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  25 <div class="section math_toolkit_extern_c_c99">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.extern_c.c99"></a><a class="link" href="c99.html" title="C99 C Functions">C99 C Functions</a>
  28 </h3></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.extern_c.c99.h0"></a>
  31         <span><a name="math_toolkit.extern_c.c99.supported_c99_functions"></a></span><a class="link" href="c99.html#math_toolkit.extern_c.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>,
 125         <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
 126         <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
 127         arguments is supported, with the return type determined by the <a class="link" href="../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
 128         type calculation rules</em></span></a>.
 129       </p>
 130 <p>
 131         For example:
 132       </p>
 133 <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>
 134 <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>
 135 <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>
 136 <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>
 137 <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>
 138 <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>
 139 </pre>
 140 <h5>
 141 <a name="math_toolkit.extern_c.c99.h1"></a>
 142         <span><a name="math_toolkit.extern_c.c99.quick_reference"></a></span><a class="link" href="c99.html#math_toolkit.extern_c.c99.quick_reference">Quick
 143         Reference</a>
 144       </h5>
 145 <p>
 146         More detailed descriptions of these functions are available in the C99 standard.
 147       </p>
 148 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
 149 <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
 150 </pre>
 151 <p>
 152         In this implementation <code class="computeroutput"><span class="identifier">float_t</span></code>
 153         is the same as type <code class="computeroutput"><span class="keyword">float</span></code>, and
 154         <code class="computeroutput"><span class="identifier">double_t</span></code> the same as type
 155         <code class="computeroutput"><span class="keyword">double</span></code> unless the preprocessor
 156         symbol FLT_EVAL_METHOD is defined, in which case these are set as follows:
 157       </p>
 158 <div class="informaltable"><table class="table">
 159 <colgroup>
 160 <col>
 161 <col>
 162 <col>
 163 </colgroup>
 164 <thead><tr>
 165 <th>
 166                 <p>
 167                   FLT_EVAL_METHOD
 168                 </p>
 169               </th>
 170 <th>
 171                 <p>
 172                   float_t
 173                 </p>
 174               </th>
 175 <th>
 176                 <p>
 177                   double_t
 178                 </p>
 179               </th>
 180 </tr></thead>
 181 <tbody>
 182 <tr>
 183 <td>
 184                 <p>
 185                   0
 186                 </p>
 187               </td>
 188 <td>
 189                 <p>
 190                   float
 191                 </p>
 192               </td>
 193 <td>
 194                 <p>
 195                   double
 196                 </p>
 197               </td>
 198 </tr>
 199 <tr>
 200 <td>
 201                 <p>
 202                   1
 203                 </p>
 204               </td>
 205 <td>
 206                 <p>
 207                   double
 208                 </p>
 209               </td>
 210 <td>
 211                 <p>
 212                   double
 213                 </p>
 214               </td>
 215 </tr>
 216 <tr>
 217 <td>
 218                 <p>
 219                   2
 220                 </p>
 221               </td>
 222 <td>
 223                 <p>
 224                   long double
 225                 </p>
 226               </td>
 227 <td>
 228                 <p>
 229                   long double
 230                 </p>
 231               </td>
 232 </tr>
 233 </tbody>
 234 </table></div>
 235 <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>
 236 <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>
 237 <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>
 238 </pre>
 239 <p>
 240         Returns the inverse hyperbolic cosine of <span class="emphasis"><em>x</em></span>.
 241       </p>
 242 <p>
 243         See also <a class="link" href="../special/inv_hyper/acosh.html" title="acosh">acosh</a>
 244         for the full template (header only) version of this function.
 245       </p>
 246 <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>
 247 <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>
 248 <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>
 249 </pre>
 250 <p>
 251         Returns the inverse hyperbolic sine of <span class="emphasis"><em>x</em></span>.
 252       </p>
 253 <p>
 254         See also <a class="link" href="../special/inv_hyper/asinh.html" title="asinh">asinh</a>
 255         for the full template (header only) version of this function.
 256       </p>
 257 <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>
 258 <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>
 259 <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>
 260 </pre>
 261 <p>
 262         Returns the inverse hyperbolic tangent of <span class="emphasis"><em>x</em></span>.
 263       </p>
 264 <p>
 265         See also <a class="link" href="../special/inv_hyper/atanh.html" title="atanh">atanh</a>
 266         for the full template (header only) version of this function.
 267       </p>
 268 <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>
 269 <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>
 270 <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>
 271 </pre>
 272 <p>
 273         Returns the cubed root of <span class="emphasis"><em>x</em></span>.
 274       </p>
 275 <p>
 276         See also <a class="link" href="../special/powers/cbrt.html" title="cbrt">cbrt</a> for
 277         the full template (header only) version of this function.
 278       </p>
 279 <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>
 280 <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>
 281 <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>
 282 </pre>
 283 <p>
 284         Returns a value with the magnitude of <span class="emphasis"><em>x</em></span> and the sign
 285         of <span class="emphasis"><em>y</em></span>.
