1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2007 Julien Pommier
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5 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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6 | //
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7 | // This Source Code Form is subject to the terms of the Mozilla
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8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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10 |
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11 | /* The sin, cos, exp, and log functions of this file come from
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12 | * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
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13 | */
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14 |
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15 | #ifndef EIGEN_MATH_FUNCTIONS_SSE_H
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16 | #define EIGEN_MATH_FUNCTIONS_SSE_H
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17 |
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18 | namespace Eigen {
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19 |
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20 | namespace internal {
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21 |
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22 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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23 | Packet4f plog<Packet4f>(const Packet4f& _x)
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24 | {
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25 | Packet4f x = _x;
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26 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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27 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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28 | _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
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29 |
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30 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
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31 |
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32 | /* the smallest non denormalized float number */
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33 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
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34 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);//-1.f/0.f);
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35 |
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36 | /* natural logarithm computed for 4 simultaneous float
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37 | return NaN for x <= 0
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38 | */
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39 | _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
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40 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
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41 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
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42 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
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43 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
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44 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
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45 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
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46 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
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47 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
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48 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
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49 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
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50 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
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51 |
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52 |
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53 | Packet4i emm0;
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54 |
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55 | Packet4f invalid_mask = _mm_cmpnge_ps(x, _mm_setzero_ps()); // not greater equal is true if x is NaN
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56 | Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());
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57 |
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58 | x = pmax(x, p4f_min_norm_pos); /* cut off denormalized stuff */
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59 | emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
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60 |
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61 | /* keep only the fractional part */
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62 | x = _mm_and_ps(x, p4f_inv_mant_mask);
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63 | x = _mm_or_ps(x, p4f_half);
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64 |
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65 | emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
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66 | Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
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67 |
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68 | /* part2:
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69 | if( x < SQRTHF ) {
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70 | e -= 1;
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71 | x = x + x - 1.0;
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72 | } else { x = x - 1.0; }
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73 | */
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74 | Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
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75 | Packet4f tmp = _mm_and_ps(x, mask);
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76 | x = psub(x, p4f_1);
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77 | e = psub(e, _mm_and_ps(p4f_1, mask));
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78 | x = padd(x, tmp);
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79 |
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80 | Packet4f x2 = pmul(x,x);
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81 | Packet4f x3 = pmul(x2,x);
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82 |
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83 | Packet4f y, y1, y2;
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84 | y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
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85 | y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
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86 | y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
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87 | y = pmadd(y , x, p4f_cephes_log_p2);
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88 | y1 = pmadd(y1, x, p4f_cephes_log_p5);
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89 | y2 = pmadd(y2, x, p4f_cephes_log_p8);
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90 | y = pmadd(y, x3, y1);
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91 | y = pmadd(y, x3, y2);
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92 | y = pmul(y, x3);
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93 |
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94 | y1 = pmul(e, p4f_cephes_log_q1);
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95 | tmp = pmul(x2, p4f_half);
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96 | y = padd(y, y1);
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97 | x = psub(x, tmp);
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98 | y2 = pmul(e, p4f_cephes_log_q2);
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99 | x = padd(x, y);
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100 | x = padd(x, y2);
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101 | // negative arg will be NAN, 0 will be -INF
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102 | return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),
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103 | _mm_and_ps(iszero_mask, p4f_minus_inf));
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104 | }
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105 |
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106 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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107 | Packet4f pexp<Packet4f>(const Packet4f& _x)
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108 | {
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109 | Packet4f x = _x;
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110 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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111 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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112 | _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
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113 |
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114 |
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115 | _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
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116 | _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
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117 |
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118 | _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
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119 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
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120 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
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121 |
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122 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
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123 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
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124 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
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125 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
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126 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
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127 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
