        "79": [0, 0.7, 0.08078, 0],
+        "80": [0, 0.7, 0.08078, 0],
+        "81": [0, 0.7, 0.03305, 0],
+        "82": [0, 0.7, 0.06259, 0],
+        "83": [0, 0.7, 0.19189, 0],
+        "84": [0, 0.7, 0.29087, 0],
+        "85": [0, 0.7, 0.25815, 0],
+        "86": [0, 0.7, 0.27523, 0],
+        "87": [0, 0.7, 0.27523, 0],
+        "88": [0, 0.7, 0.26006, 0],
+        "89": [0, 0.7, 0.2939, 0],
+        "90": [0, 0.7, 0.24037, 0]
+    },
+    "Size1-Regular": {
+        "40": [0.35001, 0.85, 0, 0],
+        "41": [0.35001, 0.85, 0, 0],
+        "47": [0.35001, 0.85, 0, 0],
+        "91": [0.35001, 0.85, 0, 0],
+        "92": [0.35001, 0.85, 0, 0],
+        "93": [0.35001, 0.85, 0, 0],
+        "123": [0.35001, 0.85, 0, 0],
+        "125": [0.35001, 0.85, 0, 0],
+        "710": [0, 0.72222, 0, 0],
+        "732": [0, 0.72222, 0, 0],
+        "770": [0, 0.72222, 0, 0],
+        "771": [0, 0.72222, 0, 0],
+        "8214": [-0.00099, 0.601, 0, 0],
+        "8593": [1e-05, 0.6, 0, 0],
+        "8595": [1e-05, 0.6, 0, 0],
+        "8657": [1e-05, 0.6, 0, 0],
+        "8659": [1e-05, 0.6, 0, 0],
+        "8719": [0.25001, 0.75, 0, 0],
+        "8720": [0.25001, 0.75, 0, 0],
+        "8721": [0.25001, 0.75, 0, 0],
+        "8730": [0.35001, 0.85, 0, 0],
+        "8739": [-0.00599, 0.606, 0, 0],
+        "8741": [-0.00599, 0.606, 0, 0],
+        "8747": [0.30612, 0.805, 0.19445, 0],
+        "8748": [0.306, 0.805, 0.19445, 0],
+        "8749": [0.306, 0.805, 0.19445, 0],
+        "8750": [0.30612, 0.805, 0.19445, 0],
+        "8896": [0.25001, 0.75, 0, 0],
+        "8897": [0.25001, 0.75, 0, 0],
+        "8898": [0.25001, 0.75, 0, 0],
+        "8899": [0.25001, 0.75, 0, 0],
+        "8968": [0.35001, 0.85, 0, 0],
+        "8969": [0.35001, 0.85, 0, 0],
+        "8970": [0.35001, 0.85, 0, 0],
+        "8971": [0.35001, 0.85, 0, 0],
+        "9168": [-0.00099, 0.601, 0, 0],
+        "10216": [0.35001, 0.85, 0, 0],
+        "10217": [0.35001, 0.85, 0, 0],
+        "10752": [0.25001, 0.75, 0, 0],
+        "10753": [0.25001, 0.75, 0, 0],
+        "10754": [0.25001, 0.75, 0, 0],
+        "10756": [0.25001, 0.75, 0, 0],
+        "10758": [0.25001, 0.75, 0, 0]
+    },
+    "Size2-Regular": {
+        "40": [0.65002, 1.15, 0, 0],
+        "41": [0.65002, 1.15, 0, 0],
+        "47": [0.65002, 1.15, 0, 0],
+        "91": [0.65002, 1.15, 0, 0],
+        "92": [0.65002, 1.15, 0, 0],
+        "93": [0.65002, 1.15, 0, 0],
+        "123": [0.65002, 1.15, 0, 0],
+        "125": [0.65002, 1.15, 0, 0],
+        "710": [0, 0.75, 0, 0],
+        "732": [0, 0.75, 0, 0],
+        "770": [0, 0.75, 0, 0],
+        "771": [0, 0.75, 0, 0],
+        "8719": [0.55001, 1.05, 0, 0],
+        "8720": [0.55001, 1.05, 0, 0],
+        "8721": [0.55001, 1.05, 0, 0],
+        "8730": [0.65002, 1.15, 0, 0],
+        "8747": [0.86225, 1.36, 0.44445, 0],
+        "8748": [0.862, 1.36, 0.44445, 0],
+        "8749": [0.862, 1.36, 0.44445, 0],
+        "8750": [0.86225, 1.36, 0.44445, 0],
+        "8896": [0.55001, 1.05, 0, 0],
+        "8897": [0.55001, 1.05, 0, 0],
+        "8898": [0.55001, 1.05, 0, 0],
+        "8899": [0.55001, 1.05, 0, 0],
+        "8968": [0.65002, 1.15, 0, 0],
+        "8969": [0.65002, 1.15, 0, 0],
+        "8970": [0.65002, 1.15, 0, 0],
+        "8971": [0.65002, 1.15, 0, 0],
+        "10216": [0.65002, 1.15, 0, 0],
+        "10217": [0.65002, 1.15, 0, 0],
+        "10752": [0.55001, 1.05, 0, 0],
+        "10753": [0.55001, 1.05, 0, 0],
+        "10754": [0.55001, 1.05, 0, 0],
+        "10756": [0.55001, 1.05, 0, 0],
+        "10758": [0.55001, 1.05, 0, 0]
+    },
+    "Size3-Regular": {
+        "40": [0.95003, 1.45, 0, 0],
+        "41": [0.95003, 1.45, 0, 0],
+        "47": [0.95003, 1.45, 0, 0],
+        "91": [0.95003, 1.45, 0, 0],
+        "92": [0.95003, 1.45, 0, 0],
+        "93": [0.95003, 1.45, 0, 0],
+        "123": [0.95003, 1.45, 0, 0],
+        "125": [0.95003, 1.45, 0, 0],
+        "710": [0, 0.75, 0, 0],
+        "732": [0, 0.75, 0, 0],
+        "770": [0, 0.75, 0, 0],
+        "771": [0, 0.75, 0, 0],
+        "8730": [0.95003, 1.45, 0, 0],
+        "8968": [0.95003, 1.45, 0, 0],
+        "8969": [0.95003, 1.45, 0, 0],
+        "8970": [0.95003, 1.45, 0, 0],
+        "8971": [0.95003, 1.45, 0, 0],
+        "10216": [0.95003, 1.45, 0, 0],
+        "10217": [0.95003, 1.45, 0, 0]
+    },
+    "Size4-Regular": {
+        "40": [1.25003, 1.75, 0, 0],
+        "41": [1.25003, 1.75, 0, 0],
+        "47": [1.25003, 1.75, 0, 0],
+        "91": [1.25003, 1.75, 0, 0],
+        "92": [1.25003, 1.75, 0, 0],
+        "93": [1.25003, 1.75, 0, 0],
+        "123": [1.25003, 1.75, 0, 0],
+        "125": [1.25003, 1.75, 0, 0],
+        "710": [0, 0.825, 0, 0],
+        "732": [0, 0.825, 0, 0],
+        "770": [0, 0.825, 0, 0],
+        "771": [0, 0.825, 0, 0],
+        "8730": [1.25003, 1.75, 0, 0],
+        "8968": [1.25003, 1.75, 0, 0],
+        "8969": [1.25003, 1.75, 0, 0],
+        "8970": [1.25003, 1.75, 0, 0],
+        "8971": [1.25003, 1.75, 0, 0],
+        "9115": [0.64502, 1.155, 0, 0],
+        "9116": [1e-05, 0.6, 0, 0],
+        "9117": [0.64502, 1.155, 0, 0],
+        "9118": [0.64502, 1.155, 0, 0],
+        "9119": [1e-05, 0.6, 0, 0],
+        "9120": [0.64502, 1.155, 0, 0],
+        "9121": [0.64502, 1.155, 0, 0],
+        "9122": [-0.00099, 0.601, 0, 0],
+        "9123": [0.64502, 1.155, 0, 0],
+        "9124": [0.64502, 1.155, 0, 0],
+        "9125": [-0.00099, 0.601, 0, 0],
+        "9126": [0.64502, 1.155, 0, 0],
+        "9127": [1e-05, 0.9, 0, 0],
+        "9128": [0.65002, 1.15, 0, 0],
+        "9129": [0.90001, 0, 0, 0],
+        "9130": [0, 0.3, 0, 0],
+        "9131": [1e-05, 0.9, 0, 0],
+        "9132": [0.65002, 1.15, 0, 0],
+        "9133": [0.90001, 0, 0, 0],
+        "9143": [0.88502, 0.915, 0, 0],
+        "10216": [1.25003, 1.75, 0, 0],
+        "10217": [1.25003, 1.75, 0, 0],
+        "57344": [-0.00499, 0.605, 0, 0],
+        "57345": [-0.00499, 0.605, 0, 0],
+        "57680": [0, 0.12, 0, 0],
+        "57681": [0, 0.12, 0, 0],
+        "57682": [0, 0.12, 0, 0],
+        "57683": [0, 0.12, 0, 0]
+    },
+    "Typewriter-Regular": {
+        "33": [0, 0.61111, 0, 0],
+        "34": [0, 0.61111, 0, 0],
+        "35": [0, 0.61111, 0, 0],
+        "36": [0.08333, 0.69444, 0, 0],
+        "37": [0.08333, 0.69444, 0, 0],
+        "38": [0, 0.61111, 0, 0],
+        "39": [0, 0.61111, 0, 0],
+        "40": [0.08333, 0.69444, 0, 0],
+        "41": [0.08333, 0.69444, 0, 0],
+        "42": [0, 0.52083, 0, 0],
+        "43": [-0.08056, 0.53055, 0, 0],
+        "44": [0.13889, 0.125, 0, 0],
+        "45": [-0.08056, 0.53055, 0, 0],
+        "46": [0, 0.125, 0, 0],
+        "47": [0.08333, 0.69444, 0, 0],
+        "48": [0, 0.61111, 0, 0],
+        "49": [0, 0.61111, 0, 0],
+        "50": [0, 0.61111, 0, 0],
+        "51": [0, 0.61111, 0, 0],
+        "52": [0, 0.61111, 0, 0],
+        "53": [0, 0.61111, 0, 0],
+        "54": [0, 0.61111, 0, 0],
+        "55": [0, 0.61111, 0, 0],
+        "56": [0, 0.61111, 0, 0],
+        "57": [0, 0.61111, 0, 0],
+        "58": [0, 0.43056, 0, 0],
+        "59": [0.13889, 0.43056, 0, 0],
+        "60": [-0.05556, 0.55556, 0, 0],
+        "61": [-0.19549, 0.41562, 0, 0],
+        "62": [-0.05556, 0.55556, 0, 0],
+        "63": [0, 0.61111, 0, 0],
+        "64": [0, 0.61111, 0, 0],
+        "65": [0, 0.61111, 0, 0],
+        "66": [0, 0.61111, 0, 0],
+        "67": [0, 0.61111, 0, 0],
+        "68": [0, 0.61111, 0, 0],
+        "69": [0, 0.61111, 0, 0],
+        "70": [0, 0.61111, 0, 0],
+        "71": [0, 0.61111, 0, 0],
+        "72": [0, 0.61111, 0, 0],
+        "73": [0, 0.61111, 0, 0],
+        "74": [0, 0.61111, 0, 0],
+        "75": [0, 0.61111, 0, 0],
+        "76": [0, 0.61111, 0, 0],
+        "77": [0, 0.61111, 0, 0],
+        "78": [0, 0.61111, 0, 0],
+        "79": [0, 0.61111, 0, 0],
+        "80": [0, 0.61111, 0, 0],
+        "81": [0.13889, 0.61111, 0, 0],
+        "82": [0, 0.61111, 0, 0],
+        "83": [0, 0.61111, 0, 0],
+        "84": [0, 0.61111, 0, 0],
+        "85": [0, 0.61111, 0, 0],
+        "86": [0, 0.61111, 0, 0],
+        "87": [0, 0.61111, 0, 0],
+        "88": [0, 0.61111, 0, 0],
+        "89": [0, 0.61111, 0, 0],
+        "90": [0, 0.61111, 0, 0],
+        "91": [0.08333, 0.69444, 0, 0],
+        "92": [0.08333, 0.69444, 0, 0],
+        "93": [0.08333, 0.69444, 0, 0],
+        "94": [0, 0.61111, 0, 0],
+        "95": [0.09514, 0, 0, 0],
+        "96": [0, 0.61111, 0, 0],
+        "97": [0, 0.43056, 0, 0],
+        "98": [0, 0.61111, 0, 0],
+        "99": [0, 0.43056, 0, 0],
+        "100": [0, 0.61111, 0, 0],
+        "101": [0, 0.43056, 0, 0],
+        "102": [0, 0.61111, 0, 0],
+        "103": [0.22222, 0.43056, 0, 0],
+        "104": [0, 0.61111, 0, 0],
+        "105": [0, 0.61111, 0, 0],
+        "106": [0.22222, 0.61111, 0, 0],
+        "107": [0, 0.61111, 0, 0],
+        "108": [0, 0.61111, 0, 0],
+        "109": [0, 0.43056, 0, 0],
+        "110": [0, 0.43056, 0, 0],
+        "111": [0, 0.43056, 0, 0],
+        "112": [0.22222, 0.43056, 0, 0],
+        "113": [0.22222, 0.43056, 0, 0],
+        "114": [0, 0.43056, 0, 0],
+        "115": [0, 0.43056, 0, 0],
+        "116": [0, 0.55358, 0, 0],
+        "117": [0, 0.43056, 0, 0],
+        "118": [0, 0.43056, 0, 0],
+        "119": [0, 0.43056, 0, 0],
+        "120": [0, 0.43056, 0, 0],
+        "121": [0.22222, 0.43056, 0, 0],
+        "122": [0, 0.43056, 0, 0],
+        "123": [0.08333, 0.69444, 0, 0],
+        "124": [0.08333, 0.69444, 0, 0],
+        "125": [0.08333, 0.69444, 0, 0],
+        "126": [0, 0.61111, 0, 0],
+        "127": [0, 0.61111, 0, 0],
+        "305": [0, 0.43056, 0, 0],
+        "567": [0.22222, 0.43056, 0, 0],
+        "768": [0, 0.61111, 0, 0],
+        "769": [0, 0.61111, 0, 0],
+        "770": [0, 0.61111, 0, 0],
+        "771": [0, 0.61111, 0, 0],
+        "772": [0, 0.56555, 0, 0],
+        "774": [0, 0.61111, 0, 0],
+        "776": [0, 0.61111, 0, 0],
+        "778": [0, 0.61111, 0, 0],
+        "780": [0, 0.56597, 0, 0],
+        "915": [0, 0.61111, 0, 0],
+        "916": [0, 0.61111, 0, 0],
+        "920": [0, 0.61111, 0, 0],
+        "923": [0, 0.61111, 0, 0],
+        "926": [0, 0.61111, 0, 0],
+        "928": [0, 0.61111, 0, 0],
+        "931": [0, 0.61111, 0, 0],
+        "933": [0, 0.61111, 0, 0],
+        "934": [0, 0.61111, 0, 0],
+        "936": [0, 0.61111, 0, 0],
+        "937": [0, 0.61111, 0, 0],
+        "2018": [0, 0.61111, 0, 0],
+        "2019": [0, 0.61111, 0, 0],
+        "8242": [0, 0.61111, 0, 0]
+    }
+};
+
+},{}],19:[function(require,module,exports){
+var utils = require("./utils");
+var ParseError = require("./ParseError");
+var parseData = require("./parseData");
+var ParseNode = parseData.ParseNode;
+
+/* This file contains a list of functions that we parse, identified by
+ * the calls to defineFunction.
+ *
+ * The first argument to defineFunction is a single name or a list of names.
+ * All functions named in such a list will share a single implementation.
+ *
+ * Each declared function can have associated properties, which
+ * include the following:
+ *
+ *  - numArgs: The number of arguments the function takes.
+ *             If this is the only property, it can be passed as a number
+ *             instead of an element of a properties object.
+ *  - argTypes: (optional) An array corresponding to each argument of the
+ *              function, giving the type of argument that should be parsed. Its
+ *              length should be equal to `numArgs + numOptionalArgs`. Valid
+ *              types:
+ *               - "size": A size-like thing, such as "1em" or "5ex"
+ *               - "color": An html color, like "#abc" or "blue"
+ *               - "original": The same type as the environment that the
+ *                             function being parsed is in (e.g. used for the
+ *                             bodies of functions like \color where the first
+ *                             argument is special and the second argument is
+ *                             parsed normally)
+ *              Other possible types (probably shouldn't be used)
+ *               - "text": Text-like (e.g. \text)
+ *               - "math": Normal math
+ *              If undefined, this will be treated as an appropriate length
+ *              array of "original" strings
+ *  - greediness: (optional) The greediness of the function to use ungrouped
+ *                arguments.
+ *
+ *                E.g. if you have an expression
+ *                  \sqrt \frac 1 2
+ *                since \frac has greediness=2 vs \sqrt's greediness=1, \frac
+ *                will use the two arguments '1' and '2' as its two arguments,
+ *                then that whole function will be used as the argument to
+ *                \sqrt. On the other hand, the expressions
+ *                  \frac \frac 1 2 3
+ *                and
+ *                  \frac \sqrt 1 2
+ *                will fail because \frac and \frac have equal greediness
+ *                and \sqrt has a lower greediness than \frac respectively. To
+ *                make these parse, we would have to change them to:
+ *                  \frac {\frac 1 2} 3
+ *                and
+ *                  \frac {\sqrt 1} 2
+ *
+ *                The default value is `1`
+ *  - allowedInText: (optional) Whether or not the function is allowed inside
+ *                   text mode (default false)
+ *  - numOptionalArgs: (optional) The number of optional arguments the function
+ *                     should parse. If the optional arguments aren't found,
+ *                     `null` will be passed to the handler in their place.
+ *                     (default 0)
+ *  - infix: (optional) Must be true if the function is an infix operator.
+ *
+ * The last argument is that implementation, the handler for the function(s).
+ * It is called to handle these functions and their arguments.
+ * It receives two arguments:
+ *  - context contains information and references provided by the parser
+ *  - args is an array of arguments obtained from TeX input
+ * The context contains the following properties:
+ *  - funcName: the text (i.e. name) of the function, including \
+ *  - parser: the parser object
+ *  - lexer: the lexer object
+ *  - positions: the positions in the overall string of the function
+ *               and the arguments.
+ * The latter three should only be used to produce error messages.
+ *
+ * The function should return an object with the following keys:
+ *  - type: The type of element that this is. This is then used in
+ *          buildHTML/buildMathML to determine which function
+ *          should be called to build this node into a DOM node
+ * Any other data can be added to the object, which will be passed
+ * in to the function in buildHTML/buildMathML as `group.value`.
+ */
+
+function defineFunction(names, props, handler) {
+    if (typeof names === "string") {
+        names = [names];
+    }
+    if (typeof props === "number") {
+        props = { numArgs: props };
+    }
+    // Set default values of functions
+    var data = {
+        numArgs: props.numArgs,
+        argTypes: props.argTypes,
+        greediness: (props.greediness === undefined) ? 1 : props.greediness,
+        allowedInText: !!props.allowedInText,
+        numOptionalArgs: props.numOptionalArgs || 0,
+        infix: !!props.infix,
+        handler: handler
+    };
+    for (var i = 0; i < names.length; ++i) {
+        module.exports[names[i]] = data;
+    }
+}
+
+// Since the corresponding buildHTML/buildMathML function expects a
+// list of elements, we normalize for different kinds of arguments
+var ordargument = function(arg) {
+    if (arg.type === "ordgroup") {
+        return arg.value;
+    } else {
+        return [arg];
+    }
+};
+
+// A normal square root
+defineFunction("\\sqrt", {
+    numArgs: 1,
+    numOptionalArgs: 1
+}, function(context, args) {
+    var index = args[0];
+    var body = args[1];
+    return {
+        type: "sqrt",
+        body: body,
+        index: index
+    };
+});
+
+// Non-mathy text, possibly in a font
+var textFunctionStyles = {
+    "\\text": undefined, "\\textrm": "mathrm", "\\textsf": "mathsf",
+    "\\texttt": "mathtt", "\\textnormal": "mathrm", "\\textbf": "mathbf",
+    "\\textit": "textit"
+};
+
+defineFunction([
+    "\\text", "\\textrm", "\\textsf", "\\texttt", "\\textnormal",
+    "\\textbf", "\\textit"
+], {
+    numArgs: 1,
+    argTypes: ["text"],
+    greediness: 2,
+    allowedInText: true
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "text",
+        body: ordargument(body),
+        style: textFunctionStyles[context.funcName]
+    };
+});
+
+// A two-argument custom color
+defineFunction("\\color", {
+    numArgs: 2,
+    allowedInText: true,
+    greediness: 3,
+    argTypes: ["color", "original"]
+}, function(context, args) {
+    var color = args[0];
+    var body = args[1];
+    return {
+        type: "color",
+        color: color.value,
+        value: ordargument(body)
+    };
+});
+
+// An overline
+defineFunction("\\overline", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "overline",
+        body: body
+    };
+});
+
+// An underline
+defineFunction("\\underline", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "underline",
+        body: body
+    };
+});
+
+// A box of the width and height
+defineFunction("\\rule", {
+    numArgs: 2,
+    numOptionalArgs: 1,
+    argTypes: ["size", "size", "size"]
+}, function(context, args) {
+    var shift = args[0];
+    var width = args[1];
+    var height = args[2];
+    return {
+        type: "rule",
+        shift: shift && shift.value,
+        width: width.value,
+        height: height.value
+    };
+});
+
+// TODO: In TeX, \mkern only accepts mu-units, and \kern does not accept
+// mu-units. In current KaTeX we relax this; both commands accept any unit.
+defineFunction(["\\kern", "\\mkern"], {
+    numArgs: 1,
+    argTypes: ["size"]
+}, function(context, args) {
+    return {
+        type: "kern",
+        dimension: args[0].value
+    };
+});
+
+// A KaTeX logo
+defineFunction("\\KaTeX", {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "katex"
+    };
+});
+
+defineFunction("\\phantom", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "phantom",
+        value: ordargument(body)
+    };
+});
+
+// Math class commands except \mathop
+defineFunction([
+    "\\mathord", "\\mathbin", "\\mathrel", "\\mathopen",
+    "\\mathclose", "\\mathpunct", "\\mathinner"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "mclass",
+        mclass: "m" + context.funcName.substr(5),
+        value: ordargument(body)
+    };
+});
+
+// Build a relation by placing one symbol on top of another
+defineFunction("\\stackrel", {
+    numArgs: 2
+}, function(context, args) {
+    var top = args[0];
+    var bottom = args[1];
+
+    var bottomop = new ParseNode("op", {
+        type: "op",
+        limits: true,
+        alwaysHandleSupSub: true,
+        symbol: false,
+        value: ordargument(bottom)
+    }, bottom.mode);
+
+    var supsub = new ParseNode("supsub", {
+        base: bottomop,
+        sup: top,
+        sub: null
+    }, top.mode);
+
+    return {
+        type: "mclass",
+        mclass: "mrel",
+        value: [supsub]
+    };
+});
+
+// \mod-type functions
+defineFunction("\\bmod", {
+    numArgs: 0
+}, function(context, args) {
+    return {
+        type: "mod",
+        modType: "bmod",
+        value: null
+    };
+});
+
+defineFunction(["\\pod", "\\pmod", "\\mod"], {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "mod",
+        modType: context.funcName.substr(1),
+        value: ordargument(body)
+    };
+});
+
+// Extra data needed for the delimiter handler down below
+var delimiterSizes = {
+    "\\bigl" : {mclass: "mopen",    size: 1},
+    "\\Bigl" : {mclass: "mopen",    size: 2},
+    "\\biggl": {mclass: "mopen",    size: 3},
+    "\\Biggl": {mclass: "mopen",    size: 4},
+    "\\bigr" : {mclass: "mclose",   size: 1},
+    "\\Bigr" : {mclass: "mclose",   size: 2},
+    "\\biggr": {mclass: "mclose",   size: 3},
+    "\\Biggr": {mclass: "mclose",   size: 4},
+    "\\bigm" : {mclass: "mrel",     size: 1},
+    "\\Bigm" : {mclass: "mrel",     size: 2},
+    "\\biggm": {mclass: "mrel",     size: 3},
+    "\\Biggm": {mclass: "mrel",     size: 4},
+    "\\big"  : {mclass: "mord",     size: 1},
+    "\\Big"  : {mclass: "mord",     size: 2},
+    "\\bigg" : {mclass: "mord",     size: 3},
+    "\\Bigg" : {mclass: "mord",     size: 4}
+};
+
+var delimiters = [
+    "(", ")", "[", "\\lbrack", "]", "\\rbrack",
+    "\\{", "\\lbrace", "\\}", "\\rbrace",
+    "\\lfloor", "\\rfloor", "\\lceil", "\\rceil",
+    "<", ">", "\\langle", "\\rangle", "\\lt", "\\gt",
+    "\\lvert", "\\rvert", "\\lVert", "\\rVert",
+    "\\lgroup", "\\rgroup", "\\lmoustache", "\\rmoustache",
+    "/", "\\backslash",
+    "|", "\\vert", "\\|", "\\Vert",
+    "\\uparrow", "\\Uparrow",
+    "\\downarrow", "\\Downarrow",
+    "\\updownarrow", "\\Updownarrow",
+    "."
+];
+
+var fontAliases = {
+    "\\Bbb": "\\mathbb",
+    "\\bold": "\\mathbf",
+    "\\frak": "\\mathfrak"
+};
+
+// Single-argument color functions
+defineFunction([
+    "\\blue", "\\orange", "\\pink", "\\red",
+    "\\green", "\\gray", "\\purple",
+    "\\blueA", "\\blueB", "\\blueC", "\\blueD", "\\blueE",
+    "\\tealA", "\\tealB", "\\tealC", "\\tealD", "\\tealE",
+    "\\greenA", "\\greenB", "\\greenC", "\\greenD", "\\greenE",
+    "\\goldA", "\\goldB", "\\goldC", "\\goldD", "\\goldE",
+    "\\redA", "\\redB", "\\redC", "\\redD", "\\redE",
+    "\\maroonA", "\\maroonB", "\\maroonC", "\\maroonD", "\\maroonE",
+    "\\purpleA", "\\purpleB", "\\purpleC", "\\purpleD", "\\purpleE",
+    "\\mintA", "\\mintB", "\\mintC",
+    "\\grayA", "\\grayB", "\\grayC", "\\grayD", "\\grayE",
+    "\\grayF", "\\grayG", "\\grayH", "\\grayI",
+    "\\kaBlue", "\\kaGreen"
+], {
+    numArgs: 1,
+    allowedInText: true,
+    greediness: 3
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "color",
+        color: "katex-" + context.funcName.slice(1),
+        value: ordargument(body)
+    };
+});
+
+// There are 2 flags for operators; whether they produce limits in
+// displaystyle, and whether they are symbols and should grow in
+// displaystyle. These four groups cover the four possible choices.
+
+// No limits, not symbols
+defineFunction([
+    "\\arcsin", "\\arccos", "\\arctan", "\\arg", "\\cos", "\\cosh",
+    "\\cot", "\\coth", "\\csc", "\\deg", "\\dim", "\\exp", "\\hom",
+    "\\ker", "\\lg", "\\ln", "\\log", "\\sec", "\\sin", "\\sinh",
+    "\\tan", "\\tanh"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: false,
+        symbol: false,
+        body: context.funcName
+    };
+});
+
+// Limits, not symbols
+defineFunction([
+    "\\det", "\\gcd", "\\inf", "\\lim", "\\liminf", "\\limsup", "\\max",
+    "\\min", "\\Pr", "\\sup"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: true,
+        symbol: false,
+        body: context.funcName
+    };
+});
+
+// No limits, symbols
+defineFunction([
+    "\\int", "\\iint", "\\iiint", "\\oint"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: false,
+        symbol: true,
+        body: context.funcName
+    };
+});
+
+// Limits, symbols
+defineFunction([
+    "\\coprod", "\\bigvee", "\\bigwedge", "\\biguplus", "\\bigcap",
+    "\\bigcup", "\\intop", "\\prod", "\\sum", "\\bigotimes",
+    "\\bigoplus", "\\bigodot", "\\bigsqcup", "\\smallint"
+], {
+    numArgs: 0
+}, function(context) {
+    return {
+        type: "op",
+        limits: true,
+        symbol: true,
+        body: context.funcName
+    };
+});
+
+// \mathop class command
+defineFunction("\\mathop", {
+    numArgs: 1
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: "op",
+        limits: false,
+        symbol: false,
+        value: ordargument(body)
+    };
+});
+
+// Fractions
+defineFunction([
+    "\\dfrac", "\\frac", "\\tfrac",
+    "\\dbinom", "\\binom", "\\tbinom",
+    "\\\\atopfrac" // can’t be entered directly
+], {
+    numArgs: 2,
+    greediness: 2
+}, function(context, args) {
+    var numer = args[0];
+    var denom = args[1];
+    var hasBarLine;
+    var leftDelim = null;
+    var rightDelim = null;
+    var size = "auto";
+
+    switch (context.funcName) {
+        case "\\dfrac":
+        case "\\frac":
+        case "\\tfrac":
+            hasBarLine = true;
+            break;
+        case "\\\\atopfrac":
+            hasBarLine = false;
+            break;
+        case "\\dbinom":
+        case "\\binom":
+        case "\\tbinom":
+            hasBarLine = false;
+            leftDelim = "(";
+            rightDelim = ")";
+            break;
+        default:
+            throw new Error("Unrecognized genfrac command");
+    }
+
+    switch (context.funcName) {
+        case "\\dfrac":
+        case "\\dbinom":
+            size = "display";
+            break;
+        case "\\tfrac":
+        case "\\tbinom":
+            size = "text";
+            break;
+    }
+
+    return {
+        type: "genfrac",
+        numer: numer,
+        denom: denom,
+        hasBarLine: hasBarLine,
+        leftDelim: leftDelim,
+        rightDelim: rightDelim,
+        size: size
+    };
+});
+
+// Left and right overlap functions
+defineFunction(["\\llap", "\\rlap"], {
+    numArgs: 1,
+    allowedInText: true
+}, function(context, args) {
+    var body = args[0];
+    return {
+        type: context.funcName.slice(1),
+        body: body
+    };
+});
+
+// Delimiter functions
+var checkDelimiter = function(delim, context) {
+    if (utils.contains(delimiters, delim.value)) {
+        return delim;
+    } else {
+        throw new ParseError(
+            "Invalid delimiter: '" + delim.value + "' after '" +
+            context.funcName + "'", delim);
+    }
+};
+
+defineFunction([
+    "\\bigl", "\\Bigl", "\\biggl", "\\Biggl",
+    "\\bigr", "\\Bigr", "\\biggr", "\\Biggr",
+    "\\bigm", "\\Bigm", "\\biggm", "\\Biggm",
+    "\\big",  "\\Big",  "\\bigg",  "\\Bigg"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var delim = checkDelimiter(args[0], context);
+
+    return {
+        type: "delimsizing",
+        size: delimiterSizes[context.funcName].size,
+        mclass: delimiterSizes[context.funcName].mclass,
+        value: delim.value
+    };
+});
+
+defineFunction([
+    "\\left", "\\right"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var delim = checkDelimiter(args[0], context);
+
+    // \left and \right are caught somewhere in Parser.js, which is
+    // why this data doesn't match what is in buildHTML.
+    return {
+        type: "leftright",
+        value: delim.value
+    };
+});
+
+defineFunction("\\middle", {
+    numArgs: 1
+}, function(context, args) {
+    var delim = checkDelimiter(args[0], context);
+    if (!context.parser.leftrightDepth) {
+        throw new ParseError("\\middle without preceding \\left", delim);
+    }
+
+    return {
+        type: "middle",
+        value: delim.value
+    };
+});
+
+// Sizing functions (handled in Parser.js explicitly, hence no handler)
+defineFunction([
+    "\\tiny", "\\scriptsize", "\\footnotesize", "\\small",
+    "\\normalsize", "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"
+], 0, null);
+
+// Style changing functions (handled in Parser.js explicitly, hence no
+// handler)
+defineFunction([
+    "\\displaystyle", "\\textstyle", "\\scriptstyle",
+    "\\scriptscriptstyle"
+], 0, null);
+
+defineFunction([
+    // styles
+    "\\mathrm", "\\mathit", "\\mathbf",
+
+    // families
+    "\\mathbb", "\\mathcal", "\\mathfrak", "\\mathscr", "\\mathsf",
+    "\\mathtt",
+
+    // aliases
+    "\\Bbb", "\\bold", "\\frak"
+], {
+    numArgs: 1,
+    greediness: 2
+}, function(context, args) {
+    var body = args[0];
+    var func = context.funcName;
+    if (func in fontAliases) {
+        func = fontAliases[func];
+    }
+    return {
+        type: "font",
+        font: func.slice(1),
+        body: body
+    };
+});
+
+// Accents
+defineFunction([
+    "\\acute", "\\grave", "\\ddot", "\\tilde", "\\bar", "\\breve",
+    "\\check", "\\hat", "\\vec", "\\dot"
+    // We don't support expanding accents yet
+    // "\\widetilde", "\\widehat"
+], {
+    numArgs: 1
+}, function(context, args) {
+    var base = args[0];
+    return {
+        type: "accent",
+        accent: context.funcName,
+        base: base
+    };
+});
+
+// Infix generalized fractions
+defineFunction(["\\over", "\\choose", "\\atop"], {
+    numArgs: 0,
+    infix: true
+}, function(context) {
+    var replaceWith;
+    switch (context.funcName) {
+        case "\\over":
+            replaceWith = "\\frac";
+            break;
+        case "\\choose":
+            replaceWith = "\\binom";
+            break;
+        case "\\atop":
+            replaceWith = "\\\\atopfrac";
+            break;
+        default:
+            throw new Error("Unrecognized infix genfrac command");
+    }
+    return {
+        type: "infix",
+        replaceWith: replaceWith,
+        token: context.token
+    };
+});
+
+// Row breaks for aligned data
+defineFunction(["\\\\", "\\cr"], {
+    numArgs: 0,
+    numOptionalArgs: 1,
+    argTypes: ["size"]
+}, function(context, args) {
+    var size = args[0];
+    return {
+        type: "cr",
+        size: size
+    };
+});
+
+// Environment delimiters
+defineFunction(["\\begin", "\\end"], {
+    numArgs: 1,
+    argTypes: ["text"]
+}, function(context, args) {
+    var nameGroup = args[0];
+    if (nameGroup.type !== "ordgroup") {
+        throw new ParseError("Invalid environment name", nameGroup);
+    }
+    var name = "";
+    for (var i = 0; i < nameGroup.value.length; ++i) {
+        name += nameGroup.value[i].value;
+    }
+    return {
+        type: "environment",
+        name: name,
+        nameGroup: nameGroup
+    };
+});
+
+},{"./ParseError":6,"./parseData":21,"./utils":25}],20:[function(require,module,exports){
+/**
+ * These objects store data about MathML nodes. This is the MathML equivalent
+ * of the types in domTree.js. Since MathML handles its own rendering, and
+ * since we're mainly using MathML to improve accessibility, we don't manage
+ * any of the styling state that the plain DOM nodes do.
+ *
+ * The `toNode` and `toMarkup` functions work simlarly to how they do in
+ * domTree.js, creating namespaced DOM nodes and HTML text markup respectively.
+ */
+
+var utils = require("./utils");
+
+/**
+ * This node represents a general purpose MathML node of any type. The
+ * constructor requires the type of node to create (for example, `"mo"` or
+ * `"mspace"`, corresponding to `<mo>` and `<mspace>` tags).
+ */
+function MathNode(type, children) {
+    this.type = type;
+    this.attributes = {};
+    this.children = children || [];
+}
+
+/**
+ * Sets an attribute on a MathML node. MathML depends on attributes to convey a
+ * semantic content, so this is used heavily.
+ */
+MathNode.prototype.setAttribute = function(name, value) {
+    this.attributes[name] = value;
+};
+
+/**
+ * Converts the math node into a MathML-namespaced DOM element.
+ */
+MathNode.prototype.toNode = function() {
+    var node = document.createElementNS(
+        "http://www.w3.org/1998/Math/MathML", this.type);
+
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            node.setAttribute(attr, this.attributes[attr]);
+        }
+    }
+
+    for (var i = 0; i < this.children.length; i++) {
+        node.appendChild(this.children[i].toNode());
+    }
+
+    return node;
+};
+
+/**
+ * Converts the math node into an HTML markup string.
+ */
+MathNode.prototype.toMarkup = function() {
+    var markup = "<" + this.type;
+
+    // Add the attributes
+    for (var attr in this.attributes) {
+        if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) {
+            markup += " " + attr + "=\"";
+            markup += utils.escape(this.attributes[attr]);
+            markup += "\"";
+        }
+    }
+
+    markup += ">";
+
+    for (var i = 0; i < this.children.length; i++) {
+        markup += this.children[i].toMarkup();
+    }
+
+    markup += "</" + this.type + ">";
+
+    return markup;
+};
+
+/**
+ * This node represents a piece of text.
