Text Generation
Transformers
PyTorch
mpt
Composer
MosaicML
llm-foundry
custom_code
text-generation-inference
File size: 28,182 Bytes
8f0448e
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
"""
Copied from https://github.com/HazyResearch/flash-attention/blob/eff9fe6b8076df59d64d7a3f464696738a3c7c24/flash_attn/flash_attn_triton.py
update imports to use 'triton_pre_mlir'

*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_pre_mlir as triton
import triton_pre_mlir.language as tl

@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, 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
    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)
    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, :])
    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)
    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)
    elif 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)
    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)
        if EVEN_N & EVEN_M:
            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)
        elif 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)
        if not EVEN_N:
            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)
            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)
        acc_o_scale = tl.exp(m_i - m_ij)
        tl.store(t_ptrs, acc_o_scale)
        acc_o_scale = tl.load(t_ptrs)
        acc_o = acc_o * acc_o_scale[:, None]
        if EVEN_N & EVEN_M:
            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)
        elif 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)
        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)
    tl.store(t_ptrs, o_scale)
    o_scale = tl.load(t_ptrs)
    acc_o = acc_o * o_scale[:, None]
    start_m = tl.program_id(0)
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m
    tl.store(lse_ptrs, lse_i)
    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)
    elif 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
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    offs_d = tl.arange(0, BLOCK_HEADDIM)
    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)
    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):
    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)
    elif 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):
    begin_m = 0 if not IS_CAUSAL else start_n * BLOCK_N // BLOCK_M * BLOCK_M
    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)
    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, :])
    dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
    dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
    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
    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)
    elif 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)
    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
        if EVEN_M & EVEN_HEADDIM:
            q = tl.load(q_ptrs)
        elif 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)
        qk = tl.dot(q, k, trans_b=True)
        if not EVEN_N:
            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()
            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
        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])
        if EVEN_M & EVEN_HEADDIM:
            do = tl.load(do_ptrs)
        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)
        if not EVEN_M & EVEN_HEADDIM:
            tl.debug_barrier()
        dp = tl.dot(do, v, trans_b=True)
        if not EVEN_HEADDIM:
            tl.debug_barrier()
        Di = tl.load(D + offs_m_curr)
        ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype)
        dk += tl.dot(ds, q, trans_a=True)
        if not EVEN_M & EVEN_HEADDIM:
            tl.debug_barrier()
        if not ATOMIC_ADD:
            if EVEN_M & EVEN_HEADDIM:
                dq = tl.load(dq_ptrs, eviction_policy='evict_last')
                dq += tl.dot(ds, k)
                tl.store(dq_ptrs, dq, eviction_policy='evict_last')
            elif 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:
            dq = tl.dot(ds, k)
            if EVEN_M & EVEN_HEADDIM:
                tl.atomic_add(dq_ptrs, dq)
            elif 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))
        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
    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'))], 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
    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
    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):
    (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, bias_type, causal, BLOCK_HEADDIM, BLOCK_M=BLOCK, BLOCK_N=BLOCK, num_warps=num_warps, num_stages=1)
    return (o, lse, softmax_scale)

def _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=None, causal=False, softmax_scale=None):
    if do.stride(-1) != 1:
        do = do.contiguous()
    (batch, seqlen_q, nheads, d) = q.shape
    (_, seqlen_k, _, _) = k.shape
    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.empty_like(q, dtype=torch.float32)
    delta = torch.empty_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)
    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, bias_type, causal, BLOCK_HEADDIM)
    dq.copy_(dq_accum)

class FlashAttnQKVPackedFunc(torch.autograd.Function):

    @staticmethod
    def forward(ctx, qkv, bias=None, causal=False, softmax_scale=None):
        """
            qkv: (batch, seqlen, 3, nheads, headdim)
            bias: optional, shape broadcastible to (batch, nheads, seqlen, seqlen).
                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen).
                ALiBi mask for non-causal would have shape (1, nheads, seqlen, seqlen)
        """
        if qkv.stride(-1) != 1:
            qkv = qkv.contiguous()
        (o, lse, ctx.softmax_scale) = _flash_attn_forward(qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], bias=bias, causal=causal, softmax_scale=softmax_scale)
        ctx.save_for_backward(qkv, o, lse, bias)
        ctx.causal = causal
        return o

    @staticmethod
    def backward(ctx, do):
        (qkv, o, lse, bias) = ctx.saved_tensors
        assert not ctx.needs_input_grad[1], 'FlashAttention does not support bias gradient yet'
        with torch.inference_mode():
            dqkv = torch.empty_like(qkv)
            _flash_attn_backward(do, qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], o, lse, dqkv[:, :, 0], dqkv[:, :, 1], dqkv[:, :, 2], bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale)
        return (dqkv, None, None, None)
flash_attn_qkvpacked_func = FlashAttnQKVPackedFunc.apply

class FlashAttnKVPackedFunc(torch.autograd.Function):

    @staticmethod
    def forward(ctx, q, kv, bias=None, causal=False, softmax_scale=None):
        """
            q: (batch, seqlen_q, nheads, headdim)
            kv: (batch, seqlen_k, 2, nheads, headdim)
            bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).
                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).
                ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)
        """
        (q, kv) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, kv]]
        (o, lse, ctx.softmax_scale) = _flash_attn_forward(q, kv[:, :, 0], kv[:, :, 1], bias=bias, causal=causal, softmax_scale=softmax_scale)
        ctx.save_for_backward(q, kv, o, lse, bias)
        ctx.causal = causal
        return o

    @staticmethod
    def backward(ctx, do):
        (q, kv, o, lse, bias) = ctx.saved_tensors
        if len(ctx.needs_input_grad) >= 3:
            assert not ctx.needs_input_grad[2], 'FlashAttention does not support bias gradient yet'
        with torch.inference_mode():
            dq = torch.empty_like(q)
            dkv = torch.empty_like(kv)
            _flash_attn_backward(do, q, kv[:, :, 0], kv[:, :, 1], o, lse, dq, dkv[:, :, 0], dkv[:, :, 1], bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale)
        return (dq, dkv, None, None, None)
flash_attn_kvpacked_func = FlashAttnKVPackedFunc.apply

class FlashAttnFunc(torch.autograd.Function):

    @staticmethod
    def forward(ctx, q, k, v, bias=None, causal=False, softmax_scale=None):
        """
            q: (batch_size, seqlen_q, nheads, headdim)
            k, v: (batch_size, seqlen_k, nheads, headdim)
            bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).
                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).
                ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)
        """
        (q, k, v) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, k, v]]
        (o, lse, ctx.softmax_scale) = _flash_attn_forward(q, k, v, bias=bias, causal=causal, softmax_scale=softmax_scale)
        ctx.save_for_backward(q, k, v, o, lse, bias)
        ctx.causal = causal
        return o

    @staticmethod
    def backward(ctx, do):
        (q, k, v, o, lse, bias) = ctx.saved_tensors
        assert not ctx.needs_input_grad[3], 'FlashAttention does not support bias gradient yet'
        with torch.inference_mode():
            dq = torch.empty_like(q)
            dk = torch.empty_like(k)
            dv = torch.empty_like(v)
            _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale)
        return (dq, dk, dv, None, None, None)
flash_attn_func = FlashAttnFunc.apply