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128 |
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129 | Packet4f tmp, fx;
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130 | Packet4i emm0;
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131 |
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132 | // clamp x
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133 | x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
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134 |
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135 | /* express exp(x) as exp(g + n*log(2)) */
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136 | fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
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137 |
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138 | #ifdef EIGEN_VECTORIZE_SSE4_1
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139 | fx = _mm_floor_ps(fx);
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140 | #else
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141 | emm0 = _mm_cvttps_epi32(fx);
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142 | tmp = _mm_cvtepi32_ps(emm0);
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143 | /* if greater, substract 1 */
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144 | Packet4f mask = _mm_cmpgt_ps(tmp, fx);
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145 | mask = _mm_and_ps(mask, p4f_1);
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146 | fx = psub(tmp, mask);
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147 | #endif
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148 |
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149 | tmp = pmul(fx, p4f_cephes_exp_C1);
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150 | Packet4f z = pmul(fx, p4f_cephes_exp_C2);
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151 | x = psub(x, tmp);
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152 | x = psub(x, z);
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153 |
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154 | z = pmul(x,x);
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155 |
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156 | Packet4f y = p4f_cephes_exp_p0;
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157 | y = pmadd(y, x, p4f_cephes_exp_p1);
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158 | y = pmadd(y, x, p4f_cephes_exp_p2);
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159 | y = pmadd(y, x, p4f_cephes_exp_p3);
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160 | y = pmadd(y, x, p4f_cephes_exp_p4);
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161 | y = pmadd(y, x, p4f_cephes_exp_p5);
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162 | y = pmadd(y, z, x);
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163 | y = padd(y, p4f_1);
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164 |
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165 | // build 2^n
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166 | emm0 = _mm_cvttps_epi32(fx);
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167 | emm0 = _mm_add_epi32(emm0, p4i_0x7f);
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168 | emm0 = _mm_slli_epi32(emm0, 23);
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169 | return pmax(pmul(y, Packet4f(_mm_castsi128_ps(emm0))), _x);
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170 | }
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171 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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172 | Packet2d pexp<Packet2d>(const Packet2d& _x)
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173 | {
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174 | Packet2d x = _x;
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175 |
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176 | _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
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177 | _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
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178 | _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
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179 |
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180 | _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
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181 | _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
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182 |
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183 | _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
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184 |
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185 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
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186 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
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187 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
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188 |
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189 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
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190 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
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191 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
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192 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
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193 |
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194 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
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195 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
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196 | static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
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197 |
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198 | Packet2d tmp, fx;
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199 | Packet4i emm0;
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200 |
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201 | // clamp x
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202 | x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
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203 | /* express exp(x) as exp(g + n*log(2)) */
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204 | fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
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205 |
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206 | #ifdef EIGEN_VECTORIZE_SSE4_1
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207 | fx = _mm_floor_pd(fx);
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208 | #else
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209 | emm0 = _mm_cvttpd_epi32(fx);
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210 | tmp = _mm_cvtepi32_pd(emm0);
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211 | /* if greater, substract 1 */
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212 | Packet2d mask = _mm_cmpgt_pd(tmp, fx);
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213 | mask = _mm_and_pd(mask, p2d_1);
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214 | fx = psub(tmp, mask);
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215 | #endif
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216 |
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217 | tmp = pmul(fx, p2d_cephes_exp_C1);
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218 | Packet2d z = pmul(fx, p2d_cephes_exp_C2);
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219 | x = psub(x, tmp);
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220 | x = psub(x, z);
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221 |
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222 | Packet2d x2 = pmul(x,x);
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223 |
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224 | Packet2d px = p2d_cephes_exp_p0;
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225 | px = pmadd(px, x2, p2d_cephes_exp_p1);
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226 | px = pmadd(px, x2, p2d_cephes_exp_p2);
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227 | px = pmul (px, x);
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228 |
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229 | Packet2d qx = p2d_cephes_exp_q0;
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230 | qx = pmadd(qx, x2, p2d_cephes_exp_q1);
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231 | qx = pmadd(qx, x2, p2d_cephes_exp_q2);
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232 | qx = pmadd(qx, x2, p2d_cephes_exp_q3);
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233 |
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234 | x = pdiv(px,psub(qx,px));
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235 | x = pmadd(p2d_2,x,p2d_1);
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236 |
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237 | // build 2^n
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238 | emm0 = _mm_cvttpd_epi32(fx);
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239 | emm0 = _mm_add_epi32(emm0, p4i_1023_0);
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240 | emm0 = _mm_slli_epi32(emm0, 20);
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241 | emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
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242 | return pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x);
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243 | }
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244 |
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245 | /* evaluation of 4 sines at onces, using SSE2 intrinsics.
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246 |
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247 | The code is the exact rewriting of the cephes sinf function.
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248 | Precision is excellent as long as x < 8192 (I did not bother to
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249 | take into account the special handling they have for greater values
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250 | -- it does not return garbage for arguments over 8192, though, but
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251 | the extra precision is missing).
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252 |
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253 | Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
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254 | surprising but correct result.
