flash_attention_triton.py

import pytest
import torch


# import os
# os.environ["TRITON_INTERPRET"] = "1"

import triton
import triton.language as tl




def is_hip():
    return triton.runtime.driver.active.get_current_target().backend == "hip"



@triton.jit
def _attn_fwd_inner(acc, l_i, m_i, q,  #
                    K_block_ptr, V_block_ptr,  #
                    start_m, qk_scale,  #
                    BLOCK_M: tl.constexpr, HEAD_DIM: tl.constexpr, BLOCK_N: tl.constexpr,  #
                    STAGE: tl.constexpr, offs_m: tl.constexpr, offs_n: tl.constexpr,  #
                    N_CTX: tl.constexpr, fp8_v: tl.constexpr):
    # range of values handled by this stage
    # 这个阶段处理的数值范围
    # inner stage=3:  for causal = False
    # inner stage=1:  for causal = True, 先运行
    # inner stage=2:  for causal = True，后运行
    if STAGE == 1:
        lo, hi = 0, start_m * BLOCK_M
    elif STAGE == 2:
        lo, hi = start_m * BLOCK_M, (start_m + 1) * BLOCK_M
        lo = tl.multiple_of(lo, BLOCK_M)
    else:
        # causal = False, inner_stage=3
        lo, hi = 0, N_CTX

    # import ipdb;ipdb.set_trace()
    K_block_ptr = tl.advance(K_block_ptr, (0, lo))
    V_block_ptr = tl.advance(V_block_ptr, (lo, 0))
    # loop over k, v and update accumulator
    # 循环遍历 k 和 v，并更新累加器。
    for start_n in range(lo, hi, BLOCK_N):
        start_n = tl.multiple_of(start_n, BLOCK_N)
        # -- compute qk ----
        # -- 计算 qk ----
        k = tl.load(K_block_ptr)
        qk = tl.dot(q, k)
        if STAGE == 2:
            mask = offs_m[:, None] >= (start_n + offs_n[None, :])
            qk = qk * qk_scale + tl.where(mask, 0, -1.0e6)
            m_ij = tl.maximum(m_i, tl.max(qk, 1))
            qk -= m_ij[:, None]
        else:
            m_ij = tl.maximum(m_i, tl.max(qk, 1) * qk_scale)
            qk = qk * qk_scale - m_ij[:, None]
        p = tl.math.exp2(qk)
        l_ij = tl.sum(p, 1)
        # -- update m_i and l_i
        # -- 更新 m_i 和 l_i
        alpha = tl.math.exp2(m_i - m_ij)
        l_i = l_i * alpha + l_ij
        # -- update output accumulator --
        # -- 更新输出累加器 --
        acc = acc * alpha[:, None] #矫正前面的pv的block计算
        # update acc
        # 更新 acc
        v = tl.load(V_block_ptr)
        if fp8_v:
            p = p.to(tl.float8e5)
        else:
            p = p.to(tl.float16)
        acc = tl.dot(p, v, acc) #pv的block计算，结果累加到acc
        # update m_i and l_i
        # 更新 m_i 和 l_i
        m_i = m_ij
        V_block_ptr = tl.advance(V_block_ptr, (BLOCK_N, 0))
        K_block_ptr = tl.advance(K_block_ptr, (0, BLOCK_N))
    return acc, l_i, m_i




# We don't run auto-tuning every time to keep the tutorial fast. Keeping
# the code below and commenting out the equivalent parameters is convenient for
# re-tuning.
# 为了重新调整，我们不会每次都运行自动调优以保持教程的快速性。
# 保留下面的代码并注释掉等效的参数是方便的做法。
configs = [
    triton.Config({'BLOCK_M': BM, 'BLOCK_N': BN}, num_stages=s, num_warps=w) \
    for BM in [64, 128]\
    for BN in [32, 64]\
    for s in ([1] if is_hip() else [3, 4, 7])\
    for w in [4, 8]\
]



def keep(conf):
    BLOCK_M = conf.kwargs["BLOCK_M"]
    BLOCK_N = conf.kwargs["BLOCK_N"]
    if BLOCK_M * BLOCK_N < 128 * 128 and conf.num_warps == 8:
        return False
    return True




