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Fused AttentionΒΆ
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)
fused-attention-batch4-head48-d64-fwd:
N_CTX Triton
0 1024.0 0.288100
1 2048.0 0.989690
2 4096.0 3.639296
3 8192.0 13.874469
fused-attention-batch4-head48-d64-bwd:
N_CTX Triton
0 1024.0 1.201267
1 2048.0 3.849011
2 4096.0 13.625783
3 8192.0 51.016705
import pytest
import torch
import triton
import triton.language as tl
@triton.jit
def _fwd_kernel(
Q, K, V, sm_scale,
L, M,
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
m_prev = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
l_prev = 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):
# -- compute qk ----
k = tl.load(k_ptrs)
qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
qk += tl.dot(q, k)
qk *= sm_scale
qk = tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), qk, float("-inf"))
# compute new m
m_curr = tl.maximum(tl.max(qk, 1), m_prev)
# correct old l
l_prev *= tl.exp(m_prev - m_curr)
# attention weights
p = tl.exp(qk - m_curr[:, None])
l_curr = tl.sum(p, 1) + l_prev
# rescale operands of matmuls
l_rcp = 1. / l_curr
p *= l_rcp[:, None]
acc *= (l_prev * l_rcp)[:, None]
# update acc
p = p.to(Q.dtype.element_ty)
v = tl.load(v_ptrs)
acc += tl.dot(p, v)
# update m_i and l_i
l_prev = l_curr
m_prev = m_curr
# update pointers
k_ptrs += BLOCK_N * stride_kn
v_ptrs += BLOCK_N * stride_vk
# 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_prev)
tl.store(m_ptrs, m_prev)
# 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, tl.trans(k))
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(tl.trans(p.to(Q.dtype.element_ty)), do)
# 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, tl.trans(v))
# compute ds = p * (dp - delta[:, None])
ds = p * dp * sm_scale
# compute dk = dot(ds.T, q)
dk += tl.dot(tl.trans(ds.to(Q.dtype.element_ty)), q)
# compute dq
dq = tl.load(dq_ptrs)
dq += tl.dot(ds.to(Q.dtype.element_ty), k)
tl.store(dq_ptrs, dq)
# 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)
empty = torch.empty(128, device="cuda")
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], 1)
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,
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=2,
)
# print(h.asm["ttgir"])
ctx.save_for_backward(q, k, v, o, L, m)
ctx.grid = grid
ctx.sm_scale = sm_scale
ctx.BLOCK_DMODEL = Lk
return o
@staticmethod
def backward(ctx, do):
BLOCK = 128
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=BLOCK, D_HEAD=ctx.BLOCK_DMODEL,
)
_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=BLOCK, BLOCK_N=BLOCK,
BLOCK_DMODEL=ctx.BLOCK_DMODEL, num_warps=8,
num_stages=1,
)
# print(h.asm["ttgir"])
return dq, dk, dv, None
attention = _attention.apply
@pytest.mark.parametrize('Z, H, N_CTX, D_HEAD', [(4, 48, 1024, 64)])
def test_op(Z, H, N_CTX, D_HEAD, dtype=torch.float16):
torch.manual_seed(20)
q = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0.1, std=0.2).requires_grad_()
k = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0.4, std=0.2).requires_grad_()
v = torch.empty((Z, H, N_CTX, D_HEAD), dtype=dtype, device="cuda").normal_(mean=0.3, std=0.2).requires_grad_()
sm_scale = 0.2
dout = torch.randn_like(q)
# reference implementation
M = torch.tril(torch.ones((N_CTX, N_CTX), device="cuda"))
p = torch.matmul(q, k.transpose(2, 3)) * sm_scale
for z in range(Z):
for h in range(H):
p[:, :, M == 0] = float("-inf")
p = torch.softmax(p.float(), dim=-1).half()
# p = torch.exp(p)
ref_out = torch.matmul(p, v)
ref_out.backward(dout)
ref_dv, v.grad = v.grad.clone(), None
ref_dk, k.grad = k.grad.clone(), None
ref_dq, q.grad = q.grad.clone(), None
# # triton implementation
tri_out = attention(q, k, v, sm_scale)
# print(ref_out)
# print(tri_out)
tri_out.backward(dout)
tri_dv, v.grad = v.grad.clone(), None
tri_dk, k.grad = k.grad.clone(), None
tri_dq, q.grad = q.grad.clone(), None
# compare
assert torch.allclose(ref_out, tri_out, atol=1e-2, rtol=0)
assert torch.allclose(ref_dv, tri_dv, atol=1e-2, rtol=0)
assert torch.allclose(ref_dk, tri_dk, atol=1e-2, rtol=0)
assert torch.allclose(ref_dq, tri_dq, atol=1e-2, rtol=0)
try:
from flash_attn.flash_attn_interface import flash_attn_func
HAS_FLASH = True
except BaseException:
HAS_FLASH = False
BATCH, N_HEADS, N_CTX, D_HEAD = 4, 48, 4096, 64
# vary seq length for fixed head and batch=4
configs = [triton.testing.Benchmark(
x_names=['N_CTX'],
x_vals=[2**i for i in range(10, 14)],
line_arg='provider',
line_vals=['triton'] + (['flash'] if HAS_FLASH else []),
line_names=['Triton'] + (['Flash'] if HAS_FLASH else []),
styles=[('red', '-'), ('blue', '-')],
ylabel='ms',
plot_name=f'fused-attention-batch{BATCH}-head{N_HEADS}-d{D_HEAD}-{mode}',
args={'H': N_HEADS, 'BATCH': BATCH, 'D_HEAD': D_HEAD, 'dtype': torch.float16, 'mode': mode}
) for mode in ['fwd', 'bwd']]
@triton.testing.perf_report(configs)
def bench_flash_attention(BATCH, H, N_CTX, D_HEAD, mode, provider, dtype=torch.float16, device="cuda"):
assert mode in ['fwd', 'bwd']
warmup = 25
rep = 100
if provider == "triton":
q = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True)
k = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True)
v = torch.randn((BATCH, H, N_CTX, D_HEAD), dtype=dtype, device="cuda", requires_grad=True)
sm_scale = 1.3
fn = lambda: attention(q, k, v, sm_scale)
if mode == 'bwd':
o = fn()
do = torch.randn_like(o)
fn = lambda: o.backward(do, retain_graph=True)
ms = triton.testing.do_bench(fn, warmup=warmup, rep=rep)
return ms
if provider == "flash":
lengths = torch.full((BATCH,), fill_value=N_CTX, device=device)
cu_seqlens = torch.zeros((BATCH + 1,), device=device, dtype=torch.int32)
cu_seqlens[1:] = lengths.cumsum(0)
qkv = torch.randn((BATCH * N_CTX, 3, H, D_HEAD), dtype=dtype, device=device, requires_grad=True)
fn = lambda: flash_attn_func(qkv, cu_seqlens, 0., N_CTX, causal=True)
if mode == 'bwd':
o = fn()
do = torch.randn_like(o)
fn = lambda: o.backward(do, retain_graph=True)
ms = triton.testing.do_bench(fn, warmup=warmup, rep=rep)
return ms
# only works on post-Ampere GPUs right now
bench_flash_attention.run(save_path='.', print_data=True)
Total running time of the script: ( 0 minutes 4.601 seconds)