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| <title>Math Built-In Functions</title> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.78.1" /> |
| <meta name="keywords" content="Math Built-In Functions" /> |
| </head> |
| <body> |
| <div class="refentry"> |
| <a id="id-1"></a> |
| <div class="titlepage"></div> |
| <div xmlns="" class="refnamediv"> |
| <h1>Math Built-In Functions</h1> |
| <p>The table below describes the list of built-in math functions. These functions can take scalar or vector arguments. Click an item in the table for details about that function.</p> |
| </div> |
| <div class="refsect1"> |
| <a id="springboard"></a> |
| <h2></h2> |
| <div class="informaltable"> |
| <table border="1"> |
| <colgroup> |
| <col align="center" class="col1" /> |
| <col align="center" class="col2" /> |
| <col align="center" class="col3" /> |
| <col align="center" class="col4" /> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="acos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">acos</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="acos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">acosh</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="acos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">acospi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="asin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">asin</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="asin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">asinh</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="asin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">asinpi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="atan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">atan</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="atan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">atan2</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="atan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">atanh</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="atan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">atanpi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="atan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">atan2pi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="cbrt.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">cbrt</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="ceil.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">ceil</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="copysign.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">copysign</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="cos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">cos</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="cos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">cosh</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="cos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">cospi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="erf.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">erfc</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="erf.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">erf</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">exp</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">exp2</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">exp10</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">expm1</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="fabs.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fabs</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="fdim.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fdim</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="floor.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">floor</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="fma.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fma</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="fmax.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fmax</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="fmin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fmin</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="fmod.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fmod</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="fract.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">fract</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="frexp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">frexp</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="hypot.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">hypot</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="ilogb.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">ilogb</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="ldexp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">ldexp</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="lgamma.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">lgamma</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="lgamma.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">lgamma_r</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">log</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">log2</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">log10</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">log1p</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">logb</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="mad.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">mad</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="mag.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">maxmag</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="mag.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">minmag</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="modf.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">modf</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="nan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">nan</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="nextafter.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">nextafter</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="pow.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">pow</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="pow.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">pown</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="pow.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">powr</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="remainder.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">remainder</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="remquo.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">remquo</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="rint.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">rint</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="rootn.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">rootn</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="round.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">round</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="sqrt.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">rsqrt</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="sin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">sin</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="sin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">sincos</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="sin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">sinh</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="sin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">sinpi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="sqrt.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">sqrt</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="tan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">tan</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="tan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">tanh</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="tan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">tanpi</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="tgamma.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">tgamma</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="trunc.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">trunc</span> |
