fla/ops/kda/wy_fast.py

# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang

import torch
import triton
import triton.language as tl

from fla.ops.utils import prepare_chunk_indices
from fla.ops.utils.op import exp2
from fla.utils import autotune_cache_kwargs, check_shared_mem


@triton.heuristics({
    'STORE_QG': lambda args: args['qg'] is not None,
    'STORE_KG': lambda args: args['kg'] is not None,
    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
        for num_warps in [2, 4, 8]
        for num_stages in [2, 3, 4]
    ],
    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'IS_VARLEN'],
    **autotune_cache_kwargs,
)
@triton.jit(do_not_specialize=['T'])
def recompute_w_u_fwd_kda_kernel(
    q,
    k,
    qg,
    kg,
    v,
    beta,
    w,
    u,
    A,
    gk,
    cu_seqlens,
    chunk_indices,
    T,
    H: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    STORE_QG: tl.constexpr,
    STORE_KG: tl.constexpr,
    IS_VARLEN: tl.constexpr,
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_h = i_bh // H, i_bh % H
    if IS_VARLEN:
        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).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:
        bos, eos = i_b * T, i_b * T + T
    p_b = tl.make_block_ptr(beta + bos*H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
    b_b = tl.load(p_b, boundary_check=(0,))

    p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    b_A = tl.load(p_A, boundary_check=(0, 1))

    for i_v in range(tl.cdiv(V, BV)):
        p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        p_u = tl.make_block_ptr(u + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        b_v = tl.load(p_v, boundary_check=(0, 1))
        b_vb = (b_v * b_b[:, None]).to(b_v.dtype)
        b_u = tl.dot(b_A, b_vb)
        tl.store(p_u, b_u.to(p_u.dtype.element_ty), boundary_check=(0, 1))

    for i_k in range(tl.cdiv(K, BK)):
        p_w = tl.make_block_ptr(w + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_kb = b_k * b_b[:, None]

        p_gk = tl.make_block_ptr(gk + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_gk = tl.load(p_gk, boundary_check=(0, 1)).to(tl.float32)
        b_kb *= exp2(b_gk)
        if STORE_QG:
            p_q = tl.make_block_ptr(q + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_qg = tl.make_block_ptr(qg + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            b_q = tl.load(p_q, boundary_check=(0, 1))
            b_qg = b_q * exp2(b_gk)
            tl.store(p_qg, b_qg.to(p_qg.dtype.element_ty), boundary_check=(0, 1))
        if STORE_KG:
            last_idx = min(i_t * BT + BT, T) - 1
            o_k = i_k * BK + tl.arange(0, BK)
            m_k = o_k < K
            b_gn = tl.load(gk + ((bos + last_idx) * H + i_h) * K + o_k, mask=m_k, other=0.).to(tl.float32)
            b_kg = b_k * tl.where((i_t * BT + tl.arange(0, BT) < T)[:, None], exp2(b_gn[None, :] - b_gk), 0)
            p_kg = tl.make_block_ptr(kg + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            tl.store(p_kg, b_kg.to(p_kg.dtype.element_ty), boundary_check=(0, 1))

        b_w = tl.dot(b_A, b_kb.to(b_k.dtype))
        tl.store(p_w, b_w.to(p_w.dtype.element_ty), boundary_check=(0, 1))


@triton.heuristics({
    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps, num_stages=num_stages)
        for num_warps in [2, 4]
        for num_stages in [2, 3, 4]
    ],
    key=['H', 'K', 'V', 'BT', 'BK', 'BV', 'IS_VARLEN'],
    **autotune_cache_kwargs,
)
@triton.jit(do_not_specialize=['T'])
def prepare_wy_repr_bwd_kda_kernel(
    k,
    v,
    beta,
    gk,
    A,
    dA,
    dw,
    du,
    dk,
    dk2,
    dv,
    db,
    dg,
    dg2,
    cu_seqlens,
    chunk_indices,
    T,
    H: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    IS_VARLEN: tl.constexpr,
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_h = i_bh // H, i_bh % H
    if IS_VARLEN:
        i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).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:
        bos, eos = i_b * T, i_b * T + T

    p_b = tl.make_block_ptr(beta + (bos*H + i_h), (T,), (H,), (i_t * BT,), (BT,), (0,))
    p_db = tl.make_block_ptr(db + (bos*H + i_h), (T,), (H,), (i_t * BT,), (BT,), (0,))
    p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))

    b_b = tl.load(p_b, boundary_check=(0,))
    b_db = tl.zeros([BT], dtype=tl.float32)
    b_A = tl.load(p_A, boundary_check=(0, 1))
    b_dA = tl.zeros([BT, BT], dtype=tl.float32)

    for i_k in range(tl.cdiv(K, BK)):
        p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        p_dk = tl.make_block_ptr(dk + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        p_dk2 = tl.make_block_ptr(dk2 + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        p_dw = tl.make_block_ptr(dw + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        p_dg = tl.make_block_ptr(dg + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        p_dg2 = tl.make_block_ptr(dg2 + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))

