specs/unified/refpages/man/html/mathFunctions.html - external/github.com/KhronosGroup/OpenCL-Registry - Git at Google

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 <body class="manpage">
 <div id="header">
 <h1>mathFunctions(3) Manual Page</h1>
 <h2 id="_name">Name</h2>
 <div class="sectionbody">
 <p>mathFunctions - Math Functions</p>
 </div>
 </div>
 <div id="content">
 <div class="sect1">
 <h2 id="_description"><a class="anchor" href="#_description"></a>Description</h2>
 <div class="sectionbody">
 <div class="paragraph">
 <p>The built-in math functions are categorized into the following:</p>
 </div>
 <div class="ulist">
 <ul>
 <li>
 <p>A list of built-in functions that have scalar or vector argument
 versions, and,</p>
 </li>
 <li>
 <p>A list of built-in functions that only take scalar <code>float</code> arguments.</p>
 </li>
 </ul>
 </div>
 <div class="paragraph">
 <p>The vector versions of the math functions operate component-wise.
 The description is per-component.</p>
 </div>
 <div class="paragraph">
 <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>
 </div>
 <div class="paragraph">
 <p>The <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#table-builtin-math" target="_blank" rel="noopener">Built-in Scalar and Vector Argument Math
 Functions</a> table describes the list of built-in math functions that can
 take scalar or vector arguments.</p>
 </div>
 <div class="paragraph">
 <p>The generic type name <code>gentype</code> indicates that the function can take any of</p>
 </div>
 <div class="ulist">
 <ul>
 <li>
 <p><code>float</code>, <code>float2</code>, <code>float3</code>, <code>float4</code>, <code>float8</code>, or <code>float16</code></p>
 </li>
 <li>
 <p><code>double</code> <sup class="footnote" id="_footnote_double-supported">[<a id="_footnoteref_1" class="footnote" href="#_footnotedef_1" title="View footnote.">1</a>]</sup>, <code>double2</code>,
 <code>double3</code>, <code>double4</code>, <code>double8</code> or <code>double16</code></p>
 </li>
 <li>
 <p><code>half</code> <sup class="footnote">[<a id="_footnoteref_2" class="footnote" href="#_footnotedef_2" title="View footnote.">2</a>]</sup>, <code>half2</code>, <code>half3</code>, <code>half4</code>,
 <code>half8</code> or <code>half16</code></p>
 </li>
 </ul>
 </div>
 <div class="paragraph">
 <p>as the type for the arguments.</p>
 </div>
 <div class="paragraph">
 <p>The generic type name <code>gentypef</code> indicates that the function can take any of</p>
 </div>
 <div class="ulist">
 <ul>
 <li>
 <p><code>float</code>, <code>float2</code>, <code>float3</code>, <code>float4</code>, <code>float8</code>, or <code>float16</code></p>
 </li>
 </ul>
 </div>
 <div class="paragraph">
 <p>as the type for the arguments.</p>
 </div>
 <div class="paragraph">
 <p>The generic type name <code>gentyped</code> <sup class="footnote">[<a id="_footnoteref_3" class="footnote" href="#_footnotedef_3" title="View footnote.">3</a>]</sup> indicates
 that the function can take any of</p>
 </div>
 <div class="ulist">
 <ul>
 <li>
 <p><code>double</code>, <code>double2</code>, <code>double3</code>, <code>double4</code>, <code>double8</code> or <code>double16</code></p>
 </li>
 </ul>
 </div>
 <div class="paragraph">
 <p>as the type for the arguments.</p>
 </div>
 <div class="paragraph">
 <p>The generic type name <code>gentypeh</code> <sup class="footnote">[<a id="_footnoteref_4" class="footnote" href="#_footnotedef_4" title="View footnote.">4</a>]</sup> indicates
 that the function can take any of</p>
 </div>
 <div class="ulist">
 <ul>
 <li>
 <p><code>half</code>, <code>half2</code>, <code>half3</code>, <code>half4</code>, <code>half8</code> or <code>half16</code></p>
 </li>
 </ul>
 </div>
 <div class="paragraph">
 <p>as the type for the arguments.</p>
 </div>
 <div class="admonitionblock note">
 <table>
 <tr>
 <td class="icon">
 <i class="fa icon-note" title="Note"></i>
 </td>
 <td class="content">
 All functions taking or returning <code>half</code> types are supported only when
 the <code>cl_khr_<wbr>fp16</code> extension macro is supported.
