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Eigen  3.3.71
Inverse_SSE.h
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 = traits<MatrixType>::Alignment,
39  ResultAlignment = traits<ResultType>::Alignment,
40  StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
41  };
42  typedef typename conditional<(MatrixType::Flags&LinearAccessBit),MatrixType const &,typename MatrixType::PlainObject>::type ActualMatrixType;
43 
44  static void run(const MatrixType& mat, ResultType& result)
45  {
46  ActualMatrixType matrix(mat);
47  const Packet4f p4f_sign_PNNP = _mm_castsi128_ps(_mm_set_epi32(0x00000000, 0x80000000, 0x80000000, 0x00000000));
48 
49  // Load the full matrix into registers
50  __m128 _L1 = matrix.template packet<MatrixAlignment>( 0);
51  __m128 _L2 = matrix.template packet<MatrixAlignment>( 4);
52  __m128 _L3 = matrix.template packet<MatrixAlignment>( 8);
53  __m128 _L4 = matrix.template packet<MatrixAlignment>(12);
54 
55  // The inverse is calculated using "Divide and Conquer" technique. The
56  // original matrix is divide into four 2x2 sub-matrices. Since each
57  // register holds four matrix element, the smaller matrices are
58  // represented as a registers. Hence we get a better locality of the
59  // calculations.
60 
61  __m128 A, B, C, D; // the four sub-matrices
62  if(!StorageOrdersMatch)
63  {
64  A = _mm_unpacklo_ps(_L1, _L2);
65  B = _mm_unpacklo_ps(_L3, _L4);
66  C = _mm_unpackhi_ps(_L1, _L2);
67  D = _mm_unpackhi_ps(_L3, _L4);
68  }
69  else
70  {
71  A = _mm_movelh_ps(_L1, _L2);
72  B = _mm_movehl_ps(_L2, _L1);
73  C = _mm_movelh_ps(_L3, _L4);
74  D = _mm_movehl_ps(_L4, _L3);
75  }
76 
77  __m128 iA, iB, iC, iD, // partial inverse of the sub-matrices
78  DC, AB;
79  __m128 dA, dB, dC, dD; // determinant of the sub-matrices
80  __m128 det, d, d1, d2;
81  __m128 rd; // reciprocal of the determinant
82 
83  // AB = A# * B
84  AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B);
85  AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E)));
86  // DC = D# * C
87  DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C);
88  DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E)));
89 
90  // dA = |A|
91  dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A);
92  dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA));
93  // dB = |B|
94  dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B);
95  dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB));
96 
97  // dC = |C|
98  dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C);
99  dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC));
100  // dD = |D|
101  dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D);
102  dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD));
103 
104  // d = trace(AB*DC) = trace(A#*B*D#*C)
105  d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);
106 
107  // iD = C*A#*B
108  iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB));
109  iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB)));
110  // iA = B*D#*C
111  iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC));
112  iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC)));
113 
114  // d = trace(AB*DC) = trace(A#*B*D#*C) [continue]
115  d = _mm_add_ps(d, _mm_movehl_ps(d, d));
116  d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1));
117  d1 = _mm_mul_ss(dA,dD);
118  d2 = _mm_mul_ss(dB,dC);
119 
120  // iD = D*|A| - C*A#*B
121  iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);
122 
123  // iA = A*|D| - B*D#*C;
124  iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);
125 
126  // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
127  det = _mm_sub_ss(_mm_add_ss(d1,d2),d);
128  rd = _mm_div_ss(_mm_set_ss(1.0f), det);
129 
130 // #ifdef ZERO_SINGULAR
131 // rd = _mm_and_ps(_mm_cmpneq_ss(det,_mm_setzero_ps()), rd);
132 // #endif
133 
134  // iB = D * (A#B)# = D*B#*A
135  iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33));
136  iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66)));
137  // iC = A * (D#C)# = A*C#*D
138  iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33));
139  iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66)));
140 
141  rd = _mm_shuffle_ps(rd,rd,0);
142  rd = _mm_xor_ps(rd, p4f_sign_PNNP);
143 
144  // iB = C*|B| - D*B#*A
