flash_bwd_kernel.h 91.1 KB
Newer Older
Tri Dao's avatar
Tri Dao committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
/***************************************************************************************************
 * Copyright (c) 2023, Tri Dao.
 ******************************************************************************/

#pragma once

#include <cute/algorithm/copy.hpp>

#include <cutlass/cutlass.h>
#include <cutlass/array.h>
#include <cutlass/numeric_types.h>

#include "block_info.h"
#include "kernel_traits.h"
#include "utils.h"
#include "softmax.h"

18
19
#include "alibi.h"

Tri Dao's avatar
Tri Dao committed
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
namespace flash {

using namespace cute;

////////////////////////////////////////////////////////////////////////////////////////////////////

template <int MMA_N,
          class... Args,
          class TiledMMA>
CUTE_HOST_DEVICE
auto
make_tiled_copy_B_warpcontiguousN(Copy_Atom<Args...> const& copy_atom,
                                  TiledMMA           const& tiled_mma) {
    using TileShape_MNK = typename TiledMMA::TiledShape_MNK;
    using AtomShape_MNK = typename TiledMMA::AtomShape_MNK;
    constexpr int AtomShape_N = decltype(size<1>(AtomShape_MNK{}))::value;
    // Divide by 2 because right now we always use 2 for the ValLayout
    constexpr int kNWarpsN = decltype(size<1>(TileShape_MNK{}))::value / AtomShape_N / 2;
    constexpr int MMAStride_N = MMA_N * AtomShape_N * 2;
    // This gives the correct layout, idk why.
    // auto t = make_tile(Layout<Shape<Shape<_8, _2>, _2>,
    //                           Stride<Stride<_1, _64>, _8> >{},
    // auto t = make_tile(Layout<Shape<_8, _2, _2>,
    //                           Stride<_1, _64, _8> >{},
    auto t = make_tile(Layout<Shape<Int<AtomShape_N>, Int<kNWarpsN>, _2>,   // (8, 2, 2) or (8, 4, 2)
                              Stride<_1, Int<MMAStride_N>, _8> >{},       // (1, 64, 8) or (1, 32, 8)
                       make_layout(size<2>(TileShape_MNK{})));
    // if (cute::thread0()) {printf("make_tiled_copy_B_warpcontiguousN "); print(t); printf("\n");  }
    return make_tiled_copy_impl(copy_atom, tiled_mma.get_layoutB_TV(), t);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template <int MMA_N,
          class... Args,
          class TiledMMA>
CUTE_HOST_DEVICE
auto
make_tiled_copy_C_warpcontiguousN(Copy_Atom<Args...> const& copy_atom,
                                  TiledMMA           const& tiled_mma) {
    using TileShape_MNK = typename TiledMMA::TiledShape_MNK;
    using AtomShape_MNK = typename TiledMMA::AtomShape_MNK;
    constexpr int AtomShape_N = decltype(size<1>(AtomShape_MNK{}))::value;
    // Divide by 2 because right now we always use 2 for the ValLayout
    constexpr int kNWarpsN = decltype(size<1>(TileShape_MNK{}))::value / AtomShape_N / 2;
    constexpr int MMAStride_N = MMA_N * AtomShape_N * 2;
    auto t = make_tile(make_layout(size<0>(TileShape_MNK{})),
                       Layout<Shape<Int<AtomShape_N>, Int<kNWarpsN>, _2>,   // (8, 2, 2) or (8, 4, 2)
                              Stride<_1, Int<MMAStride_N>, _8> >{});       // (1, 64, 8) or (1, 32, 8)
    // if (cute::thread0()) {printf("make_tiled_copy_C_warpcontiguousN "); print(t); printf("\n");  }
    return make_tiled_copy_impl(copy_atom, tiled_mma.get_layoutC_TV(), t);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

75
template <int THREADS_PER_ROW, typename Engine0, typename Layout0, typename Engine1, typename Layout1>
Tri Dao's avatar
Tri Dao committed
76
inline __device__ void dot_do_o(Tensor<Engine0, Layout0> const &do_, Tensor<Engine0, Layout0> const &o,
77
                                Tensor<Engine1, Layout1> &dP_sum, const int gdP_col_stride, const float scale) {
Tri Dao's avatar
Tri Dao committed
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
    static_assert(Layout0::rank == 3, "Only support 3D Tensor");
    static_assert(Layout1::rank == 1, "Only support 1D Tensor");
    CUTE_STATIC_ASSERT_V(do_.layout() == o.layout());
    // Reshape do_ and o from (8, kBlockM / 32, kHeadDim / 64) to (kBlockM / 32, 8 * kHeadDim / 64)
    // The last coordinate is the "page".
    Tensor do_reshaped = make_tensor(do_.data(), make_layout(get<1>(do_.layout()),
                                                             make_layout(get<0>(do_.layout()),
                                                                         get<2>(do_.layout()))));
    Tensor o_reshaped = make_tensor(o.data(), do_reshaped.layout());
    Tensor do_fp32 = flash::convert_type<float>(do_reshaped);
    Tensor o_fp32 = flash::convert_type<float>(o_reshaped);
    #pragma unroll
    for (int mi = 0; mi < size<0>(do_reshaped); ++mi) {
        float dP_sum_cur = do_fp32(mi, 0) * o_fp32(mi, 0);
        #pragma unroll
        for (int ni = 1; ni < size<1>(do_reshaped); ni++) {
            dP_sum_cur += do_fp32(mi, ni) * o_fp32(mi, ni);
        }
        flash::SumOp<float> sum_op;
        dP_sum_cur = flash::Allreduce<THREADS_PER_ROW>::run(dP_sum_cur, sum_op) * scale;
        if (threadIdx.x % THREADS_PER_ROW == 0) {
            dP_sum(mi * gdP_col_stride + threadIdx.x / THREADS_PER_ROW) = dP_sum_cur;
        }
    }
}

////////////////////////////////////////////////////////////////////////////////////////////////////

// Just compute dot(do, o) and write the result (softmax_d) to global memory as a separate kernel.
// This is used in the case where we want to parallelize the backward across seqlen_k.
template<bool Clear_dQaccum=true, typename Kernel_traits, typename Params>
inline __device__ void compute_dot_do_o(const Params &params) {
    using Element = typename Kernel_traits::Element;
    using ElementAccum = typename Kernel_traits::ElementAccum;
    using index_t = typename Kernel_traits::index_t;

    const int m_block = blockIdx.x;
    // The block index for the batch.
    const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.z;
    // The thread index.
    const int tidx = threadIdx.x;

    constexpr int kBlockM = Kernel_traits::kBlockM;
    constexpr int kHeadDim = Kernel_traits::kHeadDim;

    const BlockInfo binfo(params, bidb);
    if (m_block * kBlockM >= binfo.actual_seqlen_q) return;

    const index_t row_offset_do = binfo.q_offset(params.do_batch_stride, params.do_row_stride, bidb)
        + m_block * kBlockM * params.do_row_stride + bidh * params.do_head_stride;
    const index_t row_offset_o = binfo.q_offset(params.o_batch_stride, params.o_row_stride, bidb)
        + m_block * kBlockM * params.o_row_stride + bidh * params.o_head_stride;
132
133
    const index_t row_offset_dq_accum = binfo.q_offset(params.seqlen_q_rounded * params.h * params.d_rounded, params.h * params.d_rounded, bidb)
        + (m_block * kBlockM + (params.cu_seqlens_q == nullptr ? 0 : 128 * bidb)) * params.h * params.d_rounded + bidh * params.d_rounded;
Tri Dao's avatar
Tri Dao committed
134
135
136
137
138
139
140
    const index_t row_offset_dpsum = (bidb * params.h + bidh) * params.seqlen_q_rounded + m_block * kBlockM;

    Tensor gdO = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.do_ptr) + row_offset_do),
                             Shape<Int<kBlockM>, Int<kHeadDim>>{},
                             make_stride(params.do_row_stride, _1{}));
    Tensor gO = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.o_ptr) + row_offset_o),
                            Shape<Int<kBlockM>, Int<kHeadDim>>{},
141
                            make_stride(params.o_row_stride, _1{}));
Tri Dao's avatar
Tri Dao committed
142
    Tensor gdQaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dq_accum_ptr) + row_offset_dq_accum),
143
144
                                  Shape<Int<kBlockM>, Int<kHeadDim>>{},
                                  make_stride(params.h * params.d_rounded, _1{}));
Tri Dao's avatar
Tri Dao committed
145
146
147
    Tensor dP_sum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dsoftmax_sum) + row_offset_dpsum),
                                Shape<Int<kBlockM>>{}, Stride<_1>{});

Tri Dao's avatar
Tri Dao committed
148
149
    typename Kernel_traits::GmemTiledCopydO gmem_tiled_copy_dO;
    auto gmem_thr_copy_dO = gmem_tiled_copy_dO.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
150
151
    // TODO: careful, we're zeroing out dQaccum with type float4, but when
    // we do atomicAdds, we use type float. The layouts are different. Check this.
Tri Dao's avatar
Tri Dao committed
152
153
    typename Kernel_traits::GmemTiledCopydQaccum gmem_tiled_copy_dQaccum;
    auto gmem_thr_copy_dQaccum = gmem_tiled_copy_dQaccum.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
154
155
156

    Tensor tdOgdO = gmem_thr_copy_dO.partition_S(gdO);
    Tensor tdOgO = gmem_thr_copy_dO.partition_S(gO);
Tri Dao's avatar
Tri Dao committed
157
    Tensor tdQgdQaccum = gmem_thr_copy_dQaccum.partition_D(gdQaccum);
Tri Dao's avatar
Tri Dao committed
158
159
160
161
162
163
164
165
166
167
168
169
170

    Tensor cdO = make_identity_tensor(Shape<Int<kBlockM>, Int<kHeadDim>>{});    // (BLK_M,BLK_K) -> (blk_m,blk_k)
    Tensor tdOcdO = gmem_thr_copy_dO.partition_S(cdO);

    // Allocate predicate tensors for k
    Tensor tdOpdO = make_tensor<bool>(make_shape(size<2>(tdOgdO)));
    // Set predicates for k bounds
    #pragma unroll
    for (int k = 0; k < size(tdOpdO); ++k) {tdOpdO(k) = get<1>(tdOcdO(0, 0, k)) < params.d;}

    Tensor tdOrdO = make_fragment_like(tdOgdO);
    Tensor tdOrO = make_fragment_like(tdOgO);
    flash::copy</*Is_even_MN=*/false, /*Is_even_K=*/false, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
171
        gmem_tiled_copy_dO, tdOgdO, tdOrdO, tdOcdO, tdOpdO, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
172
173
    );
    flash::copy</*Is_even_MN=*/false, /*Is_even_K=*/false, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
174
        gmem_tiled_copy_dO, tdOgO, tdOrO, tdOcdO, tdOpdO, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
175
176
177
178
    );
    // By right we need to scale dP up by 1/p_dropout, but instead we don't and only scale the final
    // results (dQ and dK) by 1/p_dropout. So we need to keep dP_sum scaled down by p_dropout here,
    // so that (dP - dP_sum) is on the same scale.
179
    dot_do_o<Kernel_traits::kGmemThreadsPerRow>(tdOrdO, tdOrO, dP_sum,
Tri Dao's avatar
Tri Dao committed
180
181
                                                Kernel_traits::kNThreads / (Kernel_traits::kGmemThreadsPerRow), params.p_dropout);
    if (Clear_dQaccum) {
182
183
        // We're actually not zero'ing out all of dQaccum, but only the part that we're going to
        // do atomicAdds on.
Tri Dao's avatar
Tri Dao committed
184
185
        Tensor zero = make_fragment_like(tdQgdQaccum);
        clear(zero);
Tri Dao's avatar
Tri Dao committed
186
        cute::copy(gmem_tiled_copy_dQaccum, zero, tdQgdQaccum);
Tri Dao's avatar
Tri Dao committed
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
    }
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename Kernel_traits, typename Params>
inline __device__ void clear_dKVaccum(const Params &params) {
    using ElementAccum = typename Kernel_traits::ElementAccum;
    using index_t = typename Kernel_traits::index_t;

    const int n_block = blockIdx.x;
    // The block index for the batch.
    const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.z;
    // The thread index.
    const int tidx = threadIdx.x;

    constexpr int kBlockN = Kernel_traits::kBlockN;
    constexpr int kHeadDim = Kernel_traits::kHeadDim;

    const BlockInfo binfo(params, bidb);
    if (n_block * kBlockN >= binfo.actual_seqlen_k) return;

    const index_t row_offset_dkv_accum = ((bidb * params.h_k + bidh) * params.seqlen_k_rounded + n_block * kBlockN) * params.d_rounded;

    Tensor gdKaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dk_accum_ptr) + row_offset_dkv_accum),
                                  Shape<Int<kBlockN>, Int<kHeadDim>>{}, Stride<Int<kHeadDim>, _1>{});
    Tensor gdVaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dv_accum_ptr) + row_offset_dkv_accum),
                                  Shape<Int<kBlockN>, Int<kHeadDim>>{}, Stride<Int<kHeadDim>, _1>{});

Tri Dao's avatar
Tri Dao committed
218
219
220
221
    typename Kernel_traits::GmemTiledCopydQaccum gmem_tiled_copy_dKVaccum;
    auto gmem_thr_copy_dKVaccum = gmem_tiled_copy_dKVaccum.get_thread_slice(tidx);
    Tensor tdKgdKaccum = gmem_thr_copy_dKVaccum.partition_D(gdKaccum);
    Tensor tdVgdVaccum = gmem_thr_copy_dKVaccum.partition_D(gdVaccum);
Tri Dao's avatar
Tri Dao committed
222
223
    Tensor zero = make_fragment_like(tdKgdKaccum);
    clear(zero);
Tri Dao's avatar
Tri Dao committed
224
225
    cute::copy(gmem_tiled_copy_dKVaccum, zero, tdKgdKaccum);
    cute::copy(gmem_tiled_copy_dKVaccum, zero, tdVgdVaccum);
Tri Dao's avatar
Tri Dao committed
226
227
228
229
230
231
232
}

////////////////////////////////////////////////////////////////////////////////////////////////////

// Convert dQ from dQaccum (in float) to fp16/bf16.
// This is used in the case where we want to parallelize the backward across seqlen_k.
template<typename Kernel_traits, typename Params>
233
inline __device__ void convert_dQ(const Params &params, const int nsplits) {
Tri Dao's avatar
Tri Dao committed
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
    using Element = typename Kernel_traits::Element;
    using ElementAccum = typename Kernel_traits::ElementAccum;
    using index_t = typename Kernel_traits::index_t;

    // Shared memory.
    extern __shared__ char smem_[];

    const int m_block = blockIdx.x;
    // The block index for the batch.
    const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.z;
    // The thread index.
    const int tidx = threadIdx.x;

    constexpr int kBlockM = Kernel_traits::kBlockM;
    constexpr int kHeadDim = Kernel_traits::kHeadDim;

    const BlockInfo binfo(params, bidb);
    if (m_block * kBlockM >= binfo.actual_seqlen_q) return;

    const index_t row_offset_dq = binfo.q_offset(params.dq_batch_stride, params.dq_row_stride, bidb)
        + m_block * kBlockM * params.dq_row_stride + bidh * params.dq_head_stride;
257
258
    const index_t row_offset_dq_accum = binfo.q_offset(params.seqlen_q_rounded * params.h * params.d_rounded, params.h * params.d_rounded, bidb)
        + (m_block * kBlockM + (params.cu_seqlens_q == nullptr ? 0 : 128 * bidb)) * params.h * params.d_rounded + bidh * params.d_rounded;
Tri Dao's avatar
Tri Dao committed
259
260
261
262
263
264

