fla/ops/path_attn/parallel_path_bwd_inter_dkv.py

import torch
import triton
import triton.language as tl

from fla.ops.utils import prepare_chunk_indices, prepare_chunk_offsets


@triton.heuristics({
    'USE_GATE': lambda args: args['g_cumsum'] is not None,
    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
})
@triton.jit(do_not_specialize=['T'])
def parallel_path_bwd_dkv_kernel(
    q,
    k,
    v,
    g_cumsum,
    hc_whole,
    scale,
    L,
    D,
    dk,
    dv,
    do,
    dg_cumsum,
    cu_seqlens,
    indices,
    split_offsets,
    T,
    G: tl.constexpr,
    HQ: tl.constexpr,
    H: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BT: tl.constexpr,
    BS: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    S: tl.constexpr,
    IS_VARLEN: tl.constexpr,
    USE_GATE: tl.constexpr,
    NUM_BLOCKS: tl.constexpr,
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_hq = i_bh // HQ, i_bh % HQ
    i_h = i_hq // G

    if IS_VARLEN:
        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
        boh_large = tl.load(split_offsets + i_n).to(tl.int32)
        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
        T = eos - bos
    else:
        i_n = i_b
        bos, eos = i_n * T, i_n * T + T
        boh_large = i_n * tl.cdiv(T, S)

    # offset calculations

    do += (bos * HQ + i_hq) * V
    dk += (bos * HQ + i_hq) * K
    dv += (bos * HQ + i_hq) * K
    L += (bos * HQ + i_hq)
    D += (bos * HQ + i_hq)

    k += (bos * H + i_h) * K  # GQA when H!=HQ
    v += (bos * H + i_h) * V  # GQA when H!=HQ
    hc_whole += (boh_large * H + i_h) * K * K

    if USE_GATE:
        g_cumsum += (bos * HQ + i_hq)
        dg_cumsum += (bos * HQ + i_hq)

    # constants
    sm_scale = scale * 1.44269504

    # load query
    p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (i_t * BT, 0), (BT, BK), (1, 0))
    b_k = tl.load(p_k, boundary_check=(0, 1))
    p_v = tl.make_block_ptr(v, (T, V), (H*V, 1), (i_t * BT, 0), (BT, BV), (1, 0))
    b_v = tl.load(p_v, boundary_check=(0, 1))

    if USE_GATE:
        b_g_cumsum_k = tl.zeros([BT], dtype=tl.float32)
        p_g_cumsum_k = tl.make_block_ptr(g_cumsum, (T, ), (HQ, ), (i_t * BT, ), (BT, ), (0, ))
        b_g_cumsum_k += tl.load(p_g_cumsum_k, boundary_check=(0, ))
        b_dg_cumsum_k = tl.zeros([BT], dtype=tl.float32)
    else:
        b_g_cumsum_k = None
        b_dg_cumsum_k = None

    b_dk = tl.zeros([BT, BK], dtype=tl.float32)
    b_dv = tl.zeros([BT, BV], dtype=tl.float32)

    last_chunk_start = tl.floor(i_t*BT / S).to(tl.int32) * S
    idx_j = (tl.floor(i_t * BT / S).to(tl.int32) + 1).to(tl.int32)

    last_chunk_end = tl.ceil(T / BS).to(tl.int32) * BS - BS

    for offset in range(last_chunk_end, last_chunk_start+S-BS, -BS):
        p_delta = tl.make_block_ptr(D, (T, ), (HQ, ), (offset, ), (BS, ), (0, ))
        p_l = tl.make_block_ptr(L, (T, ), (HQ, ), (offset, ), (BS, ), (0, ))
        b_delta = tl.load(p_delta, boundary_check=(0, ))
        b_l = tl.load(p_l, boundary_check=(0, ))

