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import triton
import triton.language as tl
from fla.ops.utils import prepare_chunk_indices
@triton.heuristics({
'IS_VARLEN': lambda args: args['offsets'] is not None,
'USE_GATE': lambda args: args['g_cumsum'] is not None,
})
@triton.jit(do_not_specialize=['T'])
def parallel_path_bwd_intra_chunk_kernel(
q, k, v, g_cumsum, w1, w2,
L, D,
dq, dq_new, dk, dv, dw1, dw2, do, dg_cumsum,
offsets, indices,
T, scale,
G: tl.constexpr, HQ: tl.constexpr, H: tl.constexpr,
K: tl.constexpr, V: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr,
BT: tl.constexpr, S: tl.constexpr,
IS_VARLEN: tl.constexpr, USE_GATE: 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)
bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
T = eos - bos
else:
i_n = i_b
bos, eos = i_n * T, i_n * T + T
# offset calculations
k += (bos * H + i_h) * K # GQA when H!=HQ
v += (bos * H + i_h) * V # GQA when H!=HQ
w1 += (bos * H + i_h) * K
w2 += (bos * H + i_h) * K
q += (bos * HQ + i_hq) * K
dq += (bos * HQ + i_hq) * K
dq_new += (bos * HQ + i_hq) * K
dk += (bos * HQ + i_hq) * K
dv += (bos * HQ + i_hq) * V
do += (bos * HQ + i_hq) * V
dw1 += (bos * HQ + i_hq) * K
dw2 += (bos * HQ + i_hq) * K
L += (bos * HQ + i_hq)
D += (bos * HQ + i_hq)
if USE_GATE:
g_cumsum += (bos * HQ + i_hq)
dg_cumsum += (bos * HQ + i_hq)
# constants
sm_scale = scale * 1.44269504
p_do = tl.make_block_ptr(do, (T, V), (HQ*V, 1), (i_t * BT, 0), (BT, BV), (1, 0))
# [BT, BV]
b_do = tl.load(p_do, boundary_check=(0, 1))
p_delta = tl.make_block_ptr(D, (T, ), (HQ, ), (i_t * BT, ), (BT, ), (0, ))
b_delta = tl.load(p_delta, boundary_check=(0, ))
p_l = tl.make_block_ptr(L, (T, ), (HQ, ), (i_t * BT, ), (BT, ), (0, ))
b_l = tl.load(p_l, boundary_check=(0, ))
b_dq = tl.zeros([BT, BK], dtype=tl.float32)
p_dq = tl.make_block_ptr(dq, (T, K), (HQ*K, 1), (i_t * BT, 0), (BT, BK), (1, 0))
b_dq += tl.load(p_dq, boundary_check=(0, 1))
p_q = tl.make_block_ptr(q, (T, K), (HQ*K, 1), (i_t * BT, 0), (BT, BK), (1, 0))
b_q = tl.load(p_q, boundary_check=(0, 1))
if USE_GATE:
p_gq_cumsum = tl.make_block_ptr(g_cumsum, (T, ), (HQ, ), (i_t * BT, ), (BT, ), (0, ))
b_gq_cumsum = tl.load(p_gq_cumsum, boundary_check=(0, ))
b_dgq = tl.zeros([BT ], dtype=tl.float32)
else:
b_dgq = None
curr_start = (tl.floor(i_t * BT / S).to(tl.int32) * S).to(tl.int32)
for offset in range(curr_start, i_t * BT, BT):
mask = offset + tl.arange(0, BT) < T
p_k = tl.make_block_ptr(k, (T, K), (H*K, 1), (offset, 0), (BT, BK), (1, 0))
b_k = tl.load(p_k, boundary_check=(0, 1))
b_q_tmp = tl.zeros([BT, BK], dtype=tl.float32)
b_q_tmp += b_q
for i_t_small in range(i_t * BT - BT, offset, -BT):
p_w1 = tl.make_block_ptr(w1, (T, K), (H*K, 1), (i_t_small, 0), (BT, BK), (1, 0))
b_w1 = tl.load(p_w1, boundary_check=(0, 1))
p_w2 = tl.make_block_ptr(w2, (T, K), (H*K, 1), (i_t_small, 0), (BT, BK), (1, 0))
b_w2 = tl.load(p_w2, boundary_check=(0, 1))
b_A_tmp = tl.dot(b_q_tmp.to(b_w1.dtype), tl.trans(b_w1))
b_q_tmp -= tl.dot(b_A_tmp.to(b_w1.dtype), b_w2)
b_q2 = b_q_tmp.to(b_k.dtype)
b_A = tl.dot(b_q2, tl.trans(b_k))
if USE_GATE:
p_gk_cumsum = tl.make_block_ptr(g_cumsum, (T, ), (HQ, ), (offset, ), (BT, ), (0, ))