    Tensor gdQ = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dq_ptr) + row_offset_dq),
                             Shape<Int<kBlockM>, Int<kHeadDim>>{},
                             make_stride(params.dq_row_stride, _1{}));
    Tensor gdQaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dq_accum_ptr) + row_offset_dq_accum),
                                  Shape<Int<kBlockM>, Int<kHeadDim>>{},
265
                                  make_stride(params.h * params.d_rounded, _1{}));
Tri Dao's avatar
Tri Dao committed
266
267
268
269

    Tensor sdQ = make_tensor(make_smem_ptr(reinterpret_cast<Element *>(smem_)),
                             typename Kernel_traits::SmemLayoutdQ{});

Tri Dao's avatar
Tri Dao committed
270
271
272
273
    typename Kernel_traits::GmemTiledCopydQ gmem_tiled_copy_dQ;
    auto gmem_thr_copy_dQ = gmem_tiled_copy_dQ.get_thread_slice(tidx);
    typename Kernel_traits::GmemTiledCopydQaccumAtomicAdd gmem_tiled_copy_dQaccum;
    auto gmem_thr_copy_dQaccum = gmem_tiled_copy_dQaccum.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
274
275

    typename Kernel_traits::TiledMmadQ tiled_mma_dq;
Tri Dao's avatar
Tri Dao committed
276
277
    auto smem_tiled_copy_dQ = make_tiled_copy_C(typename Kernel_traits::SmemCopyAtomdQ{}, tiled_mma_dq);
    auto smem_thr_copy_dQ = smem_tiled_copy_dQ.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
278
279
280
281
    Tensor taccdQsdQ = smem_thr_copy_dQ.partition_D(sdQ);  // ((Atom,AtomNum),PIPE_M,PIPE_N)

    Tensor tdQsdQ = gmem_thr_copy_dQ.partition_S(sdQ);    // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdQgdQ = gmem_thr_copy_dQ.partition_D(gdQ);
Tri Dao's avatar
Tri Dao committed
282
    Tensor tdQgdQaccum = gmem_thr_copy_dQaccum.partition_S(gdQaccum);
Tri Dao's avatar
Tri Dao committed
283
284
285
286
287

    Tensor acc_dq = partition_fragment_C(tiled_mma_dq, Shape<Int<kBlockM>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
    CUTE_STATIC_ASSERT_V(size(acc_dq) == size(tdQgdQaccum));

    Tensor tdQrdQaccum = make_fragment_like(tdQgdQaccum);
288
289
290
291
292
293
    clear(acc_dq);
    for (int s = 0; s < nsplits; ++s) {
        cute::copy(gmem_tiled_copy_dQaccum, tdQgdQaccum, tdQrdQaccum);
        #pragma unroll
        for (int i = 0; i < size(acc_dq); ++i) { acc_dq(i) += tdQrdQaccum(i); }
        tdQgdQaccum.data() = tdQgdQaccum.data() + params.dq_accum_split_stride;
Tri Dao's avatar
Tri Dao committed
294
    }
295
296
    #pragma unroll
    for (int i = 0; i < size(acc_dq); ++i) { acc_dq(i) *= params.scale_softmax_rp_dropout; }
Tri Dao's avatar
Tri Dao committed
297
298
299
    // Convert acc_dq from fp32 to fp16
    Tensor rdQ = flash::convert_type<Element>(acc_dq);
    Tensor taccdQrdQ = smem_thr_copy_dQ.retile_S(rdQ);  // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
300
    cute::copy(smem_tiled_copy_dQ, taccdQrdQ, taccdQsdQ);
Tri Dao's avatar
Tri Dao committed
301
302
    __syncthreads();
    Tensor tdQrdQ = make_tensor<Element>(shape(tdQgdQ));
Tri Dao's avatar
Tri Dao committed
303
    cute::copy(gmem_tiled_copy_dQ, tdQsdQ, tdQrdQ);
Tri Dao's avatar
Tri Dao committed
304
305
306
307
308
309
310
311

    Tensor cdQ = make_identity_tensor(Shape<Int<kBlockM>, Int<kHeadDim>>{});    // (BLK_M,BLK_K) -> (blk_m,blk_k)
    Tensor tdQcdQ = gmem_thr_copy_dQ.partition_D(cdQ);
    Tensor tdQpdQ = make_tensor<bool>(make_shape(size<2>(tdQgdQ)));
    #pragma unroll
    for (int k = 0; k < size(tdQpdQ); ++k) { tdQpdQ(k) = get<1>(tdQcdQ(0, 0, k)) < params.d; }
    // Clear_OOB_K must be false since we don't want to write zeros to gmem
    flash::copy</*Is_even_MN=*/false, /*Is_even_K=*/false, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
Tri Dao's avatar
Tri Dao committed
312
        gmem_tiled_copy_dQ, tdQrdQ, tdQgdQ, tdQcdQ, tdQpdQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
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
    );
}

////////////////////////////////////////////////////////////////////////////////////////////////////

// Convert dK and dV from dKaccum and dVaccum (in float) to fp16/bf16.
// This is used in the case where we want to parallelize the backward across seqlen_q.
template<typename Kernel_traits, typename Params>
inline __device__ void convert_dKV(const Params &params) {
    using Element = typename Kernel_traits::Element;
    using ElementAccum = typename Kernel_traits::ElementAccum;
    using index_t = typename Kernel_traits::index_t;

    // Shared memory.
    extern __shared__ char smem_[];

    const int n_block = blockIdx.x;
    // The block index for the batch.
    const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.z;
    // The thread index.
    const int tidx = threadIdx.x;

    constexpr int kBlockN = Kernel_traits::kBlockN;
    constexpr int kHeadDim = Kernel_traits::kHeadDim;

    const BlockInfo binfo(params, bidb);
    if (n_block * kBlockN >= binfo.actual_seqlen_k) return;

    const index_t row_offset_dk = binfo.k_offset(params.dk_batch_stride, params.dk_row_stride, bidb)
        + n_block * kBlockN * params.dk_row_stride + bidh * params.dk_head_stride;
    const index_t row_offset_dv = binfo.k_offset(params.dv_batch_stride, params.dv_row_stride, bidb)
        + n_block * kBlockN * params.dv_row_stride + bidh * params.dv_head_stride;
    const index_t row_offset_dkv_accum = ((bidb * params.h_k + bidh) * params.seqlen_k_rounded
                                          + n_block * kBlockN) * params.d_rounded;

    Tensor gdK = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dk_ptr) + row_offset_dk),
                             Shape<Int<kBlockN>, Int<kHeadDim>>{},
                             make_stride(params.dk_row_stride, _1{}));
    Tensor gdV = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dv_ptr) + row_offset_dv),
                             Shape<Int<kBlockN>, Int<kHeadDim>>{},
                             make_stride(params.dv_row_stride, _1{}));
    Tensor gdKaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dk_accum_ptr) + row_offset_dkv_accum),
                                  Shape<Int<kBlockN>, Int<kHeadDim>>{},
                                  Stride<Int<kHeadDim>, _1>{});
    Tensor gdVaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dv_accum_ptr) + row_offset_dkv_accum),
                                  Shape<Int<kBlockN>, Int<kHeadDim>>{},
                                  Stride<Int<kHeadDim>, _1>{});

    Tensor sdK = make_tensor(make_smem_ptr(reinterpret_cast<Element *>(smem_)),
                             typename Kernel_traits::SmemLayoutdKV{});
    Tensor sdV = make_tensor(sdK.data() + size(sdK), typename Kernel_traits::SmemLayoutdKV{}); // (SMEM_N, SMEM_K)

Tri Dao's avatar
Tri Dao committed
367
368
369
370
    typename Kernel_traits::GmemTiledCopydQ gmem_tiled_copy_dKV;
    auto gmem_thr_copy_dKV = gmem_tiled_copy_dKV.get_thread_slice(tidx);
    typename Kernel_traits::GmemTiledCopydQaccumAtomicAdd gmem_tiled_copy_dKVaccum;
    auto gmem_thr_copy_dKVaccum = gmem_tiled_copy_dKVaccum.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
371
372

    typename Kernel_traits::TiledMmadKV tiled_mma_dkv;
Tri Dao's avatar
Tri Dao committed
373
374
    auto smem_tiled_copy_dKV = make_tiled_copy_C(typename Kernel_traits::SmemCopyAtomdKV{}, tiled_mma_dkv);
    auto smem_thr_copy_dKV = smem_tiled_copy_dKV.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
375
376
377
378
379
380
381
    Tensor taccdKsdK = smem_thr_copy_dKV.partition_D(sdK);  // ((Atom,AtomNum),PIPE_M,PIPE_N)
    Tensor taccdVsdV = smem_thr_copy_dKV.partition_D(sdV);  // ((Atom,AtomNum),PIPE_M,PIPE_N)

    Tensor tdKsdK = gmem_thr_copy_dKV.partition_S(sdK);    // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdKgdK = gmem_thr_copy_dKV.partition_D(gdK);
    Tensor tdVsdV = gmem_thr_copy_dKV.partition_S(sdV);    // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdVgdV = gmem_thr_copy_dKV.partition_D(gdV);
Tri Dao's avatar
Tri Dao committed
382
383
    Tensor tdKgdKaccum = gmem_thr_copy_dKVaccum.partition_S(gdKaccum);
    Tensor tdVgdVaccum = gmem_thr_copy_dKVaccum.partition_S(gdVaccum);
Tri Dao's avatar
Tri Dao committed
384
385
386
387
388
389
390
391

    Tensor acc_dk = partition_fragment_C(tiled_mma_dkv, Shape<Int<kBlockN>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
    Tensor acc_dv = partition_fragment_C(tiled_mma_dkv, Shape<Int<kBlockN>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
    CUTE_STATIC_ASSERT_V(size(acc_dk) == size(tdKgdKaccum));
    CUTE_STATIC_ASSERT_V(size(acc_dv) == size(tdVgdVaccum));

    Tensor tdKrdKaccum = make_fragment_like(tdKgdKaccum);
    Tensor tdVrdVaccum = make_fragment_like(tdVgdVaccum);
Tri Dao's avatar
Tri Dao committed
392
393
    cute::copy(gmem_tiled_copy_dKVaccum, tdKgdKaccum, tdKrdKaccum);
    cute::copy(gmem_tiled_copy_dKVaccum, tdVgdVaccum, tdVrdVaccum);
Tri Dao's avatar
Tri Dao committed
394
395
396
397
398
399
400
401
402
403
404
405
406
    #pragma unroll
    for (int i = 0; i < size(acc_dk); ++i) {
        acc_dk(i) = tdKrdKaccum(i) * params.scale_softmax_rp_dropout;
    }
    #pragma unroll
    for (int i = 0; i < size(acc_dv); ++i) {
        acc_dv(i) = tdVrdVaccum(i) * params.rp_dropout;
    }
    // Convert acc_dk from fp32 to fp16
    Tensor rdK = flash::convert_type<Element>(acc_dk);
    Tensor rdV = flash::convert_type<Element>(acc_dv);
    Tensor taccdKrdK = smem_thr_copy_dKV.retile_S(rdK);  // ((Atom,AtomNum), MMA_N, MMA_N)
    Tensor taccdVrdV = smem_thr_copy_dKV.retile_S(rdV);  // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
407
408
    cute::copy(smem_tiled_copy_dKV, taccdKrdK, taccdKsdK);
    cute::copy(smem_tiled_copy_dKV, taccdVrdV, taccdVsdV);
Tri Dao's avatar
Tri Dao committed
409
410
411
    __syncthreads();
    Tensor tdKrdK = make_tensor<Element>(shape(tdKgdK));
    Tensor tdVrdV = make_tensor<Element>(shape(tdVgdV));
Tri Dao's avatar
Tri Dao committed
412
413
    cute::copy(gmem_tiled_copy_dKV, tdKsdK, tdKrdK);
    cute::copy(gmem_tiled_copy_dKV, tdVsdV, tdVrdV);
Tri Dao's avatar
Tri Dao committed
414
415
416
417
418
419
420
421

    Tensor cdKV = make_identity_tensor(Shape<Int<kBlockN>, Int<kHeadDim>>{});    // (BLK_M,BLK_K) -> (blk_m,blk_k)
    Tensor tdKVcdKV = gmem_thr_copy_dKV.partition_D(cdKV);
    Tensor tdKVpdKV = make_tensor<bool>(make_shape(size<2>(tdKgdK)));
    #pragma unroll
    for (int k = 0; k < size(tdKVpdKV); ++k) { tdKVpdKV(k) = get<1>(tdKVcdKV(0, 0, k)) < params.d; }
    // Clear_OOB_K must be false since we don't want to write zeros to gmem
    flash::copy</*Is_even_MN=*/false, /*Is_even_K=*/false, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
Tri Dao's avatar
Tri Dao committed
422
        gmem_tiled_copy_dKV, tdKrdK, tdKgdK, tdKVcdKV, tdKVpdKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
423
424
    );
    flash::copy</*Is_even_MN=*/false, /*Is_even_K=*/false, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
Tri Dao's avatar
Tri Dao committed
425
        gmem_tiled_copy_dKV, tdVrdV, tdVgdV, tdKVcdKV, tdKVpdKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
426
427
428
429
430
    );
}

////////////////////////////////////////////////////////////////////////////////////////////////////

431
template<typename Kernel_traits, bool Is_dropout, bool Is_causal, bool Is_local, bool Has_alibi, bool Is_even_MN, bool Is_even_K, bool Is_first, bool Is_last, bool Seq_parallel=false, typename Params>
Tri Dao's avatar
Tri Dao committed
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
inline __device__ void compute_dq_dk_dv_1colblock(const Params &params, const int bidb, const int bidh, const int n_block) {

    using Element = typename Kernel_traits::Element;
    using ElementAccum = typename Kernel_traits::ElementAccum;
    using index_t = typename Kernel_traits::index_t;

    // Shared memory.
    extern __shared__ char smem_[];

    // The thread index.
    const int tidx = threadIdx.x;

    constexpr int kBlockM = Kernel_traits::kBlockM;
    constexpr int kBlockN = Kernel_traits::kBlockN;
    constexpr int kHeadDim = Kernel_traits::kHeadDim;
    // constexpr int kNWarps = Kernel_traits::kNWarps;
    constexpr int MMA_N_SdP = kBlockN / decltype(size<1>(typename Kernel_traits::TiledMmaSdP::TiledShape_MNK{}))::value;
    constexpr int AtomLayoutMS = Kernel_traits::AtomLayoutMSdP;
    constexpr bool Double_buffer = !Kernel_traits::No_double_buffer;

