"""
Fused Attention
===============

This is a Triton implementation of the Flash Attention v2 algorithm from Tri Dao (https://tridao.me/publications/flash2/flash2.pdf)
Credits: OpenAI kernel team

This kernel supports arbitrarily sized sequence lengths.

Extra Credits:
- Original flash attention paper (https://arxiv.org/abs/2205.14135)
- Rabe and Staats (https://arxiv.org/pdf/2112.05682v2.pdf)

"""

import pytest
import torch


import triton
import triton.language as tl

torch_dtype:tl.constexpr = torch.float16
TORCH_HAS_FP8E5 = hasattr(torch, 'float8_e5m2fnuz')
if TORCH_HAS_FP8E5:
    torch_dtype:tl.constexpr = torch.float8_e5m2fnuz

@triton.jit
def _attn_fwd_inner(
    acc, l_i, m_i, q,
    K_block_ptr, V_block_ptr,
    start_m,
    BLOCK_M: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr,
    BLOCK_N: tl.constexpr,
    STAGE: tl.constexpr,
    offs_m: tl.constexpr,
    offs_n: tl.constexpr,
    N_CTX,
    pre_load_v: tl.constexpr,
    padded_block: tl.constexpr,
    total_tokens: 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)
        K_block_ptr = tl.advance(K_block_ptr, (0, lo))
        V_block_ptr = tl.advance(V_block_ptr, (lo, 0))
    # N_CTX is the seqlen to the nearest block (round down).
    # So here, we are computing the elements for that last irregular block.
    # In the loop,  we will mask the elements of BLOCK_N that do not exist.
    elif padded_block:
        lo, hi = N_CTX, N_CTX + BLOCK_N
        lo = tl.multiple_of(lo, BLOCK_N)
        K_block_ptr = tl.advance(K_block_ptr, (0, lo))
        V_block_ptr = tl.advance(V_block_ptr, (lo, 0))
    # causal = False
    else:
        lo, hi = 0, N_CTX
    # loop over k, v and update accumulator
    for start_n in range(lo, hi, BLOCK_N):
        start_n = tl.multiple_of(start_n, BLOCK_N)
        # For padded blocks, we will overrun the tensor size if
        # we load all BLOCK_N. For others, the blocks are all within range.
        if padded_block:
            k = tl.load(K_block_ptr, boundary_check=(1,), padding_option="zero")
        else:
            k = tl.load(K_block_ptr)
        if pre_load_v:
            if padded_block:
                v = tl.load(V_block_ptr, boundary_check=(0,), padding_option="zero")
            else:
                v = tl.load(V_block_ptr)
        # -- compute qk ----
        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
        if STAGE == 2:
            mask = offs_m[:, None] >= (start_n + offs_n[None, :])
            qk = tl.where(mask, qk, float("-inf"))
        if padded_block:
            boundary = tl.full([BLOCK_M], total_tokens, dtype=tl.float32)
            mask = (start_n + offs_n[None,:]) < boundary[:,None]
            qk = tl.where(mask, qk, float("-inf"))
        qk += tl.dot(q, k)
        m_ij = tl.maximum(m_i, tl.max(qk, 1))
        qk = qk - m_ij[:, None]
        p = tl.math.exp2(qk)
        # -- update output accumulator --
        alpha = tl.math.exp2(m_i - m_ij)
        acc = acc * alpha[:, None]
        if not pre_load_v:
            if padded_block:
                v = tl.load(V_block_ptr, boundary_check=(0,), padding_option="zero")
            else:
                v = tl.load(V_block_ptr)
        acc += tl.dot(p.to(v.dtype), v)
        # -- update m_i and l_i
        l_ij = tl.sum(p, 1)
        l_i = l_i * alpha + l_ij
        # update m_i and 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


@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,
    BLOCK_DMODEL: tl.constexpr,
    STAGE: tl.constexpr,
    BLOCK_M: tl.constexpr,
    BLOCK_N: tl.constexpr,
    pre_load_v: tl.constexpr,
    need_padding: tl.constexpr,
    extra_tokens_n: tl.constexpr,
):
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    qvk_offset = off_hz * stride_qh

