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
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
|
// =================================================================================================
// This file is part of the CLBlast project. The project is licensed under Apache Version 2.0. This
// project loosely follows the Google C++ styleguide and uses a tab-size of two spaces and a max-
// width of 100 characters per line.
//
// Author(s):
// Cedric Nugteren <www.cedricnugteren.nl>
//
// This file contains an optimized matrix-multiplication kernel inspired by the paper by Matsumoto
// et al. and the tutorial on http://www.cedricnugteren.nl/tutorial.php. It is fully configurable
// (and tunable!) using more or less the same parameters/naming conventions as in the paper. It
// supports different data-types (SGEMM/DGEMM/CGEMM/ZGEMM/HGEMM) through a pre-processor define.
//
// Matrices are accessed as follows:
// A: [k*M + m], with 'k' ranging from 0:K and 'm' from 0:M (m,k,m)
// B: [k*N + n], with 'k' ranging from 0:K and 'n' from 0:N (n,k,n)
// C: [n*M + m], with 'n' ranging from 0:N and 'm' from 0:M (m,n,m)
//
// Or as an image (assuming column-major)
// K
// o-------o
// | |
// N | [B^T] |
// | |
// o-------o
// K N
// o-------o o-----o
// M | [A] | M | [C] |
// | | | |
// o-------o o-----o
//
//
// This kernel is seperated into three files. This is part 1 out of 3.
//
// =================================================================================================
// Enables loading of this file using the C++ pre-processor's #include (C++11 standard raw string
// literal). Comment-out this line for syntax-highlighting when developing.
R"(
// =================================================================================================
// Parameters set by the tuner or by the database. Here they are given a basic default value in case
// this kernel file is used outside of the CLBlast library.
#ifndef MWG
#define MWG 8 // Tile-size in dimension M (e.g. 64, 128)
#endif
#ifndef NWG
#define NWG 8 // Tile-size in dimension N (e.g. 64, 128)
#endif
#ifndef KWG
#define KWG 8 // Tile-size in dimension K (e.g. 8, 16)
#endif
#ifndef MDIMC
#define MDIMC 8 // Threads per workgroup in M-dimension (e.g. 8, 16, 32)
#endif
#ifndef NDIMC
#define NDIMC 8 // Threads per workgroup in N-dimension (e.g. 8, 16, 32)
#endif
#ifndef MDIMA
#define MDIMA 8 // Re-shaped tile dimension of matrix A: KDIMA * MDIMA
#endif
#ifndef NDIMB
#define NDIMB 8 // Re-shaped tile dimension of matrix B: KDIMB * NDIMB
#endif
#ifndef KWI
#define KWI 1 // Unroll factor of the KWG loop (smaller or equal than KWG)
#endif
#ifndef VWM
#define VWM 1 // Vector width of matrices A and C
#endif
#ifndef VWN
#define VWN 1 // Vector width of matrix B
#endif
#ifndef STRM
#define STRM 0 // Use strided access within a thread in the M-dimension (1) or not (0)
#endif
#ifndef STRN
#define STRN 0 // Use strided access within a thread in the N-dimension (1) or not (0)
#endif
#ifndef SA
#define SA 0 // Use local/shared memory to cache matrix A (1) or not (0)
