# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.

"""
Reference Flash Attention Triton Implementation

This is the Flash Attention v2 implementation from the
https://triton-lang.org/main/getting-started/tutorials/06-fused-attention.html
extracted for benchmarking purposes.
"""

import torch
import triton
import triton.language as tl
from triton.tools.tensor_descriptor import TensorDescriptor


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


def is_cuda():
    return triton.runtime.driver.active.get_current_target().backend == "cuda"


def supports_host_descriptor():
    return is_cuda() and torch.cuda.get_device_capability()[0] >= 9


def is_blackwell():
    return is_cuda() and torch.cuda.get_device_capability()[0] == 10


def is_hopper():
    return is_cuda() and torch.cuda.get_device_capability()[0] == 9


@triton.jit
def _attn_fwd_inner(
    acc,
    l_i,
    m_i,
    q,  #
    desc_k,
    desc_v,  #
    offset_y,
    dtype: tl.constexpr,
    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,
    warp_specialize: tl.constexpr,
    IS_HOPPER: tl.constexpr,
):
    # range of values handled by this stage
    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)
    # causal = False
    else:
        lo, hi = 0, N_CTX
    offsetk_y = offset_y + lo
    if dtype == tl.float8e5:
        offsetv_y = offset_y * HEAD_DIM + lo
    else:
        offsetv_y = offset_y + lo
    # loop over k, v and update accumulator
    for start_n in tl.range(lo, hi, BLOCK_N, warp_specialize=warp_specialize):
        start_n = tl.multiple_of(start_n, BLOCK_N)
        # -- compute qk ----
        k = desc_k.load([offsetk_y, 0]).T
        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)
        # -- compute correction factor
        alpha = tl.math.exp2(m_i - m_ij)
        l_ij = tl.sum(p, 1)
        # -- update output accumulator --
        if not IS_HOPPER and warp_specialize and BLOCK_M == 128 and HEAD_DIM == 128:
            BM: tl.constexpr = acc.shape[0]
            BN: tl.constexpr = acc.shape[1]
            acc0, acc1 = acc.reshape([BM, 2, BN // 2]).permute(0, 2, 1).split()
            acc0 = acc0 * alpha[:, None]
            acc1 = acc1 * alpha[:, None]
            acc = tl.join(acc0, acc1).permute(0, 2, 1).reshape([BM, BN])
        else:
            acc = acc * alpha[:, None]
        # prepare p and v for the dot
        if dtype == tl.float8e5:
            v = desc_v.load([0, offsetv_y]).T
        else:
            v = desc_v.load([offsetv_y, 0])
        p = p.to(dtype)
        # note that this non transposed v for FP8 is only supported on Blackwell
        acc = tl.dot(p, v, acc)
        # update m_i and l_i
        # place this at the end of the loop to reduce register pressure
        l_i = l_i * alpha + l_ij
        m_i = m_ij
        offsetk_y += BLOCK_N
        offsetv_y += BLOCK_N
    return acc, l_i, m_i


def _host_descriptor_pre_hook(nargs):
    BLOCK_M = nargs["BLOCK_M"]
    BLOCK_N = nargs["BLOCK_N"]
    HEAD_DIM = nargs["HEAD_DIM"]
    if not isinstance(nargs["desc_q"], TensorDescriptor):
        return
    nargs["desc_q"].block_shape = [BLOCK_M, HEAD_DIM]
    if nargs["FP8_OUTPUT"]:
        nargs["desc_v"].block_shape = [HEAD_DIM, BLOCK_N]
    else:
        nargs["desc_v"].block_shape = [BLOCK_N, HEAD_DIM]
    nargs["desc_k"].block_shape = [BLOCK_N, HEAD_DIM]
    nargs["desc_o"].block_shape = [BLOCK_M, HEAD_DIM]


if is_hip():
    NUM_STAGES_OPTIONS = [1]
elif supports_host_descriptor():
    NUM_STAGES_OPTIONS = [2, 3, 4]
else:
    NUM_STAGES_OPTIONS = [2, 3, 4]

configs = [
    triton.Config(
        {"BLOCK_M": BM, "BLOCK_N": BN},
        num_stages=s,
        num_warps=w,
        pre_hook=_host_descriptor_pre_hook,
    )
    for BM in [64, 128]
    for BN in [32, 64, 128]
    for s in NUM_STAGES_OPTIONS
    for w in [4, 8]
]


def keep(conf):
    BLOCK_M = conf.kwargs["BLOCK_M"]
    BLOCK_N = conf.kwargs["BLOCK_N"]
    return not (
        is_cuda()
        and torch.cuda.get_device_capability()[0] == 9
        and BLOCK_M * BLOCK_N < 128 * 128
        and conf.num_warps == 8
    )


def prune_invalid_configs(configs, named_args, **kwargs):
    N_CTX = kwargs["N_CTX"]
    # Filter out configs where BLOCK_M > N_CTX
    return [conf for conf in configs if conf.kwargs.get("BLOCK_M", 0) <= N_CTX]


