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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.c99"></a><a class="link" href="c99.html" title="C99 C Functions">C99 C Functions</a>
</h2></div></div></div>
<h5>
<a name="math_toolkit.c99.h0"></a>
      <span class="phrase"><a name="math_toolkit.c99.supported_c99_functions"></a></span><a class="link" href="c99.html#math_toolkit.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="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>
<h5>
<a name="math_toolkit.c99.h1"></a>
      <span class="phrase"><a name="math_toolkit.c99.quick_reference"></a></span><a class="link" href="c99.html#math_toolkit.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="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="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="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="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.svg"></span>
    </p>
<p>
      See also <a class="link" href="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="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="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="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.svg"></span>
    </p>
<p>
      See also <a class="link" href="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="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="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="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="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.svg"></span>
    </p>
<p>
      See also <a class="link" href="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="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; 2006-2010, 2012-2014 Nikhar Agrawal,
      Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
      Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
      Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<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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