 </td>
 </tr>
 </table>
 </div>
 <div class="paragraph">
 <p>For any specific use of a function with <code>gentype*</code> arguments the actual type
 has to be the same for all arguments and the return type, unless they are
 explicitly specified as an actual type.</p>
 </div>
 <table id="table-builtin-math" class="tableblock frame-all grid-all stretch">
 <caption class="title">Table 1. Built-in Scalar and Vector Argument Math Functions</caption>
 <colgroup>
 <col style="width: 50%;">
 <col style="width: 50%;">
 </colgroup>
 <thead>
 <tr>
 <th class="tableblock halign-left valign-top">Function</th>
 <th class="tableblock halign-left valign-top">Description</th>
 </tr>
 </thead>
 <tbody>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>acos</strong>(gentype)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Arc cosine function. Returns an angle in radians.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>acosh</strong>(gentype)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Inverse hyperbolic cosine. Returns an angle in radians.</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)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Arc sine function. Returns an angle in radians.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>asinh</strong>(gentype)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Inverse hyperbolic sine. Returns an angle in radians.</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. Returns an angle in radians.</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>. Returns an angle in radians.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>atanh</strong>(gentype)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Hyperbolic arc tangent. Returns an angle in radians.</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)</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)</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, where <em>x</em> is an angle in radians.</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 cosine, where <em>x</em> is an angle in radians.</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>(π <em>x</em>).</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>erfc</strong>(gentype)</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)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Error function encountered in integrating the
       <a href="https://mathworld.wolfram.com/NormalDistribution.html"><em>normal
       distribution</em></a>.</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-<em>e</em> exponential of <em>x</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>exp2</strong>(gentype)</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)</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)</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 <em>x</em> is less than or equal to <em>y</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>floor</strong>(gentype)</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 standard.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fmax</strong>(gentype <em>x</em>, gentype <em>y</em>)<br>
   gentypef <strong>fmax</strong>(gentypef <em>x</em>, float <em>y</em>)<br>
   gentyped <strong>fmax</strong>(gentyped <em>x</em>, double <em>y</em>)</p>
 <p class="tableblock">gentypeh <strong>fmax</strong>(gentypeh <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>
   gentypef <strong>fmin</strong>(gentypef <em>x</em>, float <em>y</em>)<br>
   gentyped <strong>fmin</strong>(gentyped <em>x</em>, double <em>y</em>)</p>
 <p class="tableblock">gentypeh <strong>fmin</strong>(gentypeh <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.
       <sup class="footnote">[<a id="_footnoteref_5" class="footnote" href="#_footnotedef_5" title="View footnote.">5</a>]</sup></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>, __global gentype <em>*iptr</em>)<br>
   gentype <strong>fract</strong>(gentype <em>x</em>, __local gentype <em>*iptr</em>)<br>
   gentype <strong>fract</strong>(gentype <em>x</em>, __private gentype <em>*iptr</em>)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <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>), <code>C</code>), where <code>C</code> is the constant
       <code>0x1.fffffep-1f</code> for <code>float</code> aguments, <code>0x1.fffffffffffffp-1</code> for <code>double</code>
       arguments, and <code>0x1.ffcp-1h</code> for <code>half</code> arguments.
       <strong>floor</strong>(x) is returned in <em>iptr</em>.