+ */
+function TextNode(text) {
+    this.text = text;
+}
+
+/**
+ * Converts the text node into a DOM text node.
+ */
+TextNode.prototype.toNode = function() {
+    return document.createTextNode(this.text);
+};
+
+/**
+ * Converts the text node into HTML markup (which is just the text itself).
+ */
+TextNode.prototype.toMarkup = function() {
+    return utils.escape(this.text);
+};
+
+module.exports = {
+    MathNode: MathNode,
+    TextNode: TextNode
+};
+
+},{"./utils":25}],21:[function(require,module,exports){
+/**
+ * The resulting parse tree nodes of the parse tree.
+ *
+ * It is possible to provide position information, so that a ParseNode can
+ * fulfil a role similar to a Token in error reporting.
+ * For details on the corresponding properties see Token constructor.
+ * Providing such information can lead to better error reporting.
+ *
+ * @param {string}  type       type of node, like e.g. "ordgroup"
+ * @param {?object} value      type-specific representation of the node
+ * @param {string}  mode       parse mode in action for this node,
+ *                             "math" or "text"
+ * @param {Token=} firstToken  first token of the input for this node,
+ *                             will omit position information if unset
+ * @param {Token=} lastToken   last token of the input for this node,
+ *                             will default to firstToken if unset
+ */
+function ParseNode(type, value, mode, firstToken, lastToken) {
+    this.type = type;
+    this.value = value;
+    this.mode = mode;
+    if (firstToken && (!lastToken || lastToken.lexer === firstToken.lexer)) {
+        this.lexer = firstToken.lexer;
+        this.start = firstToken.start;
+        this.end = (lastToken || firstToken).end;
+    }
+}
+
+module.exports = {
+    ParseNode: ParseNode
+};
+
+
+},{}],22:[function(require,module,exports){
+/**
+ * Provides a single function for parsing an expression using a Parser
+ * TODO(emily): Remove this
+ */
+
+var Parser = require("./Parser");
+
+/**
+ * Parses an expression using a Parser, then returns the parsed result.
+ */
+var parseTree = function(toParse, settings) {
+    if (!(typeof toParse === 'string' || toParse instanceof String)) {
+        throw new TypeError('KaTeX can only parse string typed expression');
+    }
+    var parser = new Parser(toParse, settings);
+
+    return parser.parse();
+};
+
+module.exports = parseTree;
+
+},{"./Parser":7}],23:[function(require,module,exports){
+/**
+ * This file holds a list of all no-argument functions and single-character
+ * symbols (like 'a' or ';').
+ *
+ * For each of the symbols, there are three properties they can have:
+ * - font (required): the font to be used for this symbol. Either "main" (the
+     normal font), or "ams" (the ams fonts).
+ * - group (required): the ParseNode group type the symbol should have (i.e.
+     "textord", "mathord", etc).
+     See https://github.com/Khan/KaTeX/wiki/Examining-TeX#group-types
+ * - replace: the character that this symbol or function should be
+ *   replaced with (i.e. "\phi" has a replace value of "\u03d5", the phi
+ *   character in the main font).
+ *
+ * The outermost map in the table indicates what mode the symbols should be
+ * accepted in (e.g. "math" or "text").
+ */
+
+module.exports = {
+    math: {},
+    text: {}
+};
+
+function defineSymbol(mode, font, group, replace, name) {
+    module.exports[mode][name] = {
+        font: font,
+        group: group,
+        replace: replace
+    };
+}
+
+// Some abbreviations for commonly used strings.
+// This helps minify the code, and also spotting typos using jshint.
+
+// modes:
+var math = "math";
+var text = "text";
+
+// fonts:
+var main = "main";
+var ams = "ams";
+
+// groups:
+var accent = "accent";
+var bin = "bin";
+var close = "close";
+var inner = "inner";
+var mathord = "mathord";
+var op = "op";
+var open = "open";
+var punct = "punct";
+var rel = "rel";
+var spacing = "spacing";
+var textord = "textord";
+
+// Now comes the symbol table
+
+// Relation Symbols
+defineSymbol(math, main, rel, "\u2261", "\\equiv");
+defineSymbol(math, main, rel, "\u227a", "\\prec");
+defineSymbol(math, main, rel, "\u227b", "\\succ");
+defineSymbol(math, main, rel, "\u223c", "\\sim");
+defineSymbol(math, main, rel, "\u22a5", "\\perp");
+defineSymbol(math, main, rel, "\u2aaf", "\\preceq");
+defineSymbol(math, main, rel, "\u2ab0", "\\succeq");
+defineSymbol(math, main, rel, "\u2243", "\\simeq");
+defineSymbol(math, main, rel, "\u2223", "\\mid");
+defineSymbol(math, main, rel, "\u226a", "\\ll");
+defineSymbol(math, main, rel, "\u226b", "\\gg");
+defineSymbol(math, main, rel, "\u224d", "\\asymp");
+defineSymbol(math, main, rel, "\u2225", "\\parallel");
+defineSymbol(math, main, rel, "\u22c8", "\\bowtie");
+defineSymbol(math, main, rel, "\u2323", "\\smile");
+defineSymbol(math, main, rel, "\u2291", "\\sqsubseteq");
+defineSymbol(math, main, rel, "\u2292", "\\sqsupseteq");
+defineSymbol(math, main, rel, "\u2250", "\\doteq");
+defineSymbol(math, main, rel, "\u2322", "\\frown");
+defineSymbol(math, main, rel, "\u220b", "\\ni");
+defineSymbol(math, main, rel, "\u221d", "\\propto");
+defineSymbol(math, main, rel, "\u22a2", "\\vdash");
+defineSymbol(math, main, rel, "\u22a3", "\\dashv");
+defineSymbol(math, main, rel, "\u220b", "\\owns");
+
+// Punctuation
+defineSymbol(math, main, punct, "\u002e", "\\ldotp");
+defineSymbol(math, main, punct, "\u22c5", "\\cdotp");
+
+// Misc Symbols
+defineSymbol(math, main, textord, "\u0023", "\\#");
+defineSymbol(text, main, textord, "\u0023", "\\#");
+defineSymbol(math, main, textord, "\u0026", "\\&");
+defineSymbol(text, main, textord, "\u0026", "\\&");
+defineSymbol(math, main, textord, "\u2135", "\\aleph");
+defineSymbol(math, main, textord, "\u2200", "\\forall");
+defineSymbol(math, main, textord, "\u210f", "\\hbar");
+defineSymbol(math, main, textord, "\u2203", "\\exists");
+defineSymbol(math, main, textord, "\u2207", "\\nabla");
+defineSymbol(math, main, textord, "\u266d", "\\flat");
+defineSymbol(math, main, textord, "\u2113", "\\ell");
+defineSymbol(math, main, textord, "\u266e", "\\natural");
+defineSymbol(math, main, textord, "\u2663", "\\clubsuit");
+defineSymbol(math, main, textord, "\u2118", "\\wp");
+defineSymbol(math, main, textord, "\u266f", "\\sharp");
+defineSymbol(math, main, textord, "\u2662", "\\diamondsuit");
+defineSymbol(math, main, textord, "\u211c", "\\Re");
+defineSymbol(math, main, textord, "\u2661", "\\heartsuit");
+defineSymbol(math, main, textord, "\u2111", "\\Im");
+defineSymbol(math, main, textord, "\u2660", "\\spadesuit");
+
+// Math and Text
+defineSymbol(math, main, textord, "\u2020", "\\dag");
+defineSymbol(math, main, textord, "\u2021", "\\ddag");
+
+// Large Delimiters
+defineSymbol(math, main, close, "\u23b1", "\\rmoustache");
+defineSymbol(math, main, open, "\u23b0", "\\lmoustache");
+defineSymbol(math, main, close, "\u27ef", "\\rgroup");
+defineSymbol(math, main, open, "\u27ee", "\\lgroup");
+
+// Binary Operators
+defineSymbol(math, main, bin, "\u2213", "\\mp");
+defineSymbol(math, main, bin, "\u2296", "\\ominus");
+defineSymbol(math, main, bin, "\u228e", "\\uplus");
+defineSymbol(math, main, bin, "\u2293", "\\sqcap");
+defineSymbol(math, main, bin, "\u2217", "\\ast");
+defineSymbol(math, main, bin, "\u2294", "\\sqcup");
+defineSymbol(math, main, bin, "\u25ef", "\\bigcirc");
+defineSymbol(math, main, bin, "\u2219", "\\bullet");
+defineSymbol(math, main, bin, "\u2021", "\\ddagger");
+defineSymbol(math, main, bin, "\u2240", "\\wr");
+defineSymbol(math, main, bin, "\u2a3f", "\\amalg");
+
+// Arrow Symbols
+defineSymbol(math, main, rel, "\u27f5", "\\longleftarrow");
+defineSymbol(math, main, rel, "\u21d0", "\\Leftarrow");
+defineSymbol(math, main, rel, "\u27f8", "\\Longleftarrow");
+defineSymbol(math, main, rel, "\u27f6", "\\longrightarrow");
+defineSymbol(math, main, rel, "\u21d2", "\\Rightarrow");
+defineSymbol(math, main, rel, "\u27f9", "\\Longrightarrow");
+defineSymbol(math, main, rel, "\u2194", "\\leftrightarrow");
+defineSymbol(math, main, rel, "\u27f7", "\\longleftrightarrow");
+defineSymbol(math, main, rel, "\u21d4", "\\Leftrightarrow");
+defineSymbol(math, main, rel, "\u27fa", "\\Longleftrightarrow");
+defineSymbol(math, main, rel, "\u21a6", "\\mapsto");
+defineSymbol(math, main, rel, "\u27fc", "\\longmapsto");
+defineSymbol(math, main, rel, "\u2197", "\\nearrow");
+defineSymbol(math, main, rel, "\u21a9", "\\hookleftarrow");
+defineSymbol(math, main, rel, "\u21aa", "\\hookrightarrow");
+defineSymbol(math, main, rel, "\u2198", "\\searrow");
+defineSymbol(math, main, rel, "\u21bc", "\\leftharpoonup");
+defineSymbol(math, main, rel, "\u21c0", "\\rightharpoonup");
+defineSymbol(math, main, rel, "\u2199", "\\swarrow");
+defineSymbol(math, main, rel, "\u21bd", "\\leftharpoondown");
+defineSymbol(math, main, rel, "\u21c1", "\\rightharpoondown");
+defineSymbol(math, main, rel, "\u2196", "\\nwarrow");
+defineSymbol(math, main, rel, "\u21cc", "\\rightleftharpoons");
+
+// AMS Negated Binary Relations
+defineSymbol(math, ams, rel, "\u226e", "\\nless");
+defineSymbol(math, ams, rel, "\ue010", "\\nleqslant");
+defineSymbol(math, ams, rel, "\ue011", "\\nleqq");
+defineSymbol(math, ams, rel, "\u2a87", "\\lneq");
+defineSymbol(math, ams, rel, "\u2268", "\\lneqq");
+defineSymbol(math, ams, rel, "\ue00c", "\\lvertneqq");
+defineSymbol(math, ams, rel, "\u22e6", "\\lnsim");
+defineSymbol(math, ams, rel, "\u2a89", "\\lnapprox");
+defineSymbol(math, ams, rel, "\u2280", "\\nprec");
+defineSymbol(math, ams, rel, "\u22e0", "\\npreceq");
+defineSymbol(math, ams, rel, "\u22e8", "\\precnsim");
+defineSymbol(math, ams, rel, "\u2ab9", "\\precnapprox");
+defineSymbol(math, ams, rel, "\u2241", "\\nsim");
+defineSymbol(math, ams, rel, "\ue006", "\\nshortmid");
+defineSymbol(math, ams, rel, "\u2224", "\\nmid");
+defineSymbol(math, ams, rel, "\u22ac", "\\nvdash");
+defineSymbol(math, ams, rel, "\u22ad", "\\nvDash");
+defineSymbol(math, ams, rel, "\u22ea", "\\ntriangleleft");
+defineSymbol(math, ams, rel, "\u22ec", "\\ntrianglelefteq");
+defineSymbol(math, ams, rel, "\u228a", "\\subsetneq");
+defineSymbol(math, ams, rel, "\ue01a", "\\varsubsetneq");
+defineSymbol(math, ams, rel, "\u2acb", "\\subsetneqq");
+defineSymbol(math, ams, rel, "\ue017", "\\varsubsetneqq");
+defineSymbol(math, ams, rel, "\u226f", "\\ngtr");
+defineSymbol(math, ams, rel, "\ue00f", "\\ngeqslant");
+defineSymbol(math, ams, rel, "\ue00e", "\\ngeqq");
+defineSymbol(math, ams, rel, "\u2a88", "\\gneq");
+defineSymbol(math, ams, rel, "\u2269", "\\gneqq");
+defineSymbol(math, ams, rel, "\ue00d", "\\gvertneqq");
+defineSymbol(math, ams, rel, "\u22e7", "\\gnsim");
+defineSymbol(math, ams, rel, "\u2a8a", "\\gnapprox");
+defineSymbol(math, ams, rel, "\u2281", "\\nsucc");
+defineSymbol(math, ams, rel, "\u22e1", "\\nsucceq");
+defineSymbol(math, ams, rel, "\u22e9", "\\succnsim");
+defineSymbol(math, ams, rel, "\u2aba", "\\succnapprox");
+defineSymbol(math, ams, rel, "\u2246", "\\ncong");
+defineSymbol(math, ams, rel, "\ue007", "\\nshortparallel");
+defineSymbol(math, ams, rel, "\u2226", "\\nparallel");
+defineSymbol(math, ams, rel, "\u22af", "\\nVDash");
+defineSymbol(math, ams, rel, "\u22eb", "\\ntriangleright");
+defineSymbol(math, ams, rel, "\u22ed", "\\ntrianglerighteq");
+defineSymbol(math, ams, rel, "\ue018", "\\nsupseteqq");
+defineSymbol(math, ams, rel, "\u228b", "\\supsetneq");
+defineSymbol(math, ams, rel, "\ue01b", "\\varsupsetneq");
+defineSymbol(math, ams, rel, "\u2acc", "\\supsetneqq");
+defineSymbol(math, ams, rel, "\ue019", "\\varsupsetneqq");
+defineSymbol(math, ams, rel, "\u22ae", "\\nVdash");
+defineSymbol(math, ams, rel, "\u2ab5", "\\precneqq");
+defineSymbol(math, ams, rel, "\u2ab6", "\\succneqq");
+defineSymbol(math, ams, rel, "\ue016", "\\nsubseteqq");
+defineSymbol(math, ams, bin, "\u22b4", "\\unlhd");
+defineSymbol(math, ams, bin, "\u22b5", "\\unrhd");
+
+// AMS Negated Arrows
+defineSymbol(math, ams, rel, "\u219a", "\\nleftarrow");
+defineSymbol(math, ams, rel, "\u219b", "\\nrightarrow");
+defineSymbol(math, ams, rel, "\u21cd", "\\nLeftarrow");
+defineSymbol(math, ams, rel, "\u21cf", "\\nRightarrow");
+defineSymbol(math, ams, rel, "\u21ae", "\\nleftrightarrow");
+defineSymbol(math, ams, rel, "\u21ce", "\\nLeftrightarrow");
+
+// AMS Misc
+defineSymbol(math, ams, rel, "\u25b3", "\\vartriangle");
+defineSymbol(math, ams, textord, "\u210f", "\\hslash");
+defineSymbol(math, ams, textord, "\u25bd", "\\triangledown");
+defineSymbol(math, ams, textord, "\u25ca", "\\lozenge");
+defineSymbol(math, ams, textord, "\u24c8", "\\circledS");
+defineSymbol(math, ams, textord, "\u00ae", "\\circledR");
+defineSymbol(math, ams, textord, "\u2221", "\\measuredangle");
+defineSymbol(math, ams, textord, "\u2204", "\\nexists");
+defineSymbol(math, ams, textord, "\u2127", "\\mho");
+defineSymbol(math, ams, textord, "\u2132", "\\Finv");
+defineSymbol(math, ams, textord, "\u2141", "\\Game");
+defineSymbol(math, ams, textord, "\u006b", "\\Bbbk");
+defineSymbol(math, ams, textord, "\u2035", "\\backprime");
+defineSymbol(math, ams, textord, "\u25b2", "\\blacktriangle");
+defineSymbol(math, ams, textord, "\u25bc", "\\blacktriangledown");
+defineSymbol(math, ams, textord, "\u25a0", "\\blacksquare");
+defineSymbol(math, ams, textord, "\u29eb", "\\blacklozenge");
+defineSymbol(math, ams, textord, "\u2605", "\\bigstar");
+defineSymbol(math, ams, textord, "\u2222", "\\sphericalangle");
+defineSymbol(math, ams, textord, "\u2201", "\\complement");
+defineSymbol(math, ams, textord, "\u00f0", "\\eth");
+defineSymbol(math, ams, textord, "\u2571", "\\diagup");
+defineSymbol(math, ams, textord, "\u2572", "\\diagdown");
+defineSymbol(math, ams, textord, "\u25a1", "\\square");
+defineSymbol(math, ams, textord, "\u25a1", "\\Box");
+defineSymbol(math, ams, textord, "\u25ca", "\\Diamond");
+defineSymbol(math, ams, textord, "\u00a5", "\\yen");
+defineSymbol(math, ams, textord, "\u2713", "\\checkmark");
+
+// AMS Hebrew
+defineSymbol(math, ams, textord, "\u2136", "\\beth");
+defineSymbol(math, ams, textord, "\u2138", "\\daleth");
+defineSymbol(math, ams, textord, "\u2137", "\\gimel");
+
+// AMS Greek
+defineSymbol(math, ams, textord, "\u03dd", "\\digamma");
+defineSymbol(math, ams, textord, "\u03f0", "\\varkappa");
+
+// AMS Delimiters
+defineSymbol(math, ams, open, "\u250c", "\\ulcorner");
+defineSymbol(math, ams, close, "\u2510", "\\urcorner");
+defineSymbol(math, ams, open, "\u2514", "\\llcorner");
+defineSymbol(math, ams, close, "\u2518", "\\lrcorner");
+
+// AMS Binary Relations
+defineSymbol(math, ams, rel, "\u2266", "\\leqq");
+defineSymbol(math, ams, rel, "\u2a7d", "\\leqslant");
+defineSymbol(math, ams, rel, "\u2a95", "\\eqslantless");
+defineSymbol(math, ams, rel, "\u2272", "\\lesssim");
+defineSymbol(math, ams, rel, "\u2a85", "\\lessapprox");
+defineSymbol(math, ams, rel, "\u224a", "\\approxeq");
+defineSymbol(math, ams, bin, "\u22d6", "\\lessdot");
+defineSymbol(math, ams, rel, "\u22d8", "\\lll");
+defineSymbol(math, ams, rel, "\u2276", "\\lessgtr");
+defineSymbol(math, ams, rel, "\u22da", "\\lesseqgtr");
+defineSymbol(math, ams, rel, "\u2a8b", "\\lesseqqgtr");
+defineSymbol(math, ams, rel, "\u2251", "\\doteqdot");
+defineSymbol(math, ams, rel, "\u2253", "\\risingdotseq");
+defineSymbol(math, ams, rel, "\u2252", "\\fallingdotseq");
+defineSymbol(math, ams, rel, "\u223d", "\\backsim");
+defineSymbol(math, ams, rel, "\u22cd", "\\backsimeq");
+defineSymbol(math, ams, rel, "\u2ac5", "\\subseteqq");
+defineSymbol(math, ams, rel, "\u22d0", "\\Subset");
+defineSymbol(math, ams, rel, "\u228f", "\\sqsubset");
+defineSymbol(math, ams, rel, "\u227c", "\\preccurlyeq");
+defineSymbol(math, ams, rel, "\u22de", "\\curlyeqprec");
+defineSymbol(math, ams, rel, "\u227e", "\\precsim");
+defineSymbol(math, ams, rel, "\u2ab7", "\\precapprox");
+defineSymbol(math, ams, rel, "\u22b2", "\\vartriangleleft");
+defineSymbol(math, ams, rel, "\u22b4", "\\trianglelefteq");
+defineSymbol(math, ams, rel, "\u22a8", "\\vDash");
+defineSymbol(math, ams, rel, "\u22aa", "\\Vvdash");
+defineSymbol(math, ams, rel, "\u2323", "\\smallsmile");
+defineSymbol(math, ams, rel, "\u2322", "\\smallfrown");
+defineSymbol(math, ams, rel, "\u224f", "\\bumpeq");
+defineSymbol(math, ams, rel, "\u224e", "\\Bumpeq");
+defineSymbol(math, ams, rel, "\u2267", "\\geqq");
+defineSymbol(math, ams, rel, "\u2a7e", "\\geqslant");
+defineSymbol(math, ams, rel, "\u2a96", "\\eqslantgtr");
+defineSymbol(math, ams, rel, "\u2273", "\\gtrsim");
+defineSymbol(math, ams, rel, "\u2a86", "\\gtrapprox");
+defineSymbol(math, ams, bin, "\u22d7", "\\gtrdot");
+defineSymbol(math, ams, rel, "\u22d9", "\\ggg");
+defineSymbol(math, ams, rel, "\u2277", "\\gtrless");
+defineSymbol(math, ams, rel, "\u22db", "\\gtreqless");
+defineSymbol(math, ams, rel, "\u2a8c", "\\gtreqqless");
+defineSymbol(math, ams, rel, "\u2256", "\\eqcirc");
+defineSymbol(math, ams, rel, "\u2257", "\\circeq");
+defineSymbol(math, ams, rel, "\u225c", "\\triangleq");
+defineSymbol(math, ams, rel, "\u223c", "\\thicksim");
+defineSymbol(math, ams, rel, "\u2248", "\\thickapprox");
+defineSymbol(math, ams, rel, "\u2ac6", "\\supseteqq");
+defineSymbol(math, ams, rel, "\u22d1", "\\Supset");
+defineSymbol(math, ams, rel, "\u2290", "\\sqsupset");
+defineSymbol(math, ams, rel, "\u227d", "\\succcurlyeq");
+defineSymbol(math, ams, rel, "\u22df", "\\curlyeqsucc");
+defineSymbol(math, ams, rel, "\u227f", "\\succsim");
+defineSymbol(math, ams, rel, "\u2ab8", "\\succapprox");
+defineSymbol(math, ams, rel, "\u22b3", "\\vartriangleright");
+defineSymbol(math, ams, rel, "\u22b5", "\\trianglerighteq");
+defineSymbol(math, ams, rel, "\u22a9", "\\Vdash");
+defineSymbol(math, ams, rel, "\u2223", "\\shortmid");
+defineSymbol(math, ams, rel, "\u2225", "\\shortparallel");
+defineSymbol(math, ams, rel, "\u226c", "\\between");
+defineSymbol(math, ams, rel, "\u22d4", "\\pitchfork");
+defineSymbol(math, ams, rel, "\u221d", "\\varpropto");
+defineSymbol(math, ams, rel, "\u25c0", "\\blacktriangleleft");
+defineSymbol(math, ams, rel, "\u2234", "\\therefore");
+defineSymbol(math, ams, rel, "\u220d", "\\backepsilon");
+defineSymbol(math, ams, rel, "\u25b6", "\\blacktriangleright");
+defineSymbol(math, ams, rel, "\u2235", "\\because");
+defineSymbol(math, ams, rel, "\u22d8", "\\llless");
+defineSymbol(math, ams, rel, "\u22d9", "\\gggtr");
+defineSymbol(math, ams, bin, "\u22b2", "\\lhd");
+defineSymbol(math, ams, bin, "\u22b3", "\\rhd");
+defineSymbol(math, ams, rel, "\u2242", "\\eqsim");
+defineSymbol(math, main, rel, "\u22c8", "\\Join");
+defineSymbol(math, ams, rel, "\u2251", "\\Doteq");
+
+// AMS Binary Operators
+defineSymbol(math, ams, bin, "\u2214", "\\dotplus");
+defineSymbol(math, ams, bin, "\u2216", "\\smallsetminus");
+defineSymbol(math, ams, bin, "\u22d2", "\\Cap");
+defineSymbol(math, ams, bin, "\u22d3", "\\Cup");
+defineSymbol(math, ams, bin, "\u2a5e", "\\doublebarwedge");
+defineSymbol(math, ams, bin, "\u229f", "\\boxminus");
+defineSymbol(math, ams, bin, "\u229e", "\\boxplus");
+defineSymbol(math, ams, bin, "\u22c7", "\\divideontimes");
+defineSymbol(math, ams, bin, "\u22c9", "\\ltimes");
+defineSymbol(math, ams, bin, "\u22ca", "\\rtimes");
+defineSymbol(math, ams, bin, "\u22cb", "\\leftthreetimes");
+defineSymbol(math, ams, bin, "\u22cc", "\\rightthreetimes");
+defineSymbol(math, ams, bin, "\u22cf", "\\curlywedge");
+defineSymbol(math, ams, bin, "\u22ce", "\\curlyvee");
+defineSymbol(math, ams, bin, "\u229d", "\\circleddash");
+defineSymbol(math, ams, bin, "\u229b", "\\circledast");
+defineSymbol(math, ams, bin, "\u22c5", "\\centerdot");
+defineSymbol(math, ams, bin, "\u22ba", "\\intercal");
+defineSymbol(math, ams, bin, "\u22d2", "\\doublecap");
+defineSymbol(math, ams, bin, "\u22d3", "\\doublecup");
+defineSymbol(math, ams, bin, "\u22a0", "\\boxtimes");
+
+// AMS Arrows
+defineSymbol(math, ams, rel, "\u21e2", "\\dashrightarrow");
+defineSymbol(math, ams, rel, "\u21e0", "\\dashleftarrow");
+defineSymbol(math, ams, rel, "\u21c7", "\\leftleftarrows");
+defineSymbol(math, ams, rel, "\u21c6", "\\leftrightarrows");
+defineSymbol(math, ams, rel, "\u21da", "\\Lleftarrow");
+defineSymbol(math, ams, rel, "\u219e", "\\twoheadleftarrow");
+defineSymbol(math, ams, rel, "\u21a2", "\\leftarrowtail");
+defineSymbol(math, ams, rel, "\u21ab", "\\looparrowleft");
+defineSymbol(math, ams, rel, "\u21cb", "\\leftrightharpoons");
+defineSymbol(math, ams, rel, "\u21b6", "\\curvearrowleft");
+defineSymbol(math, ams, rel, "\u21ba", "\\circlearrowleft");
+defineSymbol(math, ams, rel, "\u21b0", "\\Lsh");
+defineSymbol(math, ams, rel, "\u21c8", "\\upuparrows");
+defineSymbol(math, ams, rel, "\u21bf", "\\upharpoonleft");
+defineSymbol(math, ams, rel, "\u21c3", "\\downharpoonleft");
+defineSymbol(math, ams, rel, "\u22b8", "\\multimap");
+defineSymbol(math, ams, rel, "\u21ad", "\\leftrightsquigarrow");
+defineSymbol(math, ams, rel, "\u21c9", "\\rightrightarrows");
+defineSymbol(math, ams, rel, "\u21c4", "\\rightleftarrows");
+defineSymbol(math, ams, rel, "\u21a0", "\\twoheadrightarrow");
+defineSymbol(math, ams, rel, "\u21a3", "\\rightarrowtail");
+defineSymbol(math, ams, rel, "\u21ac", "\\looparrowright");
+defineSymbol(math, ams, rel, "\u21b7", "\\curvearrowright");
+defineSymbol(math, ams, rel, "\u21bb", "\\circlearrowright");
+defineSymbol(math, ams, rel, "\u21b1", "\\Rsh");
+defineSymbol(math, ams, rel, "\u21ca", "\\downdownarrows");
+defineSymbol(math, ams, rel, "\u21be", "\\upharpoonright");
+defineSymbol(math, ams, rel, "\u21c2", "\\downharpoonright");
+defineSymbol(math, ams, rel, "\u21dd", "\\rightsquigarrow");
+defineSymbol(math, ams, rel, "\u21dd", "\\leadsto");
+defineSymbol(math, ams, rel, "\u21db", "\\Rrightarrow");
+defineSymbol(math, ams, rel, "\u21be", "\\restriction");
+
+defineSymbol(math, main, textord, "\u2018", "`");
+defineSymbol(math, main, textord, "$", "\\$");
+defineSymbol(text, main, textord, "$", "\\$");
+defineSymbol(math, main, textord, "%", "\\%");
+defineSymbol(text, main, textord, "%", "\\%");
+defineSymbol(math, main, textord, "_", "\\_");
+defineSymbol(text, main, textord, "_", "\\_");
+defineSymbol(math, main, textord, "\u2220", "\\angle");
+defineSymbol(math, main, textord, "\u221e", "\\infty");
+defineSymbol(math, main, textord, "\u2032", "\\prime");
+defineSymbol(math, main, textord, "\u25b3", "\\triangle");
+defineSymbol(math, main, textord, "\u0393", "\\Gamma");
+defineSymbol(math, main, textord, "\u0394", "\\Delta");
+defineSymbol(math, main, textord, "\u0398", "\\Theta");
+defineSymbol(math, main, textord, "\u039b", "\\Lambda");
+defineSymbol(math, main, textord, "\u039e", "\\Xi");
+defineSymbol(math, main, textord, "\u03a0", "\\Pi");
+defineSymbol(math, main, textord, "\u03a3", "\\Sigma");
+defineSymbol(math, main, textord, "\u03a5", "\\Upsilon");
+defineSymbol(math, main, textord, "\u03a6", "\\Phi");
+defineSymbol(math, main, textord, "\u03a8", "\\Psi");
+defineSymbol(math, main, textord, "\u03a9", "\\Omega");
+defineSymbol(math, main, textord, "\u00ac", "\\neg");
+defineSymbol(math, main, textord, "\u00ac", "\\lnot");
+defineSymbol(math, main, textord, "\u22a4", "\\top");
+defineSymbol(math, main, textord, "\u22a5", "\\bot");
+defineSymbol(math, main, textord, "\u2205", "\\emptyset");
+defineSymbol(math, ams, textord, "\u2205", "\\varnothing");
+defineSymbol(math, main, mathord, "\u03b1", "\\alpha");
+defineSymbol(math, main, mathord, "\u03b2", "\\beta");
+defineSymbol(math, main, mathord, "\u03b3", "\\gamma");
+defineSymbol(math, main, mathord, "\u03b4", "\\delta");
+defineSymbol(math, main, mathord, "\u03f5", "\\epsilon");
+defineSymbol(math, main, mathord, "\u03b6", "\\zeta");
+defineSymbol(math, main, mathord, "\u03b7", "\\eta");
+defineSymbol(math, main, mathord, "\u03b8", "\\theta");
+defineSymbol(math, main, mathord, "\u03b9", "\\iota");
+defineSymbol(math, main, mathord, "\u03ba", "\\kappa");
+defineSymbol(math, main, mathord, "\u03bb", "\\lambda");
+defineSymbol(math, main, mathord, "\u03bc", "\\mu");
+defineSymbol(math, main, mathord, "\u03bd", "\\nu");
+defineSymbol(math, main, mathord, "\u03be", "\\xi");
+defineSymbol(math, main, mathord, "o", "\\omicron");
+defineSymbol(math, main, mathord, "\u03c0", "\\pi");
+defineSymbol(math, main, mathord, "\u03c1", "\\rho");
+defineSymbol(math, main, mathord, "\u03c3", "\\sigma");
+defineSymbol(math, main, mathord, "\u03c4", "\\tau");
+defineSymbol(math, main, mathord, "\u03c5", "\\upsilon");
+defineSymbol(math, main, mathord, "\u03d5", "\\phi");
+defineSymbol(math, main, mathord, "\u03c7", "\\chi");
+defineSymbol(math, main, mathord, "\u03c8", "\\psi");
+defineSymbol(math, main, mathord, "\u03c9", "\\omega");
+defineSymbol(math, main, mathord, "\u03b5", "\\varepsilon");
+defineSymbol(math, main, mathord, "\u03d1", "\\vartheta");
+defineSymbol(math, main, mathord, "\u03d6", "\\varpi");
+defineSymbol(math, main, mathord, "\u03f1", "\\varrho");
+defineSymbol(math, main, mathord, "\u03c2", "\\varsigma");
+defineSymbol(math, main, mathord, "\u03c6", "\\varphi");
+defineSymbol(math, main, bin, "\u2217", "*");
+defineSymbol(math, main, bin, "+", "+");
+defineSymbol(math, main, bin, "\u2212", "-");
+defineSymbol(math, main, bin, "\u22c5", "\\cdot");
+defineSymbol(math, main, bin, "\u2218", "\\circ");
+defineSymbol(math, main, bin, "\u00f7", "\\div");
+defineSymbol(math, main, bin, "\u00b1", "\\pm");
+defineSymbol(math, main, bin, "\u00d7", "\\times");
+defineSymbol(math, main, bin, "\u2229", "\\cap");
+defineSymbol(math, main, bin, "\u222a", "\\cup");
+defineSymbol(math, main, bin, "\u2216", "\\setminus");
+defineSymbol(math, main, bin, "\u2227", "\\land");
+defineSymbol(math, main, bin, "\u2228", "\\lor");
+defineSymbol(math, main, bin, "\u2227", "\\wedge");
+defineSymbol(math, main, bin, "\u2228", "\\vee");
+defineSymbol(math, main, textord, "\u221a", "\\surd");
+defineSymbol(math, main, open, "(", "(");
+defineSymbol(math, main, open, "[", "[");
+defineSymbol(math, main, open, "\u27e8", "\\langle");
+defineSymbol(math, main, open, "\u2223", "\\lvert");
+defineSymbol(math, main, open, "\u2225", "\\lVert");
+defineSymbol(math, main, close, ")", ")");
+defineSymbol(math, main, close, "]", "]");
+defineSymbol(math, main, close, "?", "?");
+defineSymbol(math, main, close, "!", "!");
+defineSymbol(math, main, close, "\u27e9", "\\rangle");
+defineSymbol(math, main, close, "\u2223", "\\rvert");
+defineSymbol(math, main, close, "\u2225", "\\rVert");
+defineSymbol(math, main, rel, "=", "=");
+defineSymbol(math, main, rel, "<", "<");
+defineSymbol(math, main, rel, ">", ">");
+defineSymbol(math, main, rel, ":", ":");
+defineSymbol(math, main, rel, "\u2248", "\\approx");
+defineSymbol(math, main, rel, "\u2245", "\\cong");
+defineSymbol(math, main, rel, "\u2265", "\\ge");
+defineSymbol(math, main, rel, "\u2265", "\\geq");
+defineSymbol(math, main, rel, "\u2190", "\\gets");
+defineSymbol(math, main, rel, ">", "\\gt");
+defineSymbol(math, main, rel, "\u2208", "\\in");
+defineSymbol(math, main, rel, "\u2209", "\\notin");
+defineSymbol(math, main, rel, "\u2282", "\\subset");
+defineSymbol(math, main, rel, "\u2283", "\\supset");
+defineSymbol(math, main, rel, "\u2286", "\\subseteq");
+defineSymbol(math, main, rel, "\u2287", "\\supseteq");
+defineSymbol(math, ams, rel, "\u2288", "\\nsubseteq");
+defineSymbol(math, ams, rel, "\u2289", "\\nsupseteq");
+defineSymbol(math, main, rel, "\u22a8", "\\models");
+defineSymbol(math, main, rel, "\u2190", "\\leftarrow");
+defineSymbol(math, main, rel, "\u2264", "\\le");
+defineSymbol(math, main, rel, "\u2264", "\\leq");
+defineSymbol(math, main, rel, "<", "\\lt");
+defineSymbol(math, main, rel, "\u2260", "\\ne");
+defineSymbol(math, main, rel, "\u2260", "\\neq");
+defineSymbol(math, main, rel, "\u2192", "\\rightarrow");
+defineSymbol(math, main, rel, "\u2192", "\\to");
+defineSymbol(math, ams, rel, "\u2271", "\\ngeq");
+defineSymbol(math, ams, rel, "\u2270", "\\nleq");
+defineSymbol(math, main, spacing, null, "\\!");
+defineSymbol(math, main, spacing, "\u00a0", "\\ ");
+defineSymbol(math, main, spacing, "\u00a0", "~");
+defineSymbol(math, main, spacing, null, "\\,");
+defineSymbol(math, main, spacing, null, "\\:");
+defineSymbol(math, main, spacing, null, "\\;");
+defineSymbol(math, main, spacing, null, "\\enspace");
+defineSymbol(math, main, spacing, null, "\\qquad");
+defineSymbol(math, main, spacing, null, "\\quad");
+defineSymbol(math, main, spacing, "\u00a0", "\\space");
+defineSymbol(math, main, punct, ",", ",");
+defineSymbol(math, main, punct, ";", ";");
+defineSymbol(math, main, punct, ":", "\\colon");
+defineSymbol(math, ams, bin, "\u22bc", "\\barwedge");
+defineSymbol(math, ams, bin, "\u22bb", "\\veebar");
+defineSymbol(math, main, bin, "\u2299", "\\odot");
+defineSymbol(math, main, bin, "\u2295", "\\oplus");
+defineSymbol(math, main, bin, "\u2297", "\\otimes");
+defineSymbol(math, main, textord, "\u2202", "\\partial");
+defineSymbol(math, main, bin, "\u2298", "\\oslash");
+defineSymbol(math, ams, bin, "\u229a", "\\circledcirc");
+defineSymbol(math, ams, bin, "\u22a1", "\\boxdot");
+defineSymbol(math, main, bin, "\u25b3", "\\bigtriangleup");
+defineSymbol(math, main, bin, "\u25bd", "\\bigtriangledown");
+defineSymbol(math, main, bin, "\u2020", "\\dagger");
+defineSymbol(math, main, bin, "\u22c4", "\\diamond");
+defineSymbol(math, main, bin, "\u22c6", "\\star");
+defineSymbol(math, main, bin, "\u25c3", "\\triangleleft");
+defineSymbol(math, main, bin, "\u25b9", "\\triangleright");
+defineSymbol(math, main, open, "{", "\\{");
+defineSymbol(text, main, textord, "{", "\\{");
+defineSymbol(math, main, close, "}", "\\}");
+defineSymbol(text, main, textord, "}", "\\}");
+defineSymbol(math, main, open, "{", "\\lbrace");
+defineSymbol(math, main, close, "}", "\\rbrace");
+defineSymbol(math, main, open, "[", "\\lbrack");
+defineSymbol(math, main, close, "]", "\\rbrack");
+defineSymbol(math, main, open, "\u230a", "\\lfloor");
+defineSymbol(math, main, close, "\u230b", "\\rfloor");
+defineSymbol(math, main, open, "\u2308", "\\lceil");
+defineSymbol(math, main, close, "\u2309", "\\rceil");
+defineSymbol(math, main, textord, "\\", "\\backslash");
+defineSymbol(math, main, textord, "\u2223", "|");
+defineSymbol(math, main, textord, "\u2223", "\\vert");
+defineSymbol(math, main, textord, "\u2225", "\\|");
+defineSymbol(math, main, textord, "\u2225", "\\Vert");
+defineSymbol(math, main, rel, "\u2191", "\\uparrow");
+defineSymbol(math, main, rel, "\u21d1", "\\Uparrow");
+defineSymbol(math, main, rel, "\u2193", "\\downarrow");
+defineSymbol(math, main, rel, "\u21d3", "\\Downarrow");
+defineSymbol(math, main, rel, "\u2195", "\\updownarrow");
+defineSymbol(math, main, rel, "\u21d5", "\\Updownarrow");
+defineSymbol(math, math, op, "\u2210", "\\coprod");
+defineSymbol(math, math, op, "\u22c1", "\\bigvee");
+defineSymbol(math, math, op, "\u22c0", "\\bigwedge");
+defineSymbol(math, math, op, "\u2a04", "\\biguplus");
+defineSymbol(math, math, op, "\u22c2", "\\bigcap");
+defineSymbol(math, math, op, "\u22c3", "\\bigcup");
+defineSymbol(math, math, op, "\u222b", "\\int");
+defineSymbol(math, math, op, "\u222b", "\\intop");
+defineSymbol(math, math, op, "\u222c", "\\iint");
+defineSymbol(math, math, op, "\u222d", "\\iiint");
+defineSymbol(math, math, op, "\u220f", "\\prod");
+defineSymbol(math, math, op, "\u2211", "\\sum");
+defineSymbol(math, math, op, "\u2a02", "\\bigotimes");
+defineSymbol(math, math, op, "\u2a01", "\\bigoplus");
+defineSymbol(math, math, op, "\u2a00", "\\bigodot");
+defineSymbol(math, math, op, "\u222e", "\\oint");
+defineSymbol(math, math, op, "\u2a06", "\\bigsqcup");
+defineSymbol(math, math, op, "\u222b", "\\smallint");
+defineSymbol(text, main, inner, "\u2026", "\\textellipsis");
+defineSymbol(math, main, inner, "\u2026", "\\mathellipsis");
+defineSymbol(text, main, inner, "\u2026", "\\ldots");
+defineSymbol(math, main, inner, "\u2026", "\\ldots");
+defineSymbol(math, main, inner, "\u22ef", "\\cdots");
+defineSymbol(math, main, inner, "\u22f1", "\\ddots");
+defineSymbol(math, main, textord, "\u22ee", "\\vdots");
+defineSymbol(math, main, accent, "\u00b4", "\\acute");
+defineSymbol(math, main, accent, "\u0060", "\\grave");
+defineSymbol(math, main, accent, "\u00a8", "\\ddot");
+defineSymbol(math, main, accent, "\u007e", "\\tilde");
+defineSymbol(math, main, accent, "\u00af", "\\bar");
+defineSymbol(math, main, accent, "\u02d8", "\\breve");
+defineSymbol(math, main, accent, "\u02c7", "\\check");
+defineSymbol(math, main, accent, "\u005e", "\\hat");
+defineSymbol(math, main, accent, "\u20d7", "\\vec");
+defineSymbol(math, main, accent, "\u02d9", "\\dot");
+defineSymbol(math, main, mathord, "\u0131", "\\imath");
+defineSymbol(math, main, mathord, "\u0237", "\\jmath");
+
+defineSymbol(text, main, textord, "\u2013", "--");
+defineSymbol(text, main, textord, "\u2014", "---");
+defineSymbol(text, main, textord, "\u2018", "`");
+defineSymbol(text, main, textord, "\u2019", "'");
+defineSymbol(text, main, textord, "\u201c", "``");
+defineSymbol(text, main, textord, "\u201d", "''");
+defineSymbol(math, main, textord, "\u00b0", "\\degree");
+defineSymbol(text, main, textord, "\u00b0", "\\degree");
+defineSymbol(math, main, mathord, "\u00a3", "\\pounds");
+defineSymbol(math, ams, textord, "\u2720", "\\maltese");
+defineSymbol(text, ams, textord, "\u2720", "\\maltese");
+
+defineSymbol(text, main, spacing, "\u00a0", "\\ ");
+defineSymbol(text, main, spacing, "\u00a0", " ");
+defineSymbol(text, main, spacing, "\u00a0", "~");
+
+// There are lots of symbols which are the same, so we add them in afterwards.
