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

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

Extra Credits:
- Original flash attention paper (https://arxiv.org/abs/2205.14135)
- Rabe and Staats (https://arxiv.org/pdf/2112.05682v2.pdf)
- Adam P. Goucher for simplified vector math

"""

import pytest
import torch

import triton
import triton.language as tl


@triton.jit
def max_fn(x, y):
    return tl.math.max(x, y)


@triton.jit
def _fwd_kernel(
    Q, K, V, sm_scale,
    L, 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_M: tl.constexpr, BLOCK_DMODEL: tl.constexpr,
    BLOCK_N: tl.constexpr,
    MODE: tl.constexpr,
):
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    qvk_offset = off_hz * stride_qh
    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=(N_CTX, BLOCK_DMODEL),
        strides=(stride_vk, stride_vn),
        offsets=(0, 0),
        block_shape=(BLOCK_N, BLOCK_DMODEL),
        order=(1, 0)
    )
    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)
    acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
    # causal check on every loop iteration can be expensive
    # and peeling the last iteration of the loop does not work well with ptxas
    # so we have a mode to do the causal check in a separate kernel entirely
    if MODE == 0:  # entire non-causal attention
        lo, hi = 0, N_CTX
    if MODE == 1:  # entire causal attention
        lo, hi = 0, (start_m + 1) * BLOCK_M
    if MODE == 2:  # off band-diagonal
        lo, hi = 0, start_m * BLOCK_M
    if MODE == 3:  # on band-diagonal
        l_ptrs = L + off_hz * N_CTX + offs_m
        m_ptrs = M + off_hz * N_CTX + offs_m
        m_i = tl.load(m_ptrs)
        l_i = tl.load(l_ptrs)
        acc += tl.load(O_block_ptr).to(tl.float32)
        lo, hi = start_m * BLOCK_M, (start_m + 1) * BLOCK_M
    # 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
    q = tl.load(Q_block_ptr)
    q = (q * qk_scale).to(tl.float16)
    # advance block pointers to first iteration of the loop
    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
    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)
        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
        qk += tl.dot(q, k)
        if MODE == 1 or MODE == 3:
            qk = tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), qk, float("-inf"))
        # -- compute m_ij, p, l_ij
        m_ij = tl.maximum(m_i, tl.max(qk, 1))
        p = tl.math.exp2(qk - m_ij[:, None])
        l_ij = tl.sum(p, 1)
        # -- update m_i and l_i
        alpha = tl.math.exp2(m_i - m_ij)
        l_i *= alpha
        l_i_new = l_i + l_ij
        # scale acc
        acc_scale = l_i * 0 + alpha
        acc = acc * acc_scale[:, None]
        # update acc
        v = tl.load(V_block_ptr)
        p = p.to(tl.float16)
        acc += tl.dot(p, v)
        # update m_i and l_i
        l_i = l_i_new
        m_i = m_ij
        # update pointers
        K_block_ptr = tl.advance(K_block_ptr, (0, BLOCK_N))
        V_block_ptr = tl.advance(V_block_ptr, (BLOCK_N, 0))
    # write back l and m
    acc = acc / l_i[:, None]
    l_ptrs = L + off_hz * N_CTX + offs_m
    m_ptrs = M + off_hz * N_CTX + offs_m
    tl.store(l_ptrs, l_i)
    tl.store(m_ptrs, m_i)
    # write back O
    tl.store(O_block_ptr, acc.to(tl.float16))


