1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
|
/* ************************************************************************
* Copyright 2013 Advanced Micro Devices, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
* ************************************************************************/
#include <blas-math.h>
#include <common.h>
// Type-dependant constants
template <class T>
static cl_double DELTA_0();
template<>
__template_static cl_double DELTA_0<cl_float>() { return pow(2.0, -20); }
template<>
__template_static cl_double DELTA_0<cl_double>() { return pow(2.0, -50); }
template<>
__template_static cl_double DELTA_0<FloatComplex>() { return pow(2.0, -20); }
template<>
__template_static cl_double DELTA_0<DoubleComplex>() { return pow(2.0, -50); }
size_t
trsmBlockSize(size_t elemSize)
{
/* TODO: Right now TRSM generators use block size of 16 elements for the
* double complex type, and of 32 elements for another types.
* If this changes, we have to fetch block size from TRSM generator
* somehow.
*/
return (elemSize == sizeof(DoubleComplex)) ? 16 : 32;
}
template <typename T>
void
trsmDelta(
clblasOrder order,
clblasSide side,
clblasUplo uplo,
clblasTranspose transA,
clblasDiag diag,
size_t M,
size_t N,
T *A,
size_t lda,
T *B,
size_t ldb,
T alpha,
cl_double *delta)
{
cl_double *deltaCLBLAS, s;
int i, k, j, jStart, jEnd, idx;
int zinc;
size_t z = 0;
size_t bsize;
bool isUpper;
T v;
isUpper = ((uplo == clblasUpper) && (transA == clblasNoTrans)) ||
((uplo == clblasLower) && (transA != clblasNoTrans));
deltaCLBLAS = new cl_double[M * N];
bsize = trsmBlockSize(sizeof(T));
if (side == clblasLeft) {
// Calculate delta of TRSM evaluated with the Gauss' method
for (k = 0; k < (int)N; k++) {
if (isUpper) {
for (i = (int)M - 1; i >= 0; i--) {
v = getElement<T>(order, clblasNoTrans, i, k, B, ldb);
if (diag == clblasNonUnit) {
v = v / getElement<T>(order, transA, i, i, A, lda);
}
s = module(v) * DELTA_0<T>() * module(alpha);
if (i == (int)(M - 1)) {
delta[i * N + k] = s;
}
else {
delta[i * N + k] = s + delta[(i + 1) * N + k];
}
assert(delta[i* N + k] >= 0);
}
}
else {
for (i = 0; i < (int)M; i++) {
v = getElement<T>(order, clblasNoTrans, i, k, B, ldb);
if (diag == clblasNonUnit) {
v = v / getElement<T>(order, transA, i, i, A, lda);
}
s = module(v) * DELTA_0<T>() * module(alpha);
if (i == 0) {
delta[i * N + k] = s;
}
else {
delta[i * N + k] = s + delta[(i - 1) * N + k];
}
assert(delta[i* N + k] >= 0);
}
}
}
// Calculate clblas TRSM delta
for (k = 0; k < (int)N; k++) {
for (i = 0; i < (int)M; i++) {
s = 0.0;
/*
* For the upper triangular matrix the solving process proceeds
* from the bottom to the top, and the bottommost block's
* delta influents most of all. For the lower triangular matrix
* the situation is opposite.
*/
if (isUpper) {
jStart = i / (int)bsize;
// index of the block just after the last matrix block
jEnd = ((int)M + (int)bsize - 1) / (int)bsize;
z = 1;
zinc = 1;
}
else {
jStart = 0;
jEnd = i / (int)bsize + 1;
z = jEnd - jStart;
zinc = -1;
}
for (j = jStart; j < jEnd; j++) {
idx = j * (int)bsize + i % (int)bsize;
if (idx >= (int)M) {
continue;
}
s += z * delta[idx * N + k];
z += zinc;
}
deltaCLBLAS[i * N + k] = s * bsize;
assert(deltaCLBLAS[i* N + k] >= 0);
}
}
}
else {
// Calculate delta of TRSM evaluated with the Gauss' method
for (i = 0; i < (int)M; i++) {
if (isUpper) {
for (k = 0; k < (int)N; k++) {
v = getElement<T>(order, clblasNoTrans, i, k, B, ldb);
if (diag == clblasNonUnit) {
v = v / getElement<T>(order, transA, k, k, A, lda);
}
s = module(v) * DELTA_0<T>() * module(alpha);
if (k == 0) {
delta[i * N + k] = s;
}
else {
delta[i * N + k] = s + delta[i * N + (k - 1)];
}
assert(delta[i* N + k] >= 0);
}
}
else {
for (k = (int)N - 1; k >= 0; k--) {
v = getElement<T>(order, clblasNoTrans, i, k, B, ldb);
if (diag == clblasNonUnit) {
v = v / getElement<T>(order, transA, k, k, A, lda);
}
s = module(v) * DELTA_0<T>() * module(alpha);
if (k == (int)(N - 1)) {
delta[i * N + k] = s;
}
else {
delta[i * N + k] = s + delta[i * N + (k + 1)];
}
assert(delta[i* N + k] >= 0);
}
}
}
// Calculate clblas TRSM delta
for (i = 0; i < (int)M; i++) {
for (k = 0; k < (int)N; k++) {
s = 0.0;
/*
* Approach is the same as for the left side matrix, but delta
* is calculated over the rows rather than the columns.
* Now, since the matrices are swapped, the largest and
* tightest blocks are swapped as well. Therefore, pass
* direction for the upper and lower triangular matrix is also
* swapped.
*/
if (isUpper) {
jStart = 0;
jEnd = k / (int)bsize + 1;
z = jEnd - jStart;
zinc = -1;
}
else {
jStart = k / (int)bsize;
jEnd = (k + (int)bsize - 1) / (int)bsize;
z = 1;
zinc = 1;
}
for (j = jStart; j < jEnd; j++) {
idx = j * (int)bsize + k % (int)bsize;
if (idx >= (int)N) {
continue;
}
s += z * delta[i * N + idx];
z += zinc;
}
deltaCLBLAS[i * N + k] = s * bsize;
assert(deltaCLBLAS[i* N + k] >= 0);
}
}
}
for (k = 0; k < (int)N; k++) {
for (i = 0; i < (int)M; i++) {
delta[i * N + k] += deltaCLBLAS[i * N + k];
}
}
delete[] deltaCLBLAS;
}
|