+var i;
+var ch;
+
+// All of these are textords in math mode
+var mathTextSymbols = "0123456789/@.\"";
+for (i = 0; i < mathTextSymbols.length; i++) {
+    ch = mathTextSymbols.charAt(i);
+    defineSymbol(math, main, textord, ch, ch);
+}
+
+// All of these are textords in text mode
+var textSymbols = "0123456789!@*()-=+[]\";:?/.,";
+for (i = 0; i < textSymbols.length; i++) {
+    ch = textSymbols.charAt(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// All of these are textords in text mode, and mathords in math mode
+var letters = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
+for (i = 0; i < letters.length; i++) {
+    ch = letters.charAt(i);
+    defineSymbol(math, main, mathord, ch, ch);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// Latin-1 letters
+for (i = 0x00C0; i <= 0x00D6; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+for (i = 0x00D8; i <= 0x00F6; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+for (i = 0x00F8; i <= 0x00FF; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// Cyrillic
+for (i = 0x0410; i <= 0x044F; i++) {
+    ch = String.fromCharCode(i);
+    defineSymbol(text, main, textord, ch, ch);
+}
+
+// Unicode versions of existing characters
+defineSymbol(text, main, textord, "\u2013", "–");
+defineSymbol(text, main, textord, "\u2014", "—");
+defineSymbol(text, main, textord, "\u2018", "‘");
+defineSymbol(text, main, textord, "\u2019", "’");
+defineSymbol(text, main, textord, "\u201c", "“");
+defineSymbol(text, main, textord, "\u201d", "”");
+
+},{}],24:[function(require,module,exports){
+var hangulRegex = /[\uAC00-\uD7AF]/;
+
+// This regex combines
+// - Hiragana: [\u3040-\u309F]
+// - Katakana: [\u30A0-\u30FF]
+// - CJK ideograms: [\u4E00-\u9FAF]
+// - Hangul syllables: [\uAC00-\uD7AF]
+// Notably missing are halfwidth Katakana and Romanji glyphs.
+var cjkRegex =
+    /[\u3040-\u309F]|[\u30A0-\u30FF]|[\u4E00-\u9FAF]|[\uAC00-\uD7AF]/;
+
+module.exports = {
+    cjkRegex: cjkRegex,
+    hangulRegex: hangulRegex
+};
+
+},{}],25:[function(require,module,exports){
+/**
+ * This file contains a list of utility functions which are useful in other
+ * files.
+ */
+
+/**
+ * Provide an `indexOf` function which works in IE8, but defers to native if
+ * possible.
+ */
+var nativeIndexOf = Array.prototype.indexOf;
+var indexOf = function(list, elem) {
+    if (list == null) {
+        return -1;
+    }
+    if (nativeIndexOf && list.indexOf === nativeIndexOf) {
+        return list.indexOf(elem);
+    }
+    var i = 0;
+    var l = list.length;
+    for (; i < l; i++) {
+        if (list[i] === elem) {
+            return i;
+        }
+    }
+    return -1;
+};
+
+/**
+ * Return whether an element is contained in a list
+ */
+var contains = function(list, elem) {
+    return indexOf(list, elem) !== -1;
+};
+
+/**
+ * Provide a default value if a setting is undefined
+ */
+var deflt = function(setting, defaultIfUndefined) {
+    return setting === undefined ? defaultIfUndefined : setting;
+};
+
+// hyphenate and escape adapted from Facebook's React under Apache 2 license
+
+var uppercase = /([A-Z])/g;
+var hyphenate = function(str) {
+    return str.replace(uppercase, "-$1").toLowerCase();
+};
+
+var ESCAPE_LOOKUP = {
+    "&": "&amp;",
+    ">": "&gt;",
+    "<": "&lt;",
+    "\"": "&quot;",
+    "'": "&#x27;"
+};
+
+var ESCAPE_REGEX = /[&><"']/g;
+
+function escaper(match) {
+    return ESCAPE_LOOKUP[match];
+}
+
+/**
+ * Escapes text to prevent scripting attacks.
+ *
+ * @param {*} text Text value to escape.
+ * @return {string} An escaped string.
+ */
+function escape(text) {
+    return ("" + text).replace(ESCAPE_REGEX, escaper);
+}
+
+/**
+ * A function to set the text content of a DOM element in all supported
+ * browsers. Note that we don't define this if there is no document.
+ */
+var setTextContent;
+if (typeof document !== "undefined") {
+    var testNode = document.createElement("span");
+    if ("textContent" in testNode) {
+        setTextContent = function(node, text) {
+            node.textContent = text;
+        };
+    } else {
+        setTextContent = function(node, text) {
+            node.innerText = text;
+        };
+    }
+}
+
+/**
+ * A function to clear a node.
+ */
+function clearNode(node) {
+    setTextContent(node, "");
+}
+
+module.exports = {
+    contains: contains,
+    deflt: deflt,
+    escape: escape,
+    hyphenate: hyphenate,
+    indexOf: indexOf,
+    setTextContent: setTextContent,
+    clearNode: clearNode
+};
+
+},{}]},{},[1])(1)
+});
\ No newline at end of file
diff --git a/specs/gl/katex/katex.min.css b/specs/gl/katex/katex.min.css
new file mode 100644
index 0000000..d6fb837
--- /dev/null
+++ b/specs/gl/katex/katex.min.css
@@ -0,0 +1 @@
+@font-face{font-family:KaTeX_AMS;src:url(fonts/KaTeX_AMS-Regular.eot);src:url(fonts/KaTeX_AMS-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_AMS-Regular.woff2) format('woff2'),url(fonts/KaTeX_AMS-Regular.woff) format('woff'),url(fonts/KaTeX_AMS-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Caligraphic;src:url(fonts/KaTeX_Caligraphic-Bold.eot);src:url(fonts/KaTeX_Caligraphic-Bold.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Caligraphic-Bold.woff2) format('woff2'),url(fonts/KaTeX_Caligraphic-Bold.woff) format('woff'),url(fonts/KaTeX_Caligraphic-Bold.ttf) format('truetype');font-weight:700;font-style:normal}@font-face{font-family:KaTeX_Caligraphic;src:url(fonts/KaTeX_Caligraphic-Regular.eot);src:url(fonts/KaTeX_Caligraphic-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Caligraphic-Regular.woff2) format('woff2'),url(fonts/KaTeX_Caligraphic-Regular.woff) format('woff'),url(fonts/KaTeX_Caligraphic-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Fraktur;src:url(fonts/KaTeX_Fraktur-Bold.eot);src:url(fonts/KaTeX_Fraktur-Bold.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Fraktur-Bold.woff2) format('woff2'),url(fonts/KaTeX_Fraktur-Bold.woff) format('woff'),url(fonts/KaTeX_Fraktur-Bold.ttf) format('truetype');font-weight:700;font-style:normal}@font-face{font-family:KaTeX_Fraktur;src:url(fonts/KaTeX_Fraktur-Regular.eot);src:url(fonts/KaTeX_Fraktur-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Fraktur-Regular.woff2) format('woff2'),url(fonts/KaTeX_Fraktur-Regular.woff) format('woff'),url(fonts/KaTeX_Fraktur-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Main;src:url(fonts/KaTeX_Main-Bold.eot);src:url(fonts/KaTeX_Main-Bold.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Main-Bold.woff2) format('woff2'),url(fonts/KaTeX_Main-Bold.woff) format('woff'),url(fonts/KaTeX_Main-Bold.ttf) format('truetype');font-weight:700;font-style:normal}@font-face{font-family:KaTeX_Main;src:url(fonts/KaTeX_Main-Italic.eot);src:url(fonts/KaTeX_Main-Italic.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Main-Italic.woff2) format('woff2'),url(fonts/KaTeX_Main-Italic.woff) format('woff'),url(fonts/KaTeX_Main-Italic.ttf) format('truetype');font-weight:400;font-style:italic}@font-face{font-family:KaTeX_Main;src:url(fonts/KaTeX_Main-Regular.eot);src:url(fonts/KaTeX_Main-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Main-Regular.woff2) format('woff2'),url(fonts/KaTeX_Main-Regular.woff) format('woff'),url(fonts/KaTeX_Main-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Math;src:url(fonts/KaTeX_Math-Italic.eot);src:url(fonts/KaTeX_Math-Italic.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Math-Italic.woff2) format('woff2'),url(fonts/KaTeX_Math-Italic.woff) format('woff'),url(fonts/KaTeX_Math-Italic.ttf) format('truetype');font-weight:400;font-style:italic}@font-face{font-family:KaTeX_SansSerif;src:url(fonts/KaTeX_SansSerif-Regular.eot);src:url(fonts/KaTeX_SansSerif-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_SansSerif-Regular.woff2) format('woff2'),url(fonts/KaTeX_SansSerif-Regular.woff) format('woff'),url(fonts/KaTeX_SansSerif-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Script;src:url(fonts/KaTeX_Script-Regular.eot);src:url(fonts/KaTeX_Script-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Script-Regular.woff2) format('woff2'),url(fonts/KaTeX_Script-Regular.woff) format('woff'),url(fonts/KaTeX_Script-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size1;src:url(fonts/KaTeX_Size1-Regular.eot);src:url(fonts/KaTeX_Size1-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size1-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size1-Regular.woff) format('woff'),url(fonts/KaTeX_Size1-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size2;src:url(fonts/KaTeX_Size2-Regular.eot);src:url(fonts/KaTeX_Size2-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size2-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size2-Regular.woff) format('woff'),url(fonts/KaTeX_Size2-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size3;src:url(fonts/KaTeX_Size3-Regular.eot);src:url(fonts/KaTeX_Size3-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size3-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size3-Regular.woff) format('woff'),url(fonts/KaTeX_Size3-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Size4;src:url(fonts/KaTeX_Size4-Regular.eot);src:url(fonts/KaTeX_Size4-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Size4-Regular.woff2) format('woff2'),url(fonts/KaTeX_Size4-Regular.woff) format('woff'),url(fonts/KaTeX_Size4-Regular.ttf) format('truetype');font-weight:400;font-style:normal}@font-face{font-family:KaTeX_Typewriter;src:url(fonts/KaTeX_Typewriter-Regular.eot);src:url(fonts/KaTeX_Typewriter-Regular.eot#iefix) format('embedded-opentype'),url(fonts/KaTeX_Typewriter-Regular.woff2) format('woff2'),url(fonts/KaTeX_Typewriter-Regular.woff) format('woff'),url(fonts/KaTeX_Typewriter-Regular.ttf) format('truetype');font-weight:400;font-style:normal}.katex-display{display:block;margin:1em 0;text-align:center}.katex-display>.katex{display:inline-block;text-align:initial}.katex{font:400 1.21em KaTeX_Main,Times New Roman,serif;line-height:1.2;white-space:nowrap;text-indent:0}.katex .katex-html{display:inline-block}.katex .katex-mathml{position:absolute;clip:rect(1px,1px,1px,1px);padding:0;border:0;height:1px;width:1px;overflow:hidden}.katex .base,.katex .strut{display:inline-block}.katex .mathrm{font-style:normal}.katex .textit{font-style:italic}.katex .mathit{font-family:KaTeX_Math;font-style:italic}.katex .mathbf{font-family:KaTeX_Main;font-weight:700}.katex .amsrm,.katex .mathbb{font-family:KaTeX_AMS}.katex .mathcal{font-family:KaTeX_Caligraphic}.katex .mathfrak{font-family:KaTeX_Fraktur}.katex .mathtt{font-family:KaTeX_Typewriter}.katex .mathscr{font-family:KaTeX_Script}.katex .mathsf{font-family:KaTeX_SansSerif}.katex .mainit{font-family:KaTeX_Main;font-style:italic}.katex .mord+.mop{margin-left:.16667em}.katex .mord+.mbin{margin-left:.22222em}.katex .mord+.mrel{margin-left:.27778em}.katex .mop+.mop,.katex .mop+.mord,.katex .mord+.minner{margin-left:.16667em}.katex .mop+.mrel{margin-left:.27778em}.katex .mop+.minner{margin-left:.16667em}.katex .mbin+.minner,.katex .mbin+.mop,.katex .mbin+.mopen,.katex .mbin+.mord{margin-left:.22222em}.katex .mrel+.minner,.katex .mrel+.mop,.katex .mrel+.mopen,.katex .mrel+.mord{margin-left:.27778em}.katex .mclose+.mop{margin-left:.16667em}.katex .mclose+.mbin{margin-left:.22222em}.katex .mclose+.mrel{margin-left:.27778em}.katex .mclose+.minner,.katex .minner+.mop,.katex .minner+.mord,.katex .mpunct+.mclose,.katex .mpunct+.minner,.katex .mpunct+.mop,.katex .mpunct+.mopen,.katex .mpunct+.mord,.katex .mpunct+.mpunct,.katex .mpunct+.mrel{margin-left:.16667em}.katex .minner+.mbin{margin-left:.22222em}.katex .minner+.mrel{margin-left:.27778em}.katex .minner+.minner,.katex .minner+.mopen,.katex .minner+.mpunct{margin-left:.16667em}.katex .mbin.mtight,.katex .mclose.mtight,.katex .minner.mtight,.katex .mop.mtight,.katex .mopen.mtight,.katex .mord.mtight,.katex .mpunct.mtight,.katex .mrel.mtight{margin-left:0}.katex .mclose+.mop.mtight,.katex .minner+.mop.mtight,.katex .mop+.mop.mtight,.katex .mop+.mord.mtight,.katex .mord+.mop.mtight{margin-left:.16667em}.katex .reset-textstyle.textstyle{font-size:1em}.katex .reset-textstyle.scriptstyle{font-size:.7em}.katex .reset-textstyle.scriptscriptstyle{font-size:.5em}.katex .reset-scriptstyle.textstyle{font-size:1.42857em}.katex .reset-scriptstyle.scriptstyle{font-size:1em}.katex .reset-scriptstyle.scriptscriptstyle{font-size:.71429em}.katex .reset-scriptscriptstyle.textstyle{font-size:2em}.katex .reset-scriptscriptstyle.scriptstyle{font-size:1.4em}.katex .reset-scriptscriptstyle.scriptscriptstyle{font-size:1em}.katex .style-wrap{position:relative}.katex .vlist{display:inline-block}.katex .vlist>span{display:block;height:0;position:relative}.katex .vlist>span>span{display:inline-block}.katex .vlist .baseline-fix{display:inline-table;table-layout:fixed}.katex .msupsub{text-align:left}.katex .mfrac>span>span{text-align:center}.katex .mfrac .frac-line{width:100%}.katex .mfrac .frac-line:before{border-bottom-style:solid;border-bottom-width:1px;content:"";display:block}.katex .mfrac .frac-line:after{border-bottom-style:solid;border-bottom-width:.04em;content:"";display:block;margin-top:-1px}.katex .mspace{display:inline-block}.katex .mspace.negativethinspace{margin-left:-.16667em}.katex .mspace.thinspace{width:.16667em}.katex .mspace.negativemediumspace{margin-left:-.22222em}.katex .mspace.mediumspace{width:.22222em}.katex .mspace.thickspace{width:.27778em}.katex .mspace.sixmuspace{width:.333333em}.katex .mspace.eightmuspace{width:.444444em}.katex .mspace.enspace{width:.5em}.katex .mspace.twelvemuspace{width:.666667em}.katex .mspace.quad{width:1em}.katex .mspace.qquad{width:2em}.katex .llap,.katex .rlap{width:0;position:relative}.katex .llap>.inner,.katex .rlap>.inner{position:absolute}.katex .llap>.fix,.katex .rlap>.fix{display:inline-block}.katex .llap>.inner{right:0}.katex .rlap>.inner{left:0}.katex .katex-logo .a{font-size:.75em;margin-left:-.32em;position:relative;top:-.2em}.katex .katex-logo .t{margin-left:-.23em}.katex .katex-logo .e{margin-left:-.1667em;position:relative;top:.2155em}.katex .katex-logo .x{margin-left:-.125em}.katex .rule{display:inline-block;border:0 solid;position:relative}.katex .overline .overline-line,.katex .underline .underline-line{width:100%}.katex .overline .overline-line:before,.katex .underline .underline-line:before{border-bottom-style:solid;border-bottom-width:1px;content:"";display:block}.katex .overline .overline-line:after,.katex .underline .underline-line:after{border-bottom-style:solid;border-bottom-width:.04em;content:"";display:block;margin-top:-1px}.katex .sqrt>.sqrt-sign{position:relative}.katex .sqrt .sqrt-line{width:100%}.katex .sqrt .sqrt-line:before{border-bottom-style:solid;border-bottom-width:1px;content:"";display:block}.katex .sqrt .sqrt-line:after{border-bottom-style:solid;border-bottom-width:.04em;content:"";display:block;margin-top:-1px}.katex .sqrt>.root{margin-left:.27777778em;margin-right:-.55555556em}.katex .fontsize-ensurer,.katex .sizing{display:inline-block}.katex .fontsize-ensurer.reset-size1.size1,.katex .sizing.reset-size1.size1{font-size:1em}.katex .fontsize-ensurer.reset-size1.size2,.katex .sizing.reset-size1.size2{font-size:1.4em}.katex .fontsize-ensurer.reset-size1.size3,.katex .sizing.reset-size1.size3{font-size:1.6em}.katex .fontsize-ensurer.reset-size1.size4,.katex .sizing.reset-size1.size4{font-size:1.8em}.katex .fontsize-ensurer.reset-size1.size5,.katex .sizing.reset-size1.size5{font-size:2em}.katex .fontsize-ensurer.reset-size1.size6,.katex .sizing.reset-size1.size6{font-size:2.4em}.katex .fontsize-ensurer.reset-size1.size7,.katex .sizing.reset-size1.size7{font-size:2.88em}.katex .fontsize-ensurer.reset-size1.size8,.katex .sizing.reset-size1.size8{font-size:3.46em}.katex .fontsize-ensurer.reset-size1.size9,.katex .sizing.reset-size1.size9{font-size:4.14em}.katex .fontsize-ensurer.reset-size1.size10,.katex .sizing.reset-size1.size10{font-size:4.98em}.katex .fontsize-ensurer.reset-size2.size1,.katex .sizing.reset-size2.size1{font-size:.71428571em}.katex .fontsize-ensurer.reset-size2.size2,.katex .sizing.reset-size2.size2{font-size:1em}.katex .fontsize-ensurer.reset-size2.size3,.katex .sizing.reset-size2.size3{font-size:1.14285714em}.katex .fontsize-ensurer.reset-size2.size4,.katex .sizing.reset-size2.size4{font-size:1.28571429em}.katex .fontsize-ensurer.reset-size2.size5,.katex .sizing.reset-size2.size5{font-size:1.42857143em}.katex .fontsize-ensurer.reset-size2.size6,.katex .sizing.reset-size2.size6{font-size:1.71428571em}.katex .fontsize-ensurer.reset-size2.size7,.katex .sizing.reset-size2.size7{font-size:2.05714286em}.katex .fontsize-ensurer.reset-size2.size8,.katex .sizing.reset-size2.size8{font-size:2.47142857em}.katex .fontsize-ensurer.reset-size2.size9,.katex .sizing.reset-size2.size9{font-size:2.95714286em}.katex .fontsize-ensurer.reset-size2.size10,.katex .sizing.reset-size2.size10{font-size:3.55714286em}.katex .fontsize-ensurer.reset-size3.size1,.katex .sizing.reset-size3.size1{font-size:.625em}.katex .fontsize-ensurer.reset-size3.size2,.katex .sizing.reset-size3.size2{font-size:.875em}.katex .fontsize-ensurer.reset-size3.size3,.katex .sizing.reset-size3.size3{font-size:1em}.katex .fontsize-ensurer.reset-size3.size4,.katex .sizing.reset-size3.size4{font-size:1.125em}.katex .fontsize-ensurer.reset-size3.size5,.katex .sizing.reset-size3.size5{font-size:1.25em}.katex .fontsize-ensurer.reset-size3.size6,.katex .sizing.reset-size3.size6{font-size:1.5em}.katex .fontsize-ensurer.reset-size3.size7,.katex .sizing.reset-size3.size7{font-size:1.8em}.katex .fontsize-ensurer.reset-size3.size8,.katex .sizing.reset-size3.size8{font-size:2.1625em}.katex .fontsize-ensurer.reset-size3.size9,.katex .sizing.reset-size3.size9{font-size:2.5875em}.katex .fontsize-ensurer.reset-size3.size10,.katex .sizing.reset-size3.size10{font-size:3.1125em}.katex .fontsize-ensurer.reset-size4.size1,.katex .sizing.reset-size4.size1{font-size:.55555556em}.katex .fontsize-ensurer.reset-size4.size2,.katex .sizing.reset-size4.size2{font-size:.77777778em}.katex .fontsize-ensurer.reset-size4.size3,.katex .sizing.reset-size4.size3{font-size:.88888889em}.katex .fontsize-ensurer.reset-size4.size4,.katex .sizing.reset-size4.size4{font-size:1em}.katex .fontsize-ensurer.reset-size4.size5,.katex .sizing.reset-size4.size5{font-size:1.11111111em}.katex .fontsize-ensurer.reset-size4.size6,.katex .sizing.reset-size4.size6{font-size:1.33333333em}.katex .fontsize-ensurer.reset-size4.size7,.katex .sizing.reset-size4.size7{font-size:1.6em}.katex .fontsize-ensurer.reset-size4.size8,.katex .sizing.reset-size4.size8{font-size:1.92222222em}.katex .fontsize-ensurer.reset-size4.size9,.katex .sizing.reset-size4.size9{font-size:2.3em}.katex .fontsize-ensurer.reset-size4.size10,.katex .sizing.reset-size4.size10{font-size:2.76666667em}.katex .fontsize-ensurer.reset-size5.size1,.katex .sizing.reset-size5.size1{font-size:.5em}.katex .fontsize-ensurer.reset-size5.size2,.katex .sizing.reset-size5.size2{font-size:.7em}.katex .fontsize-ensurer.reset-size5.size3,.katex .sizing.reset-size5.size3{font-size:.8em}.katex .fontsize-ensurer.reset-size5.size4,.katex .sizing.reset-size5.size4{font-size:.9em}.katex .fontsize-ensurer.reset-size5.size5,.katex .sizing.reset-size5.size5{font-size:1em}.katex .fontsize-ensurer.reset-size5.size6,.katex .sizing.reset-size5.size6{font-size:1.2em}.katex .fontsize-ensurer.reset-size5.size7,.katex .sizing.reset-size5.size7{font-size:1.44em}.katex .fontsize-ensurer.reset-size5.size8,.katex .sizing.reset-size5.size8{font-size:1.73em}.katex .fontsize-ensurer.reset-size5.size9,.katex .sizing.reset-size5.size9{font-size:2.07em}.katex .fontsize-ensurer.reset-size5.size10,.katex .sizing.reset-size5.size10{font-size:2.49em}.katex .fontsize-ensurer.reset-size6.size1,.katex .sizing.reset-size6.size1{font-size:.41666667em}.katex .fontsize-ensurer.reset-size6.size2,.katex .sizing.reset-size6.size2{font-size:.58333333em}.katex .fontsize-ensurer.reset-size6.size3,.katex .sizing.reset-size6.size3{font-size:.66666667em}.katex .fontsize-ensurer.reset-size6.size4,.katex .sizing.reset-size6.size4{font-size:.75em}.katex .fontsize-ensurer.reset-size6.size5,.katex .sizing.reset-size6.size5{font-size:.83333333em}.katex .fontsize-ensurer.reset-size6.size6,.katex .sizing.reset-size6.size6{font-size:1em}.katex .fontsize-ensurer.reset-size6.size7,.katex .sizing.reset-size6.size7{font-size:1.2em}.katex .fontsize-ensurer.reset-size6.size8,.katex .sizing.reset-size6.size8{font-size:1.44166667em}.katex .fontsize-ensurer.reset-size6.size9,.katex .sizing.reset-size6.size9{font-size:1.725em}.katex .fontsize-ensurer.reset-size6.size10,.katex .sizing.reset-size6.size10{font-size:2.075em}.katex .fontsize-ensurer.reset-size7.size1,.katex .sizing.reset-size7.size1{font-size:.34722222em}.katex .fontsize-ensurer.reset-size7.size2,.katex .sizing.reset-size7.size2{font-size:.48611111em}.katex .fontsize-ensurer.reset-size7.size3,.katex .sizing.reset-size7.size3{font-size:.55555556em}.katex .fontsize-ensurer.reset-size7.size4,.katex .sizing.reset-size7.size4{font-size:.625em}.katex .fontsize-ensurer.reset-size7.size5,.katex .sizing.reset-size7.size5{font-size:.69444444em}.katex .fontsize-ensurer.reset-size7.size6,.katex .sizing.reset-size7.size6{font-size:.83333333em}.katex .fontsize-ensurer.reset-size7.size7,.katex .sizing.reset-size7.size7{font-size:1em}.katex .fontsize-ensurer.reset-size7.size8,.katex .sizing.reset-size7.size8{font-size:1.20138889em}.katex .fontsize-ensurer.reset-size7.size9,.katex .sizing.reset-size7.size9{font-size:1.4375em}.katex .fontsize-ensurer.reset-size7.size10,.katex .sizing.reset-size7.size10{font-size:1.72916667em}.katex .fontsize-ensurer.reset-size8.size1,.katex .sizing.reset-size8.size1{font-size:.28901734em}.katex .fontsize-ensurer.reset-size8.size2,.katex .sizing.reset-size8.size2{font-size:.40462428em}.katex .fontsize-ensurer.reset-size8.size3,.katex .sizing.reset-size8.size3{font-size:.46242775em}.katex .fontsize-ensurer.reset-size8.size4,.katex .sizing.reset-size8.size4{font-size:.52023121em}.katex .fontsize-ensurer.reset-size8.size5,.katex .sizing.reset-size8.size5{font-size:.57803468em}.katex .fontsize-ensurer.reset-size8.size6,.katex .sizing.reset-size8.size6{font-size:.69364162em}.katex .fontsize-ensurer.reset-size8.size7,.katex .sizing.reset-size8.size7{font-size:.83236994em}.katex .fontsize-ensurer.reset-size8.size8,.katex .sizing.reset-size8.size8{font-size:1em}.katex .fontsize-ensurer.reset-size8.size9,.katex .sizing.reset-size8.size9{font-size:1.19653179em}.katex .fontsize-ensurer.reset-size8.size10,.katex .sizing.reset-size8.size10{font-size:1.43930636em}.katex .fontsize-ensurer.reset-size9.size1,.katex .sizing.reset-size9.size1{font-size:.24154589em}.katex .fontsize-ensurer.reset-size9.size2,.katex .sizing.reset-size9.size2{font-size:.33816425em}.katex .fontsize-ensurer.reset-size9.size3,.katex .sizing.reset-size9.size3{font-size:.38647343em}.katex .fontsize-ensurer.reset-size9.size4,.katex .sizing.reset-size9.size4{font-size:.43478261em}.katex .fontsize-ensurer.reset-size9.size5,.katex .sizing.reset-size9.size5{font-size:.48309179em}.katex .fontsize-ensurer.reset-size9.size6,.katex .sizing.reset-size9.size6{font-size:.57971014em}.katex .fontsize-ensurer.reset-size9.size7,.katex .sizing.reset-size9.size7{font-size:.69565217em}.katex .fontsize-ensurer.reset-size9.size8,.katex .sizing.reset-size9.size8{font-size:.83574879em}.katex .fontsize-ensurer.reset-size9.size9,.katex .sizing.reset-size9.size9{font-size:1em}.katex .fontsize-ensurer.reset-size9.size10,.katex .sizing.reset-size9.size10{font-size:1.20289855em}.katex .fontsize-ensurer.reset-size10.size1,.katex .sizing.reset-size10.size1{font-size:.20080321em}.katex .fontsize-ensurer.reset-size10.size2,.katex .sizing.reset-size10.size2{font-size:.2811245em}.katex .fontsize-ensurer.reset-size10.size3,.katex .sizing.reset-size10.size3{font-size:.32128514em}.katex .fontsize-ensurer.reset-size10.size4,.katex .sizing.reset-size10.size4{font-size:.36144578em}.katex .fontsize-ensurer.reset-size10.size5,.katex .sizing.reset-size10.size5{font-size:.40160643em}.katex .fontsize-ensurer.reset-size10.size6,.katex .sizing.reset-size10.size6{font-size:.48192771em}.katex .fontsize-ensurer.reset-size10.size7,.katex .sizing.reset-size10.size7{font-size:.57831325em}.katex .fontsize-ensurer.reset-size10.size8,.katex .sizing.reset-size10.size8{font-size:.69477912em}.katex .fontsize-ensurer.reset-size10.size9,.katex .sizing.reset-size10.size9{font-size:.8313253em}.katex .fontsize-ensurer.reset-size10.size10,.katex .sizing.reset-size10.size10{font-size:1em}.katex .delimsizing.size1{font-family:KaTeX_Size1}.katex .delimsizing.size2{font-family:KaTeX_Size2}.katex .delimsizing.size3{font-family:KaTeX_Size3}.katex .delimsizing.size4{font-family:KaTeX_Size4}.katex .delimsizing.mult .delim-size1>span{font-family:KaTeX_Size1}.katex .delimsizing.mult .delim-size4>span{font-family:KaTeX_Size4}.katex .nulldelimiter{display:inline-block;width:.12em}.katex .op-symbol{position:relative}.katex .op-symbol.small-op{font-family:KaTeX_Size1}.katex .op-symbol.large-op{font-family:KaTeX_Size2}.katex .accent>.vlist>span,.katex .op-limits>.vlist>span{text-align:center}.katex .accent .accent-body>span{width:0}.katex .accent .accent-body.accent-vec>span{position:relative;left:.326em}.katex .mtable .vertical-separator{display:inline-block;margin:0 -.025em;border-right:.05em solid #000}.katex .mtable .arraycolsep{display:inline-block}.katex .mtable .col-align-c>.vlist{text-align:center}.katex .mtable .col-align-l>.vlist{text-align:left}.katex .mtable .col-align-r>.vlist{text-align:right}
\ No newline at end of file
diff --git a/specs/gl/katex/katex.min.js b/specs/gl/katex/katex.min.js
new file mode 100644
index 0000000..66c0821
--- /dev/null
+++ b/specs/gl/katex/katex.min.js
@@ -0,0 +1,4 @@
