-
Notifications
You must be signed in to change notification settings - Fork 1.5k
/
Copy pathflash_attn_triton.py
1160 lines (1113 loc) · 40.1 KB
/
flash_attn_triton.py
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
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
"""
*Experimental* implementation of FlashAttention in Triton.
Tested with triton==2.0.0.dev20221202.
Triton 2.0 has a new backend (MLIR) but seems like it doesn't yet work for head dimensions
other than 64:
https://github.com/openai/triton/blob/d376020f90002757eea3ea9475d4f7cfc2ec5ead/python/triton/ops/flash_attention.py#L207
We'll update this implementation with the new Triton backend once this is fixed.
We use the FlashAttention implementation from Phil Tillet a starting point.
https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py
Changes:
- Implement both causal and non-causal attention.
- Implement both self-attention and cross-attention.
- Support arbitrary seqlens (not just multiples of 128), for both forward and backward.
- Support all head dimensions up to 128 (not just 16, 32, 64, 128), for both forward and backward.
- Support attention bias.
- Speed up the forward pass a bit, and only store the LSE instead of m and l.
- Make the backward for d=128 much faster by reducing register spilling.
- Optionally parallelize the backward pass across seqlen_k, to deal with the case of
small batch size * nheads.
Caution:
- This is an *experimental* implementation. The forward pass should be quite robust but
I'm not 100% sure that the backward pass doesn't have race conditions (due to the Triton compiler).
- This implementation has only been tested on A100.
- If you plan to use headdim other than 64 and 128, you should test for race conditions
(due to the Triton compiler), as done in tests/test_flash_attn.py
"test_flash_attn_triton_race_condition". I've tested and fixed many race conditions
for different head dimensions (40, 48, 64, 128, 80, 88, 96), but I'm still not 100% confident
that there are none left for other head dimensions.
Differences between this Triton version and the CUDA version:
- Triton version doesn't support dropout.
- Triton forward is generally faster than CUDA forward, while Triton backward is
generally slower than CUDA backward. Overall Triton forward + backward is slightly slower
than CUDA forward + backward.
- Triton version doesn't support different sequence lengths in a batch (i.e., RaggedTensor/NestedTensor).
- Triton version supports attention bias, while CUDA version doesn't.
"""
import math
import torch
import triton
import triton.language as tl
# Disabling autotune for now, set num_warps=4 if headdim=64 and num_warps=8 if headdim=128
# @triton.autotune(
# configs=[
# triton.Config({"BLOCK_M": 128, "BLOCK_N": 128}, num_warps=4, num_stages=1),
# # This config has a race condition when EVEN_M == False, disabling it for now.
# # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64}, num_warps=4, num_stages=1),
# ],
# key=['CACHE_KEY_SEQLEN_Q', 'CACHE_KEY_SEQLEN_K', 'BIAS_TYPE', 'IS_CAUSAL', 'BLOCK_HEADDIM']
# )
@triton.heuristics(
{
"EVEN_M": lambda args: args["seqlen_q"] % args["BLOCK_M"] == 0,
"EVEN_N": lambda args: args["seqlen_k"] % args["BLOCK_N"] == 0,
"EVEN_HEADDIM": lambda args: args["headdim"] == args["BLOCK_HEADDIM"],
}
)
@triton.jit
def _fwd_kernel(
Q,
K,
V,
Bias,
Out,
Lse,
TMP, # NOTE: TMP is a scratchpad buffer to workaround a compiler bug
softmax_scale,
stride_qb,
stride_qh,
stride_qm,
stride_kb,
stride_kh,
stride_kn,
stride_vb,
stride_vh,
stride_vn,
stride_bb,
stride_bh,
stride_bm,
stride_ob,
stride_oh,
stride_om,
nheads,
seqlen_q,
seqlen_k,
seqlen_q_rounded,
headdim,
CACHE_KEY_SEQLEN_Q,
CACHE_KEY_SEQLEN_K,
BIAS_TYPE: tl.constexpr,
IS_CAUSAL: tl.constexpr,
BLOCK_HEADDIM: tl.constexpr,
EVEN_M: tl.constexpr,
EVEN_N: tl.constexpr,
EVEN_HEADDIM: tl.constexpr,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
):
start_m = tl.program_id(0)
off_hb = tl.program_id(1)
off_b = off_hb // nheads
off_h = off_hb % nheads
# off_b = tl.program_id(1)
# off_h = tl.program_id(2)
# off_hb = off_b * nheads + off_h
# initialize offsets
offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
offs_n = tl.arange(0, BLOCK_N)
offs_d = tl.arange(0, BLOCK_HEADDIM)