@triton.autotune(list(filter(keep, configs)), key=["N_CTX", "HEAD_DIM"])
@triton.jit
def _attn_fwd(Q, K, V, sm_scale, M, Out,  #
              stride_qz, stride_qh, stride_qm, stride_qk,  #
              stride_kz, stride_kh, stride_kn, stride_kk,  #
              stride_vz, stride_vh, stride_vk, stride_vn,  #
              stride_oz, stride_oh, stride_om, stride_on,  #
              Z, H, N_CTX,  #
              HEAD_DIM: tl.constexpr,  #
              BLOCK_M: tl.constexpr,  #
              BLOCK_N: tl.constexpr,  #
              STAGE: tl.constexpr  #
              ):
    tl.static_assert(BLOCK_N <= HEAD_DIM)
    # grid -> [N_CTX, Z * H, 1] ->(seq_len/block_m, batch*n_heads, 1)
    # Q.shape -> [batch, n_heads, seq_n, head_dim] -> [z, h, seq_n, d]
    start_m = tl.program_id(0) #seq_len/block_m
    off_hz = tl.program_id(1) #batch*n_heads
    off_z = off_hz // H #获取batch索引
    off_h = off_hz % H #获取head索引
    # offset pointers for batch/head，基于 batch/head 的偏移指针
    qvk_offset = off_z.to(tl.int64) * stride_qz + off_h.to(tl.int64) * stride_qh


    # block pointers
    # 块指针
    # 创建一个块指针，包含了基地址、形状、步幅、偏移量和存储顺序等信息。
    # 后续offs_m, offs_n, offs_k等都是基于这个块指针的来访问块数据
    Q_block_ptr = tl.make_block_ptr(
        base=Q + qvk_offset,
        shape=(N_CTX, HEAD_DIM), #(1024, 64)
        strides=(stride_qm, stride_qk), #stride_qm: seq_len, stride_qk: head_dim (64, 1)
        offsets=(start_m * BLOCK_M, 0), #(start_m*64, 0)
        block_shape=(BLOCK_M, HEAD_DIM), #(64, 64)
        order=(1, 0),
    )
    v_order: tl.constexpr = (0, 1) if V.dtype.element_ty == tl.float8e5 else (1, 0)
    V_block_ptr = tl.make_block_ptr(
        base=V + qvk_offset,
        shape=(N_CTX, HEAD_DIM),
        strides=(stride_vk, stride_vn),
        offsets=(0, 0),
        block_shape=(BLOCK_N, HEAD_DIM),
        order=v_order,
    )
    K_block_ptr = tl.make_block_ptr(
        base=K + qvk_offset,
        shape=(HEAD_DIM, N_CTX),
        strides=(stride_kk, stride_kn),
        offsets=(0, 0),
        block_shape=(HEAD_DIM, BLOCK_N),
        order=(0, 1),
    )
    O_block_ptr = tl.make_block_ptr(
        base=Out + qvk_offset,
        shape=(N_CTX, HEAD_DIM),
        strides=(stride_om, stride_on),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, HEAD_DIM),
        order=(1, 0),
    )
    # initialize offsets
    # 初始化偏移量
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    offs_n = tl.arange(0, BLOCK_N)
    # initialize pointer to m and l、
    # 初始化 m 和 l 的指针
    m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
    l_i = tl.zeros([BLOCK_M], dtype=tl.float32) + 1.0
    acc = tl.zeros([BLOCK_M, HEAD_DIM], dtype=tl.float32)
    # load scales
    # 加载系数
    qk_scale = sm_scale
    qk_scale *= 1.44269504  # 1/log(2)
    # load q: it will stay in SRAM throughout
    # 加载 q: 它将始终保留在 SRAM 中
    q = tl.load(Q_block_ptr)
    # stage 1: off-band
    # 阶段 1: off-band
    # For causal = True, STAGE = 3 and _attn_fwd_inner gets 1 as its STAGE
    # 对于 causal = True，STAGE = 3，而 _attn_fwd_inner 的 STAGE 参数设定为 1。
    # For causal = False, STAGE = 1, and _attn_fwd_inner gets 3 as its STAGE
    # 对于 causal = False, STAGE = 1, 而 _attn_fwd_inner 的 STAGE 参数设定为 3。