       <sup class="footnote">[<a id="_footnoteref_6" class="footnote" href="#_footnotedef_6" title="View footnote.">6</a>]</sup></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>, __global int<em>n</em> *exp)<br>
   half <strong>frexp</strong>(half <em>x</em>, __global int *exp)</p>
 <p class="tableblock">  half<em>n</em> <strong>frexp</strong>(half<em>n</em> <em>x</em>, __local int<em>n</em> *exp)<br>
   half <strong>frexp</strong>(half <em>x</em>, __local int *exp)</p>
 <p class="tableblock">  half<em>n</em> <strong>frexp</strong>(half<em>n</em> <em>x</em>, __private int<em>n</em> *exp)<br>
   half <strong>frexp</strong>(half <em>x</em>, __private int *exp)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <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 <code>half</code> 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">float<em>n</em> <strong>frexp</strong>(float<em>n</em> <em>x</em>, __global int<em>n</em> *exp)<br>
   float <strong>frexp</strong>(float <em>x</em>, __global int *exp)</p>
 <p class="tableblock">  float<em>n</em> <strong>frexp</strong>(float<em>n</em> <em>x</em>, __local int<em>n</em> *exp)<br>
   float <strong>frexp</strong>(float <em>x</em>, __local int *exp)</p>
 <p class="tableblock">  float<em>n</em> <strong>frexp</strong>(float<em>n</em> <em>x</em>, __private int<em>n</em> *exp)<br>
   float <strong>frexp</strong>(float <em>x</em>, __private int *exp)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <p class="tableblock">  float<em>n</em> <strong>frexp</strong>(float<em>n</em> <em>x</em>, int<em>n</em> *exp)<br>
   float <strong>frexp</strong>(float <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 <code>float</code> 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">double<em>n</em> <strong>frexp</strong>(double<em>n</em> <em>x</em>, __global int<em>n</em> *exp)<br>
   double <strong>frexp</strong>(double <em>x</em>, __global int *exp)</p>
 <p class="tableblock">  double<em>n</em> <strong>frexp</strong>(double<em>n</em> <em>x</em>, __local int<em>n</em> *exp)<br>
   double <strong>frexp</strong>(double <em>x</em>, __local int *exp)</p>
 <p class="tableblock">  double<em>n</em> <strong>frexp</strong>(double<em>n</em> <em>x</em>, __private int<em>n</em> *exp)<br>
   double <strong>frexp</strong>(double <em>x</em>, __private int *exp)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <p class="tableblock">  double<em>n</em> <strong>frexp</strong>(double<em>n</em> <em>x</em>, int<em>n</em> *exp)<br>
   double <strong>frexp</strong>(double <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 <code>double</code> 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>(float<em>n</em> <em>x</em>)<br>
   int <strong>ilogb</strong>(float <em>x</em>)<br>
   int<em>n</em> <strong>ilogb</strong>(double<em>n</em> <em>x</em>)<br>
   int <strong>ilogb</strong>(double <em>x</em>)</p>
 <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">float<em>n</em> <strong>ldexp</strong>(float<em>n</em> <em>x</em>, int<em>n</em> <em>k</em>)<br>
   float<em>n</em> <strong>ldexp</strong>(float<em>n</em> <em>x</em>, int <em>k</em>)<br>
   float <strong>ldexp</strong>(float <em>x</em>, int <em>k</em>)<br>
   double<em>n</em> <strong>ldexp</strong>(double<em>n</em> <em>x</em>, int<em>n</em> <em>k</em>)<br>
   double<em>n</em> <strong>ldexp</strong>(double<em>n</em> <em>x</em>, int <em>k</em>)<br>
   double <strong>ldexp</strong>(double <em>x</em>, int <em>k</em>)</p>
 <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>
   float<em>n</em> <strong>lgamma_r</strong>(float<em>n</em> <em>x</em>, __global int<em>n</em> *<em>signp</em>)<br>
   float <strong>lgamma_r</strong>(float <em>x</em>, __global int *<em>signp</em>)<br>
   double<em>n</em> <strong>lgamma_r</strong>(double<em>n</em> <em>x</em>, __global int<em>n</em> *<em>signp</em>)<br>
   double <strong>lgamma_r</strong>(double <em>x</em>, __global int *<em>signp</em>)</p>
 <p class="tableblock">  half<em>n</em> <strong>lgamma_r</strong>(half<em>n</em> <em>x</em>, __global int<em>n</em> *<em>signp</em>)<br>