    # block pointers
    Q_block_ptr = tl.make_block_ptr(
        base=Q + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_qm, stride_qk),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0),
    )
    V_block_ptr = tl.make_block_ptr(
        base=V + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_vk, stride_vn),
        offsets=(0, 0),
        block_shape=(BLOCK_N, BLOCK_DMODEL),
        order=(1, 0),
    )
    K_block_ptr = tl.make_block_ptr(
        base=K + qvk_offset,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_kk, stride_kn),
        offsets=(0, 0),
        block_shape=(BLOCK_DMODEL, BLOCK_N),
        order=(0, 1),
    )
    O_block_ptr = tl.make_block_ptr(
        base=Out + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_om, stride_on),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0),
    )
    # 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, BLOCK_DMODEL], dtype=tl.float32)
    # scale sm_scale by log_2(e) and use
    # 2^x instead of exp in the loop because CSE and LICM
    # don't work as expected with `exp` in the loop
    qk_scale = sm_scale * 1.44269504
    # load q: it will stay in SRAM throughout on NV GPUs but in VGPRs on AMD GPUs
    q = tl.load(Q_block_ptr, boundary_check=(0,1), padding_option="zero")
    q = (q * qk_scale).to(q.dtype)
    # 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:
        # We don't currently support causal masking and padding.
        tl.static_assert((STAGE != 3) or not need_padding)
        # equal to N_CTX if N_CTX is already a multiple of block_M
        seqlen_aligned = N_CTX - extra_tokens_n
        if N_CTX >= BLOCK_N:
            acc, l_i, m_i = _attn_fwd_inner(
                acc, l_i, m_i, q, K_block_ptr, V_block_ptr,
                start_m,
                BLOCK_M, BLOCK_DMODEL, BLOCK_N,
                4 - STAGE, offs_m, offs_n,
                seqlen_aligned, pre_load_v,
                False, seqlen_aligned
            )
        tl.debug_barrier()
        if need_padding:
            if N_CTX < BLOCK_N:
                seqlen_aligned = 0
            acc, l_i, m_i = _attn_fwd_inner(
                acc, l_i, m_i, q, K_block_ptr, V_block_ptr,
                start_m,
                BLOCK_M, BLOCK_DMODEL, BLOCK_N,
                4 - STAGE, offs_m, offs_n,
                seqlen_aligned, pre_load_v,
                True, N_CTX,
            )
    # stage 2: on-band
    if STAGE & 2:
        # barrier makes it easier for compielr to schedule the
        # two loops independently
        tl.debug_barrier()
        acc, l_i, m_i = _attn_fwd_inner(
            acc, l_i, m_i, q, K_block_ptr, V_block_ptr,
            start_m,
            BLOCK_M, BLOCK_DMODEL, BLOCK_N,
            2, offs_m, offs_n,
            N_CTX, pre_load_v,
        )
    # epilogue
    # write back m
    acc = acc / l_i[:, None]
    m_ptrs = M + off_hz * N_CTX + offs_m
    # Check for last block_M
    overflow_size = (start_m * BLOCK_M) - N_CTX
    if overflow_size > 0:
        boundary = tl.full((BLOCK_M,), overflow_size, dtype=tl.float32)
        # This is a > check because mask being 0 blocks the store.
        m_ptrs_mask = boundary > tl.arange(0, BLOCK_M)
        tl.store(m_ptrs, m_i + tl.math.log2(l_i))
    else:
        tl.store(m_ptrs, m_i + tl.math.log2(l_i))
    tl.store(O_block_ptr, acc.to(Out.type.element_ty), boundary_check=(0,1))


