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RWKV-Runner/finetune/lora/v6/fla/ops/abc/chunk.py

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sync https://github.com/JL-er/RWKV-PEFT
2024-05-28 14:35:47 +00:00
# -*- coding: utf-8 -*-
# Copyright (c) 2023-2024, Yu Zhang, Songlin Yang
from typing import Optional, Tuple
import torch
import triton
import triton.language as tl
from fla.ops.utils import (logcumsumexp_fwd_kernel, softmax_bwd_kernel,
softmax_fwd_kernel)
from fla.utils import contiguous
@triton.jit
def chunk_abc_fwd_kernel_h(
k,
v,
z,
h,
h0,
ht,
s_k_h,
s_k_t,
s_k_d,
s_v_h,
s_v_t,
s_v_d,
s_h_h,
s_h_t,
s_h_d,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr,
NT: tl.constexpr,
NORMK: tl.constexpr,
USE_INITIAL_STATE: tl.constexpr,
STORE_FINAL_STATE: tl.constexpr
):
i_v, i_k, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
b_h = tl.zeros([BK, BV], dtype=tl.float32)
if USE_INITIAL_STATE:
p_h = tl.make_block_ptr(h0 + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
b_h += tl.load(p_h, boundary_check=(0, 1)).to(tl.float32)
if NORMK:
p_z0 = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), (i_k * BK,), (BK,), (0,))
else:
p_z0 = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), (i_v * BV,), (BV,), (0,))
b_zp = tl.load(p_z0).to(tl.float32)
for i_t in range(NT):
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1))
# [BK, BT]
b_k = tl.load(p_k, boundary_check=(0, 1))
# [BT, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
if NORMK:
p_zc = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + BT - 1) * K + i_k * BK,), (BK,), (0,))
# [BK,]
b_zc = tl.load(p_zc, boundary_check=(0,))
b_r, b_zp = tl.exp(b_zp - b_zc), b_zc
# [BK, BV]
b_h = b_h * b_r[:, None]
b_k = tl.exp(b_k - b_zc[:, None]).to(b_k.dtype)
else:
p_zc = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), ((i_t * BT + BT - 1) * V + i_v * BV,), (BV,), (0,))
# [BV,]
b_zc = tl.load(p_zc, boundary_check=(0,))
b_r, b_zp = tl.exp(b_zp - b_zc), b_zc
# [BK, BV]
b_h = b_h * b_r[None, :]
b_v = tl.exp(b_v - b_zc[None, :]).to(b_v.dtype)
# [BK, BV]
b_h += tl.dot(b_k, b_v, allow_tf32=False)
if STORE_FINAL_STATE:
p_h = tl.make_block_ptr(ht + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_fwd_kernel_intra_K(
v,
z,
o,
A,
s_v_h,
s_v_t,
s_v_d,
T: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BC: tl.constexpr,
BV: tl.constexpr,
NC: tl.constexpr
):
i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_t, i_i = i_c // NC, i_c % NC
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), ((i_t * BT + i_i * BC) * V + i_v * BV,), (BV,), (0,))
# [BV,]
b_zn = tl.load(p_zn, boundary_check=(0,))
# [BC, BV]
b_o = tl.zeros([BC, BV], dtype=tl.float32)
for i_j in range(0, i_i):
p_A = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0))
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0))
# [BC, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
# [BC, BC]
b_A = tl.load(p_A, boundary_check=(0, 1))
b_o += tl.dot(b_A, tl.exp(b_v - b_zn[None, :]).to(b_v.dtype), allow_tf32=False)
b_z = tl.load(p_z, boundary_check=(0, 1))
b_o *= tl.exp(b_zn[None, :] - b_z)
o_i = tl.arange(0, BC)
o_A = i_bh * T * BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_i * BC
m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T
for j in range(0, BC):
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T * V,), (1,), ((i_t * BT + i_i * BC + j) * V + i_v * BV,), (BV,), (0,))
