Eigen/src/LU/arch/Inverse_SSE.h - platform/external/eigen - Git at Google

 // 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
	// 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(ABDC) = trace(A#BD#C)
	d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);

	// iD = CA#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 = BD#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(ABDC) = trace(A#BD#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\| - CA#*B
	iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);

	// iA = A\|D\| - BD#*C;
	iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);

	// det = \|A\|\|D\| + \|B\|\|C\| - trace(A#BD#*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)# = DB#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)# = AC#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\| - DB#*A
	iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);

	// iC = B\|C\| - AC#*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(ABDC) = trace(A#BD#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 = CA#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 = BD#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\| - CA#*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\| - BD#*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)# = DB#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#BD#*C)
	det = _mm_add_sd(d1, d2);
	det = _mm_sub_sd(det, rd);

	// iC = A * (D#C)# = AC#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\| - DB#*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\| - AC#*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