#endif
#ifndef SB
#define SB 0 // Use local/shared memory to cache matrix B (1) or not (0)
#endif
// Helper parameters based on the above tuning parameters
#define MWI (MWG/MDIMC) // Work per work-item (M-dimension)
#define NWI (NWG/NDIMC) // Work per work-item (N-dimension)
#define KDIMA ((MDIMC*NDIMC)/(MDIMA)) // Re-shaped tile dimension of matrix A: KDIMA * MDIMA
#define KDIMB ((MDIMC*NDIMC)/(NDIMB)) // Re-shaped tile dimension of matrix B: KDIMB * NDIMB
#define MWA (MWG/MDIMA) // Amount of loads-per-thread for matrix A (M-dimension)
#define KWA (KWG/KDIMA) // Amount of loads-per-thread for matrix A (K-dimension)
#define KWB (KWG/KDIMB) // Amount of loads-per-thread for matrix B (K-dimension)
#define NWB (NWG/NDIMB) // Amount of loads-per-thread for matrix B (N-dimension)
// Settings
#ifndef USE_VECTOR_MAD
#define USE_VECTOR_MAD 0 // Unroll (0) or don't (1) unroll the vector MAD manually
#endif
#ifndef GLOBAL_MEM_FENCE
#define GLOBAL_MEM_FENCE 0 // Global synchronisation barrier for potential better performance
#endif
// =================================================================================================
// Data-widths in dimension M
#if VWM == 1
typedef real realM;
#elif VWM == 2
typedef real2 realM;
#elif VWM == 4
typedef real4 realM;
#elif VWM == 8
typedef real8 realM;
#elif VWM == 16
typedef real16 realM;
#endif
// Data-widths in dimension N
#if VWN == 1
typedef real realN;
#elif VWN == 2
typedef real2 realN;
#elif VWN == 4
typedef real4 realN;
#elif VWN == 8
typedef real8 realN;
#elif VWN == 16
typedef real16 realN;
#endif
// =================================================================================================
// Initializes the accumulation registers to zero
INLINE_FUNC void InitAccRegisters(realM cpm[NWI][MWI/VWM]) {
#pragma unroll
for (int mi=0; mi<MWI/VWM; ++mi) {
#pragma unroll
for (int ni=0; ni<NWI; ++ni) {
#if VWM == 1
SetToZero(cpm[ni][mi]);
#elif VWM == 2
SetToZero(cpm[ni][mi].x);
SetToZero(cpm[ni][mi].y);
#elif VWM == 4
SetToZero(cpm[ni][mi].x);
SetToZero(cpm[ni][mi].y);
SetToZero(cpm[ni][mi].z);
SetToZero(cpm[ni][mi].w);
#elif VWM == 8
SetToZero(cpm[ni][mi].s0);
SetToZero(cpm[ni][mi].s1);
SetToZero(cpm[ni][mi].s2);
SetToZero(cpm[ni][mi].s3);
SetToZero(cpm[ni][mi].s4);
SetToZero(cpm[ni][mi].s5);
SetToZero(cpm[ni][mi].s6);
SetToZero(cpm[ni][mi].s7);
#elif VWM == 16
SetToZero(cpm[ni][mi].s0);
SetToZero(cpm[ni][mi].s1);
SetToZero(cpm[ni][mi].s2);
SetToZero(cpm[ni][mi].s3);
SetToZero(cpm[ni][mi].s4);
SetToZero(cpm[ni][mi].s5);
SetToZero(cpm[ni][mi].s6);
SetToZero(cpm[ni][mi].s7);
SetToZero(cpm[ni][mi].s8);
SetToZero(cpm[ni][mi].s9);
SetToZero(cpm[ni][mi].sA);
SetToZero(cpm[ni][mi].sB);
SetToZero(cpm[ni][mi].sC);
SetToZero(cpm[ni][mi].sD);
SetToZero(cpm[ni][mi].sE);
SetToZero(cpm[ni][mi].sF);
#endif
}
}
}
// =================================================================================================
// Caches global off-chip memory into local (shared) memory on-chip. This function is specific for
// caching the A input matrix.
