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    27. 

  27. <a name="math_toolkit.c99"></a><a class="link" href="c99.html" title="C99 C Functions">C99 C Functions</a>
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  28. </h2></div></div></div>
    29. 

  29. <h5>
    30. 

  30. <a name="math_toolkit.c99.h0"></a>
    31. 

  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. 

  32.       C99 Functions</a>
    33. 

  33.     </h5>
    34. 

  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. 

  35. 

  36. <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
    37. 

  37. <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
    38. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  118. 

  119. <span class="special">}}}}</span> <span class="comment">// namespaces</span>
    120. 

  120. </pre>
    121. 

  121. <p>
    122. 

  122.       In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
    123. 

  123.       versions of the above functions are provided, so that calling the function
    124. 

  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. 

  125.       <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
    126. 

  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. 

  127.       type calculation rules</em></span></a>.
    128. 

  128.     </p>
    129. 

  129. <p>
    130. 

  130.       For example:
    131. 

  131.     </p>
    132. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  138. </pre>
    139. 

  139. <h5>
    140. 

  140. <a name="math_toolkit.c99.h1"></a>
    141. 

  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. 

  142.       Reference</a>
    143. 

  143.     </h5>
    144. 

  144. <p>
    145. 

  145.       More detailed descriptions of these functions are available in the C99 standard.
    146. 

  146.     </p>
    147. 

  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. 

  148. <span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
    149. 

  149. </pre>
    150. 

  150. <p>
    151. 

  151.       In this implementation <code class="computeroutput"><span class="identifier">float_t</span></code>
    152. 

  152.       is the same as type <code class="computeroutput"><span class="keyword">float</span></code>, and
    153. 

  153.       <code class="computeroutput"><span class="identifier">double_t</span></code> the same as type
    154. 

  154.       <code class="computeroutput"><span class="keyword">double</span></code> unless the preprocessor
    155. 

  155.       symbol FLT_EVAL_METHOD is defined, in which case these are set as follows:
    156. 

  156.     </p>
    157. 

  157. <div class="informaltable"><table class="table">
    158. 

  158. <colgroup>
    159. 

  159. <col>
    160. 

  160. <col>
    161. 

  161. <col>
    162. 

  162. </colgroup>
    163. 

  163. <thead><tr>
    164. 

  164. <th>
    165. 

  165.               <p>
    166. 

  166.                 FLT_EVAL_METHOD
    167. 

  167.               </p>
    168. 

  168.             </th>
    169. 

  169. <th>
    170. 

  170.               <p>
    171. 

  171.                 float_t
    172. 

  172.               </p>
    173. 

  173.             </th>
    174. 

  174. <th>
    175. 

  175.               <p>
    176. 

  176.                 double_t
    177. 

  177.               </p>
    178. 

  178.             </th>
    179. 

  179. </tr></thead>
    180. 

  180. <tbody>
    181. 

  181. <tr>
    182. 

  182. <td>
    183. 

  183.               <p>
    184. 

  184.                 0
    185. 

  185.               </p>
    186. 

  186.             </td>
    187. 

  187. <td>
    188. 

  188.               <p>
    189. 

  189.                 float
    190. 

  190.               </p>
    191. 

  191.             </td>
    192. 

  192. <td>
    193. 

  193.               <p>
    194. 

  194.                 double
    195. 

  195.               </p>
    196. 

  196.             </td>
    197. 

  197. </tr>
    198. 

  198. <tr>
    199. 

  199. <td>
    200. 

  200.               <p>
    201. 

  201.                 1
    202. 

  202.               </p>
    203. 

  203.             </td>
    204. 

  204. <td>
    205. 

  205.               <p>
    206. 

  206.                 double
    207. 

  207.               </p>
    208. 

  208.             </td>
    209. 

  209. <td>
    210. 

  210.               <p>
    211. 

  211.                 double
    212. 

  212.               </p>
    213. 

  213.             </td>
    214. 

  214. </tr>
    215. 

  215. <tr>
    216. 

  216. <td>
    217. 

  217.               <p>
    218. 

  218.                 2
    219. 

  219.               </p>
    220. 

  220.             </td>
    221. 

  221. <td>
    222. 

  222.               <p>
    223. 

  223.                 long double
    224. 

  224.               </p>
    225. 

  225.             </td>
    226. 

  226. <td>
    227. 

  227.               <p>
    228. 

  228.                 long double
    229. 

  229.               </p>
    230. 

  230.             </td>
    231. 

  231. </tr>
    232. 

  232. </tbody>
    233. 

  233. </table></div>
    234. 

  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. 

  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. 

  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. 

  237. </pre>
    238. 

  238. <p>
    239. 

  239.       Returns the inverse hyperbolic cosine of <span class="emphasis"><em>x</em></span>.
    240. 

  240.     </p>
    241. 