   half <strong>lgamma_r</strong>(half <em>x</em>, __global int *<em>signp</em>)<br></p>
 <p class="tableblock">  float<em>n</em> <strong>lgamma_r</strong>(float<em>n</em> <em>x</em>, __local int<em>n</em> *<em>signp</em>)<br>
   float <strong>lgamma_r</strong>(float <em>x</em>, __local int *<em>signp</em>)<br>
   double<em>n</em> <strong>lgamma_r</strong>(double<em>n</em> <em>x</em>, __local int<em>n</em> *<em>signp</em>)<br>
   double <strong>lgamma_r</strong>(double <em>x</em>, __local int *<em>signp</em>)</p>
 <p class="tableblock">  half<em>n</em> <strong>lgamma_r</strong>(half<em>n</em> <em>x</em>, __local int<em>n</em> *<em>signp</em>)<br>
   half <strong>lgamma_r</strong>(half <em>x</em>, __local int *<em>signp</em>)<br></p>
 <p class="tableblock">  float<em>n</em> <strong>lgamma_r</strong>(float<em>n</em> <em>x</em>, __private int<em>n</em> *<em>signp</em>)<br>
   float <strong>lgamma_r</strong>(float <em>x</em>, __private int *<em>signp</em>)<br>
   double<em>n</em> <strong>lgamma_r</strong>(double<em>n</em> <em>x</em>, __private int<em>n</em> *<em>signp</em>)<br>
   double <strong>lgamma_r</strong>(double <em>x</em>, __private int *<em>signp</em>)</p>
 <p class="tableblock">  half<em>n</em> <strong>lgamma_r</strong>(half<em>n</em> <em>x</em>, __private int<em>n</em> *<em>signp</em>)<br>
   half <strong>lgamma_r</strong>(half <em>x</em>, __private int *<em>signp</em>)<br></p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <p class="tableblock">  float<em>n</em> <strong>lgamma_r</strong>(float<em>n</em> <em>x</em>, int<em>n</em> *<em>signp</em>)<br>
   float <strong>lgamma_r</strong>(float <em>x</em>, int *<em>signp</em>)<br>
   double<em>n</em> <strong>lgamma_r</strong>(double<em>n</em> <em>x</em>, int<em>n</em> *<em>signp</em>)<br>
   double <strong>lgamma_r</strong>(double <em>x</em>, int *<em>signp</em>)</p>
 <p class="tableblock">  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)</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)</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)</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.
       On some hardware the mad instruction may provide better performance
       than expanded computation of <em>a</em> * <em>b</em> + <em>c</em>.
       <sup class="footnote">[<a id="_footnoteref_7" class="footnote" href="#_footnotedef_7" title="View footnote.">7</a>]</sup></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>
 <p class="tableblock">      <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#unified-spec" target="_blank" rel="noopener">Requires</a> support for OpenCL C 1.1 or newer.</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>
 <p class="tableblock">      <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#unified-spec" target="_blank" rel="noopener">Requires</a> support for OpenCL C 1.1 or newer.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>modf</strong>(gentype <em>x</em>, __global gentype <em>*iptr</em>)<br>
   gentype <strong>modf</strong>(gentype <em>x</em>, __local gentype <em>*iptr</em>)<br>
   gentype <strong>modf</strong>(gentype <em>x</em>, __private gentype <em>*iptr</em>)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <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">float<em>n</em> <strong>nan</strong>(uint<em>n</em> <em>nancode</em>)<br>
   float <strong>nan</strong>(uint <em>nancode</em>)<br>
   double<em>n</em> <strong>nan</strong>(ulong<em>n</em> <em>nancode</em>)<br>
   double <strong>nan</strong>(ulong <em>nancode</em>)</p>
 <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 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">float<em>n</em> <strong>pown</strong>(float<em>n</em> <em>x</em>, int<em>n</em> <em>y</em>)<br>
   float <strong>pown</strong>(float <em>x</em>, int <em>y</em>)<br>
   double<em>n</em> <strong>pown</strong>(double<em>n</em> <em>x</em>, int<em>n</em> <em>y</em>)<br>
   double <strong>pown</strong>(double <em>x</em>, int <em>y</em>)</p>
 <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">float<em>n</em> <strong>remquo</strong>(float<em>n</em> <em>x</em>, float<em>n</em> <em>y</em>, __global int<em>n</em> <em>*quo</em>)<br>
