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<a href="a16533.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> // TR1 complex -*- C++ -*-</div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> </div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> // Copyright (C) 2006-2018 Free Software Foundation, Inc.</div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> //</div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> // This file is part of the GNU ISO C++ Library. This library is free</div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> // software; you can redistribute it and/or modify it under the</div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> // terms of the GNU General Public License as published by the</div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> // Free Software Foundation; either version 3, or (at your option)</div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> // any later version.</div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> // This library is distributed in the hope that it will be useful,</div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> // but WITHOUT ANY WARRANTY; without even the implied warranty of</div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> // GNU General Public License for more details.</div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> // Under Section 7 of GPL version 3, you are granted additional</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> // permissions described in the GCC Runtime Library Exception, version</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> // 3.1, as published by the Free Software Foundation.</div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> // You should have received a copy of the GNU General Public License and</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> // a copy of the GCC Runtime Library Exception along with this program;</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> // <http://www.gnu.org/licenses/>.</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> /** @file tr1/complex</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  * This is a TR1 C++ Library header. </div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  */</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> #ifndef _GLIBCXX_TR1_COMPLEX</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> #define _GLIBCXX_TR1_COMPLEX 1</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> #pragma GCC system_header</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> #include <complex></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> </div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> namespace std _GLIBCXX_VISIBILITY(default)</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> {</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> _GLIBCXX_BEGIN_NAMESPACE_VERSION</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> namespace tr1</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> {</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  /**</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  * @addtogroup complex_numbers</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  * @{</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  */</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> #if __cplusplus >= 201103L</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  using std::acos;</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  using std::asin;</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  using std::atan;</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  using std::acosh;</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  using std::asinh;</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  using std::atanh;</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> #else</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> #endif</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  // The std::fabs return type in C++11 mode is different (just _Tp).</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> </div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> #if __cplusplus < 201103L</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  template<typename _Tp></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  inline std::complex<_Tp></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  __complex_acos(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  {</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  const std::complex<_Tp> __t = std::tr1::asin(__z);</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  const _Tp __pi_2 = 1.5707963267948966192313216916397514L;</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> #if _GLIBCXX_USE_C99_COMPLEX_TR1</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  inline __complex__ float</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  __complex_acos(__complex__ float __z)</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  { return __builtin_cacosf(__z); }</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>  inline __complex__ double</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  __complex_acos(__complex__ double __z)</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  { return __builtin_cacos(__z); }</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  inline __complex__ long double</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  __complex_acos(const __complex__ long double& __z)</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  { return __builtin_cacosl(__z); }</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  template<typename _Tp></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  inline std::complex<_Tp></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  acos(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  { return __complex_acos(__z.__rep()); }</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> #else</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  /// acos(__z) [8.1.2].</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  // Effects: Behaves the same as C99 function cacos, defined</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  // in subclause 7.3.5.1.</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  template<typename _Tp></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  inline std::complex<_Tp></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  acos(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  { return __complex_acos(__z); }</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> #endif</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  template<typename _Tp></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  inline std::complex<_Tp></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  __complex_asin(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  {</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  std::complex<_Tp> __t(-__z.imag(), __z.real());</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  __t = std::tr1::asinh(__t);</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  return std::complex<_Tp>(__t.imag(), -__t.real());</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> #if _GLIBCXX_USE_C99_COMPLEX_TR1</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  inline __complex__ float</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  __complex_asin(__complex__ float __z)</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  { return __builtin_casinf(__z); }</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> </div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  inline __complex__ double</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  __complex_asin(__complex__ double __z)</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  { return __builtin_casin(__z); }</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  inline __complex__ long double</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  __complex_asin(const __complex__ long double& __z)</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  { return __builtin_casinl(__z); }</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span> </div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  template<typename _Tp></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  inline std::complex<_Tp></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  asin(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  { return __complex_asin(__z.__rep()); }</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> #else</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  /// asin(__z) [8.1.3].</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  // Effects: Behaves the same as C99 function casin, defined</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  // in subclause 7.3.5.2.