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


@triton.jit
def _bwd_kernel_dk_dv(
    Q, K, V, sm_scale, Out, DO,
    DK, DV,
    L,
    D,
    stride_qz, stride_qh, stride_qm, stride_qk,
    stride_kz, stride_kh, stride_kn, stride_kk,
    stride_vz, stride_vh, stride_vk, stride_vn,
    Z, H, N_CTX,
    BLOCK_M: tl.constexpr, BLOCK_DMODEL: tl.constexpr,
    BLOCK_N: tl.constexpr,
):
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    # Q is consumed depending on block ID. Every block uses
    # previous block offset by BLOCK_M x D_HEAD.
    qvk_offset = off_hz * stride_qh
    qdo_offset = qvk_offset + start_m * BLOCK_M * stride_qm
    # 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_DMODEL)
    # Initialize pointers to Q, K, V
    Q_block_ptr = tl.make_block_ptr(
        base=Q + qdo_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_qm, stride_qk),
        offsets=(0, 0),
        block_shape=(BLOCK_N, BLOCK_DMODEL),
        order=(1, 0)
    )
    K_block_ptr = tl.make_block_ptr(
        base=K + qvk_offset,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_kk, stride_kn),
        offsets=(0, start_m * BLOCK_M),
        block_shape=(BLOCK_DMODEL, BLOCK_N),
        order=(0, 1)
    )
    V_block_ptr = tl.make_block_ptr(
        base=V + qvk_offset,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_vn, stride_vk),
        offsets=(0, start_m * BLOCK_M),
        block_shape=(BLOCK_DMODEL, BLOCK_N),
        order=(0, 1)
    )
    DO_block_ptr = tl.make_block_ptr(
        base=DO + qdo_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_qm, stride_qk),
        offsets=(0, 0),
        block_shape=(BLOCK_N, BLOCK_DMODEL),
        order=(1, 0)
    )
    # pointer to row-wise quantities in value-like data
    D_ptrs = D + off_hz * N_CTX
    l_ptrs = L + off_hz * N_CTX
    qk_scale = sm_scale * 1.44269504
    # load k and v: they will stay in SRAM throughout
    k = tl.load(K_block_ptr)
    k = (k * qk_scale).to(k.dtype)
    v = tl.load(V_block_ptr)
    dv = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
    dk = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
    # This lower loop bound is because of the causal mask. We create a lower triangular
    # result. The upper triangular is -inf (becomes 0 when we do e^x). As such, it can
    # be ignored in the GEMM.
    lo = start_m * BLOCK_M
    hi = N_CTX
    # loop over q, do
    for start_n in range(lo, hi, BLOCK_N):
        offs_m_curr = offs_n[:, None] + start_n
        # -- load q, do --
        q = tl.load(Q_block_ptr)
        do = tl.load(DO_block_ptr)
        # -- compute qk ----
        qk = tl.dot(q, k)
        qk = tl.where(offs_m_curr >= offs_m[None, :], qk, float("-inf"))
        l_i = tl.load(l_ptrs + offs_m_curr)
        p = tl.math.exp2(qk - l_i)
        # -- compute dv ----
        dv += tl.dot(tl.trans(p.to(do.dtype)), do)
        # compute dp = dot(v, do)
        Di = tl.load(D_ptrs + offs_m_curr)
        dp = tl.zeros([BLOCK_N, BLOCK_M], dtype=tl.float32) - Di
        dp += tl.dot(do, v)
        # compute ds = p * (dp - delta[:, None])
        ds = p * dp
        # compute dk
        dk += tl.dot(tl.trans(ds.to(Q.dtype.element_ty)), q)
        # update pointers
        Q_block_ptr = tl.advance(Q_block_ptr, (BLOCK_N, 0))
        DO_block_ptr = tl.advance(DO_block_ptr, (BLOCK_N, 0))
    # initialize pointers to output
    DK_block_ptr = tl.make_block_ptr(
        base=DK + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_kn, stride_kk),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0)
    )
    DV_block_ptr = tl.make_block_ptr(
        base=DV + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_vk, stride_vn),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0)
    )
    tl.store(DK_block_ptr, (dk * sm_scale).to(DK.dtype.element_ty))
    tl.store(DV_block_ptr, dv.to(tl.float16))

