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add flash_attn_triton.py (#28)

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- add flash_attn_triton.py (a118b32fbf005c9582045f52f1b49583377eea2c)


Co-authored-by: Vitaliy Chiley <vchiley@users.noreply.huggingface.co>

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  1. flash_attn_triton.py +484 -0
flash_attn_triton.py ADDED
@@ -0,0 +1,484 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ """
2
+ Copied from https://github.com/HazyResearch/flash-attention/blob/eff9fe6b8076df59d64d7a3f464696738a3c7c24/flash_attn/flash_attn_triton.py
3
+ update imports to use 'triton_pre_mlir'
4
+
5
+ *Experimental* implementation of FlashAttention in Triton.
6
+ Tested with triton==2.0.0.dev20221202.
7
+ Triton 2.0 has a new backend (MLIR) but seems like it doesn't yet work for head dimensions
8
+ other than 64:
9
+ https://github.com/openai/triton/blob/d376020f90002757eea3ea9475d4f7cfc2ec5ead/python/triton/ops/flash_attention.py#L207
10
+ We'll update this implementation with the new Triton backend once this is fixed.
11
+
12
+ We use the FlashAttention implementation from Phil Tillet a starting point.
13
+ https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py
14
+
15
+ Changes:
16
+ - Implement both causal and non-causal attention.
17
+ - Implement both self-attention and cross-attention.
18
+ - Support arbitrary seqlens (not just multiples of 128), for both forward and backward.
19
+ - Support all head dimensions up to 128 (not just 16, 32, 64, 128), for both forward and backward.
20
+ - Support attention bias.
21
+ - Speed up the forward pass a bit, and only store the LSE instead of m and l.
22
+ - Make the backward for d=128 much faster by reducing register spilling.
23
+ - Optionally parallelize the backward pass across seqlen_k, to deal with the case of
24
+ small batch size * nheads.
25
+
26
+ Caution:
27
+ - This is an *experimental* implementation. The forward pass should be quite robust but
28
+ I'm not 100% sure that the backward pass doesn't have race conditions (due to the Triton compiler).
29
+ - This implementation has only been tested on A100.
30
+ - If you plan to use headdim other than 64 and 128, you should test for race conditions
31
+ (due to the Triton compiler), as done in tests/test_flash_attn.py
32
+ "test_flash_attn_triton_race_condition". I've tested and fixed many race conditions
33
+ for different head dimensions (40, 48, 64, 128, 80, 88, 96), but I'm still not 100% confident
34
+ that there are none left for other head dimensions.
35
+
36
+ Differences between this Triton version and the CUDA version:
37
+ - Triton version doesn't support dropout.
38
+ - Triton forward is generally faster than CUDA forward, while Triton backward is
39
+ generally slower than CUDA backward. Overall Triton forward + backward is slightly slower
40
+ than CUDA forward + backward.
41
+ - Triton version doesn't support different sequence lengths in a batch (i.e., RaggedTensor/NestedTensor).
42
+ - Triton version supports attention bias, while CUDA version doesn't.
