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
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
|
// Copyright ©2017 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build !noasm,!gccgo,!safe
#include "textflag.h"
#define SIZE 8
#define M_DIM n+8(FP)
#define M CX
#define N_DIM m+0(FP)
#define N BX
#define TMP1 R14
#define TMP2 R15
#define X_PTR SI
#define X x_base+56(FP)
#define Y_PTR DX
#define Y y_base+96(FP)
#define A_ROW AX
#define A_PTR DI
#define INC_X R8
#define INC3_X R9
#define INC_Y R10
#define INC3_Y R11
#define LDA R12
#define LDA3 R13
#define ALPHA X15
#define BETA X14
#define INIT4 \
MOVDDUP (X_PTR), X8 \
MOVDDUP (X_PTR)(INC_X*1), X9 \
MOVDDUP (X_PTR)(INC_X*2), X10 \
MOVDDUP (X_PTR)(INC3_X*1), X11 \
MULPD ALPHA, X8 \
MULPD ALPHA, X9 \
MULPD ALPHA, X10 \
MULPD ALPHA, X11
#define INIT2 \
MOVDDUP (X_PTR), X8 \
MOVDDUP (X_PTR)(INC_X*1), X9 \
MULPD ALPHA, X8 \
MULPD ALPHA, X9
#define INIT1 \
MOVDDUP (X_PTR), X8 \
MULPD ALPHA, X8
#define KERNEL_LOAD4 \
MOVUPS (Y_PTR), X0 \
MOVUPS 2*SIZE(Y_PTR), X1
#define KERNEL_LOAD2 \
MOVUPS (Y_PTR), X0
#define KERNEL_LOAD4_INC \
MOVSD (Y_PTR), X0 \
MOVHPD (Y_PTR)(INC_Y*1), X0 \
MOVSD (Y_PTR)(INC_Y*2), X1 \
MOVHPD (Y_PTR)(INC3_Y*1), X1
#define KERNEL_LOAD2_INC \
MOVSD (Y_PTR), X0 \
MOVHPD (Y_PTR)(INC_Y*1), X0
#define KERNEL_4x4 \
MOVUPS (A_PTR), X4 \
MOVUPS 2*SIZE(A_PTR), X5 \
MOVUPS (A_PTR)(LDA*1), X6 \
MOVUPS 2*SIZE(A_PTR)(LDA*1), X7 \
MULPD X8, X4 \
MULPD X8, X5 \
MULPD X9, X6 \
MULPD X9, X7 \
ADDPD X4, X0 \
ADDPD X5, X1 \
ADDPD X6, X0 \
ADDPD X7, X1 \
MOVUPS (A_PTR)(LDA*2), X4 \
MOVUPS 2*SIZE(A_PTR)(LDA*2), X5 \
MOVUPS (A_PTR)(LDA3*1), X6 \
MOVUPS 2*SIZE(A_PTR)(LDA3*1), X7 \
MULPD X10, X4 \
MULPD X10, X5 \
MULPD X11, X6 \
MULPD X11, X7 \
ADDPD X4, X0 \
ADDPD X5, X1 \
ADDPD X6, X0 \
ADDPD X7, X1 \
ADDQ $4*SIZE, A_PTR
#define KERNEL_4x2 \
MOVUPS (A_PTR), X4 \
MOVUPS 2*SIZE(A_PTR), X5 \
MOVUPS (A_PTR)(LDA*1), X6 \
MOVUPS 2*SIZE(A_PTR)(LDA*1), X7 \
MULPD X8, X4 \
MULPD X8, X5 \
MULPD X9, X6 \
MULPD X9, X7 \
ADDPD X4, X0 \
ADDPD X5, X1 \
ADDPD X6, X0 \
ADDPD X7, X1 \
ADDQ $4*SIZE, A_PTR
#define KERNEL_4x1 \
MOVUPS (A_PTR), X4 \
