flash_attn_triton.py

# Copyright 2022 MosaicML Examples authors
# SPDX-License-Identifier: Apache-2.0

"""Triton implementation of Flash Attention.

# Copyright (c) 2022, Tri Dao.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

*Experimental* implementation of FlashAttention in Triton.
We use the FlashAttention implementation from Phil Tillet a starting point.
https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py

Changes:
- Implement both causal and non-causal attention.
- Implement both self-attention and cross-attention.
- Support arbitrary seqlens (not just multiples of 128), for both forward and backward.
- Support all head dimensions up to 128 (not just 16, 32, 64, 128), for both forward and backward.
- Support attention bias.
- Speed up the forward pass a bit, and only store the LSE instead of m and l.
- Make the backward for d=128 much faster by reducing register spilling.
- Optionally parallelize the backward pass across seqlen_k, to deal with the case of
small batch size * nheads.

Caution:
- If you plan to use headdim other than 64 and 128, you should test for race conditions
(due to the Triton compiler), as done in tests/test_flash_attn.py
"test_flash_attn_triton_race_condition". I've tested and fixed many race conditions
for different head dimensions (40, 48, 64, 128, 80, 88, 96), but I'm still not 100% confident
that there are none left for other head dimensions.
Differences between this Triton version and the CUDA version:
- Triton version doesn't support dropout.
- Triton forward is generally faster than CUDA forward.
- Triton backward is faster than CUDA backward when batch * nheads is small, and when headdim=64.
It is slightly slower when headdim=128 and batch * nheads is large.
- Triton version doesn't yet support different sequence lengths in a batch (i.e., RaggedTensor/NestedTensor).
"""

import math

import torch
import triton  # type: ignore (reportMissingImports)
import triton.language as tl  # type: ignore (reportMissingImports)
from einops import repeat