# Initialize pointers to Q, K, V
# Adding parenthesis around indexing might use int32 math instead of int64 math?
# https://github.com/openai/triton/issues/741
# I'm seeing a tiny bit of difference (5-7us)
q_ptrs = (
Q + off_b * stride_qb + off_h * stride_qh + (offs_m[:, None] * stride_qm + offs_d[None, :])
)
k_ptrs = (
K + off_b * stride_kb + off_h * stride_kh + (offs_n[:, None] * stride_kn + offs_d[None, :])
)
v_ptrs = (
V + off_b * stride_vb + off_h * stride_vh + (offs_n[:, None] * stride_vn + offs_d[None, :])
)
if BIAS_TYPE == "vector":
b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + offs_n
elif BIAS_TYPE == "matrix":
b_ptrs = (
Bias
+ off_b * stride_bb
+ off_h * stride_bh
+ (offs_m[:, None] * stride_bm + offs_n[None, :])
)
# initialize pointer to m and l
t_ptrs = TMP + off_hb * seqlen_q_rounded + offs_m
lse_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
acc_o = tl.zeros([BLOCK_M, BLOCK_HEADDIM], dtype=tl.float32)
# load q: it will stay in SRAM throughout
# [2022-10-30] TD: Triton bug - in the case of EVEN_M=True and EVEN_N=False, if we just call
# tl.load(q_ptrs), we get the wrong output!
if EVEN_M & EVEN_N:
if EVEN_HEADDIM:
q = tl.load(q_ptrs)
else:
q = tl.load(q_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
else:
if EVEN_HEADDIM:
q = tl.load(q_ptrs, mask=offs_m[:, None] < seqlen_q, other=0.0)
else:
q = tl.load(
q_ptrs, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0
)
# loop over k, v and update accumulator
end_n = seqlen_k if not IS_CAUSAL else tl.minimum((start_m + 1) * BLOCK_M, seqlen_k)
for start_n in range(0, end_n, BLOCK_N):
start_n = tl.multiple_of(start_n, BLOCK_N)
# -- compute qk ----
if EVEN_N & EVEN_M: # If we just do "if EVEN_N", there seems to be some race condition
if EVEN_HEADDIM:
k = tl.load(k_ptrs + start_n * stride_kn)
else:
k = tl.load(k_ptrs + start_n * stride_kn, mask=offs_d[None, :] < headdim, other=0.0)
else:
if EVEN_HEADDIM:
k = tl.load(
k_ptrs + start_n * stride_kn,
mask=(start_n + offs_n)[:, None] < seqlen_k,
other=0.0,
)
else:
k = tl.load(
k_ptrs + start_n * stride_kn,
mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim),
other=0.0,
)
qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
qk += tl.dot(q, k, trans_b=True)
# Trying to combine the two masks seem to make the result wrong
if not EVEN_N: # Need to mask out otherwise the softmax is wrong
qk += tl.where((start_n + offs_n)[None, :] < seqlen_k, 0, float("-inf"))
if IS_CAUSAL:
qk += tl.where(offs_m[:, None] >= (start_n + offs_n)[None, :], 0, float("-inf"))
if BIAS_TYPE != "none":
if BIAS_TYPE == "vector":
if EVEN_N:
bias = tl.load(b_ptrs + start_n).to(tl.float32)
else:
bias = tl.load(
b_ptrs + start_n, mask=(start_n + offs_n) < seqlen_k, other=0.0
).to(tl.float32)
bias = bias[None, :]
elif BIAS_TYPE == "matrix":
if EVEN_M & EVEN_N:
bias = tl.load(b_ptrs + start_n).to(tl.float32)
else:
bias = tl.load(
b_ptrs + start_n,
mask=(offs_m[:, None] < seqlen_q)
& ((start_n + offs_n)[None, :] < seqlen_k),
other=0.0,
).to(tl.float32)
