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<body class="book toc2 toc-left" style="max-width: 100;">
<div id="header">
<h1>The OpenCL Extension Specification</h1>
<div class="details">
<span id="author" class="author">Khronos OpenCL Working Group</span><br>
<span id="revnumber">version 2.2-8,</span>
<span id="revdate">Mon, 08 Oct 2018 16:50:25 +0000</span>
<br><span id="revremark">from git branch: master commit: b3cab22fcff5d8c17869907c983e259ddd7ce788</span>
</div>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#optional-extensions">1. Optional Extensions</a></li>
<li><a href="#cl_khr_fp16">2. Half Precision Floating-Point</a></li>
<li><a href="#cl_khr_gl_sharing">3. Creating an OpenCL Context from an OpenGL Context or Share Group</a></li>
<li><a href="#cl_khr_gl_sharing__memobjs">4. Creating OpenCL Memory Objects from OpenGL Objects</a></li>
<li><a href="#cl_khr_gl_event-creating">5. Creating OpenCL Event Objects from OpenGL Sync Objects</a></li>
<li><a href="#cl_khr_dx9_media_sharing">6. Creating OpenCL Memory Objects from DirectX 9 Media Surfaces</a></li>
<li><a href="#cl_khr_d3d10_sharing">7. Creating OpenCL Memory Objects from Direct3D 10 Buffers and Textures</a></li>
<li><a href="#cl_khr_d3d11_sharing">8. Creating OpenCL Memory Objects from Direct3D 11 Buffers and Textures</a></li>
<li><a href="#cl_khr_gl_depth_images">9. Sharing OpenGL and OpenGL ES Depth and Depth-Stencil Images</a></li>
<li><a href="#cl_khr_gl_msaa_sharing">10. Creating OpenCL Memory Obejcts from OpenGL MSAA Textures</a></li>
<li><a href="#cl_khr_initialize_memory">11. Local and Private Memory Initialization</a></li>
<li><a href="#cl_khr_terminate_context">12. Terminating OpenCL contexts</a></li>
<li><a href="#cl_khr_spir">13. SPIR 1.2 Binaries</a></li>
<li><a href="#cl_khr_icd-opencl">14. OpenCL Installable Client Driver (ICD)</a></li>
<li><a href="#cl_khr_subgroups">15. Subgroups</a></li>
<li><a href="#cl_khr_mipmap_image">16. Mipmaps</a></li>
<li><a href="#cl_khr_egl_image">17. Creating OpenCL Memory Objects from EGL Images</a></li>
<li><a href="#cl_khr_egl_event">18. Creating OpenCL Event Objects from EGL Sync Objects</a></li>
<li><a href="#cl_khr_priority_hints">19. Priority Hints</a></li>
<li><a href="#cl_khr_throttle_hints">20. Throttle Hints</a></li>
<li><a href="#cl_khr_subgroup_named_barrier">21. Named Barriers for Subgroups</a></li>
<li><a href="#_summary_of_changes_from_opencl_2_1">Appendix A: Summary of Changes from OpenCL 2.1</a></li>
</ul>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph">
<p>Copyright 2008-2018 The Khronos Group.</p>
</div>
<div class="paragraph">
<p>This specification is protected by copyright laws and contains material proprietary
to the Khronos Group, Inc. Except as described by these terms, 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.</p>
</div>
<div class="paragraph">
<p>Khronos Group grants a conditional copyright license to use and reproduce the
unmodified specification for any purpose, without fee or royalty, EXCEPT no licenses
to any patent, trademark or other intellectual property rights are granted under
these terms. Parties desiring to implement the specification and make use of
Khronos trademarks in relation to that implementation, and receive reciprocal patent
license protection under the Khronos IP Policy must become Adopters and confirm the
implementation as conformant under the process defined by Khronos for this
specification; see <a href="https://www.khronos.org/adopters" class="bare">https://www.khronos.org/adopters</a>.</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:
merchantability, fitness for a particular purpose, non-infringement of any
intellectual property, correctness, accuracy, completeness, timeliness, and
reliability. 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>Vulkan is a registered trademark and Khronos, OpenXR, SPIR, SPIR-V, SYCL, WebGL,
WebCL, OpenVX, OpenVG, EGL, COLLADA, glTF, NNEF, OpenKODE, OpenKCAM, StreamInput,
OpenWF, OpenSL ES, OpenMAX, OpenMAX AL, OpenMAX IL, OpenMAX DL, OpenML and DevU are
trademarks of the Khronos Group Inc. ASTC is a trademark of ARM Holdings PLC,
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>
</div>
</div>
<div class="sect1">
<h2 id="optional-extensions">1. Optional Extensions</h2>
<div class="sectionbody">
<div class="paragraph">
<p>This document describes the list of optional features supported by OpenCL
2.2.