452
    const BlockInfo</*Varlen=*/!Is_even_MN> binfo(params, bidb);
453
    if (n_block * kBlockN >= binfo.actual_seqlen_k) return;
Tri Dao's avatar
Tri Dao committed
454
455

    int m_block_max = cute::ceil_div(binfo.actual_seqlen_q, kBlockM);
Tri Dao's avatar
Tri Dao committed
456
457
458
    if (Is_local) {
        m_block_max = std::min(m_block_max, cute::ceil_div((n_block + 1) * kBlockN + binfo.actual_seqlen_q - binfo.actual_seqlen_k + params.window_size_left, kBlockM));
    }
Tri Dao's avatar
Tri Dao committed
459
460
461
462
463
464
465
466
467
468
469
470
471

    const index_t row_offset_q = binfo.q_offset(params.q_batch_stride, params.q_row_stride, bidb)
        + (m_block_max - 1) * kBlockM * params.q_row_stride + bidh * params.q_head_stride;
    const index_t row_offset_k = binfo.k_offset(params.k_batch_stride, params.k_row_stride, bidb)
        + n_block * kBlockN * params.k_row_stride + (bidh / params.h_h_k_ratio) * params.k_head_stride;
    const index_t row_offset_v = binfo.k_offset(params.v_batch_stride, params.v_row_stride, bidb)
        + n_block * kBlockN * params.v_row_stride + (bidh / params.h_h_k_ratio) * params.v_head_stride;
    const index_t row_offset_do = binfo.q_offset(params.do_batch_stride, params.do_row_stride, bidb)
        + (m_block_max - 1) * kBlockM * params.do_row_stride + bidh * params.do_head_stride;
    const index_t row_offset_o = binfo.q_offset(params.o_batch_stride, params.o_row_stride, bidb)
        + (m_block_max - 1) * kBlockM * params.o_row_stride + bidh * params.o_head_stride;
    const index_t row_offset_dq = binfo.q_offset(params.dq_batch_stride, params.dq_row_stride, bidb)
        + (m_block_max - 1) * kBlockM * params.dq_row_stride + bidh * params.dq_head_stride;
472
    const index_t row_offset_dq_accum = binfo.q_offset(params.seqlen_q_rounded * params.h * params.d_rounded, params.h * params.d_rounded, bidb)
473
474
475
        + ((m_block_max - 1) * kBlockM + (params.cu_seqlens_q == nullptr ? 0 : 128 * bidb)) * params.h * params.d_rounded + bidh * params.d_rounded
        // If deterministic, each thread block will do atomicAdd to a different dQ_accum buffer.
        + (!params.deterministic ? 0 : blockIdx.x * params.dq_accum_split_stride);
Tri Dao's avatar
Tri Dao committed
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
    const index_t row_offset_lse = (bidb * params.h + bidh) * params.seqlen_q
        + (m_block_max - 1) * kBlockM;
    const index_t row_offset_dpsum = (bidb * params.h + bidh) * params.seqlen_q_rounded
        + (m_block_max - 1) * kBlockM;

    Tensor gQ = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.q_ptr) + row_offset_q),
                            Shape<Int<kBlockM>, Int<kHeadDim>>{},
                            make_stride(params.q_row_stride, _1{}));
    Tensor gK = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.k_ptr) + row_offset_k),
                            Shape<Int<kBlockN>, Int<kHeadDim>>{},
                            make_stride(params.k_row_stride, _1{}));
    Tensor gV = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.v_ptr) + row_offset_v),
                            Shape<Int<kBlockN>, Int<kHeadDim>>{},
                            make_stride(params.v_row_stride, _1{}));
    Tensor gdO = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.do_ptr) + row_offset_do),
                             Shape<Int<kBlockM>, Int<kHeadDim>>{},
                             make_stride(params.do_row_stride, _1{}));
    Tensor gO = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.o_ptr) + row_offset_o),
                            Shape<Int<kBlockM>, Int<kHeadDim>>{},
495
                            make_stride(params.o_row_stride, _1{}));
Tri Dao's avatar
Tri Dao committed
496
497
498
499
500
    Tensor gdQ = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dq_ptr) + row_offset_dq),
                             Shape<Int<kBlockM>, Int<kHeadDim>>{},
                             make_stride(params.dq_row_stride, _1{}));
    Tensor gdQaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dq_accum_ptr) + row_offset_dq_accum),
                                  Shape<Int<kBlockM>, Int<kHeadDim>>{},
501
                                  make_stride(params.h * params.d_rounded, _1{}));
Tri Dao's avatar
Tri Dao committed
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
    Tensor gLSE = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.softmax_lse_ptr) + row_offset_lse),
                              Shape<Int<kBlockM>>{}, Stride<_1>{});
    Tensor gdPsum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dsoftmax_sum) + row_offset_dpsum),
                                Shape<Int<kBlockM>>{}, Stride<_1>{});

    Tensor sQ = make_tensor(make_smem_ptr(reinterpret_cast<Element *>(smem_)),
                            typename Kernel_traits::SmemLayoutQdO{});
    Tensor sQt = make_tensor(sQ.data(), typename Kernel_traits::SmemLayoutQdOtransposed{});
    Tensor sQtNoSwizzle = make_tensor(sQ.data(), typename Kernel_traits::SmemLayoutQdOtransposedNoSwizzle{});
    // Double buffer for sQ
    Tensor sdO = make_tensor(sQ.data() + (Double_buffer ? 2 : 1) * size(sQ), typename Kernel_traits::SmemLayoutQdO{});
    Tensor sdOt = make_tensor(sdO.data(), typename Kernel_traits::SmemLayoutQdOtransposed{});
    Tensor sdOtransposedNoSwizzle = make_tensor(sdO.data(),
                                                typename Kernel_traits::SmemLayoutQdOtransposedNoSwizzle{});
    Tensor sK = make_tensor(sdO.data() + size(sdO), typename Kernel_traits::SmemLayoutKV{});
    Tensor sV = make_tensor(sK.data() + size(sK), typename Kernel_traits::SmemLayoutKV{});
    Tensor sKt = make_tensor(sK.data(), typename Kernel_traits::SmemLayoutKtransposed{});
    Tensor sKtNoSwizzle = make_tensor(sK.data(), typename Kernel_traits::SmemLayoutKtransposedNoSwizzle{});
    Tensor sdS = make_tensor(!Kernel_traits::Is_V_in_regs ? sV.data() + size(sV) : sK.data() + size(sK),
                             typename Kernel_traits::SmemLayoutPdS{});
    Tensor sdSt = make_tensor(sdS.data(), typename Kernel_traits::SmemLayoutPdStransposed{});
    Tensor sdStNoSwizzle = make_tensor(sdS.data(), typename Kernel_traits::SmemLayoutPdStransposedNoSwizzle{});
    Tensor sP = make_tensor(sdS.data() + size(sdS), typename Kernel_traits::SmemLayoutPdS{});
    Tensor sPt = make_tensor(sP.data(), typename Kernel_traits::SmemLayoutPdStransposed{});
    Tensor sPtNoSwizzle = make_tensor(sP.data(), typename Kernel_traits::SmemLayoutPdStransposedNoSwizzle{});
    // sP and sdQ share the same memory so be careful
    Tensor sdQ = make_tensor(sP.data(), typename Kernel_traits::SmemLayoutdQ{});

Tri Dao's avatar
Tri Dao committed
530
531
    typename Kernel_traits::GmemTiledCopyQKV gmem_tiled_copy_QKV;
    auto gmem_thr_copy_QKV = gmem_tiled_copy_QKV.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
532
533
534
535
536
    using GmemTiledCopydO = std::conditional_t<
        Is_first,
        typename Kernel_traits::GmemTiledCopydO,
        typename Kernel_traits::GmemTiledCopyQKV
    >;
Tri Dao's avatar
Tri Dao committed
537
538
539
540
    GmemTiledCopydO gmem_tiled_copy_dO;
    auto gmem_thr_copy_dO = gmem_tiled_copy_dO.get_thread_slice(tidx);
    typename Kernel_traits::GmemTiledCopydQ gmem_tiled_copy_dQ;
    auto gmem_thr_copy_dQ = gmem_tiled_copy_dQ.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
541
542
543
544
545
    using GmemLayoutAtomdQaccum = std::conditional_t<
        !Seq_parallel,
        typename Kernel_traits::GmemTiledCopydQaccum,
        typename Kernel_traits::GmemTiledCopydQaccumAtomicAdd
    >;
Tri Dao's avatar
Tri Dao committed
546
547
    GmemLayoutAtomdQaccum gmem_tiled_copy_dQaccum;
    auto gmem_thr_copy_dQaccum = gmem_tiled_copy_dQaccum.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
548
549
550
551
552
553
554
555
556
557
558
559

    Tensor tQgQ = gmem_thr_copy_QKV.partition_S(gQ);
    Tensor tQsQ = gmem_thr_copy_QKV.partition_D(sQ);
    Tensor tdOgdO = gmem_thr_copy_dO.partition_S(gdO);
    Tensor tdOsdO = gmem_thr_copy_dO.partition_D(sdO);
    Tensor tdOgO = gmem_thr_copy_dO.partition_S(gO);
    Tensor tKgK = gmem_thr_copy_QKV.partition_S(gK);  // (KCPY, KCPY_N, KCPY_K)
    Tensor tKsK = gmem_thr_copy_QKV.partition_D(sK);
    Tensor tVgV = gmem_thr_copy_QKV.partition_S(gV);  // (VCPY, VCPY_N, VCPY_K)
    Tensor tVsV = gmem_thr_copy_QKV.partition_D(sV);
    Tensor tdQsdQ = gmem_thr_copy_dQ.partition_S(sdQ);    // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdQgdQ = gmem_thr_copy_dQ.partition_D(gdQ);
Tri Dao's avatar
Tri Dao committed
560
    Tensor tdQgdQaccum = gmem_thr_copy_dQaccum.partition_D(gdQaccum);
Tri Dao's avatar
Tri Dao committed
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
    // if (cute::thread0()) { print(tdQgdQaccum.layout()); printf("\n"); }
    // __syncthreads();
    // if (blockIdx.x == 0 && blockIdx.y == 0 && blockIdx.z == 0 && tidx < 64) {
    //     printf("tidx = %d, tdQgdQaccum = 0x%p\n", tidx, tdQgdQaccum.data());
    // }

    typename Kernel_traits::TiledMmaSdP tiled_mma_sdp;
    auto thr_mma_sdp = tiled_mma_sdp.get_thread_slice(tidx);
    Tensor tSrQ = thr_mma_sdp.partition_fragment_A(sQ);         // (MMA,MMA_N,MMA_K)
    Tensor tSrK = thr_mma_sdp.partition_fragment_B(sK);         // (MMA,MMA_N,MMA_K)
    Tensor tdPrdO = thr_mma_sdp.partition_fragment_A(sdO);      // (MMA,MMA_N,MMA_K)
    Tensor tdPrV = thr_mma_sdp.partition_fragment_B(sV);        // (MMA,MMA_N,MMA_K)

    typename Kernel_traits::TiledMmadKV tiled_mma_dkv;
    auto thr_mma_dkv = tiled_mma_dkv.get_thread_slice(tidx);
    Tensor tdKrdSt = thr_mma_dkv.partition_fragment_A(sdStNoSwizzle); // (MMA, MMA_N, MMA_N)
    Tensor tdKrQt = thr_mma_dkv.partition_fragment_B(sQtNoSwizzle);   // (MMA, MMA_K, MMA_N)
    Tensor tdVrPt = thr_mma_dkv.partition_fragment_A(sPtNoSwizzle);   // (MMA, MMA_N, MMA_N)
    Tensor tdVrdO = thr_mma_dkv.partition_fragment_B(sdOtransposedNoSwizzle); // (MMA, MMA_K, MMA_N)

    typename Kernel_traits::TiledMmadQ tiled_mma_dq;
    auto thr_mma_dq = tiled_mma_dq.get_thread_slice(tidx);
    Tensor tdQrdS = thr_mma_dq.partition_fragment_A(sdS);                      // (MMA, MMA_N, MMA_N)
    Tensor tdQrKt = thr_mma_dq.partition_fragment_B(sKtNoSwizzle);    // (MMA, MMA_K, MMA_N)

    Tensor acc_dk = partition_fragment_C(tiled_mma_dkv, Shape<Int<kBlockN>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
    Tensor acc_dv = partition_fragment_C(tiled_mma_dkv, Shape<Int<kBlockN>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K

    //
    // Copy Atom retiling
    //

Tri Dao's avatar
Tri Dao committed
593
594
    auto smem_tiled_copy_QdO = make_tiled_copy_A(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_sdp);
    auto smem_thr_copy_QdO = smem_tiled_copy_QdO.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
595
596
597
598
    Tensor tSsQ = smem_thr_copy_QdO.partition_S(sQ);
    Tensor tdPsdO = smem_thr_copy_QdO.partition_S(sdO);

    // auto smem_thr_copy_KV = make_tiled_copy_B(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_sdp).get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
599
600
    auto smem_tiled_copy_KV = make_tiled_copy_B_warpcontiguousN<MMA_N_SdP>(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_sdp);
    auto smem_thr_copy_KV = smem_tiled_copy_KV.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
601
602
603
604
605
606
607
608
    Tensor tSsK = smem_thr_copy_KV.partition_S(sK);
    // if (cute::thread(0, 0) && n_block == 0) { printf("sK layout: "); print(sK.layout()); printf("\n"); }
    // if (cute::thread(0, 0) && n_block == 0) { print(tSsK.layout()); printf("\n"); }
    Tensor tdPsV = smem_thr_copy_KV.partition_S(sV);

    // Partition sP and sdS to match the accumulator partitioning
    // This has to be tiled_mma_sdp, not tiled_mma_dkv
    // auto smem_thr_copy_PdS = make_tiled_copy_C(typename Kernel_traits::SmemCopyAtomPdS{}, tiled_mma_sdp).get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
609
610
    auto smem_tiled_copy_PdS = make_tiled_copy_C_warpcontiguousN<MMA_N_SdP>(typename Kernel_traits::SmemCopyAtomPdS{}, tiled_mma_sdp);
    auto smem_thr_copy_PdS = smem_tiled_copy_PdS.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
611
612
613
614
615
616
617
618
    Tensor tPsP = smem_thr_copy_PdS.partition_D(sP);      // ((Atom,AtomNum),PIPE_M,PIPE_N)
    // if (cute::thread(0, 0) && n_block == 0) { printf("sP layout: "); print(sP.layout()); printf("\n"); }
    // if (cute::thread(0, 0) && n_block == 0) { print(tPsP.layout()); printf("\n"); }
    // if (n_block == 0 && blockIdx.x == 0 && blockIdx.y == 0 && tidx < 64) {
    //     printf("tidx=%d, tPsP = 0x%p\n", tidx, tPsP.data());
    // }
    Tensor tdSsdS = smem_thr_copy_PdS.partition_D(sdS);   // ((Atom,AtomNum),PIPE_M,PIPE_N)

Tri Dao's avatar
Tri Dao committed
619
620
    auto smem_tiled_copy_PdSt = make_tiled_copy_A(typename Kernel_traits::SmemCopyAtomTransposed{}, tiled_mma_dkv);
    auto smem_thr_copy_PdSt = smem_tiled_copy_PdSt.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
621
622
623
    Tensor tdVsPt = smem_thr_copy_PdSt.partition_S(sPt);
    Tensor tdKsdSt = smem_thr_copy_PdSt.partition_S(sdSt);

