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<div class="fragment"><div class="line"><a id="l00001" 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 id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com></span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">// Copyright (C) 2021 C. Antonio Sanchez <cantonios@google.com></span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">//</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#ifndef EIGEN_COMPLEX_GPU_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#define EIGEN_COMPLEX_GPU_H</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// Many std::complex methods such as operator+, operator-, operator* and</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// operator/ are not constexpr. Due to this, GCC and older versions of clang do</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// not treat them as device functions and thus Eigen functors making use of</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// these operators fail to compile. Here, we manually specialize these</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// operators and functors for complex types when building for CUDA to enable</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// their use on-device.</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">//</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// NOTES:</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// - Compound assignment operators +=,-=,*=,/=(Scalar) will not work on device,</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// since they are already specialized in the standard. Using them will result</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// in silent kernel failures.</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// - Compiling with MSVC and using +=,-=,*=,/=(std::complex<Scalar>) will lead</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// to duplicate definition errors, since these are already specialized in</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// Visual Studio's <complex> header (contrary to the standard). This is</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// preferable to removing such definitions, which will lead to silent kernel</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// failures.</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// - Compiling with ICC requires defining _USE_COMPLEX_SPECIALIZATION_ prior</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// to the first inclusion of <complex>.</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#if defined(EIGEN_GPUCC) && defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// ICC already specializes std::complex<float> and std::complex<double></span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// operators, preventing us from making them device functions here.</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// This will lead to silent runtime errors if the operators are used on device.</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">//</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// To allow std::complex operator use on device, define _OVERRIDE_COMPLEX_SPECIALIZATION_</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// prior to first inclusion of <complex>. This prevents ICC from adding</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// its own specializations, so our custom ones below can be used instead.</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#if !(EIGEN_COMP_ICC && defined(_USE_COMPLEX_SPECIALIZATION_))</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// Import Eigen's internal operator specializations.</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="preprocessor">#define EIGEN_USING_STD_COMPLEX_OPERATORS \</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator+; \</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator-; \</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator*; \</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator/; \</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator+=; \</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator-=; \</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator*=; \</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator/=; \</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator==; \</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="preprocessor"> using Eigen::complex_operator_detail::operator!=;</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="preprocessor">#include "../../InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// Specialized std::complex overloads.</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="keyword">namespace </span>complex_operator_detail {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="keyword">template</span><<span class="keyword">typename</span> T></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>std::complex<T> complex_multiply(<span class="keyword">const</span> std::complex<T>& a, <span class="keyword">const</span> std::complex<T>& b) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">const</span> T a_real = numext::real(a);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">const</span> T a_imag = numext::imag(a);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keyword">const</span> T b_real = numext::real(b);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keyword">const</span> T b_imag = numext::imag(b);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">return</span> std::complex<T>(</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> a_real * b_real - a_imag * b_imag,</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> a_imag * b_real + a_real * b_imag);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>}</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="keyword">template</span><<span class="keyword">typename</span> T></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span>std::complex<T> complex_divide_fast(<span class="keyword">const</span> std::complex<T>& a, <span class="keyword">const</span> std::complex<T>& b) {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">const</span> T a_real = numext::real(a);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">const</span> T a_imag = numext::imag(a);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">const</span> T b_real = numext::real(b);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">const</span> T b_imag = numext::imag(b);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keyword">const</span> T norm = (b_real * b_real + b_imag * b_imag);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">return</span> std::complex<T>((a_real * b_real + a_imag * b_imag) / norm,</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> (a_imag * b_real - a_real * b_imag) / norm);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span>}</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="keyword">template</span><<span class="keyword">typename</span> T></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>std::complex<T> complex_divide_stable(<span class="keyword">const</span> std::complex<T>& a, <span class="keyword">const</span> std::complex<T>& b) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keyword">const</span> T a_real = numext::real(a);</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keyword">const</span> T a_imag = numext::imag(a);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">const</span> T b_real = numext::real(b);</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">const</span> T b_imag = numext::imag(b);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// Smith's complex division (https://arxiv.org/pdf/1210.4539.pdf),</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// guards against over/under-flow.</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> scale_imag = numext::abs(b_imag) <= numext::abs(b_real);</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">const</span> T rscale = scale_imag ? T(1) : b_real / b_imag;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">const</span> T iscale = scale_imag ? b_imag / b_real : T(1);</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">const</span> T denominator = b_real * rscale + b_imag * iscale;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">return</span> std::complex<T>((a_real * rscale + a_imag * iscale) / denominator, </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> (a_imag * rscale - a_real * iscale) / denominator);</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>}</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="keyword">template</span><<span class="keyword">typename</span> T></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span>std::complex<T> complex_divide(<span class="keyword">const</span> std::complex<T>& a, <span class="keyword">const</span> std::complex<T>& b) {</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="preprocessor">#if EIGEN_FAST_MATH</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">return</span> complex_divide_fast(a, b);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="preprocessor">#else</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keywordflow">return</span> complex_divide_stable(a, b);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span>}</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span><span class="comment">// NOTE: We cannot specialize compound assignment operators with Scalar T,</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment">// (i.e. operator@=(const T&), for @=+,-,*,/)</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">// since they are already specialized for float/double/long double within</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment">// the standard <complex> header. We also do not specialize the stream</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment">// operators.