Triton implementation of Flash Attention2.0
git clone https://github.com/kyegomez/FlashAttention2.0Triton.git
cd FlashAttention2.0Triton
python3 -m pip install -r requirements.txt
python3 -m pip install -U --index-url https://aiinfra.pkgs.visualstudio.com/PublicPackages/_packaging/Triton-Nightly/pypi/simple/ triton-nightly
python3 attention.py
Flash Attention 2.0 triton vs torch
https://github.com/kyegomez/FlashAttention20Triton
Torch
-------
length 1024: 0.32473278045654297 seconds
length 16000: 8.895928621292114 seconds
-----------------
TRITON
N_CTX Triton
0 1024.0 28.783796,ms
4 16384.0 46.376728 ms
import pytest
import torch
import triton
import triton.language as tl
@triton.jit
def max_fn(x, y):
return tl.math.max(x, y)
@triton.jit
def _fwd_kernel(
Q, K, V, sm_scale,
L,
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,
IS_CAUSAL: tl.constexpr,
):
start_m = tl.program_id(0)
off_hz = tl.program_id(1)
qvk_offset = off_hz * stride_qh
Q_block_ptr = tl.make_block_ptr(
base=Q + qvk_offset,
shape=(N_CTX, BLOCK_DMODEL),
strides=(stride_qm, stride_qk),
offsets=(start_m * BLOCK_M, 0),
block_shape=(BLOCK_M, BLOCK_DMODEL),
order=(1, 0)
)
K_block_ptr = tl.make_block_ptr(
base=K + qvk_offset,
shape=(BLOCK_DMODEL, N_CTX),
strides=(stride_kk, stride_kn),
offsets=(0, 0),
block_shape=(BLOCK_DMODEL, BLOCK_N),
order=(0, 1)
)
V_block_ptr = tl.make_block_ptr(
base=V + qvk_offset,
shape=(N_CTX, BLOCK_DMODEL),
strides=(stride_vk, stride_vn),
offsets=(0, 0),
block_shape=(BLOCK_N, BLOCK_DMODEL),
order=(1, 0)
)
# initialize offsets
offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
offs_n = tl.arange(0, BLOCK_N)
# initialize pointer to m and l
m_i = tl.zeros([BLOCK_M], dtype=tl.float32) - float("inf")
l_i = tl.zeros([BLOCK_M], dtype=tl.float32)
acc = tl.zeros([BLOCK_M, BLOCK_DMODEL], dtype=tl.float32)
# scale sm_scale by log_2(e) and use
# 2^x instead of exp in the loop because CSE and LICM
# don't work as expected with `exp` in the loop
qk_scale = sm_scale * 1.44269504
# load q: it will stay in SRAM throughout
q = tl.load(Q_block_ptr)
q = (q * qk_scale).to(tl.float16)
# loop over k, v and update accumulator
lo = 0
hi = (start_m + 1) * BLOCK_M if IS_CAUSAL else N_CTX
for start_n in range(lo, hi, BLOCK_N):
# -- load k, v --
k = tl.load(K_block_ptr)
v = tl.load(V_block_ptr)
# -- compute qk ---
qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
if IS_CAUSAL:
qk = tl.where(offs_m[:, None] >= (start_n + offs_n[None, :]), qk, float("-inf"))
qk += tl.dot(q, k)
# -- compute scaling constant ---
m_i_new = tl.maximum(m_i, tl.max(qk, 1))
alpha = tl.math.exp2(m_i - m_i_new)
p = tl.math.exp2(qk - m_i_new[:, None])
# -- scale and update acc --
acc_scale = l_i * 0 + alpha # workaround some compiler bug
acc *= acc_scale[:, None]
acc += tl.dot(p.to(tl.float16), v)
# -- update m_i and l_i --
l_i = l_i * alpha + tl.sum(p, 1)
m_i = m_i_new
# update pointers
K_block_ptr = tl.advance(K_block_ptr, (0, BLOCK_N))
V_block_ptr = tl.advance(V_block_ptr, (BLOCK_N, 0))
# write back l and m
acc = acc / l_i[:, None]
l_ptrs = L + off_hz * N_CTX + offs_m
tl.store(l_ptrs, m_i + tl.math.log2(l_i))
# write back O
O_block_ptr = tl.make_block_ptr(
base=Out + qvk_offset,
shape=(N_CTX, BLOCK_DMODEL),
strides=(stride_om, stride_on),
offsets=(start_m * BLOCK_M, 0),
block_shape=(BLOCK_M, BLOCK_DMODEL),
order=(1, 0)
)
tl.store(O_block_ptr, acc.to(tl.float16))
@triton.jit
def _bwd_preprocess(
Out, DO,
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)
# compute
delta = tl.sum(o * do, axis=1)
# write-back
tl.store(Delta + off_m, delta)
@triton.jit
def _bwd_kernel(
Q, K, V, sm_scale, Out, DO,
DQ, DK, DV,
L,
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,
CAUSAL: tl.constexpr,
):
off_hz = tl.program_id(0)
off_z = off_hz // H
off_h = off_hz % H
qk_scale = sm_scale * 1.44269504
# 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):
if CAUSAL:
lo = start_n * BLOCK_M
else:
lo = 0
# 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
l_ptrs = L + 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
if CAUSAL:
qk = tl.where(offs_m_curr[:, None] >= (offs_n[None, :]), float(0.), float("-inf"))
else:
qk = tl.zeros([BLOCK_M, BLOCK_N], dtype=tl.float32)
qk += tl.dot(q, tl.trans(k))
qk *= qk_scale
l_i = tl.load(l_ptrs + offs_m_curr)
p = tl.math.exp2(qk - l_i[:, 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, causal, sm_scale):
# 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)
BLOCK_M = 128
BLOCK_N = 64
grid = (triton.cdiv(q.shape[2], BLOCK_M), 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)
num_warps = 4 if Lk <= 64 else 8
_fwd_kernel[grid](
q, k, v, sm_scale,
L,
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_M, BLOCK_N=BLOCK_N, BLOCK_DMODEL=Lk,
IS_CAUSAL=causal,
num_warps=num_warps,
num_stages=4)
ctx.save_for_backward(q, k, v, o, L)
ctx.grid = grid
ctx.sm_scale = sm_scale
ctx.BLOCK_DMODEL = Lk
ctx.causal = causal
return o
@staticmethod
def backward(ctx, do):
BLOCK = 128
q, k, v, o, L = ctx.saved_tensors
do = do.contiguous()
dq = torch.zeros_like(q, dtype=torch.float32)
dk = torch.empty_like(k)
dv = torch.empty_like(v)
delta = torch.empty_like(L)
_bwd_preprocess[(ctx.grid[0] * ctx.grid[1], )](
o, do,
delta,
BLOCK_M=BLOCK, D_HEAD=ctx.BLOCK_DMODEL,
)
_bwd_kernel[(ctx.grid[1],)](
q, k, v, ctx.sm_scale,
o, do,
dq, dk, dv,
L, 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,
CAUSAL=ctx.causal,
num_stages=1,
)
return dq, dk, dv, None, None
attention = _attention.apply