Optional extensions may be supported by some OpenCL devices.
Optional extensions are not required to be supported by a conformant OpenCL
implementation, but are expected to be widely available; they define
functionality that is likely to move into the required feature set in a
future revision of the OpenCL specification.
A brief description of how OpenCL extensions are defined is provided below.</p>
</div>
<div class="paragraph">
<p>For OpenCL extensions approved by the OpenCL working group, the following
naming conventions are used:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>A unique <em>name string</em> of the form <code>"<strong>cl_khr_&lt;<em>name</em>&gt;</strong>"</code> is associated
with each extension.
If the extension is supported by an implementation, this string will be
present in the implementation&#8217;s CL_PLATFORM_EXTENSIONS string or
CL_DEVICE_EXTENSIONS string.</p>
</li>
<li>
<p>All API functions defined by the extension will have names of the form
<strong>cl&lt;<em>function_name</em>&gt;KHR</strong>.</p>
</li>
<li>
<p>All enumerants defined by the extension will have names of the form
<strong>CL_&lt;<em>enum_name</em>&gt;_KHR.</strong></p>
</li>
</ul>
</div>
<div class="paragraph">
<p>OpenCL extensions approved by the OpenCL working group can be <em>promoted</em> to
required core features in later revisions of OpenCL.
When this occurs, the extension specifications are merged into the core
specification.
Functions and enumerants that are part of such promoted extensions will have
the <strong>KHR</strong> affix removed.
OpenCL implementations of such later revisions must also export the name
strings of promoted extensions in the CL_PLATFORM_EXTENSIONS or
CL_DEVICE_EXTENSIONS string, and support the <strong>KHR</strong>-affixed versions of
functions and enumerants as a transition aid.</p>
</div>
<div class="paragraph">
<p>For vendor extensions, the following naming conventions are used:</p>
</div>
<div class="ulist">
<ul>
<li>
<p>A unique <em>name string</em> of the form <code>"<strong>cl_&lt;<em>vendor_name</em>&gt;_&lt;<em>name&gt;</em></strong>"</code>
is associated with each extension.
If the extension is supported by an implementation, this string will be
present in the implementation&#8217;s CL_PLATFORM_EXTENSIONS string or
CL_DEVICE_EXTENSIONS string.</p>
</li>
<li>
<p>All API functions defined by the vendor extension will have names of the
form <strong>cl&lt;<em>function_name</em>&gt;&lt;<em>vendor_name</em>&gt;</strong>.</p>
</li>
<li>
<p>All enumerants defined by the vendor extension will have names of the
form <strong>CL_&lt;<em>enum_name</em>&gt;_&lt;<em>vendor_name</em>&gt;.</strong></p>
</li>
</ul>
</div>
<div class="sect2">
<h3 id="compiler-directives-for-optional-extensions">1.1. Compiler Directives for Optional Extensions</h3>
<div class="paragraph">
<p>The <strong>#pragma OPENCL EXTENSION</strong> directive controls the behavior of the OpenCL
compiler with respect to extensions.
The <strong>#pragma OPENCL EXTENSION</strong> directive is defined as:</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code>#pragma OPENCL EXTENSION &lt;extension_name&gt; : &lt;behavior&gt;
#pragma OPENCL EXTENSION all : &lt;behavior&gt;</code></pre>
</div>
</div>
<div class="paragraph">
<p>where <em>extension_name</em> is the name of the extension.
The <em>extension_name</em> will have names of the form <strong>cl_khr_&lt;<em>name</em>&gt;</strong> for an
extension approved by the OpenCL working group and will have names of the
form <strong>cl_&lt;<em>vendor_name</em>&gt;_&lt;<em>name</em>&gt;</strong> for vendor extensions.
The token <strong>all</strong> means that the behavior applies to all extensions supported
by the compiler.
The <em>behavior</em> can be set to one of the following values given by the table
below.</p>
</div>
<table class="tableblock frame-all grid-all spread">
<colgroup>
<col style="width: 25%;">
<col style="width: 75%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>behavior</strong></th>
<th class="tableblock halign-left valign-top"><strong>Description</strong></th>
</tr>
</thead>
<tbody>
<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>.
</p><p class="tableblock"> Report an error on the <strong><code>#pragma OPENCL EXTENSION</code></strong> if the
<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>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.
</p><p class="tableblock"> 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.
</p><p class="tableblock"> Warn on the <strong><code>#pragma OPENCL EXTENSION</code></strong> if the extension <em>extension_name</em>
is not supported.</p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>The <strong><code>#pragma OPENCL EXTENSION</code></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.
The order of directives matter 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 extension directives, but only if the <em>behavior</em> is set to
<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>#pragma OPENCL EXTENSION 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>Every extension which affects the OpenCL language semantics, syntax or adds
built-in functions to the language must create a preprocessor <code>#define</code> that
matches the extension name string.
