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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 algorithm below is a reimplementation of former \src\LU\Inverse_SSE.h using PacketMath.
-// inv(M) = M#/|M|, where inv(M), M# and |M| denote the inverse of M,
-// adjugate of M and determinant of M respectively. M# is computed block-wise
-// using specific formulae. For proof, see:
-// https://lxjk.github.io/2017/09/03/Fast-4x4-Matrix-Inverse-with-SSE-SIMD-Explained.html
-// Variable names are adopted from \src\LU\Inverse_SSE.h.
-//
-// The SSE code for the 4x4 float and double matrix inverse in former (deprecated) \src\LU\Inverse_SSE.h
-// 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.
-//
-// TODO: Unify implementations of different data types (i.e. float and double).
-#ifndef EIGEN_INVERSE_SIZE_4_H
-#define EIGEN_INVERSE_SIZE_4_H
-
-namespace Eigen
-{
-namespace internal
-{
-template <typename MatrixType, typename ResultType>
-struct compute_inverse_size4<Architecture::Target, float, MatrixType, ResultType>
-{
- enum
- {
- MatrixAlignment = traits<MatrixType>::Alignment,
- ResultAlignment = traits<ResultType>::Alignment,
- StorageOrdersMatch = (MatrixType::Flags & RowMajorBit) == (ResultType::Flags & RowMajorBit)
- };
- typedef typename conditional<(MatrixType::Flags & LinearAccessBit), MatrixType const &, typename MatrixType::PlainObject>::type ActualMatrixType;
-
- static void run(const MatrixType &mat, ResultType &result)
- {
- ActualMatrixType matrix(mat);
-
- const float* data = matrix.data();
- const Index stride = matrix.innerStride();
- Packet4f _L1 = ploadt<Packet4f,MatrixAlignment>(data);
- Packet4f _L2 = ploadt<Packet4f,MatrixAlignment>(data + stride*4);
- Packet4f _L3 = ploadt<Packet4f,MatrixAlignment>(data + stride*8);
- Packet4f _L4 = ploadt<Packet4f,MatrixAlignment>(data + stride*12);
-
- // Four 2x2 sub-matrices of the input matrix
- // input = [[A, B],
- // [C, D]]
- Packet4f A, B, C, D;
-
- if (!StorageOrdersMatch)
- {
- A = vec4f_unpacklo(_L1, _L2);
- B = vec4f_unpacklo(_L3, _L4);
- C = vec4f_unpackhi(_L1, _L2);
- D = vec4f_unpackhi(_L3, _L4);
- }
- else
- {
- A = vec4f_movelh(_L1, _L2);
- B = vec4f_movehl(_L2, _L1);
- C = vec4f_movelh(_L3, _L4);
- D = vec4f_movehl(_L4, _L3);
- }
-
- Packet4f AB, DC;
-
- // AB = A# * B, where A# denotes the adjugate of A, and * denotes matrix product.
- AB = pmul(vec4f_swizzle2(A, A, 3, 3, 0, 0), B);
- AB = psub(AB, pmul(vec4f_swizzle2(A, A, 1, 1, 2, 2), vec4f_swizzle2(B, B, 2, 3, 0, 1)));
-
- // DC = D#*C
- DC = pmul(vec4f_swizzle2(D, D, 3, 3, 0, 0), C);
- DC = psub(DC, pmul(vec4f_swizzle2(D, D, 1, 1, 2, 2), vec4f_swizzle2(C, C, 2, 3, 0, 1)));
-
- // determinants of the sub-matrices
- Packet4f dA, dB, dC, dD;
-
- dA = pmul(vec4f_swizzle2(A, A, 3, 3, 1, 1), A);