+(function(e){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=e()}else if(typeof define==="function"&&define.amd){define([],e)}else{var t;if(typeof window!=="undefined"){t=window}else if(typeof global!=="undefined"){t=global}else if(typeof self!=="undefined"){t=self}else{t=this}t.katex=e()}})(function(){var e,t,r;return function a(e,t,r){function i(s,l){if(!t[s]){if(!e[s]){var o=typeof require=="function"&&require;if(!l&&o)return o(s,!0);if(n)return n(s,!0);var u=new Error("Cannot find module '"+s+"'");throw u.code="MODULE_NOT_FOUND",u}var p=t[s]={exports:{}};e[s][0].call(p.exports,function(t){var r=e[s][1][t];return i(r?r:t)},p,p.exports,a,e,t,r)}return t[s].exports}var n=typeof require=="function"&&require;for(var s=0;s<r.length;s++)i(r[s]);return i}({1:[function(e,t,r){var a=e("./src/ParseError");var i=e("./src/Settings");var n=e("./src/buildTree");var s=e("./src/parseTree");var l=e("./src/utils");var o=function(e,t,r){l.clearNode(t);var a=new i(r);var o=s(e,a);var u=n(o,e,a).toNode();t.appendChild(u)};if(typeof document!=="undefined"){if(document.compatMode!=="CSS1Compat"){typeof console!=="undefined"&&console.warn("Warning: KaTeX doesn't work in quirks mode. Make sure your "+"website has a suitable doctype.");o=function(){throw new a("KaTeX doesn't work in quirks mode.")}}}var u=function(e,t){var r=new i(t);var a=s(e,r);return n(a,e,r).toMarkup()};var p=function(e,t){var r=new i(t);return s(e,r)};t.exports={render:o,renderToString:u,__parse:p,ParseError:a}},{"./src/ParseError":6,"./src/Settings":8,"./src/buildTree":13,"./src/parseTree":22,"./src/utils":25}],2:[function(e,t,r){"use strict";function a(e){if(!e.__matchAtRelocatable){var t=e.source+"|()";var r="g"+(e.ignoreCase?"i":"")+(e.multiline?"m":"")+(e.unicode?"u":"");e.__matchAtRelocatable=new RegExp(t,r)}return e.__matchAtRelocatable}function i(e,t,r){if(e.global||e.sticky){throw new Error("matchAt(...): Only non-global regexes are supported")}var i=a(e);i.lastIndex=r;var n=i.exec(t);if(n[n.length-1]==null){n.length=n.length-1;return n}else{return null}}t.exports=i},{}],3:[function(e,t,r){var a=e("match-at");var i=e("./ParseError");function n(e){this.input=e;this.pos=0}function s(e,t,r,a){this.text=e;this.start=t;this.end=r;this.lexer=a}s.prototype.range=function(e,t){if(e.lexer!==this.lexer){return new s(t)}return new s(t,this.start,e.end,this.lexer)};var l=new RegExp("([ \r\n	]+)|"+"([!-\\[\\]-\u2027\u202a-\ud7ff\uf900-\uffff]"+"|[\ud800-\udbff][\udc00-\udfff]"+"|\\\\(?:[a-zA-Z]+|[^\ud800-\udfff])"+")");n.prototype.lex=function(){var e=this.input;var t=this.pos;if(t===e.length){return new s("EOF",t,t,this)}var r=a(l,e,t);if(r===null){throw new i("Unexpected character: '"+e[t]+"'",new s(e[t],t,t+1,this))}var n=r[2]||" ";var o=this.pos;this.pos+=r[0].length;var u=this.pos;return new s(n,o,u,this)};t.exports=n},{"./ParseError":6,"match-at":2}],4:[function(e,t,r){var a=e("./Lexer");function i(e,t){this.lexer=new a(e);this.macros=t;this.stack=[];this.discardedWhiteSpace=[]}i.prototype.nextToken=function(){for(;;){if(this.stack.length===0){this.stack.push(this.lexer.lex())}var e=this.stack.pop();var t=e.text;if(!(t.charAt(0)==="\\"&&this.macros.hasOwnProperty(t))){return e}var r=this.macros[t];if(typeof r==="string"){var i=new a(r);r=[];var n=i.lex();while(n.text!=="EOF"){r.push(n);n=i.lex()}r.reverse();this.macros[t]=r}this.stack=this.stack.concat(r)}};i.prototype.get=function(e){this.discardedWhiteSpace=[];var t=this.nextToken();if(e){while(t.text===" "){this.discardedWhiteSpace.push(t);t=this.nextToken()}}return t};i.prototype.unget=function(e){this.stack.push(e);while(this.discardedWhiteSpace.length!==0){this.stack.push(this.discardedWhiteSpace.pop())}};t.exports=i},{"./Lexer":3}],5:[function(e,t,r){function a(e){this.style=e.style;this.color=e.color;this.size=e.size;this.phantom=e.phantom;this.font=e.font;if(e.parentStyle===undefined){this.parentStyle=e.style}else{this.parentStyle=e.parentStyle}if(e.parentSize===undefined){this.parentSize=e.size}else{this.parentSize=e.parentSize}}a.prototype.extend=function(e){var t={style:this.style,size:this.size,color:this.color,parentStyle:this.style,parentSize:this.size,phantom:this.phantom,font:this.font};for(var r in e){if(e.hasOwnProperty(r)){t[r]=e[r]}}return new a(t)};a.prototype.withStyle=function(e){return this.extend({style:e})};a.prototype.withSize=function(e){return this.extend({size:e})};a.prototype.withColor=function(e){return this.extend({color:e})};a.prototype.withPhantom=function(){return this.extend({phantom:true})};a.prototype.withFont=function(e){return this.extend({font:e||this.font})};a.prototype.reset=function(){return this.extend({})};var i={"katex-blue":"#6495ed","katex-orange":"#ffa500","katex-pink":"#ff00af","katex-red":"#df0030","katex-green":"#28ae7b","katex-gray":"gray","katex-purple":"#9d38bd","katex-blueA":"#ccfaff","katex-blueB":"#80f6ff","katex-blueC":"#63d9ea","katex-blueD":"#11accd","katex-blueE":"#0c7f99","katex-tealA":"#94fff5","katex-tealB":"#26edd5","katex-tealC":"#01d1c1","katex-tealD":"#01a995","katex-tealE":"#208170","katex-greenA":"#b6ffb0","katex-greenB":"#8af281","katex-greenC":"#74cf70","katex-greenD":"#1fab54","katex-greenE":"#0d923f","katex-goldA":"#ffd0a9","katex-goldB":"#ffbb71","katex-goldC":"#ff9c39","katex-goldD":"#e07d10","katex-goldE":"#a75a05","katex-redA":"#fca9a9","katex-redB":"#ff8482","katex-redC":"#f9685d","katex-redD":"#e84d39","katex-redE":"#bc2612","katex-maroonA":"#ffbde0","katex-maroonB":"#ff92c6","katex-maroonC":"#ed5fa6","katex-maroonD":"#ca337c","katex-maroonE":"#9e034e","katex-purpleA":"#ddd7ff","katex-purpleB":"#c6b9fc","katex-purpleC":"#aa87ff","katex-purpleD":"#7854ab","katex-purpleE":"#543b78","katex-mintA":"#f5f9e8","katex-mintB":"#edf2df","katex-mintC":"#e0e5cc","katex-grayA":"#f6f7f7","katex-grayB":"#f0f1f2","katex-grayC":"#e3e5e6","katex-grayD":"#d6d8da","katex-grayE":"#babec2","katex-grayF":"#888d93","katex-grayG":"#626569","katex-grayH":"#3b3e40","katex-grayI":"#21242c","katex-kaBlue":"#314453","katex-kaGreen":"#71B307"};a.prototype.getColor=function(){if(this.phantom){return"transparent"}else{return i[this.color]||this.color}};t.exports=a},{}],6:[function(e,t,r){function a(e,t){var r="KaTeX parse error: "+e;var i;var n;if(t&&t.lexer&&t.start<=t.end){var s=t.lexer.input;i=t.start;n=t.end;if(i===s.length){r+=" at end of input: "}else{r+=" at position "+(i+1)+": "}var l=s.slice(i,n).replace(/[^]/g,"$&\u0332");var o;if(i>15){o="\u2026"+s.slice(i-15,i)}else{o=s.slice(0,i)}var u;if(n+15<s.length){u=s.slice(n,n+15)+"\u2026"}else{u=s.slice(n)}r+=o+l+u}var p=new Error(r);p.name="ParseError";p.__proto__=a.prototype;p.position=i;return p}a.prototype.__proto__=Error.prototype;t.exports=a},{}],7:[function(e,t,r){var a=e("./functions");var i=e("./environments");var n=e("./MacroExpander");var s=e("./symbols");var l=e("./utils");var o=e("./unicodeRegexes").cjkRegex;var u=e("./parseData");var p=e("./ParseError");function h(e,t){this.gullet=new n(e,t.macros);this.settings=t;this.leftrightDepth=0}var c=u.ParseNode;function m(e,t,r){this.result=e;this.isFunction=t;this.token=r}h.prototype.expect=function(e,t){if(this.nextToken.text!==e){throw new p("Expected '"+e+"', got '"+this.nextToken.text+"'",this.nextToken)}if(t!==false){this.consume()}};h.prototype.consume=function(){this.nextToken=this.gullet.get(this.mode==="math")};h.prototype.switchMode=function(e){this.gullet.unget(this.nextToken);this.mode=e;this.consume()};h.prototype.parse=function(){this.mode="math";this.consume();var e=this.parseInput();return e};h.prototype.parseInput=function(){var e=this.parseExpression(false);this.expect("EOF",false);return e};var f=["}","\\end","\\right","&","\\\\","\\cr"];h.prototype.parseExpression=function(e,t){var r=[];while(true){var i=this.nextToken;if(f.indexOf(i.text)!==-1){break}if(t&&i.text===t){break}if(e&&a[i.text]&&a[i.text].infix){break}var n=this.parseAtom();if(!n){if(!this.settings.throwOnError&&i.text[0]==="\\"){var s=this.handleUnsupportedCmd();r.push(s);continue}break}r.push(n)}return this.handleInfixNodes(r)};h.prototype.handleInfixNodes=function(e){var t=-1;var r;for(var a=0;a<e.length;a++){var i=e[a];if(i.type==="infix"){if(t!==-1){throw new p("only one infix operator per group",i.value.token)}t=a;r=i.value.replaceWith}}if(t!==-1){var n;var s;var l=e.slice(0,t);var o=e.slice(t+1);if(l.length===1&&l[0].type==="ordgroup"){n=l[0]}else{n=new c("ordgroup",l,this.mode)}if(o.length===1&&o[0].type==="ordgroup"){s=o[0]}else{s=new c("ordgroup",o,this.mode)}var u=this.callFunction(r,[n,s],null);return[new c(u.type,u,this.mode)]}else{return e}};var v=1;h.prototype.handleSupSubscript=function(e){var t=this.nextToken;var r=t.text;this.consume();var i=this.parseGroup();if(!i){if(!this.settings.throwOnError&&this.nextToken.text[0]==="\\"){return this.handleUnsupportedCmd()}else{throw new p("Expected group after '"+r+"'",t)}}else if(i.isFunction){var n=a[i.result].greediness;if(n>v){return this.parseFunction(i)}else{throw new p("Got function '"+i.result+"' with no arguments "+"as "+e,t)}}else{return i.result}};h.prototype.handleUnsupportedCmd=function(){var e=this.nextToken.text;var t=[];for(var r=0;r<e.length;r++){t.push(new c("textord",e[r],"text"))}var a=new c("text",{body:t,type:"text"},this.mode);var i=new c("color",{color:this.settings.errorColor,value:[a],type:"color"},this.mode);this.consume();return i};h.prototype.parseAtom=function(){var e=this.parseImplicitGroup();if(this.mode==="text"){return e}var t;var r;while(true){var a=this.nextToken;if(a.text==="\\limits"||a.text==="\\nolimits"){if(!e||e.type!=="op"){throw new p("Limit controls must follow a math operator",a)}else{var i=a.text==="\\limits";e.value.limits=i;e.value.alwaysHandleSupSub=true}this.consume()}else if(a.text==="^"){if(t){throw new p("Double superscript",a)}t=this.handleSupSubscript("superscript")}else if(a.text==="_"){if(r){throw new p("Double subscript",a)}r=this.handleSupSubscript("subscript")}else if(a.text==="'"){var n=new c("textord","\\prime",this.mode);var s=[n];this.consume();while(this.nextToken.text==="'"){s.push(n);this.consume()}t=new c("ordgroup",s,this.mode)}else{break}}if(t||r){return new c("supsub",{base:e,sup:t,sub:r},this.mode)}else{return e}};var d=["\\tiny","\\scriptsize","\\footnotesize","\\small","\\normalsize","\\large","\\Large","\\LARGE","\\huge","\\Huge"];var g=["\\displaystyle","\\textstyle","\\scriptstyle","\\scriptscriptstyle"];h.prototype.parseImplicitGroup=function(){var e=this.parseSymbol();if(e==null){return this.parseFunction()}var t=e.result;var r;if(t==="\\left"){var a=this.parseFunction(e);++this.leftrightDepth;r=this.parseExpression(false);--this.leftrightDepth;this.expect("\\right",false);var n=this.parseFunction();return new c("leftright",{body:r,left:a.value.value,right:n.value.value},this.mode)}else if(t==="\\begin"){var s=this.parseFunction(e);var o=s.value.name;if(!i.hasOwnProperty(o)){throw new p("No such environment: "+o,s.value.nameGroup)}var u=i[o];var h=this.parseArguments("\\begin{"+o+"}",u);var m={mode:this.mode,envName:o,parser:this,positions:h.pop()};var f=u.handler(m,h);this.expect("\\end",false);var v=this.nextToken;var y=this.parseFunction();if(y.value.name!==o){throw new p("Mismatch: \\begin{"+o+"} matched "+"by \\end{"+y.value.name+"}",v)}f.position=y.position;return f}else if(l.contains(d,t)){r=this.parseExpression(false);return new c("sizing",{size:"size"+(l.indexOf(d,t)+1),value:r},this.mode)}else if(l.contains(g,t)){r=this.parseExpression(true);return new c("styling",{style:t.slice(1,t.length-5),value:r},this.mode)}else{return this.parseFunction(e)}};h.prototype.parseFunction=function(e){if(!e){e=this.parseGroup()}if(e){if(e.isFunction){var t=e.result;var r=a[t];if(this.mode==="text"&&!r.allowedInText){throw new p("Can't use function '"+t+"' in text mode",e.token)}var i=this.parseArguments(t,r);var n=e.token;var s=this.callFunction(t,i,i.pop(),n);return new c(s.type,s,this.mode)}else{return e.result}}else{return null}};h.prototype.callFunction=function(e,t,r,i){var n={funcName:e,parser:this,positions:r,token:i};return a[e].handler(n,t)};h.prototype.parseArguments=function(e,t){var r=t.numArgs+t.numOptionalArgs;if(r===0){return[[this.pos]]}var i=t.greediness;var n=[this.pos];var s=[];for(var l=0;l<r;l++){var o=this.nextToken;var u=t.argTypes&&t.argTypes[l];var h;if(l<t.numOptionalArgs){if(u){h=this.parseGroupOfType(u,true)}else{h=this.parseGroup(true)}if(!h){s.push(null);n.push(this.pos);continue}}else{if(u){h=this.parseGroupOfType(u)}else{h=this.parseGroup()}if(!h){if(!this.settings.throwOnError&&this.nextToken.text[0]==="\\"){h=new m(this.handleUnsupportedCmd(this.nextToken.text),false)}else{throw new p("Expected group after '"+e+"'",o)}}}var c;if(h.isFunction){var f=a[h.result].greediness;if(f>i){c=this.parseFunction(h)}else{throw new p("Got function '"+h.result+"' as "+"argument to '"+e+"'",o)}}else{c=h.result}s.push(c);n.push(this.pos)}s.push(n);return s};h.prototype.parseGroupOfType=function(e,t){var r=this.mode;if(e==="original"){e=r}if(e==="color"){return this.parseColorGroup(t)}if(e==="size"){return this.parseSizeGroup(t)}this.switchMode(e);if(e==="text"){while(this.nextToken.text===" "){this.consume()}}var a=this.parseGroup(t);this.switchMode(r);return a};h.prototype.parseStringGroup=function(e,t){if(t&&this.nextToken.text!=="["){return null}var r=this.mode;this.mode="text";this.expect(t?"[":"{");var a="";var i=this.nextToken;var n=i;while(this.nextToken.text!==(t?"]":"}")){if(this.nextToken.text==="EOF"){throw new p("Unexpected end of input in "+e,i.range(this.nextToken,a))}n=this.nextToken;a+=n.text;this.consume()}this.mode=r;this.expect(t?"]":"}");return i.range(n,a)};h.prototype.parseRegexGroup=function(e,t){var r=this.mode;this.mode="text";var a=this.nextToken;var i=a;var n="";while(this.nextToken.text!=="EOF"&&e.test(n+this.nextToken.text)){i=this.nextToken;n+=i.text;this.consume()}if(n===""){throw new p("Invalid "+t+": '"+a.text+"'",a)}this.mode=r;return a.range(i,n)};h.prototype.parseColorGroup=function(e){var t=this.parseStringGroup("color",e);if(!t){return null}var r=/^(#[a-z0-9]+|[a-z]+)$/i.exec(t.text);if(!r){throw new p("Invalid color: '"+t.text+"'",t)}return new m(new c("color",r[0],this.mode),false)};h.prototype.parseSizeGroup=function(e){var t;if(!e&&this.nextToken.text!=="{"){t=this.parseRegexGroup(/^[-+]? *(?:$|\d+|\d+\.\d*|\.\d*) *[a-z]{0,2}$/,"size")}else{t=this.parseStringGroup("size",e)}if(!t){return null}var r=/([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/.exec(t.text);if(!r){throw new p("Invalid size: '"+t.text+"'",t)}var a={number:+(r[1]+r[2]),unit:r[3]};if(a.unit!=="em"&&a.unit!=="ex"&&a.unit!=="mu"){throw new p("Invalid unit: '"+a.unit+"'",t)}return new m(new c("color",a,this.mode),false)};h.prototype.parseGroup=function(e){var t=this.nextToken;if(this.nextToken.text===(e?"[":"{")){this.consume();var r=this.parseExpression(false,e?"]":null);var a=this.nextToken;this.expect(e?"]":"}");if(this.mode==="text"){this.formLigatures(r)}return new m(new c("ordgroup",r,this.mode,t,a),false)}else{return e?null:this.parseSymbol()}};h.prototype.formLigatures=function(e){var t;var r=e.length-1;for(t=0;t<r;++t){var a=e[t];var i=a.value;if(i==="-"&&e[t+1].value==="-"){if(t+1<r&&e[t+2].value==="-"){e.splice(t,3,new c("textord","---","text",a,e[t+2]));r-=2}else{e.splice(t,2,new c("textord","--","text",a,e[t+1]));r-=1}}if((i==="'"||i==="`")&&e[t+1].value===i){e.splice(t,2,new c("textord",i+i,"text",a,e[t+1]));r-=1}}};h.prototype.parseSymbol=function(){var e=this.nextToken;if(a[e.text]){this.consume();return new m(e.text,true,e)}else if(s[this.mode][e.text]){this.consume();return new m(new c(s[this.mode][e.text].group,e.text,this.mode,e),false,e)}else if(this.mode==="text"&&o.test(e.text)){this.consume();return new m(new c("textord",e.text,this.mode,e),false,e)}else{return null}};h.prototype.ParseNode=c;t.exports=h},{"./MacroExpander":4,"./ParseError":6,"./environments":16,"./functions":19,"./parseData":21,"./symbols":23,"./unicodeRegexes":24,"./utils":25}],8:[function(e,t,r){function a(e,t){return e===undefined?t:e}function i(e){e=e||{};this.displayMode=a(e.displayMode,false);this.throwOnError=a(e.throwOnError,true);this.errorColor=a(e.errorColor,"#cc0000");this.macros=e.macros||{}}t.exports=i},{}],9:[function(e,t,r){var a=e("./fontMetrics.js").sigmas;var i=[{},{},{}];var n;for(var s in a){if(a.hasOwnProperty(s)){for(n=0;n<3;n++){i[n][s]=a[s][n]}}}for(n=0;n<3;n++){i[n].emPerEx=a.xHeight[n]/a.quad[n]}function l(e,t,r,a){this.id=e;this.size=t;this.cramped=a;this.sizeMultiplier=r;this.metrics=i[t>0?t-1:0]}l.prototype.sup=function(){return y[x[this.id]]};l.prototype.sub=function(){return y[b[this.id]]};l.prototype.fracNum=function(){return y[w[this.id]]};l.prototype.fracDen=function(){return y[k[this.id]]};l.prototype.cramp=function(){return y[z[this.id]]};l.prototype.cls=function(){return d[this.size]+(this.cramped?" cramped":" uncramped")};l.prototype.reset=function(){return g[this.size]};l.prototype.isTight=function(){return this.size>=2};var o=0;var u=1;var p=2;var h=3;var c=4;var m=5;var f=6;var v=7;var d=["displaystyle textstyle","textstyle","scriptstyle","scriptscriptstyle"];var g=["reset-textstyle","reset-textstyle","reset-scriptstyle","reset-scriptscriptstyle"];var y=[new l(o,0,1,false),new l(u,0,1,true),new l(p,1,1,false),new l(h,1,1,true),new l(c,2,.7,false),new l(m,2,.7,true),new l(f,3,.5,false),new l(v,3,.5,true)];var x=[c,m,c,m,f,v,f,v];var b=[m,m,m,m,v,v,v,v];var w=[p,h,c,m,f,v,f,v];var k=[h,h,m,m,v,v,v,v];var z=[u,u,h,h,m,m,v,v];t.exports={DISPLAY:y[o],TEXT:y[p],SCRIPT:y[c],SCRIPTSCRIPT:y[f]}},{"./fontMetrics.js":17}],10:[function(e,t,r){var a=e("./domTree");var i=e("./fontMetrics");var n=e("./symbols");var s=e("./utils");var l=["\\Gamma","\\Delta","\\Theta","\\Lambda","\\Xi","\\Pi","\\Sigma","\\Upsilon","\\Phi","\\Psi","\\Omega"];var o=["\u0131","\u0237","\xa3"];var u=function(e,t,r,s,l){if(n[r][e]&&n[r][e].replace){e=n[r][e].replace}var o=i.getCharacterMetrics(e,t);var u;if(o){var p=o.italic;if(r==="text"){p=0}u=new a.symbolNode(e,o.height,o.depth,p,o.skew,l)}else{typeof console!=="undefined"&&console.warn("No character metrics for '"+e+"' in style '"+t+"'");u=new a.symbolNode(e,0,0,0,0,l)}if(s){if(s.style.isTight()){u.classes.push("mtight")}if(s.getColor()){u.style.color=s.getColor()}}return u};var p=function(e,t,r,a){if(e==="\\"||n[t][e].font==="main"){return u(e,"Main-Regular",t,r,a)}else{return u(e,"AMS-Regular",t,r,a.concat(["amsrm"]))}};var h=function(e,t,r,a,i){if(i==="mathord"){return c(e,t,r,a)}else if(i==="textord"){return u(e,"Main-Regular",t,r,a.concat(["mathrm"]))}else{throw new Error("unexpected type: "+i+" in mathDefault")}};var c=function(e,t,r,a){if(/[0-9]/.test(e.charAt(0))||s.contains(o,e)||s.contains(l,e)){return u(e,"Main-Italic",t,r,a.concat(["mainit"]))}else{return u(e,"Math-Italic",t,r,a.concat(["mathit"]))}};var m=function(e,t,r){var a=e.mode;var l=e.value;if(n[a][l]&&n[a][l].replace){l=n[a][l].replace}var p=["mord"];var m=t.font;if(m){if(m==="mathit"||s.contains(o,l)){return c(l,a,t,p)}else{var f=k[m].fontName;if(i.getCharacterMetrics(l,f)){return u(l,f,a,t,p.concat([m]))}else{return h(l,a,t,p,r)}}}else{return h(l,a,t,p,r)}};var f=function(e){var t=0;var r=0;var a=0;if(e.children){for(var i=0;i<e.children.length;i++){if(e.children[i].height>t){t=e.children[i].height}if(e.children[i].depth>r){r=e.children[i].depth}if(e.children[i].maxFontSize>a){a=e.children[i].maxFontSize}}}e.height=t;e.depth=r;e.maxFontSize=a};var v=function(e,t,r){var i=new a.span(e,t,r);f(i);return i};var d=function(e,t){e.children=t.concat(e.children);f(e)};var g=function(e){var t=new a.documentFragment(e);f(t);return t};var y=function(e,t){var r=v([],[new a.symbolNode("\u200b")]);r.style.fontSize=t/e.style.sizeMultiplier+"em";var i=v(["fontsize-ensurer","reset-"+e.size,"size5"],[r]);return i};var x=function(e,t,r,i){var n;var s;var l;if(t==="individualShift"){var o=e;e=[o[0]];n=-o[0].shift-o[0].elem.depth;s=n;for(l=1;l<o.length;l++){var u=-o[l].shift-s-o[l].elem.depth;var p=u-(o[l-1].elem.height+o[l-1].elem.depth);s=s+u;e.push({type:"kern",size:p});e.push(o[l])}}else if(t==="top"){var h=r;for(l=0;l<e.length;l++){if(e[l].type==="kern"){h-=e[l].size}else{h-=e[l].elem.height+e[l].elem.depth}}n=h}else if(t==="bottom"){n=-r}else if(t==="shift"){n=-e[0].elem.depth-r}else if(t==="firstBaseline"){n=-e[0].elem.depth}else{n=0}var c=0;for(l=0;l<e.length;l++){if(e[l].type==="elem"){c=Math.max(c,e[l].elem.maxFontSize)}}var m=y(i,c);var f=[];s=n;for(l=0;l<e.length;l++){if(e[l].type==="kern"){s+=e[l].size}else{var d=e[l].elem;var g=-d.depth-s;s+=d.height+d.depth;var x=v([],[m,d]);x.height-=g;x.depth+=g;x.style.top=g+"em";f.push(x)}}var b=v(["baseline-fix"],[m,new a.symbolNode("\u200b")]);f.push(b);var w=v(["vlist"],f);w.height=Math.max(s,w.height);w.depth=Math.max(-n,w.depth);return w};var b={size1:.5,size2:.7,size3:.8,size4:.9,size5:1,size6:1.2,size7:1.44,size8:1.73,size9:2.07,size10:2.49};var w={"\\qquad":{size:"2em",className:"qquad"},"\\quad":{size:"1em",className:"quad"},"\\enspace":{size:"0.5em",className:"enspace"},"\\;":{size:"0.277778em",className:"thickspace"},"\\:":{size:"0.22222em",className:"mediumspace"},"\\,":{size:"0.16667em",className:"thinspace"},"\\!":{size:"-0.16667em",className:"negativethinspace"}};var k={mathbf:{variant:"bold",fontName:"Main-Bold"},mathrm:{variant:"normal",fontName:"Main-Regular"},textit:{variant:"italic",fontName:"Main-Italic"},mathbb:{variant:"double-struck",fontName:"AMS-Regular"},mathcal:{variant:"script",fontName:"Caligraphic-Regular"},mathfrak:{variant:"fraktur",fontName:"Fraktur-Regular"},mathscr:{variant:"script",fontName:"Script-Regular"},mathsf:{variant:"sans-serif",fontName:"SansSerif-Regular"},mathtt:{variant:"monospace",fontName:"Typewriter-Regular"}};t.exports={fontMap:k,makeSymbol:u,mathsym:p,makeSpan:v,makeFragment:g,makeVList:x,makeOrd:m,prependChildren:d,sizingMultiplier:b,spacingFunctions:w}},{"./domTree":15,"./fontMetrics":17,"./symbols":23,"./utils":25}],11:[function(e,t,r){var a=e("./ParseError");var i=e("./Style");var n=e("./buildCommon");var s=e("./delimiter");var l=e("./domTree");var o=e("./fontMetrics");var u=e("./utils");var p=n.makeSpan;var h=function(e){return e instanceof l.span&&e.classes[0]==="mspace"};var c=function(e){return e&&e.classes[0]==="mbin"};var m=function(e,t){if(e){return u.contains(["mbin","mopen","mrel","mop","mpunct"],e.classes[0])}else{return t}};var f=function(e,t){if(e){return u.contains(["mrel","mclose","mpunct"],e.classes[0])}else{return t}};var v=function(e,t,r){var a=[];for(var i=0;i<e.length;i++){var s=e[i];var o=z(s,t);if(o instanceof l.documentFragment){Array.prototype.push.apply(a,o.children)}else{a.push(o)}}var u=null;for(i=0;i<a.length;i++){if(h(a[i])){u=u||[];u.push(a[i]);a.splice(i,1);i--}else if(u){if(a[i]instanceof l.symbolNode){a[i]=p([].concat(a[i].classes),[a[i]])}n.prependChildren(a[i],u);u=null}}if(u){Array.prototype.push.apply(a,u)}for(i=0;i<a.length;i++){if(c(a[i])&&(m(a[i-1],r)||f(a[i+1],r))){a[i].classes[0]="mord"}}return a};var d=function(e){if(e instanceof l.documentFragment){if(e.children.length){return d(e.children[e.children.length-1])}}else{if(u.contains(["mord","mop","mbin","mrel","mopen","mclose","mpunct","minner"],e.classes[0])){return e.classes[0]}}return null};var g=function(e,t){if(!e){return false}else if(e.type==="op"){return e.value.limits&&(t.style.size===i.DISPLAY.size||e.value.alwaysHandleSupSub)}else if(e.type==="accent"){return x(e.value.base)}else{return null}};var y=function(e){if(!e){return false}else if(e.type==="ordgroup"){if(e.value.length===1){return y(e.value[0])}else{return e}}else if(e.type==="color"){if(e.value.value.length===1){return y(e.value.value[0])}else{return e}}else if(e.type==="font"){return y(e.value.body)}else{return e}};var x=function(e){var t=y(e);return t.type==="mathord"||t.type==="textord"||t.type==="bin"||t.type==="rel"||t.type==="inner"||t.type==="open"||t.type==="close"||t.type==="punct"};var b=function(e,t){return p(t.concat(["sizing","reset-"+e.size,"size5",e.style.reset(),i.TEXT.cls(),"nulldelimiter"]))};var w={};w.mathord=function(e,t){return n.makeOrd(e,t,"mathord")};w.textord=function(e,t){return n.makeOrd(e,t,"textord")};w.bin=function(e,t){return n.mathsym(e.value,e.mode,t,["mbin"])};w.rel=function(e,t){return n.mathsym(e.value,e.mode,t,["mrel"])};w.open=function(e,t){return n.mathsym(e.value,e.mode,t,["mopen"])};w.close=function(e,t){return n.mathsym(e.value,e.mode,t,["mclose"])};w.inner=function(e,t){return n.mathsym(e.value,e.mode,t,["minner"])};w.punct=function(e,t){return n.mathsym(e.value,e.mode,t,["mpunct"])};w.ordgroup=function(e,t){return p(["mord",t.style.cls()],v(e.value,t.reset(),true),t)};w.text=function(e,t){var r=t.withFont(e.value.style);var a=v(e.value.body,r,true);for(var i=0;i<a.length-1;i++){if(a[i].tryCombine(a[i+1])){a.splice(i+1,1);i--}}return p(["mord","text",r.style.cls()],a,r)};w.color=function(e,t){var r=v(e.value.value,t.withColor(e.value.color),false);return new n.makeFragment(r)};w.supsub=function(e,t){if(g(e.value.base,t)){return w[e.value.base.type](e,t)}var r=z(e.value.base,t.reset());var a;var s;var u;var h;var c=t.style;var m;if(e.value.sup){m=t.withStyle(c.sup());u=z(e.value.sup,m);a=p([c.reset(),c.sup().cls()],[u],m)}if(e.value.sub){m=t.withStyle(c.sub());h=z(e.value.sub,m);s=p([c.reset(),c.sub().cls()],[h],m)}var f;var v;if(x(e.value.base)){f=0;v=0}else{f=r.height-c.metrics.supDrop;v=r.depth+c.metrics.subDrop}var y;if(c===i.DISPLAY){y=c.metrics.sup1}else if(c.cramped){y=c.metrics.sup3}else{y=c.metrics.sup2}var b=i.TEXT.sizeMultiplier*c.sizeMultiplier;var k=.5/o.metrics.ptPerEm/b+"em";var S;if(!e.value.sup){v=Math.max(v,c.metrics.sub1,h.height-.8*c.metrics.xHeight);S=n.makeVList([{type:"elem",elem:s}],"shift",v,t);S.children[0].style.marginRight=k;if(r instanceof l.symbolNode){S.children[0].style.marginLeft=-r.italic+"em"}}else if(!e.value.sub){f=Math.max(f,y,u.depth+.25*c.metrics.xHeight);S=n.makeVList([{type:"elem",elem:a}],"shift",-f,t);S.children[0].style.marginRight=k}else{f=Math.max(f,y,u.depth+.25*c.metrics.xHeight);v=Math.max(v,c.metrics.sub2);var M=o.metrics.defaultRuleThickness;if(f-u.depth-(h.height-v)<4*M){v=4*M-(f-u.depth)+h.height;var T=.8*c.metrics.xHeight-(f-u.depth);if(T>0){f+=T;v-=T}}S=n.makeVList([{type:"elem",elem:s,shift:v},{type:"elem",elem:a,shift:-f}],"individualShift",null,t);if(r instanceof l.symbolNode){S.children[0].style.marginLeft=-r.italic+"em"}S.children[0].style.marginRight=k;S.children[1].style.marginRight=k}var A=d(r)||"mord";return p([A],[r,p(["msupsub"],[S])],t)};w.genfrac=function(e,t){var r=t.style;if(e.value.size==="display"){r=i.DISPLAY}else if(e.value.size==="text"){r=i.TEXT}var a=r.fracNum();var l=r.fracDen();var u;u=t.withStyle(a);var h=z(e.value.numer,u);var c=p([r.reset(),a.cls()],[h],u);u=t.withStyle(l);var m=z(e.value.denom,u);var f=p([r.reset(),l.cls()],[m],u);var v;if(e.value.hasBarLine){v=o.metrics.defaultRuleThickness/t.style.sizeMultiplier}else{v=0}var d;var g;var y;if(r.size===i.DISPLAY.size){d=r.metrics.num1;if(v>0){g=3*v}else{g=7*o.metrics.defaultRuleThickness}y=r.metrics.denom1}else{if(v>0){d=r.metrics.num2;g=v}else{d=r.metrics.num3;g=3*o.metrics.defaultRuleThickness}y=r.metrics.denom2}var x;if(v===0){var w=d-h.depth-(m.height-y);if(w<g){d+=.5*(g-w);y+=.5*(g-w)}x=n.makeVList([{type:"elem",elem:f,shift:y},{type:"elem",elem:c,shift:-d}],"individualShift",null,t)}else{var k=r.metrics.axisHeight;if(d-h.depth-(k+.5*v)<g){d+=g-(d-h.depth-(k+.5*v))}if(k-.5*v-(m.height-y)<g){y+=g-(k-.5*v-(m.height-y))}var S=p([t.style.reset(),i.TEXT.cls(),"frac-line"]);S.height=v;var M=-(k-.5*v);x=n.makeVList([{type:"elem",elem:f,shift:y},{type:"elem",elem:S,shift:M},{type:"elem",elem:c,shift:-d}],"individualShift",null,t)}x.height*=r.sizeMultiplier/t.style.sizeMultiplier;x.depth*=r.sizeMultiplier/t.style.sizeMultiplier;var T;if(r.size===i.DISPLAY.size){T=r.metrics.delim1}else{T=r.metrics.delim2}var A;var N;if(e.value.leftDelim==null){A=b(t,["mopen"])}else{A=s.customSizedDelim(e.value.leftDelim,T,true,t.withStyle(r),e.mode,["mopen"])}if(e.value.rightDelim==null){N=b(t,["mclose"])}else{N=s.customSizedDelim(e.value.rightDelim,T,true,t.withStyle(r),e.mode,["mclose"])}return p(["mord",t.style.reset(),r.cls()],[A,p(["mfrac"],[x]),N],t)};var k=function(e,t){var r=e.number;if(e.unit==="ex"){r*=t.metrics.emPerEx}else if(e.unit==="mu"){r/=18}return r};w.array=function(e,t){var r;var i;var s=e.value.body.length;var l=0;var h=new Array(s);var c=t.style;var m=1/o.metrics.ptPerEm;var f=5*m;var v=12*m;var d=u.deflt(e.value.arraystretch,1);var g=d*v;var y=.7*g;var x=.3*g;var b=0;for(r=0;r<e.value.body.length;++r){var w=e.value.body[r];var S=y;var M=x;if(l<w.length){l=w.length}var T=new Array(w.length);for(i=0;i<w.length;++i){var A=z(w[i],t);if(M<A.depth){M=A.depth}if(S<A.height){S=A.height}T[i]=A}var N=0;if(e.value.rowGaps[r]){N=k(e.value.rowGaps[r].value,c);if(N>0){N+=x;if(M<N){M=N}N=0}}T.height=S;T.depth=M;b+=S;T.pos=b;b+=M+N;h[r]=T}var q=b/2+c.metrics.axisHeight;var R=e.value.cols||[];var E=[];var C;var D;for(i=0,D=0;i<l||D<R.length;++i,++D){var O=R[D]||{};var P=true;while(O.type==="separator"){if(!P){C=p(["arraycolsep"],[]);C.style.width=o.metrics.doubleRuleSep+"em";E.push(C)}if(O.separator==="|"){var F=p(["vertical-separator"],[]);F.style.height=b+"em";F.style.verticalAlign=-(b-q)+"em";E.push(F)}else{throw new a("Invalid separator type: "+O.separator)}D++;O=R[D]||{};P=false}if(i>=l){continue}var I;if(i>0||e.value.hskipBeforeAndAfter){I=u.deflt(O.pregap,f);if(I!