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255 | */
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256 |
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257 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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258 | Packet4f psin<Packet4f>(const Packet4f& _x)
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259 | {
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260 | Packet4f x = _x;
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261 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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262 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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263 |
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264 | _EIGEN_DECLARE_CONST_Packet4i(1, 1);
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265 | _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
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266 | _EIGEN_DECLARE_CONST_Packet4i(2, 2);
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267 | _EIGEN_DECLARE_CONST_Packet4i(4, 4);
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268 |
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269 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
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270 |
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271 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
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272 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
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273 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
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274 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
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275 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
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276 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
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277 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
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278 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
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279 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
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280 | _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
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281 |
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282 | Packet4f xmm1, xmm2, xmm3, sign_bit, y;
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283 |
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284 | Packet4i emm0, emm2;
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285 | sign_bit = x;
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286 | /* take the absolute value */
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287 | x = pabs(x);
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288 |
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289 | /* take the modulo */
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290 |
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291 | /* extract the sign bit (upper one) */
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292 | sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
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293 |
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294 | /* scale by 4/Pi */
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295 | y = pmul(x, p4f_cephes_FOPI);
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296 |
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297 | /* store the integer part of y in mm0 */
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298 | emm2 = _mm_cvttps_epi32(y);
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299 | /* j=(j+1) & (~1) (see the cephes sources) */
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300 | emm2 = _mm_add_epi32(emm2, p4i_1);
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301 | emm2 = _mm_and_si128(emm2, p4i_not1);
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302 | y = _mm_cvtepi32_ps(emm2);
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303 | /* get the swap sign flag */
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304 | emm0 = _mm_and_si128(emm2, p4i_4);
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305 | emm0 = _mm_slli_epi32(emm0, 29);
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306 | /* get the polynom selection mask
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307 | there is one polynom for 0 <= x <= Pi/4
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308 | and another one for Pi/4<x<=Pi/2
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309 |
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310 | Both branches will be computed.
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311 | */
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312 | emm2 = _mm_and_si128(emm2, p4i_2);
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313 | emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
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314 |
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315 | Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
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316 | Packet4f poly_mask = _mm_castsi128_ps(emm2);
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317 | sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
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318 |
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319 | /* The magic pass: "Extended precision modular arithmetic"
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320 | x = ((x - y * DP1) - y * DP2) - y * DP3; */
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321 | xmm1 = pmul(y, p4f_minus_cephes_DP1);
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322 | xmm2 = pmul(y, p4f_minus_cephes_DP2);
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323 | xmm3 = pmul(y, p4f_minus_cephes_DP3);
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324 | x = padd(x, xmm1);
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325 | x = padd(x, xmm2);
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326 | x = padd(x, xmm3);
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327 |
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328 | /* Evaluate the first polynom (0 <= x <= Pi/4) */
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329 | y = p4f_coscof_p0;
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330 | Packet4f z = _mm_mul_ps(x,x);
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331 |
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332 | y = pmadd(y, z, p4f_coscof_p1);
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333 | y = pmadd(y, z, p4f_coscof_p2);
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334 | y = pmul(y, z);
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335 | y = pmul(y, z);
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336 | Packet4f tmp = pmul(z, p4f_half);
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337 | y = psub(y, tmp);
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338 | y = padd(y, p4f_1);
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339 |
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340 | /* Evaluate the second polynom (Pi/4 <= x <= 0) */
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341 |
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342 | Packet4f y2 = p4f_sincof_p0;
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343 | y2 = pmadd(y2, z, p4f_sincof_p1);
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344 | y2 = pmadd(y2, z, p4f_sincof_p2);