@triton.autotune(
    configs=[
        triton.Config({
            'BLOCK_M': 128,
            'BLOCK_N': 128
        },
                      num_warps=8,
                      num_stages=1),
        # This config has a race condition when EVEN_M == False, disabling it for now.
        # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64}, num_warps=4, num_stages=1),
    ],
    key=[
        'CACHE_KEY_SEQLEN_Q', 'CACHE_KEY_SEQLEN_K', 'BIAS_TYPE', 'IS_CAUSAL',
        'BLOCK_HEADDIM'
    ])
@triton.heuristics({
    'EVEN_M': lambda args: args['seqlen_q'] % args['BLOCK_M'] == 0,
    'EVEN_N': lambda args: args['seqlen_k'] % args['BLOCK_N'] == 0,
    'EVEN_HEADDIM': lambda args: args['headdim'] == args['BLOCK_HEADDIM'],
})
@triton.jit
def _fwd_kernel(
    Q,
    K,
    V,
    Bias,
    Out,
    Lse,
    TMP,  # NOTE: TMP is a scratchpad buffer to workaround a compiler bug
    softmax_scale,
    stride_qb,
    stride_qh,
    stride_qm,
    stride_kb,
    stride_kh,
    stride_kn,
    stride_vb,
    stride_vh,
    stride_vn,
    stride_bb,
    stride_bh,
    stride_bm,
    stride_ob,
    stride_oh,
    stride_om,
    nheads,
    seqlen_q,
    seqlen_k,
    seqlen_q_rounded,
    headdim,
    CACHE_KEY_SEQLEN_Q,
    CACHE_KEY_SEQLEN_K,
    BIAS_TYPE: tl.constexpr,
    IS_CAUSAL: tl.constexpr,
    BLOCK_HEADDIM: tl.constexpr,
    EVEN_M: tl.constexpr,
    EVEN_N: tl.constexpr,
    EVEN_HEADDIM: tl.constexpr,
    BLOCK_M: tl.constexpr,
    BLOCK_N: tl.constexpr,
):
    start_m = tl.program_id(0)
    off_hb = tl.program_id(1)
    off_b = off_hb // nheads
    off_h = off_hb % nheads
    # off_b = tl.program_id(1)
    # off_h = tl.program_id(2)
    # off_hb = off_b * nheads + off_h
    # initialize offsets
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    offs_n = tl.arange(0, BLOCK_N)
    offs_d = tl.arange(0, BLOCK_HEADDIM)
    # Initialize pointers to Q, K, V
    # Adding parenthesis around indexing might use int32 math instead of int64 math?
    # https://github.com/openai/triton/issues/741
    # I'm seeing a tiny bit of difference (5-7us)
    q_ptrs = Q + off_b * stride_qb + off_h * stride_qh + (
        offs_m[:, None] * stride_qm + offs_d[None, :])
    k_ptrs = K + off_b * stride_kb + off_h * stride_kh + (
        offs_n[:, None] * stride_kn + offs_d[None, :])
    v_ptrs = V + off_b * stride_vb + off_h * stride_vh + (
        offs_n[:, None] * stride_vn + offs_d[None, :])
    if BIAS_TYPE == 'vector':
        b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + offs_n
    elif BIAS_TYPE == 'matrix':
        b_ptrs = Bias + off_b * stride_bb + off_h * stride_bh + (
            offs_m[:, None] * stride_bm + offs_n[None, :])
    else:
        raise ValueError("BIAS_TYPE must be one of {'vector', 'matrix'}")
    # initialize pointer to m and l
    t_ptrs = TMP + off_hb * seqlen_q_rounded + offs_m
    lse_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')
    m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float('inf')
    acc_o = tl.zeros([BLOCK_M, BLOCK_HEADDIM], dtype=tl.float32)
    # load q: it will stay in SRAM throughout
    # [2022-10-30] TD: Triton bug - in the case of EVEN_M=True and EVEN_N=False, if we just call
    # tl.load(q_ptrs), we get the wrong output!
    if EVEN_M & EVEN_N:
        if EVEN_HEADDIM:
            q = tl.load(q_ptrs)
        else:
            q = tl.load(q_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
    else:
        if EVEN_HEADDIM:
            q = tl.load(q_ptrs, mask=offs_m[:, None] < seqlen_q, other=0.0)
        else:
            q = tl.load(q_ptrs,
                        mask=(offs_m[:, None] < seqlen_q) &
                        (offs_d[None, :] < headdim),
                        other=0.0)
    # loop over k, v and update accumulator
    end_n = seqlen_k if not IS_CAUSAL else tl.minimum(
        (start_m + 1) * BLOCK_M, seqlen_k)
    for start_n in range(0, end_n, BLOCK_N):
        start_n = tl.multiple_of(start_n, BLOCK_N)
        # -- compute qk ----
        if EVEN_N & EVEN_M:  # If we just do "if EVEN_N", there seems to be some race condition
            if EVEN_HEADDIM:
                k = tl.load(k_ptrs + start_n * stride_kn)
            else:
                k = tl.load(k_ptrs + start_n * stride_kn,
                            mask=offs_d[None, :] < headdim,
                            other=0.0)
        else:
            if EVEN_HEADDIM:
                k = tl.load(k_ptrs + start_n * stride_kn,
                            mask=(start_n + offs_n)[:, None] < seqlen_k,
                            other=0.0)
            else:
                k = tl.load(k_ptrs + start_n * stride_kn,
                            mask=((start_n + offs_n)[:, None] < seqlen_k) &
                            (offs_d[None, :] < headdim),
                            other=0.0)
        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
        qk += tl.dot(q, k, trans_b=True)
        # Trying to combine the two masks seem to make the result wrong
        if not EVEN_N:  # Need to mask out otherwise the softmax is wrong
            qk += tl.where((start_n + offs_n)[None, :] < seqlen_k, 0,
                           float('-inf'))
        if IS_CAUSAL:
            qk += tl.where(offs_m[:, None] >= (start_n + offs_n)[None, :], 0,
                           float('-inf'))
        if BIAS_TYPE != 'none':
            if BIAS_TYPE == 'vector':
                if EVEN_N:
                    bias = tl.load(b_ptrs + start_n).to(tl.float32)
                else:
                    bias = tl.load(b_ptrs + start_n,
                                   mask=(start_n + offs_n) < seqlen_k,
                                   other=0.0).to(tl.float32)
                bias = bias[None, :]
            elif BIAS_TYPE == 'matrix':
                if EVEN_M & EVEN_N:
                    bias = tl.load(b_ptrs + start_n).to(tl.float32)
                else:
                    bias = tl.load(b_ptrs + start_n,
                                   mask=(offs_m[:, None] < seqlen_q) &
                                   ((start_n + offs_n)[None, :] < seqlen_k),
                                   other=0.0).to(tl.float32)
            else:
                raise ValueError(
                    "BIAS_TYPE must be one of {'vector', 'matrix'}")
            # Slightly faster to multiply the softmax_scale in the tl.exp below since the compiler
            # can then fuse the mult and add into an fma instruction. But if we have bias we need to
            # to multiply with softmax_scale here.
            qk = qk * softmax_scale + bias
            m_ij = tl.maximum(tl.max(qk, 1), lse_i)
            p = tl.exp(qk - m_ij[:, None])
        else:
            m_ij = tl.maximum(tl.max(qk, 1) * softmax_scale, lse_i)
            p = tl.exp(qk * softmax_scale - m_ij[:, None])
        l_ij = tl.sum(p, 1)

        # scale acc_o
        acc_o_scale = tl.exp(m_i - m_ij)

        # # -- update output accumulator --
        # BUG: have to store and immediately load
        tl.store(t_ptrs, acc_o_scale)
        acc_o_scale = tl.load(t_ptrs)
        acc_o = acc_o * acc_o_scale[:, None]
        # update acc_o
        if EVEN_N & EVEN_M:  # If we just do "if EVEN_N", there seems to be some race condition
            if EVEN_HEADDIM:
                v = tl.load(v_ptrs + start_n * stride_vn)
            else:
                v = tl.load(v_ptrs + start_n * stride_vn,
                            mask=offs_d[None, :] < headdim,
                            other=0.0)
        else:
            if EVEN_HEADDIM:
                v = tl.load(v_ptrs + start_n * stride_vn,
                            mask=(start_n + offs_n)[:, None] < seqlen_k,
                            other=0.0)
            else:
                v = tl.load(v_ptrs + start_n * stride_vn,
                            mask=((start_n + offs_n)[:, None] < seqlen_k) &
                            (offs_d[None, :] < headdim),
                            other=0.0)
        p = p.to(v.dtype)
        acc_o += tl.dot(p, v)