   float <strong>remquo</strong>(float <em>x</em>, float <em>y</em>, __global int <em>*quo</em>)</p>
 <p class="tableblock">  float<em>n</em> <strong>remquo</strong>(float<em>n</em> <em>x</em>, float<em>n</em> <em>y</em>, __local int<em>n</em> <em>*quo</em>)<br>
   float <strong>remquo</strong>(float <em>x</em>, float <em>y</em>, __local int <em>*quo</em>)</p>
 <p class="tableblock">  float<em>n</em> <strong>remquo</strong>(float<em>n</em> <em>x</em>, float<em>n</em> <em>y</em>, __private int<em>n</em> <em>*quo</em>)<br>
   float <strong>remquo</strong>(float <em>x</em>, float <em>y</em>, __private int <em>*quo</em>)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <p class="tableblock">  float<em>n</em> <strong>remquo</strong>(float<em>n</em> <em>x</em>, float<em>n</em> <em>y</em>, int<em>n</em> <em>*quo</em>)<br>
   float <strong>remquo</strong>(float <em>x</em>, float <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">double<em>n</em> <strong>remquo</strong>(double<em>n</em> <em>x</em>, double<em>n</em> <em>y</em>, __global int<em>n</em> <em>*quo</em>)<br>
   double <strong>remquo</strong>(double <em>x</em>, double <em>y</em>, __global int <em>*quo</em>)</p>
 <p class="tableblock">  double<em>n</em> <strong>remquo</strong>(double<em>n</em> <em>x</em>, double<em>n</em> <em>y</em>, __local int<em>n</em> <em>*quo</em>)<br>
   double <strong>remquo</strong>(double <em>x</em>, double <em>y</em>, __local int <em>*quo</em>)</p>
 <p class="tableblock">  double<em>n</em> <strong>remquo</strong>(double<em>n</em> <em>x</em>, double<em>n</em> <em>y</em>, __private int<em>n</em> <em>*quo</em>)<br>
   double <strong>remquo</strong>(double <em>x</em>, double <em>y</em>, __private int <em>*quo</em>)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <p class="tableblock">  double<em>n</em> <strong>remquo</strong>(double<em>n</em> <em>x</em>, double<em>n</em> <em>y</em>, int<em>n</em> <em>*quo</em>)<br>
   double <strong>remquo</strong>(double <em>x</em>, double <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">half<em>n</em> <strong>remquo</strong>(half<em>n</em> <em>x</em>, half<em>n</em> <em>y</em>, __global int<em>n</em> <em>*quo</em>)<br>
   half <strong>remquo</strong>(half <em>x</em>, half <em>y</em>, __global int <em>*quo</em>)</p>
 <p class="tableblock">  half<em>n</em> <strong>remquo</strong>(half<em>n</em> <em>x</em>, half<em>n</em> <em>y</em>, __local int<em>n</em> <em>*quo</em>)<br>
   half <strong>remquo</strong>(half <em>x</em>, half <em>y</em>, __local int <em>*quo</em>)</p>
 <p class="tableblock">  half<em>n</em> <strong>remquo</strong>(half<em>n</em> <em>x</em>, half<em>n</em> <em>y</em>, __private int<em>n</em> <em>*quo</em>)<br>
   half <strong>remquo</strong>(half <em>x</em>, half <em>y</em>, __private int <em>*quo</em>)</p>
 <p class="tableblock">  For OpenCL C 2.0 or with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <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)</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">float<em>n</em> <strong>rootn</strong>(float<em>n</em> <em>x</em>, int<em>n</em> <em>y</em>)<br>
   float <strong>rootn</strong>(float <em>x</em>, int <em>y</em>)<br>
   double<em>n</em> <strong>rootn</strong>(double<em>n</em> <em>x</em>, int<em>n</em> <em>y</em>)<br>
   double <strong>rootn</strong>(double <em>x</em>, int <em>y</em>)</p>
 <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)</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, where <em>x</em> is an angle in radians.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sincos</strong>(gentype <em>x</em>, __global gentype <em>*cosval</em>)<br>
   gentype <strong>sincos</strong>(gentype <em>x</em>, __local gentype <em>*cosval</em>)<br>
   gentype <strong>sincos</strong>(gentype <em>x</em>, __private gentype <em>*cosval</em>)</p>
 <p class="tableblock">  For OpenCL C 2.0, or OpenCL C 3.0 or newer with the
   <code>__opencl_c_<wbr>generic_<wbr>address_<wbr>space</code> feature:</p>
 <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 <em>x</em>.
