File size: 11,693 Bytes
e45d058
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
# [2022-10-23] Downloaded from https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py
# for benchmarking.
# We fixed a few dtype cast to make it work for bf16

"""

Fused Attention

===============

This is a Triton implementation of the Flash Attention algorithm

(see: Dao et al., https://arxiv.org/pdf/2205.14135v2.pdf; Rabe and Staats https://arxiv.org/pdf/2112.05682v2.pdf)

"""

import pytest
import torch
import triton
import triton.language as tl


@triton.jit
def _fwd_kernel(

    Q,

    K,

    V,

    sm_scale,

    TMP,

    L,

    M,  # NOTE: TMP is a scratchpad buffer to workaround a compiler bug

    Out,

    stride_qz,

    stride_qh,

    stride_qm,

    stride_qk,

    stride_kz,

    stride_kh,

    stride_kn,

    stride_kk,

    stride_vz,

    stride_vh,

    stride_vk,

    stride_vn,

    stride_oz,

    stride_oh,

    stride_om,

    stride_on,

    Z,

    H,

    N_CTX,

    BLOCK_M: tl.constexpr,

    BLOCK_DMODEL: tl.constexpr,

    BLOCK_N: tl.constexpr,

):
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    # 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_DMODEL)
    off_q = off_hz * stride_qh + offs_m[:, None] * stride_qm + offs_d[None, :] * stride_qk
    off_k = off_hz * stride_qh + offs_n[:, None] * stride_kn + offs_d[None, :] * stride_kk
    off_v = off_hz * stride_qh + offs_n[:, None] * stride_qm + offs_d[None, :] * stride_qk
    # Initialize pointers to Q, K, V
    q_ptrs = Q + off_q
    k_ptrs = K + off_k
    v_ptrs = V + off_v
    # initialize pointer to m and l
    t_ptrs = TMP + off_hz * N_CTX + offs_m
    m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
    l_i = tl.zeros([BLOCK_M], dtype=tl.float32)
    acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
    # load q: it will stay in SRAM throughout
    q = tl.load(q_ptrs)
    # loop over k, v and update accumulator
    for start_n in range(0, (start_m + 1) * BLOCK_M, BLOCK_N):
        start_n = tl.multiple_of(start_n, BLOCK_N)
        # -- compute qk ----
        k = tl.load(k_ptrs + start_n * stride_kn)
        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
        qk += tl.dot(q, k, trans_b=True)
        qk *= sm_scale
        qk += tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), 0, float("-inf"))
        # -- compute m_ij, p, l_ij
        m_ij = tl.max(qk, 1)
        p = tl.exp(qk - m_ij[:, None])
        l_ij = tl.sum(p, 1)
        # -- update m_i and l_i
        m_i_new = tl.maximum(m_i, m_ij)
        alpha = tl.exp(m_i - m_i_new)
        beta = tl.exp(m_ij - m_i_new)
        l_i_new = alpha * l_i + beta * l_ij
        # -- update output accumulator --
        # scale p
        p_scale = beta / l_i_new
        p = p * p_scale[:, None]
        # scale acc
        acc_scale = l_i / l_i_new * alpha
        tl.store(t_ptrs, acc_scale)
        acc_scale = tl.load(t_ptrs)  # BUG: have to store and immediately load
        acc = acc * acc_scale[:, None]
        # update acc
        v = tl.load(v_ptrs + start_n * stride_vk)
        p = p.to(v.dtype)
        acc += tl.dot(p, v)
        # update m_i and l_i
        l_i = l_i_new
        m_i = m_i_new
    # 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
    l_ptrs = L + off_hz * N_CTX + offs_m
    m_ptrs = M + off_hz * N_CTX + offs_m
    tl.store(l_ptrs, l_i)
    tl.store(m_ptrs, m_i)
    # initialize pointers to output
    offs_n = tl.arange(0, BLOCK_DMODEL)
    off_o = off_hz * stride_oh + offs_m[:, None] * stride_om + offs_n[None, :] * stride_on
    out_ptrs = Out + off_o
    tl.store(out_ptrs, acc)