@triton.jit
def _maybe_make_tensor_desc(desc_or_ptr, shape, strides, block_shape):
    if isinstance(desc_or_ptr, tl.tensor_descriptor):
        return desc_or_ptr
    else:
        return tl.make_tensor_descriptor(desc_or_ptr, shape, strides, block_shape)


@triton.autotune(
    configs=list(filter(keep, configs)),
    key=["N_CTX", "HEAD_DIM", "FP8_OUTPUT", "warp_specialize"],
    prune_configs_by={"early_config_prune": prune_invalid_configs},
)
@triton.jit
def _attn_fwd(
    sm_scale,
    M,  #
    Z,
    H,
    desc_q,
    desc_k,
    desc_v,
    desc_o,
    N_CTX,  #
    HEAD_DIM: tl.constexpr,  #
    BLOCK_M: tl.constexpr,  #
    BLOCK_N: tl.constexpr,  #
    FP8_OUTPUT: tl.constexpr,  #
    STAGE: tl.constexpr,  #
    warp_specialize: tl.constexpr,  #
    IS_HOPPER: tl.constexpr,  #
):
    dtype = tl.float8e5 if FP8_OUTPUT else tl.float16
    tl.static_assert(BLOCK_N <= HEAD_DIM)
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    off_z = off_hz // H
    off_h = off_hz % H

    y_dim = Z * H * N_CTX
    desc_q = _maybe_make_tensor_desc(
        desc_q,
        shape=[y_dim, HEAD_DIM],
        strides=[HEAD_DIM, 1],
        block_shape=[BLOCK_M, HEAD_DIM],
    )
    if FP8_OUTPUT:
        desc_v = _maybe_make_tensor_desc(
            desc_v,
            shape=[HEAD_DIM, y_dim],
            strides=[N_CTX, 1],
            block_shape=[HEAD_DIM, BLOCK_N],
        )
    else:
        desc_v = _maybe_make_tensor_desc(
            desc_v,
            shape=[y_dim, HEAD_DIM],
            strides=[HEAD_DIM, 1],
            block_shape=[BLOCK_N, HEAD_DIM],
        )
    desc_k = _maybe_make_tensor_desc(
        desc_k,
        shape=[y_dim, HEAD_DIM],
        strides=[HEAD_DIM, 1],
        block_shape=[BLOCK_N, HEAD_DIM],
    )
    desc_o = _maybe_make_tensor_desc(
        desc_o,
        shape=[y_dim, HEAD_DIM],
        strides=[HEAD_DIM, 1],
        block_shape=[BLOCK_M, HEAD_DIM],
    )

    offset_y = off_z * (N_CTX * H) + off_h * N_CTX
    qo_offset_y = offset_y + start_m * BLOCK_M
    # initialize offsets
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    offs_n = tl.arange(0, BLOCK_N)
    # initialize pointer to m and l
    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
    qk_scale = sm_scale
    qk_scale *= 1.44269504  # 1/log(2)
    # load q: it will stay in SRAM throughout
    q = desc_q.load([qo_offset_y, 0])
    # stage 1: off-band
    # For causal = True, STAGE = 3 and _attn_fwd_inner gets 1 as its STAGE
    # For causal = False, STAGE = 1, and _attn_fwd_inner gets 3 as its STAGE
    if STAGE & 1:
        acc, l_i, m_i = _attn_fwd_inner(
            acc,
            l_i,
            m_i,
            q,  #
            desc_k,
            desc_v,  #
            offset_y,
            dtype,
            start_m,
            qk_scale,  #
            BLOCK_M,
            HEAD_DIM,
            BLOCK_N,  #
            4 - STAGE,
            offs_m,
            offs_n,
            N_CTX,  #
            warp_specialize,
            IS_HOPPER,
        )
    # stage 2: on-band
    if STAGE & 2:
        acc, l_i, m_i = _attn_fwd_inner(
            acc,
            l_i,
            m_i,
            q,  #
            desc_k,
            desc_v,  #
            offset_y,
            dtype,
            start_m,
            qk_scale,  #
            BLOCK_M,
            HEAD_DIM,
            BLOCK_N,  #
            2,
            offs_m,
            offs_n,
            N_CTX,  #
            warp_specialize,
            IS_HOPPER,
        )
    # epilogue
    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)
    desc_o.store([qo_offset_y, 0], acc.to(dtype))


@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
    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
    tl.store(Delta + off_hz * N_CTX + off_m, delta)


