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SparseLU_gemm_kernel.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Gael Guennebaud <[email protected]>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_SPARSELU_GEMM_KERNEL_H
11 #define EIGEN_SPARSELU_GEMM_KERNEL_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 
24 template<typename Scalar,typename Index>
25 EIGEN_DONT_INLINE
26 void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)
27 {
28  using namespace Eigen::internal;
29 
30  typedef typename packet_traits<Scalar>::type Packet;
31  enum {
32  NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
33  PacketSize = packet_traits<Scalar>::size,
34  PM = 8, // peeling in M
35  RN = 2, // register blocking
36  RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
37  BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk
38  SM = PM*PacketSize // step along M
39  };
40  Index d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking
41  Index n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once
42  Index i0 = internal::first_aligned(A,m);
43 
44  eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_aligned(C,m)));
45 
46  // handle the non aligned rows of A and C without any optimization:
47  for(Index i=0; i<i0; ++i)
48  {
49  for(Index j=0; j<n; ++j)
50  {
51  Scalar c = C[i+j*ldc];
52  for(Index k=0; k<d; ++k)
53  c += B[k+j*ldb] * A[i+k*lda];
54  C[i+j*ldc] = c;
55  }
56  }
57  // process the remaining rows per chunk of BM rows
58  for(Index ib=i0; ib<m; ib+=BM)
59  {
60  Index actual_b = std::min<Index>(BM, m-ib); // actual number of rows
61  Index actual_b_end1 = (actual_b/SM)*SM; // actual number of rows suitable for peeling
62  Index actual_b_end2 = (actual_b/PacketSize)*PacketSize; // actual number of rows suitable for vectorization
63 
64  // Let's process two columns of B-C at once
65  for(Index j=0; j<n_end; j+=RN)
66  {
67  const Scalar* Bc0 = B+(j+0)*ldb;
68  const Scalar* Bc1 = B+(j+1)*ldb;
69 
70  for(Index k=0; k<d_end; k+=RK)
71  {
72 
73  // load and expand a RN x RK block of B
74  Packet b00, b10, b20, b30, b01, b11, b21, b31;
75  b00 = pset1<Packet>(Bc0[0]);
76  b10 = pset1<Packet>(Bc0[1]);
77  if(RK==4) b20 = pset1<Packet>(Bc0[2]);
78  if(RK==4) b30 = pset1<Packet>(Bc0[3]);
79  b01 = pset1<Packet>(Bc1[0]);
80  b11 = pset1<Packet>(Bc1[1]);
81  if(RK==4) b21 = pset1<Packet>(Bc1[2]);
82  if(RK==4) b31 = pset1<Packet>(Bc1[3]);
83 
84  Packet a0, a1, a2, a3, c0, c1, t0, t1;
85 
86  const Scalar* A0 = A+ib+(k+0)*lda;
87  const Scalar* A1 = A+ib+(k+1)*lda;
88  const Scalar* A2 = A+ib+(k+2)*lda;
89  const Scalar* A3 = A+ib+(k+3)*lda;
90 
91  Scalar* C0 = C+ib+(j+0)*ldc;
92  Scalar* C1 = C+ib+(j+1)*ldc;
93 
94  a0 = pload<Packet>(A0);
95  a1 = pload<Packet>(A1);
96  if(RK==4)
97  {
98  a2 = pload<Packet>(A2);
99  a3 = pload<Packet>(A3);
100  }
101  else
102  {
103  // workaround "may be used uninitialized in this function" warning
104  a2 = a3 = a0;
105  }
106 
107 #define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}
108 #define WORK(I) \
109  c0 = pload<Packet>(C0+i+(I)*PacketSize); \
110  c1 = pload<Packet>(C1+i+(I)*PacketSize); \
111  KMADD(c0, a0, b00, t0) \
112  KMADD(c1, a0, b01, t1) \
113  a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
114  KMADD(c0, a1, b10, t0) \
115  KMADD(c1, a1, b11, t1) \
116  a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
117  if(RK==4) KMADD(c0, a2, b20, t0) \
118  if(RK==4) KMADD(c1, a2, b21, t1) \
119  if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
120  if(RK==4) KMADD(c0, a3, b30, t0) \
121  if(RK==4) KMADD(c1, a3, b31, t1) \
122  if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
123  pstore(C0+i+(I)*PacketSize, c0); \
124  pstore(C1+i+(I)*PacketSize, c1)
125 
126  // process rows of A' - C' with aggressive vectorization and peeling
127  for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
128  {
129  EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
130  prefetch((A0+i+(5)*PacketSize));
131  prefetch((A1+i+(5)*PacketSize));
