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) 2001 Intel Corporation
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5 | // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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6 | // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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7 | //
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8 | // This Source Code Form is subject to the terms of the Mozilla
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9 | // Public License v. 2.0. If a copy of the MPL was not distributed
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10 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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11 |
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12 | // The SSE code for the 4x4 float and double matrix inverse in this file
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13 | // comes from the following Intel's library:
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14 | // http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/
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15 | //
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16 | // Here is the respective copyright and license statement:
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17 | //
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18 | // Copyright (c) 2001 Intel Corporation.
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19 | //
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20 | // Permition is granted to use, copy, distribute and prepare derivative works
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21 | // of this library for any purpose and without fee, provided, that the above
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22 | // copyright notice and this statement appear in all copies.
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23 | // Intel makes no representations about the suitability of this software for
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24 | // any purpose, and specifically disclaims all warranties.
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25 | // See LEGAL.TXT for all the legal information.
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26 |
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27 | #ifndef EIGEN_INVERSE_SSE_H
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28 | #define EIGEN_INVERSE_SSE_H
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29 |
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30 | namespace Eigen {
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31 |
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32 | namespace internal {
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33 |
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34 | template<typename MatrixType, typename ResultType>
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35 | struct compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType>
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36 | {
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37 | enum {
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38 | MatrixAlignment = bool(MatrixType::Flags&AlignedBit),
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39 | ResultAlignment = bool(ResultType::Flags&AlignedBit),
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40 | StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
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41 | };
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42 |
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43 | static void run(const MatrixType& matrix, ResultType& result)
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44 | {
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45 | EIGEN_ALIGN16 const unsigned int _Sign_PNNP[4] = { 0x00000000, 0x80000000, 0x80000000, 0x00000000 };
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46 |
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47 | // Load the full matrix into registers
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48 | __m128 _L1 = matrix.template packet<MatrixAlignment>( 0);
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49 | __m128 _L2 = matrix.template packet<MatrixAlignment>( 4);
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50 | __m128 _L3 = matrix.template packet<MatrixAlignment>( 8);
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51 | __m128 _L4 = matrix.template packet<MatrixAlignment>(12);
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52 |
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53 | // The inverse is calculated using "Divide and Conquer" technique. The
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54 | // original matrix is divide into four 2x2 sub-matrices. Since each
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55 | // register holds four matrix element, the smaller matrices are
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56 | // represented as a registers. Hence we get a better locality of the
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57 | // calculations.
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58 |
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59 | __m128 A, B, C, D; // the four sub-matrices
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60 | if(!StorageOrdersMatch)
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61 | {
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62 | A = _mm_unpacklo_ps(_L1, _L2);
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63 | B = _mm_unpacklo_ps(_L3, _L4);
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64 | C = _mm_unpackhi_ps(_L1, _L2);
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65 | D = _mm_unpackhi_ps(_L3, _L4);
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66 | }
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67 | else
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68 | {
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69 | A = _mm_movelh_ps(_L1, _L2);
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70 | B = _mm_movehl_ps(_L2, _L1);
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71 | C = _mm_movelh_ps(_L3, _L4);
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72 | D = _mm_movehl_ps(_L4, _L3);
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73 | }
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74 |
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75 | __m128 iA, iB, iC, iD, // partial inverse of the sub-matrices
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76 | DC, AB;
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77 | __m128 dA, dB, dC, dD; // determinant of the sub-matrices
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78 | __m128 det, d, d1, d2;
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79 | __m128 rd; // reciprocal of the determinant
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80 |
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81 | // AB = A# * B
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82 | AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B);
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83 | AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E)));
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84 | // DC = D# * C
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85 | DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C);
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86 | DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E)));
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87 |
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88 | // dA = |A|
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89 | dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A);
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90 | dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA));
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91 | // dB = |B|
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92 | dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B);
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93 | dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB));
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94 |
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95 | // dC = |C|
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96 | dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C);
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97 | dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC));
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98 | // dD = |D|
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99 | dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D);
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100 | dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD));
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101 |
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102 | // d = trace(AB*DC) = trace(A#*B*D#*C)
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103 | d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);
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104 |
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105 | // iD = C*A#*B
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106 | iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB));
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107 | iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB)));
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108 | // iA = B*D#*C
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109 | iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC));
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110 | iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC)));
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111 |
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112 | // d = trace(AB*DC) = trace(A#*B*D#*C) [continue]
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113 | d = _mm_add_ps(d, _mm_movehl_ps(d, d));
