Inverse_SSE.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2001 Intel Corporation
5 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
6 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
7 //
8 // This Source Code Form is subject to the terms of the Mozilla
9 // Public License v. 2.0. If a copy of the MPL was not distributed
10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11 
12 // The SSE code for the 4x4 float and double matrix inverse in this file
13 // comes from the following Intel's library:
14 // http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/
15 //
16 // Here is the respective copyright and license statement:
17 //
18 // Copyright (c) 2001 Intel Corporation.
19 //
20 // Permition is granted to use, copy, distribute and prepare derivative works
21 // of this library for any purpose and without fee, provided, that the above
22 // copyright notice and this statement appear in all copies.
23 // Intel makes no representations about the suitability of this software for
24 // any purpose, and specifically disclaims all warranties.
25 // See LEGAL.TXT for all the legal information.
26 
27 #ifndef EIGEN_INVERSE_SSE_H
28 #define EIGEN_INVERSE_SSE_H
29 
30 namespace Eigen {
31 
32 namespace internal {
33 
34 template<typename MatrixType, typename ResultType>
35 struct compute_inverse_size4<Architecture::SSE, float, MatrixType, ResultType>
36 {
37  enum {
38  MatrixAlignment = bool(MatrixType::Flags&AlignedBit),
39  ResultAlignment = bool(ResultType::Flags&AlignedBit),
40  StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
41  };
42 
43  static void run(const MatrixType& matrix, ResultType& result)
44  {
45  EIGEN_ALIGN16 const unsigned int _Sign_PNNP[4] = { 0x00000000, 0x80000000, 0x80000000, 0x00000000 };
46 
47  // Load the full matrix into registers
48  __m128 _L1 = matrix.template packet<MatrixAlignment>( 0);
49  __m128 _L2 = matrix.template packet<MatrixAlignment>( 4);
50  __m128 _L3 = matrix.template packet<MatrixAlignment>( 8);
51  __m128 _L4 = matrix.template packet<MatrixAlignment>(12);
52 
53  // The inverse is calculated using "Divide and Conquer" technique. The
54  // original matrix is divide into four 2x2 sub-matrices. Since each
55  // register holds four matrix element, the smaller matrices are
56  // represented as a registers. Hence we get a better locality of the
57  // calculations.
58 
59  __m128 A, B, C, D; // the four sub-matrices
60  if(!StorageOrdersMatch)
61  {
62  A = _mm_unpacklo_ps(_L1, _L2);
63  B = _mm_unpacklo_ps(_L3, _L4);
64  C = _mm_unpackhi_ps(_L1, _L2);
65  D = _mm_unpackhi_ps(_L3, _L4);
66  }
67  else
68  {
69  A = _mm_movelh_ps(_L1, _L2);
70  B = _mm_movehl_ps(_L2, _L1);
71  C = _mm_movelh_ps(_L3, _L4);
72  D = _mm_movehl_ps(_L4, _L3);
73  }
74 
75  __m128 iA, iB, iC, iD, // partial inverse of the sub-matrices
76  DC, AB;
77  __m128 dA, dB, dC, dD; // determinant of the sub-matrices
78  __m128 det, d, d1, d2;
79  __m128 rd; // reciprocal of the determinant
80 
81  // AB = A# * B
82  AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B);
83  AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E)));
84  // DC = D# * C
85  DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C);
86  DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E)));
87 
88  // dA = |A|
89  dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A);
90  dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA));
91  // dB = |B|
92  dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B);
93  dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB));
94 
95  // dC = |C|
96  dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C);
97  dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC));
98  // dD = |D|
99  dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D);
100  dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD));
101 
102  // d = trace(AB*DC) = trace(A#*B*D#*C)
103  d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);
104 
105  // iD = C*A#*B
106  iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB));
107  iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB)));
108  // iA = B*D#*C
109  iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC));
110  iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC)));
111 
112  // d = trace(AB*DC) = trace(A#*B*D#*C) [continue]
113  d = _mm_add_ps(d, _mm_movehl_ps(d, d));
114  d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1));
115  d1 = _mm_mul_ss(dA,dD);
116  d2 = _mm_mul_ss(dB,dC);
117 
118  // iD = D*|A| - C*A#*B
119  iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);
120 
121  // iA = A*|D| - B*D#*C;
122  iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);
123 
124  // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
