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| <a href="special__functions-inl_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * Licensed to the Apache Software Foundation (ASF) under one</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * or more contributor license agreements. See the NOTICE file</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * distributed with this work for additional information</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * regarding copyright ownership. The ASF licenses this file</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * to you under the Apache License, Version 2.0 (the</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * "License"); you may not use this file except in compliance</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * with the License. You may obtain a copy of the License at</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * http://www.apache.org/licenses/LICENSE-2.0</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * Unless required by applicable law or agreed to in writing,</span></div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * software distributed under the License is distributed on an</span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY</span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * KIND, either express or implied. See the License for the</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * specific language governing permissions and limitations</span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * under the License.</span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#ifndef MXNET_COMMON_CUDA_RTC_SPECIAL_FUNCTIONS_INL_H_</span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#define MXNET_COMMON_CUDA_RTC_SPECIAL_FUNCTIONS_INL_H_</span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  </div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <cfloat></span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <string></span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  </div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">namespace </span><a class="code" href="namespacemxnet.html">mxnet</a> {</div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">namespace </span>common {</div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span>cuda {</div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">namespace </span>rtc {</div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// This code is based on the Cephes Library availible at http://www.netlib.org/cephes</span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// The original author, Stephen Moshier, has kindly given permission to use this code</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// in mxnet. (See email below).</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">//</span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// Date: Tue, 13 Sep 2016 09:28:20 -0400</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// From: Stephen Moshier</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// To: Flunkert, Valentin</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Subject: Re: cephes code in mxnet</span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">//</span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// Hello Valentin,</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">//</span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// Thank you for writing. You are welcome to use and modify the Cephes code</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// and distribute it under the Apache license.</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">//</span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// Good luck with your project,</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// Steve Moshier</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">//</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// Cephes Math Library Release 2.2: June, 1992</span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// Copyright 1984, 1987, 1992 by Stephen L. Moshier</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// Direct inquiries to 30 Frost Street, Cambridge, MA 02140</span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">//</span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="namespacemxnet_1_1common_1_1cuda_1_1rtc.html#a65dbf14987fef106699cfead3c209512"> 52</a></span> <span class="keyword">const</span> <span class="keywordtype">char</span> <a class="code" href="namespacemxnet_1_1common_1_1cuda_1_1rtc.html#a65dbf14987fef106699cfead3c209512">special_functions_definitions</a>[] = R<span class="stringliteral">"code(</span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="stringliteral">namespace op {</span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="stringliteral">namespace special_functions {</span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="stringliteral">template<typename DType></span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="stringliteral">__device__ inline static DType trigamma(DType x);</span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="stringliteral">template<></span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="stringliteral">__device__ inline double trigamma<double>(double x) {</span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="stringliteral"> double PI(3.14159265358979323846);</span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="stringliteral"> double sign = +1;</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="stringliteral"> double result = 0;</span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="stringliteral"> if (x < 0.5) {</span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="stringliteral"> sign = -1;</span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="stringliteral"> const double sin_pi_x = sin(PI * x);</span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="stringliteral"> result -= (PI * PI) / (sin_pi_x * sin_pi_x);</span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="stringliteral"> x = 1 - x;</span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="stringliteral"> for (int i = 0; i < 6; ++i) {</span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="stringliteral"> result += 1 / (x * x);</span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="stringliteral"> x += 1;</span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="stringliteral"> const double ixx = 1 / (x*x);</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="stringliteral"> result += (1 + 1 / (2*x) + ixx * (1./6 - ixx * (1./30 - ixx * (1./42)))) / x;</span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="stringliteral"> return sign * result;</span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="stringliteral">}</span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="stringliteral">template<></span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="stringliteral">__device__ inline float trigamma<float>(float x) {</span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="stringliteral"> float PI(3.14159265358979323846);</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="stringliteral"> float sign = +1;</span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="stringliteral"> float result = 0;</span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="stringliteral"> if (x < 0.5f) {</span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="stringliteral"> sign = -1;</span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="stringliteral"> const float sin_pi_x = sinf(PI * x);</span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="stringliteral"> result -= (PI * PI) / (sin_pi_x * sin_pi_x);</span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="stringliteral"> x = 1 - x;</span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="stringliteral"> for (int i = 0; i < 6; ++i) {</span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="stringliteral"> result += 1 / (x * x);</span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="stringliteral"> x += 1;</span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="stringliteral"> const float ixx = 1 / (x*x);</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="stringliteral"> result += (1 + 1 / (2*x) + ixx * (1.f/6 - ixx * (1.f/30 - ixx * (1.f/42)))) / x;</span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="stringliteral"> return sign * result;</span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="stringliteral">}</span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="stringliteral">struct cephes {</span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="stringliteral"> /*</span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="stringliteral"> * Helper to evaluate a polynomial given an array of coefficients.