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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 categorized into the following: |
| </p> |
| <p> |
| </p> |
| <div class="itemizedlist"> |
| <ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem">A list of built-in functions that have scalar or vector argument versions, and,</li> |
| <li class="listitem">A list of built-in functions that only take scalar float arguments.</li> |
| </ul> |
| </div> |
| <p> |
| </p> |
| <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="https://www.khronos.org/registry/cl/specs/opencl-2.0-openclc.pdf#page=71" 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 © 2007-2013 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> |