MOVUPS 2*SIZE(A_PTR), X5 \
MULPD X8, X4 \
MULPD X8, X5 \
ADDPD X4, X0 \
ADDPD X5, X1 \
ADDQ $4*SIZE, A_PTR
#define STORE4 \
MOVUPS X0, (Y_PTR) \
MOVUPS X1, 2*SIZE(Y_PTR)
#define STORE4_INC \
MOVLPD X0, (Y_PTR) \
MOVHPD X0, (Y_PTR)(INC_Y*1) \
MOVLPD X1, (Y_PTR)(INC_Y*2) \
MOVHPD X1, (Y_PTR)(INC3_Y*1)
#define KERNEL_2x4 \
MOVUPS (A_PTR), X4 \
MOVUPS (A_PTR)(LDA*1), X5 \
MOVUPS (A_PTR)(LDA*2), X6 \
MOVUPS (A_PTR)(LDA3*1), X7 \
MULPD X8, X4 \
MULPD X9, X5 \
MULPD X10, X6 \
MULPD X11, X7 \
ADDPD X4, X0 \
ADDPD X5, X0 \
ADDPD X6, X0 \
ADDPD X7, X0 \
ADDQ $2*SIZE, A_PTR
#define KERNEL_2x2 \
MOVUPS (A_PTR), X4 \
MOVUPS (A_PTR)(LDA*1), X5 \
MULPD X8, X4 \
MULPD X9, X5 \
ADDPD X4, X0 \
ADDPD X5, X0 \
ADDQ $2*SIZE, A_PTR
#define KERNEL_2x1 \
MOVUPS (A_PTR), X4 \
MULPD X8, X4 \
ADDPD X4, X0 \
ADDQ $2*SIZE, A_PTR
#define STORE2 \
MOVUPS X0, (Y_PTR)
#define STORE2_INC \
MOVLPD X0, (Y_PTR) \
MOVHPD X0, (Y_PTR)(INC_Y*1)
#define KERNEL_1x4 \
MOVSD (Y_PTR), X0 \
MOVSD (A_PTR), X4 \
MOVSD (A_PTR)(LDA*1), X5 \
MOVSD (A_PTR)(LDA*2), X6 \
MOVSD (A_PTR)(LDA3*1), X7 \
MULSD X8, X4 \
MULSD X9, X5 \
MULSD X10, X6 \
MULSD X11, X7 \
ADDSD X4, X0 \
ADDSD X5, X0 \
ADDSD X6, X0 \
ADDSD X7, X0 \
MOVSD X0, (Y_PTR) \
ADDQ $SIZE, A_PTR
#define KERNEL_1x2 \
MOVSD (Y_PTR), X0 \
MOVSD (A_PTR), X4 \
MOVSD (A_PTR)(LDA*1), X5 \
MULSD X8, X4 \
MULSD X9, X5 \
ADDSD X4, X0 \
ADDSD X5, X0 \
MOVSD X0, (Y_PTR) \
ADDQ $SIZE, A_PTR
#define KERNEL_1x1 \
MOVSD (Y_PTR), X0 \
MOVSD (A_PTR), X4 \
MULSD X8, X4 \
ADDSD X4, X0 \
MOVSD X0, (Y_PTR) \
ADDQ $SIZE, A_PTR
#define SCALE_8(PTR, SCAL) \
MOVUPS (PTR), X0 \
MOVUPS 16(PTR), X1 \
MOVUPS 32(PTR), X2 \
MOVUPS 48(PTR), X3 \
MULPD SCAL, X0 \
MULPD SCAL, X1 \
MULPD SCAL, X2 \
MULPD SCAL, X3 \
MOVUPS X0, (PTR) \
MOVUPS X1, 16(PTR) \
MOVUPS X2, 32(PTR) \
MOVUPS X3, 48(PTR)
#define SCALE_4(PTR, SCAL) \
MOVUPS (PTR), X0 \
MOVUPS 16(PTR), X1 \
MULPD SCAL, X0 \
MULPD SCAL, X1 \
MOVUPS X0, (PTR) \
MOVUPS X1, 16(PTR) \
#define SCALE_2(PTR, SCAL) \
MOVUPS (PTR), X0 \
MULPD SCAL, X0 \
MOVUPS X0, (PTR) \
#define SCALE_1(PTR, SCAL) \
MOVSD (PTR), X0 \
MULSD SCAL, X0 \
MOVSD X0, (PTR) \
#define SCALEINC_4(PTR, INC, INC3, SCAL) \