        # -- update statistics
        m_i = m_ij
        l_i_new = tl.exp(lse_i - m_ij) + l_ij
        lse_i = m_ij + tl.log(l_i_new)

    o_scale = tl.exp(m_i - lse_i)
    # BUG: have to store and immediately load
    tl.store(t_ptrs, o_scale)
    o_scale = tl.load(t_ptrs)
    acc_o = acc_o * o_scale[:, None]
    # rematerialize offsets to save registers
    start_m = tl.program_id(0)
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    # write back l and m
    lse_ptrs = Lse + off_hb * seqlen_q_rounded + offs_m
    tl.store(lse_ptrs, lse_i)
    # initialize pointers to output
    offs_n = tl.arange(0, BLOCK_HEADDIM)
    out_ptrs = Out + off_b * stride_ob + off_h * stride_oh + (
        offs_m[:, None] * stride_om + offs_n[None, :])
    if EVEN_M:
        if EVEN_HEADDIM:
            tl.store(out_ptrs, acc_o)
        else:
            tl.store(out_ptrs, acc_o, mask=offs_d[None, :] < headdim)
    else:
        if EVEN_HEADDIM:
            tl.store(out_ptrs, acc_o, mask=offs_m[:, None] < seqlen_q)
        else:
            tl.store(out_ptrs,
                     acc_o,
                     mask=(offs_m[:, None] < seqlen_q) &
                     (offs_d[None, :] < headdim))


@triton.jit
def _bwd_preprocess_do_o_dot(
    Out,
    DO,
    Delta,
    stride_ob,
    stride_oh,
    stride_om,
    stride_dob,
    stride_doh,
    stride_dom,
    nheads,
    seqlen_q,
    seqlen_q_rounded,
    headdim,
    BLOCK_M: tl.constexpr,
    BLOCK_HEADDIM: tl.constexpr,
):
    start_m = tl.program_id(0)
    off_hb = tl.program_id(1)
    off_b = off_hb // nheads
    off_h = off_hb % nheads
    # initialize offsets
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    offs_d = tl.arange(0, BLOCK_HEADDIM)
    # load
    o = tl.load(Out + off_b * stride_ob + off_h * stride_oh +
                offs_m[:, None] * stride_om + offs_d[None, :],
                mask=(offs_m[:, None] < seqlen_q) & (offs_d[None, :] < headdim),
                other=0.0).to(tl.float32)
    do = tl.load(DO + off_b * stride_dob + off_h * stride_doh +
                 offs_m[:, None] * stride_dom + offs_d[None, :],
                 mask=(offs_m[:, None] < seqlen_q) &
                 (offs_d[None, :] < headdim),
                 other=0.0).to(tl.float32)
    delta = tl.sum(o * do, axis=1)
    # write-back
    tl.store(Delta + off_hb * seqlen_q_rounded + offs_m, delta)