    # For causal = False, STAGE=1, _attn_fwd_inner运行一次_attn_fwd_inner，inner_stage=3, 标准的k,v内循环
    # For causal = True, STAGE=3,  _attn_fwd_inner运行两次，第一次inner_stage=1,第二次inner_stage=2
    if STAGE & 1:
        acc, l_i, m_i = _attn_fwd_inner(acc, l_i, m_i, q, K_block_ptr, V_block_ptr,  #
                                        start_m, qk_scale,  #
                                        BLOCK_M, HEAD_DIM, BLOCK_N,  #
                                        4 - STAGE, offs_m, offs_n, N_CTX, V.dtype.element_ty == tl.float8e5  #
                                        )
    # stage 2: on-band
    # 阶段 2: on-band
    if STAGE & 2:
        # barrier makes it easier for compielr to schedule the
        # two loops independently
        acc, l_i, m_i = _attn_fwd_inner(acc, l_i, m_i, q, K_block_ptr, V_block_ptr,  #
                                        start_m, qk_scale,  #
                                        BLOCK_M, HEAD_DIM, BLOCK_N,  #
                                        2, offs_m, offs_n, N_CTX, V.dtype.element_ty == tl.float8e5  #
                                        )
    # epilogue
    # 结尾
    m_i += tl.math.log2(l_i)
    acc = acc / l_i[:, None]
    m_ptrs = M + off_hz * N_CTX + offs_m
    tl.store(m_ptrs, m_i)
    tl.store(O_block_ptr, acc.to(Out.type.element_ty))




@triton.jit
def _attn_bwd_preprocess(O, DO,  #
                         Delta,  #
                         Z, H, N_CTX,  #
                         BLOCK_M: tl.constexpr, HEAD_DIM: tl.constexpr  #
                         ):
    off_m = tl.program_id(0) * BLOCK_M + tl.arange(0, BLOCK_M)
    off_hz = tl.program_id(1)
    off_n = tl.arange(0, HEAD_DIM)
    # load
    # 加载
    o = tl.load(O + off_hz * HEAD_DIM * N_CTX + off_m[:, None] * HEAD_DIM + off_n[None, :])
    do = tl.load(DO + off_hz * HEAD_DIM * N_CTX + off_m[:, None] * HEAD_DIM + off_n[None, :]).to(tl.float32)
    delta = tl.sum(o * do, axis=1)
    # write-back
    # 写回
    tl.store(Delta + off_hz * N_CTX + off_m, delta)




# The main inner-loop logic for computing dK and dV.
# 内循环的主要逻辑是计算 dK 和 dV
@triton.jit
def _attn_bwd_dkdv(dk, dv,  #
                   Q, k, v, sm_scale,  #
                   DO,  #
                   M, D,  #
                   # shared by Q/K/V/DO.
                   # 由 Q/K/V/DO 共享
                   stride_tok, stride_d,  #
                   H, N_CTX, BLOCK_M1: tl.constexpr,  #
                   BLOCK_N1: tl.constexpr,  #
                   HEAD_DIM: tl.constexpr,  #
                   # Filled in by the wrapper.
                   # 由 wrapper 填充
                   start_n, start_m, num_steps,  #
                   MASK: tl.constexpr):
    offs_m = start_m + tl.arange(0, BLOCK_M1)
    offs_n = start_n + tl.arange(0, BLOCK_N1)
    offs_k = tl.arange(0, HEAD_DIM)
    qT_ptrs = Q + offs_m[None, :] * stride_tok + offs_k[:, None] * stride_d
    do_ptrs = DO + offs_m[:, None] * stride_tok + offs_k[None, :] * stride_d
    # BLOCK_N1 must be a multiple of BLOCK_M1, otherwise the code wouldn't work.
    # BLOCK_N1 必须是 BLOCK_M1 的倍数，否则代码将无法正常工作。
    tl.static_assert(BLOCK_N1 % BLOCK_M1 == 0)
    curr_m = start_m
    step_m = BLOCK_M1
    for blk_idx in range(num_steps):
        qT = tl.load(qT_ptrs)
        # Load m before computing qk to reduce pipeline stall.
        # 在计算 qk 前先加载 m，以减少流水线停顿。
        offs_m = curr_m + tl.arange(0, BLOCK_M1)
        m = tl.load(M + offs_m)
        qkT = tl.dot(k, qT)
        pT = tl.math.exp2(qkT - m[None, :])
        # Autoregressive masking.
        # 自回归掩码。
        if MASK:
            mask = (offs_m[None, :] >= offs_n[:, None])
            pT = tl.where(mask, pT, 0.0)
        do = tl.load(do_ptrs)
        # Compute dV.
        # 计算 dV.
        ppT = pT
        ppT = ppT.to(tl.float16)
        dv += tl.dot(ppT, do)
        # D (= delta) is pre-divided by ds_scale.
        # D（= delta）已经通过 ds_scale 进行了预除。
        Di = tl.load(D + offs_m)
        # Compute dP and dS.
        # 计算 dP 和 dS.
        dpT = tl.dot(v, tl.trans(do)).to(tl.float32)
        dsT = pT * (dpT - Di[None, :])
        dsT = dsT.to(tl.float16)
        dk += tl.dot(dsT, tl.trans(qT))
        # Increment pointers.
        # 增加指针。
        curr_m += step_m
        qT_ptrs += step_m * stride_tok
        do_ptrs += step_m * stride_tok
    return dk, dv