This <code>#define</code> would be available in the language if and only if the
extension is supported on a given implementation.</p>
</div>
<div class="paragraph">
<p><strong>Example</strong>:</p>
</div>
<div class="paragraph">
<p>An extension which adds the extension string <code>"cl_khr_3d_image_writes"</code>
should also add a preprocessor <code>#define</code> called <strong><code>cl_khr_3d_image_writes</code></strong>.
A kernel can now use this preprocessor <code>#define</code> to do something like:</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code>#ifdef cl_khr_3d_image_writes
// do something using the extension
#else
// do something else or #error!
#endif</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="getting-opencl-api-extension-function-pointers">1.2. Getting OpenCL API Extension Function Pointers</h3>
<div class="paragraph">
<p>The function
</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code>void* clGetExtensionFunctionAddressForPlatform(cl_platform_id platform,
const char *funcname)</code></pre>
</div>
</div>
<div class="paragraph">
<p>returns the address of the extension function named by <em>funcname</em> for a
given <em>platform</em> The pointer returned should be cast to a function pointer
type matching the extension function&#8217;s definition defined in the appropriate
extension specification and header file.
A return value of <code>NULL</code> indicates that the specified function does not
exist for the implementation or <em>platform</em> is not a valid platform.
A non-<code>NULL</code> return value for <strong>clGetExtensionFunctionAddressForPlatform</strong>
does not guarantee that an extension function is actually supported by the
platform.
The application must also make a corresponding query using
<strong>clGetPlatformInfo</strong>(platform, CL_PLATFORM_EXTENSIONS, &#8230;&#8203;) or
<strong>clGetDeviceInfo</strong>(device, CL_DEVICE_EXTENSIONS, &#8230;&#8203;) to determine if an
extension is supported by the OpenCL implementation.</p>
</div>
<div class="paragraph">
<p>Since there is no way to qualify the query with a
device, the function pointer returned must work for all implementations of
that extension on different devices for a platform.
The behavior of calling a device extension function on a device not
supporting that extension is undefined.</p>
</div>
<div class="paragraph">
<p><strong>clGetExtensionFunctionAddressForPlatform</strong> may not be be used to query for core
(non-extension) functions in OpenCL.
For extension functions that may be queried using
<strong>clGetExtensionFunctionAddressForPlatform</strong>, implementations may also choose to
export those functions statically from the object libraries
implementing those functions, however, portable applications cannot rely on
this behavior.</p>
</div>
<div class="paragraph">
<p>Function pointer typedefs must be declared for all extensions that add API
entrypoints.
These typedefs are a required part of the extension interface, to be
provided in an appropriate header (such as cl_ext.h if the extension is an
OpenCL extension, or cl_gl_ext.h if the extension is an OpenCL / OpenGL
sharing extension).</p>
</div>
<div class="paragraph">
<p>The following convention must be followed for all extensions affecting the
host API:</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code>#ifndef extension_name
#define extension_name 1
// all data typedefs, token #defines, prototypes, and
// function pointer typedefs for this extension
// function pointer typedefs must use the
// following naming convention
typedef CL_API_ENTRY return_type
(CL_API_CALL *clExtensionFunctionNameTAG_fn)(...);
#endif // _extension_name_</code></pre>
</div>
</div>
<div class="paragraph">
<p>where <code>TAG</code> can be <code>KHR</code>, <code>EXT</code> or <code>vendor-specific</code>.</p>
</div>
<div class="paragraph">
<p>Consider, for example, the <strong>cl_khr_gl_sharing</strong> extension.
This extension would add the following to cl_gl_ext.h:</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code>#ifndef cl_khr_gl_sharing
#define cl_khr_gl_sharing 1
// all data typedefs, token #defines, prototypes, and
// function pointer typedefs for this extension
#define CL_INVALID_GL_SHAREGROUP_REFERENCE_KHR -1000
#define CL_CURRENT_DEVICE_FOR_GL_CONTEXT_KHR 0x2006
#define CL_DEVICES_FOR_GL_CONTEXT_KHR 0x2007
#define CL_GL_CONTEXT_KHR 0x2008
#define CL_EGL_DISPLAY_KHR 0x2009
#define CL_GLX_DISPLAY_KHR 0x200A
#define CL_WGL_HDC_KHR 0x200B
#define CL_CGL_SHAREGROUP_KHR 0x200C
// function pointer typedefs must use the
// following naming convention
typedef CL_API_ENTRY cl_int
(CL_API_CALL *clGetGLContextInfoKHR_fn)(
const cl_context_properties * /* properties */,
cl_gl_context_info /* param_name */,
size_t /* param_value_size */,
void * /* param_value */,
size_t * /*param_value_size_ret*/);
#endif // cl_khr_gl_sharing</code></pre>
</div>
</div>
<div style="page-break-after: always;"></div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="cl_khr_fp16">2. Half Precision Floating-Point</h2>
<div class="sectionbody">
<div class="paragraph">
<p>This section describes the <strong>cl_khr_fp16</strong> extension.