==0){C=p(["arraycolsep"],[]);C.style.width=I+"em";E.push(C)}}var L=[];for(r=0;r<s;++r){var B=h[r];var G=B[i];if(!G){continue}var V=B.pos-q;G.depth=B.depth;G.height=B.height;L.push({type:"elem",elem:G,shift:V})}L=n.makeVList(L,"individualShift",null,t);L=p(["col-align-"+(O.align||"c")],[L]);E.push(L);if(i<l-1||e.value.hskipBeforeAndAfter){I=u.deflt(O.postgap,f);if(I!==0){C=p(["arraycolsep"],[]);C.style.width=I+"em";E.push(C)}}}h=p(["mtable"],E);return p(["mord"],[h],t)};w.spacing=function(e,t){if(e.value==="\\ "||e.value==="\\space"||e.value===" "||e.value==="~"){if(e.mode==="text"){return n.makeOrd(e,t,"textord")}else{return p(["mspace"],[n.mathsym(e.value,e.mode,t)],t)}}else{return p(["mspace",n.spacingFunctions[e.value].className],[],t)}};w.llap=function(e,t){var r=p(["inner"],[z(e.value.body,t.reset())]);var a=p(["fix"],[]);return p(["mord","llap",t.style.cls()],[r,a],t)};w.rlap=function(e,t){var r=p(["inner"],[z(e.value.body,t.reset())]);var a=p(["fix"],[]);return p(["mord","rlap",t.style.cls()],[r,a],t)};w.op=function(e,t){var r;var a;var s=false;if(e.type==="supsub"){r=e.value.sup;a=e.value.sub;e=e.value.base;s=true}var l=t.style;var h=["\\smallint"];var c=false;if(l.size===i.DISPLAY.size&&e.value.symbol&&!u.contains(h,e.value.body)){c=true}var m;var f=0;var d=0;if(e.value.symbol){var g=c?"Size2-Regular":"Size1-Regular";m=n.makeSymbol(e.value.body,g,"math",t,["mop","op-symbol",c?"large-op":"small-op"]);f=(m.height-m.depth)/2-l.metrics.axisHeight*l.sizeMultiplier;d=m.italic}else if(e.value.value){var y=v(e.value.value,t,true);m=p(["mop"],y,t)}else{var x=[];for(var b=1;b<e.value.body.length;b++){x.push(n.mathsym(e.value.body[b],e.mode))}m=p(["mop"],x,t)}if(s){m=p([],[m]);var w;var k;var S;var M;var T;if(r){T=t.withStyle(l.sup());var A=z(r,T);w=p([l.reset(),l.sup().cls()],[A],T);k=Math.max(o.metrics.bigOpSpacing1,o.metrics.bigOpSpacing3-A.depth)}if(a){T=t.withStyle(l.sub());var N=z(a,T);S=p([l.reset(),l.sub().cls()],[N],T);M=Math.max(o.metrics.bigOpSpacing2,o.metrics.bigOpSpacing4-N.height)}var q;var R;var E;if(!r){R=m.height-f;q=n.makeVList([{type:"kern",size:o.metrics.bigOpSpacing5},{type:"elem",elem:S},{type:"kern",size:M},{type:"elem",elem:m}],"top",R,t);q.children[0].style.marginLeft=-d+"em"}else if(!a){E=m.depth+f;q=n.makeVList([{type:"elem",elem:m},{type:"kern",size:k},{type:"elem",elem:w},{type:"kern",size:o.metrics.bigOpSpacing5}],"bottom",E,t);q.children[1].style.marginLeft=d+"em"}else if(!r&&!a){return m}else{E=o.metrics.bigOpSpacing5+S.height+S.depth+M+m.depth+f;
+q=n.makeVList([{type:"kern",size:o.metrics.bigOpSpacing5},{type:"elem",elem:S},{type:"kern",size:M},{type:"elem",elem:m},{type:"kern",size:k},{type:"elem",elem:w},{type:"kern",size:o.metrics.bigOpSpacing5}],"bottom",E,t);q.children[0].style.marginLeft=-d+"em";q.children[2].style.marginLeft=d+"em"}return p(["mop","op-limits"],[q],t)}else{if(e.value.symbol){m.style.top=f+"em"}return m}};w.mod=function(e,t){var r=[];if(e.value.modType==="bmod"){if(!t.style.isTight()){r.push(p(["mspace","negativemediumspace"],[],t))}r.push(p(["mspace","thickspace"],[],t))}else if(t.style.size===i.DISPLAY.size){r.push(p(["mspace","quad"],[],t))}else if(e.value.modType==="mod"){r.push(p(["mspace","twelvemuspace"],[],t))}else{r.push(p(["mspace","eightmuspace"],[],t))}if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(n.mathsym("(",e.mode))}if(e.value.modType!=="pod"){var a=[n.mathsym("m",e.mode),n.mathsym("o",e.mode),n.mathsym("d",e.mode)];if(e.value.modType==="bmod"){r.push(p(["mbin"],a,t));r.push(p(["mspace","thickspace"],[],t));if(!t.style.isTight()){r.push(p(["mspace","negativemediumspace"],[],t))}}else{Array.prototype.push.apply(r,a);r.push(p(["mspace","sixmuspace"],[],t))}}if(e.value.value){Array.prototype.push.apply(r,v(e.value.value,t,false))}if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(n.mathsym(")",e.mode))}return n.makeFragment(r)};w.katex=function(e,t){var r=p(["k"],[n.mathsym("K",e.mode)],t);var a=p(["a"],[n.mathsym("A",e.mode)],t);a.height=(a.height+.2)*.75;a.depth=(a.height-.2)*.75;var i=p(["t"],[n.mathsym("T",e.mode)],t);var s=p(["e"],[n.mathsym("E",e.mode)],t);s.height=s.height-.2155;s.depth=s.depth+.2155;var l=p(["x"],[n.mathsym("X",e.mode)],t);return p(["mord","katex-logo"],[r,a,i,s,l],t)};w.overline=function(e,t){var r=t.style;var a=z(e.value.body,t.withStyle(r.cramp()));var s=o.metrics.defaultRuleThickness/r.sizeMultiplier;var l=p([r.reset(),i.TEXT.cls(),"overline-line"]);l.height=s;l.maxFontSize=1;var u=n.makeVList([{type:"elem",elem:a},{type:"kern",size:3*s},{type:"elem",elem:l},{type:"kern",size:s}],"firstBaseline",null,t);return p(["mord","overline"],[u],t)};w.underline=function(e,t){var r=t.style;var a=z(e.value.body,t);var s=o.metrics.defaultRuleThickness/r.sizeMultiplier;var l=p([r.reset(),i.TEXT.cls(),"underline-line"]);l.height=s;l.maxFontSize=1;var u=n.makeVList([{type:"kern",size:s},{type:"elem",elem:l},{type:"kern",size:3*s},{type:"elem",elem:a}],"top",a.height,t);return p(["mord","underline"],[u],t)};w.sqrt=function(e,t){var r=t.style;var a=z(e.value.body,t.withStyle(r.cramp()));var l=o.metrics.defaultRuleThickness/r.sizeMultiplier;var u=p([r.reset(),i.TEXT.cls(),"sqrt-line"],[],t);u.height=l;u.maxFontSize=1;var h=l;if(r.id<i.TEXT.id){h=r.metrics.xHeight}var c=l+h/4;var m=(a.height+a.depth)*r.sizeMultiplier;var f=m+c+l;var v=p(["sqrt-sign"],[s.customSizedDelim("\\surd",f,false,t,e.mode)],t);var d=v.height+v.depth-l;if(d>a.height+a.depth+c){c=(c+d-a.height-a.depth)/2}var g=-(a.height+c+l)+v.height;v.style.top=g+"em";v.height-=g;v.depth+=g;var y;if(a.height===0&&a.depth===0){y=p()}else{y=n.makeVList([{type:"elem",elem:a},{type:"kern",size:c},{type:"elem",elem:u},{type:"kern",size:l}],"firstBaseline",null,t)}if(!e.value.index){return p(["mord","sqrt"],[v,y],t)}else{var x=t.withStyle(i.SCRIPTSCRIPT);var b=z(e.value.index,x);var w=p([r.reset(),i.SCRIPTSCRIPT.cls()],[b],x);var k=Math.max(v.height,y.height);var S=Math.max(v.depth,y.depth);var M=.6*(k-S);var T=n.makeVList([{type:"elem",elem:w}],"shift",-M,t);var A=p(["root"],[T]);return p(["mord","sqrt"],[A,v,y],t)}};w.sizing=function(e,t){var r=v(e.value.value,t.withSize(e.value.size),false);var a=t.style;var i=n.sizingMultiplier[e.value.size];i=i*a.sizeMultiplier;for(var s=0;s<r.length;s++){var l=u.indexOf(r[s].classes,"sizing");if(l<0){r[s].classes.push("sizing","reset-"+t.size,e.value.size,a.cls());r[s].maxFontSize=i}else if(r[s].classes[l+1]==="reset-"+e.value.size){r[s].classes[l+1]="reset-"+t.size}}return n.makeFragment(r)};w.styling=function(e,t){var r={display:i.DISPLAY,text:i.TEXT,script:i.SCRIPT,scriptscript:i.SCRIPTSCRIPT};var a=r[e.value.style];var s=t.withStyle(a);var l=v(e.value.value,s,false);for(var o=0;o<l.length;o++){var p=u.indexOf(l[o].classes,a.reset());if(p<0){l[o].classes.push(t.style.reset(),a.cls())}else{l[o].classes[p]=t.style.reset()}}return new n.makeFragment(l)};w.font=function(e,t){var r=e.value.font;return z(e.value.body,t.withFont(r))};w.delimsizing=function(e,t){var r=e.value.value;if(r==="."){return p([e.value.mclass])}return s.sizedDelim(r,e.value.size,t,e.mode,[e.value.mclass])};w.leftright=function(e,t){var r=v(e.value.body,t.reset(),true);var a=0;var i=0;var n=false;for(var l=0;l<r.length;l++){if(r[l].isMiddle){n=true}else{a=Math.max(r[l].height,a);i=Math.max(r[l].depth,i)}}var o=t.style;a*=o.sizeMultiplier;i*=o.sizeMultiplier;var u;if(e.value.left==="."){u=b(t,["mopen"])}else{u=s.leftRightDelim(e.value.left,a,i,t,e.mode,["mopen"])}r.unshift(u);if(n){for(l=1;l<r.length;l++){if(r[l].isMiddle){r[l]=s.leftRightDelim(r[l].isMiddle.value,a,i,r[l].isMiddle.options,e.mode,[])}}}var h;if(e.value.right==="."){h=b(t,["mclose"])}else{h=s.leftRightDelim(e.value.right,a,i,t,e.mode,["mclose"])}r.push(h);return p(["minner",o.cls()],r,t)};w.middle=function(e,t){var r;if(e.value.value==="."){r=b(t,[])}else{r=s.sizedDelim(e.value.value,1,t,e.mode,[]);r.isMiddle={value:e.value.value,options:t}}return r};w.rule=function(e,t){var r=p(["mord","rule"],[],t);var a=t.style;var i=0;if(e.value.shift){i=k(e.value.shift,a)}var n=k(e.value.width,a);var s=k(e.value.height,a);i/=a.sizeMultiplier;n/=a.sizeMultiplier;s/=a.sizeMultiplier;r.style.borderRightWidth=n+"em";r.style.borderTopWidth=s+"em";r.style.bottom=i+"em";r.width=n;r.height=s+i;r.depth=-i;return r};w.kern=function(e,t){var r=p(["mord","rule"],[],t);var a=t.style;var i=0;if(e.value.dimension){i=k(e.value.dimension,a)}i/=a.sizeMultiplier;r.style.marginLeft=i+"em";return r};w.accent=function(e,t){var r=e.value.base;var a=t.style;var i;if(e.type==="supsub"){var s=e;e=s.value.base;r=e.value.base;s.value.base=r;i=z(s,t.reset())}var l=z(r,t.withStyle(a.cramp()));var o;if(x(r)){var u=y(r);var h=z(u,t.withStyle(a.cramp()));o=h.skew}else{o=0}var c=Math.min(l.height,a.metrics.xHeight);var m=n.makeSymbol(e.value.accent,"Main-Regular","math",t);m.italic=0;var f=e.value.accent==="\\vec"?"accent-vec":null;var v=p(["accent-body",f],[p([],[m])]);v=n.makeVList([{type:"elem",elem:l},{type:"kern",size:-c},{type:"elem",elem:v}],"firstBaseline",null,t);v.children[1].style.marginLeft=2*o+"em";var d=p(["mord","accent"],[v],t);if(i){i.children[0]=d;i.height=Math.max(d.height,i.height);i.classes[0]="mord";return i}else{return d}};w.phantom=function(e,t){var r=v(e.value.value,t.withPhantom(),false);return new n.makeFragment(r)};w.mclass=function(e,t){var r=v(e.value.value,t,true);return p([e.value.mclass],r,t)};var z=function(e,t){if(!e){return p()}if(w[e.type]){var r=w[e.type](e,t);var i;if(t.style!==t.parentStyle){i=t.style.sizeMultiplier/t.parentStyle.sizeMultiplier;r.height*=i;r.depth*=i}if(t.size!==t.parentSize){i=n.sizingMultiplier[t.size]/n.sizingMultiplier[t.parentSize];r.height*=i;r.depth*=i}return r}else{throw new a("Got group of unknown type: '"+e.type+"'")}};var S=function(e,t){e=JSON.parse(JSON.stringify(e));var r=v(e,t,true);var a=p(["base",t.style.cls()],r,t);var i=p(["strut"]);var n=p(["strut","bottom"]);i.style.height=a.height+"em";n.style.height=a.height+a.depth+"em";n.style.verticalAlign=-a.depth+"em";var s=p(["katex-html"],[i,n,a]);s.setAttribute("aria-hidden","true");return s};t.exports=S},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./delimiter":14,"./domTree":15,"./fontMetrics":17,"./utils":25}],12:[function(e,t,r){var a=e("./buildCommon");var i=e("./fontMetrics");var n=e("./mathMLTree");var s=e("./ParseError");var l=e("./symbols");var o=e("./utils");var u=a.makeSpan;var p=a.fontMap;var h=function(e,t){if(l[t][e]&&l[t][e].replace){e=l[t][e].replace}return new n.TextNode(e)};var c=function(e,t){var r=t.font;if(!r){return null}var a=e.mode;if(r==="mathit"){return"italic"}var n=e.value;if(o.contains(["\\imath","\\jmath"],n)){return null}if(l[a][n]&&l[a][n].replace){n=l[a][n].replace}var s=p[r].fontName;if(i.getCharacterMetrics(n,s)){return p[t.font].variant}return null};var m={};m.mathord=function(e,t){var r=new n.MathNode("mi",[h(e.value,e.mode)]);var a=c(e,t);if(a){r.setAttribute("mathvariant",a)}return r};m.textord=function(e,t){var r=h(e.value,e.mode);var a=c(e,t)||"normal";var i;if(/[0-9]/.test(e.value)){i=new n.MathNode("mn",[r]);if(t.font){i.setAttribute("mathvariant",a)}}else{i=new n.MathNode("mi",[r]);i.setAttribute("mathvariant",a)}return i};m.bin=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.rel=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.open=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.close=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.inner=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);return t};m.punct=function(e){var t=new n.MathNode("mo",[h(e.value,e.mode)]);t.setAttribute("separator","true");return t};m.ordgroup=function(e,t){var r=f(e.value,t);var a=new n.MathNode("mrow",r);return a};m.text=function(e,t){var r=f(e.value.body,t);var a=new n.MathNode("mtext",r);return a};m.color=function(e,t){var r=f(e.value.value,t);var a=new n.MathNode("mstyle",r);a.setAttribute("mathcolor",e.value.color);return a};m.supsub=function(e,t){var r=[v(e.value.base,t)];if(e.value.sub){r.push(v(e.value.sub,t))}if(e.value.sup){r.push(v(e.value.sup,t))}var a;if(!e.value.sub){a="msup"}else if(!e.value.sup){a="msub"}else{a="msubsup"}var i=new n.MathNode(a,r);return i};m.genfrac=function(e,t){var r=new n.MathNode("mfrac",[v(e.value.numer,t),v(e.value.denom,t)]);if(!e.value.hasBarLine){r.setAttribute("linethickness","0px")}if(e.value.leftDelim!=null||e.value.rightDelim!=null){var a=[];if(e.value.leftDelim!=null){var i=new n.MathNode("mo",[new n.TextNode(e.value.leftDelim)]);i.setAttribute("fence","true");a.push(i)}a.push(r);if(e.value.rightDelim!=null){var s=new n.MathNode("mo",[new n.TextNode(e.value.rightDelim)]);s.setAttribute("fence","true");a.push(s)}var l=new n.MathNode("mrow",a);return l}return r};m.array=function(e,t){return new n.MathNode("mtable",e.value.body.map(function(e){return new n.MathNode("mtr",e.map(function(e){return new n.MathNode("mtd",[v(e,t)])}))}))};m.sqrt=function(e,t){var r;if(e.value.index){r=new n.MathNode("mroot",[v(e.value.body,t),v(e.value.index,t)])}else{r=new n.MathNode("msqrt",[v(e.value.body,t)])}return r};m.leftright=function(e,t){var r=f(e.value.body,t);if(e.value.left!=="."){var a=new n.MathNode("mo",[h(e.value.left,e.mode)]);a.setAttribute("fence","true");r.unshift(a)}if(e.value.right!=="."){var i=new n.MathNode("mo",[h(e.value.right,e.mode)]);i.setAttribute("fence","true");r.push(i)}var s=new n.MathNode("mrow",r);return s};m.middle=function(e,t){var r=new n.MathNode("mo",[h(e.value.middle,e.mode)]);r.setAttribute("fence","true");return r};m.accent=function(e,t){var r=new n.MathNode("mo",[h(e.value.accent,e.mode)]);var a=new n.MathNode("mover",[v(e.value.base,t),r]);a.setAttribute("accent","true");return a};m.spacing=function(e){var t;if(e.value==="\\ "||e.value==="\\space"||e.value===" "||e.value==="~"){t=new n.MathNode("mtext",[new n.TextNode("\xa0")])}else{t=new n.MathNode("mspace");t.setAttribute("width",a.spacingFunctions[e.value].size)}return t};m.op=function(e,t){var r;if(e.value.symbol){r=new n.MathNode("mo",[h(e.value.body,e.mode)])}else if(e.value.value){r=new n.MathNode("mo",f(e.value.value,t))}else{r=new n.MathNode("mi",[new n.TextNode(e.value.body.slice(1))])}return r};m.mod=function(e,t){var r=[];if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(new n.MathNode("mo",[h("(",e.mode)]))}if(e.value.modType!=="pod"){r.push(new n.MathNode("mo",[h("mod",e.mode)]))}if(e.value.value){var a=new n.MathNode("mspace");a.setAttribute("width","0.333333em");r.push(a);r=r.concat(f(e.value.value,t))}if(e.value.modType==="pod"||e.value.modType==="pmod"){r.push(new n.MathNode("mo",[h(")",e.mode)]))}return new n.MathNode("mo",r)};m.katex=function(e){var t=new n.MathNode("mtext",[new n.TextNode("KaTeX")]);return t};m.font=function(e,t){var r=e.value.font;return v(e.value.body,t.withFont(r))};m.delimsizing=function(e){var t=[];if(e.value.value!=="."){t.push(h(e.value.value,e.mode))}var r=new n.MathNode("mo",t);if(e.value.mclass==="mopen"||e.value.mclass==="mclose"){r.setAttribute("fence","true")}else{r.setAttribute("fence","false")}return r};m.styling=function(e,t){var r=f(e.value.value,t);var a=new n.MathNode("mstyle",r);var i={display:["0","true"],text:["0","false"],script:["1","false"],scriptscript:["2","false"]};var s=i[e.value.style];a.setAttribute("scriptlevel",s[0]);a.setAttribute("displaystyle",s[1]);return a};m.sizing=function(e,t){var r=f(e.value.value,t);var i=new n.MathNode("mstyle",r);i.setAttribute("mathsize",a.sizingMultiplier[e.value.size]+"em");return i};m.overline=function(e,t){var r=new n.MathNode("mo",[new n.TextNode("\u203e")]);r.setAttribute("stretchy","true");var a=new n.MathNode("mover",[v(e.value.body,t),r]);a.setAttribute("accent","true");return a};m.underline=function(e,t){var r=new n.MathNode("mo",[new n.TextNode("\u203e")]);r.setAttribute("stretchy","true");var a=new n.MathNode("munder",[v(e.value.body,t),r]);a.setAttribute("accentunder","true");return a};m.rule=function(e){var t=new n.MathNode("mrow");return t};m.kern=function(e){var t=new n.MathNode("mrow");return t};m.llap=function(e,t){var r=new n.MathNode("mpadded",[v(e.value.body,t)]);r.setAttribute("lspace","-1width");r.setAttribute("width","0px");return r};m.rlap=function(e,t){var r=new n.MathNode("mpadded",[v(e.value.body,t)]);r.setAttribute("width","0px");return r};m.phantom=function(e,t){var r=f(e.value.value,t);return new n.MathNode("mphantom",r)};m.mclass=function(e,t){var r=f(e.value.value,t);return new n.MathNode("mstyle",r)};var f=function(e,t){var r=[];for(var a=0;a<e.length;a++){var i=e[a];r.push(v(i,t))}return r};var v=function(e,t){if(!e){return new n.MathNode("mrow")}if(m[e.type]){return m[e.type](e,t)}else{throw new s("Got group of unknown type: '"+e.type+"'")}};var d=function(e,t,r){var a=f(e,r);var i=new n.MathNode("mrow",a);var s=new n.MathNode("annotation",[new n.TextNode(t)]);s.setAttribute("encoding","application/x-tex");var l=new n.MathNode("semantics",[i,s]);var o=new n.MathNode("math",[l]);return u(["katex-mathml"],[o])};t.exports=d},{"./ParseError":6,"./buildCommon":10,"./fontMetrics":17,"./mathMLTree":20,"./symbols":23,"./utils":25}],13:[function(e,t,r){var a=e("./buildHTML");var i=e("./buildMathML");var n=e("./buildCommon");var s=e("./Options");var l=e("./Settings");var o=e("./Style");var u=n.makeSpan;var p=function(e,t,r){r=r||new l({});var n=o.TEXT;if(r.displayMode){n=o.DISPLAY}var p=new s({style:n,size:"size5"});var h=i(e,t,p);var c=a(e,p);var m=u(["katex"],[h,c]);if(r.displayMode){return u(["katex-display"],[m])}else{return m}};t.exports=p},{"./Options":5,"./Settings":8,"./Style":9,"./buildCommon":10,"./buildHTML":11,"./buildMathML":12}],14:[function(e,t,r){var a=e("./ParseError");var i=e("./Style");var n=e("./buildCommon");var s=e("./fontMetrics");var l=e("./symbols");var o=e("./utils");var u=n.makeSpan;var p=function(e,t){if(l.math[e]&&l.math[e].replace){return s.getCharacterMetrics(l.math[e].replace,t)}else{return s.getCharacterMetrics(e,t)}};var h=function(e,t,r,a){return n.makeSymbol(e,"Size"+t+"-Regular",r,a)};var c=function(e,t,r,a){a=a||[];var i=u(a.concat(["style-wrap",r.style.reset(),t.cls()]),[e],r);var n=t.sizeMultiplier/r.style.sizeMultiplier;i.height*=n;i.depth*=n;i.maxFontSize=t.sizeMultiplier;return i};var m=function(e,t,r,a,i,s){var l=n.makeSymbol(e,"Main-Regular",i,a);var o=c(l,t,a,s);if(r){var u=(1-a.style.sizeMultiplier/t.sizeMultiplier)*a.style.metrics.axisHeight;o.style.top=u+"em";o.height-=u;o.depth+=u}return o};var f=function(e,t,r,a,n,s){var l=h(e,t,n,a);var o=c(u(["delimsizing","size"+t],[l],a),i.TEXT,a,s);if(r){var p=(1-a.style.sizeMultiplier)*a.style.metrics.axisHeight;o.style.top=p+"em";o.height-=p;o.depth+=p}return o};var v=function(e,t,r){var a;if(t==="Size1-Regular"){a="delim-size1"}else if(t==="Size4-Regular"){a="delim-size4"}var i=u(["delimsizinginner",a],[u([],[n.makeSymbol(e,t,r)])]);return{type:"elem",elem:i}};var d=function(e,t,r,a,s,l){var o;var h;var m;var f;o=m=f=e;h=null;var d="Size1-Regular";if(e==="\\uparrow"){m=f="\u23d0"}else if(e==="\\Uparrow"){m=f="\u2016"}else if(e==="\\downarrow"){o=m="\u23d0"}else if(e==="\\Downarrow"){o=m="\u2016"}else if(e==="\\updownarrow"){o="\\uparrow";m="\u23d0";f="\\downarrow"}else if(e==="\\Updownarrow"){o="\\Uparrow";m="\u2016";f="\\Downarrow"}else if(e==="["||e==="\\lbrack"){o="\u23a1";m="\u23a2";f="\u23a3";d="Size4-Regular"}else if(e==="]"||e==="\\rbrack"){o="\u23a4";m="\u23a5";f="\u23a6";d="Size4-Regular"}else if(e==="\\lfloor"){m=o="\u23a2";f="\u23a3";d="Size4-Regular"}else if(e==="\\lceil"){o="\u23a1";m=f="\u23a2";d="Size4-Regular"}else if(e==="\\rfloor"){m=o="\u23a5";f="\u23a6";d="Size4-Regular"}else if(e==="\\rceil"){o="\u23a4";m=f="\u23a5";d="Size4-Regular"}else if(e==="("){o="\u239b";m="\u239c";f="\u239d";d="Size4-Regular"}else if(e===")"){o="\u239e";m="\u239f";f="\u23a0";d="Size4-Regular"}else if(e==="\\{"||e==="\\lbrace"){o="\u23a7";h="\u23a8";f="\u23a9";m="\u23aa";d="Size4-Regular"}else if(e==="\\}"||e==="\\rbrace"){o="\u23ab";h="\u23ac";f="\u23ad";m="\u23aa";d="Size4-Regular"}else if(e==="\\lgroup"){o="\u23a7";f="\u23a9";m="\u23aa";d="Size4-Regular"}else if(e==="\\rgroup"){o="\u23ab";f="\u23ad";m="\u23aa";d="Size4-Regular"}else if(e==="\\lmoustache"){o="\u23a7";f="\u23ad";m="\u23aa";d="Size4-Regular"}else if(e==="\\rmoustache"){o="\u23ab";f="\u23a9";m="\u23aa";d="Size4-Regular"}else if(e==="\\surd"){o="\ue001";f="\u23b7";m="\ue000";d="Size4-Regular"}var g=p(o,d);var y=g.height+g.depth;var x=p(m,d);var b=x.height+x.depth;var w=p(f,d);var k=w.height+w.depth;var z=0;var S=1;if(h!==null){var M=p(h,d);z=M.height+M.depth;S=2}var T=y+k+z;var A=Math.ceil((t-T)/(S*b));var N=T+A*S*b;var q=a.style.metrics.axisHeight;if(r){q*=a.style.sizeMultiplier}var R=N/2-q;var E=[];E.push(v(f,d,s));var C;if(h===null){for(C=0;C<A;C++){E.push(v(m,d,s))}}else{for(C=0;C<A;C++){E.push(v(m,d,s))}E.push(v(h,d,s));for(C=0;C<A;C++){E.push(v(m,d,s))}}E.push(v(o,d,s));var D=n.makeVList(E,"bottom",R,a);return c(u(["delimsizing","mult"],[D],a),i.TEXT,a,l)};var g=["(",")","[","\\lbrack","]","\\rbrack","\\{","\\lbrace","\\}","\\rbrace","\\lfloor","\\rfloor","\\lceil","\\rceil","\\surd"];var y=["\\uparrow","\\downarrow","\\updownarrow","\\Uparrow","\\Downarrow","\\Updownarrow","|","\\|","\\vert","\\Vert","\\lvert","\\rvert","\\lVert","\\rVert","\\lgroup","\\rgroup","\\lmoustache","\\rmoustache"];var x=["<",">","\\langle","\\rangle","/","\\backslash","\\lt","\\gt"];var b=[0,1.2,1.8,2.4,3];var w=function(e,t,r,i,n){if(e==="<"||e==="\\lt"){e="\\langle"}else if(e===">"||e==="\\gt"){e="\\rangle"}if(o.contains(g,e)||o.contains(x,e)){return f(e,t,false,r,i,n)}else if(o.contains(y,e)){return d(e,b[t],false,r,i,n)}else{throw new a("Illegal delimiter: '"+e+"'")}};var k=[{type:"small",style:i.SCRIPTSCRIPT},{type:"small",style:i.SCRIPT},{type:"small",style:i.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4}];var z=[{type:"small",style:i.SCRIPTSCRIPT},{type:"small",style:i.SCRIPT},{type:"small",style:i.TEXT},{type:"stack"}];var S=[{type:"small",style:i.SCRIPTSCRIPT},{type:"small",style:i.SCRIPT},{type:"small",style:i.