# the main inner-loop logic for computing dQ
# 内循环的主要逻辑是计算 dQ
@triton.jit
def _attn_bwd_dq(dq, q, K, V,  #
                 do, m, D,
                 # shared by Q/K/V/DO.
                 # 由 Q/K/V/DO 共享
                 stride_tok, stride_d,  #
                 H, N_CTX,  #
                 BLOCK_M2: tl.constexpr,  #
                 BLOCK_N2: tl.constexpr,  #
                 HEAD_DIM: tl.constexpr,
                 # Filled in by the wrapper.
                 # 由 wrapper 填充
                 start_m, start_n, num_steps,  #
                 MASK: tl.constexpr):
    offs_m = start_m + tl.arange(0, BLOCK_M2)
    offs_n = start_n + tl.arange(0, BLOCK_N2)
    offs_k = tl.arange(0, HEAD_DIM)
    kT_ptrs = K + offs_n[None, :] * stride_tok + offs_k[:, None] * stride_d
    vT_ptrs = V + offs_n[None, :] * stride_tok + offs_k[:, None] * stride_d
    # D (= delta) is pre-divided by ds_scale.
    # D（即 delta）在使用前已经被 ds_scale 预先除以。
    Di = tl.load(D + offs_m)
    # BLOCK_M2 must be a multiple of BLOCK_N2, otherwise the code wouldn't work.
    # BLOCK_M2 必须是 BLOCK_N2 的倍数，否则代码将无法正常工作。
    tl.static_assert(BLOCK_M2 % BLOCK_N2 == 0)
    curr_n = start_n
    step_n = BLOCK_N2
    for blk_idx in range(num_steps):
        kT = tl.load(kT_ptrs)
        vT = tl.load(vT_ptrs)
        qk = tl.dot(q, kT)
        p = tl.math.exp2(qk - m)
        # Autoregressive masking.
        # 自回归掩码。
        if MASK:
            offs_n = curr_n + tl.arange(0, BLOCK_N2)
            mask = (offs_m[:, None] >= offs_n[None, :])
            p = tl.where(mask, p, 0.0)
        # Compute dP and dS.
        # 计算 dP 和 dS.
        dp = tl.dot(do, vT).to(tl.float32)
        ds = p * (dp - Di[:, None])
        ds = ds.to(tl.float16)
        # Compute dQ.
        # 计算 dQ.
        # NOTE: We need to de-scale dq in the end, because kT was pre-scaled.
        # 注意：我们需要在最后对 dq 进行反缩放，因为 kT 已经进行了预缩放。
        dq += tl.dot(ds, tl.trans(kT))
        # 增加指针。
        curr_n += step_n
        kT_ptrs += step_n * stride_tok
        vT_ptrs += step_n * stride_tok
    return dq