Tri Dao's avatar
Tri Dao committed
624
625
    auto smem_tiled_copy_QdOt = make_tiled_copy_B(typename Kernel_traits::SmemCopyAtomTransposed{}, tiled_mma_dkv);
    auto smem_thr_copy_QdOt = smem_tiled_copy_QdOt.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
626
627
628
    Tensor tdVsdOt = smem_thr_copy_QdOt.partition_S(sdOt);
    Tensor tdKsQt = smem_thr_copy_QdOt.partition_S(sQt);

Tri Dao's avatar
Tri Dao committed
629
630
    auto smem_tiled_copy_dS = make_tiled_copy_A(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_dq);
    auto smem_thr_copy_dS = smem_tiled_copy_dS.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
631
632
    Tensor tdQsdS = smem_thr_copy_dS.partition_S(sdS);

Tri Dao's avatar
Tri Dao committed
633
634
    auto smem_tiled_copy_Kt = make_tiled_copy_B(typename Kernel_traits::SmemCopyAtomTransposed{}, tiled_mma_dq);
    auto smem_thr_copy_Kt = smem_tiled_copy_Kt.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
635
636
    Tensor tdQsKt = smem_thr_copy_Kt.partition_S(sKt);

Tri Dao's avatar
Tri Dao committed
637
638
    auto smem_tiled_copy_dQ = make_tiled_copy_C(typename Kernel_traits::SmemCopyAtomdQ{}, tiled_mma_dq);
    auto smem_thr_copy_dQ = smem_tiled_copy_dQ.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
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
    Tensor taccdQsdQ = smem_thr_copy_dQ.partition_D(sdQ);  // ((Atom,AtomNum),PIPE_M,PIPE_N)

    //
    // PREDICATES
    //

    Tensor cQ = make_identity_tensor(make_shape(size<0>(sQ), size<1>(sQ)));    // (BLK_M,BLK_K) -> (blk_m,blk_k)
    Tensor cKV = make_identity_tensor(make_shape(size<0>(sK), size<1>(sK)));    // (BLK_N,BLK_K) -> (blk_n,blk_k)
    Tensor tQcQ = gmem_thr_copy_QKV.partition_D(cQ);
    Tensor tKVcKV = gmem_thr_copy_QKV.partition_D(cKV);

    // Allocate predicate tensors for k
    Tensor tQpQ = make_tensor<bool>(make_shape(size<2>(tQsQ)));
    Tensor tKVpKV = make_tensor<bool>(make_shape(size<2>(tKsK)));

    // Set predicates for k bounds
    if (!Is_even_K) {
        #pragma unroll
        for (int k = 0; k < size(tQpQ); ++k) { tQpQ(k) = get<1>(tQcQ(0, 0, k)) < params.d; }
        #pragma unroll
        for (int k = 0; k < size(tKVpKV); ++k) { tKVpKV(k) = get<1>(tKVcKV(0, 0, k)) < params.d; }
    }

    // Prologue

    // We'll advance gdQ and gdQaccum before the 1st read/write.
    tdQgdQ.data() = tdQgdQ.data() + kBlockM * params.dq_row_stride;
666
    tdQgdQaccum.data() = tdQgdQaccum.data() + kBlockM * params.h * params.d_rounded;
Tri Dao's avatar
Tri Dao committed
667
668

    int m_block = m_block_max - 1;
Tri Dao's avatar
Tri Dao committed
669
670
671
672
    int m_block_min = (!Is_causal && !Is_local)
        ? 0
        : std::max(0, (n_block * kBlockN + binfo.actual_seqlen_q - binfo.actual_seqlen_k - params.window_size_right) / kBlockM);
    // If not local, we're guaranteed that m_block_min <= m_block:
673
674
675
676
677
678
    // We checked earlier that n_block * kBlockN < actual_seqlen_k, so in the causal case,
    // n_block * kBlockN + binfo.actual_seqlen_q - binfo.actual_seqlen_k < actual_seqlen_q.
    // So m_block_min <= (actual_seqlen_q - 1) / kBlockM.
    // Recall that m_block_max = cute::ceil_div(binfo.actual_seqlen_q, kBlockM) = (actual_seqlen_q + kBlockM - 1) / kBlockM.
    // So m_block_m - 1 = (actual_seqlen_q - 1) / kBlockM.
    // We conclude that m_block_min <= m_block, so we will always have at least 1 iteration of the for loop.
Tri Dao's avatar
Tri Dao committed
679
680
681
682
    // However, if local, then this possible to have some blocks of K & V not attending to any query.
    // We might need to exit early and write 0 to dK and dV for those blocks.
    // Otherwise we get wrong result for the case where we don't enter the for loop.
    // And we might read OOB elements from gQ and gdO.
683
684
    // This also covers the case where actual_seqlen_q == 0
    if ((Is_local || !Is_even_MN) && m_block < m_block_min) {
Tri Dao's avatar
Tri Dao committed
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
        const index_t row_offset_dk = binfo.k_offset(params.dk_batch_stride, params.dk_row_stride, bidb)
          + n_block * kBlockN * params.dk_row_stride + bidh * params.dk_head_stride;
        const index_t row_offset_dv = binfo.k_offset(params.dv_batch_stride, params.dv_row_stride, bidb)
          + n_block * kBlockN * params.dv_row_stride + bidh * params.dv_head_stride;
        Tensor gdK = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dk_ptr) + row_offset_dk),
                                 Shape<Int<kBlockN>, Int<kHeadDim>>{},
                                 make_stride(params.dk_row_stride, _1{}));
        Tensor gdV = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dv_ptr) + row_offset_dv),
                                 Shape<Int<kBlockN>, Int<kHeadDim>>{},
                                 make_stride(params.dv_row_stride, _1{}));
        typename Kernel_traits::GmemTiledCopydKV gmem_tiled_copy_dKV;
        auto gmem_thr_copy_dKV = gmem_tiled_copy_dKV.get_thread_slice(tidx);
        Tensor tdKgdK = gmem_thr_copy_dKV.partition_D(gdK);
        Tensor tdVgdV = gmem_thr_copy_dKV.partition_D(gdV);
        Tensor tdKrdK = make_tensor<Element>(shape(tdKgdK));
        Tensor tdVrdV = make_tensor<Element>(shape(tdVgdV));
        clear(tdKrdK);
        clear(tdVrdV);
        Tensor cdKV = make_identity_tensor(make_shape(size<0>(gdK), size<1>(gdK)));    // (BLK_N,BLK_K) -> (blk_n,blk_k)
        Tensor tdKVcdKV = gmem_thr_copy_dKV.partition_D(cdKV);
        Tensor tdKVpdKV = make_tensor<bool>(make_shape(size<2>(tdKgdK)));
        #pragma unroll
        for (int k = 0; k < size(tdKVpdKV); ++k) { tdKVpdKV(k) = get<1>(tdKVcdKV(0, 0, k)) < params.d; }
        // Clear_OOB_K must be false since we don't want to write zeros to gmem
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
            gmem_tiled_copy_dKV, tdKrdK, tdKgdK, tdKVcdKV, tdKVpdKV, binfo.actual_seqlen_k - n_block * kBlockN
        );
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
            gmem_tiled_copy_dKV, tdVrdV, tdVgdV, tdKVcdKV, tdKVpdKV, binfo.actual_seqlen_k - n_block * kBlockN
        );
        return;
    }
Tri Dao's avatar
Tri Dao committed
717
718
719
720
721
722
723

    if (Double_buffer && m_block % 2 == 1) {  // Double buffer for sQ
        tQsQ.data() = tQsQ.data() + size(sQ);
        tSsQ.data() = tSsQ.data() + size(sQ);
        tdKsQt.data() = tdKsQt.data() + size(sQ);
    }

724
    if ((!Is_first && !Seq_parallel) || params.deterministic) { __syncthreads(); }
Tri Dao's avatar
Tri Dao committed
725
726
727

    if (Kernel_traits::Is_V_in_regs) {
        // Clear the smem tiles to account for predicated off loads
728
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
729
            gmem_tiled_copy_QKV, tVgV, tVsV, tKVcKV, tKVpKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
730
731
732
733
734
735
736
737
        );
        flash::cp_async_fence();
    }

    Tensor tdOrdO = make_fragment_like(tdOgdO);
    Tensor tdOrO = make_fragment_like(tdOgO);
    if (!Is_first) {
        // Clear the smem tiles to account for predicated off loads
738
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
739
            gmem_tiled_copy_dO, tdOgdO, tdOsdO, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
740
741
        );
    } else {
742
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
743
            gmem_tiled_copy_dO, tdOgdO, tdOrdO, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
744
        );
745
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
746
            gmem_tiled_copy_dO, tdOgO, tdOrO, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
747
748
        );
    }
749
    flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
750
        gmem_tiled_copy_QKV, tQgQ, tQsQ, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
751
752
753
754
755
756
757
758
759
760
761
    );

    Tensor caccS = make_identity_tensor(Shape<Int<kBlockM>, Int<kBlockN>>{});    // (BLK_M,BLK_N) -> (blk_m,blk_n)
    Tensor taccScS = thr_mma_sdp.partition_C(caccS);                           // (MMA,MMA_N,MMA_N)
    static_assert(decltype(size<0>(taccScS))::value == 4);
    // Convert to ((2, 2), MMA_N, MMA_N) then take only the row indices.
    Tensor taccScS_row = logical_divide(taccScS, Shape<_2>{})(make_coord(0, _), _, 0);
    Tensor lse = make_tensor<ElementAccum>(Shape<Int<decltype(size(taccScS_row))::value>>{});
    #pragma unroll
    for (int mi = 0; mi < size(lse); ++mi) {
        const int row = get<0>(taccScS_row(mi));
762
        lse(mi) = Is_even_MN || row < binfo.actual_seqlen_q - m_block * kBlockM ? gLSE(row) : INFINITY;
Tri Dao's avatar
Tri Dao committed
763
    }
764
765
766
767
    // We want LSE = inf if the row is OOB. In that case Q would be zero, K would be zero,
    // and scores would be zero. With LSE = 0, probs will be all 1's, and when we multiply
    // with V (which would be zero), we're fine. However, with ALiBi, we might modify these
    // scores, and probs can become NaN. Instead if we set LSE = inf for OOB rows, probs are always 0.
Tri Dao's avatar
Tri Dao committed
768
769

    // Tensor tKrK = make_fragment_like(tKsK);
Tri Dao's avatar
Tri Dao committed
770
771
    // // cute::copy(gmem_tiled_copy_QKV, tKgK(_, _, _, 0), tKrK);
    // cute::copy(gmem_tiled_copy_QKV, tKgK, tKrK);
Tri Dao's avatar
Tri Dao committed
772
773
    // // if (cute::thread(1, 0)) { print(tKrK); }

774
    flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
775
        gmem_tiled_copy_QKV, tKgK, tKsK, tKVcKV, tKVpKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
776
777
    );
    if (!Kernel_traits::Is_V_in_regs) {
778
        flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
779
            gmem_tiled_copy_QKV, tVgV, tVsV, tKVcKV, tKVpKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
780
781
782
783
784
785
        );
    }
    flash::cp_async_fence();

    // if (cute::thread0()) { print(tdOgdO.layout()); printf("\n"); print(tdOrdO); print(tdOrO); }
    if (Is_first) {
Tri Dao's avatar
Tri Dao committed
786
        cute::copy(tdOrdO, tdOsdO);
787
        dot_do_o<Kernel_traits::kGmemThreadsPerRow>(tdOrdO, tdOrO, gdPsum,
Tri Dao's avatar
Tri Dao committed
788
789
790
791
792
793
794
795
                                                    Kernel_traits::kNThreads / (Kernel_traits::kGmemThreadsPerRow), params.p_dropout);
    }

    if (Kernel_traits::Is_V_in_regs) {
        cute::cp_async_wait<1>();
        __syncthreads();
        Tensor tdPrV_copy_view = smem_thr_copy_KV.retile_D(tdPrV);
        CUTE_STATIC_ASSERT_V(size<1>(tdPsV) == size<1>(tdPrV_copy_view));            // M
Tri Dao's avatar
Tri Dao committed
796
        cute::copy(smem_tiled_copy_KV, tdPsV, tdPrV_copy_view);
Tri Dao's avatar
Tri Dao committed
797
798
    }

799
800
    auto seed = params.rng_state[0];
    auto offset = params.rng_state[1] + (bidb * params.h + bidh) * 32 + tidx % 32;
Tri Dao's avatar
Tri Dao committed
801
802
803
804

    clear(acc_dv);
    clear(acc_dk);

805
    float alibi_slope = !Has_alibi ? 0.0f : reinterpret_cast<float *>(params.alibi_slopes_ptr)[bidb * params.alibi_slopes_batch_stride + bidh] / params.scale_softmax;
806

Tri Dao's avatar
Tri Dao committed
807
808
809
810
811
812
813
814
815
816
817
818
819
820
    for (; m_block >= m_block_min; --m_block) {
        Tensor acc_s = partition_fragment_C(tiled_mma_sdp, Shape<Int<kBlockM>, Int<kBlockN>>{});  // (MMA=4, MMA_N, MMA_N)
        clear(acc_s);
        cute::cp_async_wait<0>();
        __syncthreads();

        Tensor dP_sum = make_fragment_like(lse);
        #pragma unroll
        for (int mi = 0; mi < size(lse); ++mi) { dP_sum(mi) = gdPsum(get<0>(taccScS_row(mi))); }

        // if (cute::thread0()) { print(sK); }
        // Tensor tSrK_copy_view = smem_thr_copy_KV.retile_D(tSrK);
        // #pragma unroll
        // for (int k = 0; k < size<2>(tSrK_copy_view); ++k) {
Tri Dao's avatar
Tri Dao committed
821
        //     cute::copy(smem_tiled_copy_KV, tSsK(_, _, k), tSrK_copy_view(_, _, k));
Tri Dao's avatar
Tri Dao committed
822
823
        // }
        // if (cute::thread0()) { print(tSrK); }
Tri Dao's avatar
Tri Dao committed
824
825
        flash::gemm(acc_s, tSrQ, tSrK, tSsQ, tSsK, tiled_mma_sdp,
                    smem_tiled_copy_QdO, smem_tiled_copy_KV, smem_thr_copy_QdO, smem_thr_copy_KV);
Tri Dao's avatar
Tri Dao committed
826
827
828
829

        // Reshape acc_s from (MMA=4, MMA_N, MMA_N) to (col=(2, MMA_N), row=(2, MMA_N))
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
        // if (cute::thread(32, 0)) { print(scores); }
830
831

        if (Has_alibi) {
832
            flash::apply_alibi<Is_causal>(
833
834
835
836
837
838
839
840
841
                scores, 
                n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
                binfo.actual_seqlen_k, 
                m_block * kBlockM + get<0>(taccScS_row(0)),
                binfo.actual_seqlen_q, 
                AtomLayoutMS * 16,
                alibi_slope
            );
        }
842