</span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="stringliteral"> */</span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="stringliteral"> template <typename DType></span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="stringliteral"> __device__ inline static DType polevl(DType x, const DType coef[], int N) {</span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="stringliteral"> DType ans;</span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="stringliteral"> DType const *p;</span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="stringliteral"> int i;</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="stringliteral"> p = coef;</span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="stringliteral"> ans = *p++;</span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="stringliteral"> i = N;</span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="stringliteral"> do {</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="stringliteral"> ans = ans * x + *p++;</span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="stringliteral"> } while ( --i );</span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="stringliteral"> return( ans );</span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="stringliteral"> /*</span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="stringliteral"> * Helper function for psi that handles double/float specific differences</span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="stringliteral"> * in the algorithm.</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="stringliteral"> */</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="stringliteral"> template<typename DType></span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="stringliteral"> __device__ inline static DType psi_helper(DType s);</span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="stringliteral"> /*</span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="stringliteral"> * Psi (digamma) function</span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="stringliteral"> * SYNOPSIS:</span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="stringliteral"> * float x, y, psif();</span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="stringliteral"> * y = psif( x );</span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="stringliteral"> * DESCRIPTION:</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="stringliteral"> * d -</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="stringliteral"> * psi(x) = -- ln | (x)</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="stringliteral"> * dx</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="stringliteral"> * is the logarithmic derivative of the gamma function.</span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="stringliteral"> * For integer x,</span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="stringliteral"> * n-1</span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="stringliteral"> * -</span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="stringliteral"> * psi(n) = -EUL + > 1/k.</span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="stringliteral"> * -</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="stringliteral"> * k=1</span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="stringliteral"> * This formula is used for 0 < n <= 10. If x is negative, it</span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="stringliteral"> * is transformed to a positive argument by the reflection</span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="stringliteral"> * formula psi(1-x) = psi(x) + pi cot(pi x).</span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="stringliteral"> * For general positive x, the argument is made greater than 10</span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="stringliteral"> * using the recurrence psi(x+1) = psi(x) + 1/x.</span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="stringliteral"> * Then the following asymptotic expansion is applied:</span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="stringliteral"> * inf. B</span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="stringliteral"> * - 2k</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="stringliteral"> * psi(x) = log(x) - 1/2x - > -------</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="stringliteral"> * - 2k</span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="stringliteral"> * k=1 2k x</span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="stringliteral"> * where the B2k are Bernoulli numbers.</span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="stringliteral"> * ACCURACY:</span></div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="stringliteral"> * Absolute error, relative when |psi| > 1 :</span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="stringliteral"> * arithmetic domain # trials peak rms</span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="stringliteral"> * IEEE -33,0 30000 8.2e-7 1.2e-7</span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="stringliteral"> * IEEE 0,33 100000 7.3e-7 7.7e-8</span></div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="stringliteral"> *</span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="stringliteral"> * ERROR MESSAGES:</span></div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="stringliteral"> * message condition value returned</span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="stringliteral"> * psi singularity x integer <=0 MAXNUMF</span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="stringliteral"> */</span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="stringliteral"> template<typename DType></span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="stringliteral"> __device__ inline static DType psi(DType x) {</span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="stringliteral"> DType p, q, nz, s, w, y;</span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="stringliteral"> int i, n, negative;</span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="stringliteral"> DType EUL(0.57721566490153286061);</span></div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="stringliteral"> DType PI(3.14159265358979323846);</span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="stringliteral"> negative = 0;</span></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="stringliteral"> nz = 0.0;</span></div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="stringliteral"> if ( x <= 0.0 ) {</span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="stringliteral"> negative = 1;</span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="stringliteral"> q = x;</span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="stringliteral"> p = ::floor(q);</span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="stringliteral"> if ( p == q ) {</span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="stringliteral"> return DBL_MAX;</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="stringliteral"> /* Remove the zeros of tan(PI x)</span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="stringliteral"> * by subtracting the nearest integer from x</span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="stringliteral"> */</span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="stringliteral"> nz = q - p;</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="stringliteral"> if ( nz != 0.5 ) {</span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="stringliteral"> if ( nz > 0.5 ) {</span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="stringliteral"> p += 1.0;</span></div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="stringliteral"> nz = q - p;</span></div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="stringliteral"> nz = PI/::tan(PI*nz);</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="stringliteral"> } else {</span></div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="stringliteral"> nz = 0.0;</span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="stringliteral"> x = 1.0 - x;</span></div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="stringliteral"> /* check for positive integer up to 10 */</span></div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="stringliteral"> if ( (x <= 10.0) && (x == ::floor(x)) ) {</span></div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="stringliteral"> y = 0.0;</span></div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="stringliteral"> n = x;</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="stringliteral"> for ( i = 1; i < n; i++ ) {</span></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="stringliteral"> w = i;</span></div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="stringliteral"> y += 1.0/w;</span></div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="stringliteral"> y -= EUL;</span></div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="stringliteral"> goto done;</span></div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="stringliteral"> s = x;</span></div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="stringliteral"> w = 0.0;</span></div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="stringliteral"> while ( s < 10.0 ) {</span></div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="stringliteral"> w += 1.0/s;</span></div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="stringliteral"> s += 1.0;</span></div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="stringliteral"> y = psi_helper(s);</span></div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="stringliteral"> y = logf(s) - (0.5/s) - y - w;</span></div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="stringliteral">done:</span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="stringliteral"> if ( negative ) {</span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="stringliteral"> y -= nz;</span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="stringliteral"> return(y);</span></div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="stringliteral">};</span></div> |
| <div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="stringliteral">template<></span></div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="stringliteral">__device__ inline double cephes::psi_helper<double>(double s) {</span></div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="stringliteral"> double z;</span></div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="stringliteral"> const double A[] = {</span></div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="stringliteral"> 8.33333333333333333333E-2,</span></div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="stringliteral"> -2.10927960927960927961E-2,</span></div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="stringliteral"> 7.57575757575757575758E-3,</span></div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="stringliteral"> -4.16666666666666666667E-3,</span></div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="stringliteral"> 3.96825396825396825397E-3,</span></div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="stringliteral"> -8.33333333333333333333E-3,</span></div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="stringliteral"> 8.33333333333333333333E-2</span></div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="stringliteral"> };</span></div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="stringliteral"> if ( s < 1.0e17 ) {</span></div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="stringliteral"> z = 1.0/(s * s);</span></div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="stringliteral"> return z * cephes::polevl<double>(z, A, 6);</span></div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="stringliteral"> } else {</span></div> |
| <div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="stringliteral"> return 0.0;</span></div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="stringliteral">}</span></div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="stringliteral">template<></span></div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="stringliteral">__device__ inline float cephes::psi_helper<float>(float s) {</span></div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="stringliteral"> float z;</span></div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="stringliteral"> const float A[] = {</span></div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="stringliteral"> -4.16666666666666666667E-3f,</span></div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="stringliteral"> 3.96825396825396825397E-3f,</span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="stringliteral"> -8.33333333333333333333E-3f,</span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="stringliteral"> 8.33333333333333333333E-2f</span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="stringliteral"> };</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="stringliteral"> if ( s < 1.0e8 ) {</span></div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="stringliteral"> z = 1.0/(s * s);</span></div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="stringliteral"> return z * cephes::polevl<float>(z, A, 3);</span></div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="stringliteral"> } else {</span></div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="stringliteral"> return 0.0;</span></div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="stringliteral"> }</span></div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="stringliteral">}</span></div> |
| <div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="stringliteral">} // namespace special_functions</span></div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="stringliteral">} // namespace op</span></div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="stringliteral">)code";</span></div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="stringliteral"></span> </div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="stringliteral">} </span><span class="comment">// namespace rtc</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> } <span class="comment">// namespace cuda</span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> } <span class="comment">// namespace common</span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> } <span class="comment">// namespace mxnet</span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  </div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="preprocessor">#endif // MXNET_COMMON_CUDA_RTC_SPECIAL_FUNCTIONS_INL_H_</span></div> |
| </div><!-- fragment --></div><!-- contents --> |
| <div class="ttc" id="anamespacemxnet_html"><div class="ttname"><a href="namespacemxnet.html">mxnet</a></div><div class="ttdoc">namespace of mxnet</div><div class="ttdef"><b>Definition:</b> api_registry.h:33</div></div> |
| <div class="ttc" id="anamespacemxnet_1_1common_1_1cuda_1_1rtc_html_a65dbf14987fef106699cfead3c209512"><div class="ttname"><a href="namespacemxnet_1_1common_1_1cuda_1_1rtc.html#a65dbf14987fef106699cfead3c209512">mxnet::common::cuda::rtc::special_functions_definitions</a></div><div class="ttdeci">const char special_functions_definitions[]</div><div class="ttdef"><b>Definition:</b> special_functions-inl.h:52</div></div> |
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