       The computed sine is the return value and computed cosine is returned
       in <em>cosval</em>, where <em>x</em> is an angle in radians.</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, where <em>x</em> is an angle in radians</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>(π <em>x</em>).</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>sqrt</strong>(gentype)</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, where <em>x</em> is an angle in radians.</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, where <em>x</em> is an angle in radians.</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>(π <em>x</em>).</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>tgamma</strong>(gentype)</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)</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 following table describes the following functions:</p>
 </div>
 <div class="ulist">
 <ul>
 <li>
 <p>A subset of functions from <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#table-builtin-math" target="_blank" rel="noopener">Built-in Scalar and Vector
 Argument Math Functions</a> that are defined with the half_ prefix.
 These functions are implemented with a minimum of 10-bits of accuracy,
 i.e. the maximum error value &lt;= 8192 ulp.</p>
 </li>
 <li>
 <p>A subset of functions from <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#table-builtin-math" target="_blank" rel="noopener">Built-in Scalar and Vector
 Argument Math Functions</a> that are defined with the native_ prefix.
 These functions may map to one or more native device instructions and
 will typically have better performance compared to the corresponding
 functions without the <code>native_</code> prefix).
 The accuracy (and in some cases the input range(s)) of these functions
 is implementation-defined.</p>
 </li>
 <li>
 <p><code>half_</code> and <code>native_</code> functions for following basic operations:
 divide and reciprocal.</p>
 </li>
 </ul>
 </div>
 <div class="paragraph">
 <p>We use the generic type name <code>gentype</code> to indicate that the functions in the
 following table can take <code>float</code>, <code>float2</code>, <code>float3</code>, <code>float4</code>, <code>float8</code> or
 <code>float16</code> as the type for the arguments.</p>
 </div>
 <div class="admonitionblock note">
 <table>
 <tr>
 <td class="icon">
 <i class="fa icon-note" title="Note"></i>
 </td>
 <td class="content">
 The use of <code>half</code> in this table does not refer to the argument and
 return types, which are 32-bit floating-point values, but to the accuracy
 requirements of the function results.
 </td>
 </tr>
 </table>
 </div>
 <table id="table-builtin-half-native-math" class="tableblock frame-all grid-all stretch">
 <caption class="title">Table 2. Built-in Scalar and Vector <em>half</em> and <em>native</em> Math Functions</caption>
 <colgroup>
 <col style="width: 50%;">
 <col style="width: 50%;">
 </colgroup>
 <thead>
 <tr>
 <th class="tableblock halign-left valign-top">Function</th>
 <th class="tableblock halign-left valign-top">Description</th>
 </tr>
 </thead>
 <tbody>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_cos</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute cosine.
       <em>x</em> is an angle in radians, and must be in the range [-2<sup>16</sup>, +2<sup>16</sup>].</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_divide</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> / <em>y</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_exp</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base-<em>e</em> exponential of <em>x</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_exp2</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base- 2 exponential of <em>x</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_exp10</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base- 10 exponential of <em>x</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_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>half_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>half_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>half_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>half_recip</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute reciprocal.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_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>half_sin</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute sine.
       <em>x</em> is an angle in radians, and must be in the range [-2<sup>16</sup>, +2<sup>16</sup>].</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>half_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>half_tan</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute tangent.
       <em>x</em> is an angle in radians, and must be in the range [-2<sup>16</sup>, +2<sup>16</sup>].</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"></td>
 <td class="tableblock halign-left valign-top"></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_cos</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute cosine over an implementation-defined range, where <em>x</em> is an
       angle in radians.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_divide</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> / <em>y</em> over an implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_exp</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base-<em>e</em> exponential of <em>x</em> over an
       implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_exp2</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base-2 exponential of <em>x</em> over an implementation-defined
       range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_exp10</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute the base-10 exponential of <em>x</em> over an implementation-defined
       range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_log</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute natural logarithm over an implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_log2</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute a base 2 logarithm over an
       implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_log10</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute a base 10 logarithm over
       an implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_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.
       The range of <em>x</em> and <em>y</em> are implementation-defined.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_recip</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute reciprocal over an implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_rsqrt</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute inverse square root over an implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_sin</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute sine over an implementation-defined range, where <em>x</em> is an
       angle in radians.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_sqrt</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute square root over an implementation-defined range.