@triton.jit
def _bwd_kernel_dq(
    Q, K, V, sm_scale, Out, DO,
    DQ,
    L,
    D,
    stride_qz, stride_qh, stride_qm, stride_qk,
    stride_kz, stride_kh, stride_kn, stride_kk,
    stride_vz, stride_vh, stride_vk, stride_vn,
    Z, H, N_CTX,
    BLOCK_M: tl.constexpr, BLOCK_DMODEL: tl.constexpr,
    BLOCK_N: tl.constexpr,
):
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    qvk_offset = off_hz * stride_qh
    # 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_DMODEL)
    # Initialize pointers to Q, K, V
    Q_block_ptr = tl.make_block_ptr(
        base=Q + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_qm, stride_qk),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0)
    )
    K_block_ptr = tl.make_block_ptr(
        base=K + qvk_offset,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_kk, stride_kn),
        offsets=(0, 0),
        block_shape=(BLOCK_DMODEL, BLOCK_N),
        order=(0, 1)
    )
    V_block_ptr = tl.make_block_ptr(
        base=V + qvk_offset,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_vn, stride_vk),
        offsets=(0, 0),
        block_shape=(BLOCK_DMODEL, BLOCK_N),
        order=(0, 1)
    )
    DO_block_ptr = tl.make_block_ptr(
        base=DO + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_qm, stride_qk),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0)
    )
    # pointer to row-wise quantities in value-like data
    D_ptrs = D + off_hz * N_CTX
    l_ptrs = L + off_hz * N_CTX
    qk_scale = sm_scale * 1.44269504
    # load q and do: they will stay in SRAM throughout
    q = tl.load(Q_block_ptr)
    q = (q * qk_scale).to(q.dtype)
    do = tl.load(DO_block_ptr)
    Di = tl.load(D_ptrs + offs_m)
    l_i = tl.load(l_ptrs + offs_m)
    dq = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
    # loop over k, v
    lo = 0
    hi = (start_m + 1) * BLOCK_M
    for start_n in range(lo, hi, BLOCK_N):
        # -- load k, v --
        k = tl.load(K_block_ptr)
        v = tl.load(V_block_ptr)
        # -- compute qk ----
        qk = tl.dot(q, k)
        qk = tl.where(offs_m[:, None] >= (offs_n[None, :] + start_n), qk, float("-inf"))
        p = tl.math.exp2(qk - l_i[:, None])
        # compute dp = dot(v, do)
        dp = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32) - Di[:, None]
        dp += tl.dot(do, v)
        # compute ds = p * (dp - delta[:, None])
        ds = p * dp
        # compute dq. Unfortunately we cannot avoid transpose here as this loop
        # uses k both normal and transpose.
        dq += tl.dot(ds.to(Q.dtype.element_ty), tl.trans(k))
        # update pointers
        K_block_ptr = tl.advance(K_block_ptr, (0, BLOCK_N))
        V_block_ptr = tl.advance(V_block_ptr, (0, BLOCK_N))
    # initialize pointers to output
    DQ_block_ptr = tl.make_block_ptr(
        base=DQ + qvk_offset,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_qm, stride_qk),
        offsets=(start_m * BLOCK_M, 0),
        block_shape=(BLOCK_M, BLOCK_DMODEL),
        order=(1, 0)
    )
    tl.store(DQ_block_ptr, (dq * sm_scale).to(tl.float16))

empty = torch.empty(128, device="cuda")


class _attention(torch.autograd.Function):
    @staticmethod
    def forward(ctx, q, k, v, causal, sm_scale, split_kernel=False):
        # shape constraints
        _, _, seqlen, Lq = q.shape
        Lk, Lv = k.shape[-1], v.shape[-1]
        assert Lq == Lk and Lk == Lv
        assert Lk in {16, 32, 64, 128}
        # For now we assume K and V seqlen = Q seqlen
        assert seqlen == k.shape[-2] and seqlen == v.shape[-2]

        # We've derived these previously from tuning the kernel
        BLOCK_M = 256 if Lq == 128 else 128
        BLOCK_N = 64 #128 if Lq == 128 else 64
        waves_per_eu = 2 if Lq == 128 else 3
        num_warps = 8 if Lq == 128 else 4
        pre_load_v = False if Lq == 128 else True
        grid = (triton.cdiv(q.shape[2], BLOCK_M), q.shape[0] * q.shape[1], 1)
        stage = 3 if causal else 1

        # Compute if we need padding and how much
        seqlen_k = k.shape[-2]

        if seqlen_k < BLOCK_N:
            need_padding = True
            extra_tokens_n = BLOCK_N - seqlen_k
            # This effectively ensures we do not slice across Q.
            assert(grid[0] == 1)
        elif seqlen_k % BLOCK_N:
            need_padding = True
            extra_tokens_n = seqlen_k % BLOCK_N
        else:
            # We don't care if BLOCK_M isn't aligned, as we
            # always boundary_check on Q and O
            need_padding = False
            extra_tokens_n = 0

        o = torch.empty_like(q, dtype=v.dtype)
        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],
            BLOCK_DMODEL=Lk,
            STAGE=stage,
            BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N,
            waves_per_eu=waves_per_eu, pre_load_v=pre_load_v,
            need_padding=need_padding, extra_tokens_n=extra_tokens_n,
            num_stages=1, num_warps=num_warps
        )

        ctx.save_for_backward(q, k, v, o, M)
        ctx.grid = grid
        ctx.sm_scale = sm_scale
        ctx.BLOCK_DMODEL = Lk
        ctx.causal = causal
        ctx.split_kernel = split_kernel
        return o