#if SA == 1
INLINE_FUNC void GlobalToLocalA(const __global realM* restrict agm, __local realM* alm,
const int kSizeM, const int tid, const int kwg) {
const int la0 = tid % MDIMA;
const int la1 = tid / MDIMA;
#pragma unroll
for (int mia=0; mia<MWA/VWM; ++mia) {
#pragma unroll
for (int kia=0; kia<KWA; ++kia) {
// Computes the indices based on strided/non-strided access
#if STRM == 0
int mg = mia + la0*(MWA/VWM);
#elif STRM == 1
int mg = la0 + mia*MDIMA;
#endif
// Computes the indices for the global memory
int kg = kia + la1*KWA;
int idm = mg + GetGroupID0() * (MWG/VWM);
int idk = kg + kwg;
// Loads the data from global memory (not transposed) into the local memory
alm[kg*(MWG/VWM) + mg] = agm[idk*(kSizeM/VWM) + idm];
}
}
}
#endif
// Same as above, but now for the B input matrix
#if SB == 1
INLINE_FUNC void GlobalToLocalB(const __global realN* restrict bgm, __local realN* blm,
const int kSizeN, const int tid, const int kwg) {
const int lb0 = tid % NDIMB;
const int lb1 = tid / NDIMB;
#pragma unroll
for (int kib=0; kib<KWB; ++kib) {
#pragma unroll
for (int nib=0; nib<NWB/VWN; ++nib) {
// Computes the indices based on strided/non-strided access
#if STRN == 0
int ng = nib + lb0*(NWB/VWN);
#elif STRN == 1
int ng = lb0 + nib*NDIMB;
#endif
// Computes the indices for the global memory
int kg = kib + lb1*KWB;
int idn = ng + GetGroupID1() * (NWG/VWN);
int idk = kg + kwg;
// Loads the data from global memory (transposed) into the local memory
blm[kg*(NWG/VWN) + ng] = bgm[idk*(kSizeN/VWN) + idn];
}
}
}
#endif
// =================================================================================================
// Caches global off-chip memory directly into per-thread private memory (registers). This function
// is specific for caching the A input matrix.
#if SA == 0
INLINE_FUNC void GlobalToPrivateA(const __global realM* restrict agm, realM apm[MWI/VWM],
const int kSizeM, const int idk, const int kwg) {
#pragma unroll
for (int mi=0; mi<MWI/VWM; ++mi) {
// Computes the indices based on strided/non-strided access
#if STRM == 0
int mg = mi + get_local_id(0)*(MWI/VWM);
#elif STRM == 1
int mg = get_local_id(0) + mi*MDIMC;
#endif
// Computes the indices for the global memory
int idm = mg + GetGroupID0() * (MWG/VWM);
// Loads the data from global memory (not transposed) and stores into registers
apm[mi] = agm[idk*(kSizeM/VWM) + idm];
}
}
#endif
// Same as above, but now for the B input matrix
#if SB == 0
INLINE_FUNC void GlobalToPrivateB(const __global realN* restrict bgm, realN bpm[NWI/VWN],
const int kSizeN, const int idk) {
#pragma unroll
for (int ni=0; ni<NWI/VWN; ++ni) {
// Computes the indices based on strided/non-strided access
#if STRN == 0
int ng = ni + get_local_id(1)*(NWI/VWN);
#elif STRN == 1
int ng = get_local_id(1) + ni*NDIMC;
#endif
// Computes the indices for the global memory
int idn = ng + GetGroupID1() * (NWG/VWN);
// Loads the data from global memory (transposed) and stores into registers
bpm[ni] = bgm[idk*(kSizeN/VWN) + idn];
}
}
#endif
// =================================================================================================
// Caches on-chip local memory into per-thread private memory (registers). This function is specific
// for caching the A input matrix.
#if SA == 1
INLINE_FUNC void LocalToPrivateA(__local realM* alm, realM apm[MWI/VWM], const int kg) {
#pragma unroll
for (int mi=0; mi<MWI/VWM; ++mi) {
#if STRM == 0
int mg = mi + get_local_id(0)*(MWI/VWM);
#elif STRM == 1
int mg = get_local_id(0) + mi*MDIMC;
#endif
apm[mi] = alm[kg*(MWG/VWM) + mg];
}
}
#endif
// Same as above, but now for the B input matrix
#if SB == 1
INLINE_FUNC void LocalToPrivateB(__local realN* blm, realN bpm[NWI/VWN], const int kg) {
#pragma unroll
for (int ni=0; ni<NWI/VWN; ++ni) {
#if STRN == 0
int ng = ni + get_local_id(1)*(NWI/VWN);
#elif STRN == 1
int ng = get_local_id(1) + ni*NDIMC;
#endif
bpm[ni] = blm[kg*(NWG/VWN) + ng];
}
}
#endif
// =================================================================================================
// End of the C++11 raw string literal
)"
// =================================================================================================
|