@triton.jit
def _bwd_preprocess(

    Out,

    DO,

    L,

    NewDO,

    Delta,

    BLOCK_M: tl.constexpr,

    D_HEAD: tl.constexpr,

):
    off_m = tl.program_id(0) * BLOCK_M + tl.arange(0, BLOCK_M)
    off_n = tl.arange(0, D_HEAD)
    # load
    o = tl.load(Out + off_m[:, None] * D_HEAD + off_n[None, :]).to(tl.float32)
    do = tl.load(DO + off_m[:, None] * D_HEAD + off_n[None, :]).to(tl.float32)
    denom = tl.load(L + off_m).to(tl.float32)
    # compute
    do = do / denom[:, None]
    delta = tl.sum(o * do, axis=1)
    # write-back
    tl.store(NewDO + off_m[:, None] * D_HEAD + off_n[None, :], do)
    tl.store(Delta + off_m, delta)


@triton.jit
def _bwd_kernel(

    Q,

    K,

    V,

    sm_scale,

    Out,

    DO,

    DQ,

    DK,

    DV,

    L,

    M,

    D,

    stride_qz,

    stride_qh,

    stride_qm,

    stride_qk,

    stride_kz,

    stride_kh,

    stride_kn,

    stride_kk,

    stride_vz,

    stride_vh,

    stride_vk,

    stride_vn,

    Z,

    H,

    N_CTX,

    num_block,

    BLOCK_M: tl.constexpr,

    BLOCK_DMODEL: tl.constexpr,

    BLOCK_N: tl.constexpr,

):
    off_hz = tl.program_id(0)
    off_z = off_hz // H
    off_h = off_hz % H
    # offset pointers for batch/head
    Q += off_z * stride_qz + off_h * stride_qh
    K += off_z * stride_qz + off_h * stride_qh
    V += off_z * stride_qz + off_h * stride_qh
    DO += off_z * stride_qz + off_h * stride_qh
    DQ += off_z * stride_qz + off_h * stride_qh
    DK += off_z * stride_qz + off_h * stride_qh
    DV += off_z * stride_qz + off_h * stride_qh
    for start_n in range(0, num_block):
        lo = start_n * BLOCK_M
        # initialize row/col offsets
        offs_qm = lo + tl.arange(0, BLOCK_M)
        offs_n = start_n * BLOCK_M + tl.arange(0, BLOCK_M)
        offs_m = tl.arange(0, BLOCK_N)
        offs_k = tl.arange(0, BLOCK_DMODEL)
        # initialize pointers to value-like data
        q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        k_ptrs = K + (offs_n[:, None] * stride_kn + offs_k[None, :] * stride_kk)
        v_ptrs = V + (offs_n[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        do_ptrs = DO + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        dq_ptrs = DQ + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        # pointer to row-wise quantities in value-like data
        D_ptrs = D + off_hz * N_CTX
        m_ptrs = M + off_hz * N_CTX
        # initialize dv amd dk
        dv = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
        dk = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
        # k and v stay in SRAM throughout
        k = tl.load(k_ptrs)
        v = tl.load(v_ptrs)
        # loop over rows
        for start_m in range(lo, num_block * BLOCK_M, BLOCK_M):
            offs_m_curr = start_m + offs_m
            # load q, k, v, do on-chip
            q = tl.load(q_ptrs)
            # recompute p = softmax(qk, dim=-1).T
            # NOTE: `do` is pre-divided by `l`; no normalization here
            qk = tl.dot(q, k, trans_b=True)
            qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), qk, float("-inf"))
            m = tl.load(m_ptrs + offs_m_curr)
            p = tl.exp(qk * sm_scale - m[:, None])
            # compute dv
            do = tl.load(do_ptrs)
            dv += tl.dot(p.to(do.dtype), do, trans_a=True)
            # compute dp = dot(v, do)
            Di = tl.load(D_ptrs + offs_m_curr)
            dp = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32) - Di[:, None]
            dp += tl.dot(do, v, trans_b=True)
            # compute ds = p * (dp - delta[:, None])
            ds = p * dp * sm_scale
            # compute dk = dot(ds.T, q)
            dk += tl.dot(ds.to(q.dtype), q, trans_a=True)
            # # compute dq
            dq = tl.load(dq_ptrs, eviction_policy="evict_last")
            dq += tl.dot(ds.to(k.dtype), k)
            tl.store(dq_ptrs, dq, eviction_policy="evict_last")
            # # increment pointers
            dq_ptrs += BLOCK_M * stride_qm
            q_ptrs += BLOCK_M * stride_qm
            do_ptrs += BLOCK_M * stride_qm
        # write-back
        dv_ptrs = DV + (offs_n[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        dk_ptrs = DK + (offs_n[:, None] * stride_kn + offs_k[None, :] * stride_kk)
        tl.store(dv_ptrs, dv)
        tl.store(dk_ptrs, dk)