@triton.jit
def _attn_bwd(Q, K, V, sm_scale,  #
              DO,  #
              DQ, DK, DV,  #
              M, D,
              # shared by Q/K/V/DO.
              # 由 Q/K/V/DO 共享
              stride_z, stride_h, stride_tok, stride_d,  #
              H, N_CTX,  #
              BLOCK_M1: tl.constexpr,  #
              BLOCK_N1: tl.constexpr,  #
              BLOCK_M2: tl.constexpr,  #
              BLOCK_N2: tl.constexpr,  #
              BLK_SLICE_FACTOR: tl.constexpr,  #
              HEAD_DIM: tl.constexpr):
    LN2: tl.constexpr = 0.6931471824645996  # = ln(2)


    bhid = tl.program_id(2)
    off_chz = (bhid * N_CTX).to(tl.int64)
    adj = (stride_h * (bhid % H) + stride_z * (bhid // H)).to(tl.int64)
    pid = tl.program_id(0)


    # offset pointers for batch/head
    # 为 batch/head 偏移指针。
    Q += adj
    K += adj
    V += adj
    DO += adj
    DQ += adj
    DK += adj
    DV += adj
    M += off_chz
    D += off_chz


    # load scales
    # 加载系数
    offs_k = tl.arange(0, HEAD_DIM)


    start_n = pid * BLOCK_N1
    start_m = start_n


    MASK_BLOCK_M1: tl.constexpr = BLOCK_M1 // BLK_SLICE_FACTOR
    offs_n = start_n + tl.arange(0, BLOCK_N1)


    dv = tl.zeros([BLOCK_N1, HEAD_DIM], dtype=tl.float32)
    dk = tl.zeros([BLOCK_N1, HEAD_DIM], dtype=tl.float32)


    # load K and V: they stay in SRAM throughout the inner loop.
    # 加载 K 和 V：它们在整个内部循环过程中保持在 SRAM 中。
    k = tl.load(K + offs_n[:, None] * stride_tok + offs_k[None, :] * stride_d)
    v = tl.load(V + offs_n[:, None] * stride_tok + offs_k[None, :] * stride_d)


    num_steps = BLOCK_N1 // MASK_BLOCK_M1


    dk, dv = _attn_bwd_dkdv(dk, dv,  #
                            Q, k, v, sm_scale,  #
                            DO,  #
                            M, D,  #
                            stride_tok, stride_d,  #
                            H, N_CTX,  #
                            MASK_BLOCK_M1, BLOCK_N1, HEAD_DIM,  #
                            start_n, start_m, num_steps,  #
                            MASK=True  #
                            )


    start_m += num_steps * MASK_BLOCK_M1
    num_steps = (N_CTX - start_m) // BLOCK_M1


    # Compute dK and dV for non-masked blocks.
    # 计算非掩码块的 dK 和 dV。
    dk, dv = _attn_bwd_dkdv(  #
        dk, dv,  #
        Q, k, v, sm_scale,  #
        DO,  #
        M, D,  #
        stride_tok, stride_d,  #
        H, N_CTX,  #
        BLOCK_M1, BLOCK_N1, HEAD_DIM,  #
        start_n, start_m, num_steps,  #
        MASK=False  #
    )


    dv_ptrs = DV + offs_n[:, None] * stride_tok + offs_k[None, :] * stride_d
    tl.store(dv_ptrs, dv)


    # Write back dK.
    # 写回 dK
    dk *= sm_scale
    dk_ptrs = DK + offs_n[:, None] * stride_tok + offs_k[None, :] * stride_d
    tl.store(dk_ptrs, dk)


    # THIS BLOCK DOES DQ:
    # 该段计算 DQ
    start_m = pid * BLOCK_M2
    end_n = start_m + BLOCK_M2


    MASK_BLOCK_N2: tl.constexpr = BLOCK_N2 // BLK_SLICE_FACTOR
    offs_m = start_m + tl.arange(0, BLOCK_M2)


    q = tl.load(Q + offs_m[:, None] * stride_tok + offs_k[None, :] * stride_d)
    dq = tl.zeros([BLOCK_M2, HEAD_DIM], dtype=tl.float32)
    do = tl.load(DO + offs_m[:, None] * stride_tok + offs_k[None, :] * stride_d)


    m = tl.load(M + offs_m)
    m = m[:, None]


