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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="idp33964592"></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 vector versions of the math functions operate
component-wise. The description is per-component.
</p>
<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 built-in math functions take scalar or vector arguments. For any specific use of these
function, the actual type has to be the same for all arguments and the return type unless
otherwise specified.
</p>
<p>
The generic type name <span class="type">gentype</span> is used to indicate that the function can
take <span class="type">float</span>, <span class="type">float2</span>, <span class="type">float3</span>, <span class="type">float4</span>,
<span class="type">float8</span>, <span class="type">float16</span>, <span class="type">double</span>, <span class="type">double2</span>,
<span class="type">double3</span>, <span class="type">double4</span>, <span class="type">double8</span>, or <span class="type">double16</span>
as the type for the arguments.
</p>
<p>
If extended with <a class="citerefentry" href="cl_khr_fp16.html"><span class="citerefentry"><span class="refentrytitle">cl_khr_fp16</span></span></a>,
generic type name <span class="type">gentype</span> may indicate <span class="type">half</span> and
<span class="type">half{2|3|4|8|16}</span> as arguments and return values.
</p>
<p>
The generic type name <span class="type">gentypef</span> is used to indicate that the function can
take <span class="type">float</span>, <span class="type">float2</span>, <span class="type">float3</span>, <span class="type">float4</span>,
<span class="type">float8</span>, or <span class="type">float16</span> as the type for the arguments.
</p>
<p>
The generic type name <span class="type">gentyped</span> is used to indicate that the function can take
<span class="type">double</span>, <span class="type">double2</span>, <span class="type">double3</span>, <span class="type">double4</span>,
<span class="type">double8</span>, or <span class="type">double16</span> as the type for the arguments.
</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-1.2.pdf#page=244" 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 © 2007-2011 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.
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