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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> <meta http-equiv="X-UA-Compatible" content="IE=9"/> <meta name="generator" content="Doxygen 1.8.14"/> <meta name="viewport" content="width=device-width, initial-scale=1"/> <title>Ruby: math.c Source File</title> <link href="../../tabs.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="../../jquery.js"></script> <script type="text/javascript" src="../../dynsections.js"></script> <link href="../../doxygen.css" rel="stylesheet" type="text/css" /> </head> <body> <div id="top"><!-- do not remove this div, it is closed by doxygen! --> <div id="titlearea"> <table cellspacing="0" cellpadding="0"> <tbody> <tr style="height: 56px;"> <td id="projectalign" style="padding-left: 0.5em;"> <div id="projectname">Ruby  <span id="projectnumber">2.1.10p492(2016-04-01revision54464)</span> </div> </td> </tr> </tbody> </table> </div> <!-- end header part --> <!-- Generated by Doxygen 1.8.14 --> <script type="text/javascript" src="../../menudata.js"></script> <script type="text/javascript" src="../../menu.js"></script> <script type="text/javascript"> /* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */ $(function() { initMenu('../../',false,false,'search.php','Search'); }); /* @license-end */</script> <div id="main-nav"></div> </div><!-- top --> <div class="header"> <div class="headertitle"> <div class="title">math.c</div> </div> </div><!--header--> <div class="contents"> <a href="../../d6/da3/math_8c.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/**********************************************************************</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"></span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> math.c -</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"></span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> $Author: nobu $</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> created at: Tue Jan 25 14:12:56 JST 1994</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"></span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Copyright (C) 1993-2007 Yukihiro Matsumoto</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"></span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">**********************************************************************/</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include "<a class="code" href="../../de/de6/ruby_2ruby_8h.html">ruby/ruby.h</a>"</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include "<a class="code" href="../../db/dde/internal_8h.html">internal.h</a>"</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include <float.h></span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include <math.h></span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <errno.h></span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor"> !defined(signbit)</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keyword">extern</span> <span class="keywordtype">int</span> <a class="code" href="../../d3/d90/missing_8h.html#a67a4a1547ffbaeabfa58b9773d5bc9bc">signbit</a>(<span class="keywordtype">double</span>);</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div><div class="line"><a name="l00023"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a02d562fc66e90d37c0ed571aaaf21f91"> 23</a></span> <span class="preprocessor">#define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM)</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be"> 25</a></span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> <a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>;</div><div class="line"><a name="l00026"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#afa48011feed589b977764fa06a9bfa80"> 26</a></span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> <a class="code" href="../../d6/da3/math_8c.html#afa48011feed589b977764fa06a9bfa80">rb_eMathDomainError</a>;</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div><div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff"> 28</a></span> <span class="preprocessor">#define Need_Float(x) do {if (!RB_TYPE_P(x, T_FLOAT)) {(x) = rb_to_float(x);}} while(0)</span></div><div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a8cabf161e2f357d85d4492baffeccb09"> 29</a></span> <span class="preprocessor">#define Need_Float2(x,y) do {\</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor"> Need_Float(x);\</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor"> Need_Float(y);\</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">} while (0)</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c"> 34</a></span> <span class="preprocessor">#define domain_error(msg) \</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor"> rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg)</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">/*</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> * Math.atan2(y, x) -> Float</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> *</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> * Computes the arc tangent given +y+ and +x+.</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> * Returns a Float in the range -PI..PI.</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"> *</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment"> *</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment"> * Codomain: [-PI, PI]</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"> *</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> * Math.atan2(-0.0, -1.0) #=> -3.141592653589793</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> * Math.atan2(-1.0, -1.0) #=> -2.356194490192345</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"> * Math.atan2(-1.0, 0.0) #=> -1.5707963267948966</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> * Math.atan2(-1.0, 1.0) #=> -0.7853981633974483</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"> * Math.atan2(-0.0, 1.0) #=> -0.0</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> * Math.atan2(0.0, 1.0) #=> 0.0</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"> * Math.atan2(1.0, 1.0) #=> 0.7853981633974483</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> * Math.atan2(1.0, 0.0) #=> 1.5707963267948966</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"> * Math.atan2(1.0, -1.0) #=> 2.356194490192345</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> * Math.atan2(0.0, -1.0) #=> 3.141592653589793</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"> *</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> */</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a5356b837d80de8e96dcfa87034987935"> 62</a></span> <a class="code" href="../../d6/da3/math_8c.html#a5356b837d80de8e96dcfa87034987935">math_atan2</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> y, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> {</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="preprocessor">#ifndef M_PI</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="preprocessor"># define M_PI 3.14159265358979323846</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordtype">double</span> dx, dy;</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <a class="code" href="../../d6/da3/math_8c.html#a8cabf161e2f357d85d4492baffeccb09">Need_Float2</a>(y, x);</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  dx = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  dy = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(y);</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">if</span> (dx == 0.0 && dy == 0.0) {</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordflow">if</span> (!<a class="code" href="../../d3/d90/missing_8h.html#a67a4a1547ffbaeabfa58b9773d5bc9bc">signbit</a>(dx))</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(dy);</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">if</span> (!<a class="code" href="../../d3/d90/missing_8h.html#a67a4a1547ffbaeabfa58b9773d5bc9bc">signbit</a>(dy))</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d6/da3/math_8c.html#ae71449b1cc6e6250b91f539153a7a0d3">M_PI</a>);</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(-<a class="code" href="../../d6/da3/math_8c.html#ae71449b1cc6e6250b91f539153a7a0d3">M_PI</a>);</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d3/d90/missing_8h.html#ae7a5ae88899707625ed6ab2ec7045583">isinf</a>(dx) && <a class="code" href="../../d3/d90/missing_8h.html#ae7a5ae88899707625ed6ab2ec7045583">isinf</a>(dy)) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"atan2"</span>);</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(atan2(dy, dx));</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> }</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">/*</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> * Math.cos(x) -> Float</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> *</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> * Computes the cosine of +x+ (expressed in radians).</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> * Returns a Float in the range -1.0..1.0.</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"> *</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> *</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> * Codomain: [-1, 1]</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"> *</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> * Math.cos(Math::PI) #=> -1.0</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> *</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> */</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#afb5fcc604398e4ccc2de7c1559057af8"> 99</a></span> <a class="code" href="../../d6/da3/math_8c.html#afb5fcc604398e4ccc2de7c1559057af8">math_cos</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> {</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(cos(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> }</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment">/*</span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"> * Math.sin(x) -> Float</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"> *</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"> * Computes the sine of +x+ (expressed in radians).</span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"> * Returns a Float in the range -1.0..1.0.</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"> *</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"> *</span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> * Codomain: [-1, 1]</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> *</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> * Math.sin(Math::PI/2) #=> 1.0</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> *</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> */</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> </div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a16d50286debaa6bb7d9bbaa40590392e"> 121</a></span> <a class="code" href="../../d6/da3/math_8c.html#a16d50286debaa6bb7d9bbaa40590392e">math_sin</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span> {</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(sin(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span> }</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> </div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">/*</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> * Math.tan(x) -> Float</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> *</span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> * Computes the tangent of +x+ (expressed in radians).</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> *</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> *</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> *</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> * Math.tan(0) #=> 0.0</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> *</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> */</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> </div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#abd660936cc59e94c26e492c2181b73df"> 143</a></span> <a class="code" href="../../d6/da3/math_8c.html#abd660936cc59e94c26e492c2181b73df">math_tan</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> {</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(tan(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> }</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> </div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">/*</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> * Math.acos(x) -> Float</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> *</span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> * Computes the arc cosine of +x+. Returns 0..PI.</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"> *</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> * Domain: [-1, 1]</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> *</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> * Codomain: [0, PI]</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> *</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> * Math.acos(0) == Math::PI/2 #=> true</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> *</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> */</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> </div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00164"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ac40c99395caa4f5562f98b381b51c390"> 164</a></span> <a class="code" href="../../d6/da3/math_8c.html#ac40c99395caa4f5562f98b381b51c390">math_acos</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span> {</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < -1.0 || 1.0 < <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"acos"</span>);</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  d = acos(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> }</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">/*</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"> * Math.asin(x) -> Float</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> *</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"> * Computes the arc sine of +x+. Returns -PI/2..PI/2.</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"> *</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"> * Domain: [-1, -1]</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> *</span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> * Codomain: [-PI/2, PI/2]</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment"> *</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"> * Math.asin(1) == Math::PI/2 #=> true</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment"> */</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span> </div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00190"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a23509ad0c21d42f95a16c41845322aab"> 190</a></span> <a class="code" href="../../d6/da3/math_8c.html#a23509ad0c21d42f95a16c41845322aab">math_asin</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> {</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < -1.0 || 1.0 < <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"asin"</span>);</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  d = asin(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> }</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> </div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment">/*</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"> * Math.atan(x) -> Float</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> *</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> * Computes the arc tangent of +x+. Returns -PI/2..PI/2.