843
844
845
846
847
848
849
        // TD [2023-07-29]: I was thinking that we don't need to mask out the elements beyond
        // actual_seqlen_k, because acc_s would be some finite value for those indices.
        // In the end when we multiply with K to get dQ, the corresponding values of K would be 0,
        // so the result would still be correct.
        // However, it's possible that the values in acc_s are so large that they overflow
        // when we multiply with dP and convert to fp16, resulting in Inf in dS and NaNs in dQ.
        // So we need to mask out the elements beyond actual_seqlen_k.
Tri Dao's avatar
Tri Dao committed
850
        if (!Is_causal && !Is_local) {
851
852
853
854
            if (!Is_even_MN && (n_block + 1) * kBlockN >= binfo.actual_seqlen_k) {
                flash::apply_mask(scores, binfo.actual_seqlen_k,
                                  n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16);
            }
Tri Dao's avatar
Tri Dao committed
855
        } else if (Is_causal) {
856
            // Putting this causal masking right after acc_s is *much* slower for some reason.
857
858
            // TD [2023-08-16]: We need the 2nd condition because if seqlen_q is long and seqlen_k is short
            // (e.g., 256 and 2), the 2nd block of seqlen_q (from 128 to 255), we're not doing causal masking.
859
            // But we still want to mask out elements beyond actual_seqlen_k.
860
            if (m_block * kBlockM < (n_block + 1) * kBlockN + binfo.actual_seqlen_q - binfo.actual_seqlen_k
861
                || (!Is_even_MN && (n_block + 1) * kBlockN >= binfo.actual_seqlen_k)) {
862
                flash::apply_mask_causal(scores, n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
863
864
                                         binfo.actual_seqlen_k, m_block * kBlockM + get<0>(taccScS_row(0)),
                                         binfo.actual_seqlen_q,
865
866
867
                                         // binfo.actual_seqlen_k, m_block * kBlockM + (tidx / 32) % AtomLayoutMS * 16 + (tidx % 32) / 4,
                                         AtomLayoutMS * 16);
            }
Tri Dao's avatar
Tri Dao committed
868
869
870
871
872
873
874
875
876
877
        } else if (Is_local) {
            if (m_block * kBlockM < (n_block + 1) * kBlockN + binfo.actual_seqlen_q - binfo.actual_seqlen_k - params.window_size_right
                || (m_block + 1) * kBlockM >= n_block * kBlockN + binfo.actual_seqlen_q - binfo.actual_seqlen_k + params.window_size_left
                || (!Is_even_MN && (n_block + 1) * kBlockN >= binfo.actual_seqlen_k)) {
                flash::apply_mask_local(scores, n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
                                        binfo.actual_seqlen_k, m_block * kBlockM + get<0>(taccScS_row(0)),
                                        binfo.actual_seqlen_q, AtomLayoutMS * 16,
                                        params.window_size_left, params.window_size_right);
            }

Tri Dao's avatar
Tri Dao committed
878
        }
879

Tri Dao's avatar
Tri Dao committed
880
881
882
883
        // if (cute::thread(32, 0)) { print(scores); }
        // Compute the exponential value.
        flash::scale_apply_exp2</*scale_max=*/false>(scores, lse, params.scale_softmax_log2);
        if (Is_dropout) {
884
885
            int warp_id = tidx / 32;
            int block_row_idx = m_block * (kBlockM / 16) + warp_id % AtomLayoutMS;
Tri Dao's avatar
Tri Dao committed
886
887
            // Need col to be multiples of 32, since we're doing dropout with block of 16 x 32
            static_assert(MMA_N_SdP % 2 == 0);
888
            int block_col_idx = n_block * (kBlockN / 32) + (warp_id / AtomLayoutMS) * (MMA_N_SdP / 2);
Tri Dao's avatar
Tri Dao committed
889
890
891
892
893
894
895
896
897
898
899
900
901
902
            Tensor scores_dropped = make_tensor(scores.data(), flash::convert_layout_rowcol_Aregs<Kernel_traits::TiledMmaSdP>(scores.layout()));
            flash::apply_dropout</*encode_dropout_in_sign_bit=*/true>(
                scores_dropped, params.p_dropout_in_uint8_t, seed, offset,
                block_row_idx, block_col_idx, AtomLayoutMS
            );
        }
        // Convert scores from fp32 to fp16/bf16
        Tensor rP = !Is_dropout
            ? flash::convert_type<Element>(scores)
            : flash::convert_type_relu<Element>(scores);
        // Reshape rP from (nrow=(2, MMA_N), ncol=(2, MMA_N)) to ((2, 2, 2), MMA_N, MMA_N / 2)
        // if using m16n8k16 or ((2, 2, 1), MMA_N, MMA_N) if using m16n8k8.
        Tensor tPrP = make_tensor(rP.data(), flash::convert_layout_rowcol_Aregs<Kernel_traits::TiledMmaSdP>(rP.layout()));
        Tensor tPaP = smem_thr_copy_PdS.retile_S(tPrP);     // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
903
        cute::copy(smem_tiled_copy_PdS, tPaP, tPsP);
Tri Dao's avatar
Tri Dao committed
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
        // if (cute::thread0()) { print(tPaP); }
        // __syncthreads();
        // if (cute::thread0()) { print(sP); }

        Tensor acc_dp = partition_fragment_C(tiled_mma_sdp, Shape<Int<kBlockM>, Int<kBlockN>>{});  // (MMA=4, MMA_N, MMA_N)
        CUTE_STATIC_ASSERT_V(size<0>(acc_dp) == size<0>(acc_s));                     // MMA
        CUTE_STATIC_ASSERT_V(size<1>(acc_dp) == size<1>(acc_s));                     // MMA
        CUTE_STATIC_ASSERT_V(size<2>(acc_dp) == size<2>(acc_s));                     // MMA

        clear(acc_dp);
        // Tensor acc_dp_reshaped = make_tensor(acc_dp.data(), flash::convert_layout_acc_rowcol(acc_dp.layout()));
        // #pragma unroll
        // for (int mi = 0; mi < size<0>(acc_dp_reshaped); ++mi) {
        //     #pragma unroll
        //     for (int ni = 0; ni < size<1>(acc_dp_reshaped); ++ni) {
        //         acc_dp_reshaped(mi, ni) = -dP_sum(mi);
        //     }
        // }

        // if (cute::thread0()) { print(dP_sum); }

        flash::gemm</*A_in_regs=*/false, /*B_in_regs=*/Kernel_traits::Is_V_in_regs>(
Tri Dao's avatar
Tri Dao committed
926
927
            acc_dp, tdPrdO, tdPrV, tdPsdO, tdPsV, tiled_mma_sdp,
            smem_tiled_copy_QdO, smem_tiled_copy_KV, smem_thr_copy_QdO, smem_thr_copy_KV
Tri Dao's avatar
Tri Dao committed
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
        );

        // Reshape acc_dp from (MMA=4, MMA_N, MMA_N) to (col=(2, MMA_N), row=(2, MMA_N))
        Tensor dS = make_tensor(acc_dp.data(), scores.layout());
        auto pointwise_mult = [](float p, float dp, float d) {
            return p * (!Is_dropout || p >= 0 ? dp - d : d);
        };
        #pragma unroll
        for (int mi = 0; mi < size<0>(dS); ++mi) {
            #pragma unroll
            for (int ni = 0; ni < size<1>(dS); ++ni) {
                dS(mi, ni) = pointwise_mult(scores(mi, ni), dS(mi, ni), dP_sum(mi));
            }
        }
        // if (cute::thread0()) { print(dS); }

        Tensor acc_dq = partition_fragment_C(tiled_mma_dq, Shape<Int<kBlockM>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
945
        tdQgdQaccum.data() = tdQgdQaccum.data() + (-int(kBlockM * params.h * params.d_rounded));
Tri Dao's avatar
Tri Dao committed
946
947
948
949
950
951
952
953
        if (Is_first || Seq_parallel) {
            clear(acc_dq);
        } else {
            // Reshape acc_dq from (4, 1, 2) to (4, 2, 1) to write to gdQaccum
            Tensor acc_dq_reshaped = make_tensor(acc_dq.data(),
                                                 make_layout(get<0>(acc_dq.layout()),
                                                             get<2>(acc_dq.layout()),
                                                             get<1>(acc_dq.layout())));
Tri Dao's avatar
Tri Dao committed
954
            cute::copy(gmem_tiled_copy_dQaccum, tdQgdQaccum, acc_dq_reshaped);
Tri Dao's avatar
Tri Dao committed
955
956
957
958
959
960
961
962
963
        }

        if (Double_buffer && m_block > m_block_min) {
            // Double buffer for sQ
            const int sQ_offset = m_block % 2 == 0 ? size(sQ) : -size(sQ);
            tQsQ.data() = tQsQ.data() + sQ_offset;
            tSsQ.data() = tSsQ.data() + sQ_offset;
            // Advance gQ
            tQgQ.data() = tQgQ.data() + (-int(kBlockM * params.q_row_stride));
Tri Dao's avatar
Tri Dao committed
964
            flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_QKV, tQgQ, tQsQ, tQcQ, tQpQ);
Tri Dao's avatar
Tri Dao committed
965
966
967
968
969
970
971
972
            flash::cp_async_fence();
        }

        Tensor dS_reshaped = make_tensor(dS.data(), acc_dp.layout());
        // Convert dS from fp32 to fp16
        Tensor tdSrdS = flash::convert_type<Element>(dS_reshaped);
        // if (cute::thread0()) { print(tPrP); }
        Tensor tdSadS = smem_thr_copy_PdS.retile_S(tdSrdS);                                          // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
973
        cute::copy(smem_tiled_copy_PdS, tdSadS, tdSsdS);
Tri Dao's avatar
Tri Dao committed
974
975
976
977
978
979
980
        __syncthreads();

        // Layout p_l = tPrP.layout();
        // Tensor tdVrPt = make_tensor(tPrP.data(), make_layout(get<0>(p_l), get<2>(p_l), get<1>(p_l)));
        // flash::gemm_A_in_regs(acc_dv, tdVrPt, tdVrdO, tdVsdOt, tiled_mma_dkv, smem_thr_copy_QdOt);
        // Tensor tdKrdSt = make_tensor(tdSrdS.data(), tdVrPt.layout());
        // flash::gemm_A_in_regs(acc_dk, tdKrdSt, tdKrQt, tdKsQt, tiled_mma_dkv, smem_thr_copy_QdOt);
Tri Dao's avatar
Tri Dao committed
981
982
        flash::gemm(acc_dv, tdVrPt, tdVrdO, tdVsPt, tdVsdOt, tiled_mma_dkv,
                    smem_tiled_copy_PdSt, smem_tiled_copy_QdOt, smem_thr_copy_PdSt, smem_thr_copy_QdOt);
Tri Dao's avatar
Tri Dao committed
983
984
985
986
987
988
989
990
991
992
        // if (cute::thread0() && n_block == 0 && m_block == 0) { print(tdVrPt); }
        // if (cute::thread0()) { print(acc_dv); }

        __syncthreads(); // Need syncthreads since we're writing to the same sdO location

        if (m_block > m_block_min) {
            // Advance gdO
            tdOgdO.data() = tdOgdO.data() + (-int(kBlockM * params.do_row_stride));
            if (Is_first) {
                tdOgO.data() = tdOgO.data() + (-int(kBlockM * params.o_row_stride));
Tri Dao's avatar
Tri Dao committed
993
994
                flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_dO, tdOgdO, tdOrdO, tQcQ, tQpQ);
                flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_dO, tdOgO, tdOrO, tQcQ, tQpQ);
Tri Dao's avatar
Tri Dao committed
995
            } else {
Tri Dao's avatar
Tri Dao committed
996
                flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_dO, tdOgdO, tdOsdO, tQcQ, tQpQ);
Tri Dao's avatar
Tri Dao committed
997
998
999
1000
                flash::cp_async_fence();
            }
        }

Tri Dao's avatar
Tri Dao committed
1001
1002
        flash::gemm(acc_dq, tdQrdS, tdQrKt, tdQsdS, tdQsKt, tiled_mma_dq,
                    smem_tiled_copy_dS, smem_tiled_copy_Kt, smem_thr_copy_dS, smem_thr_copy_Kt);
Tri Dao's avatar
Tri Dao committed
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
        // if (cute::thread0()) { print(acc_dq); }

        if (m_block > m_block_min) {
            gLSE.data() = gLSE.data() + (-int(kBlockM));
            #pragma unroll
            for (int mi = 0; mi < size(lse); ++mi) { lse(mi) = gLSE(get<0>(taccScS_row(mi))); }
            gdPsum.data() = gdPsum.data() + (-int(kBlockM));
        }

        if (!Is_last) {
            // Reshape acc_dq from (4, 1, 2) to (4, 2, 1) to write to gdQaccum
            Tensor acc_dq_reshaped = make_tensor(acc_dq.data(),
                                                 make_layout(get<0>(acc_dq.layout()),
                                                             get<2>(acc_dq.layout()),
                                                             get<1>(acc_dq.layout())));
            if (!Seq_parallel) {
Tri Dao's avatar
Tri Dao committed
1019
                cute::copy(gmem_tiled_copy_dQaccum, acc_dq_reshaped, tdQgdQaccum);
Tri Dao's avatar
Tri Dao committed
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
            } else {
                // if (cute::thread0()) { print(acc_dq.layout()); printf("\n"); print(acc_dq_reshaped.layout()); printf("\n"); print(tdQgdQaccum.layout()); printf("\n"); }
                CUTE_STATIC_ASSERT_V(size(acc_dq) == size(tdQgdQaccum));
                #pragma unroll
                for (int i = 0; i < size(acc_dq); ++i) { atomicAdd(&tdQgdQaccum(i), acc_dq(i)); }
            }
        } else {
            #pragma unroll
            for (int i = 0; i < size(acc_dq); ++i) { acc_dq(i) *= params.scale_softmax_rp_dropout; }
            // Convert acc_dq from fp32 to fp16
            Tensor rdQ = flash::convert_type<Element>(acc_dq);
            Tensor taccdQrdQ = smem_thr_copy_dQ.retile_S(rdQ);  // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
1032
            cute::copy(smem_tiled_copy_dQ, taccdQrdQ, taccdQsdQ);
Tri Dao's avatar
Tri Dao committed
1033
1034
        }

