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  25 <div class="section">
  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.c99"></a><a class="link" href="c99.html" title="C99 C Functions">C99 C Functions</a>
  28 </h2></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.c99.h0"></a>
  31       <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
  32       C99 Functions</a>
  33     </h5>
  34 <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>
  35
  36 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
  37 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
  38
  39 <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>
  40 <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>
  41 <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>
  42
  43 <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>
  44 <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>
  45 <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>
  46
  47 <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>
  48 <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>
  49 <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>
  50
  51 <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>
  52 <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>
  53 <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>
  54
  55 <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>
  56 <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>
  57 <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>
  58
  59 <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>
  60 <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>
  61 <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>
  62
  63 <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>
  64 <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>
  65 <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>
  66
  67 <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>
  68 <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>
  69 <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>
  70
  71 <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>
  72 <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>
  73 <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>
  74
  75 <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>
  76 <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>
  77 <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>
  78
  79 <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>
  80 <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>
  81 <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>
  82
  83 <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>
  84 <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>
  85 <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>
  86
  87 <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>
  88 <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>
  89 <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>
  90
  91 <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>
  92 <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>
  93 <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>
  94
  95 <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>
  96 <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>
  97 <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>
  98
  99 <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>
 100 <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>
 101 <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>
 102
 103 <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>
 104 <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>
 105 <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>
 106
 107 <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>
 108 <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>
 109 <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>
 110
 111 <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>
 112 <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>
 113 <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>
 114
 115 <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>
 116 <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>
 117 <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>
 118
 119 <span class="special">}}}}</span> <span class="comment">// namespaces</span>
 120 </pre>
 121 <p>
 122       In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
 123       versions of the above functions are provided, so that calling the function
 124       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>
 125       <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
 126       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
 127       type calculation rules</em></span></a>.
 128     </p>
 129 <p>
 130       For example:
 131     </p>
 132 <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>
 133 <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>
 134 <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>
 135 <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>
 136 <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>
 137 <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>
 138 </pre>
 139 <h5>
 140 <a name="math_toolkit.c99.h1"></a>
 141       <span class="phrase"><a name="math_toolkit.c99.quick_reference"></a></span><a class="link" href="c99.html#math_toolkit.c99.quick_reference">Quick
 142       Reference</a>
 143     </h5>
 144 <p>
 145       More detailed descriptions of these functions are available in the C99 standard.
 146     </p>
 147 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
 148 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
 149 </pre>
 150 <p>
 151       In this implementation <code class="computeroutput"><span class="identifier">float_t</span></code>
 152       is the same as type <code class="computeroutput"><span class="keyword">float</span></code>, and
 153       <code class="computeroutput"><span class="identifier">double_t</span></code> the same as type
 154       <code class="computeroutput"><span class="keyword">double</span></code> unless the preprocessor
 155       symbol FLT_EVAL_METHOD is defined, in which case these are set as follows:
 156     </p>
 157 <div class="informaltable"><table class="table">
 158 <colgroup>
 159 <col>
 160 <col>
 161 <col>
 162 </colgroup>
 163 <thead><tr>
 164 <th>
 165               <p>
 166                 FLT_EVAL_METHOD
 167               </p>
 168             </th>
 169 <th>
 170               <p>
 171                 float_t
 172               </p>
 173             </th>
 174 <th>
 175               <p>
 176                 double_t
 177               </p>
 178             </th>
 179 </tr></thead>
 180 <tbody>
 181 <tr>
 182 <td>
 183               <p>
 184                 0
 185               </p>
 186             </td>
 187 <td>
 188               <p>
 189                 float
 190               </p>
 191             </td>
 192 <td>
 193               <p>
 194                 double
 195               </p>
 196             </td>
 197 </tr>
 198 <tr>
 199 <td>
 200               <p>
 201                 1
 202               </p>
 203             </td>
 204 <td>
 205               <p>
 206                 double
 207               </p>
 208             </td>
 209 <td>
 210               <p>
 211                 double
 212               </p>
 213             </td>
 214 </tr>
 215 <tr>
 216 <td>
 217               <p>
 218                 2
 219               </p>
 220             </td>
 221 <td>
 222               <p>
 223                 long double
 224               </p>
 225             </td>
 226 <td>
 227               <p>
 228                 long double
 229               </p>
 230             </td>
 231 </tr>
 232 </tbody>
 233 </table></div>
 234 <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>
 235 <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>
 236 <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>
 237 </pre>
 238 <p>
 239       Returns the inverse hyperbolic cosine of <span class="emphasis"><em>x</em></span>.
 240     </p>
 241 <p>
 242       See also <a class="link" href="inv_hyper/acosh.html" title="acosh">acosh</a> for the
 243       full template (header only) version of this function.
 244     </p>
 245 <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>
 246 <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>
 247 <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>
 248 </pre>
 249 <p>
 250       Returns the inverse hyperbolic sine of <span class="emphasis"><em>x</em></span>.
 251     </p>
 252 <p>
 253       See also <a class="link" href="inv_hyper/asinh.html" title="asinh">asinh</a> for the
 254       full template (header only) version of this function.
 255     </p>
 256 <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>
 257 <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>
 258 <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>
 259 </pre>
 260 <p>
 261       Returns the inverse hyperbolic tangent of <span class="emphasis"><em>x</em></span>.
 262     </p>
 263 <p>
 264       See also <a class="link" href="inv_hyper/atanh.html" title="atanh">atanh</a> for the
 265       full template (header only) version of this function.