MOVSD (PTR), X0 \
MOVSD (PTR)(INC*1), X1 \
MOVSD (PTR)(INC*2), X2 \
MOVSD (PTR)(INC3*1), X3 \
MULSD SCAL, X0 \
MULSD SCAL, X1 \
MULSD SCAL, X2 \
MULSD SCAL, X3 \
MOVSD X0, (PTR) \
MOVSD X1, (PTR)(INC*1) \
MOVSD X2, (PTR)(INC*2) \
MOVSD X3, (PTR)(INC3*1)
#define SCALEINC_2(PTR, INC, SCAL) \
MOVSD (PTR), X0 \
MOVSD (PTR)(INC*1), X1 \
MULSD SCAL, X0 \
MULSD SCAL, X1 \
MOVSD X0, (PTR) \
MOVSD X1, (PTR)(INC*1)
// func GemvT(m, n int,
// alpha float64,
// a []float64, lda int,
// x []float64, incX int,
// beta float64,
// y []float64, incY int)
TEXT ·GemvT(SB), NOSPLIT, $32-128
MOVQ M_DIM, M
MOVQ N_DIM, N
CMPQ M, $0
JE end
CMPQ N, $0
JE end
MOVDDUP alpha+16(FP), ALPHA
MOVQ x_base+56(FP), X_PTR
MOVQ y_base+96(FP), Y_PTR
MOVQ a_base+24(FP), A_ROW
MOVQ incY+120(FP), INC_Y // INC_Y = incY * sizeof(float64)
MOVQ lda+48(FP), LDA // LDA = LDA * sizeof(float64)
SHLQ $3, LDA
LEAQ (LDA)(LDA*2), LDA3 // LDA3 = LDA * 3
MOVQ A_ROW, A_PTR
MOVQ incX+80(FP), INC_X // INC_X = incX * sizeof(float64)
XORQ TMP2, TMP2
MOVQ N, TMP1
SUBQ $1, TMP1
NEGQ TMP1
IMULQ INC_X, TMP1
CMPQ INC_X, $0
CMOVQLT TMP1, TMP2
LEAQ (X_PTR)(TMP2*SIZE), X_PTR
MOVQ X_PTR, X
SHLQ $3, INC_X
LEAQ (INC_X)(INC_X*2), INC3_X // INC3_X = INC_X * 3
CMPQ incY+120(FP), $1 // Check for dense vector Y (fast-path)
JNE inc
MOVSD $1.0, X0
COMISD beta+88(FP), X0
JE gemv_start
MOVSD $0.0, X0
COMISD beta+88(FP), X0
JE gemv_clear
MOVDDUP beta+88(FP), BETA
SHRQ $3, M
JZ scal4
scal8:
SCALE_8(Y_PTR, BETA)
ADDQ $8*SIZE, Y_PTR
DECQ M
JNZ scal8
scal4:
TESTQ $4, M_DIM
JZ scal2
SCALE_4(Y_PTR, BETA)
ADDQ $4*SIZE, Y_PTR
scal2:
TESTQ $2, M_DIM
JZ scal1
SCALE_2(Y_PTR, BETA)
ADDQ $2*SIZE, Y_PTR
scal1:
TESTQ $1, M_DIM
JZ prep_end
SCALE_1(Y_PTR, BETA)
JMP prep_end
gemv_clear: // beta == 0 is special cased to clear memory (no nan handling)
XORPS X0, X0
XORPS X1, X1
XORPS X2, X2
XORPS X3, X3
SHRQ $3, M
JZ clear4
clear8:
MOVUPS X0, (Y_PTR)
MOVUPS X1, 16(Y_PTR)
MOVUPS X2, 32(Y_PTR)
MOVUPS X3, 48(Y_PTR)
ADDQ $8*SIZE, Y_PTR
DECQ M
JNZ clear8
clear4:
TESTQ $4, M_DIM
JZ clear2
MOVUPS X0, (Y_PTR)
MOVUPS X1, 16(Y_PTR)
ADDQ $4*SIZE, Y_PTR
clear2:
TESTQ $2, M_DIM
JZ clear1
