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flash_attn_triton.py

@@ -0,0 +1,1112 @@
+# 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