</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment"> *</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"> *</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> * Codomain: (-PI/2, PI/2)</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"> *</span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment"> * Math.atan(0) #=> 0.0</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment"> */</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ace875924c28bd439afb8739e8c91278b"> 216</a></span> <a class="code" href="../../d6/da3/math_8c.html#ace875924c28bd439afb8739e8c91278b">math_atan</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> {</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(atan(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> }</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="preprocessor">#ifndef HAVE_COSH</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="keywordtype">double</span></div><div class="line"><a name="l00224"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a3795d3c1f1d30819be56da4e4d67f64b"> 224</a></span> <a class="code" href="../../d6/da3/math_8c.html#a3795d3c1f1d30819be56da4e4d67f64b">cosh</a>(<span class="keywordtype">double</span> x)</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span> {</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">return</span> (exp(x) + exp(-x)) / 2;</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> }</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment">/*</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment"> * Math.cosh(x) -> Float</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment"> *</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"> * Computes the hyperbolic cosine of +x+ (expressed in radians).</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"> *</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> *</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment"> * Codomain: [1, INFINITY)</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment"> *</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment"> * Math.cosh(0) #=> 1.0</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"> *</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment"> */</span></div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00245"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#afefc2a4c319791dd73f9157f682c276b"> 245</a></span> <a class="code" href="../../d6/da3/math_8c.html#afefc2a4c319791dd73f9157f682c276b">math_cosh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span> {</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d6/da3/math_8c.html#a3795d3c1f1d30819be56da4e4d67f64b">cosh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> }</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="preprocessor">#ifndef HAVE_SINH</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="keywordtype">double</span></div><div class="line"><a name="l00253"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a862012e970c977c482507064e2793b45"> 253</a></span> <a class="code" href="../../d6/da3/math_8c.html#a862012e970c977c482507064e2793b45">sinh</a>(<span class="keywordtype">double</span> x)</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> {</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">return</span> (exp(x) - exp(-x)) / 2;</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> }</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment">/*</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment"> * Math.sinh(x) -> Float</span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment"> *</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment"> * Computes the hyperbolic sine of +x+ (expressed in radians).</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment"> *</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment"> *</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment"> *</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"> * Math.sinh(0) #=> 0.0</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment"> *</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"> */</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> </div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00274"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ab326f3f4766a48575290a40fe8bf3f42"> 274</a></span> <a class="code" href="../../d6/da3/math_8c.html#ab326f3f4766a48575290a40fe8bf3f42">math_sinh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> {</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d6/da3/math_8c.html#a862012e970c977c482507064e2793b45">sinh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> }</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span> </div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="preprocessor">#ifndef HAVE_TANH</span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="keywordtype">double</span></div><div class="line"><a name="l00282"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#af85bcf153d7ae805733927f12329dac1"> 282</a></span> <a class="code" href="../../d6/da3/math_8c.html#af85bcf153d7ae805733927f12329dac1">tanh</a>(<span class="keywordtype">double</span> x)</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> {</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">return</span> <a class="code" href="../../d6/da3/math_8c.html#a862012e970c977c482507064e2793b45">sinh</a>(x) / <a class="code" href="../../d6/da3/math_8c.html#a3795d3c1f1d30819be56da4e4d67f64b">cosh</a>(x);</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> }</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">/*</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment"> * Math.tanh(x) -> Float</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment"> *</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment"> * Computes the hyperbolic tangent of +x+ (expressed in radians).</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment"> *</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment"> *</span></div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment"> * Codomain: (-1, 1)</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment"> *</span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment"> * Math.tanh(0) #=> 0.0</span></div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"> *</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"> */</span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00303"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#adfabc64c79f8be8d07b2cd744133af76"> 303</a></span> <a class="code" href="../../d6/da3/math_8c.html#adfabc64c79f8be8d07b2cd744133af76">math_tanh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span> {</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d6/da3/math_8c.html#af85bcf153d7ae805733927f12329dac1">tanh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> }</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> </div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment">/*</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment"> * Math.acosh(x) -> Float</span></div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment"> *</span></div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment"> * Computes the inverse hyperbolic cosine of +x+.</span></div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment"> *</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="comment"> * Domain: [1, INFINITY)</span></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="comment"> *</span></div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="comment"> * Codomain: [0, INFINITY)</span></div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="comment"> *</span></div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment"> * Math.acosh(1) #=> 0.0</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="comment"> *</span></div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="comment"> */</span></div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span> </div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00324"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#af6d250959ee5fbf65b4d19d827a3db78"> 324</a></span> <a class="code" href="../../d6/da3/math_8c.html#af6d250959ee5fbf65b4d19d827a3db78">math_acosh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span> {</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < 1.0) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"acosh"</span>);</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  d = <a class="code" href="../../d3/d90/missing_8h.html#adced3433618a2f01f68b7fb60bb9d95d">acosh</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span> }</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="comment">/*</span></div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="comment"> * Math.asinh(x) -> Float</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="comment"> *</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="comment"> * Computes the inverse hyperbolic sine of +x+.</span></div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="comment"> *</span></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="comment"> *</span></div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment"> *</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment"> * Math.asinh(1) #=> 0.881373587019543</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment"> *</span></div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment"> */</span></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00351"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a7ee8ba235b99f8b19e99e4c4a04f0dcc"> 351</a></span> <a class="code" href="../../d6/da3/math_8c.html#a7ee8ba235b99f8b19e99e4c4a04f0dcc">math_asinh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span> {</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d3/d90/missing_8h.html#a6fc70ff722c0d4ee5542b29f374dca50">asinh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span> }</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="comment">/*</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span> <span class="comment"> * Math.atanh(x) -> Float</span></div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="comment"> *</span></div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment"> * Computes the inverse hyperbolic tangent of +x+.</span></div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment"> *</span></div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment"> * Domain: (-1, 1)</span></div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment"> *</span></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment"> *</span></div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment"> * Math.atanh(1) #=> Infinity</span></div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="comment"> *</span></div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="comment"> */</span></div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span> </div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00372"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#af479bb3e458d54f9b0b89a1d585926ff"> 372</a></span> <a class="code" href="../../d6/da3/math_8c.html#af479bb3e458d54f9b0b89a1d585926ff">math_atanh</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span> {</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span> </div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < -1.0 || +1.0 < <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"atanh"</span>);</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="comment">/* check for pole error */</span></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> == -1.0) <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(-<a class="code" href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a>);</div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> == +1.0) <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(+<a class="code" href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a>);</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  d = <a class="code" href="../../d3/d90/missing_8h.html#a3aaf65bc2e95b04a6c8ee60ed785b750">atanh</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> }</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span> </div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="comment">/*</span></div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="comment"> * Math.exp(x) -> Float</span></div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="comment"> *</span></div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="comment"> * Returns e**x.</span></div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="comment"> *</span></div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment"> *</span></div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="comment"> * Codomain: (0, INFINITY)</span></div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment"> *</span></div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="comment"> * Math.exp(0) #=> 1.0</span></div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment"> * Math.exp(1) #=> 2.718281828459045</span></div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment"> * Math.exp(1.5) #=> 4.4816890703380645</span></div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment"> *</span></div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment"> */</span></div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span> </div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00404"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a1bacd682f5d7e0277df28b27d0abb299"> 404</a></span> <a class="code" href="../../d6/da3/math_8c.html#a1bacd682f5d7e0277df28b27d0abb299">math_exp</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span> {</div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(exp(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span> }</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span> </div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="preprocessor">#if defined __CYGWIN__</span></div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="preprocessor"># include <cygwin/version.h></span></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="preprocessor"># if CYGWIN_VERSION_DLL_MAJOR < 1005</span></div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="preprocessor"># define nan(x) nan()</span></div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="preprocessor"># endif</span></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="preprocessor"># define log(x) ((x) < 0.0 ? nan("") : log(x))</span></div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="preprocessor"># define log10(x) ((x) < 0.0 ? nan("") : log10(x))</span></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span> </div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="comment">/*</span></div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment"> * Math.log(x) -> Float</span></div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment"> * Math.log(x, base) -> Float</span></div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="comment"> *</span></div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment"> * Returns the logarithm of +x+.</span></div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"> * If additional second argument is given, it will be the base</span></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment"> * of logarithm. Otherwise it is +e+ (for the natural logarithm).