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<div class="title">MathFunctions.h</div> </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_MATHFUNCTIONS_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATHFUNCTIONS_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> dummy = <span class="keywordtype">void</span>></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">struct </span>global_math_functions_filtering_base</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>  <span class="keyword">typedef</span> T type;</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> <span class="keyword">template</span><<span class="keyword">typename</span> T> <span class="keyword">struct </span>always_void { <span class="keyword">typedef</span> <span class="keywordtype">void</span> type; };</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> <span class="keyword">template</span><<span class="keyword">typename</span> T></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">struct </span>global_math_functions_filtering_base</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <T,</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  ></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> };</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="preprocessor">#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type></span></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">* Implementation of real *</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> template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">struct </span>real_default_impl</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="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> };</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="keyword">struct </span>real_default_impl<Scalar,true></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  {</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keyword">using</span> std::real;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">return</span> real(x);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar> <span class="keyword">struct </span>real_impl : real_default_impl<Scalar> {};</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">struct </span>real_retval</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real type;</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> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</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">* Implementation of imag *</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> </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="keyword">struct </span>imag_default_impl</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">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar&)</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>  <span class="keywordflow">return</span> RealScalar(0);</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> };</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="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">struct </span>imag_default_impl<Scalar,true></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> {</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar& x)</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>  <span class="keyword">using</span> std::imag;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> imag(x);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> };</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar> <span class="keyword">struct </span>imag_impl : imag_default_impl<Scalar> {};</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="keyword">struct </span>imag_retval</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real type;</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> </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">* Implementation of real_ref *</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment">****************************************************************************/</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="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="keyword">struct </span>real_ref_impl</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar& run(Scalar& x)</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  {</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> <span class="keyword">reinterpret_cast<</span>RealScalar*<span class="keyword">></span>(&x)[0];</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  }</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  {</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">return</span> <span class="keyword">reinterpret_cast<</span><span class="keyword">const </span>RealScalar*<span class="keyword">></span>(&x)[0];</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  }</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</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">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="keyword">struct </span>real_ref_retval</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real & type;</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> };</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> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">* Implementation of imag_ref *</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment">****************************************************************************/</span></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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="keyword">struct </span>imag_ref_default_impl</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar& run(Scalar& x)</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">return</span> <span class="keyword">reinterpret_cast<</span>RealScalar*<span class="keyword">></span>(&x)[1];</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  }</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  {</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">return</span> <span class="keyword">reinterpret_cast<</span>RealScalar*<span class="keyword">></span>(&x)[1];</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  }</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> </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">struct </span>imag_ref_default_impl<Scalar, false></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>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(Scalar&)</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  {</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordflow">return</span> Scalar(0);</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  }</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">const</span> Scalar run(<span class="keyword">const</span> Scalar&)</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>  <span class="keywordflow">return</span> Scalar(0);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  }</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> };</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="keyword">struct </span>imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="keyword">struct </span>imag_ref_retval</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> {</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real & type;</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> </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment">* Implementation of conj *</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment">****************************************************************************/</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> template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">struct </span>conj_impl</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x)</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>  <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> };</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="keyword">struct </span>conj_impl<Scalar,true></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> {</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  {</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keyword">using</span> std::conj;</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">return</span> conj(x);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  }</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> };</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">struct </span>conj_retval</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> {</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">typedef</span> Scalar type;</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> };</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment">* Implementation of abs2 *</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment">****************************************************************************/</span></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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">struct </span>abs2_impl</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> {</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  {</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">return</span> x*x;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</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> </div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="keyword">template</span><<span class="keyword">typename</span> RealScalar></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">struct </span>abs2_impl<std::complex<RealScalar> ></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> {</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> std::complex<RealScalar>& x)</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>  <span class="keywordflow">return</span> real(x)*real(x) + imag(x)*imag(x);</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  }</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> };</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">struct </span>abs2_retval</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real type;</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> };</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="comment">* Implementation of norm1 *</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment">****************************************************************************/</span></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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">struct </span>norm1_default_impl</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> {</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  {</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">return</span> abs(real(x)) + abs(imag(x));</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> };</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="keyword">struct </span>norm1_default_impl<Scalar, false></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> {</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">return</span> abs(x);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> };</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="keyword">struct </span>norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">struct </span>norm1_retval</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> {</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real type;</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="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment">* Implementation of hypot *</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment">****************************************************************************/</span></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="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="keyword">struct </span>hypot_impl</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> {</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y)</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  {</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keyword">using</span> std::max;</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keyword">using</span> std::min;</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  RealScalar _x = abs(x);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  RealScalar _y = abs(y);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  RealScalar p = (max)(_x, _y);</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">if</span>(p==RealScalar(0)) <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  RealScalar q = (min)(_x, _y);</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  RealScalar qp = q/p;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">return</span> p * sqrt(RealScalar(1) + qp*qp);</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> };</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="keyword">struct </span>hypot_retval</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> {</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real type;</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> </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment">* Implementation of cast *</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> </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="keyword">template</span><<span class="keyword">typename</span> OldType, <span class="keyword">typename</span> NewType></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="keyword">struct </span>cast_impl</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> {</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keyword">static</span> <span class="keyword">inline</span> NewType run(<span class="keyword">const</span> OldType& 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>  <span class="keywordflow">return</span> <span class="keyword">static_cast<</span>NewType<span class="keyword">></span>(x);</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  }</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</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="comment">// here, for once, we're plainly returning NewType: we don't want cast to do weird things.</span></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> </div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="keyword">template</span><<span class="keyword">typename</span> OldType, <span class="keyword">typename</span> NewType></div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="keyword">inline</span> NewType cast(<span class="keyword">const</span> OldType& x)</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>  <span class="keywordflow">return</span> cast_impl<OldType, NewType>::run(x);</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> }</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="comment">* Implementation of atanh2 *</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment">****************************************************************************/</span></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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar, <span class="keywordtype">bool</span> IsInteger></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="keyword">struct </span>atanh2_default_impl</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> {</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <span class="keyword">typedef</span> Scalar retval;</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y)</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  {</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  Scalar z = x / y;</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">if</span> (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon()))</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">return</span> RealScalar(0.5) * log((y + x) / (y - x));</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">return</span> z + z*z*z / RealScalar(3);</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  }</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> </div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="keyword">struct </span>atanh2_default_impl<Scalar, true></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>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar&, <span class="keyword">const</span> Scalar&)</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  return Scalar(0);</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  }</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> };</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> template<typename Scalar></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> </div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="keyword">struct </span>atanh2_retval</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> {</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">typedef</span> Scalar type;</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> </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="comment">* Implementation of pow *</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="comment">****************************************************************************/</span></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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar, <span class="keywordtype">bool</span> IsInteger></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="keyword">struct </span>pow_default_impl</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> {</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keyword">typedef</span> Scalar retval;</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y)</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  {</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordflow">return</span> pow(x, y);</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> };</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="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="keyword">struct </span>pow_default_impl<Scalar, true></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> {</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(Scalar x, Scalar y)</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  {</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  Scalar res(1);</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">if</span>(y & 1) res *= x;</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  y >>= 1;</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">while</span>(y)</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  {</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  x *= x;</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keywordflow">if</span>(y&1) res *= x;</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  y >>= 1;</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  }</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keywordflow">return</span> res;</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> };</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="keyword">struct </span>pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};</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> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="keyword">struct </span>pow_retval</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> {</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keyword">typedef</span> Scalar type;</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> </div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment">* Implementation of random *</span></div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment">****************************************************************************/</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="keyword">template</span><<span class="keyword">typename</span> Scalar,</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="keywordtype">bool</span> IsComplex,</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordtype">bool</span> IsInteger></div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="keyword">struct </span>random_default_impl {};</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="keyword">struct </span>random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> </div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="keyword">struct </span>random_retval</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span> {</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keyword">typedef</span> Scalar type;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> };</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> </div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> template<typename Scalar></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> struct random_default_impl<Scalar, false, false></div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> {</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y)</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  {</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keywordflow">return</span> x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);</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>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run()</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  {</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="keywordflow">return</span> run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));</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> };</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="keyword">enum</span> {</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  floor_log2_terminate,</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  floor_log2_move_up,</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  floor_log2_move_down,</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  floor_log2_bogus</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span> };</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span> </div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="keyword">template</span><<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> lower, <span class="keywordtype">int</span> upper> <span class="keyword">struct </span>floor_log2_selector</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>  <span class="keyword">enum</span> { middle = (lower + upper) / 2,</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  value = (upper <= lower + 1) ? int(floor_log2_terminate)</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  : (n < (1 << middle)) ? int(floor_log2_move_down)</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  : (n==0) ? int(floor_log2_bogus)</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  : int(floor_log2_move_up)</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  };</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> };</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> </div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span> <span class="keyword">template</span><<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n,</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordtype">int</span> lower = 0,</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="keywordtype">int</span> upper = <span class="keyword">sizeof</span>(<span class="keywordtype">unsigned</span> int) * CHAR_BIT - 1,</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="keywordtype">int</span> selector = floor_log2_selector<n, lower, upper>::value></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="keyword">struct</span> floor_log2 {};</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> </div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span> <span class="keyword">template</span><<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> lower, <span class="keywordtype">int</span> upper></div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="keyword">struct </span>floor_log2<n, lower, upper, floor_log2_move_down></div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> {</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keyword">enum</span> { value = floor_log2<n, lower, floor_log2_selector<n, lower, upper>::middle>::value };</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span> };</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> </div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="keyword">template</span><<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> lower, <span class="keywordtype">int</span> upper></div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span> <span class="keyword">struct </span>floor_log2<n, lower, upper, floor_log2_move_up></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="keyword">enum</span> { value = floor_log2<n, floor_log2_selector<n, lower, upper>::middle, upper>::value };</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> };</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> </div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> <span class="keyword">template</span><<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> lower, <span class="keywordtype">int</span> upper></div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="keyword">struct </span>floor_log2<n, lower, upper, floor_log2_terminate></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> {</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keyword">enum</span> { value = (n >= ((<span class="keywordtype">unsigned</span> int)(1) << (lower+1))) ? lower+1 : lower };</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span> };</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span> <span class="keyword">template</span><<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> lower, <span class="keywordtype">int</span> upper></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="keyword">struct </span>floor_log2<n, lower, upper, floor_log2_bogus></div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> {</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="comment">// no value, error at compile time</span></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span> };</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span> </div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="keyword">struct </span>random_default_impl<Scalar, false, true></div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> {</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::NonInteger NonInteger;</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> </div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y)</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="keywordflow">return</span> x + Scalar((NonInteger(y)-x+1) * std::rand() / (RAND_MAX + NonInteger(1)));</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  }</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="keyword">static</span> <span class="keyword">inline</span> Scalar run()</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  {</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="preprocessor">#ifdef EIGEN_MAKING_DOCS</span></div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span> <span class="preprocessor"></span> <span class="keywordflow">return</span> run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> <span class="preprocessor"></span> <span class="keyword">enum</span> { rand_bits = floor_log2<(unsigned int)(RAND_MAX)+1>::value,</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  scalar_bits = <span class="keyword">sizeof</span>(Scalar) * CHAR_BIT,</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  shift = EIGEN_PLAIN_ENUM_MAX(0, <span class="keywordtype">int</span>(rand_bits) - int(scalar_bits)),</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  };</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keywordflow">return</span> Scalar((std::rand() >> shift) - offset);</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span> };</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span> </div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> <span class="keyword">struct </span>random_default_impl<Scalar, true, false></div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span> {</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keyword">static</span> <span class="keyword">inline</span> Scalar run(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y)</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  {</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">return</span> Scalar(random(real(x), real(y)),</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  random(imag(x), imag(y)));</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="keyword">static</span> <span class="keyword">inline</span> Scalar run()</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  {</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="keywordflow">return</span> Scalar(random<RealScalar>(), random<RealScalar>());</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  }</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> };</div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span> </div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> {</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> }</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> </div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(random, Scalar) random()</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="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(random, Scalar)::run();</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> }</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="comment">// end namespace internal</span></div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span> </div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> <span class="comment">* Generic math function *</span></div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span> <span class="comment">****************************************************************************/</span></div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> </div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span> <span class="keyword">namespace </span>numext {</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="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)</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>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span> } </div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span> </div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span> <span class="keyword">inline</span> <span class="keyword">typename</span> internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span> {</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordflow">return</span> internal::real_ref_impl<Scalar>::run(x);</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span> }</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)</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>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> }</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span> {</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span> }</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span> </div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span> <span class="keyword">inline</span> <span class="keyword">typename</span> internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(<span class="keyword">const</span> Scalar& x)</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span> {</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="keywordflow">return</span> internal::imag_ref_impl<Scalar>::run(x);</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span> }</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span> </div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span> {</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span> }</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span> </div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span> {</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</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">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& 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="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);</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> </div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span> {</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span> }</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span> </div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span> {</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span> }</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span> </div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span> {</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span> }</div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span> </div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span> <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span> {</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span> }</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span> </div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span> <span class="comment">// std::isfinite is non standard, so let's define our own version,</span></div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span> <span class="comment">// even though it is not very efficient.