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<div class="title">arch/SSE/MathFunctions.h</div> </div>
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<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) 2007 Julien Pommier</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a 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 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 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 name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">/* The sin, cos, exp, and log functions of this file come from</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> */</span></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="preprocessor">#ifndef EIGEN_MATH_FUNCTIONS_SSE_H</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATH_FUNCTIONS_SSE_H</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">namespace </span>Eigen {</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="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">template</span><> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> Packet4f plog<Packet4f>(<span class="keyword">const</span> Packet4f& _x)</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  Packet4f x = _x;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="comment">/* the smallest non denormalized float number */</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);<span class="comment">//-1.f/0.f);</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="comment">/* natural logarithm computed for 4 simultaneous float</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> return NaN for x <= 0</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </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>  Packet4i emm0;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  Packet4f invalid_mask = _mm_cmplt_ps(x, _mm_setzero_ps());</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  x = pmax(x, p4f_min_norm_pos); <span class="comment">/* cut off denormalized stuff */</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">/* keep only the fractional part */</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  x = _mm_and_ps(x, p4f_inv_mant_mask);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  x = _mm_or_ps(x, p4f_half);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  emm0 = _mm_sub_epi32(emm0, p4i_0x7f);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">/* part2:</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> if( x < SQRTHF ) {</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> e -= 1;</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> x = x + x - 1.0;</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> } else { x = x - 1.0; }</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  Packet4f tmp = _mm_and_ps(x, mask);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  x = psub(x, p4f_1);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  e = psub(e, _mm_and_ps(p4f_1, mask));</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  x = padd(x, tmp);</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>  Packet4f x2 = pmul(x,x);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  Packet4f x3 = pmul(x2,x);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  Packet4f y, y1, y2;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  y = pmadd(y , x, p4f_cephes_log_p2);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  y1 = pmadd(y1, x, p4f_cephes_log_p5);</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  y2 = pmadd(y2, x, p4f_cephes_log_p8);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  y = pmadd(y, x3, y1);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  y = pmadd(y, x3, y2);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  y = pmul(y, x3);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  y1 = pmul(e, p4f_cephes_log_q1);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  tmp = pmul(x2, p4f_half);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  y = padd(y, y1);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  x = psub(x, tmp);</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  y2 = pmul(e, p4f_cephes_log_q2);</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  x = padd(x, y);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  x = padd(x, y2);</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// negative arg will be NAN, 0 will be -INF</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">return</span> _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  _mm_and_ps(iszero_mask, p4f_minus_inf));</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> </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">template</span><> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> Packet4f pexp<Packet4f>(<span class="keyword">const</span> Packet4f& _x)</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  Packet4f x = _x;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);</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>  _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);</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>  _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  Packet4f tmp = _mm_setzero_ps(), fx;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  Packet4i emm0;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// clamp x</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">/* express exp(x) as exp(g + n*log(2)) */</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);</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="preprocessor">#ifdef EIGEN_VECTORIZE_SSE4_1</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="preprocessor"></span> fx = _mm_floor_ps(fx);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="preprocessor"></span> emm0 = _mm_cvttps_epi32(fx);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  tmp = _mm_cvtepi32_ps(emm0);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">/* if greater, substract 1 */</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  Packet4f mask = _mm_cmpgt_ps(tmp, fx);</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  mask = _mm_and_ps(mask, p4f_1);</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  fx = psub(tmp, mask);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  tmp = pmul(fx, p4f_cephes_exp_C1);</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  Packet4f z = pmul(fx, p4f_cephes_exp_C2);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  x = psub(x, tmp);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  x = psub(x, z);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  z = pmul(x,x);</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  Packet4f y = p4f_cephes_exp_p0;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  y = pmadd(y, x, p4f_cephes_exp_p1);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  y = pmadd(y, x, p4f_cephes_exp_p2);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  y = pmadd(y, x, p4f_cephes_exp_p3);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  y = pmadd(y, x, p4f_cephes_exp_p4);</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  y = pmadd(y, x, p4f_cephes_exp_p5);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  y = pmadd(y, z, x);</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  y = padd(y, p4f_1);</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>  <span class="comment">// build 2^n</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  emm0 = _mm_cvttps_epi32(fx);</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  emm0 = _mm_add_epi32(emm0, p4i_0x7f);</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  emm0 = _mm_slli_epi32(emm0, 23);</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">return</span> pmul(y, _mm_castsi128_ps(emm0));</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="keyword">template</span><> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> Packet2d pexp<Packet2d>(<span class="keyword">const</span> Packet2d& _x)</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  Packet2d x = _x;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);</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>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keyword">static</span> <span class="keyword">const</span> __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  Packet2d tmp = _mm_setzero_pd(), fx;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  Packet4i