</span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="comment"> *</span></div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment"> * Domain: (0, INFINITY)</span></div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span> <span class="comment"> *</span></div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="comment"> *</span></div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span> <span class="comment"> * Math.log(0) #=> -Infinity</span></div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="comment"> * Math.log(1) #=> 0.0</span></div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="comment"> * Math.log(Math::E) #=> 1.0</span></div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="comment"> * Math.log(Math::E**3) #=> 3.0</span></div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="comment"> * Math.log(12, 3) #=> 2.2618595071429146</span></div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment"> *</span></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment"> */</span></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span> </div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00441"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a8bbeb8d9b2dafbaf3344044a52374088"> 441</a></span> <a class="code" href="../../d6/da3/math_8c.html#a8bbeb8d9b2dafbaf3344044a52374088">math_log</a>(<span class="keywordtype">int</span> <a class="code" href="../../df/d77/ruby_8c.html#ad1447518f4372828b8435ae82e48499e">argc</a>, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> *<a class="code" href="../../df/d77/ruby_8c.html#af2efa898e9eed6fe6715279cb1ec35b0">argv</a>)</div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span> {</div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x, base;</div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="keywordtype">size_t</span> numbits;</div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span> </div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gaa7bed88640f01bee619f85fda09d28d7">rb_scan_args</a>(<a class="code" href="../../df/d77/ruby_8c.html#ad1447518f4372828b8435ae82e48499e">argc</a>, <a class="code" href="../../df/d77/ruby_8c.html#af2efa898e9eed6fe6715279cb1ec35b0">argv</a>, <span class="stringliteral">"11"</span>, &x, &base);</div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span> </div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d6/da3/math_8c.html#a02d562fc66e90d37c0ed571aaaf21f91">RB_BIGNUM_TYPE_P</a>(x) && <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a484dc4460a3e6eb2958238ab4559190c">RBIGNUM_POSITIVE_P</a>(x) &&</div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <a class="code" href="../../d6/d27/numeric_8c.html#a539f2dd258b96fac8f4dc9bc139d75c9">DBL_MAX_EXP</a> <= (numbits = <a class="code" href="../../d1/dcc/bignum_8c.html#a4d13f72afe245927b1eea45acde5c842">rb_absint_numwords</a>(x, 1, <a class="code" href="../../d4/db0/__sdbm_8c.html#a070d2ce7b6bb7e5c05602aa8c308d0c4">NULL</a>))) {</div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  numbits -= <a class="code" href="../../d7/deb/acosh_8c.html#aeb343417fe0051b641fc7921022c7b0d">DBL_MANT_DIG</a>;</div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  x = <a class="code" href="../../d1/dcc/bignum_8c.html#ad606505b6b476ddff0addf17454da732">rb_big_rshift</a>(x, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#af89e74d2dcf3eef15b29fa6015984af3">SIZET2NUM</a>(numbits));</div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  }</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  numbits = 0;</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  }</div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span> </div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < 0.0) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"log"</span>);</div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="comment">/* check for pole error */</span></div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> == 0.0) <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(-<a class="code" href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a>);</div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  d = log(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">if</span> (numbits)</div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  d += numbits * log(2); <span class="comment">/* log(2**numbits) */</span></div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordflow">if</span> (<a class="code" href="../../df/d77/ruby_8c.html#ad1447518f4372828b8435ae82e48499e">argc</a> == 2) {</div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(base);</div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  d /= log(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(base));</div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  }</div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span> }</div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span> </div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="preprocessor">#ifndef log2</span></div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="preprocessor">#ifndef HAVE_LOG2</span></div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="keywordtype">double</span></div><div class="line"><a name="l00477"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a38bd88274dc5594b4826fd60c8054c8e"> 477</a></span> <a class="code" href="../../d6/da3/math_8c.html#a38bd88274dc5594b4826fd60c8054c8e">log2</a>(<span class="keywordtype">double</span> x)</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span> {</div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="keywordflow">return</span> log10(x)/log10(2.0);</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span> }</div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span> <span class="keyword">extern</span> <span class="keywordtype">double</span> <a class="code" href="../../d6/da3/math_8c.html#a38bd88274dc5594b4826fd60c8054c8e">log2</a>(<span class="keywordtype">double</span>);</div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span> </div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="comment">/*</span></div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span> <span class="comment"> * Math.log2(x) -> Float</span></div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span> <span class="comment"> *</span></div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span> <span class="comment"> * Returns the base 2 logarithm of +x+.</span></div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="comment"> *</span></div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="comment"> * Domain: (0, INFINITY)</span></div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span> <span class="comment"> *</span></div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="comment"> *</span></div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="comment"> * Math.log2(1) #=> 0.0</span></div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="comment"> * Math.log2(2) #=> 1.0</span></div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="comment"> * Math.log2(32768) #=> 15.0</span></div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="comment"> * Math.log2(65536) #=> 16.0</span></div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment"> *</span></div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="comment"> */</span></div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span> </div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00504"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a70452a1a0be21ce5061086f498109f3b"> 504</a></span> <a class="code" href="../../d6/da3/math_8c.html#a70452a1a0be21ce5061086f498109f3b">math_log2</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span> {</div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordtype">size_t</span> numbits;</div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span> </div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d6/da3/math_8c.html#a02d562fc66e90d37c0ed571aaaf21f91">RB_BIGNUM_TYPE_P</a>(x) && <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a484dc4460a3e6eb2958238ab4559190c">RBIGNUM_POSITIVE_P</a>(x) &&</div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <a class="code" href="../../d6/d27/numeric_8c.html#a539f2dd258b96fac8f4dc9bc139d75c9">DBL_MAX_EXP</a> <= (numbits = <a class="code" href="../../d1/dcc/bignum_8c.html#a4d13f72afe245927b1eea45acde5c842">rb_absint_numwords</a>(x, 1, <a class="code" href="../../d4/db0/__sdbm_8c.html#a070d2ce7b6bb7e5c05602aa8c308d0c4">NULL</a>))) {</div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  numbits -= <a class="code" href="../../d7/deb/acosh_8c.html#aeb343417fe0051b641fc7921022c7b0d">DBL_MANT_DIG</a>;</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  x = <a class="code" href="../../d1/dcc/bignum_8c.html#ad606505b6b476ddff0addf17454da732">rb_big_rshift</a>(x, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#af89e74d2dcf3eef15b29fa6015984af3">SIZET2NUM</a>(numbits));</div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  }</div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  numbits = 0;</div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  }</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span> </div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < 0.0) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"log2"</span>);</div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="comment">/* check for pole error */</span></div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> == 0.0) <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(-<a class="code" href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a>);</div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  d = <a class="code" href="../../d6/da3/math_8c.html#a38bd88274dc5594b4826fd60c8054c8e">log2</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  d += numbits;</div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span> }</div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span> </div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span> <span class="comment">/*</span></div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span> <span class="comment"> * Math.log10(x) -> Float</span></div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span> <span class="comment"> *</span></div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="comment"> * Returns the base 10 logarithm of +x+.</span></div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="comment"> *</span></div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="comment"> * Domain: (0, INFINITY)</span></div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="comment"> *</span></div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="comment"> * Codomain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="comment"> *</span></div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span> <span class="comment"> * Math.log10(1) #=> 0.0</span></div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="comment"> * Math.log10(10) #=> 1.0</span></div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="comment"> * Math.log10(10**100) #=> 100.0</span></div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="comment"> *</span></div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span> <span class="comment"> */</span></div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span> </div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00546"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#aa808294660f7bf83d4fe0516ace22b8d"> 546</a></span> <a class="code" href="../../d6/da3/math_8c.html#aa808294660f7bf83d4fe0516ace22b8d">math_log10</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span> {</div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="keywordtype">size_t</span> numbits;</div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span> </div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d6/da3/math_8c.html#a02d562fc66e90d37c0ed571aaaf21f91">RB_BIGNUM_TYPE_P</a>(x) && <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a484dc4460a3e6eb2958238ab4559190c">RBIGNUM_POSITIVE_P</a>(x) &&</div><div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <a class="code" href="../../d6/d27/numeric_8c.html#a539f2dd258b96fac8f4dc9bc139d75c9">DBL_MAX_EXP</a> <= (numbits = <a class="code" href="../../d1/dcc/bignum_8c.html#a4d13f72afe245927b1eea45acde5c842">rb_absint_numwords</a>(x, 1, <a class="code" href="../../d4/db0/__sdbm_8c.html#a070d2ce7b6bb7e5c05602aa8c308d0c4">NULL</a>))) {</div><div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  numbits -= <a class="code" href="../../d7/deb/acosh_8c.html#aeb343417fe0051b641fc7921022c7b0d">DBL_MANT_DIG</a>;</div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  x = <a class="code" href="../../d1/dcc/bignum_8c.html#ad606505b6b476ddff0addf17454da732">rb_big_rshift</a>(x, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#af89e74d2dcf3eef15b29fa6015984af3">SIZET2NUM</a>(numbits));</div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  }</div><div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  numbits = 0;</div><div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  }</div><div class="line"><a name="l00559"></a><span class="lineno"> 559</span> </div><div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < 0.0) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"log10"</span>);</div><div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="comment">/* check for pole error */</span></div><div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> == 0.0) <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(-<a class="code" href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a>);</div><div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  d = log10(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="keywordflow">if</span> (numbits)</div><div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  d += numbits * log10(2); <span class="comment">/* log10(2**numbits) */</span></div><div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00570"></a><span class="lineno"> 570</span> }</div><div class="line"><a name="l00571"></a><span class="lineno"> 571</span> </div><div class="line"><a name="l00572"></a><span class="lineno"> 572</span> <span class="comment">/*</span></div><div class="line"><a name="l00573"></a><span class="lineno"> 573</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="comment"> * Math.sqrt(x) -> Float</span></div><div class="line"><a name="l00575"></a><span class="lineno"> 575</span> <span class="comment"> *</span></div><div class="line"><a name="l00576"></a><span class="lineno"> 576</span> <span class="comment"> * Returns the non-negative square root of +x+.