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4},{type:"stack"}];var M=function(e){if(e.type==="small"){return"Main-Regular"}else if(e.type==="large"){return"Size"+e.size+"-Regular"}else if(e.type==="stack"){return"Size4-Regular"}};var T=function(e,t,r,a){var i=Math.min(2,3-a.style.size);for(var n=i;n<r.length;n++){if(r[n].type==="stack"){break}var s=p(e,M(r[n]));var l=s.height+s.depth;if(r[n].type==="small"){l*=r[n].style.sizeMultiplier}if(l>t){return r[n]}}return r[r.length-1]};var A=function(e,t,r,a,i,n){if(e==="<"||e==="\\lt"){e="\\langle"}else if(e===">"||e==="\\gt"){e="\\rangle"}var s;if(o.contains(x,e)){s=k}else if(o.contains(g,e)){s=S}else{s=z}var l=T(e,t,s,a);if(l.type==="small"){return m(e,l.style,r,a,i,n)}else if(l.type==="large"){return f(e,l.size,r,a,i,n)}else if(l.type==="stack"){return d(e,t,r,a,i,n)}};var N=function(e,t,r,a,i,n){var l=a.style.metrics.axisHeight*a.style.sizeMultiplier;var o=901;var u=5/s.metrics.ptPerEm;var p=Math.max(t-l,r+l);var h=Math.max(p/500*o,2*p-u);return A(e,h,true,a,i,n)};t.exports={sizedDelim:w,customSizedDelim:A,leftRightDelim:N}},{"./ParseError":6,"./Style":9,"./buildCommon":10,"./fontMetrics":17,"./symbols":23,"./utils":25}],15:[function(e,t,r){var a=e("./unicodeRegexes");var i=e("./utils");var n=function(e){e=e.slice();for(var t=e.length-1;t>=0;t--){if(!e[t]){e.splice(t,1)}}return e.join(" ")};function s(e,t,r){this.classes=e||[];this.children=t||[];this.height=0;this.depth=0;this.maxFontSize=0;this.style={};this.attributes={};if(r){if(r.style.isTight()){this.classes.push("mtight")}if(r.getColor()){this.style.color=r.getColor()}}}s.prototype.setAttribute=function(e,t){this.attributes[e]=t};s.prototype.tryCombine=function(e){return false};s.prototype.toNode=function(){var e=document.createElement("span");e.className=n(this.classes);for(var t in this.style){if(Object.prototype.hasOwnProperty.call(this.style,t)){e.style[t]=this.style[t]}}for(var r in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,r)){e.setAttribute(r,this.attributes[r])}}for(var a=0;a<this.children.length;a++){e.appendChild(this.children[a].toNode())}return e};s.prototype.toMarkup=function(){var e="<span";if(this.classes.length){e+=' class="';e+=i.escape(n(this.classes));e+='"'}var t="";for(var r in this.style){if(this.style.hasOwnProperty(r)){t+=i.hyphenate(r)+":"+this.style[r]+";"}}if(t){e+=' style="'+i.escape(t)+'"'}for(var a in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,a)){e+=" "+a+'="';e+=i.escape(this.attributes[a]);e+='"'}}e+=">";for(var s=0;s<this.children.length;s++){e+=this.children[s].toMarkup()}e+="</span>";return e};function l(e){this.children=e||[];this.height=0;this.depth=0;this.maxFontSize=0}l.prototype.toNode=function(){var e=document.createDocumentFragment();for(var t=0;t<this.children.length;t++){e.appendChild(this.children[t].toNode())}return e};l.prototype.toMarkup=function(){var e="";for(var t=0;t<this.children.length;t++){e+=this.children[t].toMarkup()}return e};var o={"\xee":"\u0131\u0302","\xef":"\u0131\u0308","\xed":"\u0131\u0301","\xec":"\u0131\u0300"};function u(e,t,r,i,n,s,l){this.value=e||"";this.height=t||0;this.depth=r||0;this.italic=i||0;this.skew=n||0;this.classes=s||[];this.style=l||{};this.maxFontSize=0;if(a.cjkRegex.test(e)){if(a.hangulRegex.test(e)){this.classes.push("hangul_fallback")}else{this.classes.push("cjk_fallback")}}if(/[\xee\xef\xed\xec]/.test(this.value)){this.value=o[this.value]}}u.prototype.tryCombine=function(e){if(!e||!(e instanceof u)||this.italic>0||n(this.classes)!==n(e.classes)||this.skew!==e.skew||this.maxFontSize!==e.maxFontSize){return false}for(var t in this.style){if(this.style.hasOwnProperty(t)&&this.style[t]!==e.style[t]){return false}}for(t in e.style){if(e.style.hasOwnProperty(t)&&this.style[t]!==e.style[t]){return false}}this.value+=e.value;this.height=Math.max(this.height,e.height);this.depth=Math.max(this.depth,e.depth);this.italic=e.italic;return true};u.prototype.toNode=function(){var e=document.createTextNode(this.value);var t=null;if(this.italic>0){t=document.createElement("span");t.style.marginRight=this.italic+"em"}if(this.classes.length>0){t=t||document.createElement("span");t.className=n(this.classes)}for(var r in this.style){if(this.style.hasOwnProperty(r)){t=t||document.createElement("span");t.style[r]=this.style[r]}}if(t){t.appendChild(e);return t}else{return e}};u.prototype.toMarkup=function(){var e=false;var t="<span";if(this.classes.length){e=true;t+=' class="';t+=i.escape(n(this.classes));t+='"'}var r="";if(this.italic>0){r+="margin-right:"+this.italic+"em;"}for(var a in this.style){if(this.style.hasOwnProperty(a)){r+=i.hyphenate(a)+":"+this.style[a]+";"}}if(r){e=true;t+=' style="'+i.escape(r)+'"'}var s=i.escape(this.value);if(e){t+=">";t+=s;t+="</span>";return t}else{return s}};t.exports={span:s,documentFragment:l,symbolNode:u}},{"./unicodeRegexes":24,"./utils":25}],16:[function(e,t,r){var a=e("./parseData");var i=e("./ParseError");var n=e("./Style");var s=a.ParseNode;function l(e,t){var r=[];var a=[r];var n=[];while(true){var l=e.parseExpression(false,null);r.push(new s("ordgroup",l,e.mode));var o=e.nextToken.text;if(o==="&"){e.consume()}else if(o==="\\end"){break}else if(o==="\\\\"||o==="\\cr"){var u=e.parseFunction();n.push(u.value.size);r=[];a.push(r)}else{throw new i("Expected & or \\\\ or \\end",e.nextToken)}}t.body=a;t.rowGaps=n;return new s(t.type,t,e.mode)}function o(e,r,a){if(typeof e==="string"){e=[e]}if(typeof r==="number"){r={numArgs:r}}var i={numArgs:r.numArgs||0,argTypes:r.argTypes,greediness:1,allowedInText:!!r.allowedInText,numOptionalArgs:r.numOptionalArgs||0,handler:a};for(var n=0;n<e.length;++n){t.exports[e[n]]=i}}o("array",{numArgs:1},function(e,t){var r=t[0];r=r.value.map?r.value:[r];var a=r.map(function(e){var t=e.value;if("lcr".indexOf(t)!==-1){return{type:"align",align:t}}else if(t==="|"){return{type:"separator",separator:"|"}}throw new i("Unknown column alignment: "+e.value,e)});var n={type:"array",cols:a,hskipBeforeAndAfter:true};n=l(e.parser,n);return n});o(["matrix","pmatrix","bmatrix","Bmatrix","vmatrix","Vmatrix"],{},function(e){var t={matrix:null,pmatrix:["(",")"],bmatrix:["[","]"],Bmatrix:["\\{","\\}"],vmatrix:["|","|"],Vmatrix:["\\Vert","\\Vert"]}[e.envName];var r={type:"array",hskipBeforeAndAfter:false};r=l(e.parser,r);if(t){r=new s("leftright",{body:[r],left:t[0],right:t[1]},e.mode)}return r});o("cases",{},function(e){var t={type:"array",arraystretch:1.2,cols:[{type:"align",align:"l",pregap:0,postgap:n.TEXT.metrics.quad},{type:"align",align:"l",pregap:0,postgap:0}]};t=l(e.parser,t);t=new s("leftright",{body:[t],left:"\\{",right:"."},e.mode);return t});o("aligned",{},function(e){var t={type:"array",cols:[]};t=l(e.parser,t);var r=new s("ordgroup",[],e.mode);var a=0;t.value.body.forEach(function(e){var t;for(t=1;t<e.length;t+=2){e[t].value.unshift(r)}if(a<e.length){a=e.length}});for(var i=0;i<a;++i){var n="r";var o=0;if(i%2===1){n="l"}else if(i>0){o=2}t.value.cols[i]={type:"align",align:n,pregap:o,postgap:0}}return t})},{"./ParseError":6,"./Style":9,"./parseData":21}],17:[function(e,t,r){var a=e("./Style");var i=e("./unicodeRegexes").cjkRegex;var n={slant:[.25,.25,.25],space:[0,0,0],stretch:[0,0,0],shrink:[0,0,0],xHeight:[.431,.431,.431],quad:[1,1.171,1.472],extraSpace:[0,0,0],num1:[.677,.732,.925],num2:[.394,.384,.387],num3:[.444,.471,.504],denom1:[.686,.752,1.025],denom2:[.345,.344,.532],sup1:[.413,.503,.504],sup2:[.363,.431,.404],sup3:[.289,.286,.294],sub1:[.15,.143,.2],sub2:[.247,.286,.4],supDrop:[.386,.353,.494],subDrop:[.05,.071,.1],delim1:[2.39,1.7,1.98],delim2:[1.01,1.157,1.42],axisHeight:[.25,.25,.25]};var s=0;var l=0;var o=0;var u=0;var p=.431;var h=1;var c=0;var m=.04;var f=.111;var v=.166;var d=.2;var g=.6;var y=.1;var x=10;var b=2/x;var w={defaultRuleThickness:m,bigOpSpacing1:f,bigOpSpacing2:v,bigOpSpacing3:d,bigOpSpacing4:g,bigOpSpacing5:y,ptPerEm:x,doubleRuleSep:b};var k=e("./fontMetricsData");var z={"\xc0":"A","\xc1":"A","\xc2":"A","\xc3":"A","\xc4":"A","\xc5":"A","\xc6":"A","\xc7":"C","\xc8":"E","\xc9":"E","\xca":"E","\xcb":"E","\xcc":"I","\xcd":"I","\xce":"I","\xcf":"I","\xd0":"D","\xd1":"N","\xd2":"O","\xd3":"O","\xd4":"O","\xd5":"O","\xd6":"O","\xd8":"O","\xd9":"U","\xda":"U","\xdb":"U","\xdc":"U","\xdd":"Y","\xde":"o","\xdf":"B","\xe0":"a","\xe1":"a","\xe2":"a","\xe3":"a","\xe4":"a","\xe5":"a","\xe6":"a","\xe7":"c","\xe8":"e","\xe9":"e","\xea":"e","\xeb":"e","\xec":"i","\xed":"i","\xee":"i","\xef":"i","\xf0":"d","\xf1":"n","\xf2":"o","\xf3":"o","\xf4":"o","\xf5":"o","\xf6":"o","\xf8":"o","\xf9":"u","\xfa":"u","\xfb":"u","\xfc":"u","\xfd":"y","\xfe":"o","\xff":"y","\u0410":"A","\u0411":"B","\u0412":"B","\u0413":"F","\u0414":"A","\u0415":"E","\u0416":"K","\u0417":"3","\u0418":"N","\u0419":"N","\u041a":"K","\u041b":"N","\u041c":"M","\u041d":"H","\u041e":"O","\u041f":"N","\u0420":"P","\u0421":"C","\u0422":"T","\u0423":"y","\u0424":"O","\u0425":"X","\u0426":"U","\u0427":"h","\u0428":"W","\u0429":"W","\u042a":"B","\u042b":"X","\u042c":"B","\u042d":"3","\u042e":"X","\u042f":"R","\u0430":"a","\u0431":"b","\u0432":"a","\u0433":"r","\u0434":"y","\u0435":"e","\u0436":"m","\u0437":"e","\u0438":"n","\u0439":"n","\u043a":"n","\u043b":"n","\u043c":"m","\u043d":"n","\u043e":"o","\u043f":"n","\u0440":"p","\u0441":"c","\u0442":"o","\u0443":"y","\u0444":"b","\u0445":"x","\u0446":"n","\u0447":"n","\u0448":"w","\u0449":"w","\u044a":"a","\u044b":"m","\u044c":"a","\u044d":"e","\u044e":"m","\u044f":"r"};var S=function(e,t){var r=e.charCodeAt(0);if(e[0]in z){r=z[e[0]].charCodeAt(0)}else if(i.test(e[0])){r="M".charCodeAt(0)}var a=k[t][r];if(a){return{depth:a[0],height:a[1],italic:a[2],skew:a[3],width:a[4]}}};t.exports={metrics:w,sigmas:n,getCharacterMetrics:S}},{"./Style":9,"./fontMetricsData":18,"./unicodeRegexes":24}],18:[function(e,t,r){t.exports={"AMS-Regular":{65:[0,.68889,0,0],66:[0,.68889,0,0],67:[0,.68889,0,0],68:[0,.68889,0,0],69:[0,.68889,0,0],70:[0,.68889,0,0],71:[0,.68889,0,0],72:[0,.68889,0,0],73:[0,.68889,0,0],74:[.16667,.68889,0,0],75:[0,.68889,0,0],76:[0,.68889,0,0],77:[0,.68889,0,0],78:[0,.68889,0,0],79:[.16667,.68889,0,0],80:[0,.68889,0,0],81:[.16667,.68889,0,0],82:[0,.68889,0,0],83:[0,.68889,0,0],84:[0,.68889,0,0],85:[0,.68889,0,0],86:[0,.68889,0,0],87:[0,.68889,0,0],88:[0,.68889,0,0],89:[0,.68889,0,0],90:[0,.68889,0,0],107:[0,.68889,0,0],165:[0,.675,.025,0],174:[.15559,.69224,0,0],240:[0,.68889,0,0],295:[0,.68889,0,0],710:[0,.825,0,0],732:[0,.9,0,0],770:[0,.825,0,0],771:[0,.9,0,0],989:[.08167,.58167,0,0],1008:[0,.43056,.04028,0],8245:[0,.54986,0,0],8463:[0,.68889,0,0],8487:[0,.68889,0,0],8498:[0,.68889,0,0],8502:[0,.68889,0,0],8503:[0,.68889,0,0],8504:[0,.68889,0,0],8513:[0,.68889,0,0],8592:[-.03598,.46402,0,0],8594:[-.03598,.46402,0,0],8602:[-.13313,.36687,0,0],8603:[-.13313,.36687,0,0],8606:[.01354,.52239,0,0],8608:[.01354,.52239,0,0],8610:[.01354,.52239,0,0],8611:[.01354,.52239,0,0],8619:[0,.54986,0,0],8620:[0,.54986,0,0],8621:[-.13313,.37788,0,0],8622:[-.13313,.36687,0,0],8624:[0,.69224,0,0],8625:[0,.69224,0,0],8630:[0,.43056,0,0],8631:[0,.43056,0,0],8634:[.08198,.58198,0,0],8635:[.08198,.58198,0,0],8638:[.19444,.69224,0,0],8639:[.19444,.69224,0,0],8642:[.19444,.69224,0,0],8643:[.19444,.69224,0,0],8644:[.1808,.675,0,0],8646:[.1808,.675,0,0],8647:[.1808,.675,0,0],8648:[.19444,.69224,0,0],8649:[.1808,.675,0,0],8650:[.19444,.69224,0,0],8651:[.01354,.52239,0,0],8652:[.01354,.52239,0,0],8653:[-.13313,.36687,0,0],8654:[-.13313,.36687,0,0],8655:[-.13313,.36687,0,0],8666:[.13667,.63667,0,0],8667:[.13667,.63667,0,0],8669:[-.13313,.37788,0,0],8672:[-.064,.437,0,0],8674:[-.064,.437,0,0],8705:[0,.825,0,0],8708:[0,.68889,0,0],8709:[.08167,.58167,0,0],8717:[0,.43056,0,0],8722:[-.03598,.46402,0,0],8724:[.08198,.69224,0,0],8726:[.08167,.58167,0,0],8733:[0,.69224,0,0],8736:[0,.69224,0,0],8737:[0,.69224,0,0],8738:[.03517,.52239,0,0],8739:[.08167,.58167,0,0],8740:[.25142,.74111,0,0],8741:[.08167,.58167,0,0],8742:[.25142,.74111,0,0],8756:[0,.69224,0,0],8757:[0,.69224,0,0],8764:[-.13313,.36687,0,0],8765:[-.13313,.37788,0,0],8769:[-.13313,.36687,0,0],8770:[-.03625,.46375,0,0],8774:[.30274,.79383,0,0],8776:[-.01688,.48312,0,0],8778:[.08167,.58167,0,0],8782:[.06062,.54986,0,0],8783:[.06062,.54986,0,0],8785:[.08198,.58198,0,0],8786:[.08198,.58198,0,0],8787:[.08198,.58198,0,0],8790:[0,.69224,0,0],8791:[.22958,.72958,0,0],8796:[.08198,.91667,0,0],8806:[.25583,.75583,0,0],
+8807:[.25583,.75583,0,0],8808:[.25142,.75726,0,0],8809:[.25142,.75726,0,0],8812:[.25583,.75583,0,0],8814:[.20576,.70576,0,0],8815:[.20576,.70576,0,0],8816:[.30274,.79383,0,0],8817:[.30274,.79383,0,0],8818:[.22958,.72958,0,0],8819:[.22958,.72958,0,0],8822:[.1808,.675,0,0],8823:[.1808,.675,0,0],8828:[.13667,.63667,0,0],8829:[.13667,.63667,0,0],8830:[.22958,.72958,0,0],8831:[.22958,.72958,0,0],8832:[.20576,.70576,0,0],8833:[.20576,.70576,0,0],8840:[.30274,.79383,0,0],8841:[.30274,.79383,0,0],8842:[.13597,.63597,0,0],8843:[.13597,.63597,0,0],8847:[.03517,.54986,0,0],8848:[.03517,.54986,0,0],8858:[.08198,.58198,0,0],8859:[.08198,.58198,0,0],8861:[.08198,.58198,0,0],8862:[0,.675,0,0],8863:[0,.675,0,0],8864:[0,.675,0,0],8865:[0,.675,0,0],8872:[0,.69224,0,0],8873:[0,.69224,0,0],8874:[0,.69224,0,0],8876:[0,.68889,0,0],8877:[0,.68889,0,0],8878:[0,.68889,0,0],8879:[0,.68889,0,0],8882:[.03517,.54986,0,0],8883:[.03517,.54986,0,0],8884:[.13667,.63667,0,0],8885:[.13667,.63667,0,0],8888:[0,.54986,0,0],8890:[.19444,.43056,0,0],8891:[.19444,.69224,0,0],8892:[.19444,.69224,0,0],8901:[0,.54986,0,0],8903:[.08167,.58167,0,0],8905:[.08167,.58167,0,0],8906:[.08167,.58167,0,0],8907:[0,.69224,0,0],8908:[0,.69224,0,0],8909:[-.03598,.46402,0,0],8910:[0,.54986,0,0],8911:[0,.54986,0,0],8912:[.03517,.54986,0,0],8913:[.03517,.54986,0,0],8914:[0,.54986,0,0],8915:[0,.54986,0,0],8916:[0,.69224,0,0],8918:[.0391,.5391,0,0],8919:[.0391,.5391,0,0],8920:[.03517,.54986,0,0],8921:[.03517,.54986,0,0],8922:[.38569,.88569,0,0],8923:[.38569,.88569,0,0],8926:[.13667,.63667,0,0],8927:[.13667,.63667,0,0],8928:[.30274,.79383,0,0],8929:[.30274,.79383,0,0],8934:[.23222,.74111,0,0],8935:[.23222,.74111,0,0],8936:[.23222,.74111,0,0],8937:[.23222,.74111,0,0],8938:[.20576,.70576,0,0],8939:[.20576,.70576,0,0],8940:[.30274,.79383,0,0],8941:[.30274,.79383,0,0],8994:[.19444,.69224,0,0],8995:[.19444,.69224,0,0],9416:[.15559,.69224,0,0],9484:[0,.69224,0,0],9488:[0,.69224,0,0],9492:[0,.37788,0,0],9496:[0,.37788,0,0],9585:[.19444,.68889,0,0],9586:[.19444,.74111,0,0],9632:[0,.675,0,0],9633:[0,.675,0,0],9650:[0,.54986,0,0],9651:[0,.54986,0,0],9654:[.03517,.54986,0,0],9660:[0,.54986,0,0],9661:[0,.54986,0,0],9664:[.03517,.54986,0,0],9674:[.11111,.69224,0,0],9733:[.19444,.69224,0,0],10003:[0,.69224,0,0],10016:[0,.69224,0,0],10731:[.11111,.69224,0,0],10846:[.19444,.75583,0,0],10877:[.13667,.63667,0,0],10878:[.13667,.63667,0,0],10885:[.25583,.75583,0,0],10886:[.25583,.75583,0,0],10887:[.13597,.63597,0,0],10888:[.13597,.63597,0,0],10889:[.26167,.75726,0,0],10890:[.26167,.75726,0,0],10891:[.48256,.98256,0,0],10892:[.48256,.98256,0,0],10901:[.13667,.63667,0,0],10902:[.13667,.63667,0,0],10933:[.25142,.75726,0,0],10934:[.25142,.75726,0,0],10935:[.26167,.75726,0,0],10936:[.26167,.75726,0,0],10937:[.26167,.75726,0,0],10938:[.26167,.75726,0,0],10949:[.25583,.75583,0,0],10950:[.25583,.75583,0,0],10955:[.28481,.79383,0,0],10956:[.28481,.79383,0,0],57350:[.08167,.58167,0,0],57351:[.08167,.58167,0,0],57352:[.08167,.58167,0,0],57353:[0,.43056,.04028,0],57356:[.25142,.75726,0,0],57357:[.25142,.75726,0,0],57358:[.41951,.91951,0,0],57359:[.30274,.79383,0,0],57360:[.30274,.79383,0,0],57361:[.41951,.91951,0,0],57366:[.25142,.75726,0,0],57367:[.25142,.75726,0,0],57368:[.25142,.75726,0,0],57369:[.25142,.75726,0,0],57370:[.13597,.63597,0,0],57371:[.13597,.63597,0,0]},"Caligraphic-Regular":{48:[0,.43056,0,0],49:[0,.43056,0,0],50:[0,.43056,0,0],51:[.19444,.43056,0,0],52:[.19444,.43056,0,0],53:[.19444,.43056,0,0],54:[0,.64444,0,0],55:[.19444,.43056,0,0],56:[0,.64444,0,0],57:[.19444,.43056,0,0],65:[0,.68333,0,.19445],66:[0,.68333,.03041,.13889],67:[0,.68333,.05834,.13889],68:[0,.68333,.02778,.08334],69:[0,.68333,.08944,.11111],70:[0,.68333,.09931,.11111],71:[.09722,.68333,.0593,.11111],72:[0,.68333,.00965,.11111],73:[0,.68333,.07382,0],74:[.09722,.68333,.18472,.16667],75:[0,.68333,.01445,.05556],76:[0,.68333,0,.13889],77:[0,.68333,0,.13889],78:[0,.68333,.14736,.08334],79:[0,.68333,.02778,.11111],80:[0,.68333,.08222,.08334],81:[.09722,.68333,0,.11111],82:[0,.68333,0,.08334],83:[0,.68333,.075,.13889],84:[0,.68333,.25417,0],85:[0,.68333,.09931,.08334],86:[0,.68333,.08222,0],87:[0,.68333,.08222,.08334],88:[0,.68333,.14643,.13889],89:[.09722,.68333,.08222,.08334],90:[0,.68333,.07944,.13889]},"Fraktur-Regular":{33:[0,.69141,0,0],34:[0,.69141,0,0],38:[0,.69141,0,0],39:[0,.69141,0,0],40:[.24982,.74947,0,0],41:[.24982,.74947,0,0],42:[0,.62119,0,0],43:[.08319,.58283,0,0],44:[0,.10803,0,0],45:[.08319,.58283,0,0],46:[0,.10803,0,0],47:[.24982,.74947,0,0],48:[0,.47534,0,0],49:[0,.47534,0,0],50:[0,.47534,0,0],51:[.18906,.47534,0,0],52:[.18906,.47534,0,0],53:[.18906,.47534,0,0],54:[0,.69141,0,0],55:[.18906,.47534,0,0],56:[0,.69141,0,0],57:[.18906,.47534,0,0],58:[0,.47534,0,0],59:[.12604,.47534,0,0],61:[-.13099,.36866,0,0],63:[0,.69141,0,0],65:[0,.69141,0,0],66:[0,.69141,0,0],67:[0,.69141,0,0],68:[0,.69141,0,0],69:[0,.69141,0,0],70:[.12604,.69141,0,0],71:[0,.69141,0,0],72:[.06302,.69141,0,0],73:[0,.69141,0,0],74:[.12604,.69141,0,0],75:[0,.69141,0,0],76:[0,.69141,0,0],77:[0,.69141,0,0],78:[0,.69141,0,0],79:[0,.69141,0,0],80:[.18906,.69141,0,0],81:[.03781,.69141,0,0],82:[0,.69141,0,0],83:[0,.69141,0,0],84:[0,.69141,0,0],85:[0,.69141,0,0],86:[0,.69141,0,0],87:[0,.69141,0,0],88:[0,.69141,0,0],89:[.18906,.69141,0,0],90:[.12604,.69141,0,0],91:[.24982,.74947,0,0],93:[.24982,.74947,0,0],94:[0,.69141,0,0],97:[0,.47534,0,0],98:[0,.69141,0,0],99:[0,.47534,0,0],100:[0,.62119,0,0],101:[0,.47534,0,0],102:[.18906,.69141,0,0],103:[.18906,.47534,0,0],104:[.18906,.69141,0,0],105:[0,.69141,0,0],106:[0,.69141,0,0],107:[0,.69141,0,0],108:[0,.69141,0,0],109:[0,.47534,0,0],110:[0,.47534,0,0],111:[0,.47534,0,0],112:[.18906,.52396,0,0],113:[.18906,.47534,0,0],114:[0,.47534,0,0],115:[0,.47534,0,0],116:[0,.62119,0,0],117:[0,.47534,0,0],118:[0,.52396,0,0],119:[0,.52396,0,0],120:[.18906,.47534,0,0],121:[.18906,.47534,0,0],122:[.18906,.47534,0,0],8216:[0,.69141,0,0],8217:[0,.69141,0,0],58112:[0,.62119,0,0],58113:[0,.62119,0,0],58114:[.18906,.69141,0,0],58115:[.18906,.69141,0,0],58116:[.18906,.47534,0,0],58117:[0,.69141,0,0],58118:[0,.62119,0,0],58119:[0,.47534,0,0]},"Main-Bold":{33:[0,.69444,0,0],34:[0,.69444,0,0],35:[.19444,.69444,0,0],36:[.05556,.75,0,0],37:[.05556,.75,0,0],38:[0,.69444,0,0],39:[0,.69444,0,0],40:[.25,.75,0,0],41:[.25,.75,0,0],42:[0,.75,0,0],43:[.13333,.63333,0,0],44:[.19444,.15556,0,0],45:[0,.44444,0,0],46:[0,.15556,0,0],47:[.25,.75,0,0],48:[0,.64444,0,0],49:[0,.64444,0,0],50:[0,.64444,0,0],51:[0,.64444,0,0],52:[0,.64444,0,0],53:[0,.64444,0,0],54:[0,.64444,0,0],55:[0,.64444,0,0],56:[0,.64444,0,0],57:[0,.64444,0,0],58:[0,.44444,0,0],59:[.19444,.44444,0,0],60:[.08556,.58556,0,0],61:[-.10889,.39111,0,0],62:[.08556,.58556,0,0],63:[0,.69444,0,0],64:[0,.69444,0,0],65:[0,.68611,0,0],66:[0,.68611,0,0],67:[0,.68611,0,0],68:[0,.68611,0,0],69:[0,.68611,0,0],70:[0,.68611,0,0],71:[0,.68611,0,0],72:[0,.68611,0,0],73:[0,.68611,0,0],74:[0,.68611,0,0],75:[0,.68611,0,0],76:[0,.68611,0,0],77:[0,.68611,0,0],78:[0,.68611,0,0],79:[0,.68611,0,0],80:[0,.68611,0,0],81:[.19444,.68611,0,0],82:[0,.68611,0,0],83:[0,.68611,0,0],84:[0,.68611,0,0],85:[0,.68611,0,0],86:[0,.68611,.01597,0],87:[0,.68611,.01597,0],88:[0,.68611,0,0],89:[0,.68611,.02875,0],90:[0,.68611,0,0],91:[.25,.75,0,0],92:[.25,.75,0,0],93:[.25,.75,0,0],94:[0,.69444,0,0],95:[.31,.13444,.03194,0],96:[0,.69444,0,0],97:[0,.44444,0,0],98:[0,.69444,0,0],99:[0,.44444,0,0],100:[0,.69444,0,0],101:[0,.44444,0,0],102:[0,.69444,.10903,0],103:[.19444,.44444,.01597,0],104:[0,.69444,0,0],105:[0,.69444,0,0],106:[.19444,.69444,0,0],107:[0,.69444,0,0],108:[0,.69444,0,0],109:[0,.44444,0,0],110:[0,.44444,0,0],111:[0,.44444,0,0],112:[.19444,.44444,0,0],113:[.19444,.44444,0,0],114:[0,.44444,0,0],115:[0,.44444,0,0],116:[0,.63492,0,0],117:[0,.44444,0,0],118:[0,.44444,.01597,0],119:[0,.44444,.01597,0],120:[0,.44444,0,0],121:[.19444,.44444,.01597,0],122:[0,.44444,0,0],123:[.25,.75,0,0],124:[.25,.75,0,0],125:[.25,.75,0,0],126:[.35,.34444,0,0],168:[0,.69444,0,0],172:[0,.44444,0,0],175:[0,.59611,0,0],176:[0,.69444,0,0],177:[.13333,.63333,0,0],180:[0,.69444,0,0],215:[.13333,.63333,0,0],247:[.13333,.63333,0,0],305:[0,.44444,0,0],567:[.19444,.44444,0,0],710:[0,.69444,0,0],711:[0,.63194,0,0],713:[0,.59611,0,0],714:[0,.69444,0,0],715:[0,.69444,0,0],728:[0,.69444,0,0],729:[0,.69444,0,0],730:[0,.69444,0,0],732:[0,.69444,0,0],768:[0,.69444,0,0],769:[0,.69444,0,0],770:[0,.69444,0,0],771:[0,.69444,0,0],772:[0,.59611,0,0],774:[0,.69444,0,0],775:[0,.69444,0,0],776:[0,.69444,0,0],778:[0,.69444,0,0],779:[0,.69444,0,0],780:[0,.63194,0,0],824:[.19444,.69444,0,0],915:[0,.68611,0,0],916:[0,.68611,0,0],920:[0,.68611,0,0],923:[0,.68611,0,0],926:[0,.68611,0,0],928:[0,.68611,0,0],931:[0,.68611,0,0],933:[0,.68611,0,0],934:[0,.68611,0,0],936:[0,.68611,0,0],937:[0,.68611,0,0],8211:[0,.44444,.03194,0],8212:[0,.44444,.03194,0],8216:[0,.69444,0,0],8217:[0,.69444,0,0],8220:[0,.69444,0,0],8221:[0,.69444,0,0],8224:[.19444,.69444,0,0],8225:[.19444,.69444,0,0],8242:[0,.55556,0,0],8407:[0,.72444,.15486,0],8463:[0,.69444,0,0],8465:[0,.69444,0,0],8467:[0,.69444,0,0],8472:[.19444,.44444,0,0],8476:[0,.69444,0,0],8501:[0,.69444,0,0],8592:[-.10889,.39111,0,0],8593:[.19444,.69444,0,0],8594:[-.10889,.39111,0,0],8595:[.19444,.69444,0,0],8596:[-.10889,.39111,0,0],8597:[.25,.75,0,0],8598:[.19444,.69444,0,0],8599:[.19444,.69444,0,0],8600:[.19444,.69444,0,0],8601:[.19444,.69444,0,0],8636:[-.10889,.39111,0,0],8637:[-.10889,.39111,0,0],8640:[-.10889,.39111,0,0],8641:[-.10889,.39111,0,0],8656:[-.10889,.39111,0,0],8657:[.19444,.69444,0,0],8658:[-.10889,.39111,0,0],8659:[.19444,.69444,0,0],8660:[-.10889,.39111,0,0],8661:[.25,.75,0,0],8704:[0,.69444,0,0],8706:[0,.69444,.06389,0],8707:[0,.69444,0,0],8709:[.05556,.75,0,0],8711:[0,.68611,0,0],8712:[.08556,.58556,0,0],8715:[.08556,.58556,0,0],8722:[.13333,.63333,0,0],8723:[.13333,.63333,0,0],8725:[.25,.75,0,0],8726:[.25,.75,0,0],8727:[-.02778,.47222,0,0],8728:[-.02639,.47361,0,0],8729:[-.02639,.47361,0,0],8730:[.18,.82,0,0],8733:[0,.44444,0,0],8734:[0,.44444,0,0],8736:[0,.69224,0,0],8739:[.25,.75,0,0],8741:[.25,.75,0,0],8743:[0,.55556,0,0],8744:[0,.55556,0,0],8745:[0,.55556,0,0],8746:[0,.55556,0,0],8747:[.19444,.69444,.12778,0],8764:[-.10889,.39111,0,0],8768:[.19444,.69444,0,0],8771:[.00222,.50222,0,0],8776:[.02444,.52444,0,0],8781:[.00222,.50222,0,0],8801:[.00222,.50222,0,0],8804:[.19667,.69667,0,0],8805:[.19667,.69667,0,0],8810:[.08556,.58556,0,0],8811:[.08556,.58556,0,0],8826:[.08556,.58556,0,0],8827:[.08556,.58556,0,0],8834:[.08556,.58556,0,0],8835:[.08556,.58556,0,0],8838:[.19667,.69667,0,0],8839:[.19667,.69667,0,0],8846:[0,.55556,0,0],8849:[.19667,.69667,0,0],8850:[.19667,.69667,0,0],8851:[0,.55556,0,0],8852:[0,.55556,0,0],8853:[.13333,.63333,0,0],8854:[.13333,.63333,0,0],8855:[.13333,.63333,0,0],8856:[.13333,.63333,0,0],8857:[.13333,.63333,0,0],8866:[0,.69444,0,0],8867:[0,.69444,0,0],8868:[0,.69444,0,0],8869:[0,.69444,0,0],8900:[-.02639,.47361,0,0],8901:[-.02639,.47361,0,0],8902:[-.02778,.47222,0,0],8968:[.25,.75,0,0],8969:[.25,.75,0,0],8970:[.25,.75,0,0],8971:[.25,.75,0,0],8994:[-.13889,.36111,0,0],8995:[-.13889,.36111,0,0],9651:[.19444,.69444,0,0],9657:[-.02778,.47222,0,0],9661:[.19444,.69444,0,0],9667:[-.02778,.47222,0,0],9711:[.19444,.69444,0,0],9824:[.12963,.69444,0,0],9825:[.12963,.69444,0,0],9826:[.12963,.69444,0,0],9827:[.12963,.69444,0,0],9837:[0,.75,0,0],9838:[.19444,.69444,0,0],9839:[.19444,.69444,0,0],10216:[.25,.75,0,0],10217:[.25,.75,0,0],10815:[0,.68611,0,0],10927:[.19667,.69667,0,0],10928:[.19667,.69667,0,0]},"Main-Italic":{33:[0,.69444,.12417,0],34:[0,.69444,.06961,0],35:[.19444,.69444,.06616,0],37:[.05556,.75,.13639,0],38:[0,.69444,.09694,0],39:[0,.69444,.12417,0],40:[.25,.75,.16194,0],41:[.25,.75,.03694,0],42:[0,.75,.14917,0],43:[.05667,.56167,.03694,0],44:[.19444,.10556,0,0],45:[0,.43056,.02826,0],46:[0,.10556,0,0],47:[.25,.75,.16194,0],48:[0,.64444,.13556,0],49:[0,.64444,.13556,0],50:[0,.64444,.13556,0],51:[0,.64444,.13556,0],52:[.19444,.64444,.13556,0],53:[0,.64444,.13556,0],54:[0,.64444,.13556,0],55:[.19444,.64444,.13556,0],56:[0,.64444,.13556,0],57:[0,.64444,.13556,0],58:[0,.43056,.0582,0],59:[.19444,.43056,.0582,0],61:[-.13313,.36687,.06616,0],63:[0,.69444,.1225,0],64:[0,.69444,.09597,0],65:[0,.68333,0,0],66:[0,.68333,.10257,0],67:[0,.68333,.14528,0],68:[0,.68333,.09403,0],69:[0,.68333,.12028,0],70:[0,.68333,.13305,0],71:[0,.68333,.08722,0],72:[0,.68333,.16389,0],73:[0,.68333,.15806,0],74:[0,.68333,.14028,0],75:[0,.68333,.14528,0],76:[0,.68333,0,0],77:[0,.68333,.16389,0],78:[0,.68333,.16389,0],79:[0,.68333,.09403,0],80:[0,.68333,.10257,0],81:[.19444,.68333,.09403,0],82:[0,.68333,.03868,0],83:[0,.68333,.11972,0],84:[0,.68333,.13305,0],85:[0,.68333,.16389,0],86:[0,.68333,.18361,0],87:[0,.68333,.18361,0],88:[0,.68333,.15806,0],89:[0,.68333,.19383,0],90:[0,.68333,.14528,0],91:[.25,.75,.1875,0],93:[.25,.75,.10528,0],94:[0,.69444,.06646,0],95:[.31,.12056,.09208,0],97:[0,.43056,.07671,0],98:[0,.69444,.06312,0],99:[0,.43056,.05653,0],100:[0,.69444,.10333,0],101:[0,.43056,.07514,0],102:[.19444,.69444,.21194,0],103:[.19444,.43056,.08847,0],104:[0,.69444,.07671,0],105:[0,.65536,.1019,0],106:[.19444,.65536,.14467,0],107:[0,.69444,.10764,0],108:[0,.69444,.10333,0],109:[0,.43056,.07671,0],110:[0,.43056,.07671,0],111:[0,.43056,.06312,0],112:[.19444,.43056,.06312,0],113:[.19444,.43056,.08847,0],114:[0,.43056,.10764,0],115:[0,.43056,.08208,0],116:[0,.61508,.09486,0],117:[0,.43056,.07671,0],118:[0,.43056,.10764,0],119:[0,.43056,.10764,0],120:[0,.43056,.12042,0],121:[.19444,.43056,.08847,0],122:[0,.43056,.12292,0],126:[.35,.31786,.11585,0],163:[0,.69444,0,0],305:[0,.43056,0,.02778],567:[.19444,.43056,0,.08334],768:[0,.69444,0,0],769:[0,.69444,.09694,0],770:[0,.69444,.06646,0],771:[0,.66786,.11585,0],772:[0,.56167,.10333,0],774:[0,.69444,.10806,0],775:[0,.66786,.11752,0],776:[0,.66786,.10474,0],778:[0,.69444,0,0],779:[0,.69444,.1225,0],780:[0,.62847,.08295,0],915:[0,.68333,.13305,0],916:[0,.68333,0,0],920:[0,.68333,.09403,0],923:[0,.68333,0,0],926:[0,.68333,.15294,0],928:[0,.68333,.16389,0],931:[0,.68333,.12028,0],933:[0,.68333,.11111,0],934:[0,.68333,.05986,0],936:[0,.68333,.11111,0],937:[0,.68333,.10257,0],8211:[0,.43056,.09208,0],8212:[0,.