# Slightly faster to multiply the softmax_scale in the tl.exp below since the compiler
# can then fuse the mult and add into an fma instruction. But if we have bias we need to
# to multiply with softmax_scale here.
qk = qk * softmax_scale + bias
m_ij = tl.maximum(tl.max(qk, 1), lse_i)
p = tl.exp(qk - m_ij[:, None])
else:
m_ij = tl.maximum(tl.max(qk, 1) * softmax_scale, lse_i)
p = tl.exp(qk * softmax_scale - m_ij[:, None])
l_ij = tl.sum(p, 1)
# scale acc_o
acc_o_scale = tl.exp(m_i - m_ij)
# # -- update output accumulator --
# BUG: have to store and immediately load
tl.store(t_ptrs, acc_o_scale)
acc_o_scale = tl.load(t_ptrs)
acc_o = acc_o * acc_o_scale[:, None]
# update acc_o
if EVEN_N & EVEN_M: # If we just do "if EVEN_N", there seems to be some race condition
if EVEN_HEADDIM:
v = tl.load(v_ptrs + start_n * stride_vn)
else:
v = tl.load(v_ptrs + start_n * stride_vn, mask=offs_d[None, :] < headdim, other=0.0)
else:
if EVEN_HEADDIM:
v = tl.load(
v_ptrs + start_n * stride_vn,
mask=(start_n + offs_n)[:, None] < seqlen_k,
other=0.0,
)
else:
v = tl.load(
v_ptrs + start_n * stride_vn,
mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim),
other=0.0,
)
p = p.to(v.dtype)
acc_o += tl.dot(p, v)
# -- update statistics
m_i = m_ij
l_i_new = tl.exp(lse_i - m_ij) + l_ij
lse_i = m_ij + tl.log(l_i_new)
o_scale = tl.exp(m_i - lse_i)
# BUG: have to store and immediately load
tl.store(t_ptrs, o_scale)
o_scale = tl.load(t_ptrs)
acc_o = acc_o * o_scale[:, None]
# rematerialize offsets to save registers
start_m = tl.program_id(0)
offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
# write back l and m
lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m
tl.store(lse_ptrs, lse_i)
# initialize pointers to output
offs_d = tl.arange(0, BLOCK_HEADDIM)
out_ptrs = (
Out
+ off_b * stride_ob
+ off_h * stride_oh
+ (offs_m[:, None] * stride_om + offs_d[None, :])
)
if EVEN_M:
if EVEN_HEADDIM:
tl.store(out_ptrs, acc_o)
else:
tl.store(out_ptrs, acc_o, mask=offs_d[None, :] < headdim)
else:
if EVEN_HEADDIM:
tl.store(out_ptrs, acc_o, mask=offs_m[:, None] < seqlen_q)
else:
tl.store(
out_ptrs, acc_o, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim)
)
@triton.jit
def _bwd_preprocess_do_o_dot(
Out,
DO,
Delta,
stride_ob,
stride_oh,
stride_om,
stride_dob,
stride_doh,
stride_dom,
nheads,
seqlen_q,
seqlen_q_rounded,
headdim,
BLOCK_M: tl.constexpr,
BLOCK_HEADDIM: tl.constexpr,
):
start_m = tl.program_id(0)
off_hb = tl.program_id(1)
off_b = off_hb // nheads
off_h = off_hb % nheads
# initialize offsets
offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
offs_d = tl.arange(0, BLOCK_HEADDIM)
# load
o = tl.load(
Out + off_b * stride_ob + off_h * stride_oh + offs_m[:, None] * stride_om + offs_d[None, :],
mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
other=0.0,
).to(tl.float32)
do = tl.load(
DO
+ off_b * stride_dob
+ off_h * stride_doh
+ offs_m[:, None] * stride_dom
+ offs_d[None, :],
mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
other=0.0,
).to(tl.float32)
delta = tl.sum(o * do, axis=1)
# write-back
tl.store(Delta + off_hb * seqlen_q_rounded + offs_m, delta)
@triton.jit
def _bwd_store_dk_dv(
dk_ptrs,
dv_ptrs,
dk,
dv,
offs_n,
offs_d,
seqlen_k,
headdim,
EVEN_M: tl.constexpr,
EVEN_N: tl.constexpr,
EVEN_HEADDIM: tl.constexpr,
):
# [2022-11-01] TD: Same bug. In the case of EVEN_N=True and EVEN_M=False,
# if we just call tl.store(dv_ptrs), there's a race condition
if EVEN_N & EVEN_M:
if EVEN_HEADDIM:
tl.store(dv_ptrs, dv)
tl.store(dk_ptrs, dk)
else:
tl.store(dv_ptrs, dv, mask=offs_d[None, :] < headdim)
tl.store(dk_ptrs, dk, mask=offs_d[None, :] < headdim)
else:
if EVEN_HEADDIM:
tl.store(dv_ptrs, dv, mask=offs_n[:, None] < seqlen_k)
tl.store(dk_ptrs, dk, mask=offs_n[:, None] < seqlen_k)
else:
tl.store(dv_ptrs, dv, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim))
tl.store(dk_ptrs, dk, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim))
@triton.jit
def _bwd_kernel_one_col_block(
start_n,
Q,
K,
V,
Bias,
DO,
DQ,
DK,
DV,
LSE,
D,
softmax_scale,
stride_qm,
stride_kn,
stride_vn,
stride_bm,
stride_dom,
stride_dqm,
stride_dkn,
stride_dvn,
seqlen_q,
seqlen_k,
headdim,
ATOMIC_ADD: tl.constexpr,
BIAS_TYPE: tl.constexpr,
IS_CAUSAL: tl.constexpr,
BLOCK_HEADDIM: tl.constexpr,
EVEN_M: tl.constexpr,
EVEN_N: tl.constexpr,
EVEN_HEADDIM: tl.constexpr,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
):
# We need to make sure begin_m is a multiple of BLOCK_M (not BLOCK_N)
begin_m = 0 if not IS_CAUSAL else ((start_n * BLOCK_N) // BLOCK_M) * BLOCK_M
# initialize row/col offsets
offs_qm = begin_m + tl.arange(0, BLOCK_M)
offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N)
offs_m = tl.arange(0, BLOCK_M)
offs_d = tl.arange(0, BLOCK_HEADDIM)
# initialize pointers to value-like data
q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_d[None, :])
k_ptrs = K + (offs_n[:, None] * stride_kn + offs_d[None, :])
v_ptrs = V + (offs_n[:, None] * stride_vn + offs_d[None, :])
do_ptrs = DO + (offs_qm[:, None] * stride_dom + offs_d[None, :])
dq_ptrs = DQ + (offs_qm[:, None] * stride_dqm + offs_d[None, :])
if BIAS_TYPE == "vector":
b_ptrs = Bias + offs_n
elif BIAS_TYPE == "matrix":
b_ptrs = Bias + (offs_qm[:, None] * stride_bm + offs_n[None, :])
# initialize dv and dk
dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
# There seems to be some problem with Triton pipelining that makes results wrong for
# headdim=64, seqlen=(113, 255), bias_type='matrix'. In this case the for loop
# may have zero step, and pipelining with the bias matrix could screw it up.
# So we just exit early.
if begin_m >= seqlen_q:
dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])
dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])
_bwd_store_dk_dv(
dk_ptrs,
dv_ptrs,
dk,
dv,
offs_n,
offs_d,
seqlen_k,
headdim,
EVEN_M=EVEN_M,
EVEN_N=EVEN_N,
EVEN_HEADDIM=EVEN_HEADDIM,
)