@triton.jit
def _bwd_kernel_one_col_block(
    start_n,
    Q,
    K,
    V,
    Bias,
    DO,
    DQ,
    DK,
    DV,
    LSE,
    D,
    softmax_scale,
    stride_qm,
    stride_kn,
    stride_vn,
    stride_bm,
    stride_dom,
    stride_dqm,
    stride_dkn,
    stride_dvn,
    seqlen_q,
    seqlen_k,
    headdim,
    ATOMIC_ADD: tl.constexpr,
    BIAS_TYPE: tl.constexpr,
    IS_CAUSAL: tl.constexpr,
    BLOCK_HEADDIM: tl.constexpr,
    EVEN_M: tl.constexpr,
    EVEN_N: tl.constexpr,
    EVEN_HEADDIM: tl.constexpr,
    BLOCK_M: tl.constexpr,
    BLOCK_N: tl.constexpr,
):
    # We need to make sure begin_m is a multiple of BLOCK_M (not BLOCK_N)
    begin_m = 0 if not IS_CAUSAL else ((start_n * BLOCK_N) // BLOCK_M) * BLOCK_M
    # initialize row/col offsets
    offs_qm = begin_m + tl.arange(0, BLOCK_M)
    offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N)
    offs_m = tl.arange(0, BLOCK_M)
    offs_d = tl.arange(0, BLOCK_HEADDIM)
    # initialize pointers to value-like data
    q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_d[None, :])
    k_ptrs = K + (offs_n[:, None] * stride_kn + offs_d[None, :])
    v_ptrs = V + (offs_n[:, None] * stride_vn + offs_d[None, :])
    do_ptrs = DO + (offs_qm[:, None] * stride_dom + offs_d[None, :])
    dq_ptrs = DQ + (offs_qm[:, None] * stride_dqm + offs_d[None, :])
    if BIAS_TYPE == 'vector':
        b_ptrs = Bias + offs_n
    elif BIAS_TYPE == 'matrix':
        b_ptrs = Bias + (offs_qm[:, None] * stride_bm + offs_n[None, :])
    else:
        raise ValueError("BIAS_TYPE must be one of {'vector', 'matrix'}")
    # initialize dv and dk
    dv = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
    dk = tl.zeros([BLOCK_N, BLOCK_HEADDIM], dtype=tl.float32)
    # k and v stay in SRAM throughout
    # [2022-10-30] TD: Same bug as the fwd. In the case of EVEN_N=True and EVEN_M=False,
    # if we just call tl.load(k_ptrs), we get the wrong output!
    if EVEN_N & EVEN_M:
        if EVEN_HEADDIM:
            k = tl.load(k_ptrs)
            v = tl.load(v_ptrs)
        else:
            k = tl.load(k_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
            v = tl.load(v_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
    else:
        if EVEN_HEADDIM:
            k = tl.load(k_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
            v = tl.load(v_ptrs, mask=offs_n[:, None] < seqlen_k, other=0.0)
        else:
            k = tl.load(k_ptrs,
                        mask=(offs_n[:, None] < seqlen_k) &
                        (offs_d[None, :] < headdim),
                        other=0.0)
            v = tl.load(v_ptrs,
                        mask=(offs_n[:, None] < seqlen_k) &
                        (offs_d[None, :] < headdim),
                        other=0.0)
    # loop over rows
    num_block_m = tl.cdiv(seqlen_q, BLOCK_M)
    for start_m in range(begin_m, num_block_m * BLOCK_M, BLOCK_M):
        start_m = tl.multiple_of(start_m, BLOCK_M)
        offs_m_curr = start_m + offs_m
        # load q, k, v, do on-chip
        # Same bug as below. Otherwise gives wrong result for headdim=40, seqlen=(128, 117)
        if EVEN_M & EVEN_HEADDIM:
            q = tl.load(q_ptrs)
        else:
            if EVEN_HEADDIM:
                q = tl.load(q_ptrs,
                            mask=offs_m_curr[:, None] < seqlen_q,
                            other=0.0)
            else:
                q = tl.load(q_ptrs,
                            mask=(offs_m_curr[:, None] < seqlen_q) &
                            (offs_d[None, :] < headdim),
                            other=0.0)
        # recompute p = softmax(qk, dim=-1).T
        qk = tl.dot(q, k, trans_b=True)
        # Trying to combine the two masks seem to make the result wrong
        if not EVEN_N:  # Need to mask out otherwise the softmax is wrong
            qk = tl.where(offs_n[None, :] < seqlen_k, qk, float('-inf'))
        if IS_CAUSAL:
            qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), qk,
                          float('-inf'))
        if BIAS_TYPE != 'none':
            if BIAS_TYPE == 'vector':
                if EVEN_N:
                    bias = tl.load(b_ptrs).to(tl.float32)
                else:
                    bias = tl.load(b_ptrs, mask=offs_n < seqlen_k,
                                   other=0.0).to(tl.float32)
                bias = bias[None, :]
            elif BIAS_TYPE == 'matrix':
                if EVEN_M & EVEN_N:
                    bias = tl.load(b_ptrs).to(tl.float32)
                else:
                    bias = tl.load(b_ptrs,
                                   mask=(offs_m_curr[:, None] < seqlen_q) &
                                   (offs_n[None, :] < seqlen_k),
                                   other=0.0).to(tl.float32)
            else:
                raise ValueError(
                    "BIAS_TYPE must be one of {'vector', 'matrix'}")
            qk = qk * softmax_scale + bias
        # There seems to be a race condition when headdim=48/96, and dq, dk, dv are wrong.
        # Also wrong for headdim=64.
        if not (EVEN_M & EVEN_HEADDIM):
            tl.debug_barrier()
        lse_i = tl.load(LSE + offs_m_curr)
        if BIAS_TYPE == 'none':
            p = tl.exp(qk * softmax_scale - lse_i[:, None])
        else:
            p = tl.exp(qk - lse_i[:, None])
        # compute dv
        # [2022-10-30] TD: A Triton bug: if EVEN_M=True and EVEN_HEADDIM=False, if we call