</span></div><div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="comment"> *</span></div><div class="line"><a name="l00578"></a><span class="lineno"> 578</span> <span class="comment"> * Domain: [0, INFINITY)</span></div><div class="line"><a name="l00579"></a><span class="lineno"> 579</span> <span class="comment"> *</span></div><div class="line"><a name="l00580"></a><span class="lineno"> 580</span> <span class="comment"> * Codomain:[0, INFINITY)</span></div><div class="line"><a name="l00581"></a><span class="lineno"> 581</span> <span class="comment"> *</span></div><div class="line"><a name="l00582"></a><span class="lineno"> 582</span> <span class="comment"> * 0.upto(10) {|x|</span></div><div class="line"><a name="l00583"></a><span class="lineno"> 583</span> <span class="comment"> * p [x, Math.sqrt(x), Math.sqrt(x)**2]</span></div><div class="line"><a name="l00584"></a><span class="lineno"> 584</span> <span class="comment"> * }</span></div><div class="line"><a name="l00585"></a><span class="lineno"> 585</span> <span class="comment"> * #=> [0, 0.0, 0.0]</span></div><div class="line"><a name="l00586"></a><span class="lineno"> 586</span> <span class="comment"> * # [1, 1.0, 1.0]</span></div><div class="line"><a name="l00587"></a><span class="lineno"> 587</span> <span class="comment"> * # [2, 1.4142135623731, 2.0]</span></div><div class="line"><a name="l00588"></a><span class="lineno"> 588</span> <span class="comment"> * # [3, 1.73205080756888, 3.0]</span></div><div class="line"><a name="l00589"></a><span class="lineno"> 589</span> <span class="comment"> * # [4, 2.0, 4.0]</span></div><div class="line"><a name="l00590"></a><span class="lineno"> 590</span> <span class="comment"> * # [5, 2.23606797749979, 5.0]</span></div><div class="line"><a name="l00591"></a><span class="lineno"> 591</span> <span class="comment"> * # [6, 2.44948974278318, 6.0]</span></div><div class="line"><a name="l00592"></a><span class="lineno"> 592</span> <span class="comment"> * # [7, 2.64575131106459, 7.0]</span></div><div class="line"><a name="l00593"></a><span class="lineno"> 593</span> <span class="comment"> * # [8, 2.82842712474619, 8.0]</span></div><div class="line"><a name="l00594"></a><span class="lineno"> 594</span> <span class="comment"> * # [9, 3.0, 9.0]</span></div><div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="comment"> * # [10, 3.16227766016838, 10.0]</span></div><div class="line"><a name="l00596"></a><span class="lineno"> 596</span> <span class="comment"> */</span></div><div class="line"><a name="l00597"></a><span class="lineno"> 597</span> </div><div class="line"><a name="l00598"></a><span class="lineno"> 598</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00599"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a8c16a4990c2069257664bba3ead2e1a5"> 599</a></span> <a class="code" href="../../d6/da3/math_8c.html#a8c16a4990c2069257664bba3ead2e1a5">math_sqrt</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00600"></a><span class="lineno"> 600</span> {</div><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00602"></a><span class="lineno"> 602</span> </div><div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> < 0.0) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"sqrt"</span>);</div><div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="keywordflow">if</span> (<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> == 0.0) <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(0.0);</div><div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  d = sqrt(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00610"></a><span class="lineno"> 610</span> }</div><div class="line"><a name="l00611"></a><span class="lineno"> 611</span> </div><div class="line"><a name="l00612"></a><span class="lineno"> 612</span> <span class="comment">/*</span></div><div class="line"><a name="l00613"></a><span class="lineno"> 613</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00614"></a><span class="lineno"> 614</span> <span class="comment"> * Math.cbrt(x) -> Float</span></div><div class="line"><a name="l00615"></a><span class="lineno"> 615</span> <span class="comment"> *</span></div><div class="line"><a name="l00616"></a><span class="lineno"> 616</span> <span class="comment"> * Returns the cube root of +x+.</span></div><div class="line"><a name="l00617"></a><span class="lineno"> 617</span> <span class="comment"> *</span></div><div class="line"><a name="l00618"></a><span class="lineno"> 618</span> <span class="comment"> * Domain: [0, INFINITY)</span></div><div class="line"><a name="l00619"></a><span class="lineno"> 619</span> <span class="comment"> *</span></div><div class="line"><a name="l00620"></a><span class="lineno"> 620</span> <span class="comment"> * Codomain:[0, INFINITY)</span></div><div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="comment"> *</span></div><div class="line"><a name="l00622"></a><span class="lineno"> 622</span> <span class="comment"> * -9.upto(9) {|x|</span></div><div class="line"><a name="l00623"></a><span class="lineno"> 623</span> <span class="comment"> * p [x, Math.cbrt(x), Math.cbrt(x)**3]</span></div><div class="line"><a name="l00624"></a><span class="lineno"> 624</span> <span class="comment"> * }</span></div><div class="line"><a name="l00625"></a><span class="lineno"> 625</span> <span class="comment"> * #=> [-9, -2.0800838230519, -9.0]</span></div><div class="line"><a name="l00626"></a><span class="lineno"> 626</span> <span class="comment"> * # [-8, -2.0, -8.0]</span></div><div class="line"><a name="l00627"></a><span class="lineno"> 627</span> <span class="comment"> * # [-7, -1.91293118277239, -7.0]</span></div><div class="line"><a name="l00628"></a><span class="lineno"> 628</span> <span class="comment"> * # [-6, -1.81712059283214, -6.0]</span></div><div class="line"><a name="l00629"></a><span class="lineno"> 629</span> <span class="comment"> * # [-5, -1.7099759466767, -5.0]</span></div><div class="line"><a name="l00630"></a><span class="lineno"> 630</span> <span class="comment"> * # [-4, -1.5874010519682, -4.0]</span></div><div class="line"><a name="l00631"></a><span class="lineno"> 631</span> <span class="comment"> * # [-3, -1.44224957030741, -3.0]</span></div><div class="line"><a name="l00632"></a><span class="lineno"> 632</span> <span class="comment"> * # [-2, -1.25992104989487, -2.0]</span></div><div class="line"><a name="l00633"></a><span class="lineno"> 633</span> <span class="comment"> * # [-1, -1.0, -1.0]</span></div><div class="line"><a name="l00634"></a><span class="lineno"> 634</span> <span class="comment"> * # [0, 0.0, 0.0]</span></div><div class="line"><a name="l00635"></a><span class="lineno"> 635</span> <span class="comment"> * # [1, 1.0, 1.0]</span></div><div class="line"><a name="l00636"></a><span class="lineno"> 636</span> <span class="comment"> * # [2, 1.25992104989487, 2.0]</span></div><div class="line"><a name="l00637"></a><span class="lineno"> 637</span> <span class="comment"> * # [3, 1.44224957030741, 3.0]</span></div><div class="line"><a name="l00638"></a><span class="lineno"> 638</span> <span class="comment"> * # [4, 1.5874010519682, 4.0]</span></div><div class="line"><a name="l00639"></a><span class="lineno"> 639</span> <span class="comment"> * # [5, 1.7099759466767, 5.0]</span></div><div class="line"><a name="l00640"></a><span class="lineno"> 640</span> <span class="comment"> * # [6, 1.81712059283214, 6.0]</span></div><div class="line"><a name="l00641"></a><span class="lineno"> 641</span> <span class="comment"> * # [7, 1.91293118277239, 7.0]</span></div><div class="line"><a name="l00642"></a><span class="lineno"> 642</span> <span class="comment"> * # [8, 2.0, 8.0]</span></div><div class="line"><a name="l00643"></a><span class="lineno"> 643</span> <span class="comment"> * # [9, 2.0800838230519, 9.0]</span></div><div class="line"><a name="l00644"></a><span class="lineno"> 644</span> <span class="comment"> *</span></div><div class="line"><a name="l00645"></a><span class="lineno"> 645</span> <span class="comment"> */</span></div><div class="line"><a name="l00646"></a><span class="lineno"> 646</span> </div><div class="line"><a name="l00647"></a><span class="lineno"> 647</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00648"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ac37636a9964f1b04d6ffaea2a75b474d"> 648</a></span> <a class="code" href="../../d6/da3/math_8c.html#ac37636a9964f1b04d6ffaea2a75b474d">math_cbrt</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00649"></a><span class="lineno"> 649</span> {</div><div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d3/d90/missing_8h.html#a06124ca6e0c98d8ffdf0698c8f24b249">cbrt</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00652"></a><span class="lineno"> 652</span> }</div><div class="line"><a name="l00653"></a><span class="lineno"> 653</span> </div><div class="line"><a name="l00654"></a><span class="lineno"> 654</span> <span class="comment">/*</span></div><div class="line"><a name="l00655"></a><span class="lineno"> 655</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00656"></a><span class="lineno"> 656</span> <span class="comment"> * Math.frexp(x) -> [fraction, exponent]</span></div><div class="line"><a name="l00657"></a><span class="lineno"> 657</span> <span class="comment"> *</span></div><div class="line"><a name="l00658"></a><span class="lineno"> 658</span> <span class="comment"> * Returns a two-element array containing the normalized fraction (a Float)</span></div><div class="line"><a name="l00659"></a><span class="lineno"> 659</span> <span class="comment"> * and exponent (a Fixnum) of +x+.</span></div><div class="line"><a name="l00660"></a><span class="lineno"> 660</span> <span class="comment"> *</span></div><div class="line"><a name="l00661"></a><span class="lineno"> 661</span> <span class="comment"> * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]</span></div><div class="line"><a name="l00662"></a><span class="lineno"> 662</span> <span class="comment"> * fraction * 2**exponent #=> 1234.0</span></div><div class="line"><a name="l00663"></a><span class="lineno"> 663</span> <span class="comment"> */</span></div><div class="line"><a name="l00664"></a><span class="lineno"> 664</span> </div><div class="line"><a name="l00665"></a><span class="lineno"> 665</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00666"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a7a76f8ba84835bdb5163db8d5b4ce0e5"> 666</a></span> <a class="code" href="../../d6/da3/math_8c.html#a7a76f8ba84835bdb5163db8d5b4ce0e5">math_frexp</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00667"></a><span class="lineno"> 667</span> {</div><div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordtype">double</span> d;</div><div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="keywordtype">int</span> exp;</div><div class="line"><a name="l00670"></a><span class="lineno"> 670</span> </div><div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00672"></a><span class="lineno"> 672</span> </div><div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  d = frexp(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x), &exp);</div><div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordflow">return</span> <a class="code" href="../../dc/dcc/array_8c.html#af3085ceab406e3f4f4b90f383c440d6a">rb_assoc_new</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d), <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a7bce65407b21f6812267e8d5426201f0">INT2NUM</a>(exp));</div><div class="line"><a name="l00675"></a><span class="lineno"> 675</span> }</div><div class="line"><a name="l00676"></a><span class="lineno"> 676</span> </div><div class="line"><a name="l00677"></a><span class="lineno"> 677</span> <span class="comment">/*</span></div><div class="line"><a name="l00678"></a><span class="lineno"> 678</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00679"></a><span class="lineno"> 679</span> <span class="comment"> * Math.ldexp(fraction, exponent) -> float</span></div><div class="line"><a name="l00680"></a><span class="lineno"> 680</span> <span class="comment"> *</span></div><div class="line"><a name="l00681"></a><span class="lineno"> 681</span> <span class="comment"> * Returns the value of +fraction+*(2**+exponent+).</span></div><div class="line"><a name="l00682"></a><span class="lineno"> 682</span> <span class="comment"> *</span></div><div class="line"><a name="l00683"></a><span class="lineno"> 683</span> <span class="comment"> * fraction, exponent = Math.frexp(1234)</span></div><div class="line"><a name="l00684"></a><span class="lineno"> 684</span> <span class="comment"> * Math.ldexp(fraction, exponent) #=> 1234.0</span></div><div class="line"><a name="l00685"></a><span class="lineno"> 685</span> <span class="comment"> */</span></div><div class="line"><a name="l00686"></a><span class="lineno"> 686</span> </div><div class="line"><a name="l00687"></a><span class="lineno"> 687</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00688"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ae5b3da9a522de33d1e5d3208014fbdbe"> 688</a></span> <a class="code" href="../../d6/da3/math_8c.html#ae5b3da9a522de33d1e5d3208014fbdbe">math_ldexp</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> n)</div><div class="line"><a name="l00689"></a><span class="lineno"> 689</span> {</div><div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(ldexp(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x), <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a877c38180d23c5447d976c70dda89d69">NUM2INT</a>(n)));</div><div class="line"><a name="l00692"></a><span class="lineno"> 692</span> }</div><div class="line"><a name="l00693"></a><span class="lineno"> 693</span> </div><div class="line"><a name="l00694"></a><span class="lineno"> 694</span> <span class="comment">/*</span></div><div class="line"><a name="l00695"></a><span class="lineno"> 695</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00696"></a><span class="lineno"> 696</span> <span class="comment"> * Math.hypot(x, y) -> Float</span></div><div class="line"><a name="l00697"></a><span class="lineno"> 697</span> <span class="comment"> *</span></div><div class="line"><a name="l00698"></a><span class="lineno"> 698</span> <span class="comment"> * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with</span></div><div class="line"><a name="l00699"></a><span class="lineno"> 699</span> <span class="comment"> * sides +x+ and +y+.</span></div><div class="line"><a name="l00700"></a><span class="lineno"> 700</span> <span class="comment"> *</span></div><div class="line"><a name="l00701"></a><span class="lineno"> 701</span> <span class="comment"> * Math.hypot(3, 4) #=> 5.0</span></div><div class="line"><a name="l00702"></a><span class="lineno"> 702</span> <span class="comment"> */</span></div><div class="line"><a name="l00703"></a><span class="lineno"> 703</span> </div><div class="line"><a name="l00704"></a><span class="lineno"> 704</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00705"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#add0ee9545be4cafd996adb0f385f37c8"> 705</a></span> <a class="code" href="../../d6/da3/math_8c.html#add0ee9545be4cafd996adb0f385f37c8">math_hypot</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> y)</div><div class="line"><a name="l00706"></a><span class="lineno"> 706</span> {</div><div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <a class="code" href="../../d6/da3/math_8c.html#a8cabf161e2f357d85d4492baffeccb09">Need_Float2</a>(x, y);</div><div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d3/d90/missing_8h.html#a7a16d2f097e52b6a343811f3014dc1ea">hypot</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x), <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(y)));</div><div class="line"><a name="l00709"></a><span class="lineno"> 709</span> }</div><div class="line"><a name="l00710"></a><span class="lineno"> 710</span> </div><div class="line"><a name="l00711"></a><span class="lineno"> 711</span> <span class="comment">/*</span></div><div class="line"><a name="l00712"></a><span class="lineno"> 712</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00713"></a><span class="lineno"> 713</span> <span class="comment"> * Math.erf(x) -> Float</span></div><div class="line"><a name="l00714"></a><span class="lineno"> 714</span> <span class="comment"> *</span></div><div class="line"><a name="l00715"></a><span class="lineno"> 715</span> <span class="comment"> * Calculates the error function of +x+.