43
+ """
44
+ import math
45
+ import torch
46
+ import triton_pre_mlir as triton
47
+ import triton_pre_mlir.language as tl
48
+
49
+ @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']})
50
+ @triton.jit
51
+ 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):
52
+ start_m = tl.program_id(0)
53
+ off_hb = tl.program_id(1)
54
+ off_b = off_hb // nheads
55
+ off_h = off_hb % nheads
56
+ offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
57
+ offs_n = tl.arange(0, BLOCK_N)
58
+ offs_d = tl.arange(0, BLOCK_HEADDIM)
59
+ q_ptrs = Q + off_b * stride_qb + off_h * stride_qh + (offs_m[:, None] * stride_qm + offs_d[None, :])
60
+ k_ptrs = K + off_b * stride_kb + off_h * stride_kh + (offs_n[:, None] * stride_kn + offs_d[None, :])
61
+ v_ptrs = V + off_b * stride_vb + off_h * stride_vh + (offs_n[:, None] * stride_vn + offs_d[None, :])
62
+ if BIAS_TYPE == 'vector':
63
+ b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + offs_n
64
+ elif BIAS_TYPE == 'matrix':
65
+ b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + (offs_m[:, None] * stride_bm + offs_n[None, :])
66
+ t_ptrs = TMP + off_hb * seqlen_q_rounded + offs_m
67
+ lse_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')
68
+ m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')
69
+ acc_o = tl.zeros([BLOCK_M, BLOCK_HEADDIM], dtype=tl.float32)
70
+ if EVEN_M & EVEN_N:
71
+ if EVEN_HEADDIM:
72
+ q = tl.load(q_ptrs)
73
+ else:
74
+ q = tl.load(q_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
75
+ elif EVEN_HEADDIM:
76
+ q = tl.load(q_ptrs, mask=offs_m[:, None] < seqlen_q, other=0.0)
77
+ else:
78
+ q = tl.load(q_ptrs, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0)
79
+ end_n = seqlen_k if not IS_CAUSAL else tl.minimum((start_m + 1) * BLOCK_M, seqlen_k)
80
+ for start_n in range(0, end_n, BLOCK_N):
81
+ start_n = tl.multiple_of(start_n, BLOCK_N)
82
+ if EVEN_N & EVEN_M:
83
+ if EVEN_HEADDIM:
84
+ k = tl.load(k_ptrs + start_n * stride_kn)
85
+ else:
86
+ k = tl.load(k_ptrs + start_n * stride_kn, mask=offs_d[None, :] < headdim, other=0.0)
87
+ elif EVEN_HEADDIM:
88
+ k = tl.load(k_ptrs + start_n * stride_kn, mask=(start_n + offs_n)[:, None] < seqlen_k, other=0.0)
89
+ else:
90
+ k = tl.load(k_ptrs + start_n * stride_kn, mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)
91
+ qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
92
+ qk += tl.dot(q, k, trans_b=True)
93
+ if not EVEN_N:
94
+ qk += tl.where((start_n + offs_n)[None, :] < seqlen_k, 0, float('-inf'))
95
+ if IS_CAUSAL:
96
+ qk += tl.where(offs_m[:, None] >= (start_n + offs_n)[None, :], 0, float('-inf'))
97
+ if BIAS_TYPE != 'none':
98
+ if BIAS_TYPE == 'vector':
99
+ if EVEN_N:
100
+ bias = tl.load(b_ptrs + start_n).to(tl.float32)
101
+ else:
102
+ bias = tl.load(b_ptrs + start_n, mask=start_n + offs_n < seqlen_k, other=0.0).to(tl.float32)
103
+ bias = bias[None, :]
104
+ elif BIAS_TYPE == 'matrix':
105
+ if EVEN_M & EVEN_N:
106
+ bias = tl.load(b_ptrs + start_n).to(tl.float32)
107
+ else:
108
+ 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)
109
+ qk = qk * softmax_scale + bias
110
+ m_ij = tl.maximum(tl.max(qk, 1), lse_i)
111
+ p = tl.exp(qk - m_ij[:, None])
112
+ else:
113
+ m_ij = tl.maximum(tl.max(qk, 1) * softmax_scale, lse_i)
114
+ p = tl.exp(qk * softmax_scale - m_ij[:, None])