| </span> |
| </a> |
| </td> |
| <td class="auto-generated"> </td> |
| </tr> |
| </tbody> |
| </table> |
| </div> |
| <p></p> |
| <p>The table below describes the list of built-in math functions that are defined with the <code class="constant">half_</code> or <code class="constant">native_</code> prefix</p> |
| <div class="informaltable"> |
| <table border="1"> |
| <colgroup> |
| <col align="center" class="col1" /> |
| <col align="center" class="col2" /> |
| <col align="center" class="col3" /> |
| <col align="center" class="col4" /> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="cos.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ cos</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="divide.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ divide</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ exp</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ exp2</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="exp.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_exp10</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ log</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ log2</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="log.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ log10</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="pow.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ powr</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="recip.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ recip</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="sqrt.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ rsqrt</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="sin.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ sin</span> |
| </span> |
| </a> |
| </td> |
| </tr> |
| <tr> |
| <td align="center"> |
| <a class="citerefentry" href="sqrt.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ sqrt</span> |
| </span> |
| </a> |
| </td> |
| <td align="center"> |
| <a class="citerefentry" href="tan.html"> |
| <span class="citerefentry"> |
| <span class="refentrytitle">(half | native)_ tan</span> |
| </span> |
| </a> |
| </td> |
| <td class="auto-generated"> </td> |
| <td class="auto-generated"> </td> |
| </tr> |
| </tbody> |
| </table> |
| </div> |
| </div> |
| <div class="refsect1"> |
| <a id="description"></a> |
| <h2>Description</h2> |
| <p> |
| The built-in math functions are not affected by the prevailing rounding mode in the calling environment, and always return the same value as they would if called with the round to nearest even rounding mode. |
| </p> |
| <p> |
| The regular built-in math functions can take scalar or vector arguments. For any specific use of a function, the actual type has to be the same for all arguments and the return type, unless otherwise specified. For more information, see the reference page for a specific function. |
| </p> |
| <p> |
| The built-in math functions are extended with <a class="citerefentry" href="cl_khr_fp64.html"><span class="citerefentry"><span class="refentrytitle">cl_khr_fp64</span></span></a> to include appropriate versions of functions that take <span class="type">double</span> and <span class="type">double{2|3|4|8|16}</span> as arguments and return values. They are also extended with <a class="citerefentry" href="cl_khr_fp16.html"><span class="citerefentry"><span class="refentrytitle">cl_khr_fp16</span></span></a> to include appropriate versions of functions that take <span class="type">half</span> and <span class="type">half{2|3|4|8|16}</span> as arguments and return values. |
| </p> |
| <p> |
| The vector versions of the math functions operate component-wise. |
| The description is per-component. |
| </p> |
| <p> |
| Support for denormal values is optional for <code class="constant">half_</code> functions. The <code class="constant">half_</code> functions may return any result allowed by section 7.5.3, even when -cl-denorms-are-zero is not in force. Support for denormal values is implementation-defined for <code class="constant">native_</code> functions. |
| </p> |
| <p> |
| The math functions that are defined with the <code class="constant">half_</code> prefix are implemented with a minimum of 10-bits of accuracy i.e. an ULP value <= 8192 ulp. |
| </p> |
| <p> |
| The math functions that are defined with the <code class="constant">native_</code> prefix may map to one or more native device instructions and will typically have better performance compared to the corresponding functions (without the <code class="constant">native_</code> prefix) described. The accuracy (and in some cases the input range(s)) of these functions is implementation-defined. |
| </p> |
| </div> |
| <div class="refsect1"> |
| <a id="specification"></a> |
| <h2>Specification</h2> |
| <p> |
| <img src="pdficon_small1.gif" /> |
| |
| <a href="http://www.khronos.org/registry/cl/specs/opencl-1.1.pdf#page=203" target="OpenCL Spec">OpenCL Specification</a> |
| </p> |
| </div> |
| <div class="refsect1"> |
| <a id="seealso"></a> |
| <h2>Also see</h2> |
| <p> |
| <a class="citerefentry" href="mathConstants.html"><span class="citerefentry"><span class="refentrytitle">Symbolic Math Constants</span></span></a>, |
| <a class="citerefentry" href="FP_CONTRACT.html"><span class="citerefentry"><span class="refentrytitle">Floating Point Pragma</span></span></a>, |
| <a class="citerefentry" href="macroLimits.html"><span class="citerefentry"><span class="refentrytitle">Macros and Limits</span></span></a> |
| </p> |
| </div> |
| <div xmlns="" class="refsect3" lang="en" xml:lang="en"><a xmlns="http://www.w3.org/1999/xhtml" id="Copyright"></a><h4 xmlns="http://www.w3.org/1999/xhtml"></h4><img xmlns="http://www.w3.org/1999/xhtml" src="KhronosLogo.jpg" /><p xmlns="http://www.w3.org/1999/xhtml"></p>Copyright © 2007-2010 The Khronos Group Inc. |
| Permission is hereby granted, free of charge, to any person obtaining a |
| copy of this software and/or associated documentation files (the |
| "Materials"), to deal in the Materials without restriction, including |
| without limitation the rights to use, copy, modify, merge, publish, |
| distribute, sublicense, and/or sell copies of the Materials, and to |
| permit persons to whom the Materials are furnished to do so, subject to |
| the condition that this copyright notice and permission notice shall be included |
| in all copies or substantial portions of the Materials. |
| </div> |
| </div> |
| </body> |
| </html> |