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114 | d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1));
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115 | d1 = _mm_mul_ss(dA,dD);
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116 | d2 = _mm_mul_ss(dB,dC);
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117 |
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118 | // iD = D*|A| - C*A#*B
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119 | iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);
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120 |
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121 | // iA = A*|D| - B*D#*C;
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122 | iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);
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123 |
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124 | // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
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125 | det = _mm_sub_ss(_mm_add_ss(d1,d2),d);
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126 | rd = _mm_div_ss(_mm_set_ss(1.0f), det);
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127 |
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128 | // #ifdef ZERO_SINGULAR
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129 | // rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd);
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130 | // #endif
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131 |
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132 | // iB = D * (A#B)# = D*B#*A
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133 | iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33));
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134 | iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66)));
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135 | // iC = A * (D#C)# = A*C#*D
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136 | iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33));
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137 | iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66)));
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138 |
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139 | rd = _mm_shuffle_ps(rd,rd,0);
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140 | rd = _mm_xor_ps(rd, _mm_load_ps((float*)_Sign_PNNP));
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141 |
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142 | // iB = C*|B| - D*B#*A
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143 | iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);
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144 |
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145 | // iC = B*|C| - A*C#*D;
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146 | iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC);
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147 |
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148 | // iX = iX / det
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149 | iA = _mm_mul_ps(rd,iA);
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150 | iB = _mm_mul_ps(rd,iB);
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151 | iC = _mm_mul_ps(rd,iC);
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152 | iD = _mm_mul_ps(rd,iD);
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153 |
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154 | result.template writePacket<ResultAlignment>( 0, _mm_shuffle_ps(iA,iB,0x77));
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155 | result.template writePacket<ResultAlignment>( 4, _mm_shuffle_ps(iA,iB,0x22));
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156 | result.template writePacket<ResultAlignment>( 8, _mm_shuffle_ps(iC,iD,0x77));
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157 | result.template writePacket<ResultAlignment>(12, _mm_shuffle_ps(iC,iD,0x22));
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158 | }
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159 |
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160 | };
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161 |
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162 | template<typename MatrixType, typename ResultType>
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163 | struct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType>
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164 | {
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165 | enum {
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166 | MatrixAlignment = bool(MatrixType::Flags&AlignedBit),
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167 | ResultAlignment = bool(ResultType::Flags&AlignedBit),
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168 | StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
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169 | };
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170 | static void run(const MatrixType& matrix, ResultType& result)
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171 | {
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172 | const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
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173 | const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
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174 |
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175 | // The inverse is calculated using "Divide and Conquer" technique. The
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176 | // original matrix is divide into four 2x2 sub-matrices. Since each
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177 | // register of the matrix holds two element, the smaller matrices are
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178 | // consisted of two registers. Hence we get a better locality of the
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179 | // calculations.
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180 |
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181 | // the four sub-matrices
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182 | __m128d A1, A2, B1, B2, C1, C2, D1, D2;
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183 |
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184 | if(StorageOrdersMatch)
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185 | {
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186 | A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2);
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187 | A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6);
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188 | C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
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189 | C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
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190 | }
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191 | else
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192 | {
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193 | __m128d tmp;
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194 | A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2);
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195 | A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6);
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196 | tmp = A1;
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197 | A1 = _mm_unpacklo_pd(A1,A2);
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198 | A2 = _mm_unpackhi_pd(tmp,A2);
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199 | tmp = C1;
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200 | C1 = _mm_unpacklo_pd(C1,C2);
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201 | C2 = _mm_unpackhi_pd(tmp,C2);
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202 |
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203 | B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
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204 | B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
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205 | tmp = B1;
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206 | B1 = _mm_unpacklo_pd(B1,B2);
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207 | B2 = _mm_unpackhi_pd(tmp,B2);
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208 | tmp = D1;
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209 | D1 = _mm_unpacklo_pd(D1,D2);
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210 | D2 = _mm_unpackhi_pd(tmp,D2);
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211 | }
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212 |
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213 | __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, // partial invese of the sub-matrices
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214 | DC1, DC2, AB1, AB2;
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215 | __m128d dA, dB, dC, dD; // determinant of the sub-matrices
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216 | __m128d det, d1, d2, rd;
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217 |
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218 | // dA = |A|
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219 | dA = _mm_shuffle_pd(A2, A2, 1);
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220 | dA = _mm_mul_pd(A1, dA);
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221 | dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3));
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222 | // dB = |B|
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223 | dB = _mm_shuffle_pd(B2, B2, 1);
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224 | dB = _mm_mul_pd(B1, dB);
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225 | dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3));
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226 |