    @staticmethod
    def backward(ctx, do):
        # configuration is not supported
        assert(not (ctx.split_kernel and not ctx.causal))
        if torch.version.hip is not None:
            BLOCK = 64
        else:
            BLOCK = 128
        q, k, v, o, L = ctx.saved_tensors
        assert do.is_contiguous()
        assert q.stride() == k.stride() == v.stride() == o.stride() == do.stride()
        do = do.contiguous()
        dq = torch.zeros_like(q)
        dk = torch.empty_like(k)
        dv = torch.empty_like(v)
        BATCH, N_HEAD, N_CTX = q.shape[:3]
        delta = torch.empty_like(L)
        do_scaled = torch.empty_like(do)
        # Figure out what BLOCK size fwd used and adjust num_blocks accordingly.
        # If the two are the same, we don't need this but the bwd pass block size
        # is smaller than the fwd so we need this scaling to ensure we loop over all
        # values and don't skip some blocks. 
        # Alternatively we could compute a new grid but this keeps it consistent
        # with fwd and easier to reason about.
        block_scale = (q.shape[2] // ctx.grid[0]) // BLOCK
        _attn_bwd_preprocess[(ctx.grid[0] * ctx.grid[1], )](
            o, do,  #
            do_scaled, delta,  #
            BLOCK_M=block_scale * BLOCK, D_HEAD=ctx.BLOCK_DMODEL,  #
        )
        if not ctx.split_kernel:
            _bwd_kernel[(ctx.grid[1],)](
                q, k, v, ctx.sm_scale,
                o, do_scaled,
                dq, dk, dv,
                L, delta,
                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),
                q.shape[0], q.shape[1], q.shape[2],
                block_scale * ctx.grid[0],
                BLOCK_M=BLOCK, BLOCK_N=BLOCK,
                BLOCK_DMODEL=ctx.BLOCK_DMODEL, num_warps=4,
                CAUSAL=ctx.causal,
                num_stages=1,
            )
        else :
            dq = torch.zeros_like(q)
            _bwd_kernel_dk_dv[(block_scale * ctx.grid[0], ctx.grid[1])](
                q, k, v, ctx.sm_scale,
                o, do_scaled,
                dk, dv,
                L, delta,
                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),
                q.shape[0], q.shape[1], q.shape[2],
                BLOCK_M=BLOCK, BLOCK_N=BLOCK,
                BLOCK_DMODEL=ctx.BLOCK_DMODEL, num_warps=4,
                num_stages=1,
            )
            _bwd_kernel_dq[ctx.grid](
                q, k, v, ctx.sm_scale,
                o, do_scaled,
                dq,
                L, delta,
                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),
                q.shape[0], q.shape[1], q.shape[2],
                BLOCK_M=2*BLOCK, BLOCK_N=BLOCK,
                BLOCK_DMODEL=ctx.BLOCK_DMODEL, num_warps=4, waves_per_eu=1,
                num_stages=1,
            )
        # print(h.asm["ttgir"])
        return dq, dk, dv, None, None, None

attention = _attention.apply


@pytest.mark.parametrize('Z, H, N_CTX, D_HEAD',
                         [(1, 40, 19, 128),
                          (4, 48, 1024, 64),
                          (4, 48, 997, 64),
                          (4, 48, 2048, 64),
                          (4, 48, 4096, 64),
                          (4, 48, 3989, 64),
                          (4, 48, 1024, 128),
                          (4, 48, 1021, 128),
                          (4, 48, 2048, 128),
                          (4, 48, 4096, 128),
                          (4, 16, 8192, 64),
                          (4, 16, 8080, 64),
                          #(4, 48, 16384, 64)
                          ])
@pytest.mark.parametrize('causal', [False])
def test_op_fwd(Z, H, N_CTX, D_HEAD, causal, dtype=torch.float16):
    torch.manual_seed(20)
    q = torch.randn((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0., std=0.5).requires_grad_()
    k = torch.randn((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0., std=0.5).requires_grad_()
    v = torch.randn((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0., std=0.5).requires_grad_()
    if TORCH_HAS_FP8E5:
        q = q.to(torch_dtype)
        k = k.to(torch_dtype)
    sm_scale = 0.5
    dout = torch.randn_like(q, dtype=torch.float16)
    # reference implementation
    M = torch.tril(torch.ones((N_CTX, N_CTX), device="cuda"))
    p = torch.matmul(q.half(), k.transpose(2, 3).half()) * sm_scale
    if causal:
        p[:, :, M == 0] = float("-inf")
    p = torch.softmax(p.float(), dim=-1).half()
    ref_out = torch.matmul(p, v)
    # triton implementation
    tri_out = attention(q, k, v, causal, sm_scale)
    # compare
    torch.testing.assert_close(ref_out, tri_out, atol=1e-2, rtol=1e-2)


