triton_flash_atn.py

"""
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

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

# Pick the fp8 data type

# AMD E4M3B8
# Note: When picking this f8 data type, scaling is required when using f8
# for the second gemm
# TORCH_HAS_FP8E4B8 = hasattr(torch, 'float8_e4m3fnuz')

# AMD E5M2B16
TORCH_HAS_FP8E5B16 = hasattr(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):
    # 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))
    # 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)
        # -- compute qk ----
        k = tl.load(K_block_ptr)
        if pre_load_v:
            v = tl.load(V_block_ptr)
        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"))
        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:
            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


# We don't run auto-tuning everytime to keep the tutorial fast. Uncommenting
# the code below and commenting out the equivalent parameters is convenient for
# re-tuning.
@triton.autotune(
    configs=[
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 16, 'waves_per_eu': 2,
                       'slice_k_tile': 0, 'pre_load_v': False}, num_stages=1, num_warps=2),
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 16, 'waves_per_eu': 2,
                       'slice_k_tile': 32, 'pre_load_v': False}, num_stages=1, num_warps=2),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 32, 'waves_per_eu': 2,
                       'slice_k_tile': 0, 'pre_load_v': False}, num_stages=1, num_warps=1),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 32, 'waves_per_eu': 2,
                       'slice_k_tile': 32, 'pre_load_v': False}, num_stages=1, num_warps=1),
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 32, 'waves_per_eu': 2,
                       'slice_k_tile': 0, 'pre_load_v': False}, num_stages=1, num_warps=2),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 16, 'waves_per_eu': 3,
                       'slice_k_tile': 0, 'pre_load_v': True}, num_stages=1, num_warps=1),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 16, 'waves_per_eu': 3,
                       'slice_k_tile': 0, 'pre_load_v': False}, num_stages=1, num_warps=1),
    ],
    key=['Z', 'H', 'N_CTX', 'STAGE', 'BLOCK_DMODEL'],
)
@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,
              ):
    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)
    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:
        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, N_CTX,
                                        pre_load_v,
                                        )
    # 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
    tl.store(m_ptrs, m_i + tl.math.log2(l_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, D_HEAD: 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, D_HEAD)
    o = tl.load(O + off_hz * D_HEAD * N_CTX +
                off_m[:, None] * D_HEAD + off_n[None, :])
    do = tl.load(DO + off_hz * D_HEAD * N_CTX +
                 off_m[:, None] * D_HEAD + off_n[None, :]).to(tl.float32)
    delta = tl.sum(o * do, axis=1)
    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,
                   BLOCK_DMODEL: 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, BLOCK_DMODEL)
    QT_block_ptr = tl.make_block_ptr(
        base=Q,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_d, stride_tok),
        offsets=(0, start_m),
        block_shape=(BLOCK_DMODEL, BLOCK_M1),
        order=(0, 1)
    )
    DO_block_ptr = tl.make_block_ptr(
        base=DO,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_m, 0),
        block_shape=(BLOCK_M1, BLOCK_DMODEL),
        order=(1, 0)
    )
    # 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_block_ptr)
        # 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_block_ptr)
        # 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))
        dsT = pT * (dpT - Di[None, :])
        dsT = dsT.to(tl.float16)
        dk += tl.dot(dsT, tl.trans(qT))
        # Increment pointers.
        curr_m += step_m
        QT_block_ptr = tl.advance(QT_block_ptr, (0, step_m))
        DO_block_ptr = tl.advance(DO_block_ptr, (step_m, 0))
    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,
                 BLOCK_DMODEL: 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, BLOCK_DMODEL)
    KT_block_ptr = tl.make_block_ptr(
        base=K,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_d, stride_tok),
        offsets=(0, start_n),
        block_shape=(BLOCK_DMODEL, BLOCK_N2),
        order=(0, 1)
    )
    VT_block_ptr = tl.make_block_ptr(
        base=V,
        shape=(BLOCK_DMODEL, N_CTX),
        strides=(stride_d, stride_tok),
        offsets=(0, start_n),
        block_shape=(BLOCK_DMODEL, BLOCK_N2),
        order=(0, 1)
    )
    # 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_block_ptr)
        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.
        vT = tl.load(VT_block_ptr)
        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_block_ptr = tl.advance(KT_block_ptr, (0, step_n))
        VT_block_ptr = tl.advance(VT_block_ptr, (0, step_n))
    return dq


@triton.autotune(
    configs=[
        triton.Config({'BLOCK_M1': 32, 'BLOCK_N1': 64, 'BLOCK_M2': 64, 'BLOCK_N2': 32, 'BLK_SLICE_FACTOR': 1},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 32, 'BLOCK_N1': 64, 'BLOCK_M2': 64, 'BLOCK_N2': 32, 'BLK_SLICE_FACTOR': 2},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 64, 'BLOCK_N1': 128, 'BLOCK_M2': 128, 'BLOCK_N2': 64, 'BLK_SLICE_FACTOR': 1},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 64, 'BLOCK_N1': 128, 'BLOCK_M2': 128, 'BLOCK_N2': 64, 'BLK_SLICE_FACTOR': 2},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 64, 'BLOCK_N1': 64, 'BLOCK_M2': 64, 'BLOCK_N2': 64, 'BLK_SLICE_FACTOR': 1},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 64, 'BLOCK_N1': 64, 'BLOCK_M2': 64, 'BLOCK_N2': 64, 'BLK_SLICE_FACTOR': 2},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 32, 'BLOCK_N1': 128, 'BLOCK_M2': 128, 'BLOCK_N2': 32, 'BLK_SLICE_FACTOR': 1},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 32, 'BLOCK_N1': 128, 'BLOCK_M2': 128, 'BLOCK_N2': 32, 'BLK_SLICE_FACTOR': 2},
                      num_stages=1, num_warps=4),
        triton.Config({'BLOCK_M1': 32, 'BLOCK_N1': 128, 'BLOCK_M2': 128, 'BLOCK_N2': 32, 'BLK_SLICE_FACTOR': 2},
                      num_stages=1, num_warps=8),
    ],
    key=['H', 'N_CTX', 'BLOCK_DMODEL'],
)
@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 = 16, N_CTX = 1024
              H, N_CTX,
              BLOCK_DMODEL: tl.constexpr,
              BLOCK_M1: tl.constexpr,
              BLOCK_N1: tl.constexpr,
              BLOCK_M2: tl.constexpr,
              BLOCK_N2: tl.constexpr,
              BLK_SLICE_FACTOR: 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