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345 | y2 = pmul(y2, z);
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346 | y2 = pmul(y2, x);
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347 | y2 = padd(y2, x);
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348 |
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349 | /* select the correct result from the two polynoms */
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350 | y2 = _mm_and_ps(poly_mask, y2);
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351 | y = _mm_andnot_ps(poly_mask, y);
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352 | y = _mm_or_ps(y,y2);
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353 | /* update the sign */
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354 | return _mm_xor_ps(y, sign_bit);
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355 | }
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356 |
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357 | /* almost the same as psin */
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358 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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359 | Packet4f pcos<Packet4f>(const Packet4f& _x)
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360 | {
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361 | Packet4f x = _x;
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362 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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363 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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364 |
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365 | _EIGEN_DECLARE_CONST_Packet4i(1, 1);
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366 | _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
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367 | _EIGEN_DECLARE_CONST_Packet4i(2, 2);
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368 | _EIGEN_DECLARE_CONST_Packet4i(4, 4);
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369 |
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370 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
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371 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
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372 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
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373 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
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374 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
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375 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
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376 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
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377 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
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378 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
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379 | _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
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380 |
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381 | Packet4f xmm1, xmm2, xmm3, y;
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382 | Packet4i emm0, emm2;
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383 |
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384 | x = pabs(x);
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385 |
|
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386 | /* scale by 4/Pi */
|
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387 | y = pmul(x, p4f_cephes_FOPI);
|
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388 |
|
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389 | /* get the integer part of y */
|
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390 | emm2 = _mm_cvttps_epi32(y);
|
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391 | /* j=(j+1) & (~1) (see the cephes sources) */
|
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392 | emm2 = _mm_add_epi32(emm2, p4i_1);
|
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393 | emm2 = _mm_and_si128(emm2, p4i_not1);
|
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394 | y = _mm_cvtepi32_ps(emm2);
|
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395 |
|
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396 | emm2 = _mm_sub_epi32(emm2, p4i_2);
|
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397 |
|
---|
398 | /* get the swap sign flag */
|
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399 | emm0 = _mm_andnot_si128(emm2, p4i_4);
|
---|
400 | emm0 = _mm_slli_epi32(emm0, 29);
|
---|
401 | /* get the polynom selection mask */
|
---|
402 | emm2 = _mm_and_si128(emm2, p4i_2);
|
---|
403 | emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
|
---|
404 |
|
---|
405 | Packet4f sign_bit = _mm_castsi128_ps(emm0);
|
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406 | Packet4f poly_mask = _mm_castsi128_ps(emm2);
|
---|
407 |
|
---|
408 | /* The magic pass: "Extended precision modular arithmetic"
|
---|
409 | x = ((x - y * DP1) - y * DP2) - y * DP3; */
|
---|
410 | xmm1 = pmul(y, p4f_minus_cephes_DP1);
|
---|
411 | xmm2 = pmul(y, p4f_minus_cephes_DP2);
|
---|
412 | xmm3 = pmul(y, p4f_minus_cephes_DP3);
|
---|
413 | x = padd(x, xmm1);
|
---|
414 | x = padd(x, xmm2);
|
---|
415 | x = padd(x, xmm3);
|
---|
416 |
|
---|
417 | /* Evaluate the first polynom (0 <= x <= Pi/4) */
|
---|
418 | y = p4f_coscof_p0;
|
---|
419 | Packet4f z = pmul(x,x);
|
---|
420 |
|
---|
421 | y = pmadd(y,z,p4f_coscof_p1);
|
---|
422 | y = pmadd(y,z,p4f_coscof_p2);
|
---|
423 | y = pmul(y, z);
|
---|
424 | y = pmul(y, z);
|
---|
425 | Packet4f tmp = _mm_mul_ps(z, p4f_half);
|
---|
426 | y = psub(y, tmp);
|
---|
427 | y = padd(y, p4f_1);
|
---|
428 |
|
---|
429 | /* Evaluate the second polynom (Pi/4 <= x <= 0) */
|
---|
430 | Packet4f y2 = p4f_sincof_p0;
|
---|
431 | y2 = pmadd(y2, z, p4f_sincof_p1);
|
---|
432 | y2 = pmadd(y2, z, p4f_sincof_p2);
|
---|
433 | y2 = pmul(y2, z);
|
---|
434 | y2 = pmadd(y2, x, x);
|
---|
435 |
|
---|
436 | /* select the correct result from the two polynoms */
|
---|
437 | y2 = _mm_and_ps(poly_mask, y2);
|
---|
438 | y = _mm_andnot_ps(poly_mask, y);
|
---|
439 | y = _mm_or_ps(y,y2);
|
---|
440 |
|
---|
441 | /* update the sign */
|
---|
442 | return _mm_xor_ps(y, sign_bit);
|
---|
443 | }
|
---|
444 |
|
---|
445 | #if EIGEN_FAST_MATH
|
---|
446 |
|
---|
447 | // This is based on Quake3's fast inverse square root.
|
---|
448 | // For detail see here: http://www.beyond3d.com/content/articles/8/
|
---|
449 | // It lacks 1 (or 2 bits in some rare cases) of precision, and does not handle negative, +inf, or denormalized numbers correctly.
|
---|
450 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
|
---|
451 | Packet4f psqrt<Packet4f>(const Packet4f& _x)
|
---|
452 | {
|
---|
453 | Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
|
---|
454 |
|
---|
455 | /* select only the inverse sqrt of non-zero inputs */
|
---|
456 | Packet4f non_zero_mask = _mm_cmpge_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()));
|
---|
457 | Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
|
---|
458 |
|
---|
459 | x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
|
---|
460 | return pmul(_x,x);
|
---|
461 | }
|
---|
462 |
|
---|
463 | #else
|
---|
464 |
|
---|
465 | template<> EIGEN_STRONG_INLINE Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
|
---|
466 |
|
---|
467 | #endif
|
---|
468 |
|
---|
469 | template<> EIGEN_STRONG_INLINE Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
|
---|
470 |
|
---|
471 | } // end namespace internal
|
---|
472 |
|
---|
473 | } // end namespace Eigen
|
---|
474 |
|
---|
475 | #endif // EIGEN_MATH_FUNCTIONS_SSE_H
|
---|