115
+ l_ij = tl.sum(p, 1)
116
+ acc_o_scale = tl.exp(m_i - m_ij)
117
+ tl.store(t_ptrs, acc_o_scale)
118
+ acc_o_scale = tl.load(t_ptrs)
119
+ acc_o = acc_o * acc_o_scale[:, None]
120
+ if EVEN_N & EVEN_M:
121
+ if EVEN_HEADDIM:
122
+ v = tl.load(v_ptrs + start_n * stride_vn)
123
+ else:
124
+ v = tl.load(v_ptrs + start_n * stride_vn, mask=offs_d[None, :] < headdim, other=0.0)
125
+ elif EVEN_HEADDIM:
126
+ v = tl.load(v_ptrs + start_n * stride_vn, mask=(start_n + offs_n)[:, None] < seqlen_k, other=0.0)
127
+ else:
128
+ v = tl.load(v_ptrs + start_n * stride_vn, mask=((start_n + offs_n)[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)
129
+ p = p.to(v.dtype)
130
+ acc_o += tl.dot(p, v)
131
+ m_i = m_ij
132
+ l_i_new = tl.exp(lse_i - m_ij) + l_ij
133
+ lse_i = m_ij + tl.log(l_i_new)
134
+ o_scale = tl.exp(m_i - lse_i)
135
+ tl.store(t_ptrs, o_scale)
136
+ o_scale = tl.load(t_ptrs)
137
+ acc_o = acc_o * o_scale[:, None]
138
+ start_m = tl.program_id(0)
139
+ offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
140
+ lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m
141
+ tl.store(lse_ptrs, lse_i)
142
+ offs_d = tl.arange(0, BLOCK_HEADDIM)
143
+ out_ptrs = Out + off_b * stride_ob + off_h * stride_oh + (offs_m[:, None] * stride_om + offs_d[None, :])
144
+ if EVEN_M:
145
+ if EVEN_HEADDIM:
146
+ tl.store(out_ptrs, acc_o)
147
+ else:
148
+ tl.store(out_ptrs, acc_o, mask=offs_d[None, :] < headdim)
149
+ elif EVEN_HEADDIM:
150
+ tl.store(out_ptrs, acc_o, mask=offs_m[:, None] < seqlen_q)
151
+ else:
152
+ tl.store(out_ptrs, acc_o, mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim))
153
+
154
+ @triton.jit
155
+ 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):
156
+ start_m = tl.program_id(0)
157
+ off_hb = tl.program_id(1)
158
+ off_b = off_hb // nheads
159
+ off_h = off_hb % nheads
160
+ offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
161
+ offs_d = tl.arange(0, BLOCK_HEADDIM)
162
+ 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)
163
+ 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)
164
+ delta = tl.sum(o * do, axis=1)
165
+ tl.store(Delta + off_hb * seqlen_q_rounded + offs_m, delta)
166
+
167
+ @triton.jit
168
+ 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):
169
+ if EVEN_N & EVEN_M:
170
+ if EVEN_HEADDIM:
171
+ tl.store(dv_ptrs, dv)
172
+ tl.store(dk_ptrs, dk)
173
+ else:
174
+ tl.store(dv_ptrs, dv, mask=offs_d[None, :] < headdim)
175
+ tl.store(dk_ptrs, dk, mask=offs_d[None, :] < headdim)
176
+ elif EVEN_HEADDIM:
177
+ tl.store(dv_ptrs, dv, mask=offs_n[:, None] < seqlen_k)
178
+ tl.store(dk_ptrs, dk, mask=offs_n[:, None] < seqlen_k)
179
+ else:
180
+ tl.store(dv_ptrs, dv, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim))
181
+ tl.store(dk_ptrs, dk, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim))
182
+
183
+ @triton.jit
184
+ 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):
185
+ begin_m = 0 if not IS_CAUSAL else start_n * BLOCK_N // BLOCK_M * BLOCK_M
186
+ offs_qm = begin_m + tl.arange(0, BLOCK_M)
187
+ offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N)
188
+ offs_m = tl.arange(0, BLOCK_M)
189
+ offs_d = tl.arange(0, BLOCK_HEADDIM)
190
+ q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_d[None, :])
191