132  if(RK==4) prefetch((A2+i+(5)*PacketSize));
133  if(RK==4) prefetch((A3+i+(5)*PacketSize));
134  WORK(0);
135  WORK(1);
136  WORK(2);
137  WORK(3);
138  WORK(4);
139  WORK(5);
140  WORK(6);
141  WORK(7);
142  }
143  // process the remaining rows with vectorization only
144  for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
145  {
146  WORK(0);
147  }
148 #undef WORK
149  // process the remaining rows without vectorization
150  for(Index i=actual_b_end2; i<actual_b; ++i)
151  {
152  if(RK==4)
153  {
154  C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
155  C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];
156  }
157  else
158  {
159  C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
160  C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];
161  }
162  }
163 
164  Bc0 += RK;
165  Bc1 += RK;
166  } // peeled loop on k
167  } // peeled loop on the columns j
168  // process the last column (we now perform a matrux-vector product)
169  if((n-n_end)>0)
170  {
171  const Scalar* Bc0 = B+(n-1)*ldb;
172 
173  for(Index k=0; k<d_end; k+=RK)
174  {
175 
176  // load and expand a 1 x RK block of B
177  Packet b00, b10, b20, b30;
178  b00 = pset1<Packet>(Bc0[0]);
179  b10 = pset1<Packet>(Bc0[1]);
180  if(RK==4) b20 = pset1<Packet>(Bc0[2]);
181  if(RK==4) b30 = pset1<Packet>(Bc0[3]);
182 
183  Packet a0, a1, a2, a3, c0, t0/*, t1*/;
184 
185  const Scalar* A0 = A+ib+(k+0)*lda;
186  const Scalar* A1 = A+ib+(k+1)*lda;
187  const Scalar* A2 = A+ib+(k+2)*lda;
188  const Scalar* A3 = A+ib+(k+3)*lda;
189 
190  Scalar* C0 = C+ib+(n_end)*ldc;
191 
192  a0 = pload<Packet>(A0);
193  a1 = pload<Packet>(A1);
194  if(RK==4)
195  {
196  a2 = pload<Packet>(A2);
197  a3 = pload<Packet>(A3);
198  }
199  else
200  {
201  // workaround "may be used uninitialized in this function" warning
202  a2 = a3 = a0;
203  }
204 
205 #define WORK(I) \
206  c0 = pload<Packet>(C0+i+(I)*PacketSize); \
207  KMADD(c0, a0, b00, t0) \
208  a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
209  KMADD(c0, a1, b10, t0) \
210  a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
211  if(RK==4) KMADD(c0, a2, b20, t0) \
212  if(RK==4) a2 = pload<Packet>(A2+i+(I+1)*PacketSize); \
213  if(RK==4) KMADD(c0, a3, b30, t0) \
214  if(RK==4) a3 = pload<Packet>(A3+i+(I+1)*PacketSize); \
215  pstore(C0+i+(I)*PacketSize, c0);
216 
217  // agressive vectorization and peeling
218  for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
219  {
220  EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL2");
221  WORK(0);
222  WORK(1);
223  WORK(2);
224  WORK(3);
225  WORK(4);
226  WORK(5);
227  WORK(6);
228  WORK(7);
229  }
230  // vectorization only
231  for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
232  {
233  WORK(0);
234  }
235  // remaining scalars
236  for(Index i=actual_b_end2; i<actual_b; ++i)
237  {
238  if(RK==4)
239  C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
240  else
241  C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
242  }
243 
244  Bc0 += RK;
245 #undef WORK
246  }
247  }
248 
249  // process the last columns of A, corresponding to the last rows of B
250  Index rd = d-d_end;
251  if(rd>0)
252  {
253  for(Index j=0; j<n; ++j)
254  {
255  enum {
256  Alignment = PacketSize>1 ? Aligned : 0
257  };
258  typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;
259  typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;
260  if(rd==1) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b);
261 
262  else if(rd==2) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
263  + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);
264 
265  else MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
266  + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)
267  + B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);
268  }
269  }
270 
271  } // blocking on the rows of A and C
272 }
273 #undef KMADD
274 
275 } // namespace internal
276 
277 } // namespace Eigen
278 
279 #endif // EIGEN_SPARSELU_GEMM_KERNEL_H
Eigen::Aligned
Definition: Constants.h:194