        # do = tl.load(do_ptrs, mask=offs_d[None, :] < headdim, other=0.0), we get wrong outputs
        # in the case of headdim=48/96, seqlen_q & seqlen_k >= 512. If headdim=40 or seqlen < 512,
        # the output is correct.
        if EVEN_M & EVEN_HEADDIM:
            do = tl.load(do_ptrs)
        else:
            # [2022-11-01] TD: Triton bug, there's a race condition if we just use m_mask and not d_mask.
            do = tl.load(do_ptrs,
                         mask=(offs_m_curr[:, None] < seqlen_q) &
                         (offs_d[None, :] < headdim),
                         other=0.0)
        # if EVEN_M:
        #     if EVEN_HEADDIM:
        #         do = tl.load(do_ptrs)
        #     else:
        #         do = tl.load(do_ptrs, mask=offs_d[None, :] < headdim, other=0.0)
        # else:
        #     if EVEN_HEADDIM:
        #         do = tl.load(do_ptrs, mask=offs_m_curr[:, None] < seqlen_q, other=0.0)
        #     else:
        #         do = tl.load(do_ptrs, mask=(offs_m_curr[:, None] < seqlen_q)
        #                                    & (offs_d[None, :] < headdim), other=0.0)
        dv += tl.dot(p.to(do.dtype), do, trans_a=True)
        # compute dp = dot(v, do)
        # There seems to be a race condition when headdim=48/96, and dq, dk are wrong.
        # Also wrong for headdim=128, seqlen=(108, 256), and ATOMIC_ADD=True
        # Also wrong for headdim=64, seqlen=(1023, 1024), and ATOMIC_ADD=False
        if not (EVEN_M & EVEN_HEADDIM):
            tl.debug_barrier()
        dp = tl.dot(do, v, trans_b=True)
        # There's a race condition for headdim=48
        if not EVEN_HEADDIM:
            tl.debug_barrier()
        # compute ds = p * (dp - delta[:, None])
        # Putting the subtraction after the dp matmul (instead of before) is slightly faster
        Di = tl.load(D + offs_m_curr)
        # Converting ds to q.dtype here reduces register pressure and makes it much faster
        # for BLOCK_HEADDIM=128
        ds = (p * (dp - Di[:, None]) * softmax_scale).to(q.dtype)
        # compute dk = dot(ds.T, q)
        dk += tl.dot(ds, q, trans_a=True)
        # compute dq
        if not ATOMIC_ADD:
            if EVEN_M & EVEN_HEADDIM:  # Race condition if we just do EVEN_M
                dq = tl.load(dq_ptrs, eviction_policy='evict_last')
                dq += tl.dot(ds, k)
                tl.store(dq_ptrs, dq, eviction_policy='evict_last')
            else:
                if EVEN_HEADDIM:
                    dq = tl.load(dq_ptrs,
                                 mask=offs_m_curr[:, None] < seqlen_q,
                                 other=0.0,
                                 eviction_policy='evict_last')
                    dq += tl.dot(ds, k)
                    tl.store(dq_ptrs,
                             dq,
                             mask=offs_m_curr[:, None] < seqlen_q,
                             eviction_policy='evict_last')
                else:
                    dq = tl.load(dq_ptrs,
                                 mask=(offs_m_curr[:, None] < seqlen_q) &
                                 (offs_d[None, :] < headdim),
                                 other=0.0,
                                 eviction_policy='evict_last')
                    dq += tl.dot(ds, k)
                    tl.store(dq_ptrs,
                             dq,
                             mask=(offs_m_curr[:, None] < seqlen_q) &
                             (offs_d[None, :] < headdim),
                             eviction_policy='evict_last')
        else:  # If we're parallelizing across the seqlen_k dimension
            dq = tl.dot(ds, k)
            if EVEN_M & EVEN_HEADDIM:  # Race condition if we just do EVEN_M
                tl.atomic_add(dq_ptrs, dq)
            else:
                if EVEN_HEADDIM:
                    tl.atomic_add(dq_ptrs,
                                  dq,
                                  mask=offs_m_curr[:, None] < seqlen_q)
                else:
                    tl.atomic_add(dq_ptrs,
                                  dq,
                                  mask=(offs_m_curr[:, None] < seqlen_q) &
                                  (offs_d[None, :] < headdim))
        # increment pointers
        dq_ptrs += BLOCK_M * stride_dqm
        q_ptrs += BLOCK_M * stride_qm
        do_ptrs += BLOCK_M * stride_dom
        if BIAS_TYPE == 'matrix':
            b_ptrs += BLOCK_M * stride_bm
    # write-back
    dv_ptrs = DV + (offs_n[:, None] * stride_dvn + offs_d[None, :])
    dk_ptrs = DK + (offs_n[:, None] * stride_dkn + offs_d[None, :])
    # [2022-11-01] TD: Same bug. In the case of EVEN_N=True and EVEN_M=False,
    # if we just call tl.store(dv_ptrs), there's a race condition
    if EVEN_N & EVEN_M:
        if EVEN_HEADDIM:
            tl.store(dv_ptrs, dv)
            tl.store(dk_ptrs, dk)
        else:
            tl.store(dv_ptrs, dv, mask=offs_d[None, :] < headdim)
            tl.store(dk_ptrs, dk, mask=offs_d[None, :] < headdim)
    else:
        if EVEN_HEADDIM:
            tl.store(dv_ptrs, dv, mask=offs_n[:, None] < seqlen_k)
            tl.store(dk_ptrs, dk, mask=offs_n[:, None] < seqlen_k)
        else:
            tl.store(dv_ptrs,
                     dv,
                     mask=(offs_n[:, None] < seqlen_k) &
                     (offs_d[None, :] < headdim))
            tl.store(dk_ptrs,
                     dk,
                     mask=(offs_n[:, None] < seqlen_k) &
                     (offs_d[None, :] < headdim))