  241. <p>
    242. 

  242.       See also <a class="link" href="inv_hyper/acosh.html" title="acosh">acosh</a> for the
    243. 

  243.       full template (header only) version of this function.
    244. 

  244.     </p>
    245. 

  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. 

  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. 

  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. 

  248. </pre>
    249. 

  249. <p>
    250. 

  250.       Returns the inverse hyperbolic sine of <span class="emphasis"><em>x</em></span>.
    251. 

  251.     </p>
    252. 

  252. <p>
    253. 

  253.       See also <a class="link" href="inv_hyper/asinh.html" title="asinh">asinh</a> for the
    254. 

  254.       full template (header only) version of this function.
    255. 

  255.     </p>
    256. 

  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. 

  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. 

  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. 

  259. </pre>
    260. 

  260. <p>
    261. 

  261.       Returns the inverse hyperbolic tangent of <span class="emphasis"><em>x</em></span>.
    262. 

  262.     </p>
    263. 

  263. <p>
    264. 

  264.       See also <a class="link" href="inv_hyper/atanh.html" title="atanh">atanh</a> for the
    265. 

  265.       full template (header only) version of this function.
    266. 

  266.     </p>
    267. 

  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. 

  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. 

  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. 

  270. </pre>
    271. 

  271. <p>
    272. 

  272.       Returns the cubed root of <span class="emphasis"><em>x</em></span>.
    273. 

  273.     </p>
    274. 

  274. <p>
    275. 

  275.       See also <a class="link" href="powers/cbrt.html" title="cbrt">cbrt</a> for the full
    276. 

  276.       template (header only) version of this function.
    277. 

  277.     </p>
    278. 

  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. 

  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. 

  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. 

  281. </pre>
    282. 

  282. <p>
    283. 

  283.       Returns a value with the magnitude of <span class="emphasis"><em>x</em></span> and the sign of
    284. 

  284.       <span class="emphasis"><em>y</em></span>.
    285. 

  285.     </p>
    286. 

  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. 

  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. 

  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. 

  289. </pre>
    290. 

  290. <p>
    291. 

  291.       Returns the error function of <span class="emphasis"><em>x</em></span>:
    292. 

  292.     </p>
    293. 

  293. <div class="blockquote"><blockquote class="blockquote"><p>
    294. 

  294.         <span class="inlinemediaobject"><img src="../../equations/erf1.svg"></span>
    295. 

  295. 

  296.       </p></blockquote></div>
    297. 

  297. <p>
    298. 

  298.       See also <a class="link" href="sf_erf/error_function.html" title="Error Function erf and complement erfc">erf</a> for
    299. 

  299.       the full template (header only) version of this function.
    300. 

  300.     </p>
    301. 

  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. 

  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. 

  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. 

  304. </pre>
    305. 

  305. <p>
    306. 

  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. 

  307.       without the loss of precision implied by the subtraction.
    308. 

  308.     </p>
    309. 

  309. <p>
    310. 

  310.       See also <a class="link" href="sf_erf/error_function.html" title="Error Function erf and complement erfc">erfc</a> for
    311. 

  311.       the full template (header only) version of this function.
    312. 

  312.     </p>
    313. 

  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. 

  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. 

  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. 

  316. </pre>
    317. 

  317. <p>
    318. 

  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. 

  319.       without the loss of precision implied by the subtraction.
    320. 

  320.     </p>
    321. 

  321. <p>
    322. 

  322.       See also <a class="link" href="powers/expm1.html" title="expm1">expm1</a> for the full
    323. 

  323.       template (header only) version of this function.
    324. 

  324.     </p>
    325. 

  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. 

  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. 

  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. 

  328. </pre>
    329. 

  329. <p>
    330. 

  330.       Returns the larger (most positive) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
    331. 

  331.     </p>
    332. 

  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. 

  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. 

  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. 

  335. </pre>
    336. 

  336. <p>
    337. 

  337.       Returns the smaller (most negative) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
    338. 

  338.     </p>
    339. 

  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. 

  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. 

  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. 

  342. </pre>
    343. 

  343. <p>
    344. 

  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. 

  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. 

  346.       without the danger of numeric overflow implied by that formulation.
    347. 

  347.     </p>
    348. 

  348. <p>
    349. 

  349.       See also <a class="link" href="powers/hypot.html" title="hypot">hypot</a> for the full
    350. 

  350.       template (header only) version of this function.
    351. 

  351.     </p>
    352. 

  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. 

  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. 

  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. 

  355. </pre>
    356. 

  356. <p>
    357. 

  357.       Returns the log of the gamma function of <span class="emphasis"><em>x</em></span>.
    358. 

  358.     </p>
    359. 

  359. <div class="blockquote"><blockquote class="blockquote"><p>
    360. 