This extension adds support for half scalar and vector types as built-in
types that can be used for arithmetic operations, conversions etc.</p>
</div>
<div class="sect2">
<h3 id="cl_khr_fp16-additions-to-chapter-6-of-the-opencl-2.0-specification">2.1. Additions to Chapter 6 of the OpenCL 2.0 C Specification</h3>
<div class="paragraph">
<p>The list of built-in scalar, and vector data types defined in <em>tables 6.1</em>,
and <em>6.2</em> are extended to include the following:</p>
</div>
<table class="tableblock frame-all grid-all spread">
<colgroup>
<col style="width: 25%;">
<col style="width: 75%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Type</strong></th>
<th class="tableblock halign-left valign-top"><strong>Description</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half2</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">A 2-component half-precision floating-point vector.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half3</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">A 3-component half-precision floating-point vector.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half4</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">A 4-component half-precision floating-point vector.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half8</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">A 8-component half-precision floating-point vector.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half16</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">A 16-component half-precision floating-point vector.</p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>The built-in vector data types for <code>halfn</code> are also declared as appropriate
types in the OpenCL API (and header files) that can be used by an
application.
The following table describes the built-in vector data types for <code>halfn</code> as
defined in the OpenCL C programming language and the corresponding data type
available to the application:</p>
</div>
<table class="tableblock frame-all grid-all spread">
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Type in OpenCL Language</strong></th>
<th class="tableblock halign-left valign-top"><strong>API type for application</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half2</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cl_half2</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half3</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cl_half3</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half4</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cl_half4</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half8</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cl_half8</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>half16</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>cl_half16</strong></p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>The relational, equality, logical and logical unary operators described in
<em>section 6.3</em> can be used with <code>half</code> scalar and <code>halfn</code> vector types and
shall produce a scalar <code>int</code> and vector <code>shortn</code> result respectively.</p>
</div>
<div class="paragraph">
<p>The OpenCL compiler accepts an h and H suffix on floating point literals,
indicating the literal is typed as a half.</p>
</div>
<div class="sect3">
<h4 id="cl_khr_fp16-conversions">2.1.1. Conversions</h4>
<div class="paragraph">
<p>The implicit conversion rules specified in <em>section 6.2.1</em> now include the
<code>half</code> scalar and <code>halfn</code> vector data types.</p>
</div>
<div class="paragraph">
<p>The explicit casts described in <em>section 6.2.2</em> are extended to take a
<code>half</code> scalar data type and a <code>halfn</code> vector data type.</p>
</div>
<div class="paragraph">
<p>The explicit conversion functions described in <em>section 6.2.3</em> are extended
to take a <code>half</code> scalar data type and a <code>halfn</code> vector data type.</p>
</div>
<div class="paragraph">
<p>The <code>as_typen()</code> function for re-interpreting types as described in <em>section
6.2.4.2</em> is extended to allow conversion-free casts between <code>shortn</code>,
<code>ushortn</code>, and <code>halfn</code> scalar and vector data types.</p>
</div>
</div>
<div class="sect3">
<h4 id="cl_khr_fp16-math-functions">2.1.2. Math Functions</h4>
<div class="paragraph">
<p>The built-in math functions defined in <em>table 6.8</em> (also listed below) are
extended to include appropriate versions of functions that take <code>half</code>, and
<code>half{2|3|4|8|16}</code> as arguments and return values.