def init_to_zero(name):
    return lambda nargs: nargs[name].zero_()


@triton.autotune(
    configs=[
        triton.Config(
            {
                'BLOCK_M': 128,
                'BLOCK_N': 128,
                'SEQUENCE_PARALLEL': False
            },
            num_warps=8,
            num_stages=1,
            pre_hook=init_to_zero('DQ')),
        triton.Config(
            {
                'BLOCK_M': 128,
                'BLOCK_N': 128,
                'SEQUENCE_PARALLEL': True
            },
            num_warps=8,
            num_stages=1,
            pre_hook=init_to_zero('DQ')),
        # Other configs seem to give wrong results when seqlen_q % 128 != 0, disabling them for now
        # # Kernel is buggy (give wrong result) if we set BLOCK_m=128, BLOCK_n=64, num_warps=*4*
        # triton.Config({"BLOCK_M": 128, "BLOCK_N": 64, "SEQUENCE_PARALLEL": False}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')),
        # triton.Config({"BLOCK_M": 128, "BLOCK_N": 64, "SEQUENCE_PARALLEL": True}, num_warps=8, num_stages=1, pre_hook=init_to_zero('DQ')),
        # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64, "SEQUENCE_PARALLEL": False}, num_warps=4, num_stages=1, pre_hook=init_to_zero('DQ')),
        # triton.Config({"BLOCK_M": 64, "BLOCK_N": 64, "SEQUENCE_PARALLEL": True}, num_warps=4, num_stages=1, pre_hook=init_to_zero('DQ')),
    ],
    key=[
        'CACHE_KEY_SEQLEN_Q', 'CACHE_KEY_SEQLEN_K', 'BIAS_TYPE', 'IS_CAUSAL',
        'BLOCK_HEADDIM'
    ],
)
@triton.heuristics({
    'EVEN_M': lambda args: args['seqlen_q'] % args['BLOCK_M'] == 0,
    'EVEN_N': lambda args: args['seqlen_k'] % args['BLOCK_N'] == 0,
    'EVEN_HEADDIM': lambda args: args['headdim'] == args['BLOCK_HEADDIM'],
})
@triton.jit
def _bwd_kernel(
    Q,
    K,
    V,
    Bias,
    DO,
    DQ,
    DK,
    DV,
    LSE,
    D,
    softmax_scale,
    stride_qb,
    stride_qh,
    stride_qm,
    stride_kb,
    stride_kh,
    stride_kn,
    stride_vb,
    stride_vh,
    stride_vn,
    stride_bb,
    stride_bh,
    stride_bm,
    stride_dob,
    stride_doh,
    stride_dom,
    stride_dqb,
    stride_dqh,
    stride_dqm,
    stride_dkb,
    stride_dkh,
    stride_dkn,
    stride_dvb,
    stride_dvh,
    stride_dvn,
    nheads,
    seqlen_q,
    seqlen_k,
    seqlen_q_rounded,
    headdim,
    CACHE_KEY_SEQLEN_Q,
    CACHE_KEY_SEQLEN_K,
    BIAS_TYPE: tl.constexpr,
    IS_CAUSAL: tl.constexpr,
    BLOCK_HEADDIM: tl.constexpr,
    SEQUENCE_PARALLEL: tl.constexpr,
    EVEN_M: tl.constexpr,
    EVEN_N: tl.constexpr,
    EVEN_HEADDIM: tl.constexpr,
    BLOCK_M: tl.constexpr,
    BLOCK_N: tl.constexpr,
):
    off_hb = tl.program_id(1)
    off_b = off_hb // nheads
    off_h = off_hb % nheads
    # offset pointers for batch/head
    Q += off_b * stride_qb + off_h * stride_qh
    K += off_b * stride_kb + off_h * stride_kh
    V += off_b * stride_vb + off_h * stride_vh
    DO += off_b * stride_dob + off_h * stride_doh
    DQ += off_b * stride_dqb + off_h * stride_dqh
    DK += off_b * stride_dkb + off_h * stride_dkh
    DV += off_b * stride_dvb + off_h * stride_dvh
    if BIAS_TYPE != 'none':
        Bias += off_b * stride_bb + off_h * stride_bh
    # pointer to row-wise quantities in value-like data
    D += off_hb * seqlen_q_rounded
    LSE += off_hb * seqlen_q_rounded
    if not SEQUENCE_PARALLEL:
        num_block_n = tl.cdiv(seqlen_k, BLOCK_N)
        for start_n in range(0, num_block_n):
            _bwd_kernel_one_col_block(start_n,
                                      Q,
                                      K,
                                      V,
                                      Bias,
                                      DO,
                                      DQ,
                                      DK,
                                      DV,
                                      LSE,
                                      D,
                                      softmax_scale,
                                      stride_qm,
                                      stride_kn,
                                      stride_vn,
                                      stride_bm,
                                      stride_dom,
                                      stride_dqm,
                                      stride_dkn,
                                      stride_dvn,
                                      seqlen_q,
                                      seqlen_k,
                                      headdim,
                                      ATOMIC_ADD=False,
                                      BIAS_TYPE=BIAS_TYPE,
                                      IS_CAUSAL=IS_CAUSAL,
                                      BLOCK_HEADDIM=BLOCK_HEADDIM,
                                      EVEN_M=EVEN_M,
                                      EVEN_N=EVEN_N,
                                      EVEN_HEADDIM=EVEN_HEADDIM,
                                      BLOCK_M=BLOCK_M,
                                      BLOCK_N=BLOCK_N)
    else:
        start_n = tl.program_id(0)
        _bwd_kernel_one_col_block(start_n,
                                  Q,
                                  K,
                                  V,
                                  Bias,
                                  DO,
                                  DQ,
                                  DK,
                                  DV,
                                  LSE,
                                  D,
                                  softmax_scale,
                                  stride_qm,
                                  stride_kn,
                                  stride_vn,
                                  stride_bm,
                                  stride_dom,
                                  stride_dqm,
                                  stride_dkn,
                                  stride_dvn,
                                  seqlen_q,
                                  seqlen_k,
                                  headdim,
                                  ATOMIC_ADD=True,
                                  BIAS_TYPE=BIAS_TYPE,
                                  IS_CAUSAL=IS_CAUSAL,
                                  BLOCK_HEADDIM=BLOCK_HEADDIM,
                                  EVEN_M=EVEN_M,
                                  EVEN_N=EVEN_N,
                                  EVEN_HEADDIM=EVEN_HEADDIM,
                                  BLOCK_M=BLOCK_M,
                                  BLOCK_N=BLOCK_N)


def _flash_attn_forward(q, k, v, bias=None, causal=False, softmax_scale=None):
    # shape constraints
    batch, seqlen_q, nheads, d = q.shape
    _, seqlen_k, _, _ = k.shape
    assert k.shape == (batch, seqlen_k, nheads, d)
    assert v.shape == (batch, seqlen_k, nheads, d)
    assert d <= 128, 'FlashAttention only support head dimensions up to 128'
    assert q.dtype == k.dtype == v.dtype, 'All tensors must have the same type'
    assert q.dtype in [torch.float16,
                       torch.bfloat16], 'Only support fp16 and bf16'
    assert q.is_cuda and k.is_cuda and v.is_cuda
    softmax_scale = softmax_scale or 1.0 / math.sqrt(d)