 266     </p>
 267 <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>
 268 <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>
 269 <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>
 270 </pre>
 271 <p>
 272       Returns the cubed root of <span class="emphasis"><em>x</em></span>.
 273     </p>
 274 <p>
 275       See also <a class="link" href="powers/cbrt.html" title="cbrt">cbrt</a> for the full
 276       template (header only) version of this function.
 277     </p>
 278 <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>
 279 <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>
 280 <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>
 281 </pre>
 282 <p>
 283       Returns a value with the magnitude of <span class="emphasis"><em>x</em></span> and the sign of
 284       <span class="emphasis"><em>y</em></span>.
 285     </p>
 286 <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>
 287 <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>
 288 <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>
 289 </pre>
 290 <p>
 291       Returns the error function of <span class="emphasis"><em>x</em></span>:
 292     </p>
 293 <p>
 294       <span class="inlinemediaobject"><img src="../../equations/erf1.svg"></span>
 295     </p>
 296 <p>
 297       See also <a class="link" href="sf_erf/error_function.html" title="Error Functions">erf</a> for
 298       the full template (header only) version of this function.
 299     </p>
 300 <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>
 301 <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>
 302 <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>
 303 </pre>
 304 <p>
 305       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>
 306       without the loss of precision implied by the subtraction.
 307     </p>
 308 <p>
 309       See also <a class="link" href="sf_erf/error_function.html" title="Error Functions">erfc</a> for
 310       the full template (header only) version of this function.
 311     </p>
 312 <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>
 313 <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>
 314 <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>
 315 </pre>
 316 <p>
 317       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>
 318       without the loss of precision implied by the subtraction.
 319     </p>
 320 <p>
 321       See also <a class="link" href="powers/expm1.html" title="expm1">expm1</a> for the full
 322       template (header only) version of this function.
 323     </p>
 324 <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>
 325 <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>
 326 <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>
 327 </pre>
 328 <p>
 329       Returns the larger (most positive) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
 330     </p>
 331 <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>
 332 <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>
 333 <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>
 334 </pre>
 335 <p>
 336       Returns the smaller (most negative) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
 337     </p>
 338 <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>
 339 <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>
 340 <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>
 341 </pre>
 342 <p>
 343       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>
 344       <span class="special">+</span> <span class="identifier">y</span><span class="special">*</span><span class="identifier">y</span><span class="special">)</span></code>
 345       without the danger of numeric overflow implied by that formulation.
 346     </p>
 347 <p>
 348       See also <a class="link" href="powers/hypot.html" title="hypot">hypot</a> for the full
 349       template (header only) version of this function.
 350     </p>
 351 <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>
 352 <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>
 353 <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>
 354 </pre>
 355 <p>
 356       Returns the log of the gamma function of <span class="emphasis"><em>x</em></span>.
 357     </p>
 358 <p>
 359       <span class="inlinemediaobject"><img src="../../equations/lgamm1.svg"></span>
 360     </p>
 361 <p>
 362       See also <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> for the
 363       full template (header only) version of this function.
 364     </p>
 365 <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>
 366 <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>
 367 <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>
 368 </pre>
 369 <p>
 370       Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
 371       a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code>:
 372       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>
 373     </p>
 374 <p>
 375       See also <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> for the full
 376       template (header only) version of this function.
 377     </p>
 378 <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>
 379 <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>
 380 <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>
 381 </pre>
 382 <p>
 383       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
 384       formulation.
 385     </p>
 386 <p>
 387       See also <a class="link" href="powers/log1p.html" title="log1p">log1p</a> for the full
 388       template (header only) version of this function.
 389     </p>
 390 <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>
 391 <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>
 392 <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>
 393 </pre>
 394 <p>
 395       Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
 396       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>
 397       <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
 398     </p>
 399 <p>
 400       See also <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> for the full
 401       template (header only) version of this function.
 402     </p>
 403 <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>
 404 <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>
 405 <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>
 406 </pre>
 407 <p>
 408       Returns the next representable floating point number after <span class="emphasis"><em>x</em></span>
 409       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>.
 410     </p>
 411 <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>
 412 <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>
 413 <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>
 414 </pre>
 415 <p>
 416       As <code class="computeroutput"><span class="identifier">nextafter</span></code>, but with <span class="emphasis"><em>y</em></span>
 417       always expressed as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
 418     </p>
 419 <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>
 420 <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>
 421 <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>
 422 </pre>
 423 <p>
 424       Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer: equivalent
 425       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>
 426     </p>
 427 <p>
 428       See also <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> for the full
 429       template (header only) version of this function.
 430     </p>
 431 <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>
 432 <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>
 433 <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>
 434 </pre>
 435 <p>
 436       Returns the gamma function of <span class="emphasis"><em>x</em></span>:
 437     </p>
 438 <p>
 439       <span class="inlinemediaobject"><img src="../../equations/gamm1.svg"></span>
 440     </p>
 441 <p>
 442       See also <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a> for the
 443       full template (header only) version of this function.
 444     </p>
 445 <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>
 446 <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>
 447 <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>
 448 </pre>
 449 <p>
 450       Returns <span class="emphasis"><em>x</em></span> truncated to the nearest integer.
 451     </p>
 452 <p>
 453       See also <a class="link" href="rounding/trunc.html" title="Truncation Functions">trunc</a> for the full
 454       template (header only) version of this function.
 455     </p>
 456 <p>
 457       See also <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1124.pdf" target="_top">C99
 458       ISO Standard</a>
 459     </p>
 460 </div>
 461 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 462 <td align="left"></td>
 463 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 464       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 465       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 466       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 467         Distributed under the Boost Software License, Version 1.0. (See accompanying
 468         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>)
 469       </p>
 470 </div></td>
 471 </tr></table>
 472 <hr>
 473 <div class="spirit-nav">
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