Tri Dao's avatar
Tri Dao committed
1035
1036
        flash::gemm(acc_dk, tdKrdSt, tdKrQt, tdKsdSt, tdKsQt, tiled_mma_dkv,
                    smem_tiled_copy_PdSt, smem_tiled_copy_QdOt, smem_thr_copy_PdSt, smem_thr_copy_QdOt);
Tri Dao's avatar
Tri Dao committed
1037
1038
1039
1040
1041
1042
1043
1044
        // if (cute::thread0()) { print(acc_dk); }
        if (Double_buffer) {  // Double buffer for sQ
            tdKsQt.data() = tdKsQt.data() + (m_block % 2 == 0 ? size(sQ) : -size(sQ));
        }
        if (!Double_buffer && m_block > m_block_min) {
            __syncthreads();
            // Advance gQ
            tQgQ.data() = tQgQ.data() + (-int(kBlockM * params.q_row_stride));
Tri Dao's avatar
Tri Dao committed
1045
            flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_QKV, tQgQ, tQsQ, tQcQ, tQpQ);
Tri Dao's avatar
Tri Dao committed
1046
1047
1048
1049
            flash::cp_async_fence();
        }

        if (Is_first && m_block > m_block_min) {
Tri Dao's avatar
Tri Dao committed
1050
            cute::copy(tdOrdO, tdOsdO);
1051
            dot_do_o<Kernel_traits::kGmemThreadsPerRow>(tdOrdO, tdOrO, gdPsum,
Tri Dao's avatar
Tri Dao committed
1052
1053
1054
1055
1056
1057
                                                        Kernel_traits::kNThreads / (Kernel_traits::kGmemThreadsPerRow), params.p_dropout);
        }

        if (Is_last) {
            __syncthreads();
            Tensor tdQrdQ = make_tensor<Element>(shape(tdQgdQ));
Tri Dao's avatar
Tri Dao committed
1058
            cute::copy(gmem_tiled_copy_dQ, tdQsdQ, tdQrdQ);
Tri Dao's avatar
Tri Dao committed
1059
1060
1061
1062
1063
            tdQgdQ.data() = tdQgdQ.data() + (-int(kBlockM * params.dq_row_stride));
            Tensor cdQ = make_identity_tensor(Shape<Int<kBlockM>, Int<kHeadDim>>{});    // (BLK_M,BLK_K) -> (blk_m,blk_k)
            Tensor tdQcdQ = gmem_thr_copy_dQ.partition_D(cdQ);
            #pragma unroll
            for (int m = 0; m < size<1>(tdQgdQ); ++m) {
1064
                if (Is_even_MN || get<0>(tdQcdQ(0, m, 0)) < binfo.actual_seqlen_q - m_block * kBlockM) {
Tri Dao's avatar
Tri Dao committed
1065
                    cute::copy(gmem_tiled_copy_dQ, tdQrdQ(_, m, _), tdQgdQ(_, m, _));
Tri Dao's avatar
Tri Dao committed
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
                }
            }
        }

    }

    // Epilogue

    if (Is_dropout) {
        #pragma unroll
        for (int i = 0; i < size(acc_dv); ++i) { acc_dv(i) *= params.rp_dropout; }
    }
    #pragma unroll
    for (int i = 0; i < size(acc_dk); ++i) { acc_dk(i) *= params.scale_softmax_rp_dropout; }

    // Convert acc_dv from fp32 to fp16
    Tensor rdK = flash::convert_type<Element>(acc_dk);
    Tensor rdV = flash::convert_type<Element>(acc_dv);

    Tensor sdK = make_tensor(sK.data(), typename Kernel_traits::SmemLayoutdKV{});  // (SMEM_N, SMEM_K)
    Tensor sdV = make_tensor(sdK.data() + size(sdK), typename Kernel_traits::SmemLayoutdKV{}); // (SMEM_N, SMEM_K)

    // Partition sdV and sdK to match the accumulator partitioning
Tri Dao's avatar
Tri Dao committed
1089
1090
    auto smem_tiled_copy_dKV = make_tiled_copy_C(typename Kernel_traits::SmemCopyAtomdKV{}, tiled_mma_dkv);
    auto smem_thr_copy_dKV = smem_tiled_copy_dKV.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1091
1092
1093
1094
1095
    Tensor taccdKrdK = smem_thr_copy_dKV.retile_S(rdK);       // ((Atom,AtomNum), MMA_N, MMA_N)
    Tensor taccdKsdK = smem_thr_copy_dKV.partition_D(sdK);   // ((Atom,AtomNum),PIPE_M,PIPE_N)
    Tensor taccdVrdV = smem_thr_copy_dKV.retile_S(rdV);       // ((Atom,AtomNum), MMA_N, MMA_N)
    Tensor taccdVsdV = smem_thr_copy_dKV.partition_D(sdV);    // ((Atom,AtomNum),PIPE_M,PIPE_N)

1096
1097
1098
1099
1100
    // We need syncthreads here since we're writing to the same location as sK and sV.
    // Without syncthreads, some thread might modify the location of sK while another thread
    // is reading it for dQ gemm, leading to a race condition.
    // If Is_last, there's already a __syncthreads() at the end of the loop.
    if (!Is_last) { __syncthreads(); }
Tri Dao's avatar
Tri Dao committed
1101

Tri Dao's avatar
Tri Dao committed
1102
1103
    cute::copy(smem_tiled_copy_dKV, taccdKrdK, taccdKsdK);
    cute::copy(smem_tiled_copy_dKV, taccdVrdV, taccdVsdV);
Tri Dao's avatar
Tri Dao committed
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115

    const index_t row_offset_dk = binfo.k_offset(params.dk_batch_stride, params.dk_row_stride, bidb)
       + n_block * kBlockN * params.dk_row_stride + bidh * params.dk_head_stride;
    const index_t row_offset_dv = binfo.k_offset(params.dv_batch_stride, params.dv_row_stride, bidb)
       + n_block * kBlockN * params.dv_row_stride + bidh * params.dv_head_stride;
    Tensor gdK = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dk_ptr) + row_offset_dk),
                             Shape<Int<kBlockN>, Int<kHeadDim>>{},
                             make_stride(params.dk_row_stride, _1{}));
    Tensor gdV = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dv_ptr) + row_offset_dv),
                             Shape<Int<kBlockN>, Int<kHeadDim>>{},
                             make_stride(params.dv_row_stride, _1{}));

Tri Dao's avatar
Tri Dao committed
1116
1117
    typename Kernel_traits::GmemTiledCopydKV gmem_tiled_copy_dKV;
    auto gmem_thr_copy_dKV = gmem_tiled_copy_dKV.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1118
1119
1120
1121
1122
1123
1124
    Tensor tdKsdK = gmem_thr_copy_dKV.partition_S(sdK);   // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdKgdK = gmem_thr_copy_dKV.partition_D(gdK);
    Tensor tdVsdV = gmem_thr_copy_dKV.partition_S(sdV);   // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdVgdV = gmem_thr_copy_dKV.partition_D(gdV);

    __syncthreads();
    Tensor tdKrdK = make_tensor<Element>(shape(tdKgdK));
Tri Dao's avatar
Tri Dao committed
1125
    cute::copy(gmem_tiled_copy_dKV, tdKsdK, tdKrdK);
Tri Dao's avatar
Tri Dao committed
1126
    Tensor tdVrdV = make_tensor<Element>(shape(tdVgdV));
Tri Dao's avatar
Tri Dao committed
1127
    cute::copy(gmem_tiled_copy_dKV, tdVsdV, tdVrdV);
Tri Dao's avatar
Tri Dao committed
1128
1129
1130
1131
1132
1133
    Tensor cdKV = make_identity_tensor(make_shape(size<0>(sdK), size<1>(sdK)));    // (BLK_N,BLK_K) -> (blk_n,blk_k)
    Tensor tdKVcdKV = gmem_thr_copy_dKV.partition_D(cdKV);
    Tensor tdKVpdKV = make_tensor<bool>(make_shape(size<2>(tdKgdK)));
    #pragma unroll
    for (int k = 0; k < size(tdKVpdKV); ++k) { tdKVpdKV(k) = get<1>(tdKVcdKV(0, 0, k)) < params.d; }
    // Clear_OOB_K must be false since we don't want to write zeros to gmem
1134
    flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
Tri Dao's avatar
Tri Dao committed
1135
        gmem_tiled_copy_dKV, tdKrdK, tdKgdK, tdKVcdKV, tdKVpdKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
1136
    );
1137
    flash::copy<Is_even_MN, Is_even_K, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
Tri Dao's avatar
Tri Dao committed
1138
        gmem_tiled_copy_dKV, tdVrdV, tdVgdV, tdKVcdKV, tdKVpdKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
1139
1140
1141
1142
1143
1144
    );

}

////////////////////////////////////////////////////////////////////////////////////////////////////

1145
template<typename Kernel_traits, bool Is_dropout, bool Is_causal, bool Has_alibi, bool Is_even_N, bool Is_even_K, typename Params>
Tri Dao's avatar
Tri Dao committed
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
inline __device__ void compute_dq_dk_dv_1rowblock(const Params &params, const int bidb, const int bidh, const int m_block) {

    using Element = typename Kernel_traits::Element;
    using ElementAccum = typename Kernel_traits::ElementAccum;
    using index_t = typename Kernel_traits::index_t;

    // Shared memory.
    extern __shared__ char smem_[];

    // The thread index.
    const int tidx = threadIdx.x;

    constexpr int kBlockM = Kernel_traits::kBlockM;
    constexpr int kBlockN = Kernel_traits::kBlockN;
    constexpr int kHeadDim = Kernel_traits::kHeadDim;
    // constexpr int kNWarps = Kernel_traits::kNWarps;
    constexpr int MMA_N_SdP = kBlockN / decltype(size<1>(typename Kernel_traits::TiledMmaSdP::TiledShape_MNK{}))::value;
    constexpr int AtomLayoutMS = Kernel_traits::AtomLayoutMSdP;

    const BlockInfo</*Varlen=*/!Is_even_N> binfo(params, bidb);
    if (m_block * kBlockM >= binfo.actual_seqlen_q || binfo.actual_seqlen_k == 0) return;

    int n_block_max = cute::ceil_div(binfo.actual_seqlen_k, kBlockN);
    if (Is_causal) {
        n_block_max = std::min(n_block_max, cute::ceil_div((m_block + 1) * kBlockM, kBlockN));
    }

    // We iterate over the blocks in reverse order. This is because the last block is the only one
    // that needs masking when we read K and V from global memory. Moreover, iterating in reverse
    // might save us 1 register (we just need n_block instead of both n_block and n_block_max).

    const index_t row_offset_q = binfo.q_offset(params.q_batch_stride, params.q_row_stride, bidb)
        + m_block * kBlockM * params.q_row_stride + bidh * params.q_head_stride;
    // We move K and V to the last block.
    const index_t row_offset_k = binfo.k_offset(params.k_batch_stride, params.k_row_stride, bidb)
        + (n_block_max - 1) * kBlockN * params.k_row_stride + (bidh / params.h_h_k_ratio) * params.k_head_stride;
    const index_t row_offset_v = binfo.k_offset(params.v_batch_stride, params.v_row_stride, bidb)
        + (n_block_max - 1) * kBlockN * params.v_row_stride + (bidh / params.h_h_k_ratio) * params.v_head_stride;
    const index_t row_offset_do = binfo.q_offset(params.do_batch_stride, params.do_row_stride, bidb)
        + m_block * kBlockM * params.do_row_stride + bidh * params.do_head_stride;
    const index_t row_offset_o = binfo.q_offset(params.o_batch_stride, params.o_row_stride, bidb)
1187
        + m_block * kBlockM * params.o_row_stride + bidh * params.o_head_stride;
Tri Dao's avatar
Tri Dao committed
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
    // We'll advance gdKaccum and gdVaccum before the first write.
    const index_t row_offset_dkv_accum = ((bidb * params.h_k + (bidh / params.h_h_k_ratio)) * params.seqlen_k_rounded
                                          + n_block_max * kBlockN) * params.d_rounded;
    const index_t row_offset_lse = (bidb * params.h + bidh) * params.seqlen_q + m_block * kBlockM;

    // We assume that params.d == kHeadDim for now
    Tensor gQ = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.q_ptr) + row_offset_q),
                            Shape<Int<kBlockM>, Int<kHeadDim>>{},
                            make_stride(params.q_row_stride, _1{}));
    Tensor gK = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.k_ptr) + row_offset_k),
                            Shape<Int<kBlockN>, Int<kHeadDim>>{},
                            make_stride(params.k_row_stride, _1{}));
    Tensor gV = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.v_ptr) + row_offset_v),
                            Shape<Int<kBlockN>, Int<kHeadDim>>{},
                            make_stride(params.v_row_stride, _1{}));
    Tensor gdO = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.do_ptr) + row_offset_do),
                             Shape<Int<kBlockM>, Int<kHeadDim>>{},
                             make_stride(params.do_row_stride, _1{}));
    Tensor gO = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.o_ptr) + row_offset_o),
                            Shape<Int<kBlockM>, Int<kHeadDim>>{},
1208
                            make_stride(params.o_row_stride, _1{}));
Tri Dao's avatar
Tri Dao committed
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
    Tensor gdKaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dk_accum_ptr) + row_offset_dkv_accum),
                                  Shape<Int<kBlockN>, Int<kHeadDim>>{},
                                  Stride<Int<kHeadDim>, _1>{});
    Tensor gdVaccum = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.dv_accum_ptr) + row_offset_dkv_accum),
                                  Shape<Int<kBlockN>, Int<kHeadDim>>{},
                                  Stride<Int<kHeadDim>, _1>{});
    Tensor gLSE = make_tensor(make_gmem_ptr(reinterpret_cast<ElementAccum *>(params.softmax_lse_ptr) + row_offset_lse),
                              Shape<Int<kBlockM>>{}, Stride<_1>{});

    Tensor sQ = make_tensor(make_smem_ptr(reinterpret_cast<Element *>(smem_)),
                            typename Kernel_traits::SmemLayoutQdO{});
    Tensor sQt = make_tensor(sQ.data(), typename Kernel_traits::SmemLayoutQdOtransposed{});
    Tensor sQtNoSwizzle = make_tensor(sQ.data(), typename Kernel_traits::SmemLayoutQdOtransposedNoSwizzle{});
    Tensor sdO = make_tensor(sQ.data() + size(sQ), typename Kernel_traits::SmemLayoutQdO{});
    Tensor sdOt = make_tensor(sdO.data(), typename Kernel_traits::SmemLayoutQdOtransposed{});
    Tensor sdOtransposedNoSwizzle = make_tensor(sdO.data(),
                                                typename Kernel_traits::SmemLayoutQdOtransposedNoSwizzle{});
    Tensor sK = make_tensor(sdO.data() + size(sdO), typename Kernel_traits::SmemLayoutKV{});
    // Double buffer for sK
    Tensor sV = make_tensor(sK.data() + 2 * size(sK), typename Kernel_traits::SmemLayoutKV{});
    Tensor sKt = make_tensor(sK.data(), typename Kernel_traits::SmemLayoutKtransposed{});
    Tensor sKtNoSwizzle = make_tensor(sK.data(), typename Kernel_traits::SmemLayoutKtransposedNoSwizzle{});
    Tensor sdS = make_tensor(sV.data() + size(sV), typename Kernel_traits::SmemLayoutPdS{});
    Tensor sdSt = make_tensor(sdS.data(), typename Kernel_traits::SmemLayoutPdStransposed{});
    Tensor sdStNoSwizzle = make_tensor(sdS.data(), typename Kernel_traits::SmemLayoutPdStransposedNoSwizzle{});
    Tensor sP = make_tensor(sdS.data() + size(sdS), typename Kernel_traits::SmemLayoutPdS{});
    Tensor sPt = make_tensor(sP.data(), typename Kernel_traits::SmemLayoutPdStransposed{});
    Tensor sPtNoSwizzle = make_tensor(sP.data(), typename Kernel_traits::SmemLayoutPdStransposedNoSwizzle{});
    Tensor sdPsum = make_tensor(make_smem_ptr(reinterpret_cast<ElementAccum *>(sdS.data().get())),
                                Shape<Int<kBlockM>>{});

Tri Dao's avatar
Tri Dao committed
1240
1241
1242
1243
1244
1245
    typename Kernel_traits::GmemTiledCopyQKV gmem_tiled_copy_QKV;
    auto gmem_thr_copy_QKV = gmem_tiled_copy_QKV.get_thread_slice(tidx);
    typename Kernel_traits::GmemTiledCopydO gmem_tiled_copy_dO;
    auto gmem_thr_copy_dO = gmem_tiled_copy_dO.get_thread_slice(tidx);
    typename Kernel_traits::GmemTiledCopydQaccumAtomicAdd gmem_tiled_copy_dKVaccum;
    auto gmem_thr_copy_dKVaccum = gmem_tiled_copy_dKVaccum.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255