@pytest.mark.parametrize('Z, H, N_CTX, D_HEAD',
                         [(4, 48, 1024, 64),
                          (4, 48, 2048, 64),
                          (4, 48, 4096, 64),
                          (1, 16, 8192, 64),
                          ])
def test_op_bwd(Z, H, N_CTX, D_HEAD, dtype=torch.float16):
    torch.manual_seed(20)
    causal = True
    q = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0., std=0.5).requires_grad_()
    k = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0., std=0.5).requires_grad_()
    v = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0., std=0.5).requires_grad_()

    sm_scale = 0.5
    split_kernel = True
    dout = torch.randn_like(q)
    # reference implementation
    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()
    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
    tri_out = attention(q, k, v, causal, sm_scale, split_kernel)
    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
    torch.testing.assert_close(ref_out, tri_out, atol=1e-2, rtol=0)
    if torch.version.hip is None:
        torch.testing.assert_close(ref_dv, tri_dv, atol=1e-2, rtol=0)
    # The current block size for MI200 series is 64x64. This results in
    # larger differences in float results due to rounding.
    else:
        torch.testing.assert_close(ref_dv, tri_dv, atol=5e-2, rtol=0)
    torch.testing.assert_close(ref_dk, tri_dk, atol=5e-2, rtol=1e-2)
    torch.testing.assert_close(ref_dq, tri_dq, atol=5e-2, rtol=1e-2)


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

# vary seq length for fixed head and batch=4
configs = []
for mode in ['fwd']:
    for D_HEAD in [128]:
        if mode == 'bwd' and D_HEAD == 128:
            continue
        for causal in [False]:
            if mode == 'bwd' and causal == False:
                continue
            configs.append(triton.testing.Benchmark(
                x_names=['BATCH', 'H','N_CTX'],
                x_vals=[(16, 16, 1024),
                        (8, 16, 2048),
                        (4, 16, 4096),
                        (2, 16, 8192),
                        (1, 16, 16384),
                        (2, 48, 1024),
                        (2, 48, 2048),
                        (2, 48, 4096),
                        (2, 48, 8192),
                        (2, 48, 16384),
                        (8, 16, 1989),
                        (4, 16, 4097),
                        (2, 16, 8122),
                        (1, 16, 16281),
                        (2, 48, 1021),
                        (2, 48, 2001),
                        (2, 48, 3996),
                        (2, 48, 8181),
                        ],
                line_arg='provider',
                line_vals=['triton'] + (['flash'] if HAS_FLASH else []),
                line_names=['Triton'] + ([f'Flash-{FLASH_VER}'] if HAS_FLASH else []),
                styles=[('red', '-'), ('blue', '-')],
                ylabel='ms',
                plot_name=f'fused-attention-{mode}-d{D_HEAD}-causal={causal}',
                args={
                    'D_HEAD': D_HEAD,
                    'dtype': torch.float16,
                    'mode': mode,
                    'causal': causal})
            )


@triton.testing.perf_report(configs)
def bench_flash_attention(
    BATCH, H, N_CTX, D_HEAD, causal, mode, provider, dtype=torch.float16, device="cuda"
):
    assert mode in ["fwd", "bwd"]
    warmup = 25
    rep = 100
    split_kernel = False
    # Bwd pass only supports causal=True right now
    if mode == 'bwd':
        causal = True
        split_kernel = True
    if provider == "triton":
        q = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True)
        k = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True)
        v = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True)
        if mode == "fwd":
            q = q.to(torch_dtype)
            k = k.to(torch_dtype)
        sm_scale = 1.3
        fn = lambda: attention(q, k, v, causal, sm_scale, split_kernel)
        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, D_HEAD), 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 * D_HEAD
    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


# only works on post-Ampere GPUs right now
bench_flash_attention.run(save_path=".", print_data=True)