+ k_ptrs = K + (offs_n[:, None] * stride_kn + offs_d[None, :])
192
+ v_ptrs = V + (offs_n[:, None] * stride_vn + offs_d[None, :])
193
+ do_ptrs = DO + (offs_qm[:, None] * stride_dom + offs_d[None, :])
194
+ dq_ptrs = DQ + (offs_qm[:, None] * stride_dqm + offs_d[None, :])
195
+ if BIAS_TYPE == 'vector':
196
+ b_ptrs = Bias + offs_n
197
+ elif BIAS_TYPE == 'matrix':
198
+ b_ptrs = Bias + (offs_qm[:, None] * stride_bm + offs_n[None, :])
199
+ dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
200
+ dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
201
+ if begin_m >= seqlen_q:
202
+ dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])
203
+ dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])
204
+ _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)
205
+ return
206
+ if EVEN_N & EVEN_M:
207
+ if EVEN_HEADDIM:
208
+ k = tl.load(k_ptrs)
209
+ v = tl.load(v_ptrs)
210
+ else:
211
+ k = tl.load(k_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
212
+ v = tl.load(v_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
213
+ elif EVEN_HEADDIM:
214
+ k = tl.load(k_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
215
+ v = tl.load(v_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
216
+ else:
217
+ k = tl.load(k_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)
218
+ v = tl.load(v_ptrs, mask=(offs_n[:, None] < seqlen_k) & (offs_d[None, :] < headdim), other=0.0)
219
+ num_block_m = tl.cdiv(seqlen_q, BLOCK_M)
220
+ for start_m in range(begin_m, num_block_m * BLOCK_M, BLOCK_M):
221
+ start_m = tl.multiple_of(start_m, BLOCK_M)
222
+ offs_m_curr = start_m + offs_m
223
+ if EVEN_M & EVEN_HEADDIM:
224
+ q = tl.load(q_ptrs)
225
+ elif EVEN_HEADDIM:
226
+ q = tl.load(q_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0)
227
+ else:
228
+ q = tl.load(q_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0)
229
+ qk = tl.dot(q, k, trans_b=True)
230
+ if not EVEN_N:
231
+ qk = tl.where(offs_n[None, :] < seqlen_k, qk, float('-inf'))
232
+ if IS_CAUSAL:
233
+ qk = tl.where(offs_m_curr[:, None] >= offs_n[None, :], qk, float('-inf'))
234
+ if BIAS_TYPE != 'none':
235
+ tl.debug_barrier()
236
+ if BIAS_TYPE == 'vector':
237
+ if EVEN_N:
238
+ bias = tl.load(b_ptrs).to(tl.float32)
239
+ else:
240
+ bias = tl.load(b_ptrs, mask=offs_n < seqlen_k, other=0.0).to(tl.float32)
241
+ bias = bias[None, :]
242
+ elif BIAS_TYPE == 'matrix':
243
+ if EVEN_M & EVEN_N:
244
+ bias = tl.load(b_ptrs).to(tl.float32)
245
+ else:
246
+ bias = tl.load(b_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_n[None, :] < seqlen_k), other=0.0).to(tl.float32)
247
+ qk = qk * softmax_scale + bias
248
+ if not EVEN_M & EVEN_HEADDIM:
249
+ tl.debug_barrier()
250
+ lse_i = tl.load(LSE + offs_m_curr)
251
+ if BIAS_TYPE == 'none':
252
+ p = tl.exp(qk * softmax_scale - lse_i[:, None])
253
+ else:
254
+ p = tl.exp(qk - lse_i[:, None])
255
+ if EVEN_M & EVEN_HEADDIM:
256
+ do = tl.load(do_ptrs)
257
+ else:
258
+ do = tl.load(do_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0)
259
+ dv += tl.dot(p.to(do.dtype), do, trans_a=True)
260
+ if not EVEN_M & EVEN_HEADDIM:
261
+ tl.debug_barrier()
262
+ dp = tl.dot(do, v, trans_b=True)
263
+ if not EVEN_HEADDIM:
264
+ tl.debug_barrier()
265
+ Di = tl.load(D + offs_m_curr)
266
+ ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype)
