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Diffstat (limited to 'Eigen/src/LU/arch/Inverse_SSE.h')
| -rw-r--r-- | Eigen/src/LU/arch/Inverse_SSE.h | 152 |
1 files changed, 152 insertions, 0 deletions
diff --git a/Eigen/src/LU/arch/Inverse_SSE.h b/Eigen/src/LU/arch/Inverse_SSE.h new file mode 100644 index 000000000..371861aa5 --- /dev/null +++ b/Eigen/src/LU/arch/Inverse_SSE.h @@ -0,0 +1,152 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 1999 Intel Corporation +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +// The SSE code for the 4x4 float matrix inverse in this file comes from the file +// ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf +// See page ii of that document for legal stuff. Not being lawyers, we just assume +// here that if Intel makes this document publically available, with source code +// and detailed explanations, it's because they want their CPUs to be fed with +// good code, and therefore they presumably don't mind us using it in Eigen. + +#ifndef EIGEN_INVERSE_SSE_H +#define EIGEN_INVERSE_SSE_H + +template<typename MatrixType, typename ResultType> +struct ei_compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType> +{ + static void run(const MatrixType& matrix, ResultType& result) + { + // Variables (Streaming SIMD Extensions registers) which will contain cofactors and, later, the + // lines of the inverted matrix. + __m128 minor0, minor1, minor2, minor3; + + // Variables which will contain the lines of the reference matrix and, later (after the transposition), + // the columns of the original matrix. + __m128 row0, row1, row2, row3; + + // Temporary variables and the variable that will contain the matrix determinant. + __m128 det, tmp1; + + // Matrix transposition + const float *src = matrix.data(); + tmp1 = _mm_loadh_pi(_mm_loadl_pi(tmp1, (__m64*)(src)), (__m64*)(src+ 4)); + row1 = _mm_loadh_pi(_mm_loadl_pi(row1, (__m64*)(src+8)), (__m64*)(src+12)); + row0 = _mm_shuffle_ps(tmp1, row1, 0x88); + row1 = _mm_shuffle_ps(row1, tmp1, 0xDD); + tmp1 = _mm_loadh_pi(_mm_loadl_pi(tmp1, (__m64*)(src+ 2)), (__m64*)(src+ 6)); + row3 = _mm_loadh_pi(_mm_loadl_pi(row3, (__m64*)(src+10)), (__m64*)(src+14)); + row2 = _mm_shuffle_ps(tmp1, row3, 0x88); + row3 = _mm_shuffle_ps(row3, tmp1, 0xDD); + + + // Cofactors calculation. Because in the process of cofactor computation some pairs in three- + // element products are repeated, it is not reasonable to load these pairs anew every time. The + // values in the registers with these pairs are formed using shuffle instruction. Cofactors are + // calculated row by row (4 elements are placed in 1 SP FP SIMD floating point register). + + tmp1 = _mm_mul_ps(row2, row3); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); + minor0 = _mm_mul_ps(row1, tmp1); + minor1 = _mm_mul_ps(row0, tmp1); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); + minor0 = _mm_sub_ps(_mm_mul_ps(row1, tmp1), minor0); + minor1 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor1); + minor1 = _mm_shuffle_ps(minor1, minor1, 0x4E); + // ----------------------------------------------- + tmp1 = _mm_mul_ps(row1, row2); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); + minor0 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor0); + minor3 = _mm_mul_ps(row0, tmp1); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); + minor0 = _mm_sub_ps(minor0, _mm_mul_ps(row3, tmp1)); + minor3 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor3); + minor3 = _mm_shuffle_ps(minor3, minor3, 0x4E); + // ----------------------------------------------- + tmp1 = _mm_mul_ps(_mm_shuffle_ps(row1, row1, 0x4E), row3); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); + row2 = _mm_shuffle_ps(row2, row2, 0x4E); + minor0 = _mm_add_ps(_mm_mul_ps(row2, tmp1), minor0); + minor2 = _mm_mul_ps(row0, tmp1); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); + minor0 = _mm_sub_ps(minor0, _mm_mul_ps(row2, tmp1)); + minor2 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor2); + minor2 = _mm_shuffle_ps(minor2, minor2, 0x4E); + // ----------------------------------------------- + tmp1 = _mm_mul_ps(row0, row1); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); + minor2 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor2); + minor3 = _mm_sub_ps(_mm_mul_ps(row2, tmp1), minor3); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); + minor2 = _mm_sub_ps(_mm_mul_ps(row3, tmp1), minor2); + minor3 = _mm_sub_ps(minor3, _mm_mul_ps(row2, tmp1)); + // ----------------------------------------------- + tmp1 = _mm_mul_ps(row0, row3); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); + minor1 = _mm_sub_ps(minor1, _mm_mul_ps(row2, tmp1)); + minor2 = _mm_add_ps(_mm_mul_ps(row1, tmp1), minor2); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); + minor1 = _mm_add_ps(_mm_mul_ps(row2, tmp1), minor1); + minor2 = _mm_sub_ps(minor2, _mm_mul_ps(row1, tmp1)); + // ----------------------------------------------- + tmp1 = _mm_mul_ps(row0, row2); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); + minor1 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor1); + minor3 = _mm_sub_ps(minor3, _mm_mul_ps(row1, tmp1)); + tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); + minor1 = _mm_sub_ps(minor1, _mm_mul_ps(row3, tmp1)); + minor3 = _mm_add_ps(_mm_mul_ps(row1, tmp1), minor3); + + // Evaluation of determinant and its reciprocal value. In the original Intel document, + // 1/det was evaluated using a fast rcpps command with subsequent approximation using + // the Newton-Raphson algorithm. Here, we go for a IEEE-compliant division instead, + // so as to not compromise precision at all. + det = _mm_mul_ps(row0, minor0); + det = _mm_add_ps(_mm_shuffle_ps(det, det, 0x4E), det); + det = _mm_add_ss(_mm_shuffle_ps(det, det, 0xB1), det); + // tmp1= _mm_rcp_ss(det); + // det= _mm_sub_ss(_mm_add_ss(tmp1, tmp1), _mm_mul_ss(det, _mm_mul_ss(tmp1, tmp1))); + det = _mm_div_ps(ei_pset1<float>(1.0f), det); // <--- yay, one original line not copied from Intel + det = _mm_shuffle_ps(det, det, 0x00); + // warning, Intel's variable naming is very confusing: now 'det' is 1/det ! + + // Multiplication of cofactors by 1/det. Storing the inverse matrix to the address in pointer src. + minor0 = _mm_mul_ps(det, minor0); + float *dst = result.data(); + _mm_storel_pi((__m64*)(dst), minor0); + _mm_storeh_pi((__m64*)(dst+2), minor0); + minor1 = _mm_mul_ps(det, minor1); + _mm_storel_pi((__m64*)(dst+4), minor1); + _mm_storeh_pi((__m64*)(dst+6), minor1); + minor2 = _mm_mul_ps(det, minor2); + _mm_storel_pi((__m64*)(dst+ 8), minor2); + _mm_storeh_pi((__m64*)(dst+10), minor2); + minor3 = _mm_mul_ps(det, minor3); + _mm_storel_pi((__m64*)(dst+12), minor3); + _mm_storeh_pi((__m64*)(dst+14), minor3); + } +}; + +#endif // EIGEN_INVERSE_SSE_H +
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