    offs_k = tl.arange(0, BLOCK_DMODEL)

    start_n = pid * BLOCK_N1
    # This assignment is important. It is what allows us to pick the diagonal
    # blocks. Later, when we want to do the lower triangular, we update start_m
    # after the first dkdv call.
    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, BLOCK_DMODEL], dtype=tl.float32)
    dk = tl.zeros([BLOCK_N1, BLOCK_DMODEL], dtype=tl.float32)

    K_block_ptr = tl.make_block_ptr(
        base=K,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_n, 0),
        block_shape=(BLOCK_N1, BLOCK_DMODEL),
        order=(1, 0),
    )
    V_block_ptr = tl.make_block_ptr(
        base=V,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_n, 0),
        block_shape=(BLOCK_N1, BLOCK_DMODEL),
        order=(1, 0),
    )

    # load K and V: they stay in SRAM throughout the inner loop for dkdv.
    k = tl.load(K_block_ptr)
    v = tl.load(V_block_ptr)

    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, BLOCK_DMODEL,
                            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, BLOCK_DMODEL,
        start_n, start_m, num_steps,
        MASK=False
    )

    DV_block_ptrs = tl.make_block_ptr(
        base=DV,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_n, 0),
        block_shape=(BLOCK_N1, BLOCK_DMODEL),
        order=(1, 0)
    )
    tl.store(DV_block_ptrs, dv.to(tl.float16))

    # Write back dK.
    dk *= sm_scale
    DK_block_ptrs = tl.make_block_ptr(
        base=DK,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_n, 0),
        block_shape=(BLOCK_N1, BLOCK_DMODEL),
        order=(1, 0)
    )
    tl.store(DK_block_ptrs, dk.to(tl.float16))

    # 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_block_ptr = tl.make_block_ptr(
        base=Q,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_m, 0),
        block_shape=(BLOCK_M2, BLOCK_DMODEL),
        order=(1, 0)
    )

    DO_block_ptr = tl.make_block_ptr(
        base=DO,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_m, 0),
        block_shape=(BLOCK_M2, BLOCK_DMODEL),
        order=(1, 0)
    )
    q = tl.load(Q_block_ptr)
    do = tl.load(DO_block_ptr)
    dq = tl.zeros([BLOCK_M2, BLOCK_DMODEL], dtype=tl.float32)

    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, BLOCK_DMODEL,
                      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, BLOCK_DMODEL,
                      start_m, end_n - num_steps * BLOCK_N2, num_steps,
                      MASK=False
                      )
    # Write back dQ.
    DQ_block_ptr = tl.make_block_ptr(
        base=DQ,
        shape=(N_CTX, BLOCK_DMODEL),
        strides=(stride_tok, stride_d),
        offsets=(start_m, 0),
        block_shape=(BLOCK_M2, BLOCK_DMODEL),
        order=(1, 0)
    )
    dq *= LN2
    tl.store(DQ_block_ptr, dq.to(tl.float16))


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


class _attention(torch.autograd.Function):

    @staticmethod
    def forward(ctx, q, k, v, causal, sm_scale):
        # shape constraints
        Lq, Lk, Lv = q.shape[-1], k.shape[-1], v.shape[-1]
        assert Lq == Lk and Lk == Lv
        assert Lk in {16, 32, 64, 128}
        o = torch.empty_like(q, dtype=v.dtype)
        if torch.version.hip is None:
            BLOCK_M = 128
            BLOCK_N = 64 if Lk <= 64 else 32
            num_stages = 4 if Lk <= 64 else 3
            num_warps = 4 if Lk <= 64 else 8
            # Tuning for H100
            if torch.cuda.get_device_capability()[0] == 9:
                num_warps = 8
                num_stages = 7 if Lk >= 64 else 3
        stage = 3 if causal else 1

        def grid(META): return (
            triton.cdiv(q.shape[2], META['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],
            BLOCK_DMODEL=Lk,
            STAGE=stage,
        )

        # restore the grid for bwd kernel
        best_config = _attn_fwd.get_best_config()
        block_m = int(best_config.__str__().split(",")[0].split("BLOCK_M:")[1])
        grid = (triton.cdiv(q.shape[2], block_m), q.shape[0] * q.shape[1], 1)

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

    @staticmethod
    def backward(ctx, do):
        if torch.version.hip is not None:
            BLOCK = 64
        else:
            BLOCK = 128
        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, 1
        BLOCK_M1, BLOCK_N1, BLOCK_M2, BLOCK_N2 = 32, 64, 64, 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)
        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, D_HEAD=ctx.BLOCK_DMODEL
        )

        def grid(META): return (
            triton.cdiv(N_CTX, META['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_DMODEL=ctx.BLOCK_DMODEL
        )

        return dq, dk, dv, None, None


attention = _attention.apply