267
+ dk += tl.dot(ds, q, trans_a=True)
268
+ if not EVEN_M & EVEN_HEADDIM:
269
+ tl.debug_barrier()
270
+ if not ATOMIC_ADD:
271
+ if EVEN_M & EVEN_HEADDIM:
272
+ dq = tl.load(dq_ptrs, eviction_policy='evict_last')
273
+ dq += tl.dot(ds, k)
274
+ tl.store(dq_ptrs, dq, eviction_policy='evict_last')
275
+ elif EVEN_HEADDIM:
276
+ dq = tl.load(dq_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0, eviction_policy='evict_last')
277
+ dq += tl.dot(ds, k)
278
+ tl.store(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q, eviction_policy='evict_last')
279
+ else:
280
+ dq = tl.load(dq_ptrs, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), other=0.0, eviction_policy='evict_last')
281
+ dq += tl.dot(ds, k)
282
+ tl.store(dq_ptrs, dq, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim), eviction_policy='evict_last')
283
+ else:
284
+ dq = tl.dot(ds, k)
285
+ if EVEN_M & EVEN_HEADDIM:
286
+ tl.atomic_add(dq_ptrs, dq)
287
+ elif EVEN_HEADDIM:
288
+ tl.atomic_add(dq_ptrs, dq, mask=offs_m_curr[:, None] < seqlen_q)
289
+ else:
290
+ tl.atomic_add(dq_ptrs, dq, mask=(offs_m_curr[:, None] < seqlen_q) & (offs_d[None, :] < headdim))
291
+ dq_ptrs += BLOCK_M * stride_dqm
292
+ q_ptrs += BLOCK_M * stride_qm
293
+ do_ptrs += BLOCK_M * stride_dom
294
+ if BIAS_TYPE == 'matrix':
295
+ b_ptrs += BLOCK_M * stride_bm
296
+ dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])
297
+ dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])
298
+ _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)
299
+
300
+ def init_to_zero(name):
301
+ return lambda nargs: nargs[name].zero_()
302
+
303
+ @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'])
304
+ @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']})
305
+ @triton.jit
306
+ 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):
307
+ off_hb = tl.program_id(1)
308
+ off_b = off_hb // nheads
309
+ off_h = off_hb % nheads
310
+ Q += off_b * stride_qb + off_h * stride_qh
311
+ K += off_b * stride_kb + off_h * stride_kh
312
+ V += off_b * stride_vb + off_h * stride_vh
313
+ DO += off_b * stride_dob + off_h * stride_doh
314
+ DQ += off_b * stride_dqb + off_h * stride_dqh
315
+ DK += off_b * stride_dkb + off_h * stride_dkh
316
+ DV += off_b * stride_dvb + off_h * stride_dvh
317
+ if BIAS_TYPE != 'none':
318
+ Bias += off_b * stride_bb + off_h * stride_bh
319
+ D += off_hb * seqlen_q_rounded
320
+ LSE += off_hb * seqlen_q_rounded
321
+ if not SEQUENCE_PARALLEL:
322
+ num_block_n = tl.cdiv(seqlen_k, BLOCK_N)
323
+ for start_n in range(0, num_block_n):
324
+ _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)
325
+ else:
326
+ start_n = tl.program_id(0)
327
+ _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)
328
+
329
+ def _flash_attn_forward(q, k, v, bias=None, causal=False, softmax_scale=None):
330
+ (batch, seqlen_q, nheads, d) = q.shape
331
+ (_, seqlen_k, _, _) = k.shape
332
+ assert k.shape == (batch, seqlen_k, nheads, d)
333
+ assert v.shape == (batch, seqlen_k, nheads, d)
334
+ assert d <= 128, 'FlashAttention only support head dimensions up to 128'
335
+ assert q.dtype == k.dtype == v.dtype, 'All tensors must have the same type'
336
+ assert q.dtype in [torch.float16, torch.bfloat16], 'Only support fp16 and bf16'
337
+ assert q.is_cuda and k.is_cuda and v.is_cuda
338
+ softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
339
+ has_bias = bias is not None
340
+ bias_type = 'none'
341
+ if has_bias:
342
+ assert bias.dtype in [q.dtype, torch.float]
343
+ assert bias.is_cuda
344
+ assert bias.dim() == 4
345
+ if bias.stride(-1) != 1:
346
+ bias = bias.contiguous()
347
+ if bias.shape[2:] == (1, seqlen_k):
348
+ bias_type = 'vector'
349
+ elif bias.shape[2:] == (seqlen_q, seqlen_k):
350
+ bias_type = 'matrix'
351
+ else:
352
+ raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k) or (seqlen_q, seqlen_k)')
353
+ bias = bias.expand(batch, nheads, seqlen_q, seqlen_k)
354
+ bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0)
355
+ seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
356
+ lse = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32)
357
+ tmp = torch.empty((batch, nheads, seqlen_q_rounded), device=q.device, dtype=torch.float32)
358
+ o = torch.empty_like(q)
359
+ BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
360
+ BLOCK = 128
361
+ num_warps = 4 if d <= 64 else 8
362
+ grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)
363
+ _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)
364
+ return (o, lse, softmax_scale)
365
+
366
+ def _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=None, causal=False, softmax_scale=None):
367
+ if do.stride(-1) != 1:
368
+ do = do.contiguous()
369
+ (batch, seqlen_q, nheads, d) = q.shape
370
+ (_, seqlen_k, _, _) = k.shape
371
+ assert d <= 128
372
+ seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
373
+ assert lse.shape == (batch, nheads, seqlen_q_rounded)
374
+ assert q.stride(-1) == k.stride(-1) == v.stride(-1) == o.stride(-1) == 1
375
+ assert dq.stride(-1) == dk.stride(-1) == dv.stride(-1) == 1
376
+ softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
377
+ dq_accum = torch.empty_like(q, dtype=torch.float32)
378
+ delta = torch.empty_like(lse)
379
+ BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
380
+ grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)
381
+ _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)
382
+ has_bias = bias is not None
383
+ bias_type = 'none'
384
+ if has_bias:
385
+ assert bias.dtype in [q.dtype, torch.float]
386
+ assert bias.is_cuda
387
+ assert bias.dim() == 4
388
+ assert bias.stride(-1) == 1
389
+ if bias.shape[2:] == (1, seqlen_k):
390
+ bias_type = 'vector'
391
+ elif bias.shape[2:] == (seqlen_q, seqlen_k):
392
+ bias_type = 'matrix'
393
+ else:
394
+ raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k) or (seqlen_q, seqlen_k)')
395
+ bias = bias.expand(batch, nheads, seqlen_q, seqlen_k)
396
+ bias_strides = (bias.stride(0), bias.stride(1), bias.stride(2)) if has_bias else (0, 0, 0)
397
+ grid = lambda META: (triton.cdiv(seqlen_k, META['BLOCK_N']) if META['SEQUENCE_PARALLEL'] else 1, batch * nheads)
398
+ _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)
399
+ dq.copy_(dq_accum)
400
+
401
+ class FlashAttnQKVPackedFunc(torch.autograd.Function):
402
+
403
+ @staticmethod
404
+ def forward(ctx, qkv, bias=None, causal=False, softmax_scale=None):
405
+ """
406
+ qkv: (batch, seqlen, 3, nheads, headdim)
407
+ bias: optional, shape broadcastible to (batch, nheads, seqlen, seqlen).
408
+ For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen).