    # Compute dQ for masked (diagonal) blocks.
    # 计算掩码（对角线）块的 dQ。
    # NOTE: This code scans each row of QK^T backward (from right to left,
    # but inside each call to _attn_bwd_dq, from left to right), but that's
    # not due to anything important.  I just wanted to reuse the loop
    # structure for dK & dV above as much as possible.
    # 注意：这段代码逆向扫描每行 QK^T（从右向左，但在每次调用 _attn_bwd_dq 内部，
    # 从左向右），但这并不重要。我只是希望尽可能多地重用上述 dK 和 dV 的循环结构。
    num_steps = BLOCK_M2 // MASK_BLOCK_N2
    dq = _attn_bwd_dq(dq, q, K, V,  #
                      do, m, D,  #
                      stride_tok, stride_d,  #
                      H, N_CTX,  #
                      BLOCK_M2, MASK_BLOCK_N2, HEAD_DIM,  #
                      start_m, end_n - num_steps * MASK_BLOCK_N2, num_steps,  #
                      MASK=True  #
                      )
    end_n -= num_steps * MASK_BLOCK_N2
    # stage 2
    # 阶段 2
    num_steps = end_n // BLOCK_N2
    dq = _attn_bwd_dq(dq, q, K, V,  #
                      do, m, D,  #
                      stride_tok, stride_d,  #
                      H, N_CTX,  #
                      BLOCK_M2, BLOCK_N2, HEAD_DIM,  #
                      start_m, end_n - num_steps * BLOCK_N2, num_steps,  #
                      MASK=False  #
                      )
    # Write back dQ.
    # 写回 dQ
    dq_ptrs = DQ + offs_m[:, None] * stride_tok + offs_k[None, :] * stride_d
    dq *= LN2
    tl.store(dq_ptrs, dq)




class _attention(torch.autograd.Function):


    @staticmethod
    def forward(ctx, q, k, v, causal, sm_scale):
        # shape constraints
        # 形状约束
        HEAD_DIM_Q, HEAD_DIM_K = q.shape[-1], k.shape[-1]
        # when v is in float8_e5m2 it is transposed.
        # 当 v 在 float8_e5m2 格式下时，进行转置。
        HEAD_DIM_V = v.shape[-1]
        assert HEAD_DIM_Q == HEAD_DIM_K and HEAD_DIM_K == HEAD_DIM_V
        assert HEAD_DIM_K in {16, 32, 64, 128, 256}
        o = torch.empty_like(q)
        stage = 3 if causal else 1
        extra_kern_args = {}
        # Tuning for AMD target
        # 为 AMD 设备调整
        if is_hip():
            waves_per_eu = 3 if HEAD_DIM_K <= 64 else 2
            extra_kern_args = {"waves_per_eu": waves_per_eu, "allow_flush_denorm": True}

        # q.shape -> [batch, n_heads, seq_n, head_dim] -> [4, 32, 1024, 64]
        grid = lambda args: (triton.cdiv(q.shape[2], args["BLOCK_M"]), q.shape[0] * q.shape[1], 1)
        M = torch.empty((q.shape[0], q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32)
        _attn_fwd[grid](
            q, k, v, sm_scale, M, o,  #
            q.stride(0), q.stride(1), q.stride(2), q.stride(3),  #
            k.stride(0), k.stride(1), k.stride(2), k.stride(3),  #
            v.stride(0), v.stride(1), v.stride(2), v.stride(3),  #
            o.stride(0), o.stride(1), o.stride(2), o.stride(3),  #
            q.shape[0], q.shape[1],  #
            N_CTX=q.shape[2],  #
            HEAD_DIM=HEAD_DIM_K,  #
            STAGE=stage,  #
            **extra_kern_args)


        ctx.save_for_backward(q, k, v, o, M)
        ctx.grid = grid
        ctx.sm_scale = sm_scale
        ctx.HEAD_DIM = HEAD_DIM_K
        ctx.causal = causal
        return o