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227 | // AB = A# * B
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228 | AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3));
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229 | AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0));
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230 | AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3)));
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231 | AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0)));
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232 |
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233 | // dC = |C|
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234 | dC = _mm_shuffle_pd(C2, C2, 1);
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235 | dC = _mm_mul_pd(C1, dC);
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236 | dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3));
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237 | // dD = |D|
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238 | dD = _mm_shuffle_pd(D2, D2, 1);
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239 | dD = _mm_mul_pd(D1, dD);
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240 | dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3));
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241 |
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242 | // DC = D# * C
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243 | DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3));
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244 | DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0));
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245 | DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3)));
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246 | DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0)));
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247 |
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248 | // rd = trace(AB*DC) = trace(A#*B*D#*C)
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249 | d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0));
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250 | d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3));
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251 | rd = _mm_add_pd(d1, d2);
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252 | rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3));
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253 |
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254 | // iD = C*A#*B
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255 | iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0));
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256 | iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0));
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257 | iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3)));
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258 | iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3)));
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259 |
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260 | // iA = B*D#*C
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261 | iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0));
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262 | iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0));
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263 | iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3)));
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264 | iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3)));
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265 |
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266 | // iD = D*|A| - C*A#*B
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267 | dA = _mm_shuffle_pd(dA,dA,0);
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268 | iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1);
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269 | iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2);
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270 |
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271 | // iA = A*|D| - B*D#*C;
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272 | dD = _mm_shuffle_pd(dD,dD,0);
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273 | iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1);
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274 | iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2);
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275 |
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276 | d1 = _mm_mul_sd(dA, dD);
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277 | d2 = _mm_mul_sd(dB, dC);
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278 |
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279 | // iB = D * (A#B)# = D*B#*A
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280 | iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1));
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281 | iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1));
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282 | iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2)));
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283 | iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2)));
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284 |
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285 | // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
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286 | det = _mm_add_sd(d1, d2);
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287 | det = _mm_sub_sd(det, rd);
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288 |
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289 | // iC = A * (D#C)# = A*C#*D
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290 | iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1));
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291 | iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1));
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292 | iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2)));
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293 | iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2)));
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294 |
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295 | rd = _mm_div_sd(_mm_set_sd(1.0), det);
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296 | // #ifdef ZERO_SINGULAR
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297 | // rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd);
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298 | // #endif
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299 | rd = _mm_shuffle_pd(rd,rd,0);
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300 |
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301 | // iB = C*|B| - D*B#*A
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302 | dB = _mm_shuffle_pd(dB,dB,0);
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303 | iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1);
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304 | iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2);
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305 |
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306 | d1 = _mm_xor_pd(rd, _Sign_PN);
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307 | d2 = _mm_xor_pd(rd, _Sign_NP);
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308 |
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309 | // iC = B*|C| - A*C#*D;
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310 | dC = _mm_shuffle_pd(dC,dC,0);
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311 | iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1);
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312 | iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2);
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313 |
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314 | result.template writePacket<ResultAlignment>( 0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1)); // iA# / det
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315 | result.template writePacket<ResultAlignment>( 4, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2));
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316 | result.template writePacket<ResultAlignment>( 2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1)); // iB# / det
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317 | result.template writePacket<ResultAlignment>( 6, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2));
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318 | result.template writePacket<ResultAlignment>( 8, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1)); // iC# / det
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319 | result.template writePacket<ResultAlignment>(12, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2));
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320 | result.template writePacket<ResultAlignment>(10, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1)); // iD# / det
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321 | result.template writePacket<ResultAlignment>(14, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2));
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322 | }
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323 | };
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324 |
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325 | } // end namespace internal
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326 |
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327 | } // end namespace Eigen
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328 |
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329 | #endif // EIGEN_INVERSE_SSE_H
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