@triton.jit
def _bwd_preprocess(
    Out, DO, L,
    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(Out + 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)
    denom = tl.load(L + off_m).to(tl.float32)
    # compute
    do = do / denom[:, None]
    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(
    Q, K, V, sm_scale, Out, DO,
    DQ, DK, DV,
    L, M,
    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,
    num_block,
    BLOCK_M: tl.constexpr, BLOCK_DMODEL: tl.constexpr,
    BLOCK_N: tl.constexpr,
    MODE: tl.constexpr,
):
    off_hz = tl.program_id(0)
    off_z = off_hz // H
    off_h = off_hz % H
    qk_scale = sm_scale * 1.44269504
    # offset pointers for batch/head
    Q += off_z * stride_qz + off_h * stride_qh
    K += off_z * stride_qz + off_h * stride_qh
    V += off_z * stride_qz + off_h * stride_qh
    DO += off_z * stride_qz + off_h * stride_qh
    DQ += off_z * stride_qz + off_h * stride_qh
    DK += off_z * stride_qz + off_h * stride_qh
    DV += off_z * stride_qz + off_h * stride_qh
    for start_n in range(0, num_block):
        if MODE == 0:
            lo = 0
        else:
            lo = start_n * BLOCK_M
        # initialize row/col offsets
        offs_qm = lo + tl.arange(0, BLOCK_M)
        offs_n = start_n * BLOCK_M + tl.arange(0, BLOCK_M)
        offs_m = tl.arange(0, BLOCK_N)
        offs_k = tl.arange(0, BLOCK_DMODEL)
        # initialize pointers to value-like data
        q_ptrs = Q + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        k_ptrs = K + (offs_n[:, None] * stride_kn + offs_k[None, :] * stride_kk)
        v_ptrs = V + (offs_n[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        do_ptrs = DO + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        dq_ptrs = DQ + (offs_qm[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        # pointer to row-wise quantities in value-like data
        D_ptrs = D + off_hz * N_CTX
        m_ptrs = M + off_hz * N_CTX
        # initialize dv amd dk
        dv = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
        dk = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
        # k and v stay in SRAM throughout
        k = tl.load(k_ptrs)
        v = tl.load(v_ptrs)
        # loop over rows
        for start_m in range(lo, num_block * BLOCK_M, BLOCK_M):
            offs_m_curr = start_m + offs_m
            # load q, k, v, do on-chip
            q = tl.load(q_ptrs)
            # recompute p = softmax(qk, dim=-1).T
            # NOTE: `do` is pre-divided by `l`; no normalization here
            # if MODE == 1:
            if MODE == 1:
                qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), float(0.), float("-inf"))
            else:
                qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
            qk += tl.dot(q, tl.trans(k))
            qk *= qk_scale
            m = tl.load(m_ptrs + offs_m_curr)
            p = tl.math.exp2(qk - m[:, None])
            # compute dv
            do = tl.load(do_ptrs)
            dv += tl.dot(tl.trans(p.to(Q.dtype.element_ty)), do)
            # compute dp = dot(v, do)
            Di = tl.load(D_ptrs + offs_m_curr)
            dp = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32) - Di[:, None]
            dp += tl.dot(do, tl.trans(v))
            # compute ds = p * (dp - delta[:, None])
            ds = p * dp * sm_scale
            # compute dk = dot(ds.T, q)
            dk += tl.dot(tl.trans(ds.to(Q.dtype.element_ty)), q)
            # compute dq
            dq = tl.load(dq_ptrs)
            dq += tl.dot(ds.to(Q.dtype.element_ty), k)
            tl.store(dq_ptrs, dq)
            # increment pointers
            dq_ptrs += BLOCK_M * stride_qm
            q_ptrs += BLOCK_M * stride_qm
            do_ptrs += BLOCK_M * stride_qm
        # write-back
        dv_ptrs = DV + (offs_n[:, None] * stride_qm + offs_k[None, :] * stride_qk)
        dk_ptrs = DK + (offs_n[:, None] * stride_kn + offs_k[None, :] * stride_kk)
        tl.store(dv_ptrs, dv)
        tl.store(dk_ptrs, dk)