# [BC,]
b_A = tl.load(A + o_A + j, mask=m_A, other=0)
# [BV,]
b_v = tl.load(p_v, boundary_check=(0,)).to(tl.float32)
# [BC, BV]
# avoid 0 * inf = inf
m_i = o_i[:, None] >= j
b_o += tl.where(m_i, b_A[:, None] * tl.exp(b_v[None, :] - b_z), 0)
p_o = tl.make_block_ptr(o + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_fwd_kernel_K(
q,
k,
z,
h,
o,
A,
s_k_h,
s_k_t,
s_k_d,
s_v_h,
s_v_t,
s_v_d,
s_h_h,
s_h_t,
s_h_d,
scale,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr
):
i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_p = tl.maximum(i_t * BT - 1, 0)
o_i = tl.arange(0, BT)
m_s = o_i[:, None] >= o_i[None, :]
b_o = tl.zeros([BT, BV], dtype=tl.float32)
b_A = tl.zeros([BT, BT], dtype=tl.float32)
for i_k in range(tl.cdiv(K, BK)):
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
# [BT, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_q = (b_q * scale).to(b_q.dtype)
# [BK, BT]
b_k = tl.load(p_k, boundary_check=(0, 1))
# [BK, BV]
b_h = tl.load(p_h, boundary_check=(0, 1))
# [BT, BV]
b_o += tl.dot(b_q, b_h, allow_tf32=False)
# [BT, BT]
b_A += tl.dot(b_q, b_k, allow_tf32=False)
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_o = tl.make_block_ptr(o + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
# [BT, BV]
b_z = tl.load(p_z, boundary_check=(0, 1))
# [BT, BV]
p_zp = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), (i_p * V + i_v * BV,), (BV,), (0,))
b_zp = tl.load(p_zp, boundary_check=(0,))
b_o = b_o * tl.exp(b_zp[None, :] - b_z)
tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
p_A = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
# [BT, BT]
b_A = tl.where(m_s, b_A, 0.)
if i_v == 0:
tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_fwd_kernel_intra_V(
q,
k,
z,
A,
s_k_h,
s_k_t,
s_k_d,
scale,
T: tl.constexpr,
K: tl.constexpr,
BT: tl.constexpr,
BC: tl.constexpr,
BK: tl.constexpr,
NC: tl.constexpr
):
i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_t, i_i, i_j = i_c // (NC * NC), (i_c % (NC * NC)) // NC, (i_c % (NC * NC)) % NC
n_bh = tl.num_programs(2)
if i_i > i_j:
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1))
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
p_A = tl.make_block_ptr(A + (i_k*n_bh+i_bh)*T*BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_i * BC) * K + i_k * BK,), (BK,), (0,))
# [BK,]
b_zn = tl.load(p_zn, boundary_check=(0,))
# [BC, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_z = tl.load(p_z, boundary_check=(0, 1))
b_q = (b_q * tl.exp(b_zn[None, :] - b_z) * scale).to(b_q.dtype)
# [BK, BC]
b_k = tl.load(p_k, boundary_check=(0, 1))
b_k = tl.exp(b_k - b_zn[:, None]).to(b_k.dtype)
# [BC, BC]
b_A = tl.dot(b_q, b_k, allow_tf32=False)
tl.store(p_A, b_A.to(A.dtype.element_ty), boundary_check=(0, 1))
elif i_i == i_j:
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_j * BC) * K + i_k * BK,), (BK,), (0,))
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
# [BC, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_z = tl.load(p_z, boundary_check=(0, 1))
o_i = tl.arange(0, BC)
o_A = (i_bh + i_k * n_bh) * T * BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_j * BC
m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T
for j in range(0, BC):
# [BK,]
b_k = tl.load(p_k, boundary_check=(0,)).to(tl.float32)
# [BC,]
b_A = tl.sum(b_q * tl.exp(b_k[None, :] - b_z) * scale, 1)
b_A = tl.where(o_i >= j, b_A, 0.)
