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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 <gael.guennebaud@inria.fr>
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
13namespace Eigen {
14
15namespace internal {
16
17
24template<typename Scalar>
25EIGEN_DONT_INLINE
26void 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_default_aligned(A,m);
43
44 eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_default_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 matrix-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::Solve
Pseudo expression representing a solving operation.
Definition Solve.h:63
Eigen::Aligned
@ Aligned
Definition Constants.h:235
Eigen::internal::packet_traits
Definition GenericPacketMath.h:90
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