</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="preprocessor">#define EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(T) \</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="preprocessor">std::complex<T> operator+(const std::complex<T>& a) { return a; } \</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="preprocessor">std::complex<T> operator-(const std::complex<T>& a) { \</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="preprocessor"> return std::complex<T>(-numext::real(a), -numext::imag(a)); \</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="preprocessor">std::complex<T> operator+(const std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="preprocessor"> return std::complex<T>(numext::real(a) + numext::real(b), numext::imag(a) + numext::imag(b)); \</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="preprocessor">std::complex<T> operator+(const std::complex<T>& a, const T& b) { \</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="preprocessor"> return std::complex<T>(numext::real(a) + b, numext::imag(a)); \</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="preprocessor">std::complex<T> operator+(const T& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="preprocessor"> return std::complex<T>(a + numext::real(b), numext::imag(b)); \</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="preprocessor">std::complex<T> operator-(const std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="preprocessor"> return std::complex<T>(numext::real(a) - numext::real(b), numext::imag(a) - numext::imag(b)); \</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="preprocessor">std::complex<T> operator-(const std::complex<T>& a, const T& b) { \</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="preprocessor"> return std::complex<T>(numext::real(a) - b, numext::imag(a)); \</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="preprocessor">std::complex<T> operator-(const T& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="preprocessor"> return std::complex<T>(a - numext::real(b), -numext::imag(b)); \</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="preprocessor">std::complex<T> operator*(const std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span><span class="preprocessor"> return complex_multiply(a, b); \</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="preprocessor">std::complex<T> operator*(const std::complex<T>& a, const T& b) { \</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="preprocessor"> return std::complex<T>(numext::real(a) * b, numext::imag(a) * b); \</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="preprocessor">std::complex<T> operator*(const T& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="preprocessor"> return std::complex<T>(a * numext::real(b), a * numext::imag(b)); \</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="preprocessor">std::complex<T> operator/(const std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="preprocessor"> return complex_divide(a, b); \</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="preprocessor">std::complex<T> operator/(const std::complex<T>& a, const T& b) { \</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="preprocessor"> return std::complex<T>(numext::real(a) / b, numext::imag(a) / b); \</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><span class="preprocessor">std::complex<T> operator/(const T& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="preprocessor"> return complex_divide(std::complex<T>(a, 0), b); \</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="preprocessor">std::complex<T>& operator+=(std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span><span class="preprocessor"> numext::real_ref(a) += numext::real(b); \</span></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span><span class="preprocessor"> numext::imag_ref(a) += numext::imag(b); \</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="preprocessor"> return a; \</span></div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span><span class="preprocessor">std::complex<T>& operator-=(std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span><span class="preprocessor"> numext::real_ref(a) -= numext::real(b); \</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span><span class="preprocessor"> numext::imag_ref(a) -= numext::imag(b); \</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="preprocessor"> return a; \</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span><span class="preprocessor">std::complex<T>& operator*=(std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span><span class="preprocessor"> a = complex_multiply(a, b); \</span></div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span><span class="preprocessor"> return a; \</span></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span><span class="preprocessor">std::complex<T>& operator/=(std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span><span class="preprocessor"> a = complex_divide(a, b); \</span></div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="preprocessor"> return a; \</span></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span><span class="preprocessor">bool operator==(const std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span><span class="preprocessor"> return numext::real(a) == numext::real(b) && numext::imag(a) == numext::imag(b); \</span></div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span><span class="preprocessor">bool operator==(const std::complex<T>& a, const T& b) { \</span></div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span><span class="preprocessor"> return numext::real(a) == b && numext::imag(a) == 0; \</span></div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span><span class="preprocessor">bool operator==(const T& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span><span class="preprocessor"> return a == numext::real(b) && 0 == numext::imag(b); \</span></div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span><span class="preprocessor">bool operator!=(const std::complex<T>& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span><span class="preprocessor"> return !(a == b); \</span></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span><span class="preprocessor">bool operator!=(const std::complex<T>& a, const T& b) { \</span></div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span><span class="preprocessor"> return !(a == b); \</span></div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span><span class="preprocessor">} \</span></div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span><span class="preprocessor"> \</span></div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span><span class="preprocessor">EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \</span></div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span><span class="preprocessor">bool operator!=(const T& a, const std::complex<T>& b) { \</span></div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span><span class="preprocessor"> return !(a == b); \</span></div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span><span class="preprocessor">}</span></div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span><span class="comment">// Do not specialize for long double, since that reduces to double on device.</span></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span>EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(<span class="keywordtype">float</span>)</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span>EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(<span class="keywordtype">double</span>)</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> </div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span><span class="preprocessor">#undef EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS</span></div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> </div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> </div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span>} <span class="comment">// namespace complex_operator_detail</span></div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span>EIGEN_USING_STD_COMPLEX_OPERATORS</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span><span class="keyword">namespace </span>numext {</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span>EIGEN_USING_STD_COMPLEX_OPERATORS</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span>} <span class="comment">// namespace numext</span></div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span>EIGEN_USING_STD_COMPLEX_OPERATORS</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span>} <span class="comment">// namespace internal</span></div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span>} <span class="comment">// namespace Eigen</span></div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span><span class="preprocessor">#endif </span><span class="comment">// !(EIGEN_COMP_ICC && _USE_COMPLEX_SPECIALIZATION_)</span></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> </div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_GPUCC && EIGEN_GPU_COMPILE_PHASE</span></div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> </div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_COMPLEX_GPU_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
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