tl.store(A + o_A + j, b_A.to(b_q.dtype), mask=m_A)
p_k = tl.advance(p_k, (K,))
@triton.jit
def chunk_abc_fwd_kernel_V(
q,
v,
z,
h,
o,
A,
s_k_h,
s_k_t,
s_k_d,
s_v_h,
s_v_t,
s_v_d,
s_h_h,
s_h_t,
s_h_d,
scale,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr
):
i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_p = tl.maximum(i_t * BT - 1, 0)
b_o = tl.zeros([BT, BV], dtype=tl.float32)
for i_k in range(tl.cdiv(K, BK)):
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_zp = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), (i_p * K + i_k * BK,), (BK,), (0,))
# [BT, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_q = (b_q * scale).to(b_q.dtype)
# [BT, BK]
b_z = tl.load(p_z, boundary_check=(0, 1))
# [BT, BK]
b_zp = tl.load(p_zp, boundary_check=(0,))
b_q = (b_q * tl.exp(b_zp[None, :] - b_z)).to(b_q.dtype)
# [BK, BV]
b_h = tl.load(p_h, boundary_check=(0, 1))
# works but dkw, owing to divine benevolence
# [BT, BV]
if i_k >= 0:
b_o += tl.dot(b_q, b_h, allow_tf32=False)
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_o = tl.make_block_ptr(o + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_A = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
# [BT, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
# [BT, BT]
b_A = tl.load(p_A, boundary_check=(0, 1))
b_o += tl.dot(b_A, b_v, allow_tf32=False)
tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_bwd_kernel_dh(
q,
z,
do,
dh,
s_k_h,
s_k_t,
s_k_d,
s_v_h,
s_v_t,
s_v_d,
s_h_h,
s_h_t,
s_h_d,
scale,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr,
NT: tl.constexpr,
NORMK: tl.constexpr
):
i_k, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
b_dh = tl.zeros([BK, BV], dtype=tl.float32)
b_zp = tl.full([BK if NORMK else BV], float('inf'), dtype=tl.float32)
for i_t in range(NT - 1, -1, -1):
i_p = tl.maximum(i_t * BT - 1, 0)
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K*V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
# [BK, BT]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_q = (b_q * scale).to(b_q.dtype)
# [BT, BV]
b_do = tl.load(p_do, boundary_check=(0, 1))
tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1))
if NORMK:
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_zc = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), (i_p * K + i_k * BK,), (BK,), (0,))
# [BK,]
b_zc = tl.load(p_zc, boundary_check=(0,))
b_r, b_zp = tl.exp(b_zc - b_zp), b_zc
# [BK, BT]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_q = (b_q * tl.exp(b_zc[:, None] - b_z)).to(b_q.dtype)
# [BK, BV]
b_dh = b_dh * b_r[:, None]
else:
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_zc = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), (i_p * V + i_v * BV,), (BV,), (0,))
# [BV,]
b_zc = tl.load(p_zc, boundary_check=(0,))
b_r, b_zp = tl.exp(b_zc - b_zp), b_zc
# [BT, BV]
b_z = tl.load(p_z, boundary_check=(0,))
b_do = (b_do * tl.exp(b_zc[None, :] - b_z)).to(b_do.dtype)
# [BK, BV]
b_dh = b_dh * b_r[None, :]
# [BK, BV]
b_dh += tl.dot(b_q, b_do, allow_tf32=False)
@triton.jit
def chunk_abc_bwd_kernel_V(
k,
v,
z,
h,
A,
do,
dh,
dq,
dk,
dv,
dA,
s_k_h,
s_k_t,
s_k_d,
s_v_h,
s_v_t,
s_v_d,
s_h_h,
s_h_t,
s_h_d,
scale,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr
):
i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_p = tl.maximum(i_t * BT - 1, 0)
n_bh = tl.num_programs(2)
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_zc = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + BT - 1) * K + i_k * BK,), (BK,), (0,))