emm0;</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="comment">// clamp x</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="comment">/* express exp(x) as exp(g + n*log(2)) */</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);</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="preprocessor">#ifdef EIGEN_VECTORIZE_SSE4_1</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="preprocessor"></span> fx = _mm_floor_pd(fx);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="preprocessor"></span> emm0 = _mm_cvttpd_epi32(fx);</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  tmp = _mm_cvtepi32_pd(emm0);</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">/* if greater, substract 1 */</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  Packet2d mask = _mm_cmpgt_pd(tmp, fx);</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  mask = _mm_and_pd(mask, p2d_1);</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  fx = psub(tmp, mask);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  tmp = pmul(fx, p2d_cephes_exp_C1);</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  Packet2d z = pmul(fx, p2d_cephes_exp_C2);</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  x = psub(x, tmp);</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  x = psub(x, z);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  Packet2d x2 = pmul(x,x);</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>  Packet2d px = p2d_cephes_exp_p0;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  px = pmadd(px, x2, p2d_cephes_exp_p1);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  px = pmadd(px, x2, p2d_cephes_exp_p2);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  px = pmul (px, 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>  Packet2d qx = p2d_cephes_exp_q0;</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  qx = pmadd(qx, x2, p2d_cephes_exp_q1);</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  qx = pmadd(qx, x2, p2d_cephes_exp_q2);</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  qx = pmadd(qx, x2, p2d_cephes_exp_q3);</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>  x = pdiv(px,psub(qx,px));</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  x = pmadd(p2d_2,x,p2d_1);</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">// build 2^n</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  emm0 = _mm_cvttpd_epi32(fx);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  emm0 = _mm_add_epi32(emm0, p4i_1023_0);</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  emm0 = _mm_slli_epi32(emm0, 20);</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">return</span> pmul(x, _mm_castsi128_pd(emm0));</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> }</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment">/* evaluation of 4 sines at onces, using SSE2 intrinsics.</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"> The code is the exact rewriting of the cephes sinf function.</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment"> Precision is excellent as long as x < 8192 (I did not bother to</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment"> take into account the special handling they have for greater values</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment"> -- it does not return garbage for arguments over 8192, though, but</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment"> the extra precision is missing).</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"></span></div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"> Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> surprising but correct result.</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">template</span><> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> Packet4f psin<Packet4f>(<span class="keyword">const</span> Packet4f& _x)</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>  Packet4f x = _x;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</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>  _EIGEN_DECLARE_CONST_Packet4i(1, 1);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  _EIGEN_DECLARE_CONST_Packet4i(2, 2);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  _EIGEN_DECLARE_CONST_Packet4i(4, 4);</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>  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);</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>  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); <span class="comment">// 4 / M_PI</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;</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>  Packet4i emm0, emm2;</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  sign_bit = x;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">/* take the absolute value */</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  x = pabs(x);</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> </div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">/* take the modulo */</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="comment">/* extract the sign bit (upper one) */</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> </div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="comment">/* scale by 4/Pi */</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  y = pmul(x, p4f_cephes_FOPI);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="comment">/* store the integer part of y in mm0 */</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  emm2 = _mm_cvttps_epi32(y);</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">/* j=(j+1) & (~1) (see the cephes sources) */</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  emm2 = _mm_add_epi32(emm2, p4i_1);</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  emm2 = _mm_and_si128(emm2, p4i_not1);</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  y = _mm_cvtepi32_ps(emm2);</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="comment">/* get the swap sign flag */</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  emm0 = _mm_and_si128(emm2, p4i_4);</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  emm0 = _mm_slli_epi32(emm0, 29);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="comment">/* get the polynom selection mask</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="comment"> there is one polynom for 0 <= x <= Pi/4</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="comment"> and another one for Pi/4<x<=Pi/2</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment"></span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> Both branches will be computed.</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  emm2 = _mm_and_si128(emm2, p4i_2);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  Packet4f poly_mask = _mm_castsi128_ps(emm2);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);</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="comment">/* The magic pass: "Extended precision modular arithmetic"</span></div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="comment"> x = ((x - y * DP1) - y * DP2) - y * DP3; */</span></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  xmm1 = pmul(y, p4f_minus_cephes_DP1);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  xmm2 = pmul(y, p4f_minus_cephes_DP2);</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  xmm3 = pmul(y, p4f_minus_cephes_DP3);</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  x = padd(x, xmm1);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  x = padd(x, xmm2);</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  x = padd(x, xmm3);</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="comment">/* Evaluate the first polynom (0 <= x <= Pi/4) */</span></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  y = p4f_coscof_p0;</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  Packet4f z = _mm_mul_ps(x,x);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  y = pmadd(y, z, p4f_coscof_p1);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  y = pmadd(y, z, p4f_coscof_p2);</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  y = pmul(y, z);</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  y = pmul(y, z);</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  Packet4f tmp = pmul(z, p4f_half);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  y = psub(y, tmp);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  y = padd(y, p4f_1);</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="comment">/* Evaluate