# [2022-10-23] Downloaded from https://github.com/openai/triton/blob/master/python/tutorials/06-fused-attention.py
# for benchmarking.
# We fixed a few dtype cast to make it work for bf16

"""
Fused Attention
===============
This is a Triton implementation of the Flash Attention algorithm
(see: Dao et al., https://arxiv.org/pdf/2205.14135v2.pdf; Rabe and Staats https://arxiv.org/pdf/2112.05682v2.pdf)
"""

import pytest
import torch
import triton
import triton.language as tl


@triton.jit
def _fwd_kernel(
    Q,
    K,
    V,
    sm_scale,
    TMP,
    L,
    M,  # NOTE: TMP is a scratchpad buffer to workaround a compiler bug
    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,
):
    start_m = tl.program_id(0)
    off_hz = tl.program_id(1)
    # 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)
    off_q = off_hz * stride_qh + offs_m[:, None] * stride_qm + offs_d[None, :] * stride_qk
    off_k = off_hz * stride_qh + offs_n[:, None] * stride_kn + offs_d[None, :] * stride_kk
    off_v = off_hz * stride_qh + offs_n[:, None] * stride_qm + offs_d[None, :] * stride_qk
    # Initialize pointers to Q, K, V
    q_ptrs = Q + off_q
    k_ptrs = K + off_k
    v_ptrs = V + off_v
    # initialize pointer to m and l
    t_ptrs = TMP + off_hz * N_CTX + offs_m
    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)
    # load q: it will stay in SRAM throughout
    q = tl.load(q_ptrs)
    # loop over k, v and update accumulator
    for start_n in range(0, (start_m + 1) * BLOCK_M, BLOCK_N):
        start_n = tl.multiple_of(start_n, BLOCK_N)
        # -- compute qk ----
        k = tl.load(k_ptrs + start_n * stride_kn)
        qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
        qk += tl.dot(q, k, trans_b=True)
        qk *= sm_scale
        qk += tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), 0, float("-inf"))
        # -- compute m_ij, p, l_ij
        m_ij = tl.max(qk, 1)
        p = tl.exp(qk - m_ij[:, None])
        l_ij = tl.sum(p, 1)
        # -- update m_i and l_i
        m_i_new = tl.maximum(m_i, m_ij)
        alpha = tl.exp(m_i - m_i_new)
        beta = tl.exp(m_ij - m_i_new)
        l_i_new = alpha * l_i + beta * l_ij
        # -- update output accumulator --
        # scale p
        p_scale = beta / l_i_new
        p = p * p_scale[:, None]
        # scale acc
        acc_scale = l_i / l_i_new * alpha
        tl.store(t_ptrs, acc_scale)
        acc_scale = tl.load(t_ptrs)  # BUG: have to store and immediately load
        acc = acc * acc_scale[:, None]
        # update acc
        v = tl.load(v_ptrs + start_n * stride_vk)
        p = p.to(v.dtype)
        acc += tl.dot(p, v)
        # update m_i and l_i
        l_i = l_i_new
        m_i = m_i_new
    # rematerialize offsets to save registers
    start_m = tl.program_id(0)
    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
    # write back l and m
    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)
    # initialize pointers to output
    offs_n = tl.arange(0, BLOCK_DMODEL)
    off_o = off_hz * stride_oh + offs_m[:, None] * stride_om + offs_n[None, :] * stride_on
    out_ptrs = Out + off_o
    tl.store(out_ptrs, acc)


@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,
):
    off_hz = tl.program_id(0)
    off_z = off_hz // H
    off_h = off_hz % H
    # 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):
        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
            qk = tl.dot(q, k, trans_b=True)
            qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), qk, float("-inf"))
            m = tl.load(m_ptrs + offs_m_curr)
            p = tl.exp(qk * sm_scale - m[:, None])
            # compute dv
            do = tl.load(do_ptrs)
            dv += tl.dot(p.to(do.dtype), do, trans_a=True)
            # 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, v, trans_b=True)
            # compute ds = p * (dp - delta[:, None])
            ds = p * dp * sm_scale
            # compute dk = dot(ds.T, q)
            dk += tl.dot(ds.to(q.dtype), q, trans_a=True)
            # # compute dq
            dq = tl.load(dq_ptrs, eviction_policy="evict_last")
            dq += tl.dot(ds.to(k.dtype), k)
            tl.store(dq_ptrs, dq, eviction_policy="evict_last")
            # # 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)


class _attention(torch.autograd.Function):
    @staticmethod
    def forward(ctx, q, k, v, sm_scale):
        BLOCK = 128
        # 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)
        grid = (triton.cdiv(q.shape[2], BLOCK), q.shape[0] * q.shape[1])
        tmp = torch.empty(
            (q.shape[0] * q.shape[1], q.shape[2]), device=q.device, dtype=torch.float32
        )
        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

        _fwd_kernel[grid](
            q,
            k,
            v,
            sm_scale,
            tmp,
            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,
            BLOCK_N=BLOCK,
            BLOCK_DMODEL=Lk,
            num_warps=num_warps,
            num_stages=1,
        )
        ctx.save_for_backward(q, k, v, o, L, m)
        ctx.BLOCK = BLOCK
        ctx.grid = grid
        ctx.sm_scale = sm_scale
        ctx.BLOCK_DMODEL = Lk
        return o

    @staticmethod
    def backward(ctx, do):
        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)
        _bwd_preprocess[(ctx.grid[0] * ctx.grid[1],)](
            o,
            do,
            l,
            do_scaled,
            delta,
            BLOCK_M=ctx.BLOCK,
            D_HEAD=ctx.BLOCK_DMODEL,
        )

        # NOTE: kernel currently buggy for other values of `num_warps`
        num_warps = 8
        _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=ctx.BLOCK,
            BLOCK_N=ctx.BLOCK,
            BLOCK_DMODEL=ctx.BLOCK_DMODEL,
            num_warps=num_warps,
            num_stages=1,
        )
        return dq.to(q.dtype), dk, dv, None


attention = _attention.apply