</span></div><div class="line"><a name="l00716"></a><span class="lineno"> 716</span> <span class="comment"> *</span></div><div class="line"><a name="l00717"></a><span class="lineno"> 717</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00718"></a><span class="lineno"> 718</span> <span class="comment"> *</span></div><div class="line"><a name="l00719"></a><span class="lineno"> 719</span> <span class="comment"> * Codomain: (-1, 1)</span></div><div class="line"><a name="l00720"></a><span class="lineno"> 720</span> <span class="comment"> *</span></div><div class="line"><a name="l00721"></a><span class="lineno"> 721</span> <span class="comment"> * Math.erf(0) #=> 0.0</span></div><div class="line"><a name="l00722"></a><span class="lineno"> 722</span> <span class="comment"> *</span></div><div class="line"><a name="l00723"></a><span class="lineno"> 723</span> <span class="comment"> */</span></div><div class="line"><a name="l00724"></a><span class="lineno"> 724</span> </div><div class="line"><a name="l00725"></a><span class="lineno"> 725</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00726"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#acbdd1532a592ce8f5aba7e6bd9cc0d3f"> 726</a></span> <a class="code" href="../../d6/da3/math_8c.html#acbdd1532a592ce8f5aba7e6bd9cc0d3f">math_erf</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00727"></a><span class="lineno"> 727</span> {</div><div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d3/d90/missing_8h.html#a3206afc394d28919ee875c60c436a949">erf</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00730"></a><span class="lineno"> 730</span> }</div><div class="line"><a name="l00731"></a><span class="lineno"> 731</span> </div><div class="line"><a name="l00732"></a><span class="lineno"> 732</span> <span class="comment">/*</span></div><div class="line"><a name="l00733"></a><span class="lineno"> 733</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00734"></a><span class="lineno"> 734</span> <span class="comment"> * Math.erfc(x) -> Float</span></div><div class="line"><a name="l00735"></a><span class="lineno"> 735</span> <span class="comment"> *</span></div><div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="comment"> * Calculates the complementary error function of x.</span></div><div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="comment"> *</span></div><div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="comment"> * Domain: (-INFINITY, INFINITY)</span></div><div class="line"><a name="l00739"></a><span class="lineno"> 739</span> <span class="comment"> *</span></div><div class="line"><a name="l00740"></a><span class="lineno"> 740</span> <span class="comment"> * Codomain: (0, 2)</span></div><div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="comment"> *</span></div><div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="comment"> * Math.erfc(0) #=> 1.0</span></div><div class="line"><a name="l00743"></a><span class="lineno"> 743</span> <span class="comment"> *</span></div><div class="line"><a name="l00744"></a><span class="lineno"> 744</span> <span class="comment"> */</span></div><div class="line"><a name="l00745"></a><span class="lineno"> 745</span> </div><div class="line"><a name="l00746"></a><span class="lineno"> 746</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00747"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a54b397857b1683d0413b5a17ff58b240"> 747</a></span> <a class="code" href="../../d6/da3/math_8c.html#a54b397857b1683d0413b5a17ff58b240">math_erfc</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00748"></a><span class="lineno"> 748</span> {</div><div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d3/d90/missing_8h.html#ab2ce4909e68033b22fd3de49a5e6e388">erfc</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x)));</div><div class="line"><a name="l00751"></a><span class="lineno"> 751</span> }</div><div class="line"><a name="l00752"></a><span class="lineno"> 752</span> </div><div class="line"><a name="l00753"></a><span class="lineno"> 753</span> <span class="comment">/*</span></div><div class="line"><a name="l00754"></a><span class="lineno"> 754</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00755"></a><span class="lineno"> 755</span> <span class="comment"> * Math.gamma(x) -> Float</span></div><div class="line"><a name="l00756"></a><span class="lineno"> 756</span> <span class="comment"> *</span></div><div class="line"><a name="l00757"></a><span class="lineno"> 757</span> <span class="comment"> * Calculates the gamma function of x.</span></div><div class="line"><a name="l00758"></a><span class="lineno"> 758</span> <span class="comment"> *</span></div><div class="line"><a name="l00759"></a><span class="lineno"> 759</span> <span class="comment"> * Note that gamma(n) is same as fact(n-1) for integer n > 0.</span></div><div class="line"><a name="l00760"></a><span class="lineno"> 760</span> <span class="comment"> * However gamma(n) returns float and can be an approximation.</span></div><div class="line"><a name="l00761"></a><span class="lineno"> 761</span> <span class="comment"> *</span></div><div class="line"><a name="l00762"></a><span class="lineno"> 762</span> <span class="comment"> * def fact(n) (1..n).inject(1) {|r,i| r*i } end</span></div><div class="line"><a name="l00763"></a><span class="lineno"> 763</span> <span class="comment"> * 1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }</span></div><div class="line"><a name="l00764"></a><span class="lineno"> 764</span> <span class="comment"> * #=> [1, 1.0, 1]</span></div><div class="line"><a name="l00765"></a><span class="lineno"> 765</span> <span class="comment"> * # [2, 1.0, 1]</span></div><div class="line"><a name="l00766"></a><span class="lineno"> 766</span> <span class="comment"> * # [3, 2.0, 2]</span></div><div class="line"><a name="l00767"></a><span class="lineno"> 767</span> <span class="comment"> * # [4, 6.0, 6]</span></div><div class="line"><a name="l00768"></a><span class="lineno"> 768</span> <span class="comment"> * # [5, 24.0, 24]</span></div><div class="line"><a name="l00769"></a><span class="lineno"> 769</span> <span class="comment"> * # [6, 120.0, 120]</span></div><div class="line"><a name="l00770"></a><span class="lineno"> 770</span> <span class="comment"> * # [7, 720.0, 720]</span></div><div class="line"><a name="l00771"></a><span class="lineno"> 771</span> <span class="comment"> * # [8, 5040.0, 5040]</span></div><div class="line"><a name="l00772"></a><span class="lineno"> 772</span> <span class="comment"> * # [9, 40320.0, 40320]</span></div><div class="line"><a name="l00773"></a><span class="lineno"> 773</span> <span class="comment"> * # [10, 362880.0, 362880]</span></div><div class="line"><a name="l00774"></a><span class="lineno"> 774</span> <span class="comment"> * # [11, 3628800.0, 3628800]</span></div><div class="line"><a name="l00775"></a><span class="lineno"> 775</span> <span class="comment"> * # [12, 39916800.0, 39916800]</span></div><div class="line"><a name="l00776"></a><span class="lineno"> 776</span> <span class="comment"> * # [13, 479001600.0, 479001600]</span></div><div class="line"><a name="l00777"></a><span class="lineno"> 777</span> <span class="comment"> * # [14, 6227020800.0, 6227020800]</span></div><div class="line"><a name="l00778"></a><span class="lineno"> 778</span> <span class="comment"> * # [15, 87178291200.0, 87178291200]</span></div><div class="line"><a name="l00779"></a><span class="lineno"> 779</span> <span class="comment"> * # [16, 1307674368000.0, 1307674368000]</span></div><div class="line"><a name="l00780"></a><span class="lineno"> 780</span> <span class="comment"> * # [17, 20922789888000.0, 20922789888000]</span></div><div class="line"><a name="l00781"></a><span class="lineno"> 781</span> <span class="comment"> * # [18, 355687428096000.0, 355687428096000]</span></div><div class="line"><a name="l00782"></a><span class="lineno"> 782</span> <span class="comment"> * # [19, 6.402373705728e+15, 6402373705728000]</span></div><div class="line"><a name="l00783"></a><span class="lineno"> 783</span> <span class="comment"> * # [20, 1.21645100408832e+17, 121645100408832000]</span></div><div class="line"><a name="l00784"></a><span class="lineno"> 784</span> <span class="comment"> * # [21, 2.43290200817664e+18, 2432902008176640000]</span></div><div class="line"><a name="l00785"></a><span class="lineno"> 785</span> <span class="comment"> * # [22, 5.109094217170944e+19, 51090942171709440000]</span></div><div class="line"><a name="l00786"></a><span class="lineno"> 786</span> <span class="comment"> * # [23, 1.1240007277776077e+21, 1124000727777607680000]</span></div><div class="line"><a name="l00787"></a><span class="lineno"> 787</span> <span class="comment"> * # [24, 2.5852016738885062e+22, 25852016738884976640000]</span></div><div class="line"><a name="l00788"></a><span class="lineno"> 788</span> <span class="comment"> * # [25, 6.204484017332391e+23, 620448401733239439360000]</span></div><div class="line"><a name="l00789"></a><span class="lineno"> 789</span> <span class="comment"> * # [26, 1.5511210043330954e+25, 15511210043330985984000000]</span></div><div class="line"><a name="l00790"></a><span class="lineno"> 790</span> <span class="comment"> *</span></div><div class="line"><a name="l00791"></a><span class="lineno"> 791</span> <span class="comment"> */</span></div><div class="line"><a name="l00792"></a><span class="lineno"> 792</span> </div><div class="line"><a name="l00793"></a><span class="lineno"> 793</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00794"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a52534f854e9b5876b237fe29edafb8cd"> 794</a></span> <a class="code" href="../../d6/da3/math_8c.html#a52534f854e9b5876b237fe29edafb8cd">math_gamma</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00795"></a><span class="lineno"> 795</span> {</div><div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> fact_table[] = {</div><div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <span class="comment">/* fact(0) */</span> 1.0,</div><div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  <span class="comment">/* fact(1) */</span> 1.0,</div><div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  <span class="comment">/* fact(2) */</span> 2.0,</div><div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  <span class="comment">/* fact(3) */</span> 6.0,</div><div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  <span class="comment">/* fact(4) */</span> 24.0,</div><div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  <span class="comment">/* fact(5) */</span> 120.0,</div><div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  <span class="comment">/* fact(6) */</span> 720.0,</div><div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  <span class="comment">/* fact(7) */</span> 5040.0,</div><div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  <span class="comment">/* fact(8) */</span> 40320.0,</div><div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  <span class="comment">/* fact(9) */</span> 362880.0,</div><div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  <span class="comment">/* fact(10) */</span> 3628800.0,</div><div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  <span class="comment">/* fact(11) */</span> 39916800.0,</div><div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  <span class="comment">/* fact(12) */</span> 479001600.0,</div><div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  <span class="comment">/* fact(13) */</span> 6227020800.0,</div><div class="line"><a name="l00811"></a><span class="lineno"> 811</span>  <span class="comment">/* fact(14) */</span> 87178291200.0,</div><div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  <span class="comment">/* fact(15) */</span> 1307674368000.0,</div><div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  <span class="comment">/* fact(16) */</span> 20922789888000.0,</div><div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  <span class="comment">/* fact(17) */</span> 355687428096000.0,</div><div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  <span class="comment">/* fact(18) */</span> 6402373705728000.0,</div><div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  <span class="comment">/* fact(19) */</span> 121645100408832000.0,</div><div class="line"><a name="l00817"></a><span class="lineno"> 817</span>  <span class="comment">/* fact(20) */</span> 2432902008176640000.0,</div><div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  <span class="comment">/* fact(21) */</span> 51090942171709440000.0,</div><div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  <span class="comment">/* fact(22) */</span> 1124000727777607680000.0,</div><div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  <span class="comment">/* fact(23)=25852016738884976640000 needs 56bit mantissa which is</span></div><div class="line"><a name="l00821"></a><span class="lineno"> 821</span> <span class="comment"> * impossible to represent exactly in IEEE 754 double which have</span></div><div class="line"><a name="l00822"></a><span class="lineno"> 822</span> <span class="comment"> * 53bit mantissa. */</span></div><div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  };</div><div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  <span class="keywordtype">double</span> intpart, fracpart;</div><div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d3/d90/missing_8h.html#ae7a5ae88899707625ed6ab2ec7045583">isinf</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>) && <a class="code" href="../../d3/d90/missing_8h.html#a67a4a1547ffbaeabfa58b9773d5bc9bc">signbit</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>)) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"gamma"</span>);</div><div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  fracpart = modf(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, &intpart);</div><div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  <span class="keywordflow">if</span> (fracpart == 0.0) {</div><div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  <span class="keywordflow">if</span> (intpart < 0) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"gamma"</span>);</div><div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  <span class="keywordflow">if</span> (0 < intpart &&</div><div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  intpart - 1 < (<span class="keywordtype">double</span>)<a class="code" href="../../d5/d97/etc_8c.html#a4ac8fee05a285361c33a2b0d9c2d555c">numberof</a>(fact_table)) {</div><div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(fact_table[(<span class="keywordtype">int</span>)intpart - 1]);</div><div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  }</div><div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  }</div><div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  d = <a class="code" href="../../d3/d90/missing_8h.html#a64f1679e2eb7ba3a8f9ffb3ffb252a3e">tgamma</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>);</div><div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00840"></a><span class="lineno"> 840</span> }</div><div class="line"><a name="l00841"></a><span class="lineno"> 841</span> </div><div class="line"><a name="l00842"></a><span class="lineno"> 842</span> <span class="comment">/*</span></div><div class="line"><a name="l00843"></a><span class="lineno"> 843</span> <span class="comment"> * call-seq:</span></div><div class="line"><a name="l00844"></a><span class="lineno"> 844</span> <span class="comment"> * Math.lgamma(x) -> [float, -1 or 1]</span></div><div class="line"><a name="l00845"></a><span class="lineno"> 845</span> <span class="comment"> *</span></div><div class="line"><a name="l00846"></a><span class="lineno"> 846</span> <span class="comment"> * Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+.</span></div><div class="line"><a name="l00847"></a><span class="lineno"> 847</span> <span class="comment"> *</span></div><div class="line"><a name="l00848"></a><span class="lineno"> 848</span> <span class="comment"> * Math.lgamma(x) is same as</span></div><div class="line"><a name="l00849"></a><span class="lineno"> 849</span> <span class="comment"> * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]</span></div><div class="line"><a name="l00850"></a><span class="lineno"> 850</span> <span class="comment"> * but avoid overflow by Math.gamma(x) for large x.