1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2001 Intel Corporation 5 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud (at) inria.fr> 6 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 7 // 8 // This Source Code Form is subject to the terms of the Mozilla 9 // Public License v. 2.0. If a copy of the MPL was not distributed 10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 11 12 // The SSE code for the 4x4 float and double matrix inverse in this file 13 // comes from the following Intel's library: 14 // http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/ 15 // 16 // Here is the respective copyright and license statement: 17 // 18 // Copyright (c) 2001 Intel Corporation. 19 // 20 // Permition is granted to use, copy, distribute and prepare derivative works 21 // of this library for any purpose and without fee, provided, that the above 22 // copyright notice and this statement appear in all copies. 23 // Intel makes no representations about the suitability of this software for 24 // any purpose, and specifically disclaims all warranties. 25 // See LEGAL.TXT for all the legal information. 26 27 #ifndef EIGEN_INVERSE_SSE_H 28 #define EIGEN_INVERSE_SSE_H 29 30 namespace Eigen { 31 32 namespace internal { 33 34 template<typename MatrixType, typename ResultType> 35 struct compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType> 36 { 37 enum { 38 MatrixAlignment = bool(MatrixType::Flags&AlignedBit), 39 ResultAlignment = bool(ResultType::Flags&AlignedBit), 40 StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit) 41 }; 42 43 static void run(const MatrixType& matrix, ResultType& result) 44 { 45 EIGEN_ALIGN16 const unsigned int _Sign_PNNP[4] = { 0x00000000, 0x80000000, 0x80000000, 0x00000000 }; 46 47 // Load the full matrix into registers 48 __m128 _L1 = matrix.template packet<MatrixAlignment>( 0); 49 __m128 _L2 = matrix.template packet<MatrixAlignment>( 4); 50 __m128 _L3 = matrix.template packet<MatrixAlignment>( 8); 51 __m128 _L4 = matrix.template packet<MatrixAlignment>(12); 52 53 // The inverse is calculated using "Divide and Conquer" technique. The 54 // original matrix is divide into four 2x2 sub-matrices. Since each 55 // register holds four matrix element, the smaller matrices are 56 // represented as a registers. Hence we get a better locality of the 57 // calculations. 58 59 __m128 A, B, C, D; // the four sub-matrices 60 if(!StorageOrdersMatch) 61 { 62 A = _mm_unpacklo_ps(_L1, _L2); 63 B = _mm_unpacklo_ps(_L3, _L4); 64 C = _mm_unpackhi_ps(_L1, _L2); 65 D = _mm_unpackhi_ps(_L3, _L4); 66 } 67 else 68 { 69 A = _mm_movelh_ps(_L1, _L2); 70 B = _mm_movehl_ps(_L2, _L1); 71 C = _mm_movelh_ps(_L3, _L4); 72 D = _mm_movehl_ps(_L4, _L3); 73 } 74 75 __m128 iA, iB, iC, iD, // partial inverse of the sub-matrices 76 DC, AB; 77 __m128 dA, dB, dC, dD; // determinant of the sub-matrices 78 __m128 det, d, d1, d2; 79 __m128 rd; // reciprocal of the determinant 80 81 // AB = A# * B 82 AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B); 83 AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E))); 84 // DC = D# * C 85 DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C); 86 DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E))); 87 88 // dA = |A| 89 dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A); 90 dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA)); 91 // dB = |B| 92 dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B); 93 dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB)); 94 95 // dC = |C| 96 dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C); 97 dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC)); 98 // dD = |D| 99 dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D); 100 dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD)); 101 102 // d = trace(AB*DC) = trace(A#*B*D#*C) 103 d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB); 104 105 // iD = C*A#*B 106 iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB)); 107 iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB))); 108 // iA = B*D#*C 109 iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC)); 110 iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC))); 111 112 // d = trace(AB*DC) = trace(A#*B*D#*C) [continue] 113 d = _mm_add_ps(d, _mm_movehl_ps(d, d)); 114 d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1)); 115 d1 = _mm_mul_ss(dA,dD); 116 d2 = _mm_mul_ss(dB,dC); 117 118 // iD = D*|A| - C*A#*B 119 iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD); 120 121 // iA = A*|D| - B*D#*C; 122 iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA); 123 124 // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C) 125 det = _mm_sub_ss(_mm_add_ss(d1,d2),d); 126 rd = _mm_div_ss(_mm_set_ss(1.0f), det); 127 128 // #ifdef ZERO_SINGULAR 129 // rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd); 130 // #endif 131 132 // iB = D * (A#B)# = D*B#*A 133 iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33)); 134 iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66))); 135 // iC = A * (D#C)# = A*C#*D 136 iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33)); 137 iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66))); 138 139 rd = _mm_shuffle_ps(rd,rd,0); 140 rd = _mm_xor_ps(rd, _mm_load_ps((float*)_Sign_PNNP)); 141 142 // iB = C*|B| - D*B#*A 143 iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB); 144 145 // iC = B*|C| - A*C#*D; 146 iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC); 147 148 // iX = iX / det 149 iA = _mm_mul_ps(rd,iA); 150 iB = _mm_mul_ps(rd,iB); 151 iC = _mm_mul_ps(rd,iC); 152 iD = _mm_mul_ps(rd,iD); 153 154 result.template writePacket<ResultAlignment>( 0, _mm_shuffle_ps(iA,iB,0x77)); 155 result.template writePacket<ResultAlignment>( 4, _mm_shuffle_ps(iA,iB,0x22)); 156 result.template writePacket<ResultAlignment>( 8, _mm_shuffle_ps(iC,iD,0x77)); 157 result.template writePacket<ResultAlignment>(12, _mm_shuffle_ps(iC,iD,0x22)); 158 } 159 160 }; 161 162 template<typename MatrixType, typename ResultType> 163 struct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType> 164 { 165 enum { 166 MatrixAlignment = bool(MatrixType::Flags&AlignedBit), 167 ResultAlignment = bool(ResultType::Flags&AlignedBit), 168 StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit) 169 }; 170 static void run(const MatrixType& matrix, ResultType& result) 171 { 172 const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0)); 173 const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0)); 174 175 // The inverse is calculated using "Divide and Conquer" technique. The 176 // original matrix is divide into four 2x2 sub-matrices. Since each 177 // register of the matrix holds two element, the smaller matrices are 178 // consisted of two registers. Hence we get a better locality of the 179 // calculations. 