145  iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);
146 
147  // iC = B*|C| - A*C#*D;
148  iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC);
149 
150  // iX = iX / det
151  iA = _mm_mul_ps(rd,iA);
152  iB = _mm_mul_ps(rd,iB);
153  iC = _mm_mul_ps(rd,iC);
154  iD = _mm_mul_ps(rd,iD);
155 
156  Index res_stride = result.outerStride();
157  float* res = result.data();
158  pstoret<float, Packet4f, ResultAlignment>(res+0, _mm_shuffle_ps(iA,iB,0x77));
159  pstoret<float, Packet4f, ResultAlignment>(res+res_stride, _mm_shuffle_ps(iA,iB,0x22));
160  pstoret<float, Packet4f, ResultAlignment>(res+2*res_stride, _mm_shuffle_ps(iC,iD,0x77));
161  pstoret<float, Packet4f, ResultAlignment>(res+3*res_stride, _mm_shuffle_ps(iC,iD,0x22));
162  }
163 
164 };
165 
166 template<typename MatrixType, typename ResultType>
167 struct compute_inverse_size4<Architecture::SSE, double, MatrixType, ResultType>
168 {
169  enum {
170  MatrixAlignment = traits<MatrixType>::Alignment,
171  ResultAlignment = traits<ResultType>::Alignment,
172  StorageOrdersMatch = (MatrixType::Flags&RowMajorBit) == (ResultType::Flags&RowMajorBit)
173  };
174  typedef typename conditional<(MatrixType::Flags&LinearAccessBit),MatrixType const &,typename MatrixType::PlainObject>::type ActualMatrixType;
175 
176  static void run(const MatrixType& mat, ResultType& result)
177  {
178  ActualMatrixType matrix(mat);
179  const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
180  const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
181 
182  // The inverse is calculated using "Divide and Conquer" technique. The
183  // original matrix is divide into four 2x2 sub-matrices. Since each
184  // register of the matrix holds two elements, the smaller matrices are
185  // consisted of two registers. Hence we get a better locality of the
186  // calculations.
187 
188  // the four sub-matrices
189  __m128d A1, A2, B1, B2, C1, C2, D1, D2;
190 
191  if(StorageOrdersMatch)
192  {
193  A1 = matrix.template packet<MatrixAlignment>( 0); B1 = matrix.template packet<MatrixAlignment>( 2);
194  A2 = matrix.template packet<MatrixAlignment>( 4); B2 = matrix.template packet<MatrixAlignment>( 6);
195  C1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
196  C2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
197  }
198  else
199  {
200  __m128d tmp;
201  A1 = matrix.template packet<MatrixAlignment>( 0); C1 = matrix.template packet<MatrixAlignment>( 2);
202  A2 = matrix.template packet<MatrixAlignment>( 4); C2 = matrix.template packet<MatrixAlignment>( 6);
203  tmp = A1;
204  A1 = _mm_unpacklo_pd(A1,A2);
205  A2 = _mm_unpackhi_pd(tmp,A2);
206  tmp = C1;
207  C1 = _mm_unpacklo_pd(C1,C2);
208  C2 = _mm_unpackhi_pd(tmp,C2);
209 
210  B1 = matrix.template packet<MatrixAlignment>( 8); D1 = matrix.template packet<MatrixAlignment>(10);
211  B2 = matrix.template packet<MatrixAlignment>(12); D2 = matrix.template packet<MatrixAlignment>(14);
212  tmp = B1;
213  B1 = _mm_unpacklo_pd(B1,B2);
214  B2 = _mm_unpackhi_pd(tmp,B2);
215  tmp = D1;
216  D1 = _mm_unpacklo_pd(D1,D2);
217  D2 = _mm_unpackhi_pd(tmp,D2);
218  }
219 
220  __m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, // partial invese of the sub-matrices
221  DC1, DC2, AB1, AB2;
222  __m128d dA, dB, dC, dD; // determinant of the sub-matrices
223  __m128d det, d1, d2, rd;
224 
225  // dA = |A|
226  dA = _mm_shuffle_pd(A2, A2, 1);
227  dA = _mm_mul_pd(A1, dA);
228  dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3));
229  // dB = |B|
230  dB = _mm_shuffle_pd(B2, B2, 1);
231  dB = _mm_mul_pd(B1, dB);
232  dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3));
233 
234  // AB = A# * B
235  AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3));
236  AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0));
237  AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3)));
238  AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0)));
239 
240  // dC = |C|
241  dC = _mm_shuffle_pd(C2, C2, 1);
242  dC = _mm_mul_pd(C1, dC);
243  dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3));
244  // dD = |D|
245  dD = _mm_shuffle_pd(D2, D2, 1);
246  dD = _mm_mul_pd(D1, dD);
247  dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3));
248 
249  // DC = D# * C
250  DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3));