# The main inner-loop logic for computing dK and dV.
@triton.jit
def _attn_bwd_dkdv(
    dk,
    dv,  #
    Q,
    k,
    v,
    sm_scale,  #
    DO,  #
    M,
    D,  #
    # shared by Q/K/V/DO.
    stride_tok,
    stride_d,  #
    H,
    N_CTX,
    BLOCK_M1: tl.constexpr,  #
    BLOCK_N1: tl.constexpr,  #
    HEAD_DIM: tl.constexpr,  #
    # Filled in by the wrapper.
    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.
    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.
        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.
        if MASK:
            mask = offs_m[None, :] >= offs_n[:, None]
            pT = tl.where(mask, pT, 0.0)
        do = tl.load(do_ptrs)
        # Compute dV.
        ppT = pT
        ppT = ppT.to(tl.float16)
        dv += tl.dot(ppT, do)
        # D (= delta) is pre-divided by ds_scale.
        Di = tl.load(D + offs_m)
        # Compute dP and 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.
        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
@triton.jit
def _attn_bwd_dq(
    dq,
    q,
    K,
    V,  #
    do,
    m,
    D,
    # shared by Q/K/V/DO.
    stride_tok,
    stride_d,  #
    H,
    N_CTX,  #
    BLOCK_M2: tl.constexpr,  #
    BLOCK_N2: tl.constexpr,  #
    HEAD_DIM: tl.constexpr,
    # Filled in by the wrapper.
    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.
    Di = tl.load(D + offs_m)
    # BLOCK_M2 must be a multiple of BLOCK_N2, otherwise the code wouldn't work.
    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.
        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.
        dp = tl.dot(do, vT).to(tl.float32)
        ds = p * (dp - Di[:, None])
        ds = ds.to(tl.float16)
        # Compute dQ.
        # NOTE: We need to de-scale dq in the end, because kT was pre-scaled.
        dq += tl.dot(ds, tl.trans(kT))
        # Increment pointers.
        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.
    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
    Q += adj
    K += adj
    V += adj
    DO += adj
    DQ += adj
    DK += adj
    DV += adj
    M += off_chz
    D += off_chz

    # load scales
    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.
    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.
    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.
    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:
    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.
    # 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.
    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
    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.
    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):  # noqa: N801
    @staticmethod
    def forward(ctx, q, k, v, causal, sm_scale, warp_specialize=True):
        # shape constraints
        HEAD_DIM_Q, HEAD_DIM_K = q.shape[-1], k.shape[-1]
        # when v is in float8_e5m2 it is transposed.
        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
        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}

        M = torch.empty(
            (q.shape[0], q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32
        )
        # Use device_descriptor for Hopper + warpspec.
        if supports_host_descriptor() and not (is_hopper() and warp_specialize):
            # Note that on Hopper we cannot perform a FP8 dot with a non-transposed second tensor
            y_dim = q.shape[0] * q.shape[1] * q.shape[2]

            dummy_block = [1, 1]
            desc_q = TensorDescriptor(
                q,
                shape=[y_dim, HEAD_DIM_K],
                strides=[HEAD_DIM_K, 1],
                block_shape=dummy_block,
            )
            if q.dtype == torch.float8_e5m2:
                desc_v = TensorDescriptor(
                    v,
                    shape=[HEAD_DIM_K, y_dim],
                    strides=[q.shape[2], 1],
                    block_shape=dummy_block,
                )
            else:
                desc_v = TensorDescriptor(
                    v,
                    shape=[y_dim, HEAD_DIM_K],
                    strides=[HEAD_DIM_K, 1],
                    block_shape=dummy_block,
                )
            desc_k = TensorDescriptor(
                k,
                shape=[y_dim, HEAD_DIM_K],
                strides=[HEAD_DIM_K, 1],
                block_shape=dummy_block,
            )
            desc_o = TensorDescriptor(
                o,
                shape=[y_dim, HEAD_DIM_K],
                strides=[HEAD_DIM_K, 1],
                block_shape=dummy_block,
            )
        else:
            desc_q = q
            desc_v = v
            desc_k = k
            desc_o = o

        def alloc_fn(size: int, align: int, _):
            return torch.empty(size, dtype=torch.int8, device="cuda")

        triton.set_allocator(alloc_fn)

        def grid(META):
            return (
                triton.cdiv(q.shape[2], META["BLOCK_M"]),
                q.shape[0] * q.shape[1],
                1,
            )

        ctx.grid = grid
        if is_blackwell() and warp_specialize:
            if HEAD_DIM_K == 128 and q.dtype == torch.float16:
                extra_kern_args["maxnreg"] = 168
            else:
                extra_kern_args["maxnreg"] = 80
        _attn_fwd[grid](
            sm_scale,
            M,  #
            q.shape[0],
            q.shape[1],  #
            desc_q,
            desc_k,
            desc_v,
            desc_o,  #
            N_CTX=q.shape[2],  #
            HEAD_DIM=HEAD_DIM_K,  #
            FP8_OUTPUT=q.dtype == torch.float8_e5m2,  #
            STAGE=stage,  #
            warp_specialize=warp_specialize,  #
            IS_HOPPER=is_hopper(),  #
            **extra_kern_args
        )

        ctx.save_for_backward(q, k, v, o, M)
        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, None, None


# Main attention function export
reference_attention = _attention.apply