<code>gentype</code> now also includes <code>half</code>, <code>half2</code>, <code>half3</code>, <code>half4</code>, <code>half8</code>, and
<code>half16</code>.</p>
</div>
<div class="paragraph">
<p>For any specific use of a function, the actual type has to be the same for
all arguments and the return type.</p>
</div>
<table class="tableblock frame-all grid-all spread">
<caption class="title">Table 1. <em>Half Precision Built-in Math Functions</em></caption>
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Function</strong></th>
<th class="tableblock halign-left valign-top"><strong>Description</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>acos</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Arc cosine function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>acosh</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Inverse hyperbolic cosine.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>acospi</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>acos</strong> (<em>x</em>) / π.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>asin</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Arc sine function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>asinh</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Inverse hyperbolic sine.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>asinpi</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>asin</strong> (<em>x</em>) / π.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>atan</strong> (gentype <em>y_over_x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Arc tangent function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>atan2</strong> (gentype <em>y</em>, gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Arc tangent of <em>y</em> / <em>x</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>atanh</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Hyperbolic arc tangent.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>atanpi</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>atan</strong> (<em>x</em>) / π.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>atan2pi</strong> (gentype <em>y</em>, gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>atan2</strong> (<em>y</em>, <em>x</em>) / π.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>cbrt</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute cube-root.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>ceil</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Round to integral value using the round to positive infinity rounding
mode.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>copysign</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> with its sign changed to match the sign of <em>y</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>cos</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute cosine.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>cosh</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute hyperbolic consine.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>cospi</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>cos</strong><em>x</em>).</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>erfc</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Complementary error function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>erf</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Error function encountered in integrating the normal distribution.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>exp</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base- e exponential of <em>x</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>exp2</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Exponential base 2 function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>exp10</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Exponential base 10 function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>expm1</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <em>e<sup>x</sup></em>- 1.0.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fabs</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute absolute value of a floating-point number.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fdim</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><em>x</em> - <em>y</em> if <em>x</em> &gt; <em>y</em>, +0 if x is less than or equal to y.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>floor</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Round to integral value using the round to negative infinity rounding
mode.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fma</strong> (gentype <em>a</em>, gentype <em>b</em>, gentype <em>c</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the correctly rounded floating-point representation of the sum of
<em>c</em> with the infinitely precise product of <em>a</em> and <em>b</em>.
Rounding of intermediate products shall not occur.
Edge case behavior is per the IEEE 754-2008.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fmax</strong> (gentype x, gentype y)<br>
gentype <strong>fmax</strong> (gentype <em>x</em>, half <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>.
If one argument is a NaN, <strong>fmax()</strong> returns the other argument.
If both arguments are NaNs, <strong>fmax()</strong> returns a NaN.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fmin</strong> (gentype <em>x</em>, gentype <em>y</em>)<br>
gentype <strong>fmin</strong> (gentype <em>x</em>, half <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>.
If one argument is a NaN, <strong>fmin()</strong> returns the other argument.
If both arguments are NaNs, <strong>fmin()</strong> returns a NaN.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fmod</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Modulus.
Returns <em>x</em> - <em>y</em> * <strong>trunc</strong> (<em>x</em>/<em>y</em>) .</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fract</strong> (gentype <em>x</em>, gentype *<em>iptr</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <strong>fmin</strong>( <em>x</em> - <strong>floor</strong> (<em>x</em>), 0x1.ffcp-1f ).
</p><p class="tableblock"> <strong>floor</strong>(x) is returned in <em>iptr</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half<em>n</em> <strong>frexp</strong> (half<em>n</em> <em>x</em>, int<em>n</em> *exp)<br>
half <strong>frexp</strong> (half <em>x</em>, int *exp)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Extract mantissa and exponent from <em>x</em>.
For each component the mantissa returned is a float with magnitude in the
interval [1/2, 1) or 0.
Each component of <em>x</em> equals mantissa returned * 2<em><sup>exp</sup></em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>hypot</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute the value of the square root of <em>x</em><sup>2</sup>+ <em>y</em><sup>2</sup> without undue
overflow or underflow.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">int<em>n</em> <strong>ilogb</strong> (half<em>n</em> <em>x</em>)<br>
int <strong>ilogb</strong> (half <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Return the exponent as an integer value.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half<em>n</em> <strong>ldexp</strong> (half<em>n</em> <em>x</em>, int<em>n</em> <em>k</em>)<br>
half<em>n</em> <strong>ldexp</strong> (half<em>n</em> <em>x</em>, int <em>k</em>)<br>
half <strong>ldexp</strong> (half <em>x</em>, int <em>k</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Multiply <em>x</em> by 2 to the power <em>k</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>lgamma</strong> (gentype <em>x</em>)<br>
half<em>n</em> <strong>lgamma_r</strong> (half<em>n</em> <em>x</em>, int<em>n</em> *<em>signp</em>)<br>
half <strong>lgamma_r</strong> (half <em>x</em>, int *<em>signp</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Log gamma function.
Returns the natural logarithm of the absolute value of the gamma function.
The sign of the gamma function is returned in the <em>signp</em> argument of
<strong>lgamma_r</strong>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>log</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute natural logarithm.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>log2</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute a base 2 logarithm.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>log10</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute a base 10 logarithm.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>log1p</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute log<sub>e</sub>(1.0 + <em>x</em>) .</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>logb</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute the exponent of <em>x</em>, which is the integral part of
log<em><sub>r</sub></em>|<em>x</em>|.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>mad</strong> (gentype <em>a</em>, gentype <em>b</em>, gentype <em>c</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>mad</strong> computes <em>a</em> * <em>b</em> + <em>c</em>.