return
# k and v stay in SRAM throughout
# [2022-10-30] TD: Same bug as the fwd. In the case of EVEN_N=True and EVEN_M=False,
# if we just call tl.load(k_ptrs), we get the wrong output!
if EVEN_N & EVEN_M:
if EVEN_HEADDIM:
k = tl.load(k_ptrs)
v = tl.load(v_ptrs)
else:
k = tl.load(k_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
v = tl.load(v_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
else:
if EVEN_HEADDIM:
k = tl.load(k_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
v = tl.load(v_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
else:
k = tl.load(
k_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0
)
v = tl.load(
v_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0
)
# loop over rows
num_block_m = tl.cdiv(seqlen_q, BLOCK_M)
for start_m in range(begin_m, num_block_m * BLOCK_M, BLOCK_M):
start_m = tl.multiple_of(start_m, BLOCK_M)
offs_m_curr = start_m + offs_m
# load q, k, v, do on-chip
# Same bug as below. Otherwise gives wrong result for headdim=40, seqlen=(128, 117)
if EVEN_M & EVEN_HEADDIM:
q = tl.load(q_ptrs)
else:
if EVEN_HEADDIM:
q = tl.load(q_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0)
else:
q = tl.load(
q_ptrs,
mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
other=0.0,
)
# recompute p = softmax(qk, dim=-1).T
qk = tl.dot(q, k, trans_b=True)
# Trying to combine the two masks seem to make the result wrong
if not EVEN_N: # Need to mask out otherwise the softmax is wrong
qk = tl.where(offs_n[None, :] < seqlen_k, qk, float("-inf"))
if IS_CAUSAL:
qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), qk, float("-inf"))
if BIAS_TYPE != "none":
tl.debug_barrier() # Race condition otherwise
if BIAS_TYPE == "vector":
if EVEN_N:
bias = tl.load(b_ptrs).to(tl.float32)
else:
bias = tl.load(b_ptrs, mask=offs_n < seqlen_k, other=0.0).to(tl.float32)
bias = bias[None, :]
elif BIAS_TYPE == "matrix":
if EVEN_M & EVEN_N:
bias = tl.load(b_ptrs).to(tl.float32)
else:
bias = tl.load(
b_ptrs,
mask=(offs_m_curr[:, None] < seqlen_q) & (offs_n[None, :] < seqlen_k),
other=0.0,
).to(tl.float32)
qk = qk * softmax_scale + bias
# There seems to be a race condition when headdim=48/96, and dq, dk, dv are wrong.
# Also wrong for headdim=64.
if not (EVEN_M & EVEN_HEADDIM):
tl.debug_barrier()
lse_i = tl.load(LSE + offs_m_curr)
if BIAS_TYPE == "none":
p = tl.exp(qk * softmax_scale - lse_i[:, None])
else:
p = tl.exp(qk - lse_i[:, None])
# compute dv
# [2022-10-30] TD: A Triton bug: if EVEN_M=True and EVEN_HEADDIM=False, if we call
# do = tl.load(do_ptrs, mask=offs_d[None, :] < headdim, other=0.0), we get wrong outputs
# in the case of headdim=48/96, seqlen_q & seqlen_k >= 512. If headdim=40 or seqlen < 512,
# the output is correct.
if EVEN_M & EVEN_HEADDIM:
do = tl.load(do_ptrs)
else:
# [2022-11-01] TD: Triton bug, there's a race condition if we just use m_mask and not d_mask.
do = tl.load(
do_ptrs,
mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
other=0.0,
)
# if EVEN_M:
# if EVEN_HEADDIM:
# do = tl.load(do_ptrs)
# else:
# do = tl.load(do_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
# else:
# if EVEN_HEADDIM:
# do = tl.load(do_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0)
# else:
# do = tl.load(do_ptrs, mask=(offs_m_curr[:, None] < seqlen_q)
# & (offs_d[None, :] < headdim), other=0.0)
dv += tl.dot(p.to(do.dtype), do, trans_a=True)
# compute dp = dot(v, do)
# There seems to be a race condition when headdim=48/96, and dq, dk are wrong.
# Also wrong for headdim=128, seqlen=(108, 256), and ATOMIC_ADD=True
# Also wrong for headdim=64, seqlen=(1023, 1024), and ATOMIC_ADD=False
if not (EVEN_M & EVEN_HEADDIM):