class _attention(torch.autograd.Function):
    @staticmethod
    def forward(ctx, q, k, v, sm_scale):
        BLOCK = 128
        # shape constraints
        Lq, Lk, Lv = q.shape[-1], k.shape[-1], v.shape[-1]
        assert Lq == Lk and Lk == Lv
        assert Lk in {16, 32, 64, 128}
        o = torch.empty_like(q)
        grid = (triton.cdiv(q.shape[2], BLOCK), q.shape[0] * q.shape[1])
        tmp = torch.empty(
            (q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32
        )
        L = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32)
        m = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32)
        num_warps = 4 if Lk <= 64 else 8

        _fwd_kernel[grid](
            q,
            k,
            v,
            sm_scale,
            tmp,
            L,
            m,
            o,
            q.stride(0),
            q.stride(1),
            q.stride(2),
            q.stride(3),
            k.stride(0),
            k.stride(1),
            k.stride(2),
            k.stride(3),
            v.stride(0),
            v.stride(1),
            v.stride(2),
            v.stride(3),
            o.stride(0),
            o.stride(1),
            o.stride(2),
            o.stride(3),
            q.shape[0],
            q.shape[1],
            q.shape[2],
            BLOCK_M=BLOCK,
            BLOCK_N=BLOCK,
            BLOCK_DMODEL=Lk,
            num_warps=num_warps,
            num_stages=1,
        )
        ctx.save_for_backward(q, k, v, o, L, m)
        ctx.BLOCK = BLOCK
        ctx.grid = grid
        ctx.sm_scale = sm_scale
        ctx.BLOCK_DMODEL = Lk
        return o

    @staticmethod
    def backward(ctx, do):
        q, k, v, o, l, m = ctx.saved_tensors
        do = do.contiguous()
        dq = torch.zeros_like(q, dtype=torch.float32)
        dk = torch.empty_like(k)
        dv = torch.empty_like(v)
        do_scaled = torch.empty_like(do)
        delta = torch.empty_like(l)
        _bwd_preprocess[(ctx.grid[0] * ctx.grid[1],)](
            o,
            do,
            l,
            do_scaled,
            delta,
            BLOCK_M=ctx.BLOCK,
            D_HEAD=ctx.BLOCK_DMODEL,
        )

        # NOTE: kernel currently buggy for other values of `num_warps`
        num_warps = 8
        _bwd_kernel[(ctx.grid[1],)](
            q,
            k,
            v,
            ctx.sm_scale,
            o,
            do_scaled,
            dq,
            dk,
            dv,
            l,
            m,
            delta,
            q.stride(0),
            q.stride(1),
            q.stride(2),
            q.stride(3),
            k.stride(0),
            k.stride(1),
            k.stride(2),
            k.stride(3),
            v.stride(0),
            v.stride(1),
            v.stride(2),
            v.stride(3),
            q.shape[0],
            q.shape[1],
            q.shape[2],
            ctx.grid[0],
            BLOCK_M=ctx.BLOCK,
            BLOCK_N=ctx.BLOCK,
            BLOCK_DMODEL=ctx.BLOCK_DMODEL,
            num_warps=num_warps,
            num_stages=1,
        )
        return dq.to(q.dtype), dk, dv, None


attention = _attention.apply