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Diffstat (limited to 'third_party/eigen3/Eigen/src/LU/arch/Inverse_SSE.h')
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1 files changed, 329 insertions, 0 deletions
diff --git a/third_party/eigen3/Eigen/src/LU/arch/Inverse_SSE.h b/third_party/eigen3/Eigen/src/LU/arch/Inverse_SSE.h new file mode 100644 index 0000000000..60b7a23763 --- /dev/null +++ b/third_party/eigen3/Eigen/src/LU/arch/Inverse_SSE.h @@ -0,0 +1,329 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2001 Intel Corporation +// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +// The SSE code for the 4x4 float and double matrix inverse in this file +// comes from the following Intel's library: +// http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/ +// +// Here is the respective copyright and license statement: +// +// Copyright (c) 2001 Intel Corporation. +// +// Permition is granted to use, copy, distribute and prepare derivative works +// of this library for any purpose and without fee, provided, that the above +// copyright notice and this statement appear in all copies. +// Intel makes no representations about the suitability of this software for +// any purpose, and specifically disclaims all warranties. +// See LEGAL.TXT for all the legal information. + +#ifndef EIGEN_INVERSE_SSE_H +#define EIGEN_INVERSE_SSE_H + +namespace Eigen { + +namespace internal { + +template<typename MatrixType, typename ResultType> +struct compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType> +{ + enum { + MatrixAlignment = bool(MatrixType::Flags&AlignedBit), + ResultAlignment = bool(ResultType::Flags&AlignedBit), + StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit) + }; + + static void run(const MatrixType& matrix, ResultType& result) + { + EIGEN_ALIGN16 const unsigned int _Sign_PNNP[4] = { 0x00000000, 0x80000000, 0x80000000, 0x00000000 }; + + // Load the full matrix into registers + __m128 _L1 = matrix.template packet<MatrixAlignment>( 0); + __m128 _L2 = matrix.template packet<MatrixAlignment>( 4); + __m128 _L3 = matrix.template packet<MatrixAlignment>( 8); + __m128 _L4 = matrix.template packet<MatrixAlignment>(12); + + // The inverse is calculated using "Divide and Conquer" technique. The + // original matrix is divide into four 2x2 sub-matrices. Since each + // register holds four matrix element, the smaller matrices are + // represented as a registers. Hence we get a better locality of the + // calculations. + + __m128 A, B, C, D; // the four sub-matrices + if(!StorageOrdersMatch) + { + A = _mm_unpacklo_ps(_L1, _L2); + B = _mm_unpacklo_ps(_L3, _L4); + C = _mm_unpackhi_ps(_L1, _L2); + D = _mm_unpackhi_ps(_L3, _L4); + } + else + { + A = _mm_movelh_ps(_L1, _L2); + B = _mm_movehl_ps(_L2, _L1); + C = _mm_movelh_ps(_L3, _L4); + D = _mm_movehl_ps(_L4, _L3); + } + + __m128 iA, iB, iC, iD, // partial inverse of the sub-matrices + DC, AB; + __m128 dA, dB, dC, dD; // determinant of the sub-matrices + __m128 det, d, d1, d2; + __m128 rd; // reciprocal of the determinant + + // AB = A# * B + AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B); + AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E))); + // DC = D# * C + DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C); + DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E))); + + // dA = |A| + dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A); + dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA)); + // dB = |B| + dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B); + dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB)); + + // dC = |C| + dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C); + dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC)); + // dD = |D| + dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D); + dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD)); + + // d = trace(AB*DC) = trace(A#*B*D#*C) + d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB); + + // iD = C*A#*B + iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB)); + iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB))); + // iA = B*D#*C + iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC)); + iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC))); + + // d = trace(AB*DC) = trace(A#*B*D#*C) [continue] + d = _mm_add_ps(d, _mm_movehl_ps(d, d)); + d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1)); + d1 = _mm_mul_ss(dA,dD); + d2 = _mm_mul_ss(dB,dC); + + // iD = D*|A| - C*A#*B + iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD); + + // iA = A*|D| - B*D#*C; + iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA); + + // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C) + det = _mm_sub_ss(_mm_add_ss(d1,d2),d); + rd = _mm_div_ss(_mm_set_ss(1.0f), det); + +// #ifdef ZERO_SINGULAR +// rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd); +// #endif + + // iB = D * (A#B)# = D*B#*A + iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33)); + iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66))); + // iC = A * (D#C)# = A*C#*D + iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33)); + iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66))); + + rd = _mm_shuffle_ps(rd,rd,0); + rd = _mm_xor_ps(rd, _mm_load_ps((float*)_Sign_PNNP)); + + // iB = C*|B| - D*B#*A + iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB); + + // iC = B*|C| - A*C#*D; + iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC); + + // iX = iX / det + iA = _mm_mul_ps(rd,iA); + iB = _mm_mul_ps(rd,iB); + iC = _mm_mul_ps(rd,iC); + iD = _mm_mul_ps(rd,iD); + + result.template writePacket<ResultAlignment>( 0, _mm_shuffle_ps(iA,iB,0x77)); + result.template writePacket<ResultAlignment>( 4, _mm_shuffle_ps(iA,iB,0x22)); + result.template writePacket<ResultAlignment>( 8, _mm_shuffle_ps(iC,iD,0x77)); + result.template writePacket<ResultAlignment>(12, _mm_shuffle_ps(iC,iD,0x22)); + } + +}; + +template<typename MatrixType, typename ResultType> +struct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType> +{ + enum { + MatrixAlignment = bool(MatrixType::Flags&AlignedBit), + ResultAlignment = bool(ResultType::Flags&AlignedBit), + StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit) + }; + static