43056,.09208,0],8216:[0,.69444,.12417,0],8217:[0,.69444,.12417,0],8220:[0,.69444,.1685,0],8221:[0,.69444,.06961,0],8463:[0,.68889,0,0]},"Main-Regular":{32:[0,0,0,0],33:[0,.69444,0,0],34:[0,.69444,0,0],35:[.19444,.69444,0,0],36:[.05556,.75,0,0],37:[.05556,.75,0,0],38:[0,.69444,0,0],39:[0,.69444,0,0],40:[.25,.75,0,0],41:[.25,.75,0,0],42:[0,.75,0,0],43:[.08333,.58333,0,0],44:[.19444,.10556,0,0],45:[0,.43056,0,0],46:[0,.10556,0,0],47:[.25,.75,0,0],48:[0,.64444,0,0],49:[0,.64444,0,0],50:[0,.64444,0,0],51:[0,.64444,0,0],52:[0,.64444,0,0],53:[0,.64444,0,0],54:[0,.64444,0,0],55:[0,.64444,0,0],56:[0,.64444,0,0],57:[0,.64444,0,0],58:[0,.43056,0,0],59:[.19444,.43056,0,0],60:[.0391,.5391,0,0],61:[-.13313,.36687,0,0],62:[.0391,.5391,0,0],63:[0,.69444,0,0],64:[0,.69444,0,0],65:[0,.68333,0,0],66:[0,.68333,0,0],67:[0,.68333,0,0],68:[0,.68333,0,0],69:[0,.68333,0,0],70:[0,.68333,0,0],71:[0,.68333,0,0],72:[0,.68333,0,0],73:[0,.68333,0,0],74:[0,.68333,0,0],75:[0,.68333,0,0],76:[0,.68333,0,0],77:[0,.68333,0,0],78:[0,.68333,0,0],79:[0,.68333,0,0],80:[0,.68333,0,0],81:[.19444,.68333,0,0],82:[0,.68333,0,0],83:[0,.68333,0,0],84:[0,.68333,0,0],85:[0,.68333,0,0],86:[0,.68333,.01389,0],87:[0,.68333,.01389,0],88:[0,.68333,0,0],89:[0,.68333,.025,0],90:[0,.68333,0,0],91:[.25,.75,0,0],92:[.25,.75,0,0],93:[.25,.75,0,0],94:[0,.69444,0,0],95:[.31,.12056,.02778,0],96:[0,.69444,0,0],97:[0,.43056,0,0],98:[0,.69444,0,0],99:[0,.43056,0,0],100:[0,.69444,0,0],101:[0,.43056,0,0],102:[0,.69444,.07778,0],103:[.19444,.43056,.01389,0],104:[0,.69444,0,0],105:[0,.66786,0,0],106:[.19444,.66786,0,0],107:[0,.69444,0,0],108:[0,.69444,0,0],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,0],112:[.19444,.43056,0,0],113:[.19444,.43056,0,0],114:[0,.43056,0,0],115:[0,.43056,0,0],116:[0,.61508,0,0],117:[0,.43056,0,0],118:[0,.43056,.01389,0],119:[0,.43056,.01389,0],120:[0,.43056,0,0],121:[.19444,.43056,.01389,0],122:[0,.43056,0,0],123:[.25,.75,0,0],124:[.25,.75,0,0],125:[.25,.75,0,0],126:[.35,.31786,0,0],160:[0,0,0,0],168:[0,.66786,0,0],172:[0,.43056,0,0],175:[0,.56778,0,0],176:[0,.69444,0,0],177:[.08333,.58333,0,0],180:[0,.69444,0,0],215:[.08333,.58333,0,0],247:[.08333,.58333,0,0],305:[0,.43056,0,0],567:[.19444,.43056,0,0],710:[0,.69444,0,0],711:[0,.62847,0,0],713:[0,.56778,0,0],714:[0,.69444,0,0],715:[0,.69444,0,0],728:[0,.69444,0,0],729:[0,.66786,0,0],730:[0,.69444,0,0],732:[0,.66786,0,0],768:[0,.69444,0,0],769:[0,.69444,0,0],770:[0,.69444,0,0],771:[0,.66786,0,0],772:[0,.56778,0,0],774:[0,.69444,0,0],775:[0,.66786,0,0],776:[0,.66786,0,0],778:[0,.69444,0,0],779:[0,.69444,0,0],780:[0,.62847,0,0],824:[.19444,.69444,0,0],915:[0,.68333,0,0],916:[0,.68333,0,0],920:[0,.68333,0,0],923:[0,.68333,0,0],926:[0,.68333,0,0],928:[0,.68333,0,0],931:[0,.68333,0,0],933:[0,.68333,0,0],934:[0,.68333,0,0],936:[0,.68333,0,0],937:[0,.68333,0,0],8211:[0,.43056,.02778,0],8212:[0,.43056,.02778,0],8216:[0,.69444,0,0],8217:[0,.69444,0,0],8220:[0,.69444,0,0],8221:[0,.69444,0,0],8224:[.19444,.69444,0,0],8225:[.19444,.69444,0,0],8230:[0,.12,0,0],8242:[0,.55556,0,0],8407:[0,.71444,.15382,0],8463:[0,.68889,0,0],8465:[0,.69444,0,0],8467:[0,.69444,0,.11111],8472:[.19444,.43056,0,.11111],8476:[0,.69444,0,0],8501:[0,.69444,0,0],8592:[-.13313,.36687,0,0],8593:[.19444,.69444,0,0],8594:[-.13313,.36687,0,0],8595:[.19444,.69444,0,0],8596:[-.13313,.36687,0,0],8597:[.25,.75,0,0],8598:[.19444,.69444,0,0],8599:[.19444,.69444,0,0],8600:[.19444,.69444,0,0],8601:[.19444,.69444,0,0],8614:[.011,.511,0,0],8617:[.011,.511,0,0],8618:[.011,.511,0,0],8636:[-.13313,.36687,0,0],8637:[-.13313,.36687,0,0],8640:[-.13313,.36687,0,0],8641:[-.13313,.36687,0,0],8652:[.011,.671,0,0],8656:[-.13313,.36687,0,0],8657:[.19444,.69444,0,0],8658:[-.13313,.36687,0,0],8659:[.19444,.69444,0,0],8660:[-.13313,.36687,0,0],8661:[.25,.75,0,0],8704:[0,.69444,0,0],8706:[0,.69444,.05556,.08334],8707:[0,.69444,0,0],8709:[.05556,.75,0,0],8711:[0,.68333,0,0],8712:[.0391,.5391,0,0],8715:[.0391,.5391,0,0],8722:[.08333,.58333,0,0],8723:[.08333,.58333,0,0],8725:[.25,.75,0,0],8726:[.25,.75,0,0],8727:[-.03472,.46528,0,0],8728:[-.05555,.44445,0,0],8729:[-.05555,.44445,0,0],8730:[.2,.8,0,0],8733:[0,.43056,0,0],8734:[0,.43056,0,0],8736:[0,.69224,0,0],8739:[.25,.75,0,0],8741:[.25,.75,0,0],8743:[0,.55556,0,0],8744:[0,.55556,0,0],8745:[0,.55556,0,0],8746:[0,.55556,0,0],8747:[.19444,.69444,.11111,0],8764:[-.13313,.36687,0,0],8768:[.19444,.69444,0,0],8771:[-.03625,.46375,0,0],8773:[-.022,.589,0,0],8776:[-.01688,.48312,0,0],8781:[-.03625,.46375,0,0],8784:[-.133,.67,0,0],8800:[.215,.716,0,0],8801:[-.03625,.46375,0,0],8804:[.13597,.63597,0,0],8805:[.13597,.63597,0,0],8810:[.0391,.5391,0,0],8811:[.0391,.5391,0,0],8826:[.0391,.5391,0,0],8827:[.0391,.5391,0,0],8834:[.0391,.5391,0,0],8835:[.0391,.5391,0,0],8838:[.13597,.63597,0,0],8839:[.13597,.63597,0,0],8846:[0,.55556,0,0],8849:[.13597,.63597,0,0],8850:[.13597,.63597,0,0],8851:[0,.55556,0,0],8852:[0,.55556,0,0],8853:[.08333,.58333,0,0],8854:[.08333,.58333,0,0],8855:[.08333,.58333,0,0],8856:[.08333,.58333,0,0],8857:[.08333,.58333,0,0],8866:[0,.69444,0,0],8867:[0,.69444,0,0],8868:[0,.69444,0,0],8869:[0,.69444,0,0],8872:[.249,.75,0,0],8900:[-.05555,.44445,0,0],8901:[-.05555,.44445,0,0],8902:[-.03472,.46528,0,0],8904:[.005,.505,0,0],8942:[.03,.9,0,0],8943:[-.19,.31,0,0],8945:[-.1,.82,0,0],8968:[.25,.75,0,0],8969:[.25,.75,0,0],8970:[.25,.75,0,0],8971:[.25,.75,0,0],8994:[-.14236,.35764,0,0],8995:[-.14236,.35764,0,0],9136:[.244,.744,0,0],9137:[.244,.744,0,0],9651:[.19444,.69444,0,0],9657:[-.03472,.46528,0,0],9661:[.19444,.69444,0,0],9667:[-.03472,.46528,0,0],9711:[.19444,.69444,0,0],9824:[.12963,.69444,0,0],9825:[.12963,.69444,0,0],9826:[.12963,.69444,0,0],9827:[.12963,.69444,0,0],9837:[0,.75,0,0],9838:[.19444,.69444,0,0],9839:[.19444,.69444,0,0],10216:[.25,.75,0,0],10217:[.25,.75,0,0],10222:[.244,.744,0,0],10223:[.244,.744,0,0],10229:[.011,.511,0,0],10230:[.011,.511,0,0],10231:[.011,.511,0,0],10232:[.024,.525,0,0],10233:[.024,.525,0,0],10234:[.024,.525,0,0],10236:[.011,.511,0,0],10815:[0,.68333,0,0],10927:[.13597,.63597,0,0],10928:[.13597,.63597,0,0]},"Math-BoldItalic":{47:[.19444,.69444,0,0],65:[0,.68611,0,0],66:[0,.68611,.04835,0],67:[0,.68611,.06979,0],68:[0,.68611,.03194,0],69:[0,.68611,.05451,0],70:[0,.68611,.15972,0],71:[0,.68611,0,0],72:[0,.68611,.08229,0],73:[0,.68611,.07778,0],74:[0,.68611,.10069,0],75:[0,.68611,.06979,0],76:[0,.68611,0,0],77:[0,.68611,.11424,0],78:[0,.68611,.11424,0],79:[0,.68611,.03194,0],80:[0,.68611,.15972,0],81:[.19444,.68611,0,0],82:[0,.68611,.00421,0],83:[0,.68611,.05382,0],84:[0,.68611,.15972,0],85:[0,.68611,.11424,0],86:[0,.68611,.25555,0],87:[0,.68611,.15972,0],88:[0,.68611,.07778,0],89:[0,.68611,.25555,0],90:[0,.68611,.06979,0],97:[0,.44444,0,0],98:[0,.69444,0,0],99:[0,.44444,0,0],100:[0,.69444,0,0],101:[0,.44444,0,0],102:[.19444,.69444,.11042,0],103:[.19444,.44444,.03704,0],104:[0,.69444,0,0],105:[0,.69326,0,0],106:[.19444,.69326,.0622,0],107:[0,.69444,.01852,0],108:[0,.69444,.0088,0],109:[0,.44444,0,0],110:[0,.44444,0,0],111:[0,.44444,0,0],112:[.19444,.44444,0,0],113:[.19444,.44444,.03704,0],114:[0,.44444,.03194,0],115:[0,.44444,0,0],116:[0,.63492,0,0],117:[0,.44444,0,0],118:[0,.44444,.03704,0],119:[0,.44444,.02778,0],120:[0,.44444,0,0],121:[.19444,.44444,.03704,0],122:[0,.44444,.04213,0],915:[0,.68611,.15972,0],916:[0,.68611,0,0],920:[0,.68611,.03194,0],923:[0,.68611,0,0],926:[0,.68611,.07458,0],928:[0,.68611,.08229,0],931:[0,.68611,.05451,0],933:[0,.68611,.15972,0],934:[0,.68611,0,0],936:[0,.68611,.11653,0],937:[0,.68611,.04835,0],945:[0,.44444,0,0],946:[.19444,.69444,.03403,0],947:[.19444,.44444,.06389,0],948:[0,.69444,.03819,0],949:[0,.44444,0,0],950:[.19444,.69444,.06215,0],951:[.19444,.44444,.03704,0],952:[0,.69444,.03194,0],953:[0,.44444,0,0],954:[0,.44444,0,0],955:[0,.69444,0,0],956:[.19444,.44444,0,0],957:[0,.44444,.06898,0],958:[.19444,.69444,.03021,0],959:[0,.44444,0,0],960:[0,.44444,.03704,0],961:[.19444,.44444,0,0],962:[.09722,.44444,.07917,0],963:[0,.44444,.03704,0],964:[0,.44444,.13472,0],965:[0,.44444,.03704,0],966:[.19444,.44444,0,0],967:[.19444,.44444,0,0],968:[.19444,.69444,.03704,0],969:[0,.44444,.03704,0],977:[0,.69444,0,0],981:[.19444,.69444,0,0],982:[0,.44444,.03194,0],1009:[.19444,.44444,0,0],1013:[0,.44444,0,0]},"Math-Italic":{47:[.19444,.69444,0,0],65:[0,.68333,0,.13889],66:[0,.68333,.05017,.08334],67:[0,.68333,.07153,.08334],68:[0,.68333,.02778,.05556],69:[0,.68333,.05764,.08334],70:[0,.68333,.13889,.08334],71:[0,.68333,0,.08334],72:[0,.68333,.08125,.05556],73:[0,.68333,.07847,.11111],74:[0,.68333,.09618,.16667],75:[0,.68333,.07153,.05556],76:[0,.68333,0,.02778],77:[0,.68333,.10903,.08334],78:[0,.68333,.10903,.08334],79:[0,.68333,.02778,.08334],80:[0,.68333,.13889,.08334],81:[.19444,.68333,0,.08334],82:[0,.68333,.00773,.08334],83:[0,.68333,.05764,.08334],84:[0,.68333,.13889,.08334],85:[0,.68333,.10903,.02778],86:[0,.68333,.22222,0],87:[0,.68333,.13889,0],88:[0,.68333,.07847,.08334],89:[0,.68333,.22222,0],90:[0,.68333,.07153,.08334],97:[0,.43056,0,0],98:[0,.69444,0,0],99:[0,.43056,0,.05556],100:[0,.69444,0,.16667],101:[0,.43056,0,.05556],102:[.19444,.69444,.10764,.16667],103:[.19444,.43056,.03588,.02778],104:[0,.69444,0,0],105:[0,.65952,0,0],106:[.19444,.65952,.05724,0],107:[0,.69444,.03148,0],108:[0,.69444,.01968,.08334],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,.05556],112:[.19444,.43056,0,.08334],113:[.19444,.43056,.03588,.08334],114:[0,.43056,.02778,.05556],115:[0,.43056,0,.05556],116:[0,.61508,0,.08334],117:[0,.43056,0,.02778],118:[0,.43056,.03588,.02778],119:[0,.43056,.02691,.08334],120:[0,.43056,0,.02778],121:[.19444,.43056,.03588,.05556],122:[0,.43056,.04398,.05556],915:[0,.68333,.13889,.08334],916:[0,.68333,0,.16667],920:[0,.68333,.02778,.08334],923:[0,.68333,0,.16667],926:[0,.68333,.07569,.08334],928:[0,.68333,.08125,.05556],931:[0,.68333,.05764,.08334],933:[0,.68333,.13889,.05556],934:[0,.68333,0,.08334],936:[0,.68333,.11,.05556],937:[0,.68333,.05017,.08334],945:[0,.43056,.0037,.02778],946:[.19444,.69444,.05278,.08334],947:[.19444,.43056,.05556,0],948:[0,.69444,.03785,.05556],949:[0,.43056,0,.08334],950:[.19444,.69444,.07378,.08334],951:[.19444,.43056,.03588,.05556],952:[0,.69444,.02778,.08334],953:[0,.43056,0,.05556],954:[0,.43056,0,0],955:[0,.69444,0,0],956:[.19444,.43056,0,.02778],957:[0,.43056,.06366,.02778],958:[.19444,.69444,.04601,.11111],959:[0,.43056,0,.05556],960:[0,.43056,.03588,0],961:[.19444,.43056,0,.08334],962:[.09722,.43056,.07986,.08334],963:[0,.43056,.03588,0],964:[0,.43056,.1132,.02778],965:[0,.43056,.03588,.02778],966:[.19444,.43056,0,.08334],967:[.19444,.43056,0,.05556],968:[.19444,.69444,.03588,.11111],969:[0,.43056,.03588,0],977:[0,.69444,0,.08334],981:[.19444,.69444,0,.08334],982:[0,.43056,.02778,0],1009:[.19444,.43056,0,.08334],1013:[0,.43056,0,.05556]},"Math-Regular":{65:[0,.68333,0,.13889],66:[0,.68333,.05017,.08334],67:[0,.68333,.07153,.08334],68:[0,.68333,.02778,.05556],69:[0,.68333,.05764,.08334],70:[0,.68333,.13889,.08334],71:[0,.68333,0,.08334],72:[0,.68333,.08125,.05556],73:[0,.68333,.07847,.11111],74:[0,.68333,.09618,.16667],75:[0,.68333,.07153,.05556],76:[0,.68333,0,.02778],77:[0,.68333,.10903,.08334],78:[0,.68333,.10903,.08334],79:[0,.68333,.02778,.08334],80:[0,.68333,.13889,.08334],81:[.19444,.68333,0,.08334],82:[0,.68333,.00773,.08334],83:[0,.68333,.05764,.08334],84:[0,.68333,.13889,.08334],85:[0,.68333,.10903,.02778],86:[0,.68333,.22222,0],87:[0,.68333,.13889,0],88:[0,.68333,.07847,.08334],89:[0,.68333,.22222,0],90:[0,.68333,.07153,.08334],97:[0,.43056,0,0],98:[0,.69444,0,0],99:[0,.43056,0,.05556],100:[0,.69444,0,.16667],101:[0,.43056,0,.05556],102:[.19444,.69444,.10764,.16667],103:[.19444,.43056,.03588,.02778],104:[0,.69444,0,0],105:[0,.65952,0,0],106:[.19444,.65952,.05724,0],107:[0,.69444,.03148,0],108:[0,.69444,.01968,.08334],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,.05556],112:[.19444,.43056,0,.08334],113:[.19444,.43056,.03588,.08334],114:[0,.43056,.02778,.05556],115:[0,.43056,0,.05556],116:[0,.61508,0,.08334],117:[0,.43056,0,.02778],118:[0,.43056,.03588,.02778],119:[0,.43056,.02691,.08334],120:[0,.43056,0,.02778],121:[.19444,.43056,.03588,.05556],122:[0,.43056,.04398,.05556],915:[0,.68333,.13889,.08334],916:[0,.68333,0,.16667],920:[0,.68333,.02778,.08334],923:[0,.68333,0,.16667],926:[0,.68333,.07569,.08334],928:[0,.68333,.08125,.05556],931:[0,.68333,.05764,.08334],933:[0,.68333,.13889,.05556],934:[0,.68333,0,.08334],936:[0,.68333,.11,.05556],937:[0,.68333,.05017,.08334],945:[0,.43056,.0037,.02778],946:[.19444,.69444,.05278,.08334],947:[.19444,.43056,.05556,0],948:[0,.69444,.03785,.05556],949:[0,.43056,0,.08334],950:[.19444,.69444,.07378,.08334],951:[.19444,.43056,.03588,.05556],952:[0,.69444,.02778,.08334],953:[0,.43056,0,.05556],954:[0,.43056,0,0],955:[0,.69444,0,0],956:[.19444,.43056,0,.02778],957:[0,.43056,.06366,.02778],958:[.19444,.69444,.04601,.11111],959:[0,.43056,0,.05556],960:[0,.43056,.03588,0],961:[.19444,.43056,0,.08334],962:[.09722,.43056,.07986,.08334],963:[0,.43056,.03588,0],964:[0,.43056,.1132,.02778],965:[0,.43056,.03588,.02778],966:[.19444,.43056,0,.08334],967:[.19444,.43056,0,.05556],968:[.19444,.69444,.03588,.11111],969:[0,.43056,.03588,0],977:[0,.69444,0,.08334],981:[.19444,.69444,0,.08334],982:[0,.43056,.02778,0],1009:[.19444,.43056,0,.08334],1013:[0,.43056,0,.05556]},"SansSerif-Regular":{33:[0,.69444,0,0],34:[0,.69444,0,0],35:[.19444,.69444,0,0],36:[.05556,.75,0,0],37:[.05556,.75,0,0],38:[0,.69444,0,0],39:[0,.69444,0,0],40:[.25,.75,0,0],41:[.25,.75,0,0],42:[0,.75,0,0],43:[.08333,.58333,0,0],44:[.125,.08333,0,0],45:[0,.44444,0,0],46:[0,.08333,0,0],47:[.25,.75,0,0],48:[0,.65556,0,0],49:[0,.65556,0,0],50:[0,.65556,0,0],51:[0,.65556,0,0],52:[0,.65556,0,0],53:[0,.65556,0,0],54:[0,.65556,0,0],55:[0,.65556,0,0],56:[0,.65556,0,0],57:[0,.65556,0,0],58:[0,.44444,0,0],59:[.125,.44444,0,0],61:[-.13,.37,0,0],63:[0,.69444,0,0],64:[0,.69444,0,0],65:[0,.69444,0,0],66:[0,.69444,0,0],67:[0,.69444,0,0],68:[0,.69444,0,0],69:[0,.69444,0,0],70:[0,.69444,0,0],71:[0,.69444,0,0],72:[0,.69444,0,0],73:[0,.69444,0,0],74:[0,.69444,0,0],75:[0,.69444,0,0],76:[0,.69444,0,0],77:[0,.69444,0,0],78:[0,.69444,0,0],79:[0,.69444,0,0],80:[0,.69444,0,0],81:[.125,.69444,0,0],82:[0,.69444,0,0],83:[0,.69444,0,0],84:[0,.69444,0,0],85:[0,.69444,0,0],86:[0,.69444,.01389,0],87:[0,.69444,.01389,0],88:[0,.69444,0,0],89:[0,.69444,.025,0],90:[0,.69444,0,0],91:[.25,.75,0,0],93:[.25,.75,0,0],94:[0,.69444,0,0],95:[.35,.09444,.02778,0],97:[0,.44444,0,0],98:[0,.69444,0,0],99:[0,.44444,0,0],100:[0,.69444,0,0],101:[0,.44444,0,0],102:[0,.69444,.06944,0],103:[.19444,.44444,.01389,0],104:[0,.69444,0,0],105:[0,.67937,0,0],106:[.19444,.67937,0,0],107:[0,.69444,0,0],108:[0,.69444,0,0],109:[0,.44444,0,0],110:[0,.44444,0,0],111:[0,.44444,0,0],112:[.19444,.44444,0,0],113:[.19444,.44444,0,0],114:[0,.44444,.01389,0],115:[0,.44444,0,0],116:[0,.57143,0,0],117:[0,.44444,0,0],118:[0,.44444,.01389,0],119:[0,.44444,.01389,0],120:[0,.44444,0,0],121:[.19444,.44444,.01389,0],122:[0,.44444,0,0],126:[.35,.32659,0,0],305:[0,.44444,0,0],567:[.19444,.44444,0,0],768:[0,.69444,0,0],769:[0,.69444,0,0],770:[0,.69444,0,0],771:[0,.67659,0,0],772:[0,.60889,0,0],774:[0,.69444,0,0],775:[0,.67937,0,0],776:[0,.67937,0,0],778:[0,.69444,0,0],779:[0,.69444,0,0],780:[0,.63194,0,0],915:[0,.69444,0,0],916:[0,.69444,0,0],920:[0,.69444,0,0],923:[0,.69444,0,0],926:[0,.69444,0,0],928:[0,.69444,0,0],931:[0,.69444,0,0],933:[0,.69444,0,0],934:[0,.69444,0,0],936:[0,.69444,0,0],937:[0,.69444,0,0],8211:[0,.44444,.02778,0],8212:[0,.44444,.02778,0],8216:[0,.69444,0,0],8217:[0,.69444,0,0],8220:[0,.69444,0,0],8221:[0,.69444,0,0]},"Script-Regular":{65:[0,.7,.22925,0],66:[0,.7,.04087,0],67:[0,.7,.1689,0],68:[0,.7,.09371,0],69:[0,.7,.18583,0],70:[0,.7,.13634,0],71:[0,.7,.17322,0],72:[0,.7,.29694,0],73:[0,.7,.19189,0],74:[.27778,.7,.19189,0],75:[0,.7,.31259,0],76:[0,.7,.19189,0],77:[0,.7,.15981,0],78:[0,.7,.3525,0],79:[0,.7,.08078,0],80:[0,.7,.08078,0],81:[0,.7,.03305,0],82:[0,.7,.06259,0],83:[0,.7,.19189,0],84:[0,.7,.29087,0],85:[0,.7,.25815,0],86:[0,.7,.27523,0],87:[0,.7,.27523,0],88:[0,.7,.26006,0],89:[0,.7,.2939,0],90:[0,.7,.24037,0]},"Size1-Regular":{40:[.35001,.85,0,0],41:[.35001,.85,0,0],47:[.35001,.85,0,0],91:[.35001,.85,0,0],92:[.35001,.85,0,0],93:[.35001,.85,0,0],123:[.35001,.85,0,0],125:[.35001,.85,0,0],710:[0,.72222,0,0],732:[0,.72222,0,0],770:[0,.72222,0,0],771:[0,.72222,0,0],8214:[-99e-5,.601,0,0],8593:[1e-5,.6,0,0],8595:[1e-5,.6,0,0],8657:[1e-5,.6,0,0],8659:[1e-5,.6,0,0],8719:[.25001,.75,0,0],8720:[.25001,.75,0,0],8721:[.25001,.75,0,0],8730:[.35001,.85,0,0],8739:[-.00599,.606,0,0],8741:[-.00599,.606,0,0],8747:[.30612,.805,.19445,0],8748:[.306,.805,.19445,0],8749:[.306,.805,.19445,0],8750:[.30612,.805,.19445,0],8896:[.25001,.75,0,0],8897:[.25001,.75,0,0],8898:[.25001,.75,0,0],8899:[.25001,.75,0,0],8968:[.35001,.85,0,0],8969:[.35001,.85,0,0],8970:[.35001,.85,0,0],8971:[.35001,.85,0,0],9168:[-99e-5,.601,0,0],10216:[.35001,.85,0,0],10217:[.35001,.85,0,0],10752:[.25001,.75,0,0],10753:[.25001,.75,0,0],10754:[.25001,.75,0,0],10756:[.25001,.75,0,0],10758:[.25001,.75,0,0]},"Size2-Regular":{40:[.65002,1.15,0,0],41:[.65002,1.15,0,0],47:[.65002,1.15,0,0],91:[.65002,1.15,0,0],92:[.65002,1.15,0,0],93:[.65002,1.15,0,0],123:[.65002,1.15,0,0],125:[.65002,1.15,0,0],710:[0,.75,0,0],732:[0,.75,0,0],770:[0,.75,0,0],771:[0,.75,0,0],8719:[.55001,1.05,0,0],8720:[.55001,1.05,0,0],8721:[.55001,1.05,0,0],8730:[.65002,1.15,0,0],8747:[.86225,1.36,.44445,0],8748:[.862,1.36,.44445,0],8749:[.862,1.36,.44445,0],8750:[.86225,1.36,.44445,0],8896:[.55001,1.05,0,0],8897:[.55001,1.05,0,0],8898:[.55001,1.05,0,0],8899:[.55001,1.05,0,0],8968:[.65002,1.15,0,0],8969:[.65002,1.15,0,0],8970:[.65002,1.15,0,0],8971:[.65002,1.15,0,0],10216:[.65002,1.15,0,0],10217:[.65002,1.15,0,0],10752:[.55001,1.05,0,0],10753:[.55001,1.05,0,0],10754:[.55001,1.05,0,0],
+10756:[.55001,1.05,0,0],10758:[.55001,1.05,0,0]},"Size3-Regular":{40:[.95003,1.45,0,0],41:[.95003,1.45,0,0],47:[.95003,1.45,0,0],91:[.95003,1.45,0,0],92:[.95003,1.45,0,0],93:[.95003,1.45,0,0],123:[.95003,1.45,0,0],125:[.95003,1.45,0,0],710:[0,.75,0,0],732:[0,.75,0,0],770:[0,.75,0,0],771:[0,.75,0,0],8730:[.95003,1.45,0,0],8968:[.95003,1.45,0,0],8969:[.95003,1.45,0,0],8970:[.95003,1.45,0,0],8971:[.95003,1.45,0,0],10216:[.95003,1.45,0,0],10217:[.95003,1.45,0,0]},"Size4-Regular":{40:[1.25003,1.75,0,0],41:[1.25003,1.75,0,0],47:[1.25003,1.75,0,0],91:[1.25003,1.75,0,0],92:[1.25003,1.75,0,0],93:[1.25003,1.75,0,0],123:[1.25003,1.75,0,0],125:[1.25003,1.75,0,0],710:[0,.825,0,0],732:[0,.825,0,0],770:[0,.825,0,0],771:[0,.825,0,0],8730:[1.25003,1.75,0,0],8968:[1.25003,1.75,0,0],8969:[1.25003,1.75,0,0],8970:[1.25003,1.75,0,0],8971:[1.25003,1.75,0,0],9115:[.64502,1.155,0,0],9116:[1e-5,.6,0,0],9117:[.64502,1.155,0,0],9118:[.64502,1.155,0,0],9119:[1e-5,.6,0,0],9120:[.64502,1.155,0,0],9121:[.64502,1.155,0,0],9122:[-99e-5,.601,0,0],9123:[.64502,1.155,0,0],9124:[.64502,1.155,0,0],9125:[-99e-5,.601,0,0],9126:[.64502,1.155,0,0],9127:[1e-5,.9,0,0],9128:[.65002,1.15,0,0],9129:[.90001,0,0,0],9130:[0,.3,0,0],9131:[1e-5,.9,0,0],9132:[.65002,1.15,0,0],9133:[.90001,0,0,0],9143:[.88502,.915,0,0],10216:[1.25003,1.75,0,0],10217:[1.25003,1.75,0,0],57344:[-.00499,.605,0,0],57345:[-.00499,.605,0,0],57680:[0,.12,0,0],57681:[0,.12,0,0],57682:[0,.12,0,0],57683:[0,.12,0,0]},"Typewriter-Regular":{33:[0,.61111,0,0],34:[0,.61111,0,0],35:[0,.61111,0,0],36:[.08333,.69444,0,0],37:[.08333,.69444,0,0],38:[0,.61111,0,0],39:[0,.61111,0,0],40:[.08333,.69444,0,0],41:[.08333,.69444,0,0],42:[0,.52083,0,0],43:[-.08056,.53055,0,0],44:[.13889,.125,0,0],45:[-.08056,.53055,0,0],46:[0,.125,0,0],47:[.08333,.69444,0,0],48:[0,.61111,0,0],49:[0,.61111,0,0],50:[0,.61111,0,0],51:[0,.61111,0,0],52:[0,.61111,0,0],53:[0,.61111,0,0],54:[0,.61111,0,0],55:[0,.61111,0,0],56:[0,.61111,0,0],57:[0,.61111,0,0],58:[0,.43056,0,0],59:[.13889,.43056,0,0],60:[-.05556,.55556,0,0],61:[-.19549,.41562,0,0],62:[-.05556,.55556,0,0],63:[0,.61111,0,0],64:[0,.61111,0,0],65:[0,.61111,0,0],66:[0,.61111,0,0],67:[0,.61111,0,0],68:[0,.61111,0,0],69:[0,.61111,0,0],70:[0,.61111,0,0],71:[0,.61111,0,0],72:[0,.61111,0,0],73:[0,.61111,0,0],74:[0,.61111,0,0],75:[0,.61111,0,0],76:[0,.61111,0,0],77:[0,.61111,0,0],78:[0,.61111,0,0],79:[0,.61111,0,0],80:[0,.61111,0,0],81:[.13889,.61111,0,0],82:[0,.61111,0,0],83:[0,.61111,0,0],84:[0,.61111,0,0],85:[0,.61111,0,0],86:[0,.61111,0,0],87:[0,.61111,0,0],88:[0,.61111,0,0],89:[0,.61111,0,0],90:[0,.61111,0,0],91:[.08333,.69444,0,0],92:[.08333,.69444,0,0],93:[.08333,.69444,0,0],94:[0,.61111,0,0],95:[.09514,0,0,0],96:[0,.61111,0,0],97:[0,.43056,0,0],98:[0,.61111,0,0],99:[0,.43056,0,0],100:[0,.61111,0,0],101:[0,.43056,0,0],102:[0,.61111,0,0],103:[.22222,.43056,0,0],104:[0,.61111,0,0],105:[0,.61111,0,0],106:[.22222,.61111,0,0],107:[0,.61111,0,0],108:[0,.61111,0,0],109:[0,.43056,0,0],110:[0,.43056,0,0],111:[0,.43056,0,0],112:[.22222,.43056,0,0],113:[.22222,.43056,0,0],114:[0,.43056,0,0],115:[0,.43056,0,0],116:[0,.55358,0,0],117:[0,.43056,0,0],118:[0,.43056,0,0],119:[0,.43056,0,0],120:[0,.43056,0,0],121:[.22222,.43056,0,0],122:[0,.43056,0,0],123:[.08333,.69444,0,0],124:[.08333,.69444,0,0],125:[.08333,.69444,0,0],126:[0,.61111,0,0],127:[0,.61111,0,0],305:[0,.43056,0,0],567:[.22222,.43056,0,0],768:[0,.61111,0,0],769:[0,.61111,0,0],770:[0,.61111,0,0],771:[0,.61111,0,0],772:[0,.56555,0,0],774:[0,.61111,0,0],776:[0,.61111,0,0],778:[0,.61111,0,0],780:[0,.56597,0,0],915:[0,.61111,0,0],916:[0,.61111,0,0],920:[0,.61111,0,0],923:[0,.61111,0,0],926:[0,.61111,0,0],928:[0,.61111,0,0],931:[0,.61111,0,0],933:[0,.61111,0,0],934:[0,.61111,0,0],936:[0,.61111,0,0],937:[0,.61111,0,0],2018:[0,.61111,0,0],2019:[0,.61111,0,0],8242:[0,.61111,0,0]}}},{}],19:[function(e,t,r){var a=e("./utils");var i=e("./ParseError");var n=e("./parseData");var s=n.ParseNode;function l(e,r,a){if(typeof e==="string"){e=[e]}if(typeof r==="number"){r={numArgs:r}}var i={numArgs:r.numArgs,argTypes:r.argTypes,greediness:r.greediness===undefined?1:r.greediness,allowedInText:!!r.allowedInText,numOptionalArgs:r.numOptionalArgs||0,infix:!!r.infix,handler:a};for(var n=0;n<e.length;++n){t.exports[e[n]]=i}}var o=function(e){if(e.type==="ordgroup"){return e.value}else{return[e]}};l("\\sqrt",{numArgs:1,numOptionalArgs:1},function(e,t){var r=t[0];var a=t[1];return{type:"sqrt",body:a,index:r}});var u={"\\text":undefined,"\\textrm":"mathrm","\\textsf":"mathsf","\\texttt":"mathtt","\\textnormal":"mathrm","\\textbf":"mathbf","\\textit":"textit"};l(["\\text","\\textrm","\\textsf","\\texttt","\\textnormal","\\textbf","\\textit"],{numArgs:1,argTypes:["text"],greediness:2,allowedInText:true},function(e,t){var r=t[0];return{type:"text",body:o(r),style:u[e.funcName]}});l("\\color",{numArgs:2,allowedInText:true,greediness:3,argTypes:["color","original"]},function(e,t){var r=t[0];var a=t[1];return{type:"color",color:r.value,value:o(a)}});l("\\overline",{numArgs:1},function(e,t){var r=t[0];return{type:"overline",body:r}});l("\\underline",{numArgs:1},function(e,t){var r=t[0];return{type:"underline",body:r}});l("\\rule",{numArgs:2,numOptionalArgs:1,argTypes:["size","size","size"]},function(e,t){var r=t[0];var a=t[1];var i=t[2];return{type:"rule",shift:r&&r.value,width:a.value,height:i.value}});l(["\\kern","\\mkern"],{numArgs:1,argTypes:["size"]},function(e,t){return{type:"kern",dimension:t[0].value}});l("\\KaTeX",{numArgs:0},function(e){return{type:"katex"}});l("\\phantom",{numArgs:1},function(e,t){var r=t[0];return{type:"phantom",value:o(r)}});l(["\\mathord","\\mathbin","\\mathrel","\\mathopen","\\mathclose","\\mathpunct","\\mathinner"],{numArgs:1},function(e,t){var r=t[0];return{type:"mclass",mclass:"m"+e.funcName.substr(5),value:o(r)}});l("\\stackrel",{numArgs:2},function(e,t){var r=t[0];var a=t[1];var i=new s("op",{type:"op",limits:true,alwaysHandleSupSub:true,symbol:false,value:o(a)},a.mode);var n=new s("supsub",{base:i,sup:r,sub:null},r.mode);return{type:"mclass",mclass:"mrel",value:[n]}});l("\\bmod",{numArgs:0},function(e,t){return{type:"mod",modType:"bmod",value:null}});l(["\\pod","\\pmod","\\mod"],{numArgs:1},function(e,t){var r=t[0];return{type:"mod",modType:e.funcName.substr(1),value:o(r)}});var p={"\\bigl":{mclass:"mopen",size:1},"\\Bigl":{mclass:"mopen",size:2},"\\biggl":{mclass:"mopen",size:3},"\\Biggl":{mclass:"mopen",size:4},"\\bigr":{mclass:"mclose",size:1},"\\Bigr":{mclass:"mclose",size:2},"\\biggr":{mclass:"mclose",size:3},"\\Biggr":{mclass:"mclose",size:4},"\\bigm":{mclass:"mrel",size:1},"\\Bigm":{mclass:"mrel",size:2},"\\biggm":{mclass:"mrel",size:3},"\\Biggm":{mclass:"mrel",size:4},"\\big":{mclass:"mord",size:1},"\\Big":{mclass:"mord",size:2},"\\bigg":{mclass:"mord",size:3},"\\Bigg":{mclass:"mord",size:4}};var h=["(",")","[","\\lbrack","]","\\rbrack","\\{","\\lbrace","\\}","\\rbrace","\\lfloor","\\rfloor","\\lceil","\\rceil","<",">","\\langle","\\rangle","\\lt","\\gt","\\lvert","\\rvert","\\lVert","\\rVert","\\lgroup","\\rgroup","\\lmoustache","\\rmoustache","/","\\backslash","|","\\vert","\\|","\\Vert","\\uparrow","\\Uparrow","\\downarrow","\\Downarrow","\\updownarrow","\\Updownarrow","."];var c={"\\Bbb":"\\mathbb","\\bold":"\\mathbf","\\frak":"\\mathfrak"};l(["\\blue","\\orange","\\pink","\\red","\\green","\\gray","\\purple","\\blueA","\\blueB","\\blueC","\\blueD","\\blueE","\\tealA","\\tealB","\\tealC","\\tealD","\\tealE","\\greenA","\\greenB","\\greenC","\\greenD","\\greenE","\\goldA","\\goldB","\\goldC","\\goldD","\\goldE","\\redA","\\redB","\\redC","\\redD","\\redE","\\maroonA","\\maroonB","\\maroonC","\\maroonD","\\maroonE","\\purpleA","\\purpleB","\\purpleC","\\purpleD","\\purpleE","\\mintA","\\mintB","\\mintC","\\grayA","\\grayB","\\grayC","\\grayD","\\grayE","\\grayF","\\grayG","\\grayH","\\grayI","\\kaBlue","\\kaGreen"],{numArgs:1,allowedInText:true,greediness:3},function(e,t){var r=t[0];return{type:"color",color:"katex-"+e.funcName.slice(1),value:o(r)}});l(["\\arcsin","\\arccos","\\arctan","\\arg","\\cos","\\cosh","\\cot","\\coth","\\csc","\\deg","\\dim","\\exp","\\hom","\\ker","\\lg","\\ln","\\log","\\sec","\\sin","\\sinh","\\tan","\\tanh"],{numArgs:0},function(e){return{type:"op",limits:false,symbol:false,body:e.funcName}});l(["\\det","\\gcd","\\inf","\\lim","\\liminf","\\limsup","\\max","\\min","\\Pr","\\sup"],{numArgs:0},function(e){return{type:"op",limits:true,symbol:false,body:e.funcName}});l(["\\int","\\iint","\\iiint","\\oint"],{numArgs:0},function(e){return{type:"op",limits:false,symbol:true,body:e.funcName}});l(["\\coprod","\\bigvee","\\bigwedge","\\biguplus","\\bigcap","\\bigcup","\\intop","\\prod","\\sum","\\bigotimes","\\bigoplus","\\bigodot","\\bigsqcup","\\smallint"],{numArgs:0},function(e){return{type:"op",limits:true,symbol:true,body:e.funcName}});l("\\mathop",{numArgs:1},function(e,t){var r=t[0];return{type:"op",limits:false,symbol:false,value:o(r)}});l(["\\dfrac","\\frac","\\tfrac","\\dbinom","\\binom","\\tbinom","\\\\atopfrac"],{numArgs:2,greediness:2},function(e,t){var r=t[0];var a=t[1];var i;var n=null;var s=null;var l="auto";switch(e.funcName){case"\\dfrac":case"\\frac":case"\\tfrac":i=true;break;case"\\\\atopfrac":i=false;break;case"\\dbinom":case"\\binom":case"\\tbinom":i=false;n="(";s=")";break;default:throw new Error("Unrecognized genfrac command")}switch(e.funcName){case"\\dfrac":case"\\dbinom":l="display";break;case"\\tfrac":case"\\tbinom":l="text";break}return{type:"genfrac",numer:r,denom:a,hasBarLine:i,leftDelim:n,rightDelim:s,size:l}});l(["\\llap","\\rlap"],{numArgs:1,allowedInText:true},function(e,t){var r=t[0];return{type:e.funcName.slice(1),body:r}});var m=function(e,t){if(a.contains(h,e.value)){return e}else{throw new i("Invalid delimiter: '"+e.value+"' after '"+t.funcName+"'",e)}};l(["\\bigl","\\Bigl","\\biggl","\\Biggl","\\bigr","\\Bigr","\\biggr","\\Biggr","\\bigm","\\Bigm","\\biggm","\\Biggm","\\big","\\Big","\\bigg","\\Bigg"],{numArgs:1},function(e,t){var r=m(t[0],e);return{type:"delimsizing",size:p[e.funcName].size,mclass:p[e.funcName].mclass,value:r.value}});l(["\\left","\\right"],{numArgs:1},function(e,t){var r=m(t[0],e);return{type:"leftright",value:r.value}});l("\\middle",{numArgs:1},function(e,t){var r=m(t[0],e);if(!e.parser.leftrightDepth){throw new i("\\middle without preceding \\left",r)}return{type:"middle",value:r.value}});l(["\\tiny","\\scriptsize","\\footnotesize","\\small","\\normalsize","\\large","\\Large","\\LARGE","\\huge","\\Huge"],0,null);l(["\\displaystyle","\\textstyle","\\scriptstyle","\\scriptscriptstyle"],0,null);l(["\\mathrm","\\mathit","\\mathbf","\\mathbb","\\mathcal","\\mathfrak","\\mathscr","\\mathsf","\\mathtt","\\Bbb","\\bold","\\frak"],{numArgs:1,greediness:2},function(e,t){var r=t[0];var a=e.funcName;if(a in c){a=c[a]}return{type:"font",font:a.slice(1),body:r}});l(["\\acute","\\grave","\\ddot","\\tilde","\\bar","\\breve","\\check","\\hat","\\vec","\\dot"],{numArgs:1},function(e,t){var r=t[0];return{type:"accent",accent:e.funcName,base:r}});l(["\\over","\\choose","\\atop"],{numArgs:0,infix:true},function(e){var t;switch(e.funcName){case"\\over":t="\\frac";break;case"\\choose":t="\\binom";break;case"\\atop":t="\\\\atopfrac";break;default:throw new Error("Unrecognized infix genfrac command")}return{type:"infix",replaceWith:t,token:e.token}});l(["\\\\","\\cr"],{numArgs:0,numOptionalArgs:1,argTypes:["size"]},function(e,t){var r=t[0];return{type:"cr",size:r}});l(["\\begin","\\end"],{numArgs:1,argTypes:["text"]},function(e,t){var r=t[0];if(r.type!