    @staticmethod
    def backward(ctx, do):
        q, k, v, o, M = ctx.saved_tensors
        assert do.is_contiguous()
        assert q.stride() == k.stride() == v.stride() == o.stride() == do.stride()
        dq = torch.empty_like(q)
        dk = torch.empty_like(k)
        dv = torch.empty_like(v)
        BATCH, N_HEAD, N_CTX = q.shape[:3]
        PRE_BLOCK = 128
        NUM_WARPS, NUM_STAGES = 4, 5
        BLOCK_M1, BLOCK_N1, BLOCK_M2, BLOCK_N2 = 32, 128, 128, 32
        BLK_SLICE_FACTOR = 2
        RCP_LN2 = 1.4426950408889634  # = 1.0 / ln(2)
        arg_k = k
        arg_k = arg_k * (ctx.sm_scale * RCP_LN2)
        PRE_BLOCK = 128
        assert N_CTX % PRE_BLOCK == 0
        pre_grid = (N_CTX // PRE_BLOCK, BATCH * N_HEAD)
        delta = torch.empty_like(M)
        _attn_bwd_preprocess[pre_grid](
            o, do,  #
            delta,  #
            BATCH, N_HEAD, N_CTX,  #
            BLOCK_M=PRE_BLOCK, HEAD_DIM=ctx.HEAD_DIM  #
        )
        grid = (N_CTX // BLOCK_N1, 1, BATCH * N_HEAD)
        _attn_bwd[grid](
            q, arg_k, v, ctx.sm_scale, do, dq, dk, dv,  #
            M, delta,  #
            q.stride(0), q.stride(1), q.stride(2), q.stride(3),  #
            N_HEAD, N_CTX,  #
            BLOCK_M1=BLOCK_M1, BLOCK_N1=BLOCK_N1,  #
            BLOCK_M2=BLOCK_M2, BLOCK_N2=BLOCK_N2,  #
            BLK_SLICE_FACTOR=BLK_SLICE_FACTOR,  #
            HEAD_DIM=ctx.HEAD_DIM,  #
            num_warps=NUM_WARPS,  #
            num_stages=NUM_STAGES  #
        )


        return dq, dk, dv, None, None




attention = _attention.apply




@pytest.mark.parametrize("Z, H, N_CTX, HEAD_DIM", [(1, 2, 1024, 64)])
@pytest.mark.parametrize("causal", [True])
def test_op(Z, H, N_CTX, HEAD_DIM, causal, dtype=torch.float16):
    torch.manual_seed(20)
    q = (torch.empty((Z, H, N_CTX, HEAD_DIM), dtype=dtype, device="cuda").normal_(mean=0.0, std=0.5).requires_grad_())
    k = (torch.empty((Z, H, N_CTX, HEAD_DIM), dtype=dtype, device="cuda").normal_(mean=0.0, std=0.5).requires_grad_())
    v = (torch.empty((Z, H, N_CTX, HEAD_DIM), dtype=dtype, device="cuda").normal_(mean=0.0, std=0.5).requires_grad_())
    sm_scale = 0.5
    dout = torch.randn_like(q)
    # reference implementation
    # 参考实现
    M = torch.tril(torch.ones((N_CTX, N_CTX), device="cuda"))
    p = torch.matmul(q, k.transpose(2, 3)) * sm_scale
    if causal:
        p[:, :, M == 0] = float("-inf")
    p = torch.softmax(p.float(), dim=-1).half()
    # p = torch.exp(p)
    ref_out = torch.matmul(p, v)
    ref_out.backward(dout)
    ref_dv, v.grad = v.grad.clone(), None
    ref_dk, k.grad = k.grad.clone(), None
    ref_dq, q.grad = q.grad.clone(), None
    # triton implementation
    # triton 实现
    tri_out = attention(q, k, v, causal, sm_scale).half()
    tri_out.backward(dout)
    tri_dv, v.grad = v.grad.clone(), None
    tri_dk, k.grad = k.grad.clone(), None
    tri_dq, q.grad = q.grad.clone(), None
    # compare
    # 比较
    assert torch.allclose(ref_out, tri_out, atol=1e-2, rtol=0)
    rtol = 0.0
    # Relative tolerance workaround for known hardware limitation of MI200 GPU.
    # 针对 MI200 GPU 已知的硬件限制，使用相对容差的解决方法。
    # For details see https://pytorch.org/docs/stable/notes/numerical_accuracy.html#reduced-precision-fp16-and-bf16-gemms-and-convolutions-on-amd-instinct-mi200-devices
    # 详情见 https://pytorch.org/docs/stable/notes/numerical_accuracy.html#reduced-precision-fp16-and-bf16-gemms-and-convolutions-on-amd-instinct-mi200-devices
    if torch.version.hip is not None and triton.runtime.driver.active.get_current_target().arch == "gfx90a":
        rtol = 1e-2
    assert torch.allclose(ref_dv, tri_dv, atol=1e-2, rtol=rtol)
    assert torch.allclose(ref_dk, tri_dk, atol=1e-2, rtol=rtol)
    assert torch.allclose(ref_dq, tri_dq, atol=1e-2, rtol=rtol)




try:
    from flash_attn.flash_attn_interface import \
        flash_attn_qkvpacked_func as flash_attn_func
    HAS_FLASH = True
except BaseException:
    HAS_FLASH = False