b_gk_cumsum = tl.load(p_gk_cumsum, boundary_check=(0, ))
b_A = b_A + b_gq_cumsum[:, None] - b_gk_cumsum[None, :]
b_A = tl.where((i_t * BT + tl.arange(0, BT) < T)[:, None], b_A, float("-inf")) # avoid nan
b_A_softmax = tl.math.exp2(b_A * sm_scale - b_l[:, None])
b_dv = tl.dot(tl.trans(b_A_softmax.to(b_do.dtype)), b_do)
tl.atomic_add(
dv + ((offset + tl.arange(0, BT)) * HQ * V)[:, None] + tl.arange(0, BV)[None, :],
b_dv.to(dv.dtype.element_ty),
mask=mask[:, None],
sem='relaxed',
)
p_v = tl.make_block_ptr(v, (T, V), (V*H, 1), (offset, 0), (BT, BV), (1, 0))
b_v = tl.load(p_v, boundary_check=(0, 1))
b_dp = tl.dot(b_do, tl.trans(b_v))
b_dA = ((b_dp - b_delta[:, None]) * b_A_softmax * scale)
if USE_GATE:
b_dgk = -tl.sum(b_dA, axis=0)
tl.atomic_add(dg_cumsum + (offset + tl.arange(0, BT)) * HQ, b_dgk, mask=mask, sem='relaxed')
b_dgq += tl.sum(b_dA, axis=1)
b_dA = b_dA.to(b_v.dtype)
b_dk = tl.dot(tl.trans(b_dA), b_q2)
tl.atomic_add(dk + (offset + tl.arange(0, BT))[:, None] * HQ*K + tl.arange(0,
BK)[None, :], b_dk, mask=mask[:, None], sem='relaxed')
p_w1 = tl.make_block_ptr(w1, (T, K), (H*K, 1), (offset, 0), (BT, BK), (1, 0))
b_w1 = tl.load(p_w1, boundary_check=(0, 1))
p_w2 = tl.make_block_ptr(w2, (T, K), (H*K, 1), (offset, 0), (BT, BK), (1, 0))
b_w2 = tl.load(p_w2, boundary_check=(0, 1))
b_dA2 = tl.dot(b_dq.to(b_w2.dtype), tl.trans(b_w2)).to(b_v.dtype)
b_A2 = tl.dot(b_q2.to(b_w1.dtype), tl.trans(b_w1)).to(b_v.dtype)
b_dw2 = -tl.dot(tl.trans(b_A2), b_dq.to(b_v.dtype))
tl.atomic_add(dw2 + (offset + tl.arange(0, BT))[:, None] * HQ*K + tl.arange(0,
BK)[None, :], b_dw2, mask=mask[:, None], sem='relaxed')
b_dw1 = -tl.dot(tl.trans(b_dA2), b_q2.to(b_v.dtype))
tl.atomic_add(dw1 + (offset + tl.arange(0, BT))[:, None] * HQ*K + tl.arange(0,
BK)[None, :], b_dw1, mask=mask[:, None], sem='relaxed')
b_dq -= tl.dot(b_dA2, b_w1.to(b_v.dtype))
b_dq += tl.dot(b_dA.to(b_k.dtype), b_k)
p_dq_new = tl.make_block_ptr(dq_new, (T, K), (HQ*K, 1), (i_t * BT, 0), (BT, BK), (1, 0))
tl.store(p_dq_new, b_dq.to(dq_new.dtype.element_ty), boundary_check=(0, 1))
mask = i_t * BT + tl.arange(0, BT) < T
if USE_GATE:
tl.atomic_add(dg_cumsum + (i_t * BT + tl.arange(0, BT)) * HQ, b_dgq, mask=mask, sem='relaxed')
def parallel_path_bwd_intra_chunk_fn(
q, k, v, g_cumsum, w1, w2,
dq, dk, dv, dg_cumsum, dw1, dw2, do,
scale, L, D,
cu_seqlens,
S, BT,
):
assert dk.dtype == dv.dtype == dw1.dtype == dw2.dtype == torch.float32, 'atomic_add requires float32'
B, T, HQ, K = q.shape
assert dk.shape == dq.shape
V = v.shape[-1]
H = k.shape[-2]
G = HQ // H
indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
NT = triton.cdiv(T, BT) if cu_seqlens is None else len(indices)
dq_new = torch.empty_like(dq, dtype=q.dtype)
parallel_path_bwd_intra_chunk_kernel[(NT, B*HQ)](
q=q, k=k, v=v, g_cumsum=g_cumsum,
w1=w1, w2=w2, L=L, D=D,
dq=dq, dq_new=dq_new, dk=dk, dv=dv, dw1=dw1, dw2=dw2,
do=do, dg_cumsum=dg_cumsum,
offsets=cu_seqlens, indices=indices,
T=T, S=S, BT=BT, scale=scale,
G=G, HQ=HQ, H=H, K=K, V=V,
BK=triton.next_power_of_2(K), BV=triton.next_power_of_2(V),
)
return dq_new, dk, dv, dw1, dw2, dg_cumsum
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