</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  template<typename _Tp></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  inline std::complex<_Tp></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  asin(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  { return __complex_asin(__z); }</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> #endif</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  </div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  template<typename _Tp></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  std::complex<_Tp></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  __complex_atan(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  {</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  const _Tp __r2 = __z.real() * __z.real();</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  _Tp __num = __z.imag() + _Tp(1.0);</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  _Tp __den = __z.imag() - _Tp(1.0);</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>  __num = __r2 + __num * __num;</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  __den = __r2 + __den * __den;</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> </div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  _Tp(0.25) * log(__num / __den));</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  }</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> #if _GLIBCXX_USE_C99_COMPLEX_TR1</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  inline __complex__ float</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  __complex_atan(__complex__ float __z)</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  { return __builtin_catanf(__z); }</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  inline __complex__ double</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  __complex_atan(__complex__ double __z)</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  { return __builtin_catan(__z); }</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  inline __complex__ long double</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  __complex_atan(const __complex__ long double& __z)</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  { return __builtin_catanl(__z); }</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  template<typename _Tp></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  inline std::complex<_Tp></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  atan(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  { return __complex_atan(__z.__rep()); }</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> #else</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  /// atan(__z) [8.1.4].</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  // Effects: Behaves the same as C99 function catan, defined</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  // in subclause 7.3.5.3.</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  template<typename _Tp></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  inline std::complex<_Tp></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  atan(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  { return __complex_atan(__z); }</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> #endif</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  template<typename _Tp></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  std::complex<_Tp></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  __complex_acosh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  {</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  // Kahan's formula.</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</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> #if _GLIBCXX_USE_C99_COMPLEX_TR1</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  inline __complex__ float</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  __complex_acosh(__complex__ float __z)</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  { return __builtin_cacoshf(__z); }</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span> </div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  inline __complex__ double</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  __complex_acosh(__complex__ double __z)</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  { return __builtin_cacosh(__z); }</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>  inline __complex__ long double</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  __complex_acosh(const __complex__ long double& __z)</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  { return __builtin_cacoshl(__z); }</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  template<typename _Tp></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  inline std::complex<_Tp></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  acosh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  { return __complex_acosh(__z.__rep()); }</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> #else</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  /// acosh(__z) [8.1.5].</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  // Effects: Behaves the same as C99 function cacosh, defined</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  // in subclause 7.3.6.1.</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  template<typename _Tp></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  inline std::complex<_Tp></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  acosh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  { return __complex_acosh(__z); }</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> #endif</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> </div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  template<typename _Tp></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  std::complex<_Tp></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  __complex_asinh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  {</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  std::complex<_Tp> __t((__z.real() - __z.imag())</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  * (__z.real() + __z.imag()) + _Tp(1.0),</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  _Tp(2.0) * __z.real() * __z.imag());</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  __t = std::sqrt(__t);</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>  return std::log(__t + __z);</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> </div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> #if _GLIBCXX_USE_C99_COMPLEX_TR1</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  inline __complex__ float</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  __complex_asinh(__complex__ float __z)</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  { return __builtin_casinhf(__z); }</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  inline __complex__ double</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  __complex_asinh(__complex__ double __z)</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  { return __builtin_casinh(__z); }</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> </div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  inline __complex__ long double</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  __complex_asinh(const __complex__ long double& __z)</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  { return __builtin_casinhl(__z); }</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>  template<typename _Tp></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  inline std::complex<_Tp></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  asinh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  { return __complex_asinh(__z.__rep()); }</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> #else</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  /// asinh(__z) [8.1.6].</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  // Effects: Behaves the same as C99 function casin, defined</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  // in subclause 7.3.6.2.</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  template<typename _Tp></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  inline std::complex<_Tp></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  asinh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  { return __complex_asinh(__z); }</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> #endif</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  template<typename _Tp></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  std::complex<_Tp></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  __complex_atanh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  {</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  const _Tp __i2 = __z.imag() * __z.imag();</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  _Tp __num = _Tp(1.0) + __z.real();</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  _Tp __den = _Tp(1.0) - __z.real();</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  __num = __i2 + __num * __num;</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  __den = __i2 + __den * __den;</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> </div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  }</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> #if _GLIBCXX_USE_C99_COMPLEX_TR1</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  inline __complex__ float</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  __complex_atanh(__complex__ float __z)</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  { return __builtin_catanhf(__z); }</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>  inline __complex__ double</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  __complex_atanh(__complex__ double __z)</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  { return __builtin_catanh(__z); }</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>  inline __complex__ long double</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  __complex_atanh(const __complex__ long double& __z)</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  { return __builtin_catanhl(__z); }</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>  template<typename _Tp></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  inline std::complex<_Tp></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  atanh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  { return __complex_atanh(__z.