The function may compute <em>a</em> * <em>b</em> + <em>c</em> with reduced accuracy
in the embedded profile. See the SPIR-V OpenCL environment specification
for details. On some hardware the mad instruction may provide better
performance than expanded computation of <em>a</em> * <em>b</em> + <em>c</em>.
</p><p class="tableblock"> Note: For some usages, e.g. <strong>mad</strong>(a, b, -a*b), the half precision
definition of <strong>mad</strong>() is loose enough that almost any result is allowed
from <strong>mad</strong>() for some values of a and b.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>maxmag</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> if |<em>x</em>| &gt; |<em>y</em>|, <em>y</em> if |<em>y</em>| &gt; |<em>x</em>|, otherwise
<strong>fmax</strong>(<em>x</em>, <em>y</em>).</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>minmag</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> if |<em>x</em>| &lt; |<em>y</em>|, <em>y</em> if |<em>y</em>| &lt; |<em>x</em>|, otherwise
<strong>fmin</strong>(<em>x</em>, <em>y</em>).</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>modf</strong> (gentype <em>x</em>, gentype *<em>iptr</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Decompose a floating-point number.
The <strong>modf</strong> function breaks the argument <em>x</em> into integral and fractional
parts, each of which has the same sign as the argument.
It stores the integral part in the object pointed to by <em>iptr</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half<em>n</em> <strong>nan</strong> (ushort<em>n</em> <em>nancode</em>)<br>
half <strong>nan</strong> (ushort <em>nancode</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a quiet NaN.
The <em>nancode</em> may be placed in the significand of the resulting NaN.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>nextafter</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Computes the next representable half-precision floating-point value
following <em>x</em> in the direction of <em>y</em>.
Thus, if <em>y</em> is less than <em>x</em>, <strong>nextafter</strong>() returns the largest
representable floating-point number less than <em>x</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>pow</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <em>x</em> to the power <em>y</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half<em>n</em> <strong>pown</strong> (half<em>n</em> <em>x</em>, int<em>n</em> <em>y</em>)<br>
half <strong>pown</strong> (half <em>x</em>, int <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <em>x</em> to the power <em>y</em>, where <em>y</em> is an integer.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>powr</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <em>x</em> to the power <em>y</em>, where <em>x</em> is &gt;= 0.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>remainder</strong> (gentype <em>x</em>, gentype <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute the value <em>r</em> such that <em>r</em> = <em>x</em> - <em>n</em>*<em>y</em>, where <em>n</em> is the
integer nearest the exact value of <em>x</em>/<em>y</em>.
If there are two integers closest to <em>x</em>/<em>y</em>, <em>n</em> shall be the even one.
If <em>r</em> is zero, it is given the same sign as <em>x</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half<em>n</em> <strong>remquo</strong> (half<em>n</em> <em>x</em>, half<em>n</em> <em>y</em>, int<em>n</em> *<em>quo</em>)<br>
half <strong>remquo</strong> (half <em>x</em>, half <em>y</em>, int *<em>quo</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">The <strong>remquo</strong> function computes the value r such that <em>r</em> = <em>x</em> - <em>k</em>*<em>y</em>,
where <em>k</em> is the integer nearest the exact value of <em>x</em>/<em>y</em>.
If there are two integers closest to <em>x</em>/<em>y</em>, <em>k</em> shall be the even one.
If <em>r</em> is zero, it is given the same sign as <em>x</em>.
This is the same value that is returned by the <strong>remainder</strong> function.
<strong>remquo</strong> also calculates the lower seven bits of the integral quotient
<em>x</em>/<em>y</em>, and gives that value the same sign as <em>x</em>/<em>y</em>.
It stores this signed value in the object pointed to by <em>quo</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>rint</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Round to integral value (using round to nearest even rounding mode) in
floating-point format.
Refer to section 7.1 for description of rounding modes.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half<em>n</em> <strong>rootn</strong> (half<em>n</em> <em>x</em>, int<em>n</em> <em>y</em>)<br>
half <strong>rootn</strong> (half <em>x</em>, int <em>y</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <em>x</em> to the power 1/<em>y</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>round</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Return the integral value nearest to <em>x</em> rounding halfway cases away from
zero, regardless of the current rounding direction.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>rsqrt</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute inverse square root.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sin</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute sine.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sincos</strong> (gentype <em>x</em>, gentype *<em>cosval</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute sine and cosine of x.
The computed sine is the return value and computed cosine is returned in
<em>cosval</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sinh</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute hyperbolic sine.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sinpi</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>sin</strong><em>x</em>).</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sqrt</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute square root.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>tan</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute tangent.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>tanh</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute hyperbolic tangent.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>tanpi</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute <strong>tan</strong><em>x</em>).</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>tgamma</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute the gamma function.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>trunc</strong> (gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Round to integral value using the round to zero rounding mode.</p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>The <strong>FP_FAST_FMA_HALF</strong> macro indicates whether the <strong>fma()</strong> family of
functions are fast compared with direct code for half precision
floating-point.