        p_q = tl.make_block_ptr(q + ((bos.to(tl.int64) * NUM_BLOCKS + idx_j) * HQ + i_hq) * K, (T, K),
                                (HQ*K*NUM_BLOCKS, 1), (offset, 0), (BS, BK), (1, 0))
        b_q = tl.load(p_q, boundary_check=(0, 1))
        b_A = tl.dot(b_k, tl.trans(b_q).to(b_k.dtype))
        if USE_GATE:
            p_g_cumsum_q = tl.make_block_ptr(g_cumsum, (T, ), (HQ, ), (offset, ), (BS, ), (0, ))
            b_g_cumsum_q = tl.load(p_g_cumsum_q, boundary_check=(0, ))
            b_A = b_A + b_g_cumsum_q[None, :] - b_g_cumsum_k[:, None]
            b_A = tl.where((offset + tl.arange(0, BS) < T)[None, :], b_A, float("-inf"))  # avoid nan
        b_A_softmax = tl.math.exp2(b_A * sm_scale - b_l[None, :])
        p_do = tl.make_block_ptr(do, (T, V), (HQ*V, 1), (offset, 0), (BS, BV), (1, 0))
        b_do = tl.load(p_do, boundary_check=(0, 1))
        b_dv += tl.dot(b_A_softmax.to(b_do.dtype), b_do)
        b_dp = tl.dot(b_v, tl.trans(b_do))

        b_dA = ((b_dp - b_delta[None, :]) * b_A_softmax * scale)
        if USE_GATE:
            b_dg_cumsum_k -= tl.sum(b_dA, axis=1)
        b_dk += tl.dot(b_dA.to(b_q.dtype), b_q)

    p_dk = tl.make_block_ptr(dk, (T, K), (HQ*K, 1), (i_t * BT, 0), (BT, BK), (1, 0))
    tl.store(p_dk, b_dk.to(dk.dtype.element_ty), boundary_check=(0, 1))
    mask = i_t * BT + tl.arange(0, BT) < T
    tl.atomic_add(
        dv + (i_t * BT + tl.arange(0, BT))[:, None] * HQ * V + tl.arange(0, BV)[None, :],
        b_dv,
        mask=mask[:, None],
        sem='relaxed',
    )
    if USE_GATE:
        tl.atomic_add(dg_cumsum + (i_t * BT + tl.arange(0, BT)) * HQ, b_dg_cumsum_k, mask=mask, sem='relaxed')


def parallel_path_bwd_dkv_fn(
    q, k, v, g_cumsum, do, dv, dg_cumsum,
    hc_whole, scale, L, D,
    cu_seqlens,
    S, BT, BS,
    chunk_indices: torch.LongTensor | None = None,
):
    B, T, num_blocks, HQ, K = q.shape
    V = v.shape[-1]
    H = k.shape[-2]
    G = HQ // H

    if chunk_indices is None and cu_seqlens is not None:
        chunk_indices = prepare_chunk_indices(cu_seqlens, BT)
    indices = chunk_indices
    split_offsets = prepare_chunk_offsets(cu_seqlens, S) if cu_seqlens is not None else None
    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(indices)

    if cu_seqlens is not None:
        assert split_offsets[-1] == hc_whole.shape[0]

    dk = torch.empty(B, T, HQ, K, dtype=torch.float32, device=q.device)

    parallel_path_bwd_dkv_kernel[(NT, B*HQ)](
        q=q,
        k=k,
        v=v,
        g_cumsum=g_cumsum,
        hc_whole=hc_whole,
        scale=scale,
        L=L,
        D=D,
        dk=dk,
        dv=dv,
        do=do,
        dg_cumsum=dg_cumsum,
        cu_seqlens=cu_seqlens,
        indices=indices,
        split_offsets=split_offsets,
        T=T,
        S=S,
        BT=BT,
        BS=BS,
        G=G,
        HQ=HQ,
        H=H,
        K=K,
        V=V,
        BK=triton.next_power_of_2(K),
        BV=triton.next_power_of_2(V),
        num_warps=8 if (BT == 128 and K == 128) else 4,
        NUM_BLOCKS=num_blocks,
    )
    return dk, dv, dg_cumsum