=="ordgroup"){throw new i("Invalid environment name",r)}var a="";for(var n=0;n<r.value.length;++n){a+=r.value[n].value}return{type:"environment",name:a,nameGroup:r}})},{"./ParseError":6,"./parseData":21,"./utils":25}],20:[function(e,t,r){var a=e("./utils");function i(e,t){this.type=e;this.attributes={};this.children=t||[]}i.prototype.setAttribute=function(e,t){this.attributes[e]=t};i.prototype.toNode=function(){var e=document.createElementNS("http://www.w3.org/1998/Math/MathML",this.type);for(var t in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,t)){e.setAttribute(t,this.attributes[t])}}for(var r=0;r<this.children.length;r++){e.appendChild(this.children[r].toNode())}return e};i.prototype.toMarkup=function(){var e="<"+this.type;for(var t in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,t)){e+=" "+t+'="';e+=a.escape(this.attributes[t]);e+='"'}}e+=">";for(var r=0;r<this.children.length;r++){e+=this.children[r].toMarkup()}e+="</"+this.type+">";return e};function n(e){this.text=e}n.prototype.toNode=function(){return document.createTextNode(this.text)};n.prototype.toMarkup=function(){return a.escape(this.text)};t.exports={MathNode:i,TextNode:n}},{"./utils":25}],21:[function(e,t,r){function a(e,t,r,a,i){this.type=e;this.value=t;this.mode=r;if(a&&(!i||i.lexer===a.lexer)){this.lexer=a.lexer;this.start=a.start;this.end=(i||a).end}}t.exports={ParseNode:a}},{}],22:[function(e,t,r){var a=e("./Parser");var i=function(e,t){if(!(typeof e==="string"||e instanceof String)){throw new TypeError("KaTeX can only parse string typed expression")}var r=new a(e,t);return r.parse()};t.exports=i},{"./Parser":7}],23:[function(e,t,r){t.exports={math:{},text:{}};function a(e,r,a,i,n){t.exports[e][n]={font:r,group:a,replace:i}}var i="math";var n="text";var s="main";var l="ams";var o="accent";var u="bin";var p="close";var h="inner";var c="mathord";var m="op";var f="open";var v="punct";var d="rel";var g="spacing";var y="textord";a(i,s,d,"\u2261","\\equiv");a(i,s,d,"\u227a","\\prec");a(i,s,d,"\u227b","\\succ");a(i,s,d,"\u223c","\\sim");a(i,s,d,"\u22a5","\\perp");a(i,s,d,"\u2aaf","\\preceq");a(i,s,d,"\u2ab0","\\succeq");a(i,s,d,"\u2243","\\simeq");a(i,s,d,"\u2223","\\mid");a(i,s,d,"\u226a","\\ll");a(i,s,d,"\u226b","\\gg");a(i,s,d,"\u224d","\\asymp");a(i,s,d,"\u2225","\\parallel");a(i,s,d,"\u22c8","\\bowtie");a(i,s,d,"\u2323","\\smile");a(i,s,d,"\u2291","\\sqsubseteq");a(i,s,d,"\u2292","\\sqsupseteq");a(i,s,d,"\u2250","\\doteq");a(i,s,d,"\u2322","\\frown");a(i,s,d,"\u220b","\\ni");a(i,s,d,"\u221d","\\propto");a(i,s,d,"\u22a2","\\vdash");a(i,s,d,"\u22a3","\\dashv");a(i,s,d,"\u220b","\\owns");a(i,s,v,".","\\ldotp");a(i,s,v,"\u22c5","\\cdotp");a(i,s,y,"#","\\#");a(n,s,y,"#","\\#");a(i,s,y,"&","\\&");a(n,s,y,"&","\\&");a(i,s,y,"\u2135","\\aleph");a(i,s,y,"\u2200","\\forall");a(i,s,y,"\u210f","\\hbar");a(i,s,y,"\u2203","\\exists");a(i,s,y,"\u2207","\\nabla");a(i,s,y,"\u266d","\\flat");a(i,s,y,"\u2113","\\ell");a(i,s,y,"\u266e","\\natural");a(i,s,y,"\u2663","\\clubsuit");a(i,s,y,"\u2118","\\wp");a(i,s,y,"\u266f","\\sharp");a(i,s,y,"\u2662","\\diamondsuit");a(i,s,y,"\u211c","\\Re");a(i,s,y,"\u2661","\\heartsuit");a(i,s,y,"\u2111","\\Im");a(i,s,y,"\u2660","\\spadesuit");a(i,s,y,"\u2020","\\dag");a(i,s,y,"\u2021","\\ddag");a(i,s,p,"\u23b1","\\rmoustache");a(i,s,f,"\u23b0","\\lmoustache");a(i,s,p,"\u27ef","\\rgroup");a(i,s,f,"\u27ee","\\lgroup");a(i,s,u,"\u2213","\\mp");a(i,s,u,"\u2296","\\ominus");a(i,s,u,"\u228e","\\uplus");a(i,s,u,"\u2293","\\sqcap");a(i,s,u,"\u2217","\\ast");a(i,s,u,"\u2294","\\sqcup");a(i,s,u,"\u25ef","\\bigcirc");a(i,s,u,"\u2219","\\bullet");a(i,s,u,"\u2021","\\ddagger");a(i,s,u,"\u2240","\\wr");a(i,s,u,"\u2a3f","\\amalg");a(i,s,d,"\u27f5","\\longleftarrow");a(i,s,d,"\u21d0","\\Leftarrow");a(i,s,d,"\u27f8","\\Longleftarrow");a(i,s,d,"\u27f6","\\longrightarrow");a(i,s,d,"\u21d2","\\Rightarrow");a(i,s,d,"\u27f9","\\Longrightarrow");a(i,s,d,"\u2194","\\leftrightarrow");a(i,s,d,"\u27f7","\\longleftrightarrow");a(i,s,d,"\u21d4","\\Leftrightarrow");a(i,s,d,"\u27fa","\\Longleftrightarrow");a(i,s,d,"\u21a6","\\mapsto");a(i,s,d,"\u27fc","\\longmapsto");a(i,s,d,"\u2197","\\nearrow");a(i,s,d,"\u21a9","\\hookleftarrow");a(i,s,d,"\u21aa","\\hookrightarrow");a(i,s,d,"\u2198","\\searrow");a(i,s,d,"\u21bc","\\leftharpoonup");a(i,s,d,"\u21c0","\\rightharpoonup");a(i,s,d,"\u2199","\\swarrow");a(i,s,d,"\u21bd","\\leftharpoondown");a(i,s,d,"\u21c1","\\rightharpoondown");a(i,s,d,"\u2196","\\nwarrow");a(i,s,d,"\u21cc","\\rightleftharpoons");a(i,l,d,"\u226e","\\nless");a(i,l,d,"\ue010","\\nleqslant");a(i,l,d,"\ue011","\\nleqq");a(i,l,d,"\u2a87","\\lneq");a(i,l,d,"\u2268","\\lneqq");a(i,l,d,"\ue00c","\\lvertneqq");a(i,l,d,"\u22e6","\\lnsim");a(i,l,d,"\u2a89","\\lnapprox");a(i,l,d,"\u2280","\\nprec");a(i,l,d,"\u22e0","\\npreceq");a(i,l,d,"\u22e8","\\precnsim");a(i,l,d,"\u2ab9","\\precnapprox");a(i,l,d,"\u2241","\\nsim");a(i,l,d,"\ue006","\\nshortmid");a(i,l,d,"\u2224","\\nmid");a(i,l,d,"\u22ac","\\nvdash");a(i,l,d,"\u22ad","\\nvDash");a(i,l,d,"\u22ea","\\ntriangleleft");a(i,l,d,"\u22ec","\\ntrianglelefteq");a(i,l,d,"\u228a","\\subsetneq");a(i,l,d,"\ue01a","\\varsubsetneq");a(i,l,d,"\u2acb","\\subsetneqq");a(i,l,d,"\ue017","\\varsubsetneqq");a(i,l,d,"\u226f","\\ngtr");a(i,l,d,"\ue00f","\\ngeqslant");a(i,l,d,"\ue00e","\\ngeqq");a(i,l,d,"\u2a88","\\gneq");a(i,l,d,"\u2269","\\gneqq");a(i,l,d,"\ue00d","\\gvertneqq");a(i,l,d,"\u22e7","\\gnsim");a(i,l,d,"\u2a8a","\\gnapprox");a(i,l,d,"\u2281","\\nsucc");a(i,l,d,"\u22e1","\\nsucceq");a(i,l,d,"\u22e9","\\succnsim");a(i,l,d,"\u2aba","\\succnapprox");a(i,l,d,"\u2246","\\ncong");a(i,l,d,"\ue007","\\nshortparallel");a(i,l,d,"\u2226","\\nparallel");a(i,l,d,"\u22af","\\nVDash");a(i,l,d,"\u22eb","\\ntriangleright");a(i,l,d,"\u22ed","\\ntrianglerighteq");a(i,l,d,"\ue018","\\nsupseteqq");a(i,l,d,"\u228b","\\supsetneq");a(i,l,d,"\ue01b","\\varsupsetneq");a(i,l,d,"\u2acc","\\supsetneqq");a(i,l,d,"\ue019","\\varsupsetneqq");a(i,l,d,"\u22ae","\\nVdash");a(i,l,d,"\u2ab5","\\precneqq");a(i,l,d,"\u2ab6","\\succneqq");a(i,l,d,"\ue016","\\nsubseteqq");a(i,l,u,"\u22b4","\\unlhd");a(i,l,u,"\u22b5","\\unrhd");a(i,l,d,"\u219a","\\nleftarrow");a(i,l,d,"\u219b","\\nrightarrow");a(i,l,d,"\u21cd","\\nLeftarrow");a(i,l,d,"\u21cf","\\nRightarrow");a(i,l,d,"\u21ae","\\nleftrightarrow");a(i,l,d,"\u21ce","\\nLeftrightarrow");a(i,l,d,"\u25b3","\\vartriangle");a(i,l,y,"\u210f","\\hslash");a(i,l,y,"\u25bd","\\triangledown");a(i,l,y,"\u25ca","\\lozenge");a(i,l,y,"\u24c8","\\circledS");a(i,l,y,"\xae","\\circledR");a(i,l,y,"\u2221","\\measuredangle");a(i,l,y,"\u2204","\\nexists");a(i,l,y,"\u2127","\\mho");a(i,l,y,"\u2132","\\Finv");a(i,l,y,"\u2141","\\Game");a(i,l,y,"k","\\Bbbk");a(i,l,y,"\u2035","\\backprime");a(i,l,y,"\u25b2","\\blacktriangle");a(i,l,y,"\u25bc","\\blacktriangledown");a(i,l,y,"\u25a0","\\blacksquare");a(i,l,y,"\u29eb","\\blacklozenge");a(i,l,y,"\u2605","\\bigstar");a(i,l,y,"\u2222","\\sphericalangle");a(i,l,y,"\u2201","\\complement");a(i,l,y,"\xf0","\\eth");a(i,l,y,"\u2571","\\diagup");a(i,l,y,"\u2572","\\diagdown");a(i,l,y,"\u25a1","\\square");a(i,l,y,"\u25a1","\\Box");a(i,l,y,"\u25ca","\\Diamond");a(i,l,y,"\xa5","\\yen");a(i,l,y,"\u2713","\\checkmark");a(i,l,y,"\u2136","\\beth");a(i,l,y,"\u2138","\\daleth");a(i,l,y,"\u2137","\\gimel");a(i,l,y,"\u03dd","\\digamma");a(i,l,y,"\u03f0","\\varkappa");a(i,l,f,"\u250c","\\ulcorner");a(i,l,p,"\u2510","\\urcorner");a(i,l,f,"\u2514","\\llcorner");a(i,l,p,"\u2518","\\lrcorner");a(i,l,d,"\u2266","\\leqq");a(i,l,d,"\u2a7d","\\leqslant");a(i,l,d,"\u2a95","\\eqslantless");a(i,l,d,"\u2272","\\lesssim");a(i,l,d,"\u2a85","\\lessapprox");a(i,l,d,"\u224a","\\approxeq");a(i,l,u,"\u22d6","\\lessdot");a(i,l,d,"\u22d8","\\lll");a(i,l,d,"\u2276","\\lessgtr");a(i,l,d,"\u22da","\\lesseqgtr");a(i,l,d,"\u2a8b","\\lesseqqgtr");a(i,l,d,"\u2251","\\doteqdot");a(i,l,d,"\u2253","\\risingdotseq");a(i,l,d,"\u2252","\\fallingdotseq");a(i,l,d,"\u223d","\\backsim");a(i,l,d,"\u22cd","\\backsimeq");a(i,l,d,"\u2ac5","\\subseteqq");a(i,l,d,"\u22d0","\\Subset");a(i,l,d,"\u228f","\\sqsubset");a(i,l,d,"\u227c","\\preccurlyeq");a(i,l,d,"\u22de","\\curlyeqprec");a(i,l,d,"\u227e","\\precsim");a(i,l,d,"\u2ab7","\\precapprox");a(i,l,d,"\u22b2","\\vartriangleleft");a(i,l,d,"\u22b4","\\trianglelefteq");a(i,l,d,"\u22a8","\\vDash");a(i,l,d,"\u22aa","\\Vvdash");a(i,l,d,"\u2323","\\smallsmile");a(i,l,d,"\u2322","\\smallfrown");a(i,l,d,"\u224f","\\bumpeq");a(i,l,d,"\u224e","\\Bumpeq");a(i,l,d,"\u2267","\\geqq");a(i,l,d,"\u2a7e","\\geqslant");a(i,l,d,"\u2a96","\\eqslantgtr");a(i,l,d,"\u2273","\\gtrsim");a(i,l,d,"\u2a86","\\gtrapprox");a(i,l,u,"\u22d7","\\gtrdot");a(i,l,d,"\u22d9","\\ggg");a(i,l,d,"\u2277","\\gtrless");a(i,l,d,"\u22db","\\gtreqless");a(i,l,d,"\u2a8c","\\gtreqqless");a(i,l,d,"\u2256","\\eqcirc");a(i,l,d,"\u2257","\\circeq");a(i,l,d,"\u225c","\\triangleq");a(i,l,d,"\u223c","\\thicksim");a(i,l,d,"\u2248","\\thickapprox");a(i,l,d,"\u2ac6","\\supseteqq");a(i,l,d,"\u22d1","\\Supset");a(i,l,d,"\u2290","\\sqsupset");a(i,l,d,"\u227d","\\succcurlyeq");a(i,l,d,"\u22df","\\curlyeqsucc");a(i,l,d,"\u227f","\\succsim");a(i,l,d,"\u2ab8","\\succapprox");a(i,l,d,"\u22b3","\\vartriangleright");a(i,l,d,"\u22b5","\\trianglerighteq");a(i,l,d,"\u22a9","\\Vdash");a(i,l,d,"\u2223","\\shortmid");a(i,l,d,"\u2225","\\shortparallel");a(i,l,d,"\u226c","\\between");a(i,l,d,"\u22d4","\\pitchfork");a(i,l,d,"\u221d","\\varpropto");a(i,l,d,"\u25c0","\\blacktriangleleft");a(i,l,d,"\u2234","\\therefore");a(i,l,d,"\u220d","\\backepsilon");a(i,l,d,"\u25b6","\\blacktriangleright");a(i,l,d,"\u2235","\\because");a(i,l,d,"\u22d8","\\llless");a(i,l,d,"\u22d9","\\gggtr");a(i,l,u,"\u22b2","\\lhd");a(i,l,u,"\u22b3","\\rhd");a(i,l,d,"\u2242","\\eqsim");a(i,s,d,"\u22c8","\\Join");a(i,l,d,"\u2251","\\Doteq");a(i,l,u,"\u2214","\\dotplus");a(i,l,u,"\u2216","\\smallsetminus");a(i,l,u,"\u22d2","\\Cap");a(i,l,u,"\u22d3","\\Cup");a(i,l,u,"\u2a5e","\\doublebarwedge");a(i,l,u,"\u229f","\\boxminus");a(i,l,u,"\u229e","\\boxplus");a(i,l,u,"\u22c7","\\divideontimes");a(i,l,u,"\u22c9","\\ltimes");a(i,l,u,"\u22ca","\\rtimes");a(i,l,u,"\u22cb","\\leftthreetimes");a(i,l,u,"\u22cc","\\rightthreetimes");a(i,l,u,"\u22cf","\\curlywedge");a(i,l,u,"\u22ce","\\curlyvee");a(i,l,u,"\u229d","\\circleddash");a(i,l,u,"\u229b","\\circledast");a(i,l,u,"\u22c5","\\centerdot");a(i,l,u,"\u22ba","\\intercal");a(i,l,u,"\u22d2","\\doublecap");a(i,l,u,"\u22d3","\\doublecup");a(i,l,u,"\u22a0","\\boxtimes");a(i,l,d,"\u21e2","\\dashrightarrow");a(i,l,d,"\u21e0","\\dashleftarrow");a(i,l,d,"\u21c7","\\leftleftarrows");a(i,l,d,"\u21c6","\\leftrightarrows");a(i,l,d,"\u21da","\\Lleftarrow");a(i,l,d,"\u219e","\\twoheadleftarrow");a(i,l,d,"\u21a2","\\leftarrowtail");a(i,l,d,"\u21ab","\\looparrowleft");a(i,l,d,"\u21cb","\\leftrightharpoons");a(i,l,d,"\u21b6","\\curvearrowleft");a(i,l,d,"\u21ba","\\circlearrowleft");a(i,l,d,"\u21b0","\\Lsh");a(i,l,d,"\u21c8","\\upuparrows");a(i,l,d,"\u21bf","\\upharpoonleft");a(i,l,d,"\u21c3","\\downharpoonleft");a(i,l,d,"\u22b8","\\multimap");a(i,l,d,"\u21ad","\\leftrightsquigarrow");a(i,l,d,"\u21c9","\\rightrightarrows");a(i,l,d,"\u21c4","\\rightleftarrows");a(i,l,d,"\u21a0","\\twoheadrightarrow");a(i,l,d,"\u21a3","\\rightarrowtail");a(i,l,d,"\u21ac","\\looparrowright");a(i,l,d,"\u21b7","\\curvearrowright");a(i,l,d,"\u21bb","\\circlearrowright");a(i,l,d,"\u21b1","\\Rsh");a(i,l,d,"\u21ca","\\downdownarrows");a(i,l,d,"\u21be","\\upharpoonright");a(i,l,d,"\u21c2","\\downharpoonright");a(i,l,d,"\u21dd","\\rightsquigarrow");a(i,l,d,"\u21dd","\\leadsto");a(i,l,d,"\u21db","\\Rrightarrow");a(i,l,d,"\u21be","\\restriction");a(i,s,y,"\u2018","`");a(i,s,y,"$","\\$");a(n,s,y,"$","\\$");a(i,s,y,"%","\\%");a(n,s,y,"%","\\%");a(i,s,y,"_","\\_");a(n,s,y,"_","\\_");a(i,s,y,"\u2220","\\angle");a(i,s,y,"\u221e","\\infty");a(i,s,y,"\u2032","\\prime");a(i,s,y,"\u25b3","\\triangle");a(i,s,y,"\u0393","\\Gamma");a(i,s,y,"\u0394","\\Delta");a(i,s,y,"\u0398","\\Theta");a(i,s,y,"\u039b","\\Lambda");a(i,s,y,"\u039e","\\Xi");a(i,s,y,"\u03a0","\\Pi");a(i,s,y,"\u03a3","\\Sigma");a(i,s,y,"\u03a5","\\Upsilon");a(i,s,y,"\u03a6","\\Phi");a(i,s,y,"\u03a8","\\Psi");a(i,s,y,"\u03a9","\\Omega");a(i,s,y,"\xac","\\neg");a(i,s,y,"\xac","\\lnot");a(i,s,y,"\u22a4","\\top");a(i,s,y,"\u22a5","\\bot");a(i,s,y,"\u2205","\\emptyset");a(i,l,y,"\u2205","\\varnothing");a(i,s,c,"\u03b1","\\alpha");a(i,s,c,"\u03b2","\\beta");a(i,s,c,"\u03b3","\\gamma");a(i,s,c,"\u03b4","\\delta");a(i,s,c,"\u03f5","\\epsilon");a(i,s,c,"\u03b6","\\zeta");a(i,s,c,"\u03b7","\\eta");a(i,s,c,"\u03b8","\\theta");a(i,s,c,"\u03b9","\\iota");a(i,s,c,"\u03ba","\\kappa");a(i,s,c,"\u03bb","\\lambda");a(i,s,c,"\u03bc","\\mu");a(i,s,c,"\u03bd","\\nu");a(i,s,c,"\u03be","\\xi");a(i,s,c,"o","\\omicron");a(i,s,c,"\u03c0","\\pi");a(i,s,c,"\u03c1","\\rho");a(i,s,c,"\u03c3","\\sigma");a(i,s,c,"\u03c4","\\tau");a(i,s,c,"\u03c5","\\upsilon");a(i,s,c,"\u03d5","\\phi");a(i,s,c,"\u03c7","\\chi");a(i,s,c,"\u03c8","\\psi");a(i,s,c,"\u03c9","\\omega");a(i,s,c,"\u03b5","\\varepsilon");a(i,s,c,"\u03d1","\\vartheta");a(i,s,c,"\u03d6","\\varpi");a(i,s,c,"\u03f1","\\varrho");a(i,s,c,"\u03c2","\\varsigma");a(i,s,c,"\u03c6","\\varphi");a(i,s,u,"\u2217","*");a(i,s,u,"+","+");a(i,s,u,"\u2212","-");a(i,s,u,"\u22c5","\\cdot");a(i,s,u,"\u2218","\\circ");a(i,s,u,"\xf7","\\div");a(i,s,u,"\xb1","\\pm");a(i,s,u,"\xd7","\\times");a(i,s,u,"\u2229","\\cap");a(i,s,u,"\u222a","\\cup");a(i,s,u,"\u2216","\\setminus");a(i,s,u,"\u2227","\\land");a(i,s,u,"\u2228","\\lor");a(i,s,u,"\u2227","\\wedge");a(i,s,u,"\u2228","\\vee");a(i,s,y,"\u221a","\\surd");a(i,s,f,"(","(");a(i,s,f,"[","[");a(i,s,f,"\u27e8","\\langle");a(i,s,f,"\u2223","\\lvert");a(i,s,f,"\u2225","\\lVert");a(i,s,p,")",")");a(i,s,p,"]","]");a(i,s,p,"?","?");a(i,s,p,"!","!");a(i,s,p,"\u27e9","\\rangle");a(i,s,p,"\u2223","\\rvert");a(i,s,p,"\u2225","\\rVert");a(i,s,d,"=","=");a(i,s,d,"<","<");a(i,s,d,">",">");a(i,s,d,":",":");a(i,s,d,"\u2248","\\approx");a(i,s,d,"\u2245","\\cong");a(i,s,d,"\u2265","\\ge");a(i,s,d,"\u2265","\\geq");a(i,s,d,"\u2190","\\gets");a(i,s,d,">","\\gt");a(i,s,d,"\u2208","\\in");a(i,s,d,"\u2209","\\notin");a(i,s,d,"\u2282","\\subset");a(i,s,d,"\u2283","\\supset");a(i,s,d,"\u2286","\\subseteq");a(i,s,d,"\u2287","\\supseteq");a(i,l,d,"\u2288","\\nsubseteq");a(i,l,d,"\u2289","\\nsupseteq");a(i,s,d,"\u22a8","\\models");a(i,s,d,"\u2190","\\leftarrow");a(i,s,d,"\u2264","\\le");a(i,s,d,"\u2264","\\leq");a(i,s,d,"<","\\lt");a(i,s,d,"\u2260","\\ne");a(i,s,d,"\u2260","\\neq");a(i,s,d,"\u2192","\\rightarrow");a(i,s,d,"\u2192","\\to");a(i,l,d,"\u2271","\\ngeq");a(i,l,d,"\u2270","\\nleq");a(i,s,g,null,"\\!");a(i,s,g,"\xa0","\\ ");a(i,s,g,"\xa0","~");a(i,s,g,null,"\\,");a(i,s,g,null,"\\:");a(i,s,g,null,"\\;");a(i,s,g,null,"\\enspace");a(i,s,g,null,"\\qquad");a(i,s,g,null,"\\quad");a(i,s,g,"\xa0","\\space");a(i,s,v,",",",");a(i,s,v,";",";");a(i,s,v,":","\\colon");a(i,l,u,"\u22bc","\\barwedge");a(i,l,u,"\u22bb","\\veebar");a(i,s,u,"\u2299","\\odot");a(i,s,u,"\u2295","\\oplus");a(i,s,u,"\u2297","\\otimes");a(i,s,y,"\u2202","\\partial");a(i,s,u,"\u2298","\\oslash");a(i,l,u,"\u229a","\\circledcirc");a(i,l,u,"\u22a1","\\boxdot");a(i,s,u,"\u25b3","\\bigtriangleup");a(i,s,u,"\u25bd","\\bigtriangledown");a(i,s,u,"\u2020","\\dagger");a(i,s,u,"\u22c4","\\diamond");a(i,s,u,"\u22c6","\\star");a(i,s,u,"\u25c3","\\triangleleft");a(i,s,u,"\u25b9","\\triangleright");a(i,s,f,"{","\\{");a(n,s,y,"{","\\{");a(i,s,p,"}","\\}");a(n,s,y,"}","\\}");a(i,s,f,"{","\\lbrace");a(i,s,p,"}","\\rbrace");a(i,s,f,"[","\\lbrack");a(i,s,p,"]","\\rbrack");a(i,s,f,"\u230a","\\lfloor");a(i,s,p,"\u230b","\\rfloor");a(i,s,f,"\u2308","\\lceil");a(i,s,p,"\u2309","\\rceil");a(i,s,y,"\\","\\backslash");a(i,s,y,"\u2223","|");a(i,s,y,"\u2223","\\vert");a(i,s,y,"\u2225","\\|");a(i,s,y,"\u2225","\\Vert");a(i,s,d,"\u2191","\\uparrow");a(i,s,d,"\u21d1","\\Uparrow");a(i,s,d,"\u2193","\\downarrow");a(i,s,d,"\u21d3","\\Downarrow");a(i,s,d,"\u2195","\\updownarrow");a(i,s,d,"\u21d5","\\Updownarrow");a(i,i,m,"\u2210","\\coprod");a(i,i,m,"\u22c1","\\bigvee");a(i,i,m,"\u22c0","\\bigwedge");a(i,i,m,"\u2a04","\\biguplus");a(i,i,m,"\u22c2","\\bigcap");a(i,i,m,"\u22c3","\\bigcup");a(i,i,m,"\u222b","\\int");a(i,i,m,"\u222b","\\intop");a(i,i,m,"\u222c","\\iint");a(i,i,m,"\u222d","\\iiint");a(i,i,m,"\u220f","\\prod");a(i,i,m,"\u2211","\\sum");a(i,i,m,"\u2a02","\\bigotimes");a(i,i,m,"\u2a01","\\bigoplus");a(i,i,m,"\u2a00","\\bigodot");a(i,i,m,"\u222e","\\oint");a(i,i,m,"\u2a06","\\bigsqcup");a(i,i,m,"\u222b","\\smallint");a(n,s,h,"\u2026","\\textellipsis");a(i,s,h,"\u2026","\\mathellipsis");a(n,s,h,"\u2026","\\ldots");a(i,s,h,"\u2026","\\ldots");a(i,s,h,"\u22ef","\\cdots");a(i,s,h,"\u22f1","\\ddots");a(i,s,y,"\u22ee","\\vdots");a(i,s,o,"\xb4","\\acute");a(i,s,o,"`","\\grave");a(i,s,o,"\xa8","\\ddot");a(i,s,o,"~","\\tilde");a(i,s,o,"\xaf","\\bar");a(i,s,o,"\u02d8","\\breve");a(i,s,o,"\u02c7","\\check");a(i,s,o,"^","\\hat");a(i,s,o,"\u20d7","\\vec");a(i,s,o,"\u02d9","\\dot");a(i,s,c,"\u0131","\\imath");a(i,s,c,"\u0237","\\jmath");a(n,s,y,"\u2013","--");a(n,s,y,"\u2014","---");a(n,s,y,"\u2018","`");a(n,s,y,"\u2019","'");a(n,s,y,"\u201c","``");a(n,s,y,"\u201d","''");a(i,s,y,"\xb0","\\degree");a(n,s,y,"\xb0","\\degree");a(i,s,c,"\xa3","\\pounds");a(i,l,y,"\u2720","\\maltese");a(n,l,y,"\u2720","\\maltese");a(n,s,g,"\xa0","\\ ");a(n,s,g,"\xa0"," ");a(n,s,g,"\xa0","~");var x;var b;var w='0123456789/@."';for(x=0;x<w.length;x++){b=w.charAt(x);a(i,s,y,b,b)}var k='0123456789!@*()-=+[]";:?/.,';for(x=0;x<k.length;x++){b=k.charAt(x);a(n,s,y,b,b)}var z="abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";for(x=0;x<z.length;x++){b=z.charAt(x);a(i,s,c,b,b);a(n,s,y,b,b)}for(x=192;x<=214;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}for(x=216;x<=246;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}for(x=248;x<=255;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}for(x=1040;x<=1103;x++){b=String.fromCharCode(x);a(n,s,y,b,b)}a(n,s,y,"\u2013","\u2013");a(n,s,y,"\u2014","\u2014");a(n,s,y,"\u2018","\u2018");a(n,s,y,"\u2019","\u2019");a(n,s,y,"\u201c","\u201c");a(n,s,y,"\u201d","\u201d")},{}],24:[function(e,t,r){var a=/[\uAC00-\uD7AF]/;var i=/[\u3040-\u309F]|[\u30A0-\u30FF]|[\u4E00-\u9FAF]|[\uAC00-\uD7AF]/;t.exports={cjkRegex:i,hangulRegex:a}},{}],25:[function(e,t,r){var a=Array.prototype.indexOf;var i=function(e,t){if(e==null){return-1}if(a&&e.indexOf===a){return e.indexOf(t)}var r=0;var i=e.length;for(;r<i;r++){if(e[r]===t){return r}}return-1};var n=function(e,t){return i(e,t)!==-1};var s=function(e,t){return e===undefined?t:e};var l=/([A-Z])/g;var o=function(e){return e.replace(l,"-$1").toLowerCase()};var u={"&":"&amp;",">":"&gt;","<":"&lt;",'"':"&quot;","'":"&#x27;"};var p=/[&><"']/g;function h(e){return u[e]}function c(e){return(""+e).replace(p,h)}var m;if(typeof document!=="undefined"){var f=document.createElement("span");if("textContent"in f){m=function(e,t){e.textContent=t}}else{m=function(e,t){e.innerText=t}}}function v(e){m(e,"")}t.exports={contains:n,deflt:s,escape:c,hyphenate:o,indexOf:i,setTextContent:m,clearNode:v}},{}]},{},[1])(1)});
diff --git a/xml/glx.xml b/xml/glx.xml
index 810d55f..6fadd17 100644
--- a/xml/glx.xml
+++ b/xml/glx.xml
@@ -1086,7 +1086,7 @@
             <param><ptype>Display</ptype> *<name>dpy</name></param>
             <param><ptype>Window</ptype> <name>overlay</name></param>
             <param><ptype>Window</ptype> <name>underlay</name></param>
-            <param>long *<name>pTransparentIndex</name></param>
+            <param>unsigned long *<name>pTransparentIndex</name></param>
         </command>
         <command>
             <proto>int <name>glXGetVideoDeviceNV</name></proto>
@@ -1252,7 +1252,7 @@
             <param><ptype>GLuint</ptype> *<name>count</name></param>
         </command>
         <command>
-            <proto>int <name>glXQueryGLXPbufferSGIX</name></proto>
+            <proto>void <name>glXQueryGLXPbufferSGIX</name></proto>
             <param><ptype>Display</ptype> *<name>dpy</name></param>
             <param><ptype>GLXPbufferSGIX</ptype> <name>pbuf</name></param>
             <param>int <name>attribute</name></param>
@@ -1393,8 +1393,8 @@
             <param><ptype>GLboolean</ptype> <name>bBlock</name></param>
         </command>
         <command>
-            <proto><ptype>Bool</ptype> <name>glXSet3DfxModeMESA</name></proto>
-            <param>int <name>mode</name></param>
+            <proto><ptype>GLboolean</ptype> <name>glXSet3DfxModeMESA</name></proto>
+            <param>GLint <name>mode</name></param>
         </command>
         <command>
             <proto>void <name>glXSwapBuffers</name></proto>
diff --git a/xml/wgl.xml b/xml/wgl.xml
index 49277ed..c3b3630 100644
--- a/xml/wgl.xml
+++ b/xml/wgl.xml
@@ -538,7 +538,7 @@
         </command>
         <command>
             <proto><ptype>BOOL</ptype> <name>wglBindVideoDeviceNV</name></proto>
-            <param><ptype>HDC</ptype> <name>hDC</name></param>
+            <param><ptype>HDC</ptype> <name>hDc</name></param>
             <param>unsigned int <name>uVideoSlot</name></param>
             <param><ptype>HVIDEOOUTPUTDEVICENV</ptype> <name>hVideoDevice</name></param>
             <param>const int *<name>piAttribList</name></param>
@@ -781,7 +781,7 @@
         </command>
         <command>
             <proto>int <name>wglEnumerateVideoDevicesNV</name></proto>
-            <param><ptype>HDC</ptype> <name>hDC</name></param>
+            <param><ptype>HDC</ptype> <name>hDc</name></param>
             <param><ptype>HVIDEOOUTPUTDEVICENV</ptype> *<name>phDeviceList</name></param>
         </command>
         <command>
@@ -912,7 +912,7 @@
         <command>
             <proto><ptype>INT</ptype> <name>wglGetGPUInfoAMD</name></proto>
             <param><ptype>UINT</ptype> <name>id</name></param>
-            <param>int <name>property</name></param>
+            <param><ptype>INT</ptype> <name>property</name></param>
             <param><ptype>GLenum</ptype> <name>dataType</name></param>
             <param><ptype>UINT</ptype> <name>size</name></param>
             <param>void *<name>data</name></param>
@@ -1235,7 +1235,7 @@
         <command>
             <proto><ptype>INT64</ptype> <name>wglSwapLayerBuffersMscOML</name></proto>
             <param><ptype>HDC</ptype> <name>hdc</name></param>
-            <param>int <name>fuPlanes</name></param>
+            <param><ptype>INT</ptype> <name>fuPlanes</name></param>
             <param><ptype>INT64</ptype> <name>target_msc</name></param>
             <param><ptype>INT64</ptype> <name>divisor</name></param>
             <param><ptype>INT64</ptype> <name>remainder</name></param>