- dA = psub(dA, vec4f_movehl(dA, dA));
-
- dB = pmul(vec4f_swizzle2(B, B, 3, 3, 1, 1), B);
- dB = psub(dB, vec4f_movehl(dB, dB));
-
- dC = pmul(vec4f_swizzle2(C, C, 3, 3, 1, 1), C);
- dC = psub(dC, vec4f_movehl(dC, dC));
-
- dD = pmul(vec4f_swizzle2(D, D, 3, 3, 1, 1), D);
- dD = psub(dD, vec4f_movehl(dD, dD));
-
- Packet4f d, d1, d2;
-
- d = pmul(vec4f_swizzle2(DC, DC, 0, 2, 1, 3), AB);
- d = padd(d, vec4f_movehl(d, d));
- d = padd(d, vec4f_swizzle2(d, d, 1, 0, 0, 0));
- d1 = pmul(dA, dD);
- d2 = pmul(dB, dC);
-
- // determinant of the input matrix, det = |A||D| + |B||C| - trace(A#*B*D#*C)
- Packet4f det = vec4f_duplane(psub(padd(d1, d2), d), 0);
-
- // reciprocal of the determinant of the input matrix, rd = 1/det
- Packet4f rd = pdiv(pset1<Packet4f>(1.0f), det);
-
- // Four sub-matrices of the inverse
- Packet4f iA, iB, iC, iD;
-
- // iD = D*|A| - C*A#*B
- iD = pmul(vec4f_swizzle2(C, C, 0, 0, 2, 2), vec4f_movelh(AB, AB));
- iD = padd(iD, pmul(vec4f_swizzle2(C, C, 1, 1, 3, 3), vec4f_movehl(AB, AB)));
- iD = psub(pmul(D, vec4f_duplane(dA, 0)), iD);
-
- // iA = A*|D| - B*D#*C
- iA = pmul(vec4f_swizzle2(B, B, 0, 0, 2, 2), vec4f_movelh(DC, DC));
- iA = padd(iA, pmul(vec4f_swizzle2(B, B, 1, 1, 3, 3), vec4f_movehl(DC, DC)));
- iA = psub(pmul(A, vec4f_duplane(dD, 0)), iA);
-
- // iB = C*|B| - D * (A#B)# = C*|B| - D*B#*A
- iB = pmul(D, vec4f_swizzle2(AB, AB, 3, 0, 3, 0));
- iB = psub(iB, pmul(vec4f_swizzle2(D, D, 1, 0, 3, 2), vec4f_swizzle2(AB, AB, 2, 1, 2, 1)));
- iB = psub(pmul(C, vec4f_duplane(dB, 0)), iB);
-
- // iC = B*|C| - A * (D#C)# = B*|C| - A*C#*D
- iC = pmul(A, vec4f_swizzle2(DC, DC, 3, 0, 3, 0));
- iC = psub(iC, pmul(vec4f_swizzle2(A, A, 1, 0, 3, 2), vec4f_swizzle2(DC, DC, 2, 1, 2, 1)));
- iC = psub(pmul(B, vec4f_duplane(dC, 0)), iC);
-
- const float sign_mask[4] = {0.0f, numext::bit_cast<float>(0x80000000u), numext::bit_cast<float>(0x80000000u), 0.0f};
- const Packet4f p4f_sign_PNNP = ploadu<Packet4f>(sign_mask);
- rd = pxor(rd, p4f_sign_PNNP);
- iA = pmul(iA, rd);
- iB = pmul(iB, rd);
- iC = pmul(iC, rd);
- iD = pmul(iD, rd);
-
- Index res_stride = result.outerStride();
- float *res = result.data();
-
- pstoret<float, Packet4f, ResultAlignment>(res + 0, vec4f_swizzle2(iA, iB, 3, 1, 3, 1));
- pstoret<float, Packet4f, ResultAlignment>(res + res_stride, vec4f_swizzle2(iA, iB, 2, 0, 2, 0));
- pstoret<float, Packet4f, ResultAlignment>(res + 2 * res_stride, vec4f_swizzle2(iC, iD, 3, 1, 3, 1));
- pstoret<float, Packet4f, ResultAlignment>(res + 3 * res_stride, vec4f_swizzle2(iC, iD, 2, 0, 2, 0));
- }
-};
-
-#if !(defined EIGEN_VECTORIZE_NEON && !(EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG))
-// same algorithm as above, except that each operand is split into
-// halves for two registers to hold.