251  DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0));
252  DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3)));
253  DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0)));
254 
255  // rd = trace(AB*DC) = trace(A#*B*D#*C)
256  d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0));
257  d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3));
258  rd = _mm_add_pd(d1, d2);
259  rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3));
260 
261  // iD = C*A#*B
262  iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0));
263  iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0));
264  iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3)));
265  iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3)));
266 
267  // iA = B*D#*C
268  iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0));
269  iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0));
270  iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3)));
271  iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3)));
272 
273  // iD = D*|A| - C*A#*B
274  dA = _mm_shuffle_pd(dA,dA,0);
275  iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1);
276  iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2);
277 
278  // iA = A*|D| - B*D#*C;
279  dD = _mm_shuffle_pd(dD,dD,0);
280  iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1);
281  iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2);
282 
283  d1 = _mm_mul_sd(dA, dD);
284  d2 = _mm_mul_sd(dB, dC);
285 
286  // iB = D * (A#B)# = D*B#*A
287  iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1));
288  iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1));
289  iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2)));
290  iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2)));
291 
292  // det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
293  det = _mm_add_sd(d1, d2);
294  det = _mm_sub_sd(det, rd);
295 
296  // iC = A * (D#C)# = A*C#*D
297  iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1));
298  iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1));
299  iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2)));
300  iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2)));
301 
302  rd = _mm_div_sd(_mm_set_sd(1.0), det);
303 // #ifdef ZERO_SINGULAR
304 // rd = _mm_and_pd(_mm_cmpneq_sd(det,_mm_setzero_pd()), rd);
305 // #endif
306  rd = _mm_shuffle_pd(rd,rd,0);
307 
308  // iB = C*|B| - D*B#*A
309  dB = _mm_shuffle_pd(dB,dB,0);
310  iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1);
311  iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2);
312 
313  d1 = _mm_xor_pd(rd, _Sign_PN);
314  d2 = _mm_xor_pd(rd, _Sign_NP);
315 
316  // iC = B*|C| - A*C#*D;
317  dC = _mm_shuffle_pd(dC,dC,0);
318  iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1);
319  iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2);
320 
321  Index res_stride = result.outerStride();
322  double* res = result.data();
323  pstoret<double, Packet2d, ResultAlignment>(res+0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1));
324  pstoret<double, Packet2d, ResultAlignment>(res+res_stride, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2));
325  pstoret<double, Packet2d, ResultAlignment>(res+2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1));
326  pstoret<double, Packet2d, ResultAlignment>(res+res_stride+2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2));
327  pstoret<double, Packet2d, ResultAlignment>(res+2*res_stride, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1));
328  pstoret<double, Packet2d, ResultAlignment>(res+3*res_stride, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2));
329  pstoret<double, Packet2d, ResultAlignment>(res+2*res_stride+2,_mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1));
330  pstoret<double, Packet2d, ResultAlignment>(res+3*res_stride+2,_mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2));
331  }
332 };
333 
334 } // end namespace internal
335 
336 } // end namespace Eigen
337 
338 #endif // EIGEN_INVERSE_SSE_H
Eigen
Namespace containing all symbols from the Eigen library.
Definition: Core:309
Eigen::RowMajorBit
const unsigned int RowMajorBit
Definition: Constants.h:61
Eigen::LinearAccessBit
const unsigned int LinearAccessBit
Definition: Constants.h:125
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33