void run(const MatrixType& matrix, ResultType& result) + { + const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0)); + const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0)); + + // The inverse is calculated using "Divide and Conquer" technique. The + // original matrix is divide into four 2x2 sub-matrices. Since each + // register of the matrix holds two element, the smaller matrices are + // consisted of two registers. Hence we get a better locality of the + // calculations. + + // the four sub-matrices + __m128d A1, A2, B1, B2, C1, C2, D1, D2; + + if(StorageOrdersMatch) + { + A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2); + A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6); + C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10); + C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14); + } + else + { + __m128d tmp; + A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2); + A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6); + tmp = A1; + A1 = _mm_unpacklo_pd(A1,A2); + A2 = _mm_unpackhi_pd(tmp,A2); + tmp = C1; + C1 = _mm_unpacklo_pd(C1,C2); + C2 = _mm_unpackhi_pd(tmp,C2); + + B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10); + B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14); + tmp = B1; + B1 = _mm_unpacklo_pd(B1,B2); + B2 = _mm_unpackhi_pd(tmp,B2); + tmp = D1; + D1 = _mm_unpacklo_pd(D1,D2); + D2 = _mm_unpackhi_pd(tmp,D2); + } + + __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, // partial invese of the sub-matrices + DC1, DC2, AB1, AB2; + __m128d dA, dB, dC, dD; // determinant of the sub-matrices + __m128d det, d1, d2, rd; + + // dA = |A| + dA = _mm_shuffle_pd(A2, A2, 1); + dA = _mm_mul_pd(A1, dA); + dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3)); + // dB = |B| + dB = _mm_shuffle_pd(B2, B2, 1); + dB = _mm_mul_pd(B1, dB); + dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3)); + + // AB = A# * B + AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3)); + AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0)); + AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3))); + AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0))); + + // dC = |C| + dC = _mm_shuffle_pd(C2, C2, 1); + dC = _mm_mul_pd(C1, dC); + dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3)); + // dD = |D| + dD = _mm_shuffle_pd(D2, D2, 1); + dD = _mm_mul_pd(D1, dD); + dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3)); + + // DC = D# * C + DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3)); + DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0)); + DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3))); + DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0))); + + // rd = trace(AB*DC) = trace(A#*B*D#*C) + d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0)); + d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3)); + rd = _mm_add_pd(d1, d2); + rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3)); + + // iD = C*A#*B + iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0)); + iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0)); + iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3))); + iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3))); + + // iA = B*D#*C + iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0)); + iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0)); + iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3))); + iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3))); + + // iD = D*|A| - C*A#*B + dA = _mm_shuffle_pd(dA,dA,0); + iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1); + iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2); + + // iA = A*|D| - B*D#*C; + dD = _mm_shuffle_pd(dD,dD,0); + iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1); + iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2); + + d1 = _mm_mul_sd(dA, dD); + d2 = _mm_mul_sd(dB, dC); + + // iB = D * (A#B)# = D*B#*A + iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1)); + iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1)); + iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2))); + iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2))); + + // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C) + det = _mm_add_sd(d1, d2); + det = _mm_sub_sd(det, rd); + + // iC = A * (D#C)# = A*C#*D + iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1)); + iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1)); + iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2))); + iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2))); + + rd = _mm_div_sd(_mm_set_sd(1.0), det); +// #ifdef ZERO_SINGULAR +// rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd); +// #endif + rd = _mm_shuffle_pd(rd,rd,0); + + // iB = C*|B| - D*B#*A + dB = _mm_shuffle_pd(dB,dB,0); + iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1); + iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2); + + d1 = _mm_xor_pd(rd, _Sign_PN); + d2 = _mm_xor_pd(rd, _Sign_NP); + + // iC = B*|C| - A*C#*D; + dC = _mm_shuffle_pd(dC,dC,0); + iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1); + iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2); + + result.template writePacket<ResultAlignment>( 0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1)); // iA# / det + result.template writePacket<ResultAlignment>( 4, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2)); + result.template writePacket<ResultAlignment>( 2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1)); // iB# / det + result.template writePacket<ResultAlignment>( 6, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2)); + result.template writePacket<ResultAlignment>( 8, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1)); // iC# / det + result.template writePacket<ResultAlignment>(12, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2)); + result.template writePacket<ResultAlignment>(10, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1)); // iD# / det + result.template writePacket<ResultAlignment>(14, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2)); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_INVERSE_SSE_H |