-template <typename MatrixType, typename ResultType>
-struct compute_inverse_size4<Architecture::Target, double, MatrixType, ResultType>
-{
- enum
- {
- MatrixAlignment = traits<MatrixType>::Alignment,
- ResultAlignment = traits<ResultType>::Alignment,
- StorageOrdersMatch = (MatrixType::Flags & RowMajorBit) == (ResultType::Flags & RowMajorBit)
- };
- typedef typename conditional<(MatrixType::Flags & LinearAccessBit),
- MatrixType const &,
- typename MatrixType::PlainObject>::type
- ActualMatrixType;
-
- static void run(const MatrixType &mat, ResultType &result)
- {
- ActualMatrixType matrix(mat);
-
- // Four 2x2 sub-matrices of the input matrix, each is further divided into upper and lower
- // row e.g. A1, upper row of A, A2, lower row of A
- // input = [[A, B], = [[[A1, [B1,
- // [C, D]] A2], B2]],
- // [[C1, [D1,
- // C2], D2]]]
-
- Packet2d A1, A2, B1, B2, C1, C2, D1, D2;
-
- const double* data = matrix.data();
- const Index stride = matrix.innerStride();
- if (StorageOrdersMatch)
- {
- A1 = ploadt<Packet2d,MatrixAlignment>(data + stride*0);
- B1 = ploadt<Packet2d,MatrixAlignment>(data + stride*2);
- A2 = ploadt<Packet2d,MatrixAlignment>(data + stride*4);
- B2 = ploadt<Packet2d,MatrixAlignment>(data + stride*6);
- C1 = ploadt<Packet2d,MatrixAlignment>(data + stride*8);
- D1 = ploadt<Packet2d,MatrixAlignment>(data + stride*10);
- C2 = ploadt<Packet2d,MatrixAlignment>(data + stride*12);
- D2 = ploadt<Packet2d,MatrixAlignment>(data + stride*14);
- }
- else
- {
- Packet2d temp;
- A1 = ploadt<Packet2d,MatrixAlignment>(data + stride*0);
- C1 = ploadt<Packet2d,MatrixAlignment>(data + stride*2);
- A2 = ploadt<Packet2d,MatrixAlignment>(data + stride*4);
- C2 = ploadt<Packet2d,MatrixAlignment>(data + stride*6);
- temp = A1;
- A1 = vec2d_unpacklo(A1, A2);
- A2 = vec2d_unpackhi(temp, A2);
-
- temp = C1;
- C1 = vec2d_unpacklo(C1, C2);
- C2 = vec2d_unpackhi(temp, C2);
-
- B1 = ploadt<Packet2d,MatrixAlignment>(data + stride*8);
- D1 = ploadt<Packet2d,MatrixAlignment>(data + stride*10);
- B2 = ploadt<Packet2d,MatrixAlignment>(data + stride*12);
- D2 = ploadt<Packet2d,MatrixAlignment>(data + stride*14);
-
- temp = B1;
- B1 = vec2d_unpacklo(B1, B2);
- B2 = vec2d_unpackhi(temp, B2);
-
- temp = D1;
- D1 = vec2d_unpacklo(D1, D2);
- D2 = vec2d_unpackhi(temp, D2);
- }
-
- // determinants of the sub-matrices
- Packet2d dA, dB, dC, dD;
-
- dA = vec2d_swizzle2(A2, A2, 1);
- dA = pmul(A1, dA);
- dA = psub(dA, vec2d_duplane(dA, 1));
-
- dB = vec2d_swizzle2(B2, B2, 1);
- dB = pmul(B1, dB);
- dB = psub(dB, vec2d_duplane(dB, 1));
-
- dC = vec2d_swizzle2(C2, C2, 1);
- dC = pmul(C1, dC);
- dC = psub(dC, vec2d_duplane(dC, 1));
-
- dD = vec2d_swizzle2(D2, D2, 1);
- dD = pmul(D1, dD);
- dD = psub(dD, vec2d_duplane(dD, 1));
-
- Packet2d DC1, DC2, AB1, AB2;
-
- // AB = A# * B, where A# denotes the adjugate of A, and * denotes matrix product.
- AB1 = pmul(B1, vec2d_duplane(A2, 1));
- AB2 = pmul(B2, vec2d_duplane(A1, 0));
- AB1 = psub(AB1, pmul(B2, vec2d_duplane(A1, 1)));
- AB2 = psub(AB2, pmul(B1, vec2d_duplane(A2, 0)));
-
- // DC = D#*C
- DC1 = pmul(C1, vec2d_duplane(D2, 1));
- DC2 = pmul(C2, vec2d_duplane(D1, 0));
- DC1 = psub(DC1, pmul(C2, vec2d_duplane(D1, 1)));
- DC2 = psub(DC2, pmul(C1, vec2d_duplane(D2, 0)));
-
- Packet2d d1, d2;
-
- // determinant of the input matrix, det = |A||D| + |B||C| - trace(A#*B*D#*C)
