Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/Eigen/src/LU/arch/Inverse_SSE.h b/Eigen/src/LU/arch/Inverse_SSE.h
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+// 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