       The maximum error is implementation-defined.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>native_tan</strong>(gentype <em>x</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute tangent over an implementation-defined range, where <em>x</em> is an
       angle in radians.
       The maximum error is implementation-defined.</p></td>
 </tr>
 </tbody>
 </table>
 <div class="paragraph">
 <p>Support for denormal values is optional for <strong>half_</strong> functions.
 The <strong>half_</strong> functions may return any result allowed by
 <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#edge-case-behavior-in-flush-to-zero-mode" target="_blank" rel="noopener">Edge Case Behavior</a>, even when
 <code>-cl-denorms-are-zero</code> (see <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#opencl-spec" target="_blank" rel="noopener">section 5.8.4.2 of the OpenCL
 Specification</a>) is not in force.
 Support for denormal values is implementation-defined for <strong>native_</strong>
 functions.</p>
 </div>
 </div>
 </div>
 <div class="sect1">
 <h2 id="_see_also"><a class="anchor" href="#_see_also"></a>See Also</h2>
 <div class="sectionbody">
 <div class="paragraph">
 <p><a href="commonFunctions.html">commonFunctions</a>, <a href="integerFunctions.html">integerFunctions</a></p>
 </div>
 </div>
 </div>
 <div class="sect1">
 <h2 id="_document_notes"><a class="anchor" href="#_document_notes"></a>Document Notes</h2>
 <div class="sectionbody">
 <div class="paragraph">
 <p>For more information, see the <a href="https://www.khronos.org/registry/OpenCL/specs/3.0-unified/html/OpenCL_C.html#math-functions" target="_blank" rel="noopener">OpenCL C Specification</a></p>
 </div>
 <div class="paragraph">
 <p>This page is extracted from the OpenCL C Specification.
 Fixes and changes should be made to the Specification, not directly.</p>
 </div>
 </div>
 </div>
 <div class="sect1">
 <h2 id="_copyright"><a class="anchor" href="#_copyright"></a>Copyright</h2>
 <div class="sectionbody">
 <div class="paragraph">
 <p>Copyright 2014-2026 The Khronos Group Inc.</p>
 </div>
 <div class="paragraph">
 <p>SPDX-License-Identifier: CC-BY-4.0</p>
 </div>
 </div>
 </div>
 </div>
 <div id="footnotes">
 <hr>
 <div class="footnote" id="_footnotedef_1">
 <a href="#_footnoteref_1">1</a>. Only if double precision is supported. In OpenCL C 3.0 this will be indicated by the presence of the <code>__opencl_c_<wbr>fp64</code> feature macro.
 </div>
 <div class="footnote" id="_footnotedef_2">
 <a href="#_footnoteref_2">2</a>. Only if the <code>cl_khr_<wbr>fp16</code> extension is supported and has been enabled.
 </div>
 <div class="footnote" id="_footnotedef_3">
 <a href="#_footnoteref_3">3</a>. Only if double precision is supported. In OpenCL C 3.0 this will be indicated by the presence of the <code>__opencl_c_<wbr>fp64</code> feature macro.
 </div>
 <div class="footnote" id="_footnotedef_4">
 <a href="#_footnoteref_4">4</a>. Only if the <code>cl_khr_<wbr>fp16</code> extension is supported and has been enabled.
 </div>
 <div class="footnote" id="_footnotedef_5">
 <a href="#_footnoteref_5">5</a>. <strong>fmin</strong> and <strong>fmax</strong> behave as defined by C99 and may not match the IEEE 754-2008 definition for <strong>minNum</strong> and <strong>maxNum</strong> with regard to signaling NaNs. Specifically, signaling NaNs may behave as quiet NaNs.
 </div>
 <div class="footnote" id="_footnotedef_6">
 <a href="#_footnoteref_6">6</a>. The <strong>min</strong>() operator is there to prevent <strong>fract</strong>(-small) from returning 1.0. It returns the largest positive floating-point number less than 1.0.
 </div>
 <div class="footnote" id="_footnotedef_7">
 <a href="#_footnoteref_7">7</a>. The user is cautioned that for some usages, e.g. <strong>mad</strong>(a, b, -a*b), the definition of <strong>mad</strong>() is loose enough in the embedded profile or with half-precision arguments that almost any result is allowed from <strong>mad</strong>() for some values of a and b.
 </div>
 </div>

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