</span></div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span> <span class="keyword">template</span><<span class="keyword">typename</span> T> bool (isfinite)(<span class="keyword">const</span> T& x)</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span> {</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="keywordflow">return</span> x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span> }</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span> </div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span> } <span class="comment">// end namespace numext</span></div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span> </div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span> </div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span> <span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span> <span class="comment">* Implementation of fuzzy comparisons *</span></div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span> <span class="comment">****************************************************************************/</span></div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span> </div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar,</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  <span class="keywordtype">bool</span> IsComplex,</div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  <span class="keywordtype">bool</span> IsInteger></div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span> <span class="keyword">struct </span>scalar_fuzzy_default_impl {};</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span> </div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span> <span class="keyword">struct </span>scalar_fuzzy_default_impl<Scalar, false, false></div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span> {</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  <span class="keyword">template</span><<span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isMuchSmallerThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> OtherScalar& y, <span class="keyword">const</span> RealScalar& prec)</div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  {</div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  <span class="keywordflow">return</span> abs(x) <= abs(y) * prec;</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  }</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApprox(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar& prec)</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  {</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="keyword">using</span> std::min;</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  <span class="keywordflow">return</span> abs(x - y) <= (min)(abs(x), abs(y)) * prec;</div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  }</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApproxOrLessThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar& prec)</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  {</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <span class="keywordflow">return</span> x <= y || isApprox(x, y, prec);</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> };</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span> </div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span> <span class="keyword">struct </span>scalar_fuzzy_default_impl<Scalar, false, true></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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keyword">template</span><<span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isMuchSmallerThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar&, <span class="keyword">const</span> RealScalar&)</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="keywordflow">return</span> x == Scalar(0);</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  }</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApprox(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar&)</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  {</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="keywordflow">return</span> x == y;</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  }</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApproxOrLessThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar&)</div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  {</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  <span class="keywordflow">return</span> x <= y;</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> };</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span> </div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span> <span class="keyword">struct </span>scalar_fuzzy_default_impl<Scalar, true, false></div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span> {</div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keyword">template</span><<span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isMuchSmallerThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> OtherScalar& y, <span class="keyword">const</span> RealScalar& prec)</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  {</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  <span class="keywordflow">return</span> numext::abs2(x) <= numext::abs2(y) * prec * prec;</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  }</div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApprox(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar& prec)</div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  {</div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  <span class="keyword">using</span> std::min;</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  <span class="keywordflow">return</span> numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec;</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</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> </div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span> <span class="keyword">struct </span>scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span> </div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar, <span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isMuchSmallerThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> OtherScalar& y,</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  <span class="keyword">typename</span> NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span> {</div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="keywordflow">return</span> scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);</div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span> }</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span> </div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApprox(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y,</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <span class="keyword">typename</span> NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span> {</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  <span class="keywordflow">return</span> scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span> }</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span> </div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApproxOrLessThan(<span class="keyword">const</span> Scalar& x, <span class="keyword">const</span> Scalar& y,</div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="keyword">typename</span> NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span> {</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  <span class="keywordflow">return</span> scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);</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> </div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span> <span class="comment">/******************************************</span></div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span> <span class="comment">*** The special case of the bool type ***</span></div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span> <span class="comment">******************************************/</span></div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span> </div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span> <span class="keyword">template</span><> <span class="keyword">struct </span>random_impl<bool></div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span> {</div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> run()</div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  {</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <span class="keywordflow">return</span> random<int>(0,1)==0 ? <span class="keyword">false</span> : <span class="keyword">true</span>;</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  }</div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span> };</div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span> </div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="keyword">template</span><> <span class="keyword">struct </span>scalar_fuzzy_impl<bool></div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span> {</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  <span class="keyword">typedef</span> <span class="keywordtype">bool</span> RealScalar;</div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  </div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  <span class="keyword">template</span><<span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isMuchSmallerThan(<span class="keyword">const</span> <span class="keywordtype">bool</span>& x, <span class="keyword">const</span> <span class="keywordtype">bool</span>&, <span class="keyword">const</span> <span class="keywordtype">bool</span>&)</div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  {</div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  <span class="keywordflow">return</span> !x;</div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  }</div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  </div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApprox(<span class="keywordtype">bool</span> x, <span class="keywordtype">bool</span> y, <span class="keywordtype">bool</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="keywordflow">return</span> x == y;</div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  }</div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span> </div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isApproxOrLessThan(<span class="keyword">const</span> <span class="keywordtype">bool</span>& x, <span class="keyword">const</span> <span class="keywordtype">bool</span>& y, <span class="keyword">const</span> <span class="keywordtype">bool</span>&)</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  {</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  <span class="keywordflow">return</span> (!x) || y;</div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  }</div>
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  </div>
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span> };</div>
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span> </div>
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  </div>
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span> </div>
<div class="line"><a name="l00766"></a><span class="lineno"> 766</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00767"></a><span class="lineno"> 767</span> </div>
<div class="line"><a name="l00768"></a><span class="lineno"> 768</span> <span class="preprocessor">#endif // EIGEN_MATHFUNCTIONS_H</span></div>
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