</span></div><div class="line"><a name="l00851"></a><span class="lineno"> 851</span> <span class="comment"> *</span></div><div class="line"><a name="l00852"></a><span class="lineno"> 852</span> <span class="comment"> * Math.lgamma(0) #=> [Infinity, 1]</span></div><div class="line"><a name="l00853"></a><span class="lineno"> 853</span> <span class="comment"> *</span></div><div class="line"><a name="l00854"></a><span class="lineno"> 854</span> <span class="comment"> */</span></div><div class="line"><a name="l00855"></a><span class="lineno"> 855</span> </div><div class="line"><a name="l00856"></a><span class="lineno"> 856</span> <span class="keyword">static</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00857"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ad1b067d8013ceadb03dcb86594fd27c0"> 857</a></span> <a class="code" href="../../d6/da3/math_8c.html#ad1b067d8013ceadb03dcb86594fd27c0">math_lgamma</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> obj, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> x)</div><div class="line"><a name="l00858"></a><span class="lineno"> 858</span> {</div><div class="line"><a name="l00859"></a><span class="lineno"> 859</span>  <span class="keywordtype">double</span> <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, d;</div><div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  <span class="keywordtype">int</span> sign=1;</div><div class="line"><a name="l00861"></a><span class="lineno"> 861</span>  <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> v;</div><div class="line"><a name="l00862"></a><span class="lineno"> 862</span>  <a class="code" href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a>(x);</div><div class="line"><a name="l00863"></a><span class="lineno"> 863</span>  <a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a> = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a>(x);</div><div class="line"><a name="l00864"></a><span class="lineno"> 864</span>  <span class="comment">/* check for domain error */</span></div><div class="line"><a name="l00865"></a><span class="lineno"> 865</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d3/d90/missing_8h.html#ae7a5ae88899707625ed6ab2ec7045583">isinf</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>)) {</div><div class="line"><a name="l00866"></a><span class="lineno"> 866</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d3/d90/missing_8h.html#a67a4a1547ffbaeabfa58b9773d5bc9bc">signbit</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>)) <a class="code" href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a>(<span class="stringliteral">"lgamma"</span>);</div><div class="line"><a name="l00867"></a><span class="lineno"> 867</span>  <span class="keywordflow">return</span> <a class="code" href="../../dc/dcc/array_8c.html#af3085ceab406e3f4f4b90f383c440d6a">rb_assoc_new</a>(<a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a>), <a class="code" href="../../de/de6/ruby_2ruby_8h.html#ac55fae7f748afd3fc2533d0d7d06cf5a">INT2FIX</a>(1));</div><div class="line"><a name="l00868"></a><span class="lineno"> 868</span>  }</div><div class="line"><a name="l00869"></a><span class="lineno"> 869</span>  d = <a class="code" href="../../d3/d90/missing_8h.html#ae9eff89386f38b111e9c83a8106bd2f1">lgamma_r</a>(<a class="code" href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a>, &sign);</div><div class="line"><a name="l00870"></a><span class="lineno"> 870</span>  v = <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(d);</div><div class="line"><a name="l00871"></a><span class="lineno"> 871</span>  <span class="keywordflow">return</span> <a class="code" href="../../dc/dcc/array_8c.html#af3085ceab406e3f4f4b90f383c440d6a">rb_assoc_new</a>(v, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#ac55fae7f748afd3fc2533d0d7d06cf5a">INT2FIX</a>(sign));</div><div class="line"><a name="l00872"></a><span class="lineno"> 872</span> }</div><div class="line"><a name="l00873"></a><span class="lineno"> 873</span> </div><div class="line"><a name="l00874"></a><span class="lineno"> 874</span> </div><div class="line"><a name="l00875"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f"> 875</a></span> <span class="preprocessor">#define exp1(n) \</span></div><div class="line"><a name="l00876"></a><span class="lineno"> 876</span> <span class="preprocessor">VALUE \</span></div><div class="line"><a name="l00877"></a><span class="lineno"> 877</span> <span class="preprocessor">rb_math_##n(VALUE x)\</span></div><div class="line"><a name="l00878"></a><span class="lineno"> 878</span> <span class="preprocessor">{\</span></div><div class="line"><a name="l00879"></a><span class="lineno"> 879</span> <span class="preprocessor"> return math_##n(rb_mMath, x);\</span></div><div class="line"><a name="l00880"></a><span class="lineno"> 880</span> <span class="preprocessor">}</span></div><div class="line"><a name="l00881"></a><span class="lineno"> 881</span> </div><div class="line"><a name="l00882"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#acbc6f26bba8a2899bbc6fdec7597ed9b"> 882</a></span> <span class="preprocessor">#define exp2(n) \</span></div><div class="line"><a name="l00883"></a><span class="lineno"> 883</span> <span class="preprocessor">VALUE \</span></div><div class="line"><a name="l00884"></a><span class="lineno"> 884</span> <span class="preprocessor">rb_math_##n(VALUE x, VALUE y)\</span></div><div class="line"><a name="l00885"></a><span class="lineno"> 885</span> <span class="preprocessor">{\</span></div><div class="line"><a name="l00886"></a><span class="lineno"> 886</span> <span class="preprocessor"> return math_##n(rb_mMath, x, y);\</span></div><div class="line"><a name="l00887"></a><span class="lineno"> 887</span> <span class="preprocessor">}</span></div><div class="line"><a name="l00888"></a><span class="lineno"> 888</span> </div><div class="line"><a name="l00889"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a5176537e13e9fa1e2b365bc0e4072496"> 889</a></span> <a class="code" href="../../d6/da3/math_8c.html#acbc6f26bba8a2899bbc6fdec7597ed9b">exp2</a>(atan2)</div><div class="line"><a name="l00890"></a><span class="lineno"> 890</span> <a class="code" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a>(cos)</div><div class="line"><a name="l00891"></a><span class="lineno"> 891</span> <a class="code" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a>(<a class="code" href="../../d6/da3/math_8c.html#a3795d3c1f1d30819be56da4e4d67f64b">cosh</a>)</div><div class="line"><a name="l00892"></a><span class="lineno"> 892</span> <a class="code" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a>(exp)</div><div class="line"><a name="l00893"></a><span class="lineno"> 893</span> <a class="code" href="../../d6/da3/math_8c.html#acbc6f26bba8a2899bbc6fdec7597ed9b">exp2</a>(<a class="code" href="../../d3/d90/missing_8h.html#a7a16d2f097e52b6a343811f3014dc1ea">hypot</a>)</div><div class="line"><a name="l00894"></a><span class="lineno"> 894</span> </div><div class="line"><a name="l00895"></a><span class="lineno"> 895</span> <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="line"><a name="l00896"></a><span class="lineno"> 896</span> <a class="code" href="../../db/dde/internal_8h.html#abb43f72d4164363c6dc398886e3c0ccc">rb_math_log</a>(<span class="keywordtype">int</span> <a class="code" href="../../df/d77/ruby_8c.html#ad1447518f4372828b8435ae82e48499e">argc</a>, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a> *<a class="code" href="../../df/d77/ruby_8c.html#af2efa898e9eed6fe6715279cb1ec35b0">argv</a>)</div><div class="line"><a name="l00897"></a><span class="lineno"> 897</span> {</div><div class="line"><a name="l00898"></a><span class="lineno"> 898</span>  <span class="keywordflow">return</span> <a class="code" href="../../d6/da3/math_8c.html#a8bbeb8d9b2dafbaf3344044a52374088">math_log</a>(<a class="code" href="../../df/d77/ruby_8c.html#ad1447518f4372828b8435ae82e48499e">argc</a>, <a class="code" href="../../df/d77/ruby_8c.html#af2efa898e9eed6fe6715279cb1ec35b0">argv</a>);</div><div class="line"><a name="l00899"></a><span class="lineno"> 899</span> }</div><div class="line"><a name="l00900"></a><span class="lineno"> 900</span> </div><div class="line"><a name="l00901"></a><span class="lineno"><a class="line" href="../../d6/da3/math_8c.html#a2af6ea30e0db6e9a09166de533efa534"> 901</a></span> <a class="code" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a>(sin)</div><div class="line"><a name="l00902"></a><span class="lineno"> 902</span> <a class="code" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a>(<a class="code" href="../../d6/da3/math_8c.html#a862012e970c977c482507064e2793b45">sinh</a>)</div><div class="line"><a name="l00903"></a><span class="lineno"> 903</span> <a class="code" href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a>(sqrt)</div><div class="line"><a name="l00904"></a><span class="lineno"> 904</span> </div><div class="line"><a name="l00905"></a><span class="lineno"> 905</span> </div><div class="line"><a name="l00906"></a><span class="lineno"> 906</span> <span class="comment">/*</span></div><div class="line"><a name="l00907"></a><span class="lineno"> 907</span> <span class="comment"> * Document-class: Math::DomainError</span></div><div class="line"><a name="l00908"></a><span class="lineno"> 908</span> <span class="comment"> *</span></div><div class="line"><a name="l00909"></a><span class="lineno"> 909</span> <span class="comment"> * Raised when a mathematical function is evaluated outside of its</span></div><div class="line"><a name="l00910"></a><span class="lineno"> 910</span> <span class="comment"> * domain of definition.</span></div><div class="line"><a name="l00911"></a><span class="lineno"> 911</span> <span class="comment"> *</span></div><div class="line"><a name="l00912"></a><span class="lineno"> 912</span> <span class="comment"> * For example, since +cos+ returns values in the range -1..1,</span></div><div class="line"><a name="l00913"></a><span class="lineno"> 913</span> <span class="comment"> * its inverse function +acos+ is only defined on that interval:</span></div><div class="line"><a name="l00914"></a><span class="lineno"> 914</span> <span class="comment"> *</span></div><div class="line"><a name="l00915"></a><span class="lineno"> 915</span> <span class="comment"> * Math.acos(42)</span></div><div class="line"><a name="l00916"></a><span class="lineno"> 916</span> <span class="comment"> *</span></div><div class="line"><a name="l00917"></a><span class="lineno"> 917</span> <span class="comment"> * <em>produces:</em></span></div><div class="line"><a name="l00918"></a><span class="lineno"> 918</span> <span class="comment"> *</span></div><div class="line"><a name="l00919"></a><span class="lineno"> 919</span> <span class="comment"> * Math::DomainError: Numerical argument is out of domain - "acos"</span></div><div class="line"><a name="l00920"></a><span class="lineno"> 920</span> <span class="comment"> */</span></div><div class="line"><a name="l00921"></a><span class="lineno"> 921</span> </div><div class="line"><a name="l00922"></a><span class="lineno"> 922</span> <span class="comment">/*</span></div><div class="line"><a name="l00923"></a><span class="lineno"> 923</span> <span class="comment"> * Document-class: Math</span></div><div class="line"><a name="l00924"></a><span class="lineno"> 924</span> <span class="comment"> *</span></div><div class="line"><a name="l00925"></a><span class="lineno"> 925</span> <span class="comment"> * The Math module contains module functions for basic</span></div><div class="line"><a name="l00926"></a><span class="lineno"> 926</span> <span class="comment"> * trigonometric and transcendental functions. See class</span></div><div class="line"><a name="l00927"></a><span class="lineno"> 927</span> <span class="comment"> * Float for a list of constants that</span></div><div class="line"><a name="l00928"></a><span class="lineno"> 928</span> <span class="comment"> * define Ruby's floating point accuracy.</span></div><div class="line"><a name="l00929"></a><span class="lineno"> 929</span> <span class="comment"> *</span></div><div class="line"><a name="l00930"></a><span class="lineno"> 930</span> <span class="comment"> * Domains and codomains are given only for real (not complex) numbers.</span></div><div class="line"><a name="l00931"></a><span class="lineno"> 931</span> <span class="comment"> */</span></div><div class="line"><a name="l00932"></a><span class="lineno"> 932</span> </div><div class="line"><a name="l00933"></a><span class="lineno"> 933</span> </div><div class="line"><a name="l00934"></a><span class="lineno"> 934</span> <span class="keywordtype">void</span></div><div class="line"><a name="l00935"></a><span class="lineno"> 935</span> Init_Math(<span class="keywordtype">void</span>)</div><div class="line"><a name="l00936"></a><span class="lineno"> 936</span> {</div><div class="line"><a name="l00937"></a><span class="lineno"> 937</span>  <a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a> = <a class="code" href="../../de/ddf/group__class.html#ga911071d40f9312e49a774ea0e1b12869">rb_define_module</a>(<span class="stringliteral">"Math"</span>);</div><div class="line"><a name="l00938"></a><span class="lineno"> 938</span>  <a class="code" href="../../d6/da3/math_8c.html#afa48011feed589b977764fa06a9bfa80">rb_eMathDomainError</a> = <a class="code" href="../../de/ddf/group__class.html#ga5266deadce0318d830a1e63c0933b898">rb_define_class_under</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"DomainError"</span>, <a class="code" href="../../db/dcc/error_8c.html#a3fc1bd0a9e1211aef38f81d600345ed9">rb_eStandardError</a>);</div><div class="line"><a name="l00939"></a><span class="lineno"> 939</span> </div><div class="line"><a name="l00940"></a><span class="lineno"> 940</span> <span class="preprocessor">#ifdef M_PI</span></div><div class="line"><a name="l00941"></a><span class="lineno"> 941</span>  <span class="comment">/* Definition of the mathematical constant PI as a Float number. */</span></div><div class="line"><a name="l00942"></a><span class="lineno"> 942</span>  <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a861b20872f7d24f1c5f2da5261037322">rb_define_const</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"PI"</span>, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(<a class="code" href="../../d6/da3/math_8c.html#ae71449b1cc6e6250b91f539153a7a0d3">M_PI</a>));</div><div class="line"><a name="l00943"></a><span class="lineno"> 943</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00944"></a><span class="lineno"> 944</span>  <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a861b20872f7d24f1c5f2da5261037322">rb_define_const</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"PI"</span>, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(atan(1.0)*4.0));</div><div class="line"><a name="l00945"></a><span class="lineno"> 945</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00946"></a><span class="lineno"> 946</span> </div><div class="line"><a name="l00947"></a><span class="lineno"> 947</span> <span class="preprocessor">#ifdef M_E</span></div><div class="line"><a name="l00948"></a><span class="lineno"> 948</span>  <span class="comment">/* Definition of the mathematical constant E (e) as a Float number. */</span></div><div class="line"><a name="l00949"></a><span class="lineno"> 949</span>  <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a861b20872f7d24f1c5f2da5261037322">rb_define_const</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"E"</span>, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(M_E));</div><div class="line"><a name="l00950"></a><span class="lineno"> 950</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a861b20872f7d24f1c5f2da5261037322">rb_define_const</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"E"</span>, <a class="code" href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a>(exp(1.0)));</div><div class="line"><a name="l00952"></a><span class="lineno"> 952</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00953"></a><span class="lineno"> 953</span> </div><div class="line"><a name="l00954"></a><span class="lineno"> 954</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"atan2"</span>, <a class="code" href="../../d6/da3/math_8c.html#a5356b837d80de8e96dcfa87034987935">math_atan2</a>, 