180 181 // the four sub-matrices 182 __m128d A1, A2, B1, B2, C1, C2, D1, D2; 183 184 if(StorageOrdersMatch) 185 { 186 A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2); 187 A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6); 188 C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10); 189 C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14); 190 } 191 else 192 { 193 __m128d tmp; 194 A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2); 195 A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6); 196 tmp = A1; 197 A1 = _mm_unpacklo_pd(A1,A2); 198 A2 = _mm_unpackhi_pd(tmp,A2); 199 tmp = C1; 200 C1 = _mm_unpacklo_pd(C1,C2); 201 C2 = _mm_unpackhi_pd(tmp,C2); 202 203 B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10); 204 B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14); 205 tmp = B1; 206 B1 = _mm_unpacklo_pd(B1,B2); 207 B2 = _mm_unpackhi_pd(tmp,B2); 208 tmp = D1; 209 D1 = _mm_unpacklo_pd(D1,D2); 210 D2 = _mm_unpackhi_pd(tmp,D2); 211 } 212 213 __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, // partial invese of the sub-matrices 214 DC1, DC2, AB1, AB2; 215 __m128d dA, dB, dC, dD; // determinant of the sub-matrices 216 __m128d det, d1, d2, rd; 217 218 // dA = |A| 219 dA = _mm_shuffle_pd(A2, A2, 1); 220 dA = _mm_mul_pd(A1, dA); 221 dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3)); 222 // dB = |B| 223 dB = _mm_shuffle_pd(B2, B2, 1); 224 dB = _mm_mul_pd(B1, dB); 225 dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3)); 226 227 // AB = A# * B 228 AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3)); 229 AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0)); 230 AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3))); 231 AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0))); 232 233 // dC = |C| 234 dC = _mm_shuffle_pd(C2, C2, 1); 235 dC = _mm_mul_pd(C1, dC); 236 dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3)); 237 // dD = |D| 238 dD = _mm_shuffle_pd(D2, D2, 1); 239 dD = _mm_mul_pd(D1, dD); 240 dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3)); 241 242 // DC = D# * C 243 DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3)); 244 DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0)); 245 DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3))); 246 DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0))); 247 248 // rd = trace(AB*DC) = trace(A#*B*D#*C) 249 d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0)); 250 d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3)); 251 rd = _mm_add_pd(d1, d2); 252 rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3)); 253 254 // iD = C*A#*B 255 iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0)); 256 iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0)); 257 iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3))); 258 iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3))); 259 260 // iA = B*D#*C 261 iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0)); 262 iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0)); 263 iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3))); 264 iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3))); 265 266 // iD = D*|A| - C*A#*B 267 dA = _mm_shuffle_pd(dA,dA,0); 268 iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1); 269 iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2); 270 271 // iA = A*|D| - B*D#*C; 272 dD = _mm_shuffle_pd(dD,dD,0); 273 iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1); 274 iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2); 275 276 d1 = _mm_mul_sd(dA, dD); 277 d2 = _mm_mul_sd(dB, dC); 278 279 // iB = D * (A#B)# = D*B#*A 280 iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1)); 281 iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1)); 282 iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2))); 283 iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2))); 284 285 // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C) 286 det = _mm_add_sd(d1, d2); 287 det = _mm_sub_sd(det, rd); 288 289 // iC = A * (D#C)# = A*C#*D 290 iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1)); 291 iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1)); 292 iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2))); 293 iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2))); 294 295 rd = _mm_div_sd(_mm_set_sd(1.0), det); 296 // #ifdef ZERO_SINGULAR 297 // rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd); 298 // #endif 299 rd = _mm_shuffle_pd(rd,rd,0); 300 301 // iB = C*|B| - D*B#*A 302 dB = _mm_shuffle_pd(dB,dB,0); 303 iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1); 304 iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2); 305 306 d1 = _mm_xor_pd(rd, _Sign_PN); 307 d2 = _mm_xor_pd(rd, _Sign_NP); 308 309 // iC = B*|C| - A*C#*D; 310 dC = _mm_shuffle_pd(dC,dC,0); 311 iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1); 312 iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2); 313 314 result.template writePacket<ResultAlignment>( 0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1)); // iA# / det 315 result.template writePacket<ResultAlignment>( 4, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2)); 316 result.template writePacket<ResultAlignment>( 2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1)); // iB# / det 317 result.template writePacket<ResultAlignment>( 6, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2)); 318 result.template writePacket<ResultAlignment>( 8, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1)); // iC# / det 319 result.template writePacket<ResultAlignment>(12, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2)); 320 result.template writePacket<ResultAlignment>(10, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1)); // iD# / det 321 result.template writePacket<ResultAlignment>(14, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2)); 322 } 323 }; 324 325 } // end namespace internal 326 327 } // end namespace Eigen 328 329 #endif // EIGEN_INVERSE_SSE_H 330