        # [BT, BK]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        p_gk = tl.make_block_ptr(gk + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_gk_exp = exp2(tl.load(p_gk, boundary_check=(0, 1)))
        b_kbg = b_k * b_b[:, None] * b_gk_exp
        b_dw = tl.load(p_dw, boundary_check=(0, 1))

        b_dA += tl.dot(b_dw, tl.trans(b_kbg).to(b_dw.dtype))
        b_dkbg = tl.dot(b_A, b_dw)
        b_dk = b_dkbg * b_gk_exp * b_b[:, None] + tl.load(p_dk, boundary_check=(0, 1))
        b_db += tl.sum(b_dkbg * b_k * b_gk_exp, 1)
        b_dg = b_kbg * b_dkbg + tl.load(p_dg, boundary_check=(0, 1))

        tl.store(p_dk2, b_dk.to(p_dk2.dtype.element_ty), boundary_check=(0, 1))
        tl.store(p_dg2, b_dg.to(p_dg2.dtype.element_ty), boundary_check=(0, 1))

    for i_v in range(tl.cdiv(V, BV)):
        p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        p_dv = tl.make_block_ptr(dv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        p_du = tl.make_block_ptr(du + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        b_v = tl.load(p_v, boundary_check=(0, 1))
        b_vb = (b_v * b_b[:, None]).to(b_v.dtype)
        b_du = tl.load(p_du, boundary_check=(0, 1))
        b_dA += tl.dot(b_du, tl.trans(b_vb))
        b_dvb = tl.dot(b_A, b_du)
        b_dv = b_dvb * b_b[:, None]
        b_db += tl.sum(b_dvb * b_v, 1)
        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))

    o_t = i_t * BT + tl.arange(0, BT)
    m_t = o_t < T
    m_A = (o_t[:, None] > o_t[None, :]) & (m_t[:, None] & m_t)
    b_dA = tl.where(m_A, b_dA, 0)
    b_dA = tl.dot(b_dA.to(b_A.dtype), b_A)
    b_dA = tl.dot(b_A, b_dA.to(b_A.dtype))

    b_dA = tl.where(m_A, -b_dA, 0)

    # if using gk, save dA first and handle dk in another kernel
    p_dA = tl.make_block_ptr(dA + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    tl.store(p_dA, b_dA.to(p_dA.dtype.element_ty), boundary_check=(0, 1))
    tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0,))


def recompute_w_u_fwd(
    k: torch.Tensor,
    v: torch.Tensor,
    beta: torch.Tensor,
    A: torch.Tensor,
    q: torch.Tensor | None = None,
    gk: torch.Tensor | None = None,
    cu_seqlens: torch.LongTensor | None = None,
    chunk_indices: torch.LongTensor | None = None,
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor | None, torch.Tensor | None]:
    B, T, H, K, V = *k.shape, v.shape[-1]
    BT = A.shape[-1]
    BK = 64
    BV = 64

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

    w = torch.empty_like(k)
    u = torch.empty_like(v)
    qg = torch.empty_like(q) if q is not None else None
    kg = torch.empty_like(k) if gk is not None else None
    recompute_w_u_fwd_kda_kernel[(NT, B*H)](
        q=q,
        k=k,
        qg=qg,
        kg=kg,
        v=v,
        beta=beta,
        w=w,
        u=u,
        A=A,
        gk=gk,
        cu_seqlens=cu_seqlens,
        chunk_indices=chunk_indices,
        T=T,
        H=H,
        K=K,
        V=V,
        BT=BT,
        BK=BK,
        BV=BV,
    )
    return w, u, qg, kg


def prepare_wy_repr_bwd(
    k: torch.Tensor,
    v: torch.Tensor,
    beta: torch.Tensor,
    gk: torch.Tensor,
    A: torch.Tensor,
    dk: torch.Tensor,
    dw: torch.Tensor,
    du: torch.Tensor,
    dg: torch.Tensor,
    cu_seqlens: torch.LongTensor | None = None,
    chunk_indices: torch.LongTensor | None = None,
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
    B, T, H, K, V = *k.shape, v.shape[-1]
    BT = 64
    if chunk_indices is None and cu_seqlens is not None:
        chunk_indices = prepare_chunk_indices(cu_seqlens, BT)
    NT = triton.cdiv(T, BT) if cu_seqlens is None else len(chunk_indices)
    CONST_TILING = 64 if check_shared_mem() else 32
    BK = min(max(triton.next_power_of_2(K), 16), CONST_TILING)
    BV = min(max(triton.next_power_of_2(V), 16), CONST_TILING)

    dk2 = torch.empty_like(dk, dtype=torch.float)
    dv = torch.empty_like(v)
    dg2 = torch.empty_like(gk, dtype=torch.float)
    dA = torch.empty_like(A, dtype=torch.float)
    db = torch.empty_like(beta, dtype=torch.float)
    prepare_wy_repr_bwd_kda_kernel[(NT, B * H)](
        k=k,
        v=v,
        beta=beta,
        gk=gk,
        A=A,
        dA=dA,
        dw=dw,
        du=du,
        dk=dk,
        dk2=dk2,
        dv=dv,
        db=db,
        dg=dg,
        dg2=dg2,
        cu_seqlens=cu_seqlens,
        chunk_indices=chunk_indices,
        T=T,
        H=H,
        K=K,
        V=V,
        BT=BT,
        BK=BK,
        BV=BV,
    )
    dk = dk2
    dg = dg2
    return dk, dv, db, dg, dA