2);</div><div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"cos"</span>, <a class="code" href="../../d6/da3/math_8c.html#afb5fcc604398e4ccc2de7c1559057af8">math_cos</a>, 1);</div><div class="line"><a name="l00956"></a><span class="lineno"> 956</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"sin"</span>, <a class="code" href="../../d6/da3/math_8c.html#a16d50286debaa6bb7d9bbaa40590392e">math_sin</a>, 1);</div><div class="line"><a name="l00957"></a><span class="lineno"> 957</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"tan"</span>, <a class="code" href="../../d6/da3/math_8c.html#abd660936cc59e94c26e492c2181b73df">math_tan</a>, 1);</div><div class="line"><a name="l00958"></a><span class="lineno"> 958</span> </div><div class="line"><a name="l00959"></a><span class="lineno"> 959</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"acos"</span>, <a class="code" href="../../d6/da3/math_8c.html#ac40c99395caa4f5562f98b381b51c390">math_acos</a>, 1);</div><div class="line"><a name="l00960"></a><span class="lineno"> 960</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"asin"</span>, <a class="code" href="../../d6/da3/math_8c.html#a23509ad0c21d42f95a16c41845322aab">math_asin</a>, 1);</div><div class="line"><a name="l00961"></a><span class="lineno"> 961</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"atan"</span>, <a class="code" href="../../d6/da3/math_8c.html#ace875924c28bd439afb8739e8c91278b">math_atan</a>, 1);</div><div class="line"><a name="l00962"></a><span class="lineno"> 962</span> </div><div class="line"><a name="l00963"></a><span class="lineno"> 963</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"cosh"</span>, <a class="code" href="../../d6/da3/math_8c.html#afefc2a4c319791dd73f9157f682c276b">math_cosh</a>, 1);</div><div class="line"><a name="l00964"></a><span class="lineno"> 964</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"sinh"</span>, <a class="code" href="../../d6/da3/math_8c.html#ab326f3f4766a48575290a40fe8bf3f42">math_sinh</a>, 1);</div><div class="line"><a name="l00965"></a><span class="lineno"> 965</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"tanh"</span>, <a class="code" href="../../d6/da3/math_8c.html#adfabc64c79f8be8d07b2cd744133af76">math_tanh</a>, 1);</div><div class="line"><a name="l00966"></a><span class="lineno"> 966</span> </div><div class="line"><a name="l00967"></a><span class="lineno"> 967</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"acosh"</span>, <a class="code" href="../../d6/da3/math_8c.html#af6d250959ee5fbf65b4d19d827a3db78">math_acosh</a>, 1);</div><div class="line"><a name="l00968"></a><span class="lineno"> 968</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"asinh"</span>, <a class="code" href="../../d6/da3/math_8c.html#a7ee8ba235b99f8b19e99e4c4a04f0dcc">math_asinh</a>, 1);</div><div class="line"><a name="l00969"></a><span class="lineno"> 969</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"atanh"</span>, <a class="code" href="../../d6/da3/math_8c.html#af479bb3e458d54f9b0b89a1d585926ff">math_atanh</a>, 1);</div><div class="line"><a name="l00970"></a><span class="lineno"> 970</span> </div><div class="line"><a name="l00971"></a><span class="lineno"> 971</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"exp"</span>, <a class="code" href="../../d6/da3/math_8c.html#a1bacd682f5d7e0277df28b27d0abb299">math_exp</a>, 1);</div><div class="line"><a name="l00972"></a><span class="lineno"> 972</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"log"</span>, <a class="code" href="../../d6/da3/math_8c.html#a8bbeb8d9b2dafbaf3344044a52374088">math_log</a>, -1);</div><div class="line"><a name="l00973"></a><span class="lineno"> 973</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"log2"</span>, <a class="code" href="../../d6/da3/math_8c.html#a70452a1a0be21ce5061086f498109f3b">math_log2</a>, 1);</div><div class="line"><a name="l00974"></a><span class="lineno"> 974</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"log10"</span>, <a class="code" href="../../d6/da3/math_8c.html#aa808294660f7bf83d4fe0516ace22b8d">math_log10</a>, 1);</div><div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"sqrt"</span>, <a class="code" href="../../d6/da3/math_8c.html#a8c16a4990c2069257664bba3ead2e1a5">math_sqrt</a>, 1);</div><div class="line"><a name="l00976"></a><span class="lineno"> 976</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"cbrt"</span>, <a class="code" href="../../d6/da3/math_8c.html#ac37636a9964f1b04d6ffaea2a75b474d">math_cbrt</a>, 1);</div><div class="line"><a name="l00977"></a><span class="lineno"> 977</span> </div><div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"frexp"</span>, <a class="code" href="../../d6/da3/math_8c.html#a7a76f8ba84835bdb5163db8d5b4ce0e5">math_frexp</a>, 1);</div><div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"ldexp"</span>, <a class="code" href="../../d6/da3/math_8c.html#ae5b3da9a522de33d1e5d3208014fbdbe">math_ldexp</a>, 2);</div><div class="line"><a name="l00980"></a><span class="lineno"> 980</span> </div><div class="line"><a name="l00981"></a><span class="lineno"> 981</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"hypot"</span>, <a class="code" href="../../d6/da3/math_8c.html#add0ee9545be4cafd996adb0f385f37c8">math_hypot</a>, 2);</div><div class="line"><a name="l00982"></a><span class="lineno"> 982</span> </div><div class="line"><a name="l00983"></a><span class="lineno"> 983</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"erf"</span>, <a class="code" href="../../d6/da3/math_8c.html#acbdd1532a592ce8f5aba7e6bd9cc0d3f">math_erf</a>, 1);</div><div class="line"><a name="l00984"></a><span class="lineno"> 984</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"erfc"</span>, <a class="code" href="../../d6/da3/math_8c.html#a54b397857b1683d0413b5a17ff58b240">math_erfc</a>, 1);</div><div class="line"><a name="l00985"></a><span class="lineno"> 985</span> </div><div class="line"><a name="l00986"></a><span class="lineno"> 986</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"gamma"</span>, <a class="code" href="../../d6/da3/math_8c.html#a52534f854e9b5876b237fe29edafb8cd">math_gamma</a>, 1);</div><div class="line"><a name="l00987"></a><span class="lineno"> 987</span>  <a class="code" href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a>(<a class="code" href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a>, <span class="stringliteral">"lgamma"</span>, <a class="code" href="../../d6/da3/math_8c.html#ad1b067d8013ceadb03dcb86594fd27c0">math_lgamma</a>, 1);</div><div class="line"><a name="l00988"></a><span class="lineno"> 988</span> }</div><div class="ttc" id="util_8c_html_ade11f3df9cc63f54fa743250c646e270"><div class="ttname"><a href="../../de/df1/util_8c.html#ade11f3df9cc63f54fa743250c646e270">d0</a></div><div class="ttdeci">#define d0</div></div> <div class="ttc" id="math_8c_html_a7ee8ba235b99f8b19e99e4c4a04f0dcc"><div class="ttname"><a href="../../d6/da3/math_8c.html#a7ee8ba235b99f8b19e99e4c4a04f0dcc">math_asinh</a></div><div class="ttdeci">static VALUE math_asinh(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00351">math.c:351</a></div></div> <div class="ttc" id="error_8c_html_a3fc1bd0a9e1211aef38f81d600345ed9"><div class="ttname"><a href="../../db/dcc/error_8c.html#a3fc1bd0a9e1211aef38f81d600345ed9">rb_eStandardError</a></div><div class="ttdeci">VALUE rb_eStandardError</div><div class="ttdef"><b>Definition:</b> <a href="../../db/dcc/error_8c_source.html#l00546">error.c:546</a></div></div> <div class="ttc" id="missing_8h_html_a06124ca6e0c98d8ffdf0698c8f24b249"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a06124ca6e0c98d8ffdf0698c8f24b249">cbrt</a></div><div class="ttdeci">RUBY_EXTERN double cbrt(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../df/df9/cbrt_8c_source.html#l00004">cbrt.c:4</a></div></div> <div class="ttc" id="math_8c_html_ace3ce83aa2174da24c293be7b3ce375f"><div class="ttname"><a href="../../d6/da3/math_8c.html#ace3ce83aa2174da24c293be7b3ce375f">exp1</a></div><div class="ttdeci">#define exp1(n)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00875">math.c:875</a></div></div> <div class="ttc" id="math_8c_html_a862012e970c977c482507064e2793b45"><div class="ttname"><a href="../../d6/da3/math_8c.html#a862012e970c977c482507064e2793b45">sinh</a></div><div class="ttdeci">double sinh(double x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00253">math.c:253</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_a7bce65407b21f6812267e8d5426201f0"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#a7bce65407b21f6812267e8d5426201f0">INT2NUM</a></div><div class="ttdeci">#define INT2NUM(x)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l01296">ruby.h:1296</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_a877c38180d23c5447d976c70dda89d69"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#a877c38180d23c5447d976c70dda89d69">NUM2INT</a></div><div class="ttdeci">#define NUM2INT(x)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l00630">ruby.h:630</a></div></div> <div class="ttc" id="missing_8h_html_a67a4a1547ffbaeabfa58b9773d5bc9bc"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a67a4a1547ffbaeabfa58b9773d5bc9bc">signbit</a></div><div class="ttdeci">RUBY_EXTERN int signbit(double x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d8/de8/signbit_8c_source.html#l00005">signbit.c:5</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html">ruby.h</a></div></div> <div class="ttc" id="math_8c_html_a38bd88274dc5594b4826fd60c8054c8e"><div class="ttname"><a href="../../d6/da3/math_8c.html#a38bd88274dc5594b4826fd60c8054c8e">log2</a></div><div class="ttdeci">double log2(double x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00477">math.c:477</a></div></div> <div class="ttc" id="math_8c_html_a5356b837d80de8e96dcfa87034987935"><div class="ttname"><a href="../../d6/da3/math_8c.html#a5356b837d80de8e96dcfa87034987935">math_atan2</a></div><div class="ttdeci">static VALUE math_atan2(VALUE obj, VALUE y, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00062">math.c:62</a></div></div> <div class="ttc" id="math_8c_html_af479bb3e458d54f9b0b89a1d585926ff"><div class="ttname"><a href="../../d6/da3/math_8c.html#af479bb3e458d54f9b0b89a1d585926ff">math_atanh</a></div><div class="ttdeci">static VALUE math_atanh(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00372">math.c:372</a></div></div> <div class="ttc" id="math_8c_html_afa48011feed589b977764fa06a9bfa80"><div class="ttname"><a href="../../d6/da3/math_8c.html#afa48011feed589b977764fa06a9bfa80">rb_eMathDomainError</a></div><div class="ttdeci">VALUE rb_eMathDomainError</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00026">math.c:26</a></div></div> <div class="ttc" id="math_8c_html_a3a296753a4888c10f9fb62be65dc95be"><div class="ttname"><a href="../../d6/da3/math_8c.html#a3a296753a4888c10f9fb62be65dc95be">rb_mMath</a></div><div class="ttdeci">VALUE rb_mMath</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00025">math.c:25</a></div></div> <div class="ttc" id="group__class_html_ga5266deadce0318d830a1e63c0933b898"><div class="ttname"><a href="../../de/ddf/group__class.html#ga5266deadce0318d830a1e63c0933b898">rb_define_class_under</a></div><div class="ttdeci">VALUE rb_define_class_under(VALUE outer, const char *name, VALUE super)</div><div class="ttdoc">Defines a class under the namespace of outer. </div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d0c/class_8c_source.html#l00657">class.c:657</a></div></div> <div class="ttc" id="math_8c_html_a3795d3c1f1d30819be56da4e4d67f64b"><div class="ttname"><a href="../../d6/da3/math_8c.html#a3795d3c1f1d30819be56da4e4d67f64b">cosh</a></div><div class="ttdeci">double cosh(double x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00224">math.c:224</a></div></div> <div class="ttc" id="missing_8h_html_a64f1679e2eb7ba3a8f9ffb3ffb252a3e"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a64f1679e2eb7ba3a8f9ffb3ffb252a3e">tgamma</a></div><div class="ttdeci">RUBY_EXTERN double tgamma(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../db/d3a/tgamma_8c_source.html#l00072">tgamma.c:72</a></div></div> <div class="ttc" id="math_8c_html_a02d562fc66e90d37c0ed571aaaf21f91"><div class="ttname"><a href="../../d6/da3/math_8c.html#a02d562fc66e90d37c0ed571aaaf21f91">RB_BIGNUM_TYPE_P</a></div><div class="ttdeci">#define RB_BIGNUM_TYPE_P(x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00023">math.c:23</a></div></div> <div class="ttc" id="math_8c_html_ae5b3da9a522de33d1e5d3208014fbdbe"><div class="ttname"><a href="../../d6/da3/math_8c.html#ae5b3da9a522de33d1e5d3208014fbdbe">math_ldexp</a></div><div class="ttdeci">static VALUE math_ldexp(VALUE obj, VALUE x, VALUE n)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00688">math.c:688</a></div></div> <div class="ttc" id="missing_8h_html_ae9eff89386f38b111e9c83a8106bd2f1"><div class="ttname"><a href="../../d3/d90/missing_8h.html#ae9eff89386f38b111e9c83a8106bd2f1">lgamma_r</a></div><div class="ttdeci">RUBY_EXTERN double lgamma_r(double, int *)</div><div class="ttdef"><b>Definition:</b> <a href="../../d3/d84/lgamma__r_8c_source.html#l00063">lgamma_r.c:63</a></div></div> <div class="ttc" id="math_8c_html_a1bacd682f5d7e0277df28b27d0abb299"><div class="ttname"><a href="../../d6/da3/math_8c.html#a1bacd682f5d7e0277df28b27d0abb299">math_exp</a></div><div class="ttdeci">static VALUE math_exp(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00404">math.c:404</a></div></div> <div class="ttc" id="internal_8h_html_abb43f72d4164363c6dc398886e3c0ccc"><div class="ttname"><a href="../../db/dde/internal_8h.html#abb43f72d4164363c6dc398886e3c0ccc">rb_math_log</a></div><div class="ttdeci">VALUE rb_math_log(int argc, VALUE *argv)</div></div> <div class="ttc" id="ruby_2ruby_8h_html_a484dc4460a3e6eb2958238ab4559190c"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#a484dc4460a3e6eb2958238ab4559190c">RBIGNUM_POSITIVE_P</a></div><div class="ttdeci">#define RBIGNUM_POSITIVE_P(b)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l01097">ruby.h:1097</a></div></div> <div class="ttc" id="math_8c_html_aa808294660f7bf83d4fe0516ace22b8d"><div class="ttname"><a href="../../d6/da3/math_8c.html#aa808294660f7bf83d4fe0516ace22b8d">math_log10</a></div><div class="ttdeci">static VALUE math_log10(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00546">math.c:546</a></div></div> <div class="ttc" id="math_8c_html_af85bcf153d7ae805733927f12329dac1"><div class="ttname"><a href="../../d6/da3/math_8c.html#af85bcf153d7ae805733927f12329dac1">tanh</a></div><div class="ttdeci">double tanh(double x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00282">math.c:282</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_a861b20872f7d24f1c5f2da5261037322"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#a861b20872f7d24f1c5f2da5261037322">rb_define_const</a></div><div class="ttdeci">void rb_define_const(VALUE, const char *, VALUE)</div><div class="ttdef"><b>Definition:</b> <a href="../../d0/d2a/variable_8c_source.html#l02228">variable.c:2228</a></div></div> <div class="ttc" id="missing_8h_html_adced3433618a2f01f68b7fb60bb9d95d"><div class="ttname"><a href="../../d3/d90/missing_8h.html#adced3433618a2f01f68b7fb60bb9d95d">acosh</a></div><div class="ttdeci">RUBY_SYMBOL_EXPORT_BEGIN RUBY_EXTERN double acosh(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../d7/deb/acosh_8c_source.html#l00036">acosh.c:36</a></div></div> <div class="ttc" id="ruby_8c_html_ad1447518f4372828b8435ae82e48499e"><div class="ttname"><a href="../../df/d77/ruby_8c.html#ad1447518f4372828b8435ae82e48499e">argc</a></div><div class="ttdeci">int argc</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d77/ruby_8c_source.html#l00131">ruby.c:131</a></div></div> <div class="ttc" id="missing_8h_html_ab2ce4909e68033b22fd3de49a5e6e388"><div class="ttname"><a href="../../d3/d90/missing_8h.html#ab2ce4909e68033b22fd3de49a5e6e388">erfc</a></div><div