MOVUPS X0, (Y_PTR)
ADDQ $2*SIZE, Y_PTR
clear1:
TESTQ $1, M_DIM
JZ prep_end
MOVSD X0, (Y_PTR)
prep_end:
MOVQ Y, Y_PTR
MOVQ M_DIM, M
gemv_start:
SHRQ $2, N
JZ c2
c4:
// LOAD 4
INIT4
MOVQ M_DIM, M
SHRQ $2, M
JZ c4r2
c4r4:
// 4x4 KERNEL
KERNEL_LOAD4
KERNEL_4x4
STORE4
ADDQ $4*SIZE, Y_PTR
DECQ M
JNZ c4r4
c4r2:
TESTQ $2, M_DIM
JZ c4r1
// 4x2 KERNEL
KERNEL_LOAD2
KERNEL_2x4
STORE2
ADDQ $2*SIZE, Y_PTR
c4r1:
TESTQ $1, M_DIM
JZ c4end
// 4x1 KERNEL
KERNEL_1x4
ADDQ $SIZE, Y_PTR
c4end:
LEAQ (X_PTR)(INC_X*4), X_PTR
MOVQ Y, Y_PTR
LEAQ (A_ROW)(LDA*4), A_ROW
MOVQ A_ROW, A_PTR
DECQ N
JNZ c4
c2:
TESTQ $2, N_DIM
JZ c1
// LOAD 2
INIT2
MOVQ M_DIM, M
SHRQ $2, M
JZ c2r2
c2r4:
// 2x4 KERNEL
KERNEL_LOAD4
KERNEL_4x2
STORE4
ADDQ $4*SIZE, Y_PTR
DECQ M
JNZ c2r4
c2r2:
TESTQ $2, M_DIM
JZ c2r1
// 2x2 KERNEL
KERNEL_LOAD2
KERNEL_2x2
STORE2
ADDQ $2*SIZE, Y_PTR
c2r1:
TESTQ $1, M_DIM
JZ c2end
// 2x1 KERNEL
KERNEL_1x2
ADDQ $SIZE, Y_PTR
c2end:
LEAQ (X_PTR)(INC_X*2), X_PTR
MOVQ Y, Y_PTR
LEAQ (A_ROW)(LDA*2), A_ROW
MOVQ A_ROW, A_PTR
c1:
TESTQ $1, N_DIM
JZ end
// LOAD 1
INIT1
MOVQ M_DIM, M
SHRQ $2, M
JZ c1r2
c1r4:
// 1x4 KERNEL
KERNEL_LOAD4
KERNEL_4x1
STORE4
ADDQ $4*SIZE, Y_PTR
DECQ M
JNZ c1r4
c1r2:
TESTQ $2, M_DIM
JZ c1r1
// 1x2 KERNEL
KERNEL_LOAD2
KERNEL_2x1
STORE2
ADDQ $2*SIZE, Y_PTR
c1r1:
TESTQ $1, M_DIM
JZ end
// 1x1 KERNEL
KERNEL_1x1
end:
RET
inc: // Algorithm for incX != 0 ( split loads in kernel )
XORQ TMP2, TMP2
MOVQ M, TMP1
SUBQ $1, TMP1
IMULQ INC_Y, TMP1
NEGQ TMP1
CMPQ INC_Y, $0
CMOVQLT TMP1, TMP2
LEAQ (Y_PTR)(TMP2*SIZE), Y_PTR
MOVQ Y_PTR, Y
SHLQ $3, INC_Y
LEAQ (INC_Y)(INC_Y*2), INC3_Y // INC3_Y = INC_Y * 3
MOVSD $1.0, X0
COMISD beta+88(FP), X0
JE inc_gemv_start
MOVSD $0.0, X0
COMISD beta+88(FP), X0
JE inc_gemv_clear
MOVDDUP beta+88(FP), BETA
SHRQ $2, M
JZ inc_scal2
inc_scal4:
SCALEINC_4(Y_PTR, INC_Y, INC3_Y, BETA)
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
DECQ M
JNZ inc_scal4
inc_scal2:
TESTQ $2, M_DIM
JZ inc_scal1
SCALEINC_2(Y_PTR, INC_Y, BETA)
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
inc_scal1:
TESTQ $1, M_DIM
JZ inc_prep_end
SCALE_1(Y_PTR, BETA)
JMP inc_prep_end