    Tensor tQgQ = gmem_thr_copy_QKV.partition_S(gQ);
    Tensor tQsQ = gmem_thr_copy_QKV.partition_D(sQ);
    Tensor tdOgdO = gmem_thr_copy_dO.partition_S(gdO);
    Tensor tdOsdO = gmem_thr_copy_dO.partition_D(sdO);
    Tensor tdOgO = gmem_thr_copy_dO.partition_S(gO);
    Tensor tKgK = gmem_thr_copy_QKV.partition_S(gK);  // (KCPY, KCPY_N, KCPY_K)
    Tensor tKsK = gmem_thr_copy_QKV.partition_D(sK);
    Tensor tVgV = gmem_thr_copy_QKV.partition_S(gV);  // (VCPY, VCPY_N, VCPY_K)
    Tensor tVsV = gmem_thr_copy_QKV.partition_D(sV);
Tri Dao's avatar
Tri Dao committed
1256
1257
    Tensor tdKgdKaccum = gmem_thr_copy_dKVaccum.partition_D(gdKaccum);
    Tensor tdVgdVaccum = gmem_thr_copy_dKVaccum.partition_D(gdVaccum);
Tri Dao's avatar
Tri Dao committed
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283

    typename Kernel_traits::TiledMmaSdP tiled_mma_sdp;
    auto thr_mma_sdp = tiled_mma_sdp.get_thread_slice(tidx);
    Tensor tSrQ = thr_mma_sdp.partition_fragment_A(sQ);         // (MMA,MMA_N,MMA_K)
    Tensor tSrK = thr_mma_sdp.partition_fragment_B(sK);         // (MMA,MMA_N,MMA_K)
    Tensor tdPrdO = thr_mma_sdp.partition_fragment_A(sdO);      // (MMA,MMA_N,MMA_K)
    Tensor tdPrV = thr_mma_sdp.partition_fragment_B(sV);        // (MMA,MMA_N,MMA_K)

    typename Kernel_traits::TiledMmadKV tiled_mma_dkv;
    auto thr_mma_dkv = tiled_mma_dkv.get_thread_slice(tidx);
    Tensor tdKrdSt = thr_mma_dkv.partition_fragment_A(sdStNoSwizzle); // (MMA, MMA_N, MMA_N)
    Tensor tdKrQt = thr_mma_dkv.partition_fragment_B(sQtNoSwizzle);   // (MMA, MMA_K, MMA_N)
    Tensor tdVrPt = thr_mma_dkv.partition_fragment_A(sPtNoSwizzle);   // (MMA, MMA_N, MMA_N)
    Tensor tdVrdO = thr_mma_dkv.partition_fragment_B(sdOtransposedNoSwizzle); // (MMA, MMA_K, MMA_N)

    typename Kernel_traits::TiledMmadQ tiled_mma_dq;
    auto thr_mma_dq = tiled_mma_dq.get_thread_slice(tidx);
    Tensor tdQrdS = thr_mma_dq.partition_fragment_A(sdS);                      // (MMA, MMA_N, MMA_N)
    Tensor tdQrKt  = thr_mma_dq.partition_fragment_B(sKtNoSwizzle);    // (MMA, MMA_K, MMA_N)

    Tensor acc_dq = partition_fragment_C(tiled_mma_dq, Shape<Int<kBlockM>, Int<kHeadDim>>{});  // MMA, MMA_M_SdP, MMA_K

    //
    // Copy Atom retiling
    //

Tri Dao's avatar
Tri Dao committed
1284
1285
    auto smem_tiled_copy_QdO = make_tiled_copy_A(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_sdp);
    auto smem_thr_copy_QdO = smem_tiled_copy_QdO.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1286
1287
1288
    Tensor tSsQ = smem_thr_copy_QdO.partition_S(sQ);
    Tensor tdPsdO = smem_thr_copy_QdO.partition_S(sdO);

Tri Dao's avatar
Tri Dao committed
1289
1290
    auto smem_tiled_copy_KV = make_tiled_copy_B_warpcontiguousN<MMA_N_SdP>(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_sdp);
    auto smem_thr_copy_KV = smem_tiled_copy_KV.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1291
1292
1293
1294
1295
    Tensor tSsK = smem_thr_copy_KV.partition_S(sK);
    Tensor tdPsV = smem_thr_copy_KV.partition_S(sV);

    // Partition sP and sdS to match the accumulator partitioning
    // This has to be tiled_mma_sdp, not tiled_mma_dkv
Tri Dao's avatar
Tri Dao committed
1296
1297
    auto smem_tiled_copy_PdS = make_tiled_copy_C_warpcontiguousN<MMA_N_SdP>(typename Kernel_traits::SmemCopyAtomPdS{}, tiled_mma_sdp);
    auto smem_thr_copy_PdS = smem_tiled_copy_PdS.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1298
1299
1300
    Tensor tPsP = smem_thr_copy_PdS.partition_D(sP);      // ((Atom,AtomNum),PIPE_M,PIPE_N)
    Tensor tdSsdS = smem_thr_copy_PdS.partition_D(sdS);   // ((Atom,AtomNum),PIPE_M,PIPE_N)

Tri Dao's avatar
Tri Dao committed
1301
1302
    auto smem_tiled_copy_PdSt = make_tiled_copy_A(typename Kernel_traits::SmemCopyAtomTransposed{}, tiled_mma_dkv);
    auto smem_thr_copy_PdSt = smem_tiled_copy_PdSt.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1303
1304
1305
    Tensor tdVsPt = smem_thr_copy_PdSt.partition_S(sPt);
    Tensor tdKsdSt = smem_thr_copy_PdSt.partition_S(sdSt);

Tri Dao's avatar
Tri Dao committed
1306
1307
    auto smem_tiled_copy_QdOt = make_tiled_copy_B(typename Kernel_traits::SmemCopyAtomTransposed{}, tiled_mma_dkv);
    auto smem_thr_copy_QdOt = smem_tiled_copy_QdOt.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1308
1309
1310
    Tensor tdVsdOt = smem_thr_copy_QdOt.partition_S(sdOt);
    Tensor tdKsQt = smem_thr_copy_QdOt.partition_S(sQt);

Tri Dao's avatar
Tri Dao committed
1311
1312
    auto smem_tiled_copy_dS = make_tiled_copy_A(typename Kernel_traits::SmemCopyAtom{}, tiled_mma_dq);
    auto smem_thr_copy_dS = smem_tiled_copy_dS.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1313
1314
    Tensor tdQsdS = smem_thr_copy_dS.partition_S(sdS);

Tri Dao's avatar
Tri Dao committed
1315
1316
    auto smem_tiled_copy_Kt = make_tiled_copy_B(typename Kernel_traits::SmemCopyAtomTransposed{}, tiled_mma_dq);
    auto smem_thr_copy_Kt = smem_tiled_copy_Kt.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
    Tensor tdQsKt = smem_thr_copy_Kt.partition_S(sKt);

    //
    // PREDICATES
    //

    // Construct identity layout for sQ and sK
    Tensor cQ = make_identity_tensor(make_shape(size<0>(sQ), size<1>(sQ)));    // (BLK_M,BLK_K) -> (blk_m,blk_k)
    Tensor cKV = make_identity_tensor(make_shape(size<0>(sK), size<1>(sK)));    // (BLK_N,BLK_K) -> (blk_n,blk_k)
    // Repeat the partitioning with identity layouts
    Tensor tQcQ = gmem_thr_copy_QKV.partition_S(cQ);       // (ACPY,ACPY_M,ACPY_K) -> (blk_m,blk_k)
    Tensor tKVcKV = gmem_thr_copy_QKV.partition_S(cKV);   // (BCPY,BCPY_N,BCPY_K) -> (blk_n,blk_k)

    // Allocate predicate tensors for k
    Tensor tQpQ = make_tensor<bool>(make_shape(size<2>(tQsQ)));
    Tensor tKVpKV = make_tensor<bool>(make_shape(size<2>(tKsK)));

    // Set predicates for k bounds
    if (!Is_even_K) {
        #pragma unroll
        for (int k = 0; k < size(tQpQ); ++k) { tQpQ(k) = get<1>(tQcQ(0, 0, k)) < params.d; }
        #pragma unroll
        for (int k = 0; k < size(tKVpKV); ++k) { tKVpKV(k) = get<1>(tKVcKV(0, 0, k)) < params.d; }
    }

    // Prologue

    Tensor tdOrdO = make_fragment_like(tdOgdO);
    Tensor tdOrO = make_fragment_like(tdOgO);

    // TODO: Might need to exit early and write 0 to gdQ.

    flash::copy</*Is_even_MN=*/false, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
1350
        gmem_tiled_copy_dO, tdOgdO, tdOrdO, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
1351
1352
    );
    flash::copy</*Is_even_MN=*/false, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
1353
        gmem_tiled_copy_dO, tdOgO, tdOrO, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
1354
1355
1356
1357
    );

    Tensor tQrQ = make_fragment_like(tQgQ);
    flash::copy</*Is_even_MN=*/false, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
1358
        gmem_tiled_copy_QKV, tQgQ, tQsQ, tQcQ, tQpQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
    );

    int n_block = n_block_max - 1;
    if (n_block % 2 == 1) {
        tKsK.data() = tKsK.data() + size(sK);
        tSsK.data() = tSsK.data() + size(sK);
        tdQsKt.data() = tdQsKt.data() + size(sK);
    }

    flash::copy<Is_even_N, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
1369
        gmem_tiled_copy_QKV, tKgK, tKsK, tKVcKV, tKVpKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
1370
1371
    );
    flash::copy<Is_even_N, Is_even_K, /*Clear_OOB_MN=*/true>(
Tri Dao's avatar
Tri Dao committed
1372
        gmem_tiled_copy_QKV, tVgV, tVsV, tKVcKV, tKVpKV, binfo.actual_seqlen_k - n_block * kBlockN
Tri Dao's avatar
Tri Dao committed
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
    );

    Tensor caccS = make_identity_tensor(Shape<Int<kBlockM>, Int<kBlockN>>{});    // (BLK_M,BLK_N) -> (blk_m,blk_n)
    Tensor taccScS = thr_mma_sdp.partition_C(caccS);                           // (MMA,MMA_N,MMA_N)
    static_assert(decltype(size<0>(taccScS))::value == 4);
    // Convert to ((2, 2), MMA_N, MMA_N) then take only the row indices.
    Tensor taccScS_row = logical_divide(taccScS, Shape<_2>{})(make_coord(0, _), _, 0);
    Tensor lse = make_tensor<ElementAccum>(Shape<Int<decltype(size(taccScS_row))::value>>{});
    #pragma unroll
    for (int mi = 0; mi < size(lse); ++mi) {
        const int row = get<0>(taccScS_row(mi));
        lse(mi) = row < binfo.actual_seqlen_q - m_block * kBlockM ? gLSE(row) : 0;
    }

    cute::cp_async_fence();

    Tensor dP_sum = make_fragment_like(lse);
Tri Dao's avatar
Tri Dao committed
1390
    cute::copy(tdOrdO, tdOsdO);
Tri Dao's avatar
Tri Dao committed
1391
    dot_do_o<Kernel_traits::kGmemThreadsPerRow>(
1392
        tdOrdO, tdOrO, sdPsum,
Tri Dao's avatar
Tri Dao committed
1393
1394
1395
1396
1397
1398
        Kernel_traits::kNThreads / (Kernel_traits::kGmemThreadsPerRow), params.p_dropout
    );
    __syncthreads();
    #pragma unroll
    for (int mi = 0; mi < size(dP_sum); ++mi) { dP_sum(mi) = sdPsum(get<0>(taccScS_row(mi))); }

1399
1400
    auto seed = params.rng_state[0];
    auto offset = params.rng_state[1] + (bidb * params.h + bidh) * 32 + tidx % 32;
Tri Dao's avatar
Tri Dao committed
1401
1402
1403

    clear(acc_dq);

1404
    float alibi_slope = !Has_alibi ? 0.0f : reinterpret_cast<float *>(params.alibi_slopes_ptr)[bidb * params.alibi_slopes_batch_stride + bidh] / params.scale_softmax;
1405

Tri Dao's avatar
Tri Dao committed
1406
1407
1408
1409
1410
1411
    for (; n_block >= 0; --n_block) {
        Tensor acc_s = partition_fragment_C(tiled_mma_sdp, Shape<Int<kBlockM>, Int<kBlockN>>{});  // (MMA=4, MMA_M_SdP, MMA_N)
        clear(acc_s);
        flash::cp_async_wait<0>();
        __syncthreads();

Tri Dao's avatar
Tri Dao committed
1412
1413
        flash::gemm(acc_s, tSrQ, tSrK, tSsQ, tSsK, tiled_mma_sdp,
                    smem_tiled_copy_QdO, smem_tiled_copy_KV, smem_thr_copy_QdO, smem_thr_copy_KV);
Tri Dao's avatar
Tri Dao committed
1414
1415
1416

        // Reshape acc_s from (MMA=4, MMA_N, MMA_N) to (col=(2, MMA_N), row=(2, MMA_N))
        Tensor scores = make_tensor(acc_s.data(), flash::convert_layout_acc_rowcol(acc_s.layout()));
1417
1418

        if (Has_alibi) {
1419
            flash::apply_alibi<Is_causal>(
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
                scores, 
                n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
                binfo.actual_seqlen_k, 
                m_block * kBlockM + get<0>(taccScS_row(0)),
                binfo.actual_seqlen_q, 
                AtomLayoutMS * 16,
                alibi_slope
            );
        }

Tri Dao's avatar
Tri Dao committed
1430
1431
1432
1433
1434
        // We don't need to mask out the elements beyond actual_seqlen_k, because acc_s would
        // be some finite value for those indices. In the end when we multiply with K to get dQ,
        // the corresponding values of K would be 0, so the result would still be correct.
        if (Is_causal && m_block * kBlockM < (n_block + 1) * kBlockN) {
            flash::apply_mask_causal(scores, n_block * kBlockN + (tidx / 32 / AtomLayoutMS) * MMA_N_SdP * 16,
1435
                                     binfo.actual_seqlen_k, m_block * kBlockM + get<0>(taccScS_row(0)),
Tri Dao's avatar
Tri Dao committed
1436
                                     // binfo.actual_seqlen_k, m_block * kBlockM + (tidx / 32) % AtomLayoutMS * 16 + (tidx % 32) / 4,
1437
                                     binfo.actual_seqlen_q,
Tri Dao's avatar
Tri Dao committed
1438
1439
                                     AtomLayoutMS * 16);
        }
1440

