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# -*- coding: utf-8 -*-
# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang
from typing import Optional, Tuple
import torch
import triton
import triton.language as tl
from fla.utils import check_shared_mem, is_intel_alchemist, use_cuda_graph
# https://github.com/intel/intel-xpu-backend-for-triton/issues/3449
triton_config = {'grf_mode': 'large'} if is_intel_alchemist else {}
@triton.heuristics({
'USE_OFFSETS': lambda args: args['offsets'] is not None
})
@triton.autotune(
configs=[
triton.Config(triton_config, num_warps=num_warps, num_stages=num_stages)
for num_warps in [2, 4, 8, 16, 32]
for num_stages in [2, 3, 4]
],
key=['BT', 'BK', 'BV'],
use_cuda_graph=use_cuda_graph,
)
@triton.jit(do_not_specialize=['T'])
def bwd_prepare_wy_repr_kernel(
A_ab_inv,
A_ak,
ag,
v,
dw,
du,
dv,
dv0,
dag,
dAak,
dAab,
offsets,
indices,
T,
H: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr,
USE_OFFSETS: tl.constexpr,
HEAD_FIRST: 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 USE_OFFSETS:
i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
T = eos - bos
else:
bos, eos = i_b * T, i_b * T + T
if HEAD_FIRST:
p_Aab_inv_t = tl.make_block_ptr(A_ab_inv + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1))
p_Aak_t = tl.make_block_ptr(A_ak + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1))
p_dAak = tl.make_block_ptr(dAak + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
p_dAab = tl.make_block_ptr(dAab + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
else:
p_Aak_t = tl.make_block_ptr(A_ak + (bos*H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))
p_Aab_inv_t = tl.make_block_ptr(A_ab_inv + (bos*H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))
p_dAak = tl.make_block_ptr(dAak + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
p_dAab = tl.make_block_ptr(dAab + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
b_A_ab_inv_t = tl.load(p_Aab_inv_t, boundary_check=(0, 1))
b_A_ak_t = tl.load(p_Aak_t, boundary_check=(0, 1))
b_A_ak_t = tl.where(tl.arange(0, BT)[:, None] < tl.arange(0, BT)[None, :], b_A_ak_t, 0)
b_A_ab_inv_t = tl.where(tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :], b_A_ab_inv_t, 0)
b_A_tmp_t = tl.dot(b_A_ak_t, b_A_ab_inv_t).to(v.dtype.element_ty)
b_dA_tmp = tl.zeros([BT, BT], dtype=tl.float32)
for i_v in range(tl.cdiv(V, BV)):
if HEAD_FIRST:
p_v = tl.make_block_ptr(v + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dv = tl.make_block_ptr(dv + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dv0 = tl.make_block_ptr(dv0 + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_du = tl.make_block_ptr(du + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
else:
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_dv0 = tl.make_block_ptr(dv0 + (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_du = tl.load(p_du, boundary_check=(0, 1))
b_dA_tmp += tl.dot(b_du.to(b_v.dtype), tl.trans(b_v))
b_dv0 = tl.load(p_dv0, boundary_check=(0, 1))
b_dv = b_dv0 + tl.dot(b_A_tmp_t, b_du)
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
b_dA_tmp = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA_tmp, 0)
b_dA_ak = tl.dot(b_A_ab_inv_t, b_dA_tmp)
b_dA_ak = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA_ak, 0)
tl.store(p_dAak, b_dA_ak, boundary_check=(0, 1))
b_dA_ab_inv = tl.dot(b_dA_tmp, b_A_ak_t)
for i_k in range(tl.cdiv(K, BK)):
if HEAD_FIRST:
p_ag = tl.make_block_ptr(ag + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dag = tl.make_block_ptr(dag + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dw = tl.make_block_ptr(dw + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
else:
p_ag = tl.make_block_ptr(ag + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dag = tl.make_block_ptr(dag + (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))
b_ag = tl.load(p_ag, boundary_check=(0, 1))
b_dw = tl.load(p_dw, boundary_check=(0, 1))
b_dA_ab_inv += tl.dot(b_dw, tl.trans(b_ag))
b_dag = tl.dot(b_A_ab_inv_t.to(b_dw.dtype), b_dw)
tl.store(p_dag, b_dag.to(p_dag.dtype.element_ty), boundary_check=(0, 1))
# if we know dL/dA^(-1), for dL/dA, we can use the following formula:
# dL/dA = -(A^(-1))^T @ (dL/dA^(-1)) @ (A^(-1))^T
# in the fwd pass we use fwd substitution to calculate (I-lower(A_ab))^-1.
# denote A = I - lower(A_ab), B = A^-1
# in the backward pass.
# dL/dA = -(B)^T @ (dL/dB) @ B^T
# dL/dA_ab = lower(B^T @ dL/dB @ B^T)
b_dA_ab_inv = tl.where(tl.arange(0, BT)[:, None] >= tl.arange(0, BT)[None, :], b_dA_ab_inv, 0)
b_dA_ab_inv = tl.dot(b_A_ab_inv_t, b_dA_ab_inv)
b_dA_ab_inv = tl.dot(b_dA_ab_inv, b_A_ab_inv_t)
b_dA_ab_inv = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA_ab_inv, 0)
tl.store(p_dAab, b_dA_ab_inv, boundary_check=(0, 1))
def chunk_dplr_bwd_wy(
A_ab_inv: torch.Tensor,
A_ak: torch.Tensor,
v: torch.Tensor,
ag: torch.Tensor,
dw: torch.Tensor,
du: torch.Tensor,
dv0: torch.Tensor,
offsets: Optional[torch.LongTensor],
indices: Optional[torch.LongTensor],
head_first: bool,
chunk_size: int,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
A_ab_inv, A_ak, v, ag, dw, du = map(lambda x: x.contiguous(), [A_ab_inv, A_ak, v, ag, dw, du])
if head_first:
B, H, T, K, V = *dw.shape, du.shape[-1]
else:
B, T, H, K, V = *dw.shape, du.shape[-1]
BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
NT = triton.cdiv(T, BT) if offsets is None else len(indices)
BK = min(triton.next_power_of_2(K), 64)
BV = min(triton.next_power_of_2(V), 64) if check_shared_mem() else min(triton.next_power_of_2(V), 32)
dA_ab = torch.empty_like(A_ab_inv, dtype=torch.float)
dA_ak = torch.empty_like(A_ak, dtype=torch.float)
dv = torch.empty_like(v)
dag = torch.empty_like(ag)
bwd_prepare_wy_repr_kernel[(NT, B * H)](
A_ab_inv=A_ab_inv,
A_ak=A_ak,
ag=ag,
v=v,
dw=dw,
du=du,
dv=dv,
dv0=dv0,
dag=dag,
dAak=dA_ak,
dAab=dA_ab,
offsets=offsets,
indices=indices,
T=T,
H=H,
K=K,
V=V,
BT=BT,
BK=BK,
BV=BV,
HEAD_FIRST=head_first
)
return dA_ab, dA_ak, dv, dag
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