__rep()); }</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> #else</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  /// atanh(__z) [8.1.7].</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  // Effects: Behaves the same as C99 function catanh, defined</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  // in subclause 7.3.6.3.</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  template<typename _Tp></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  inline std::complex<_Tp></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  atanh(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  { return __complex_atanh(__z); }</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> #endif</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> #endif // C++11</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span> </div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  template<typename _Tp></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  inline std::complex<_Tp></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  /// fabs(__z) [8.1.8].</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  // Effects: Behaves the same as C99 function cabs, defined</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  // in subclause 7.3.8.1.</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  fabs(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  { return std::abs(__z); }</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  /// Additional overloads [8.1.9].</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span> #if __cplusplus < 201103L</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  template<typename _Tp></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  inline typename __gnu_cxx::__promote<_Tp>::__type</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  arg(_Tp __x)</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  {</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  : __type();</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> #else</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  return std::arg(std::complex<__type>(__x));</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span> #endif</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  }</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>  template<typename _Tp></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  inline typename __gnu_cxx::__promote<_Tp>::__type</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  imag(_Tp)</div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  { return _Tp(); }</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span> </div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  template<typename _Tp></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  inline typename __gnu_cxx::__promote<_Tp>::__type</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  norm(_Tp __x)</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  {</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  return __type(__x) * __type(__x);</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  }</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span> </div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  template<typename _Tp></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  inline typename __gnu_cxx::__promote<_Tp>::__type</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  real(_Tp __x)</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  { return __x; }</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> #endif</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  template<typename _Tp, typename _Up></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type></div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  pow(const std::complex<_Tp>& __x, const _Up& __y)</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  {</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  return std::pow(std::complex<__type>(__x), __type(__y));</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  }</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>  template<typename _Tp, typename _Up></div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  pow(const _Tp& __x, const std::complex<_Up>& __y)</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  {</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  return std::pow(__type(__x), std::complex<__type>(__y));</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  }</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span> </div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  template<typename _Tp, typename _Up></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  {</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  return std::pow(std::complex<__type>(__x),</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  std::complex<__type>(__y));</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  }</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span> </div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  using std::arg;</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  template<typename _Tp></div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  inline std::complex<_Tp></div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  conj(const std::complex<_Tp>& __z)</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  { return std::conj(__z); }</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span> </div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  template<typename _Tp></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type></div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  conj(_Tp __x)</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  { return __x; }</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span> </div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  using std::imag;</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  using std::norm;</div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  using std::polar;</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span> </div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  template<typename _Tp, typename _Up></div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type></div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  polar(const _Tp& __rho, const _Up& __theta)</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  {</div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  return std::polar(__type(__rho), __type(__theta));</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span> </div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  using std::real;</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  template<typename _Tp></div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  inline std::complex<_Tp></div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  pow(const std::complex<_Tp>& __x, const _Tp& __y)</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  { return std::pow(__x, __y); }</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span> </div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  template<typename _Tp></div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  inline std::complex<_Tp></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  pow(const _Tp& __x, const std::complex<_Tp>& __y)</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  { return std::pow(__x, __y); }</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>  template<typename _Tp></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  inline std::complex<_Tp></div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y)</div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  { return std::pow(__x, __y); }</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span> </div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span> // @} group complex_numbers</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span> }</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span> _GLIBCXX_END_NAMESPACE_VERSION</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> </div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> #endif // _GLIBCXX_TR1_COMPLEX</div></div><!-- fragment --></div><!-- contents -->
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