  360.         <span class="inlinemediaobject"><img src="../../equations/lgamm1.svg"></span>
    361. 

  361. 

  362.       </p></blockquote></div>
    363. 

  363. <p>
    364. 

  364.       See also <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> for the
    365. 

  365.       full template (header only) version of this function.
    366. 

  366.     </p>
    367. 

  367. <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>
    368. 

  368. <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>
    369. 

  369. <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>
    370. 

  370. </pre>
    371. 

  371. <p>
    372. 

  372.       Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
    373. 

  373.       a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code>:
    374. 

  374.       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>
    375. 

  375.     </p>
    376. 

  376. <p>
    377. 

  377.       See also <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> for the full
    378. 

  378.       template (header only) version of this function.
    379. 

  379.     </p>
    380. 

  380. <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>
    381. 

  381. <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>
    382. 

  382. <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>
    383. 

  383. </pre>
    384. 

  384. <p>
    385. 

  385.       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
    386. 

  386.       formulation.
    387. 

  387.     </p>
    388. 

  388. <p>
    389. 

  389.       See also <a class="link" href="powers/log1p.html" title="log1p">log1p</a> for the full
    390. 

  390.       template (header only) version of this function.
    391. 

  391.     </p>
    392. 

  392. <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>
    393. 

  393. <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>
    394. 

  394. <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>
    395. 

  395. </pre>
    396. 

  396. <p>
    397. 

  397.       Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer as
    398. 

  398.       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>
    399. 

  399.       <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
    400. 

  400.     </p>
    401. 

  401. <p>
    402. 

  402.       See also <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> for the full
    403. 

  403.       template (header only) version of this function.
    404. 

  404.     </p>
    405. 

  405. <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>
    406. 

  406. <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>
    407. 

  407. <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>
    408. 

  408. </pre>
    409. 

  409. <p>
    410. 

  410.       Returns the next representable floating point number after <span class="emphasis"><em>x</em></span>
    411. 

  411.       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>.
    412. 

  412.     </p>
    413. 

  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. 

  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. 

  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. 

  416. </pre>
    417. 

  417. <p>
    418. 

  418.       As <code class="computeroutput"><span class="identifier">nextafter</span></code>, but with <span class="emphasis"><em>y</em></span>
    419. 

  419.       always expressed as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
    420. 

  420.     </p>
    421. 

  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. 

  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. 

  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. 

  424. </pre>
    425. 

  425. <p>
    426. 

  426.       Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer: equivalent
    427. 

  427.       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. 

  428.     </p>
    429. 

  429. <p>
    430. 

  430.       See also <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> for the full
    431. 

  431.       template (header only) version of this function.
    432. 

  432.     </p>
    433. 

  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. 

  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. 

  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. 

  436. </pre>
    437. 

  437. <p>
    438. 

  438.       Returns the gamma function of <span class="emphasis"><em>x</em></span>:
    439. 

  439.     </p>
    440. 

  440. <div class="blockquote"><blockquote class="blockquote"><p>
    441. 

  441.         <span class="inlinemediaobject"><img src="../../equations/gamm1.svg"></span>
    442. 

  442. 

  443.       </p></blockquote></div>
    444. 

  444. <p>
    445. 

  445.       See also <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a> for the
    446. 

  446.       full template (header only) version of this function.
    447. 

  447.     </p>
    448. 

  448. <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>
    449. 

  449. <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>
    450. 

  450. <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>
    451. 

  451. </pre>
    452. 

  452. <p>
    453. 

  453.       Returns <span class="emphasis"><em>x</em></span> truncated to the nearest integer.
    454. 

  454.     </p>
    455. 

  455. <p>
    456. 

  456.       See also <a class="link" href="rounding/trunc.html" title="Truncation Functions">trunc</a> for the full
    457. 

  457.       template (header only) version of this function.
    458. 

  458.     </p>
    459. 

  459. <p>
    460. 

  460.       See also <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1124.pdf" target="_top">C99
    461. 

  461.       ISO Standard</a>
    462. 

  462.     </p>
    463. 

  463. </div>
    464. 

  464. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    465. 

  465. <td align="left"></td>
    466. 

  466. <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
    467. 

  467.       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
    468. 

  468.       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
    469. 

  469.       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
    470. 

  470.       Daryle Walker and Xiaogang Zhang<p>
    471. 

  471.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    472. 

  472.         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>)
    473. 

  473.       </p>
    474. 

  474. </div></td>
    475. 

  475. </tr></table>
    476. 

  476. <hr>
    477. 

  477. <div class="spirit-nav">
    478. 

  478. <a accesskey="p" href="main_tr1.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="tr1_ref.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
    479. 

  479. </div>
    480. 

  480. </body>
    481. 

  481. </html>
    482.