 286       </p>
 287 <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>
 288 <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>
 289 <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>
 290 </pre>
 291 <p>
 292         Returns the error function of <span class="emphasis"><em>x</em></span>:
 293       </p>
 294 <p>
 295         <span class="inlinemediaobject"><img src="../../../equations/erf1.png"></span>
 296       </p>
 297 <p>
 298         See also <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erf</a>
 299         for the full template (header only) version of this function.
 300       </p>
 301 <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>
 302 <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>
 303 <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>
 304 </pre>
 305 <p>
 306         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>
 307         without the loss of precision implied by the subtraction.
 308       </p>
 309 <p>
 310         See also <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erfc</a>
 311         for the full template (header only) version of this function.
 312       </p>
 313 <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>
 314 <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>
 315 <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>
 316 </pre>
 317 <p>
 318         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>
 319         without the loss of precision implied by the subtraction.
 320       </p>
 321 <p>
 322         See also <a class="link" href="../special/powers/expm1.html" title="expm1">expm1</a> for
 323         the full template (header only) version of this function.
 324       </p>
 325 <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>
 326 <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>
 327 <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>
 328 </pre>
 329 <p>
 330         Returns the larger (most positive) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
 331       </p>
 332 <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>
 333 <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>
 334 <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>
 335 </pre>
 336 <p>
 337         Returns the smaller (most negative) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
 338       </p>
 339 <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>
 340 <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>
 341 <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>
 342 </pre>
 343 <p>
 344         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>
 345         <span class="special">+</span> <span class="identifier">y</span><span class="special">*</span><span class="identifier">y</span><span class="special">)</span></code>
 346         without the danger of numeric overflow implied by that formulation.
 347       </p>
 348 <p>
 349         See also <a class="link" href="../special/powers/hypot.html" title="hypot">hypot</a> for
 350         the full template (header only) version of this function.
 351       </p>
 352 <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>
 353 <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>
 354 <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>
 355 </pre>
 356 <p>
 357         Returns the log of the gamma function of <span class="emphasis"><em>x</em></span>.
 358       </p>
 359 <p>
 360         <span class="inlinemediaobject"><img src="../../../equations/lgamm1.png"></span>
 361       </p>
 362 <p>
 363         See also <a class="link" href="../special/sf_gamma/lgamma.html" title="Log Gamma">lgamma</a>
 364         for the full template (header only) version of this function.
 365       </p>
 366 <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>
 367 <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>
 368 <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>
 369 </pre>
 370 <p>
 371         Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
 372         a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code>:
 373         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>
 374       </p>
 375 <p>
 376         See also <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> for
 377         the full template (header only) version of this function.
 378       </p>
 379 <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>
 380 <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>
 381 <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>
 382 </pre>
 383 <p>
 384         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
 385         that formulation.
 386       </p>
 387 <p>
 388         See also <a class="link" href="../special/powers/log1p.html" title="log1p">log1p</a> for
 389         the full template (header only) version of this function.
 390       </p>
 391 <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>
 392 <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>
 393 <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>
 394 </pre>
 395 <p>
 396         Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
 397         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>
 398       </p>
 399 <p>
 400         See also <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> for
 401         the full 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
 410         <code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
 411         <span class="identifier">y</span></code>.
 412       </p>
 413 <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>
 414 <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>
 415 <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>
 416 </pre>
 417 <p>
 418         As <code class="computeroutput"><span class="identifier">nextafter</span></code>, but with <span class="emphasis"><em>y</em></span>
 419         always expressed as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
 420       </p>
 421 <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>
 422 <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>
 423 <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>
 424 </pre>
 425 <p>
 426         Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer:
 427         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>
 428       </p>
 429 <p>
 430         See also <a class="link" href="../utils/rounding/round.html" title="Rounding Functions">round</a> for
 431         the full template (header only) version of this function.
 432       </p>
 433 <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>
 434 <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>
 435 <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>
 436 </pre>
 437 <p>
 438         Returns the gamma function of <span class="emphasis"><em>x</em></span>:
 439       </p>
 440 <p>
 441         <span class="inlinemediaobject"><img src="../../../equations/gamm1.png"></span>
 442       </p>
 443 <p>
 444         See also <a class="link" href="../special/sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 445         for the full template (header only) version of this function.
 446       </p>
 447 <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>
 448 <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>
 449 <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>
 450 </pre>
 451 <p>
 452         Returns <span class="emphasis"><em>x</em></span> truncated to the nearest integer.
 453       </p>
 454 <p>
 455         See also <a class="link" href="../utils/rounding/trunc.html" title="Truncation Functions">trunc</a> for
 456         the full template (header only) version of this function.
 457       </p>
 458 <p>
 459         See also <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1124.pdf" target="_top">C99
 460         ISO Standard</a>
 461       </p>
 462 </div>
 463 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 464 <td align="left"></td>
 465 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
 466       Lalande, Johan R&#229;de, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<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>)
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