the second polynom (Pi/4 <= x <= 0) */</span></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>  Packet4f y2 = p4f_sincof_p0;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  y2 = pmadd(y2, z, p4f_sincof_p1);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  y2 = pmadd(y2, z, p4f_sincof_p2);</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  y2 = pmul(y2, z);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  y2 = pmul(y2, x);</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  y2 = padd(y2, x);</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> </div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">/* select the correct result from the two polynoms */</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  y2 = _mm_and_ps(poly_mask, y2);</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  y = _mm_andnot_ps(poly_mask, y);</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  y = _mm_or_ps(y,y2);</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">/* update the sign */</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keywordflow">return</span> _mm_xor_ps(y, sign_bit);</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> }</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="comment">/* almost the same as psin */</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="keyword">template</span><> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> Packet4f pcos<Packet4f>(<span class="keyword">const</span> Packet4f& _x)</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>  Packet4f x = _x;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> </div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  _EIGEN_DECLARE_CONST_Packet4i(1, 1);</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  _EIGEN_DECLARE_CONST_Packet4i(2, 2);</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  _EIGEN_DECLARE_CONST_Packet4i(4, 4);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); <span class="comment">// 4 / M_PI</span></div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> </div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  Packet4i emm0, emm2;</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  x = pabs(x);</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>  <span class="comment">/* scale by 4/Pi */</span></div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  y = pmul(x, p4f_cephes_FOPI);</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> </div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="comment">/* get the integer part of y */</span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  emm2 = _mm_cvttps_epi32(y);</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="comment">/* j=(j+1) & (~1) (see the cephes sources) */</span></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  emm2 = _mm_add_epi32(emm2, p4i_1);</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  emm2 = _mm_and_si128(emm2, p4i_not1);</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  y = _mm_cvtepi32_ps(emm2);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> </div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  emm2 = _mm_sub_epi32(emm2, p4i_2);</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>  <span class="comment">/* get the swap sign flag */</span></div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  emm0 = _mm_andnot_si128(emm2, p4i_4);</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  emm0 = _mm_slli_epi32(emm0, 29);</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="comment">/* get the polynom selection mask */</span></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  emm2 = _mm_and_si128(emm2, p4i_2);</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());</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>  Packet4f sign_bit = _mm_castsi128_ps(emm0);</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  Packet4f poly_mask = _mm_castsi128_ps(emm2);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> </div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="comment">/* The magic pass: "Extended precision modular arithmetic"</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment"> x = ((x - y * DP1) - y * DP2) - y * DP3; */</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  xmm1 = pmul(y, p4f_minus_cephes_DP1);</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  xmm2 = pmul(y, p4f_minus_cephes_DP2);</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  xmm3 = pmul(y, p4f_minus_cephes_DP3);</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  x = padd(x, xmm1);</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  x = padd(x, xmm2);</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  x = padd(x, xmm3);</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="comment">/* Evaluate the first polynom (0 <= x <= Pi/4) */</span></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  y = p4f_coscof_p0;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  Packet4f z = pmul(x,x);</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span> </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  y = pmadd(y,z,p4f_coscof_p1);</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  y = pmadd(y,z,p4f_coscof_p2);</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  y = pmul(y, z);</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  y = pmul(y, z);</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  Packet4f tmp = _mm_mul_ps(z, p4f_half);</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  y = psub(y, tmp);</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  y = padd(y, p4f_1);</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> </div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="comment">/* Evaluate the second polynom (Pi/4 <= x <= 0) */</span></div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  Packet4f y2 = p4f_sincof_p0;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  y2 = pmadd(y2, z, p4f_sincof_p1);</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  y2 = pmadd(y2, z, p4f_sincof_p2);</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  y2 = pmul(y2, z);</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  y2 = pmadd(y2, x, x);</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>  <span class="comment">/* select the correct result from the two polynoms */</span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  y2 = _mm_and_ps(poly_mask, y2);</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  y = _mm_andnot_ps(poly_mask, y);</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  y = _mm_or_ps(y,y2);</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="comment">/* update the sign */</span></div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">return</span> _mm_xor_ps(y, sign_bit);</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> }</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="comment">// This is based on Quake3's fast inverse square root.</span></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="comment">// For detail see here: http://www.beyond3d.com/content/articles/8/</span></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="keyword">template</span><> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> Packet4f psqrt<Packet4f>(<span class="keyword">const</span> Packet4f& _x)</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> {</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  Packet4f half = pmul(_x, pset1<Packet4f>(.5f));</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="comment">/* select only the inverse sqrt of non-zero inputs */</span></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  Packet4f non_zero_mask = _mm_cmpge_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()));</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));</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>  x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keywordflow">return</span> pmul(_x,x);</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span> }</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> </div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span> </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span> } <span class="comment">// end namespace Eigen</span></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> <span class="preprocessor">#endif // EIGEN_MATH_FUNCTIONS_SSE_H</span></div>
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