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)
        BLOCK_M = 128
        BLOCK_N = 64
        grid = (triton.cdiv(q.shape[2], BLOCK_M), q.shape[0] * q.shape[1], 1)
        L = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32)
        m = torch.empty((q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32)

        num_warps = 4 if Lk <= 64 else 8
        if causal:
            modes = [1] if q.shape[2] <= 2048 else [2, 3]
        else:
            modes = [0]
        for mode in modes:
            _fwd_kernel[grid](
                q, k, v, sm_scale,
                L, 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], q.shape[2],
                BLOCK_M=BLOCK_M, BLOCK_N=BLOCK_N, BLOCK_DMODEL=Lk,
                MODE=mode,
                num_warps=num_warps,
                num_stages=4)

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

    @staticmethod
    def backward(ctx, do):
        BLOCK = 128
        q, k, v, o, l, m = ctx.saved_tensors
        do = do.contiguous()
        dq = torch.zeros_like(q, dtype=torch.float32)
        dk = torch.empty_like(k)
        dv = torch.empty_like(v)
        do_scaled = torch.empty_like(do)
        delta = torch.empty_like(l)
        if ctx.causal:
            mode = 1
        else:
            mode = 0
        _bwd_preprocess[(ctx.grid[0] * ctx.grid[1], )](
            o, do, l,
            do_scaled, delta,
            BLOCK_M=BLOCK, D_HEAD=ctx.BLOCK_DMODEL,
        )
        _bwd_kernel[(ctx.grid[1],)](
            q, k, v, ctx.sm_scale,
            o, do_scaled,
            dq, dk, dv,
            l, m,
            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],
            ctx.grid[0],
            BLOCK_M=BLOCK, BLOCK_N=BLOCK,
            BLOCK_DMODEL=ctx.BLOCK_DMODEL, num_warps=8,
            MODE=mode,
            num_stages=1,
        )
        return dq, dk, dv, None, None


attention = _attention.apply


@pytest.mark.parametrize('Z, H, N_CTX, D_HEAD', [(6, 9, 1024, 64)])
@pytest.mark.parametrize('causal', [False, True])
def test_op(Z, H, N_CTX, D_HEAD, causal, dtype=torch.float16):
    torch.manual_seed(20)
    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
    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()
    # 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
    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
    assert torch.allclose(ref_out, tri_out, atol=1e-2, rtol=0)
    assert torch.allclose(ref_dv, tri_dv, atol=1e-2, rtol=0)
    assert torch.allclose(ref_dk, tri_dk, atol=1e-2, rtol=0)
    assert torch.allclose(ref_dq, tri_dq, atol=1e-2, rtol=0)


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

BATCH, N_HEADS, N_CTX, D_HEAD = 4, 48, 4096, 64
# vary seq length for fixed head and batch=4
configs = [triton.testing.Benchmark(
    x_names=['N_CTX'],
    x_vals=[2**i for i in range(10, 15)],
    line_arg='provider',
    line_vals=['triton'] + (['flash'] if HAS_FLASH else []),
    line_names=['Triton'] + (['Flash'] if HAS_FLASH else []),
    styles=[('red', '-'), ('blue', '-')],
    ylabel='ms',
    plot_name=f'fused-attention-batch{BATCH}-head{N_HEADS}-d{D_HEAD}-{mode}',
    args={'H': N_HEADS, 'BATCH': BATCH, 'D_HEAD': D_HEAD, 'dtype': torch.float16, 'mode': mode, 'causal': causal}
) for mode in ['fwd'] for causal in [False]]


@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
    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)
        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":
        lengths = torch.full((BATCH,), fill_value=N_CTX, device=device)
        cu_seqlens = torch.zeros((BATCH + 1,), device=device, dtype=torch.int32)
        cu_seqlens[1:] = lengths.cumsum(0)
        qkv = torch.randn((BATCH * N_CTX, 3, H, D_HEAD), dtype=dtype, device=device, requires_grad=True)
        fn = lambda: flash_attn_func(qkv, cu_seqlens, 0., N_CTX, 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. * 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)