tl.debug_barrier()
dp = tl.dot(do, v, trans_b=True)
# There's a race condition for headdim=48
if not EVEN_HEADDIM:
tl.debug_barrier()
# compute ds = p * (dp - delta[:, None])
# Putting the subtraction after the dp matmul (instead of before) is slightly faster
Di = tl.load(D + offs_m_curr)
# Converting ds to q.dtype here reduces register pressure and makes it much faster
# for BLOCK_HEADDIM=128
ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype)
# compute dk = dot(ds.T, q)
dk += tl.dot(ds, q, trans_a=True)
# compute dq
if not (
EVEN_M & EVEN_HEADDIM
): # Otherewise there's a race condition when BIAS_TYPE='matrix'
tl.debug_barrier()
if not ATOMIC_ADD:
if EVEN_M & EVEN_HEADDIM: # Race condition if we just do EVEN_M
dq = tl.load(dq_ptrs, eviction_policy="evict_last")
dq += tl.dot(ds, k)
tl.store(dq_ptrs, dq, eviction_policy="evict_last")
else:
if EVEN_HEADDIM:
dq = tl.load(
dq_ptrs,
mask=offs_m_curr[:, None] < seqlen_q,
other=0.0,
eviction_policy="evict_last",
)
dq += tl.dot(ds, k)
tl.store(
dq_ptrs,
dq,
mask=offs_m_curr[:, None] < seqlen_q,
eviction_policy="evict_last",
)
else:
dq = tl.load(
dq_ptrs,
mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
other=0.0,
eviction_policy="evict_last",
)
dq += tl.dot(ds, k)
tl.store(
dq_ptrs,
dq,
mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
eviction_policy="evict_last",
)
else: # If we're parallelizing across the seqlen_k dimension
dq = tl.dot(ds, k)
if EVEN_M & EVEN_HEADDIM: # Race condition if we just do EVEN_M
tl.atomic_add(dq_ptrs, dq)
else:
if EVEN_HEADDIM:
tl.atomic_add(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q)
else:
tl.atomic_add(
dq_ptrs,
dq,
mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
)
# increment pointers
dq_ptrs += BLOCK_M * stride_dqm
q_ptrs += BLOCK_M * stride_qm
do_ptrs += BLOCK_M * stride_dom
if BIAS_TYPE == "matrix":
b_ptrs += BLOCK_M * stride_bm
# write-back
dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])
dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])
_bwd_store_dk_dv(
dk_ptrs,
dv_ptrs,
dk,
dv,
offs_n,
offs_d,
seqlen_k,
headdim,
EVEN_M=EVEN_M,
EVEN_N=EVEN_N,
EVEN_HEADDIM=EVEN_HEADDIM,
)
def init_to_zero(name):
return lambda nargs: nargs[name].zero_()
@triton.autotune(
configs=[
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 128, "SEQUENCE_PARALLEL": False},
num_warps=8,
num_stages=1,
pre_hook=init_to_zero("DQ"),
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 128, "SEQUENCE_PARALLEL": True},
num_warps=8,
num_stages=1,
pre_hook=init_to_zero("DQ"),
),
# Other configs seem to give wrong results when seqlen_q % 128 != 0, disabling them for now
# # Kernel is buggy (give wrong result) if we set BLOCK_m=128, BLOCK_n=64, num_warps=*4*
# triton.Config({"BLOCK_M": 128, "BLOCK_N": 64, "SEQUENCE_PARALLEL": False}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')),
# triton.Config({"BLOCK_M": 128, "BLOCK_N": 64, "SEQUENCE_PARALLEL": True}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')),
# triton.Config({"BLOCK_M": 64, "BLOCK_N": 64, "SEQUENCE_PARALLEL": False}, num_warps=4, num_stages=1, pre_hook=init_to_zero('DQ')),
# triton.Config({"BLOCK_M": 64, "BLOCK_N": 64, "SEQUENCE_PARALLEL": True}, num_warps=4, num_stages=1, pre_hook=init_to_zero('DQ')),
],
key=["CACHE_KEY_SEQLEN_Q", "CACHE_KEY_SEQLEN_K", "BIAS_TYPE", "IS_CAUSAL", "BLOCK_HEADDIM"],
)
@triton.heuristics(
{
