sdk/2.2/docs/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">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/2.2/html/OpenCL_C.html#table-builtin-math" target="_blank" rel="noopener">following table</a> describes the list of built-in
 math functions that can take scalar or vector arguments.
 We use the generic type name <code>gentype</code> to indicate that the function can
 take <code>float</code>, <code>float2</code>, <code>float3</code>, <code>float4</code>, <code>float8</code>, <code>float16</code>, <code>double</code>,
 <code>double2</code>, <code>double3</code>, <code>double4</code>, <code>double8</code> or <code>double16</code> as the type for the
 arguments.
 We use the generic type name <code>gentypef</code> to indicate that the function 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.
 We use the generic type name <code>gentyped</code> to indicate that the function can
 take <code>double</code>, <code>double2</code>, <code>double3</code>, <code>double4</code>, <code>double8</code> or <code>double16</code> as
 the type for the arguments.
 For any specific use of a function, the actual type has to be the same for
 all arguments and the return type, unless otherwise specified.</p>
 </div>
 <table id="table-builtin-math" class="tableblock frame-all grid-all stretch">
 <caption class="title">Table 1. Scalar and Vector Argument Built-in Math Function Table</caption>
 <colgroup>
 <col style="width: 50%;">
 <col style="width: 50%;">
 </colgroup>
 <tbody>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock"><strong>Function</strong></p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock"><strong>Description</strong></p></td>
 </tr>
 <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="http://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 y.</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></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><sup>29</sup>(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></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>y</em> if <em>y</em> &lt; <em>x</em>, otherwise it returns <em>x</em>.
       If one argument is a NaN, <strong>fmin</strong>() returns the other argument.
       If both arguments are NaNs, <strong>fmin</strong>() returns a NaN.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fmod</strong>(gentype <em>x</em>, gentype <em>y</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Modulus.
       Returns <em>x</em> - <em>y</em> * <strong>trunc</strong>(<em>x</em>/<em>y</em>).</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>fract</strong>(gentype <em>x</em>, gentype <em>*iptr</em>)<sup>30</sup></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>0x1.fffffep-1f</code>).
       <strong>floor</strong>(x) is returned in <em>iptr</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>, 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>, 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>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">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></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></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>, 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></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.  See the SPIR-V OpenCL environment specification
     for details. On some hardware the mad instruction may provide better
     performance than expanded computation of <em>a</em> * <em>b</em> + <em>c</em>.<sup>31</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></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>minmag</strong>(gentype <em>x</em>, gentype <em>y</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Returns <em>x</em> if |<em>x</em>| &lt; |<em>y</em>|, <em>y</em> if |<em>y</em>| &lt; |<em>x</em>|, otherwise
       <strong>fmin</strong>(<em>x</em>, <em>y</em>).</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>modf</strong>(gentype <em>x</em>, gentype *<em>iptr</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Decompose a floating-point number.
       The <strong>modf</strong> function breaks the argument <em>x</em> into integral and
       fractional parts, each of which has the same sign as the argument.
       It stores the integral part in the object pointed to by <em>iptr</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">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></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 single-precision floating-point value
       following <em>x</em> in the direction of <em>y</em>.
       Thus, if <em>y</em> is less than <em>x</em>, <strong>nextafter</strong>() returns the largest
       representable floating-point number less than <em>x</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">gentype <strong>pow</strong>(gentype <em>x</em>, gentype <em>y</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute <em>x</em> to the power <em>y</em>.</p></td>
 </tr>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock">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></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>, 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>, 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">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<em>n</em> <strong>rootn</strong>(double <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>, gentype *<em>cosval</em>)</p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock">Compute sine and cosine of x.
       The computed sine is the return value and computed cosine is returned
       in <em>cosval</em>, 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>[29] <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.</p>
 </div>
 <div class="paragraph">
 <p>[30] 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.</p>
 </div>
 <div class="paragraph">
 <p>[31] 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 that almost any result is allowed from
 <strong>mad</strong>() for some values of a and b.</p>
 </div>
 <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/2.2/html/OpenCL_C.html#table-builtin-math" class="bare" target="_blank" rel="noopener">https://www.khronos.org/registry/OpenCL/specs/2.2/html/OpenCL_C.html#table-builtin-math</a> that are defined with
 the half_ prefix .
 These functions are implemented with a minimum of 10-bits of accuracy,
 i.e. an ULP value &lt;= 8192 ulp.</p>
 </li>
 <li>
 <p>A subset of functions from <a href="https://www.khronos.org/registry/OpenCL/specs/2.2/html/OpenCL_C.html#table-builtin-math" class="bare" target="_blank" rel="noopener">https://www.khronos.org/registry/OpenCL/specs/2.2/html/OpenCL_C.html#table-builtin-math</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) described in
 <a href="https://www.khronos.org/registry/OpenCL/specs/2.2/html/OpenCL_C.html#table-builtin-math" class="bare" target="_blank" rel="noopener">https://www.khronos.org/registry/OpenCL/specs/2.2/html/OpenCL_C.html#table-builtin-math</a>.
 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>
 <table id="table-builtin-half-native-math" class="tableblock frame-all grid-all stretch">
 <caption class="title">Table 2. Scalar and Vector Argument Built-in <em>half</em> and <em>native</em> Math Functions</caption>
 <colgroup>
 <col style="width: 50%;">
 <col style="width: 50%;">
 </colgroup>
 <tbody>
 <tr>
 <td class="tableblock halign-left valign-top"><p class="tableblock"><strong>Function</strong></p></td>
 <td class="tableblock halign-left valign-top"><p class="tableblock"><strong>Description</strong></p></td>
 </tr>
 <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/2.2/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/2.2/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">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">Document Notes</h2>
 <div class="sectionbody">
 <div class="paragraph">
 <p>For more information, see the <a href="https://www.khronos.org/registry/OpenCL/specs/2.2/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">Copyright</h2>
 <div class="sectionbody">
 <div class="paragraph">
 <p>Copyright (c) 2014-2020 Khronos Group. This work is licensed under a
 <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank" rel="noopener">Creative Commons
 Attribution 4.0 International License</a>.</p>
 </div>
 </div>
 </div>
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