125  det = _mm_sub_ss(_mm_add_ss(d1,d2),d);
126  rd = _mm_div_ss(_mm_set_ss(1.0f), det);
127 
128 // #ifdef ZERO_SINGULAR
129 // rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd);
130 // #endif
131 
132  // iB = D * (A#B)# = D*B#*A
133  iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33));
134  iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66)));
135  // iC = A * (D#C)# = A*C#*D
136  iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33));
137  iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66)));
138 
139  rd = _mm_shuffle_ps(rd,rd,0);
140  rd = _mm_xor_ps(rd, _mm_load_ps((float*)_Sign_PNNP));
141 
142  // iB = C*|B| - D*B#*A
143  iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);
144 
145  // iC = B*|C| - A*C#*D;
146  iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC);
147 
148  // iX = iX / det
149  iA = _mm_mul_ps(rd,iA);
150  iB = _mm_mul_ps(rd,iB);
151  iC = _mm_mul_ps(rd,iC);
152  iD = _mm_mul_ps(rd,iD);
153 
154  result.template writePacket<ResultAlignment>( 0, _mm_shuffle_ps(iA,iB,0x77));
155  result.template writePacket<ResultAlignment>( 4, _mm_shuffle_ps(iA,iB,0x22));
156  result.template writePacket<ResultAlignment>( 8, _mm_shuffle_ps(iC,iD,0x77));
157  result.template writePacket<ResultAlignment>(12, _mm_shuffle_ps(iC,iD,0x22));
158  }
159 
160 };
161 
162 template<typename MatrixType, typename ResultType>
163 struct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType>
164 {
165  enum {
166  MatrixAlignment = bool(MatrixType::Flags&AlignedBit),
167  ResultAlignment = bool(ResultType::Flags&AlignedBit),
168  StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
169  };
170  static void run(const MatrixType& matrix, ResultType& result)
171  {
172  const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
173  const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
174 
175  // The inverse is calculated using "Divide and Conquer" technique. The
176  // original matrix is divide into four 2x2 sub-matrices. Since each
177  // register of the matrix holds two element, the smaller matrices are
178  // consisted of two registers. Hence we get a better locality of the
179  // calculations.
180 
181  // the four sub-matrices
182  __m128d A1, A2, B1, B2, C1, C2, D1, D2;
183 
184  if(StorageOrdersMatch)
185  {
186  A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2);
187  A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6);
188  C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
189  C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
190  }
191  else
192  {
193  __m128d tmp;
194  A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2);
195  A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6);
196  tmp = A1;
197  A1 = _mm_unpacklo_pd(A1,A2);
198  A2 = _mm_unpackhi_pd(tmp,A2);
199  tmp = C1;
200  C1 = _mm_unpacklo_pd(C1,C2);
201  C2 = _mm_unpackhi_pd(tmp,C2);
202 
203  B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
204  B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
205  tmp = B1;
206  B1 = _mm_unpacklo_pd(B1,B2);
207  B2 = _mm_unpackhi_pd(tmp,B2);
208  tmp = D1;
209  D1 = _mm_unpacklo_pd(D1,D2);
210  D2 = _mm_unpackhi_pd(tmp,D2);
211  }
212 
213  __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, // partial invese of the sub-matrices
214  DC1, DC2, AB1, AB2;
215  __m128d dA, dB, dC, dD; // determinant of the sub-matrices
216  __m128d det, d1, d2, rd;
217 
218  // dA = |A|
219  dA = _mm_shuffle_pd(A2, A2, 1);
220  dA = _mm_mul_pd(A1, dA);
221  dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3));
222  // dB = |B|
223  dB = _mm_shuffle_pd(B2, B2, 1);
224  dB = _mm_mul_pd(B1, dB);
225  dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3));
226 
227  // AB = A# * B
228  AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3));
229  AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0));
230  AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3)));
231  AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0)));
232 
233  // dC = |C|
234  dC = _mm_shuffle_pd(C2, C2, 1);
235  dC = _mm_mul_pd(C1, dC);
236  dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3));
237  // dD = |D|
238  dD = _mm_shuffle_pd(D2, D2, 1);
239  dD = _mm_mul_pd(D1, dD);
240  dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3));
241 
242  // DC = D# * C
243  DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3));
244  DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0));
245  DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3)));
246  DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0)));
247 
248  // rd = trace(AB*DC) = trace(A#*B*D#*C)
249  d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0));
250  d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3));