inc_gemv_clear: // beta == 0 is special-cased to clear memory (no nan handling)
XORPS X0, X0
XORPS X1, X1
XORPS X2, X2
XORPS X3, X3
SHRQ $2, M
JZ inc_clear2
inc_clear4:
MOVSD X0, (Y_PTR)
MOVSD X1, (Y_PTR)(INC_Y*1)
MOVSD X2, (Y_PTR)(INC_Y*2)
MOVSD X3, (Y_PTR)(INC3_Y*1)
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
DECQ M
JNZ inc_clear4
inc_clear2:
TESTQ $2, M_DIM
JZ inc_clear1
MOVSD X0, (Y_PTR)
MOVSD X1, (Y_PTR)(INC_Y*1)
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
inc_clear1:
TESTQ $1, M_DIM
JZ inc_prep_end
MOVSD X0, (Y_PTR)
inc_prep_end:
MOVQ Y, Y_PTR
MOVQ M_DIM, M
inc_gemv_start:
SHRQ $2, N
JZ inc_c2
inc_c4:
// LOAD 4
INIT4
MOVQ M_DIM, M
SHRQ $2, M
JZ inc_c4r2
inc_c4r4:
// 4x4 KERNEL
KERNEL_LOAD4_INC
KERNEL_4x4
STORE4_INC
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
DECQ M
JNZ inc_c4r4
inc_c4r2:
TESTQ $2, M_DIM
JZ inc_c4r1
// 4x2 KERNEL
KERNEL_LOAD2_INC
KERNEL_2x4
STORE2_INC
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
inc_c4r1:
TESTQ $1, M_DIM
JZ inc_c4end
// 4x1 KERNEL
KERNEL_1x4
ADDQ INC_Y, Y_PTR
inc_c4end:
LEAQ (X_PTR)(INC_X*4), X_PTR
MOVQ Y, Y_PTR
LEAQ (A_ROW)(LDA*4), A_ROW
MOVQ A_ROW, A_PTR
DECQ N
JNZ inc_c4
inc_c2:
TESTQ $2, N_DIM
JZ inc_c1
// LOAD 2
INIT2
MOVQ M_DIM, M
SHRQ $2, M
JZ inc_c2r2
inc_c2r4:
// 2x4 KERNEL
KERNEL_LOAD4_INC
KERNEL_4x2
STORE4_INC
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
DECQ M
JNZ inc_c2r4
inc_c2r2:
TESTQ $2, M_DIM
JZ inc_c2r1
// 2x2 KERNEL
KERNEL_LOAD2_INC
KERNEL_2x2
STORE2_INC
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
inc_c2r1:
TESTQ $1, M_DIM
JZ inc_c2end
// 2x1 KERNEL
KERNEL_1x2
ADDQ INC_Y, Y_PTR
inc_c2end:
LEAQ (X_PTR)(INC_X*2), X_PTR
MOVQ Y, Y_PTR
LEAQ (A_ROW)(LDA*2), A_ROW
MOVQ A_ROW, A_PTR
inc_c1:
TESTQ $1, N_DIM
JZ inc_end
// LOAD 1
INIT1
MOVQ M_DIM, M
SHRQ $2, M
JZ inc_c1r2
inc_c1r4:
// 1x4 KERNEL
KERNEL_LOAD4_INC
KERNEL_4x1
STORE4_INC
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
DECQ M
JNZ inc_c1r4
inc_c1r2:
TESTQ $2, M_DIM
JZ inc_c1r1
// 1x2 KERNEL
KERNEL_LOAD2_INC
KERNEL_2x1
STORE2_INC
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
inc_c1r1:
TESTQ $1, M_DIM
JZ inc_end
// 1x1 KERNEL
KERNEL_1x1
inc_end:
RET
|