"EVEN_M": lambda args: args["seqlen_q"] % args["BLOCK_M"] == 0,
"EVEN_N": lambda args: args["seqlen_k"] % args["BLOCK_N"] == 0,
"EVEN_HEADDIM": lambda args: args["headdim"] == args["BLOCK_HEADDIM"],
}
)
@triton.jit
def _bwd_kernel(
Q,
K,
V,
Bias,
DO,
DQ,
DK,
DV,
LSE,
D,
softmax_scale,
stride_qb,
stride_qh,
stride_qm,
stride_kb,
stride_kh,
stride_kn,
stride_vb,
stride_vh,
stride_vn,
stride_bb,
stride_bh,
stride_bm,
stride_dob,
stride_doh,
stride_dom,
stride_dqb,
stride_dqh,
stride_dqm,
stride_dkb,
stride_dkh,
stride_dkn,
stride_dvb,
stride_dvh,
stride_dvn,
nheads,
seqlen_q,
seqlen_k,
seqlen_q_rounded,
headdim,
CACHE_KEY_SEQLEN_Q,
CACHE_KEY_SEQLEN_K,
BIAS_TYPE: tl.constexpr,
IS_CAUSAL: tl.constexpr,
BLOCK_HEADDIM: tl.constexpr,
SEQUENCE_PARALLEL: tl.constexpr,
EVEN_M: tl.constexpr,
EVEN_N: tl.constexpr,
EVEN_HEADDIM: tl.constexpr,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
):
off_hb = tl.program_id(1)
off_b = off_hb // nheads
off_h = off_hb % nheads
# offset pointers for batch/head
Q += off_b * stride_qb + off_h * stride_qh
K += off_b * stride_kb + off_h * stride_kh
V += off_b * stride_vb + off_h * stride_vh
DO += off_b * stride_dob + off_h * stride_doh
DQ += off_b * stride_dqb + off_h * stride_dqh
DK += off_b * stride_dkb + off_h * stride_dkh
DV += off_b * stride_dvb + off_h * stride_dvh
if BIAS_TYPE != "none":
Bias += off_b * stride_bb + off_h * stride_bh
# pointer to row-wise quantities in value-like data
D += off_hb * seqlen_q_rounded
LSE += off_hb * seqlen_q_rounded
if not SEQUENCE_PARALLEL:
num_block_n = tl.cdiv(seqlen_k, BLOCK_N)
for start_n in range(0, num_block_n):
_bwd_kernel_one_col_block(
start_n,
Q,
K,
V,
Bias,
DO,
DQ,
DK,
DV,
LSE,
D,
softmax_scale,
stride_qm,
stride_kn,
stride_vn,
stride_bm,
stride_dom,
stride_dqm,
stride_dkn,
stride_dvn,
seqlen_q,
seqlen_k,
headdim,
ATOMIC_ADD=False,
BIAS_TYPE=BIAS_TYPE,
IS_CAUSAL=IS_CAUSAL,
BLOCK_HEADDIM=BLOCK_HEADDIM,
EVEN_M=EVEN_M,
EVEN_N=EVEN_N,
EVEN_HEADDIM=EVEN_HEADDIM,
BLOCK_M=BLOCK_M,
BLOCK_N=BLOCK_N,
)
else:
start_n = tl.program_id(0)
_bwd_kernel_one_col_block(
start_n,
Q,
K,
V,
Bias,
DO,
DQ,
DK,
DV,
LSE,
D,
softmax_scale,
stride_qm,
stride_kn,
stride_vn,
stride_bm,
stride_dom,
stride_dqm,
stride_dkn,
stride_dvn,
seqlen_q,
seqlen_k,
headdim,
ATOMIC_ADD=True,
BIAS_TYPE=BIAS_TYPE,
IS_CAUSAL=IS_CAUSAL,
BLOCK_HEADDIM=BLOCK_HEADDIM,
EVEN_M=EVEN_M,
EVEN_N=EVEN_N,
EVEN_HEADDIM=EVEN_HEADDIM,
BLOCK_M=BLOCK_M,
BLOCK_N=BLOCK_N,
)
def _flash_attn_forward(q, k, v, bias=None, causal=False, softmax_scale=None):
# shape constraints
batch, seqlen_q, nheads, d = q.shape
_, seqlen_k, _, _ = k.shape
assert k.shape == (batch, seqlen_k, nheads, d)
assert v.shape == (batch, seqlen_k, nheads, d)
assert d <= 128, "FlashAttention only support head dimensions up to 128"
assert q.dtype == k.dtype == v.dtype, "All tensors must have the same type"
assert q.dtype in [torch.float16, torch.bfloat16], "Only support fp16 and bf16"
assert q.is_cuda and k.is_cuda and v.is_cuda
softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
has_bias = bias is not None
bias_type = "none"
if has_bias:
assert bias.dtype in [q.dtype, torch.float]
assert bias.is_cuda
assert bias.dim() == 4
if bias.stride(-1) != 1:
bias = bias.contiguous()
if bias.shape[2:] == (1, seqlen_k):
bias_type = "vector"
elif bias.shape[2:] == (seqlen_q, seqlen_k):
bias_type = "matrix"
else:
raise RuntimeError(
"Last 2 dimensions of bias must be (1, seqlen_k)" " or (seqlen_q, seqlen_k)"
)
bias = bias.expand(batch, nheads, seqlen_q, seqlen_k)
bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0)
seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
lse = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32)
tmp = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32)
o = torch.empty_like(q)
BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
BLOCK = 128
num_warps = 4 if d <= 64 else 8
grid = lambda META: (triton.cdiv(seqlen_q, META["BLOCK_M"]), batch * nheads)
_fwd_kernel[grid](
q,
k,
v,
bias,
o,
lse,
tmp,
softmax_scale,
q.stride(0),
q.stride(2),
q.stride(1),
k.stride(0),
k.stride(2),
k.stride(1),
v.stride(0),
v.stride(2),
v.stride(1),
*bias_strides,
o.stride(0),
o.stride(2),
o.stride(1),
nheads,
seqlen_q,
seqlen_k,
seqlen_q_rounded,
d,
seqlen_q // 32,
seqlen_k // 32, # key for triton cache (limit number of compilations)
# Can't use kwargs here because triton autotune expects key to be args, not kwargs
# IS_CAUSAL=causal, BLOCK_HEADDIM=d,
bias_type,
causal,
BLOCK_HEADDIM,
BLOCK_M=BLOCK,
BLOCK_N=BLOCK,
num_warps=num_warps,
num_stages=1,
)
return o, lse, softmax_scale # softmax_scale could have been updated
def _flash_attn_backward(
do, q, k, v, o, lse, dq, dk, dv, bias=None, causal=False, softmax_scale=None
):
# Make sure that the last dimension is contiguous
if do.stride(-1) != 1:
do = do.contiguous()
batch, seqlen_q, nheads, d = q.shape
_, seqlen_k, _, _ = k.shape
# assert d in {16, 32, 64, 128}
assert d <= 128
seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
assert lse.shape == (batch, nheads, seqlen_q_rounded)
assert q.stride(-1) == k.stride(-1) == v.stride(-1) == o.stride(-1) == 1
assert dq.stride(-1) == dk.stride(-1) == dv.stride(-1) == 1
softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
# dq_accum = torch.zeros_like(q, dtype=torch.float32)
dq_accum = torch.empty_like(q, dtype=torch.float32)
delta = torch.empty_like(lse)
# delta = torch.zeros_like(lse)
BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
grid = lambda META: (triton.cdiv(seqlen_q, META["BLOCK_M"]), batch * nheads)
_bwd_preprocess_do_o_dot[grid](
o,
do,
delta,
o.stride(0),
o.stride(2),
o.stride(1),
do.stride(0),
do.stride(2),
do.stride(1),
nheads,
seqlen_q,
seqlen_q_rounded,
d,
BLOCK_M=128,
BLOCK_HEADDIM=BLOCK_HEADDIM,
)
has_bias = bias is not None
bias_type = "none"
if has_bias:
assert bias.dtype in [q.dtype, torch.float]
assert bias.is_cuda
assert bias.dim() == 4
assert bias.stride(-1) == 1
if bias.shape[2:] == (1, seqlen_k):
bias_type = "vector"
elif bias.shape[2:] == (seqlen_q, seqlen_k):
bias_type = "matrix"
else:
raise RuntimeError(
"Last 2 dimensions of bias must be (1, seqlen_k)" " or (seqlen_q, seqlen_k)"
)
bias = bias.expand(batch, nheads, seqlen_q, seqlen_k)
bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0)
# BLOCK_M = 128
# BLOCK_N = 64
# num_warps = 4
grid = lambda META: (
triton.cdiv(seqlen_k, META["BLOCK_N"]) if META["SEQUENCE_PARALLEL"] else 1,
batch * nheads,
)
_bwd_kernel[grid](
q,
k,
v,
bias,
do,
dq_accum,
dk,
dv,
lse,
delta,
softmax_scale,
q.stride(0),
q.stride(2),
q.stride(1),
k.stride(0),
k.stride(2),
k.stride(1),
v.stride(0),
v.stride(2),
v.stride(1),
*bias_strides,
do.stride(0),
do.stride(2),
do.stride(1),
dq_accum.stride(0),
dq_accum.stride(2),
dq_accum.stride(1),
dk.stride(0),
dk.stride(2),
dk.stride(1),
dv.stride(0),
dv.stride(2),
dv.stride(1),
nheads,
seqlen_q,
seqlen_k,
seqlen_q_rounded,
d,
seqlen_q // 32,
seqlen_k // 32, # key for triton cache (limit number of compilations)
# Can't use kwargs here because triton autotune expects key to be args, not kwargs