If defined, the <strong>FP_FAST_FMA_HALF</strong> macro shall indicate that the <strong>fma()</strong>
function generally executes about as fast as, or faster than, a multiply and
an add of <strong>half</strong> operands</p>
</div>
<div class="paragraph">
<p>The macro names given in the following list must use the values specified.
These constant expressions are suitable for use in #if preprocessing
directives.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="CodeRay highlight"><code>#define HALF_DIG 3
#define HALF_MANT_DIG 11
#define HALF_MAX_10_EXP +4
#define HALF_MAX_EXP +16
#define HALF_MIN_10_EXP -4
#define HALF_MIN_EXP -13
#define HALF_RADIX 2
#define HALF_MAX 0x1.ffcp15h
#define HALF_MIN 0x1.0p-14h
#define HALF_EPSILON 0x1.0p-10h</code></pre>
</div>
</div>
<div class="paragraph">
<p>The following table describes the built-in macro names given above in the
OpenCL C programming language and the corresponding macro names available to
the application.</p>
</div>
<table class="tableblock frame-all grid-all spread">
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Macro in OpenCL Language</strong></th>
<th class="tableblock halign-left valign-top"><strong>Macro for application</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_DIG</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_DIG</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MANT_DIG</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MANT_DIG</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MAX_10_EXP</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MAX_10_EXP</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MAX_EXP</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MAX_EXP</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MIN_10_EXP</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MIN_10_EXP</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MIN_EXP</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MIN_EXP</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_RADIX</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_RADIX</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MAX</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MAX</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_MIN</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_MIN</strong></p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>HALF_EPSILSON</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>CL_HALF_EPSILON</strong></p></td>
</tr>
</tbody>
</table>
<div class="paragraph">
<p>The following constants are also available.
They are of type <code>half</code> and are accurate within the precision of the <code>half</code>
type.</p>
</div>
<table class="tableblock frame-all grid-all spread">
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Constant</strong></th>
<th class="tableblock halign-left valign-top"><strong>Description</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_E_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of e</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_LOG2E_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of log<sub>2</sub>e</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_LOG10E_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of log<sub>10</sub>e</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_LN2_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of log<sub>e</sub>2</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_LN10_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of log<sub>e</sub>10</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_PI_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of π</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_PI_2_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of π / 2</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_PI_4_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of π / 4</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_1_PI_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of 1 / π</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_2_PI_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of 2 / π</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_2_SQRTPI_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of 2 / √π</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_SQRT2_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of √2</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock"><strong>M_SQRT1_2_H</strong></p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Value of 1 / √2</p></td>
</tr>
</tbody>
</table>
</div>
<div class="sect3">
<h4 id="cl_khr_fp16-common-functions">2.1.3. Common Functions</h4>
<div class="paragraph">
<p>The built-in common functions defined in <em>table 6.12</em> (also listed below)
are extended to include appropriate versions of functions that take <code>half</code>,
and <code>half{2|3|4|8|16}</code> as arguments and return values.
gentype now also includes <code>half</code>, <code>half2</code>, <code>half3</code>, <code>half4</code>, <code>half8</code> and
<code>half16</code>.
These are described below.</p>
</div>
<table class="tableblock frame-all grid-all spread">
<caption class="title">Table 2. <em>Half Precision Built-in Common Functions</em></caption>
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Function</strong></th>
<th class="tableblock halign-left valign-top"><strong>Description</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>clamp</strong> (<br>
gentype <em>x</em>, gentype <em>minval</em>, gentype <em>maxval</em>)
</p><p class="tableblock"> gentype <strong>clamp</strong> (<br>
gentype <em>x</em>, half <em>minval</em>, half <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>).
</p><p class="tableblock"> 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">gentype <strong>degrees</strong> (gentype <em>radians</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Converts <em>radians</em> to degrees,<br>
i.e. (180 / π) * <em>radians</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>max</strong> (gentype <em>x</em>, gentype <em>y</em>)<br>
gentype <strong>max</strong> (gentype <em>x</em>, half <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>.
If <em>x</em> and <em>y</em> are infinite or NaN, the return values are undefined.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>min</strong> (gentype <em>x</em>, gentype <em>y</em>)<br>
gentype <strong>min</strong> (gentype <em>x</em>, half <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>.