409
+ ALiBi mask for non-causal would have shape (1, nheads, seqlen, seqlen)
410
+ """
411
+ if qkv.stride(-1) != 1:
412
+ qkv = qkv.contiguous()
413
+ (o, lse, ctx.softmax_scale) = _flash_attn_forward(qkv[:, :, 0], qkv[:, :, 1], qkv[:, :, 2], bias=bias, causal=causal, softmax_scale=softmax_scale)
414
+ ctx.save_for_backward(qkv, o, lse, bias)
415
+ ctx.causal = causal
416
+ return o
417
+
418
+ @staticmethod
419
+ def backward(ctx, do):
420
+ (qkv, o, lse, bias) = ctx.saved_tensors
421
+ assert not ctx.needs_input_grad[1], 'FlashAttention does not support bias gradient yet'
422
+ with torch.inference_mode():
423
+ dqkv = torch.empty_like(qkv)
424
+ _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)
425
+ return (dqkv, None, None, None)
426
+ flash_attn_qkvpacked_func = FlashAttnQKVPackedFunc.apply
427
+
428
+ class FlashAttnKVPackedFunc(torch.autograd.Function):
429
+
430
+ @staticmethod
431
+ def forward(ctx, q, kv, bias=None, causal=False, softmax_scale=None):
432
+ """
433
+ q: (batch, seqlen_q, nheads, headdim)
434
+ kv: (batch, seqlen_k, 2, nheads, headdim)
435
+ bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).
436
+ For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).
437
+ ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)
438
+ """
439
+ (q, kv) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, kv]]
440
+ (o, lse, ctx.softmax_scale) = _flash_attn_forward(q, kv[:, :, 0], kv[:, :, 1], bias=bias, causal=causal, softmax_scale=softmax_scale)
441
+ ctx.save_for_backward(q, kv, o, lse, bias)
442
+ ctx.causal = causal
443
+ return o
444
+
445
+ @staticmethod
446
+ def backward(ctx, do):
447
+ (q, kv, o, lse, bias) = ctx.saved_tensors
448
+ if len(ctx.needs_input_grad) >= 3:
449
+ assert not ctx.needs_input_grad[2], 'FlashAttention does not support bias gradient yet'
450
+ with torch.inference_mode():
451
+ dq = torch.empty_like(q)
452
+ dkv = torch.empty_like(kv)
453
+ _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)
454
+ return (dq, dkv, None, None, None)
455
+ flash_attn_kvpacked_func = FlashAttnKVPackedFunc.apply
456
+
457
+ class FlashAttnFunc(torch.autograd.Function):
458
+
459
+ @staticmethod
460
+ def forward(ctx, q, k, v, bias=None, causal=False, softmax_scale=None):
461
+ """
462
+ q: (batch_size, seqlen_q, nheads, headdim)
463
+ k, v: (batch_size, seqlen_k, nheads, headdim)
464
+ bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).
465
+ For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).
466
+ ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)
467
+ """
468
+ (q, k, v) = [x if x.stride(-1) == 1 else x.contiguous() for x in [q, k, v]]
469
+ (o, lse, ctx.softmax_scale) = _flash_attn_forward(q, k, v, bias=bias, causal=causal, softmax_scale=softmax_scale)
470
+ ctx.save_for_backward(q, k, v, o, lse, bias)
471
+ ctx.causal = causal
472
+ return o
473
+
474
+ @staticmethod
475
+ def backward(ctx, do):
476
+ (q, k, v, o, lse, bias) = ctx.saved_tensors
477
+ assert not ctx.needs_input_grad[3], 'FlashAttention does not support bias gradient yet'
478
+ with torch.inference_mode():
479
+ dq = torch.empty_like(q)
480
+ dk = torch.empty_like(k)
481
+ dv = torch.empty_like(v)
482
+ _flash_attn_backward(do, q, k, v, o, lse, dq, dk, dv, bias=bias, causal=ctx.causal, softmax_scale=ctx.softmax_scale)
483
+ return (dq, dk, dv, None, None, None)
484
+ flash_attn_func = FlashAttnFunc.apply