- Packet2d det;
-
- // reciprocal of the determinant of the input matrix, rd = 1/det
- Packet2d rd;
-
- d1 = pmul(AB1, vec2d_swizzle2(DC1, DC2, 0));
- d2 = pmul(AB2, vec2d_swizzle2(DC1, DC2, 3));
- rd = padd(d1, d2);
- rd = padd(rd, vec2d_duplane(rd, 1));
-
- d1 = pmul(dA, dD);
- d2 = pmul(dB, dC);
-
- det = padd(d1, d2);
- det = psub(det, rd);
- det = vec2d_duplane(det, 0);
- rd = pdiv(pset1<Packet2d>(1.0), det);
-
- // rows of four sub-matrices of the inverse
- Packet2d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2;
-
- // iD = D*|A| - C*A#*B
- iD1 = pmul(AB1, vec2d_duplane(C1, 0));
- iD2 = pmul(AB1, vec2d_duplane(C2, 0));
- iD1 = padd(iD1, pmul(AB2, vec2d_duplane(C1, 1)));
- iD2 = padd(iD2, pmul(AB2, vec2d_duplane(C2, 1)));
- dA = vec2d_duplane(dA, 0);
- iD1 = psub(pmul(D1, dA), iD1);
- iD2 = psub(pmul(D2, dA), iD2);
-
- // iA = A*|D| - B*D#*C
- iA1 = pmul(DC1, vec2d_duplane(B1, 0));
- iA2 = pmul(DC1, vec2d_duplane(B2, 0));
- iA1 = padd(iA1, pmul(DC2, vec2d_duplane(B1, 1)));
- iA2 = padd(iA2, pmul(DC2, vec2d_duplane(B2, 1)));
- dD = vec2d_duplane(dD, 0);
- iA1 = psub(pmul(A1, dD), iA1);
- iA2 = psub(pmul(A2, dD), iA2);
-
- // iB = C*|B| - D * (A#B)# = C*|B| - D*B#*A
- iB1 = pmul(D1, vec2d_swizzle2(AB2, AB1, 1));
- iB2 = pmul(D2, vec2d_swizzle2(AB2, AB1, 1));
- iB1 = psub(iB1, pmul(vec2d_swizzle2(D1, D1, 1), vec2d_swizzle2(AB2, AB1, 2)));
- iB2 = psub(iB2, pmul(vec2d_swizzle2(D2, D2, 1), vec2d_swizzle2(AB2, AB1, 2)));
- dB = vec2d_duplane(dB, 0);
- iB1 = psub(pmul(C1, dB), iB1);
- iB2 = psub(pmul(C2, dB), iB2);
-
- // iC = B*|C| - A * (D#C)# = B*|C| - A*C#*D
- iC1 = pmul(A1, vec2d_swizzle2(DC2, DC1, 1));
- iC2 = pmul(A2, vec2d_swizzle2(DC2, DC1, 1));
- iC1 = psub(iC1, pmul(vec2d_swizzle2(A1, A1, 1), vec2d_swizzle2(DC2, DC1, 2)));
- iC2 = psub(iC2, pmul(vec2d_swizzle2(A2, A2, 1), vec2d_swizzle2(DC2, DC1, 2)));
- dC = vec2d_duplane(dC, 0);
- iC1 = psub(pmul(B1, dC), iC1);
- iC2 = psub(pmul(B2, dC), iC2);
-
- const double sign_mask1[2] = {0.0, numext::bit_cast<double>(0x8000000000000000ull)};
- const double sign_mask2[2] = {numext::bit_cast<double>(0x8000000000000000ull), 0.0};
- const Packet2d sign_PN = ploadu<Packet2d>(sign_mask1);
- const Packet2d sign_NP = ploadu<Packet2d>(sign_mask2);
- d1 = pxor(rd, sign_PN);
- d2 = pxor(rd, sign_NP);
-
- Index res_stride = result.outerStride();
- double *res = result.data();
- pstoret<double, Packet2d, ResultAlignment>(res + 0, pmul(vec2d_swizzle2(iA2, iA1, 3), d1));
- pstoret<double, Packet2d, ResultAlignment>(res + res_stride, pmul(vec2d_swizzle2(iA2, iA1, 0), d2));
- pstoret<double, Packet2d, ResultAlignment>(res + 2, pmul(vec2d_swizzle2(iB2, iB1, 3), d1));
- pstoret<double, Packet2d, ResultAlignment>(res + res_stride + 2, pmul(vec2d_swizzle2(iB2, iB1, 0), d2));
- pstoret<double, Packet2d, ResultAlignment>(res + 2 * res_stride, pmul(vec2d_swizzle2(iC2, iC1, 3), d1));
- pstoret<double, Packet2d, ResultAlignment>(res + 3 * res_stride, pmul(vec2d_swizzle2(iC2, iC1, 0), d2));
- pstoret<double, Packet2d, ResultAlignment>(res + 2 * res_stride + 2, pmul(vec2d_swizzle2(iD2, iD1, 3), d1));
- pstoret<double, Packet2d, ResultAlignment>(res + 3 * res_stride + 2, pmul(vec2d_swizzle2(iD2, iD1, 0), d2));
- }
-};
-#endif
-} // namespace internal
-} // namespace Eigen
-#endif
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