    has_bias = bias is not None
    bias_type = 'none'
    if has_bias:
        assert bias.dtype in [q.dtype, torch.float]
        assert bias.is_cuda
        assert bias.dim() == 4
        if bias.stride(-1) != 1:
            bias = bias.contiguous()
        if bias.shape[2:] == (1, seqlen_k):
            bias_type = 'vector'
        elif bias.shape[2:] == (seqlen_q, seqlen_k):
            bias_type = 'matrix'
        else:
            raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k)'
                               ' or (seqlen_q, seqlen_k)')
        if bias.shape[:2] == (1, nheads):
            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
        elif bias.shape[:2] == (batch, 1):
            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
        elif bias.shape[:2] == (1, 1):
            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
        assert bias.shape[:2] == (
            batch, nheads
        ), f'First 2 dimensions of bias must be broadcastible to (batch, nheads) = ({batch, nheads}). Bias has shape: {bias.shape}'
    assert bias is not None  # for type checking
    bias_strides = (bias.stride(0), bias.stride(1),
                    bias.stride(2)) if has_bias else (0, 0, 0)

    seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
    lse = torch.empty((batch, nheads, seqlen_q_rounded),
                      device=q.device,
                      dtype=torch.float32)
    tmp = torch.empty((batch, nheads, seqlen_q_rounded),
                      device=q.device,
                      dtype=torch.float32)
    o = torch.empty_like(q)

    BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
    # BLOCK = 128
    # num_warps = 4 if d <= 64 else 8
    grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)
    _fwd_kernel[grid](  # type: ignore
        q,
        k,
        v,
        bias,
        o,
        lse,
        tmp,
        softmax_scale,
        q.stride(0),
        q.stride(2),
        q.stride(1),
        k.stride(0),
        k.stride(2),
        k.stride(1),
        v.stride(0),
        v.stride(2),
        v.stride(1),
        *bias_strides,
        o.stride(0),
        o.stride(2),
        o.stride(1),
        nheads,
        seqlen_q,
        seqlen_k,
        seqlen_q_rounded,
        d,
        seqlen_q // 32,
        seqlen_k // 32,  # key for triton cache (limit number of compilations)
        # Can't use kwargs here because triton autotune expects key to be args, not kwargs
        # IS_CAUSAL=causal, BLOCK_HEADDIM=d,
        bias_type,
        causal,
        BLOCK_HEADDIM,
        # BLOCK_M=BLOCK, BLOCK_N=BLOCK,
        # num_warps=num_warps,
        # num_stages=1,
    )
    return o, lse, softmax_scale  # softmax_scale could have been updated


def _flash_attn_backward(do,
                         q,
                         k,
                         v,
                         o,
                         lse,
                         dq,
                         dk,
                         dv,
                         bias=None,
                         causal=False,
                         softmax_scale=None):
    # Make sure that the last dimension is contiguous
    if do.stride(-1) != 1:
        do = do.contiguous()
    batch, seqlen_q, nheads, d = q.shape
    _, seqlen_k, _, _ = k.shape
    # assert d in {16, 32, 64, 128}
    assert d <= 128
    seqlen_q_rounded = math.ceil(seqlen_q / 128) * 128
    assert lse.shape == (batch, nheads, seqlen_q_rounded)
    assert q.stride(-1) == k.stride(-1) == v.stride(-1) == o.stride(-1) == 1
    assert dq.stride(-1) == dk.stride(-1) == dv.stride(-1) == 1
    softmax_scale = softmax_scale or 1.0 / math.sqrt(d)
    # dq_accum = torch.zeros_like(q, dtype=torch.float32)
    dq_accum = torch.empty_like(q, dtype=torch.float32)
    delta = torch.empty_like(lse)
    # delta = torch.zeros_like(lse)

    BLOCK_HEADDIM = max(triton.next_power_of_2(d), 16)
    grid = lambda META: (triton.cdiv(seqlen_q, META['BLOCK_M']), batch * nheads)
    _bwd_preprocess_do_o_dot[grid](  # type: ignore
        o,
        do,
        delta,
        o.stride(0),
        o.stride(2),
        o.stride(1),
        do.stride(0),
        do.stride(2),
        do.stride(1),
        nheads,
        seqlen_q,
        seqlen_q_rounded,
        d,
        BLOCK_M=128,
        BLOCK_HEADDIM=BLOCK_HEADDIM,
    )

    has_bias = bias is not None
    bias_type = 'none'
    if has_bias:
        assert bias.dtype in [q.dtype, torch.float]
        assert bias.is_cuda
        assert bias.dim() == 4
        assert bias.stride(-1) == 1
        if bias.shape[2:] == (1, seqlen_k):
            bias_type = 'vector'
        elif bias.shape[2:] == (seqlen_q, seqlen_k):
            bias_type = 'matrix'
        else:
            raise RuntimeError('Last 2 dimensions of bias must be (1, seqlen_k)'
                               ' or (seqlen_q, seqlen_k)')
        if bias.shape[:2] == (1, nheads):
            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
        elif bias.shape[:2] == (batch, 1):
            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
        elif bias.shape[:2] == (1, 1):
            bias = repeat(bias, '1 h ... -> b h ...', b=batch)
            bias = repeat(bias, 'b 1 ... -> b h ...', h=nheads)
        assert bias.shape[:2] == (
            batch, nheads
        ), f'First 2 dimensions of bias must be broadcastible to (batch, nheads) = ({batch, nheads}). Bias has shape: {bias.shape}'
    assert bias is not None  # type checking
    bias_strides = (bias.stride(0), bias.stride(1),
                    bias.stride(2)) if has_bias else (0, 0, 0)