TORCH_HAS_FP8 = hasattr(torch, 'float8_e5m2')
BATCH, N_HEADS, HEAD_DIM = 4, 32, 64
# vary seq length for fixed head and batch=4
# 对于固定的 head 和 batch 为 4，变化序列长度。
configs = []
for mode in ["fwd", "bwd"]:
    for causal in [True]: # delete true
        if mode == "bwd" and not causal:
            continue
        configs.append(
            triton.testing.Benchmark(
                x_names=["N_CTX"],
                x_vals=[2**i for i in range(10, 15)],
                line_arg="provider",
                line_vals=["triton-fp16"] + (["triton-fp8"] if TORCH_HAS_FP8 else []) +
                (["flash"] if HAS_FLASH else []),
                line_names=["Triton [FP16]"] + (["Triton [FP8]"] if TORCH_HAS_FP8 else []) +
                (["Flash-2"] if HAS_FLASH else []),
                styles=[("red", "-"), ("blue", "-")],
                ylabel="ms",
                plot_name=f"fused-attention-batch{BATCH}-head{N_HEADS}-d{HEAD_DIM}-{mode}-causal={causal}",
                args={
                    "H": N_HEADS,
                    "BATCH": BATCH,
                    "HEAD_DIM": HEAD_DIM,
                    "mode": mode,
                    "causal": causal,
                },
            ))




@triton.testing.perf_report(configs)
def bench_flash_attention(BATCH, H, N_CTX, HEAD_DIM, causal, mode, provider, device="cuda"):
    assert mode in ["fwd", "bwd"]
    warmup = 25
    rep = 100
    dtype = torch.float16
    if "triton" in provider:
        q = torch.randn((BATCH, H, N_CTX, HEAD_DIM), dtype=dtype, device=device, requires_grad=True)
        k = torch.randn((BATCH, H, N_CTX, HEAD_DIM), dtype=dtype, device=device, requires_grad=True)
        v = torch.randn((BATCH, H, N_CTX, HEAD_DIM), dtype=dtype, device=device, requires_grad=True)
        if mode == "fwd" and "fp8" in provider:
            q = q.to(torch.float8_e5m2)
            k = k.to(torch.float8_e5m2)
            v = v.permute(0, 1, 3, 2).contiguous()
            v = v.permute(0, 1, 3, 2)
            v = v.to(torch.float8_e5m2)
        sm_scale = 1.3
        fn = lambda: attention(q, k, v, causal, sm_scale)
        if mode == "bwd":
            o = fn()
            do = torch.randn_like(o)
            fn = lambda: o.backward(do, retain_graph=True)
        ms = triton.testing.do_bench(fn, warmup=warmup, rep=rep)
    if provider == "flash":
        qkv = torch.randn((BATCH, N_CTX, 3, H, HEAD_DIM), dtype=dtype, device=device, requires_grad=True)
        fn = lambda: flash_attn_func(qkv, causal=causal)
        if mode == "bwd":
            o = fn()
            do = torch.randn_like(o)
            fn = lambda: o.backward(do, retain_graph=True)
        ms = triton.testing.do_bench(fn, warmup=warmup, rep=rep)
    flops_per_matmul = 2.0 * BATCH * H * N_CTX * N_CTX * HEAD_DIM
    total_flops = 2 * flops_per_matmul
    if causal:
        total_flops *= 0.5
    if mode == "bwd":
        total_flops *= 2.5  # 2.0(bwd) + 0.5(recompute)
    return total_flops / ms * 1e-9




if __name__ == "__main__":
    # only works on post-Ampere GPUs right now
    # 目前只适用于安培架构 GPU。
    bench_flash_attention.run(save_path=".", print_data=True)