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 <div class="titlepage"><div><div><h3 class="title">
 <a name="math_toolkit.extern_c.c99"></a><a class="link" href="c99.html" title="C99 C Functions"> C99 C Functions</a>
 </h3></div></div></div>
 <a name="math_toolkit.extern_c.c99.supported_c99_functions"></a><h5>
 <a name="id1172292"></a>
         <a class="link" href="c99.html#math_toolkit.extern_c.c99.supported_c99_functions">Supported
         C99 Functions</a>
       </h5>
 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>

 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>

 <span class="keyword">double</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">acoshf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">acoshl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">asinhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">asinhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">atanhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">atanhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">cbrtf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cbrtl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">copysign</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">copysignf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">copysignl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">erf</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">erff</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">erfc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">erfcf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfcl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">expm1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">expm1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expm1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">fmax</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">fmaxf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmaxl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">fmin</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">fminf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fminl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">hypot</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">hypotf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypotl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">lgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">lgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">log1p</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">log1pf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log1pl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="identifier">lroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="identifier">lroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">nextafterf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nextafterl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">nexttoward</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">nexttowardf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nexttowardl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">roundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">roundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">tgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">tgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="keyword">double</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">truncf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">truncl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>

 <span class="special">}}}}</span> <span class="comment">// namespaces
 </span></pre>
 <p>
         In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
         versions of the above functions are provided, so that calling the function
         with any mixture of <code class="computeroutput"><span class="keyword">float</span></code>,
         <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
         <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
         arguments is supported, with the return type determined by the <a class="link" href="../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
         type calculation rules</em></span></a>.
       </p>
 <p>
         For example:
       </p>
 <pre class="programlisting"><span class="identifier">acoshf</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span>  <span class="comment">// float version, returns float.
 </span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span>   <span class="comment">// also calls the float version and returns float.
 </span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span>    <span class="comment">// double version, returns double.
 </span><span class="identifier">acoshl</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span>  <span class="comment">// long double version, returns a long double.
 </span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span>   <span class="comment">// also calls the long double version.
 </span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>      <span class="comment">// integer argument is treated as a double, returns double.
 </span></pre>
 <a name="math_toolkit.extern_c.c99.quick_reference"></a><h5>
 <a name="id1176218"></a>
         <a class="link" href="c99.html#math_toolkit.extern_c.c99.quick_reference">Quick Reference</a>
       </h5>
 <p>
         More detailed descriptions of these functions are available in the C99 standard.
       </p>
 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
 </pre>
 <p>
         In this implementation <code class="computeroutput"><span class="identifier">float_t</span></code>
         is the same as type <code class="computeroutput"><span class="keyword">float</span></code>, and
         <code class="computeroutput"><span class="identifier">double_t</span></code> the same as type
         <code class="computeroutput"><span class="keyword">double</span></code> unless the preprocessor
         symbol FLT_EVAL_METHOD is defined, in which case these are set as follows:
       </p>
 <div class="informaltable"><table class="table">
 <colgroup>
 <col>
 <col>
 <col>
 </colgroup>
 <thead><tr>
 <th>
                 <p>
                   FLT_EVAL_METHOD
                 </p>
               </th>
 <th>
                 <p>
                   float_t
                 </p>
               </th>
 <th>
                 <p>
                   double_t
                 </p>
               </th>
 </tr></thead>
 <tbody>
 <tr>
 <td>
                 <p>
                   0
                 </p>
               </td>
 <td>
                 <p>
                   float
                 </p>
               </td>
 <td>
                 <p>
                   double
                 </p>
               </td>
 </tr>
 <tr>
 <td>
                 <p>
                   1
                 </p>
               </td>
 <td>
                 <p>
                   double
                 </p>
               </td>
 <td>
                 <p>
                   double
                 </p>
               </td>
 </tr>
 <tr>
 <td>
                 <p>
                   2
                 </p>
               </td>
 <td>
                 <p>
                   long double
                 </p>
               </td>
 <td>
                 <p>
                   long double
                 </p>
               </td>
 </tr>
 </tbody>
 </table></div>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">acoshf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">acoshl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the inverse hyperbolic cosine of <span class="emphasis"><em>x</em></span>.
       </p>
 <p>
         See also <a class="link" href="../special/inv_hyper/acosh.html" title="acosh">acosh</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">asinhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">asinhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the inverse hyperbolic sine of <span class="emphasis"><em>x</em></span>.
       </p>
 <p>
         See also <a class="link" href="../special/inv_hyper/asinh.html" title="asinh">asinh</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">atanhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">atanhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the inverse hyperbolic tangent of <span class="emphasis"><em>x</em></span>.