class="ttdeci">RUBY_EXTERN double erfc(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../dd/dcf/erf_8c_source.html#l00081">erf.c:81</a></div></div> <div class="ttc" id="math_8c_html_adfabc64c79f8be8d07b2cd744133af76"><div class="ttname"><a href="../../d6/da3/math_8c.html#adfabc64c79f8be8d07b2cd744133af76">math_tanh</a></div><div class="ttdeci">static VALUE math_tanh(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00303">math.c:303</a></div></div> <div class="ttc" id="missing_8h_html_ae7a5ae88899707625ed6ab2ec7045583"><div class="ttname"><a href="../../d3/d90/missing_8h.html#ae7a5ae88899707625ed6ab2ec7045583">isinf</a></div><div class="ttdeci">RUBY_EXTERN int isinf(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d89/isinf_8c_source.html#l00056">isinf.c:56</a></div></div> <div class="ttc" id="etc_8c_html_a4ac8fee05a285361c33a2b0d9c2d555c"><div class="ttname"><a href="../../d5/d97/etc_8c.html#a4ac8fee05a285361c33a2b0d9c2d555c">numberof</a></div><div class="ttdeci">#define numberof(array)</div><div class="ttdef"><b>Definition:</b> <a href="../../d5/d97/etc_8c_source.html#l00602">etc.c:602</a></div></div> <div class="ttc" id="group__defmethod_html_gafc7122dde38ecff13de3e9d19a30aaeb"><div class="ttname"><a href="../../d7/d19/group__defmethod.html#gafc7122dde38ecff13de3e9d19a30aaeb">rb_define_module_function</a></div><div class="ttdeci">void rb_define_module_function(VALUE module, const char *name, VALUE(*func)(ANYARGS), int argc)</div><div class="ttdoc">Defines a module function for module. </div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d0c/class_8c_source.html#l01661">class.c:1661</a></div></div> <div class="ttc" id="math_8c_html_a8c16a4990c2069257664bba3ead2e1a5"><div class="ttname"><a href="../../d6/da3/math_8c.html#a8c16a4990c2069257664bba3ead2e1a5">math_sqrt</a></div><div class="ttdeci">static VALUE math_sqrt(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00599">math.c:599</a></div></div> <div class="ttc" id="missing_8h_html_a3aaf65bc2e95b04a6c8ee60ed785b750"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a3aaf65bc2e95b04a6c8ee60ed785b750">atanh</a></div><div class="ttdeci">RUBY_EXTERN double atanh(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../d7/deb/acosh_8c_source.html#l00075">acosh.c:75</a></div></div> <div class="ttc" id="math_8c_html_a8cabf161e2f357d85d4492baffeccb09"><div class="ttname"><a href="../../d6/da3/math_8c.html#a8cabf161e2f357d85d4492baffeccb09">Need_Float2</a></div><div class="ttdeci">#define Need_Float2(x, y)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00029">math.c:29</a></div></div> <div class="ttc" id="missing_8h_html_a7a16d2f097e52b6a343811f3014dc1ea"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a7a16d2f097e52b6a343811f3014dc1ea">hypot</a></div><div class="ttdeci">RUBY_EXTERN double hypot(double, double)</div><div class="ttdef"><b>Definition:</b> <a href="../../d1/db2/hypot_8c_source.html#l00006">hypot.c:6</a></div></div> <div class="ttc" id="group__defmethod_html_gaa7bed88640f01bee619f85fda09d28d7"><div class="ttname"><a href="../../d7/d19/group__defmethod.html#gaa7bed88640f01bee619f85fda09d28d7">rb_scan_args</a></div><div class="ttdeci">int rb_scan_args(int argc, const VALUE *argv, const char *fmt,...)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d0c/class_8c_source.html#l01719">class.c:1719</a></div></div> <div class="ttc" id="math_8c_html_acbdd1532a592ce8f5aba7e6bd9cc0d3f"><div class="ttname"><a href="../../d6/da3/math_8c.html#acbdd1532a592ce8f5aba7e6bd9cc0d3f">math_erf</a></div><div class="ttdeci">static VALUE math_erf(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00726">math.c:726</a></div></div> <div class="ttc" id="array_8c_html_af3085ceab406e3f4f4b90f383c440d6a"><div class="ttname"><a href="../../dc/dcc/array_8c.html#af3085ceab406e3f4f4b90f383c440d6a">rb_assoc_new</a></div><div class="ttdeci">VALUE rb_assoc_new(VALUE car, VALUE cdr)</div><div class="ttdef"><b>Definition:</b> <a href="../../dc/dcc/array_8c_source.html#l00620">array.c:620</a></div></div> <div class="ttc" id="internal_8h_html"><div class="ttname"><a href="../../db/dde/internal_8h.html">internal.h</a></div></div> <div class="ttc" id="math_8c_html_a8bbeb8d9b2dafbaf3344044a52374088"><div class="ttname"><a href="../../d6/da3/math_8c.html#a8bbeb8d9b2dafbaf3344044a52374088">math_log</a></div><div class="ttdeci">static VALUE math_log(int argc, VALUE *argv)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00441">math.c:441</a></div></div> <div class="ttc" id="math_8c_html_a7b67ef047e33f3c6a76b26c3b4d5334c"><div class="ttname"><a href="../../d6/da3/math_8c.html#a7b67ef047e33f3c6a76b26c3b4d5334c">domain_error</a></div><div class="ttdeci">#define domain_error(msg)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00034">math.c:34</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_a3c1d4bfc6a81af60bdcb48744c35f760"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#a3c1d4bfc6a81af60bdcb48744c35f760">VALUE</a></div><div class="ttdeci">unsigned long VALUE</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l00088">ruby.h:88</a></div></div> <div class="ttc" id="missing_8h_html_a6fc70ff722c0d4ee5542b29f374dca50"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a6fc70ff722c0d4ee5542b29f374dca50">asinh</a></div><div class="ttdeci">RUBY_EXTERN double asinh(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../d7/deb/acosh_8c_source.html#l00052">acosh.c:52</a></div></div> <div class="ttc" id="missing_8h_html_a956e2723d559858d08644ac99146e910"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a956e2723d559858d08644ac99146e910">INFINITY</a></div><div class="ttdeci">#define INFINITY</div><div class="ttdef"><b>Definition:</b> <a href="../../d3/d90/missing_8h_source.html#l00141">missing.h:141</a></div></div> <div class="ttc" id="acosh_8c_html_aeb343417fe0051b641fc7921022c7b0d"><div class="ttname"><a href="../../d7/deb/acosh_8c.html#aeb343417fe0051b641fc7921022c7b0d">DBL_MANT_DIG</a></div><div class="ttdeci">#define DBL_MANT_DIG</div><div class="ttdef"><b>Definition:</b> <a href="../../d7/deb/acosh_8c_source.html#l00019">acosh.c:19</a></div></div> <div class="ttc" id="numeric_8c_html_a539f2dd258b96fac8f4dc9bc139d75c9"><div class="ttname"><a href="../../d6/d27/numeric_8c.html#a539f2dd258b96fac8f4dc9bc139d75c9">DBL_MAX_EXP</a></div><div class="ttdeci">#define DBL_MAX_EXP</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/d27/numeric_8c_source.html#l00058">numeric.c:58</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_aa7311e0d10f373b0bb50c41522dc3981"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#aa7311e0d10f373b0bb50c41522dc3981">RFLOAT_VALUE</a></div><div class="ttdeci">#define RFLOAT_VALUE(v)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l00814">ruby.h:814</a></div></div> <div class="ttc" id="math_8c_html_ae71449b1cc6e6250b91f539153a7a0d3"><div class="ttname"><a href="../../d6/da3/math_8c.html#ae71449b1cc6e6250b91f539153a7a0d3">M_PI</a></div><div class="ttdeci">#define M_PI</div></div> <div class="ttc" id="ruby_2ruby_8h_html_ac55fae7f748afd3fc2533d0d7d06cf5a"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#ac55fae7f748afd3fc2533d0d7d06cf5a">INT2FIX</a></div><div class="ttdeci">#define INT2FIX(i)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l00231">ruby.h:231</a></div></div> <div class="ttc" id="math_8c_html_afb5fcc604398e4ccc2de7c1559057af8"><div class="ttname"><a href="../../d6/da3/math_8c.html#afb5fcc604398e4ccc2de7c1559057af8">math_cos</a></div><div class="ttdeci">static VALUE math_cos(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00099">math.c:99</a></div></div> <div class="ttc" id="math_8c_html_ac40c99395caa4f5562f98b381b51c390"><div class="ttname"><a href="../../d6/da3/math_8c.html#ac40c99395caa4f5562f98b381b51c390">math_acos</a></div><div class="ttdeci">static VALUE math_acos(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00164">math.c:164</a></div></div> <div class="ttc" id="math_8c_html_ace875924c28bd439afb8739e8c91278b"><div class="ttname"><a href="../../d6/da3/math_8c.html#ace875924c28bd439afb8739e8c91278b">math_atan</a></div><div class="ttdeci">static VALUE math_atan(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00216">math.c:216</a></div></div> <div class="ttc" id="math_8c_html_a54b397857b1683d0413b5a17ff58b240"><div class="ttname"><a href="../../d6/da3/math_8c.html#a54b397857b1683d0413b5a17ff58b240">math_erfc</a></div><div class="ttdeci">static VALUE math_erfc(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00747">math.c:747</a></div></div> <div class="ttc" id="math_8c_html_af6d250959ee5fbf65b4d19d827a3db78"><div class="ttname"><a href="../../d6/da3/math_8c.html#af6d250959ee5fbf65b4d19d827a3db78">math_acosh</a></div><div class="ttdeci">static VALUE math_acosh(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00324">math.c:324</a></div></div> <div class="ttc" id="math_8c_html_ac37636a9964f1b04d6ffaea2a75b474d"><div class="ttname"><a href="../../d6/da3/math_8c.html#ac37636a9964f1b04d6ffaea2a75b474d">math_cbrt</a></div><div class="ttdeci">static VALUE math_cbrt(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00648">math.c:648</a></div></div> <div class="ttc" id="math_8c_html_a70452a1a0be21ce5061086f498109f3b"><div class="ttname"><a href="../../d6/da3/math_8c.html#a70452a1a0be21ce5061086f498109f3b">math_log2</a></div><div class="ttdeci">static VALUE math_log2(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00504">math.c:504</a></div></div> <div class="ttc" id="math_8c_html_a7a76f8ba84835bdb5163db8d5b4ce0e5"><div class="ttname"><a href="../../d6/da3/math_8c.html#a7a76f8ba84835bdb5163db8d5b4ce0e5">math_frexp</a></div><div class="ttdeci">static VALUE math_frexp(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00666">math.c:666</a></div></div> <div class="ttc" id="bignum_8c_html_a4d13f72afe245927b1eea45acde5c842"><div class="ttname"><a href="../../d1/dcc/bignum_8c.html#a4d13f72afe245927b1eea45acde5c842">rb_absint_numwords</a></div><div class="ttdeci">size_t rb_absint_numwords(VALUE val, size_t word_numbits, size_t *nlz_bits_ret)</div><div class="ttdef"><b>Definition:</b> <a href="../../d1/dcc/bignum_8c_source.html#l03366">bignum.c:3366</a></div></div> <div class="ttc" id="math_8c_html_a16d50286debaa6bb7d9bbaa40590392e"><div class="ttname"><a href="../../d6/da3/math_8c.html#a16d50286debaa6bb7d9bbaa40590392e">math_sin</a></div><div class="ttdeci">static VALUE math_sin(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00121">math.c:121</a></div></div> <div class="ttc" id="math_8c_html_a23509ad0c21d42f95a16c41845322aab"><div class="ttname"><a href="../../d6/da3/math_8c.html#a23509ad0c21d42f95a16c41845322aab">math_asin</a></div><div class="ttdeci">static VALUE math_asin(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00190">math.c:190</a></div></div> <div class="ttc" id="bignum_8c_html_ad606505b6b476ddff0addf17454da732"><div class="ttname"><a href="../../d1/dcc/bignum_8c.html#ad606505b6b476ddff0addf17454da732">rb_big_rshift</a></div><div class="ttdeci">VALUE rb_big_rshift(VALUE x, VALUE y)</div><div class="ttdef"><b>Definition:</b> <a href="../../d1/dcc/bignum_8c_source.html#l06798">bignum.c:6798</a></div></div> <div class="ttc" id="math_8c_html_abd660936cc59e94c26e492c2181b73df"><div class="ttname"><a href="../../d6/da3/math_8c.html#abd660936cc59e94c26e492c2181b73df">math_tan</a></div><div class="ttdeci">static VALUE math_tan(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00143">math.c:143</a></div></div> <div class="ttc" id="group__class_html_ga911071d40f9312e49a774ea0e1b12869"><div class="ttname"><a href="../../de/ddf/group__class.html#ga911071d40f9312e49a774ea0e1b12869">rb_define_module</a></div><div class="ttdeci">VALUE rb_define_module(const char *name)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d0c/class_8c_source.html#l00727">class.c:727</a></div></div> <div class="ttc" id="__sdbm_8c_html_a070d2ce7b6bb7e5c05602aa8c308d0c4"><div class="ttname"><a href="../../d4/db0/__sdbm_8c.html#a070d2ce7b6bb7e5c05602aa8c308d0c4">NULL</a></div><div class="ttdeci">#define NULL</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/db0/__sdbm_8c_source.html#l00102">_sdbm.c:102</a></div></div> <div class="ttc" id="math_8c_html_a52534f854e9b5876b237fe29edafb8cd"><div class="ttname"><a href="../../d6/da3/math_8c.html#a52534f854e9b5876b237fe29edafb8cd">math_gamma</a></div><div class="ttdeci">static VALUE math_gamma(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00794">math.c:794</a></div></div> <div class="ttc" id="math_8c_html_acbc6f26bba8a2899bbc6fdec7597ed9b"><div class="ttname"><a href="../../d6/da3/math_8c.html#acbc6f26bba8a2899bbc6fdec7597ed9b">exp2</a></div><div class="ttdeci">#define exp2(n)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00882">math.c:882</a></div></div> <div class="ttc" id="math_8c_html_add0ee9545be4cafd996adb0f385f37c8"><div class="ttname"><a href="../../d6/da3/math_8c.html#add0ee9545be4cafd996adb0f385f37c8">math_hypot</a></div><div class="ttdeci">static VALUE math_hypot(VALUE obj, VALUE x, VALUE y)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00705">math.c:705</a></div></div> <div class="ttc" id="missing_8h_html_a3206afc394d28919ee875c60c436a949"><div class="ttname"><a href="../../d3/d90/missing_8h.html#a3206afc394d28919ee875c60c436a949">erf</a></div><div class="ttdeci">RUBY_EXTERN double erf(double)</div><div class="ttdef"><b>Definition:</b> <a href="../../dd/dcf/erf_8c_source.html#l00071">erf.c:71</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_af89e74d2dcf3eef15b29fa6015984af3"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#af89e74d2dcf3eef15b29fa6015984af3">SIZET2NUM</a></div><div class="ttdeci">#define SIZET2NUM(v)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l00262">ruby.h:262</a></div></div> <div class="ttc" id="math_8c_html_afefc2a4c319791dd73f9157f682c276b"><div class="ttname"><a href="../../d6/da3/math_8c.html#afefc2a4c319791dd73f9157f682c276b">math_cosh</a></div><div class="ttdeci">static VALUE math_cosh(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00245">math.c:245</a></div></div> <div class="ttc" id="ruby_8c_html_af2efa898e9eed6fe6715279cb1ec35b0"><div class="ttname"><a href="../../df/d77/ruby_8c.html#af2efa898e9eed6fe6715279cb1ec35b0">argv</a></div><div class="ttdeci">char ** argv</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d77/ruby_8c_source.html#l00132">ruby.c:132</a></div></div> <div class="ttc" id="ruby_2ruby_8h_html_a4affd02e0f0fe17593cd4ecd78cf9064"><div class="ttname"><a href="../../de/de6/ruby_2ruby_8h.html#a4affd02e0f0fe17593cd4ecd78cf9064">DBL2NUM</a></div><div class="ttdeci">#define DBL2NUM(dbl)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/de6/ruby_2ruby_8h_source.html#l00815">ruby.h:815</a></div></div> <div class="ttc" id="math_8c_html_ad1b067d8013ceadb03dcb86594fd27c0"><div class="ttname"><a href="../../d6/da3/math_8c.html#ad1b067d8013ceadb03dcb86594fd27c0">math_lgamma</a></div><div class="ttdeci">static VALUE math_lgamma(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00857">math.c:857</a></div></div> <div class="ttc" id="math_8c_html_ab326f3f4766a48575290a40fe8bf3f42"><div class="ttname"><a href="../../d6/da3/math_8c.html#ab326f3f4766a48575290a40fe8bf3f42">math_sinh</a></div><div class="ttdeci">static VALUE math_sinh(VALUE obj, VALUE x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00274">math.c:274</a></div></div> <div class="ttc" id="math_8c_html_a6334fd559b7bdb66aa45e5c56b3955ff"><div class="ttname"><a href="../../d6/da3/math_8c.html#a6334fd559b7bdb66aa45e5c56b3955ff">Need_Float</a></div><div class="ttdeci">#define Need_Float(x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d6/da3/math_8c_source.html#l00028">math.c:28</a></div></div> </div><!-- fragment --></div><!-- contents --> <!-- start footer part --> <hr class="footer"/><address class="footer"><small> Generated by  <a 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