If <em>x</em> and <em>y</em> are infinite or NaN, the return values are undefined.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>mix</strong> (gentype <em>x</em>, gentype <em>y</em>, gentype <em>a</em>)<br>
gentype <strong>mix</strong> (gentype <em>x</em>, gentype <em>y</em>, half <em>a</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the linear blend of <em>x</em> and <em>y</em> implemented as:
</p><p class="tableblock"> <em>x</em> + (<em>y</em> - <em>x)</em> * <em>a</em>
</p><p class="tableblock"> <em>a</em> must be a value in the range 0.0 &#8230;&#8203; 1.0.
If <em>a</em> is not in the range 0.0 &#8230;&#8203; 1.0, the return values are undefined.
</p><p class="tableblock"> Note: The half precision <strong>mix</strong> function can be implemented using contractions such as <strong>mad</strong> or <strong>fma</strong>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>radians</strong> (gentype <em>degrees</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Converts <em>degrees</em> to radians, i.e. (π / 180) * <em>degrees</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>step</strong> (gentype <em>edge</em>, gentype <em>x</em>)<br>
gentype <strong>step</strong> (half <em>edge</em>, gentype <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">gentype <strong>smoothstep</strong> (<br>
gentype <em>edge0</em>, gentype <em>edge1</em>, gentype <em>x</em>)
</p><p class="tableblock"> gentype <strong>smoothstep</strong> (<br>
half <em>edge0</em>, half <em>edge1</em>, gentype <em>x</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns 0.0 if <em>x</em> &lt;= <em>edge0</em> and 1.0 if <em>x</em> &gt;= <em>edge1</em> and performs
smooth Hermite interpolation between 0 and 1 when <em>edge0</em> &lt; <em>x</em> &lt; <em>edge1</em>.
This is useful in cases where you would want a threshold function with a
smooth transition.
</p><p class="tableblock"> This is equivalent to:
</p><p class="tableblock"> gentype <em>t</em>;<br>
<em>t</em> = clamp ((<em>x</em> - <em>edge0</em>) / (<em>edge1</em> - <em>edge0</em>), 0, 1);<br>
return <em>t</em> * <em>t</em> * (3 - 2 * <em>t</em>);<br>
</p><p class="tableblock"> Results are undefined if <em>edge0</em> &gt;= <em>edge1</em>.
</p><p class="tableblock"> Note: The half precision <strong>smoothstep</strong> function can be implemented using contractions such as <strong>mad</strong> or <strong>fma</strong>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sign</strong> (gentype <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> = -0.0, +0.0 if <em>x</em> = +0.0, or -1.0 if
<em>x</em> &lt; 0.
Returns 0.0 if <em>x</em> is a NaN.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="sect3">
<h4 id="cl_khr_fp16-geometric-functions">2.1.4. Geometric Functions</h4>
<div class="paragraph">
<p>The built-in geometric functions defined in <em>table 6.13</em> (also listed below)
are extended to include appropriate versions of functions that take <code>half</code>,
and <code>half{2|3|4}</code> as arguments and return values.
gentype now also includes <code>half</code>, <code>half2</code>, <code>half3</code> and <code>half4</code>.
These are described below.</p>
</div>
<div class="paragraph">
<p>Note: The half precision geometric functions can be implemented using
contractions such as <strong>mad</strong> or <strong>fma</strong>.</p>
</div>
<table class="tableblock frame-all grid-all spread">
<caption class="title">Table 3. <em>Half Precision Built-in Geometric Functions</em></caption>
<colgroup>
<col style="width: 50%;">
<col style="width: 50%;">
</colgroup>
<thead>
<tr>
<th class="tableblock halign-left valign-top"><strong>Function</strong></th>
<th class="tableblock halign-left valign-top"><strong>Description</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half4 <strong>cross</strong> (half4 <em>p0</em>, half4 <em>p1</em>)<br>
half3 <strong>cross</strong> (half3 <em>p0</em>, half3 <em>p1</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns the cross product of <em>p0.xyz</em> and <em>p1.xyz</em>.
The <em>w</em> component of the result will be 0.0.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half <strong>dot</strong> (gentype <em>p0</em>, gentype <em>p1</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Compute the dot product of <em>p0</em> and <em>p1</em>.</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half <strong>distance</strong> (gentype <em>p0</em>, gentype <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>.
This is calculated as <strong>length</strong>(<em>p0</em> - <em>p1</em>).</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">half <strong>length</strong> (gentype <em>p</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Return the length of vector x, i.e.,<br>
sqrt( <em>p.x</em><sup>2</sup> + <em>p.y</em><sup>2</sup> + &#8230;&#8203; )</p></td>
</tr>
<tr>
<td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>normalize</strong> (gentype <em>p</em>)</p></td>
<td class="tableblock halign-left valign-top"><p class="tableblock">Returns a vector in the same direction as <em>p</em> but with a length of 1.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="sect3">
<h4 id="cl_khr_fp16-relational-functions">2.1.5. Relational Functions</h4>
<div <