Tri Dao's avatar
Tri Dao committed
1441
1442
1443
        // Compute the exponential value.
        flash::scale_apply_exp2</*scale_max=*/false>(scores, lse, params.scale_softmax_log2);
        if (Is_dropout) {
1444
1445
            int warp_id = tidx / 32;
            int block_row_idx = m_block * (kBlockM / 16) + warp_id % AtomLayoutMS;
Tri Dao's avatar
Tri Dao committed
1446
1447
            // Need col to be multiples of 32, since we're doing dropout with block of 16 x 32
            static_assert(MMA_N_SdP % 2 == 0);
1448
            int block_col_idx = n_block * (kBlockN / 32) + (warp_id / AtomLayoutMS) * (MMA_N_SdP / 2);
Tri Dao's avatar
Tri Dao committed
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
            Tensor scores_dropped = make_tensor(scores.data(), flash::convert_layout_rowcol_Aregs<Kernel_traits::TiledMmaSdP>(scores.layout()));
            flash::apply_dropout</*encode_dropout_in_sign_bit=*/true>(
                scores_dropped, params.p_dropout_in_uint8_t, seed, offset,
                block_row_idx, block_col_idx, AtomLayoutMS
            );
        }
        // Convert scores from fp32 to fp16/bf16
        Tensor rP = !Is_dropout
            ? flash::convert_type<Element>(scores)
            : flash::convert_type_relu<Element>(scores);
        // Reshape rP from (nrow=(2, MMA_N), ncol=(2, MMA_N)) to ((2, 2, 2), MMA_N, MMA_N / 2)
        // if using m16n8k16 or ((2, 2, 1), MMA_N, MMA_N) if using m16n8k8.
        Tensor tPrP = make_tensor(rP.data(), flash::convert_layout_rowcol_Aregs<Kernel_traits::TiledMmaSdP>(rP.layout()));
        Tensor tPaP = smem_thr_copy_PdS.retile_S(tPrP);     // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
1463
        cute::copy(smem_tiled_copy_PdS, tPaP, tPsP);
Tri Dao's avatar
Tri Dao committed
1464
1465
1466
1467
1468
1469
1470

        Tensor acc_dp = partition_fragment_C(tiled_mma_sdp, Shape<Int<kBlockM>, Int<kBlockN>>{});  // (MMA=4, MMA_N, MMA_N)
        CUTE_STATIC_ASSERT_V(size<0>(acc_dp) == size<0>(acc_s));                     // MMA
        CUTE_STATIC_ASSERT_V(size<1>(acc_dp) == size<1>(acc_s));                     // MMA
        CUTE_STATIC_ASSERT_V(size<2>(acc_dp) == size<2>(acc_s));                     // MMA

        clear(acc_dp);
Tri Dao's avatar
Tri Dao committed
1471
1472
        flash::gemm(acc_dp, tdPrdO, tdPrV, tdPsdO, tdPsV, tiled_mma_sdp,
                    smem_tiled_copy_QdO, smem_tiled_copy_KV, smem_thr_copy_QdO, smem_thr_copy_KV);
Tri Dao's avatar
Tri Dao committed
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490

        // Reshape acc_dp from (MMA=4, MMA_N, MMA_N) to (col=(2, MMA_N), row=(2, MMA_N))
        Tensor dS = make_tensor(acc_dp.data(), scores.layout());
        auto pointwise_mult = [](float p, float dp, float d) {
            return p * (!Is_dropout || p >= 0 ? dp - d : d);
        };
        #pragma unroll
        for (int mi = 0; mi < size<0>(dS); ++mi) {
            #pragma unroll
            for (int ni = 0; ni < size<1>(dS); ++ni) {
                dS(mi, ni) = pointwise_mult(scores(mi, ni), dS(mi, ni), dP_sum(mi));
            }
        }

        Tensor dS_reshaped = make_tensor(dS.data(), acc_dp.layout());
        // Convert dS from fp32 to fp16
        Tensor tdSrdS = flash::convert_type<Element>(dS_reshaped);
        Tensor tdSadS = smem_thr_copy_PdS.retile_S(tdSrdS);                                          // ((Atom,AtomNum), MMA_N, MMA_N)
Tri Dao's avatar
Tri Dao committed
1491
        cute::copy(smem_tiled_copy_PdS, tdSadS, tdSsdS);
Tri Dao's avatar
Tri Dao committed
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
        __syncthreads();

        if (n_block > 0) {
            // Double buffer for sK
            const int sK_offset = n_block % 2 == 0 ? size(sK) : -size(sK);
            tKsK.data() = tKsK.data() + sK_offset;
            tSsK.data() = tSsK.data() + sK_offset;
            // Advance gK, gV
            tKgK.data() = tKgK.data() + (-int(kBlockN * params.k_row_stride));
            tVgV.data() = tVgV.data() + (-int(kBlockN * params.v_row_stride));
Tri Dao's avatar
Tri Dao committed
1502
1503
            flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_QKV, tKgK, tKsK, tKVcKV, tKVpKV);
            flash::copy</*Is_even_MN=*/true, Is_even_K>(gmem_tiled_copy_QKV, tVgV, tVsV, tKVcKV, tKVpKV);
Tri Dao's avatar
Tri Dao committed
1504
1505
1506
1507
1508
1509
1510
            // This cp_async_fence needs to be in the if block, otherwise the synchronization
            // isn't right and we get race conditions.
            cute::cp_async_fence();
        }

        Tensor acc_dv = partition_fragment_C(tiled_mma_dkv, Shape<Int<kBlockN>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
        clear(acc_dv);
Tri Dao's avatar
Tri Dao committed
1511
1512
        flash::gemm(acc_dv, tdVrPt, tdVrdO, tdVsPt, tdVsdOt, tiled_mma_dkv,
                    smem_tiled_copy_PdSt, smem_tiled_copy_QdOt, smem_thr_copy_PdSt, smem_thr_copy_QdOt);
Tri Dao's avatar
Tri Dao committed
1513
1514
1515
1516
1517
1518
1519
1520
        // if (threadIdx.x == 0 && blockIdx.y == 0 && blockIdx.z == 0) { print(acc_dv); }
        tdVgdVaccum.data() = tdVgdVaccum.data() + (-int(kBlockN * params.d_rounded));
        #pragma unroll
        for (int i = 0; i < size(acc_dv); ++i) { atomicAdd(&tdVgdVaccum(i), acc_dv(i)); }

        __syncthreads();
        Tensor acc_dk = partition_fragment_C(tiled_mma_dkv, Shape<Int<kBlockN>, Int<kHeadDim>>{});  // MMA, MMA_N, MMA_K
        clear(acc_dk);
Tri Dao's avatar
Tri Dao committed
1521
1522
        flash::gemm(acc_dk, tdKrdSt, tdKrQt, tdKsdSt, tdKsQt, tiled_mma_dkv,
                    smem_tiled_copy_PdSt, smem_tiled_copy_QdOt, smem_thr_copy_PdSt, smem_thr_copy_QdOt);
Tri Dao's avatar
Tri Dao committed
1523
1524
1525
1526
        tdKgdKaccum.data() = tdKgdKaccum.data() + (-int(kBlockN * params.d_rounded));
        #pragma unroll
        for (int i = 0; i < size(acc_dk); ++i) { atomicAdd(&tdKgdKaccum(i), acc_dk(i)); }

Tri Dao's avatar
Tri Dao committed
1527
1528
        flash::gemm(acc_dq, tdQrdS, tdQrKt, tdQsdS, tdQsKt, tiled_mma_dq,
                    smem_tiled_copy_dS, smem_tiled_copy_Kt, smem_thr_copy_dS, smem_thr_copy_Kt);
Tri Dao's avatar
Tri Dao committed
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
        // Double buffer for sK
        tdQsKt.data() = tdQsKt.data() + (n_block % 2 == 0 ? size(sK) : -size(sK));

    }

    // Epilogue

    #pragma unroll
    for (int i = 0; i < size(acc_dq); ++i) { acc_dq(i) *= params.scale_softmax_rp_dropout; }
    // Convert acc_dq from fp32 to fp16
    Tensor rdQ = flash::convert_type<Element>(acc_dq);

    Tensor sdQ = make_tensor(sQ.data(), typename Kernel_traits::SmemLayoutdQ{});

    // Partition sdV and sdK to match the accumulator partitioning
Tri Dao's avatar
Tri Dao committed
1544
1545
    auto smem_tiled_copy_dQ = make_tiled_copy_C(typename Kernel_traits::SmemCopyAtomdQ{}, tiled_mma_dq);
    auto smem_thr_copy_dQ = smem_tiled_copy_dQ.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1546
1547
1548
1549
    Tensor taccdQrdQ = smem_thr_copy_dQ.retile_S(rdQ);  // ((Atom,AtomNum), MMA_N, MMA_N)
    Tensor taccdQsdQ = smem_thr_copy_dQ.partition_D(sdQ);  // ((Atom,AtomNum),PIPE_M,PIPE_N)

    __syncthreads();
Tri Dao's avatar
Tri Dao committed
1550
    cute::copy(smem_tiled_copy_dQ, taccdQrdQ, taccdQsdQ);
Tri Dao's avatar
Tri Dao committed
1551
1552
1553
1554
1555
1556
1557

    const index_t row_offset_dq = binfo.q_offset(params.dq_batch_stride, params.dq_row_stride, bidb)
        + m_block * kBlockM * params.dq_row_stride + bidh * params.dq_head_stride;
    Tensor gdQ = make_tensor(make_gmem_ptr(reinterpret_cast<Element *>(params.dq_ptr) + row_offset_dq),
                             Shape<Int<kBlockM>, Int<kHeadDim>>{},
                             make_stride(params.dq_row_stride, _1{}));

Tri Dao's avatar
Tri Dao committed
1558
1559
    typename Kernel_traits::GmemTiledCopydQ gmem_tiled_copy_dQ;
    auto gmem_thr_copy_dQ = gmem_tiled_copy_dQ.get_thread_slice(tidx);
Tri Dao's avatar
Tri Dao committed
1560
1561
1562
1563
1564
1565
    Tensor tdQsdQ = gmem_thr_copy_dQ.partition_S(sdQ);    // ((Atom,AtomNum),ATOM_M,ATOM_N)
    Tensor tdQgdQ = gmem_thr_copy_dQ.partition_D(gdQ);

    __syncthreads();

    Tensor tdQrdQ = make_tensor<Element>(shape(tdQgdQ));
Tri Dao's avatar
Tri Dao committed
1566
    cute::copy(gmem_tiled_copy_dQ, tdQsdQ, tdQrdQ);
Tri Dao's avatar
Tri Dao committed
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576

    Tensor cdQ = make_identity_tensor(Shape<Int<kBlockM>, Int<kHeadDim>>{});    // (BLK_M,BLK_K) -> (blk_m,blk_k)
    Tensor tdQcdQ = gmem_thr_copy_dQ.partition_D(cdQ);
    Tensor tdQpdQ = make_tensor<bool>(make_shape(size<2>(tdQgdQ)));
    if (!Is_even_K) {
        #pragma unroll
        for (int k = 0; k < size(tdQpdQ); ++k) { tdQpdQ(k) = get<1>(tdQcdQ(0, 0, k)) < params.d; }
    }
    // Clear_OOB_K must be false since we don't want to write zeros to gmem
    flash::copy</*Is_even_MN=*/false, Is_even_K, /*Clear_OOB_MN=*/false, /*Clear_OOB_K=*/false>(
Tri Dao's avatar
Tri Dao committed
1577
        gmem_tiled_copy_dQ, tdQrdQ, tdQgdQ, tdQcdQ, tdQpdQ, binfo.actual_seqlen_q - m_block * kBlockM
Tri Dao's avatar
Tri Dao committed
1578
1579
1580
1581
1582
    );
}

////////////////////////////////////////////////////////////////////////////////////////////////////

1583
template<typename Kernel_traits, bool Is_dropout, bool Is_causal, bool Has_alibi, bool Is_even_M, bool Is_even_K, typename Params>
Tri Dao's avatar
Tri Dao committed
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
inline __device__ void compute_dq_dk_dv(const Params &params) {

    // The block index for the batch.
    const int bidb = blockIdx.x;
    // const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.y;
    // const int bidh = blockIdx.z;
    // The thread index.
    const int tidx = threadIdx.x;

    const int n_block_max = (params.seqlen_k + Kernel_traits::kBlockN - 1) / Kernel_traits::kBlockN;
    if (n_block_max == 1) {
1597
        compute_dq_dk_dv_1colblock<Kernel_traits, Is_dropout, Is_causal, Has_alibi, Is_even_M, Is_even_K, true, true>(params, bidb, bidh, 0);
Tri Dao's avatar
Tri Dao committed
1598
1599
    } else {
        // Iterating backward from n_block_max - 1 to 0 might save 1 register
1600
        compute_dq_dk_dv_1colblock<Kernel_traits, Is_dropout, Is_causal, Has_alibi, Is_even_M, Is_even_K, true, false>(params, bidb, bidh, n_block_max - 1);
Tri Dao's avatar
Tri Dao committed
1601
        for (int n_block = n_block_max - 2; n_block > 0; n_block--) {
1602
            compute_dq_dk_dv_1colblock<Kernel_traits, Is_dropout, Is_causal, Has_alibi, Is_even_M, Is_even_K, false, false>(params, bidb, bidh, n_block);
Tri Dao's avatar
Tri Dao committed
1603
        }
1604
        compute_dq_dk_dv_1colblock<Kernel_traits, Is_dropout, Is_causal, Has_alibi, Is_even_M, Is_even_K, false, true>(params, bidb, bidh, 0);
Tri Dao's avatar
Tri Dao committed
1605
1606
1607
1608
1609
    }
}

////////////////////////////////////////////////////////////////////////////////////////////////////

1610
template<typename Kernel_traits, bool Is_dropout, bool Is_causal, bool Is_local, bool Has_alibi, bool Is_even_MN, bool Is_even_K, typename Params>
Tri Dao's avatar
Tri Dao committed
1611
1612
1613
1614
1615
1616
1617
inline __device__ void compute_dq_dk_dv_seqk_parallel(const Params &params) {

    // The block index for the batch.
    const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.z;

1618
1619
1620
1621
    // If deterministic, each thread block will do atomicAdd to a different dQ_accum buffer.
    for (int n_block = blockIdx.x; n_block < (params.seqlen_k + Kernel_traits::kBlockN - 1) / Kernel_traits::kBlockN; n_block += gridDim.x) {
        compute_dq_dk_dv_1colblock<Kernel_traits, Is_dropout, Is_causal, Is_local, Has_alibi, Is_even_MN, Is_even_K, false, false, /*Seq_parallel=*/true>(params, bidb, bidh, n_block);
    }
Tri Dao's avatar
Tri Dao committed
1622
1623
1624
1625
}

////////////////////////////////////////////////////////////////////////////////////////////////////

1626
template<typename Kernel_traits, bool Is_dropout, bool Is_causal, bool Has_alibi, bool Is_even_N, bool Is_even_K, typename Params>
Tri Dao's avatar
Tri Dao committed
1627
1628
1629
1630
1631
1632
1633
1634
inline __device__ void compute_dq_dk_dv_seqq_parallel(const Params &params) {

    const int m_block = blockIdx.x;
    // The block index for the batch.
    const int bidb = blockIdx.y;
    // The block index for the head.
    const int bidh = blockIdx.z;

1635
    compute_dq_dk_dv_1rowblock<Kernel_traits, Is_dropout, Is_causal, Has_alibi, Is_even_N, Is_even_K>(params, bidb, bidh, m_block);
Tri Dao's avatar
Tri Dao committed
1636
1637
1638
1639
}

////////////////////////////////////////////////////////////////////////////////////////////////////
} // namespace flash