    # BLOCK_M = 128
    # BLOCK_N = 64
    # num_warps = 4
    grid = lambda META: (triton.cdiv(seqlen_k, META['BLOCK_N'])
                         if META['SEQUENCE_PARALLEL'] else 1, batch * nheads)
    _bwd_kernel[grid](  # type: ignore
        q,
        k,
        v,
        bias,
        do,
        dq_accum,
        dk,
        dv,
        lse,
        delta,
        softmax_scale,
        q.stride(0),
        q.stride(2),
        q.stride(1),
        k.stride(0),
        k.stride(2),
        k.stride(1),
        v.stride(0),
        v.stride(2),
        v.stride(1),
        *bias_strides,
        do.stride(0),
        do.stride(2),
        do.stride(1),
        dq_accum.stride(0),
        dq_accum.stride(2),
        dq_accum.stride(1),
        dk.stride(0),
        dk.stride(2),
        dk.stride(1),
        dv.stride(0),
        dv.stride(2),
        dv.stride(1),
        nheads,
        seqlen_q,
        seqlen_k,
        seqlen_q_rounded,
        d,
        seqlen_q // 32,
        seqlen_k // 32,  # key for triton cache (limit number of compilations)
        # Can't use kwargs here because triton autotune expects key to be args, not kwargs
        # IS_CAUSAL=causal, BLOCK_HEADDIM=d,
        bias_type,
        causal,
        BLOCK_HEADDIM,
        # SEQUENCE_PARALLEL=False,
        # BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N,
        # num_warps=num_warps,
        # num_stages=1,
    )
    dq.copy_(dq_accum)


class _FlashAttnQKVPackedFunc(torch.autograd.Function):

    @staticmethod
    def forward(ctx, qkv, bias=None, causal=False, softmax_scale=None):
        """Forward pass for packed FlashAttention.

        Args:
            ctx: autograd context
            qkv: (batch, seqlen, 3, nheads, headdim)
            bias: optional, shape broadcastible to (batch, nheads, seqlen, seqlen).
                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen).
                ALiBi mask for non-causal would have shape (1, nheads, seqlen, seqlen)
            causal (bool): whether to incorporate causal attention masking
            softmax_scale (float, optional): scale factor for softmax
        """
        # Make sure that the last dimension is contiguous
        if qkv.stride(-1) != 1:
            qkv = qkv.contiguous()
        o, lse, ctx.softmax_scale = _flash_attn_forward(
            qkv[:, :, 0],
            qkv[:, :, 1],
            qkv[:, :, 2],
            bias=bias,
            causal=causal,
            softmax_scale=softmax_scale)
        ctx.save_for_backward(qkv, o, lse, bias)
        ctx.causal = causal
        return o

    @staticmethod
    def backward(ctx, do):
        qkv, o, lse, bias = ctx.saved_tensors
        assert not ctx.needs_input_grad[
            1], 'FlashAttention does not support bias gradient yet'
        # Triton's autotune causes the Tensor._version to change, and so Pytorch autograd
        # does a memcpy. To avoid this we run in inference_mode, which doesn't track the version.
        with torch.inference_mode():
            dqkv = torch.empty_like(qkv)
            _flash_attn_backward(do,
                                 qkv[:, :, 0],
                                 qkv[:, :, 1],
                                 qkv[:, :, 2],
                                 o,
                                 lse,
                                 dqkv[:, :, 0],
                                 dqkv[:, :, 1],
                                 dqkv[:, :, 2],
                                 bias=bias,
                                 causal=ctx.causal,
                                 softmax_scale=ctx.softmax_scale)
        return dqkv, None, None, None


flash_attn_qkvpacked_func = _FlashAttnQKVPackedFunc.apply


class _FlashAttnFunc(torch.autograd.Function):

    @staticmethod
    def forward(ctx, q, k, v, bias=None, causal=False, softmax_scale=None):
        """Forward pass for FlashAttention.

        Args:
            ctx: autograd context
            q: (batch_size, seqlen_q, nheads, headdim)
            k: (batch_size, seqlen_k, nheads, headdim)
            v: (batch_size, seqlen_k, nheads, headdim)
            bias: optional, shape broadcastible to (batch, nheads, seqlen_q, seqlen_k).
                For example, ALiBi mask for causal would have shape (1, nheads, 1, seqlen_k).
                ALiBi mask for non-causal would have shape (1, nheads, seqlen_q, seqlen_k)
            causal (bool): whether to incorporate causal attention masking
            softmax_scale (float, optional): scale factor for softmax
        """
        # Make sure that the last dimension is contiguous
        q, k, v = [
            x if x.stride(-1) == 1 else x.contiguous() for x in [q, k, v]
        ]
        o, lse, ctx.softmax_scale = _flash_attn_forward(
            q, k, v, bias=bias, causal=causal, softmax_scale=softmax_scale)
        ctx.save_for_backward(q, k, v, o, lse, bias)
        ctx.causal = causal
        return o

    @staticmethod
    def backward(ctx, do):
        q, k, v, o, lse, bias = ctx.saved_tensors
        assert not ctx.needs_input_grad[
            3], 'FlashAttention does not support bias gradient yet'
        # Triton's autotune causes the Tensor._version to change, and so Pytorch autograd
        # does a memcpy. To avoid this we run in inference_mode, which doesn't track the version.
        with torch.inference_mode():
            dq = torch.empty_like(q)
            dk = torch.empty_like(k)
            dv = torch.empty_like(v)
            _flash_attn_backward(do,
                                 q,
                                 k,
                                 v,
                                 o,
                                 lse,
                                 dq,
                                 dk,
                                 dv,
                                 bias=bias,
                                 causal=ctx.causal,
                                 softmax_scale=ctx.softmax_scale)
        return dq, dk, dv, None, None, None


flash_attn_func = _FlashAttnFunc.apply