       </p>
 <p>
         See also <a class="link" href="../special/inv_hyper/atanh.html" title="atanh">atanh</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">cbrtf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cbrtl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the cubed root of <span class="emphasis"><em>x</em></span>.
       </p>
 <p>
         See also <a class="link" href="../special/powers/cbrt.html" title="cbrt">cbrt</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">copysign</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">copysignf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">copysignl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 </pre>
 <p>
         Returns a value with the magnitude of <span class="emphasis"><em>x</em></span> and the sign
         of <span class="emphasis"><em>y</em></span>.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">erf</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">erff</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the error function of <span class="emphasis"><em>x</em></span>:
       </p>
 <p>
         <span class="inlinemediaobject"><img src="../../../equations/erf1.png"></span>
       </p>
 <p>
         See also <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erf</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">erfc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">erfcf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfcl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the complementary error function of <span class="emphasis"><em>x</em></span> <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">erf</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code>
         without the loss of precision implied by the subtraction.
       </p>
 <p>
         See also <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erfc</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">expm1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">expm1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expm1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns <code class="computeroutput"><span class="identifier">exp</span><span class="special">(</span><span class="identifier">x</span><span class="special">)-</span><span class="number">1</span></code>
         without the loss of precision implied by the subtraction.
       </p>
 <p>
         See also <a class="link" href="../special/powers/expm1.html" title="expm1">expm1</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">fmax</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">fmaxf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmaxl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 </pre>
 <p>
         Returns the larger (most positive) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">fmin</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">fminf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fminl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 </pre>
 <p>
         Returns the smaller (most negative) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">hypot</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">hypotf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypotl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 </pre>
 <p>
         Returns <code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">x</span><span class="special">*</span><span class="identifier">x</span>
         <span class="special">+</span> <span class="identifier">y</span><span class="special">*</span><span class="identifier">y</span><span class="special">)</span></code>
         without the danger of numeric overflow implied by that formulation.
       </p>
 <p>
         See also <a class="link" href="../special/powers/hypot.html" title="hypot">hypot</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">lgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">lgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the log of the gamma function of <span class="emphasis"><em>x</em></span>.
       </p>
 <p>
         <span class="inlinemediaobject"><img src="../../../equations/lgamm1.png"></span>
       </p>
 <p>
         See also <a class="link" href="../special/sf_gamma/lgamma.html" title="Log Gamma">lgamma</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
         a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code>:
         equivalent to <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
       </p>
 <p>
         See also <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">log1p</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">log1pf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log1pl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code> without the loss of precision implied by
         that formulation.
       </p>
 <p>
         See also <a class="link" href="../special/powers/log1p.html" title="log1p">log1p</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="identifier">lroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="identifier">lroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
         a <code class="computeroutput"><span class="keyword">long</span></code>: equivalent to <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
       </p>
 <p>
         See also <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">nextafterf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nextafterl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 </pre>
 <p>
         Returns the next representable floating point number after <span class="emphasis"><em>x</em></span>
         in the direction of <span class="emphasis"><em>y</em></span>, or <span class="emphasis"><em>x</em></span> if
         <code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
         <span class="identifier">y</span></code>.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">nexttoward</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">nexttowardf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nexttowardl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
 </pre>
 <p>
         As <code class="computeroutput"><span class="identifier">nextafter</span></code>, but with <span class="emphasis"><em>y</em></span>
         always expressed as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">roundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">roundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer:
         equivalent to <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
       </p>
 <p>
         See also <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> for
         the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">tgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">tgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns the gamma function of <span class="emphasis"><em>x</em></span>:
       </p>
 <p>
         <span class="inlinemediaobject"><img src="../../../equations/gamm1.png"></span>
       </p>
 <p>
         See also <a class="link" href="../special/sf_gamma/tgamma.html" title="Gamma">tgamma</a>
         for the full template (header only) version of this function.
       </p>
 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">float</span> <span class="identifier">truncf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
 <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">truncl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
 </pre>
 <p>
         Returns <span class="emphasis"><em>x</em></span> truncated to the nearest integer.
       </p>
 <p>
         See also <a class="link" href="../utils/rounding/trunc.html" title="Truncation Functions">trunc</a> for
         the full template (header only) version of this function.
       </p>
 <p>
         See also <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1124.pdf" target="_top">C99
         ISO Standard</a>
       </p>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 <td align="left"></td>
 <td align="right"><div class="copyright-footer">Copyright &#169; 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow,
       Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de, Gautam Sewani and
       Thijs van den Berg<p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
       </p>
 </div></td>
 </tr></table>
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