251  rd = _mm_add_pd(d1, d2);
252  rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3));
253 
254  // iD = C*A#*B
255  iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0));
256  iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0));
257  iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3)));
258  iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3)));
259 
260  // iA = B*D#*C
261  iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0));
262  iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0));
263  iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3)));
264  iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3)));
265 
266  // iD = D*|A| - C*A#*B
267  dA = _mm_shuffle_pd(dA,dA,0);
268  iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1);
269  iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2);
270 
271  // iA = A*|D| - B*D#*C;
272  dD = _mm_shuffle_pd(dD,dD,0);
273  iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1);
274  iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2);
275 
276  d1 = _mm_mul_sd(dA, dD);
277  d2 = _mm_mul_sd(dB, dC);
278 
279  // iB = D * (A#B)# = D*B#*A
280  iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1));
281  iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1));
282  iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2)));
283  iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2)));
284 
285  // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
286  det = _mm_add_sd(d1, d2);
287  det = _mm_sub_sd(det, rd);
288 
289  // iC = A * (D#C)# = A*C#*D
290  iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1));
291  iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1));
292  iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2)));
293  iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2)));
294 
295  rd = _mm_div_sd(_mm_set_sd(1.0), det);
296 // #ifdef ZERO_SINGULAR
297 // rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd);
298 // #endif
299  rd = _mm_shuffle_pd(rd,rd,0);
300 
301  // iB = C*|B| - D*B#*A
302  dB = _mm_shuffle_pd(dB,dB,0);
303  iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1);
304  iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2);
305 
306  d1 = _mm_xor_pd(rd, _Sign_PN);
307  d2 = _mm_xor_pd(rd, _Sign_NP);
308 
309  // iC = B*|C| - A*C#*D;
310  dC = _mm_shuffle_pd(dC,dC,0);
311  iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1);
312  iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2);
313 
314  result.template writePacket<ResultAlignment>( 0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1)); // iA# / det
315  result.template writePacket<ResultAlignment>( 4, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2));
316  result.template writePacket<ResultAlignment>( 2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1)); // iB# / det
317  result.template writePacket<ResultAlignment>( 6, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2));
318  result.template writePacket<ResultAlignment>( 8, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1)); // iC# / det
319  result.template writePacket<ResultAlignment>(12, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2));
320  result.template writePacket<ResultAlignment>(10, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1)); // iD# / det
321  result.template writePacket<ResultAlignment>(14, _mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2));
322  }
323 };
324 
325 } // end namespace internal
326 
327 } // end namespace Eigen
328 
329 #endif // EIGEN_INVERSE_SSE_H
EIGEN_ALIGN16
#define EIGEN_ALIGN16
Definition: Core/util/Macros.h:269
B1
#define B1
Definition: hydroscal_model.hpp:85
B2
#define B2
Definition: hydroscal_model.hpp:89
Eigen
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: matrix.hpp:471
A1
#define A1
Definition: hydroscal_model.hpp:84
Eigen::RowMajorBit
const unsigned int RowMajorBit
Definition: eigen3/Eigen/src/Core/util/Constants.h:53
Eigen::AlignedBit
const unsigned int AlignedBit
Definition: eigen3/Eigen/src/Core/util/Constants.h:147
A2
#define A2
Definition: hydroscal_model.hpp:88
Eigen::internal::compute_inverse_size4
Definition: Inverse.h:215
Eigen::internal::compute_inverse_size4< Architecture::SSE, double, MatrixType, ResultType >::run
static void run(const MatrixType &matrix, ResultType &result)
Definition: Inverse_SSE.h:170
Eigen::internal::compute_inverse_size4< Architecture::SSE, float, MatrixType, ResultType >::run
static void run(const MatrixType &matrix, ResultType &result)
Definition: Inverse_SSE.h:43
C1
#define C1
Definition: hydroscal_model.hpp:86
C2
#define C2
Definition: hydroscal_model.hpp:90

acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:34:43