p_A = tl.make_block_ptr(A + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1))
# [BK,]
b_zc = tl.load(p_zc, boundary_check=(0,))
# [BT, BK]
b_k = tl.load(p_k, boundary_check=(0, 1))
b_k = tl.exp(b_k - b_zc[None, :]).to(b_k.dtype)
# [BT, BT]
b_A = tl.load(p_A, boundary_check=(0, 1))
b_dq = tl.zeros([BT, BK], dtype=tl.float32)
b_dk = tl.zeros([BT, BK], dtype=tl.float32)
b_dA = tl.zeros([BT, BT], dtype=tl.float32)
for i_v in range(tl.cdiv(V, BV)):
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * V * K, (V, K), (s_h_d, s_h_t), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K*V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_dv = tl.make_block_ptr(dv + (i_k*n_bh+i_bh) * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
# [BT, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
# [BV, BK]
b_h = tl.load(p_h, boundary_check=(0, 1))
# [BT, BV]
b_do = tl.load(p_do, boundary_check=(0, 1))
# [BK, BV]
b_dh = tl.load(p_dh, boundary_check=(0, 1))
# [BT, BV]
b_dv = tl.dot(b_k, b_dh, allow_tf32=False)
if i_k == 0:
b_dv += tl.dot(b_A, b_do, allow_tf32=False)
b_do = (b_do * scale).to(b_do.dtype)
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
# [BT, BT]
b_dA += tl.dot(b_do, tl.trans(b_v), allow_tf32=False)
# [BT, BK]
b_dq += tl.dot(b_do, b_h, allow_tf32=False)
# [BT, BK]
b_dk += tl.dot(b_v, tl.trans(b_dh), allow_tf32=False)
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_zp = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), (i_p * K + i_k * BK,), (BK,), (0,))
# [BK,]
b_zp = tl.load(p_zp, boundary_check=(0,))
# [BT, BK]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_z = tl.exp(b_zp[None, :] - b_z)
# [BT, BK]
b_dq = b_dq * b_z
b_dk = b_dk * b_k
p_dq = tl.make_block_ptr(dq + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dk = tl.make_block_ptr(dk + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dA = tl.make_block_ptr(dA + i_bh * T * BT, (T, BT,), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
o_i = tl.arange(0, BT)
m_s = o_i[:, None] >= o_i[None, :]
# [BT, BT]
b_dA = tl.where(m_s, b_dA, 0.).to(b_k.dtype)
if i_k == 0:
tl.store(p_dA, b_dA.to(p_dA.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_bwd_kernel_intra_V(
q,
k,
z,
dA,
dq,
dk,
s_k_h,
s_k_t,
s_k_d,
T: tl.constexpr,
K: tl.constexpr,
BT: tl.constexpr,
BC: tl.constexpr,
BK: tl.constexpr,
NC: tl.constexpr
):
i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_t, i_i = i_c // NC, i_c % NC
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_i * BC) * K + i_k * BK,), (BK,), (0,))
# [BK,]
b_zn = tl.load(p_zn, boundary_check=(0,))
# [BC, BK]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_zq = tl.exp(b_zn[None, :] - b_z)
b_dq = tl.zeros([BC, BK], dtype=tl.float32)
for i_j in range(0, i_i):
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0))
p_dA = tl.make_block_ptr(dA + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0))
# [BC, BK]
b_k = tl.load(p_k, boundary_check=(0, 1))
b_kz = tl.exp(b_k - b_zn[None, :]).to(b_k.dtype)
# [BC, BC]
b_dA = tl.load(p_dA, boundary_check=(0, 1))
# [BC, BK]
b_dq += tl.dot(b_dA, b_kz, allow_tf32=False)
b_dq *= b_zq
o_i = tl.arange(0, BC)
o_dA = i_bh * T * BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_i * BC
m_dA = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T
for j in range(0, BC):
p_kj = tl.make_block_ptr(k + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i*BC+j) * K + i_k * BK,), (BK,), (0,))
# [BC,]
b_dA = tl.load(dA + o_dA + j, mask=m_dA, other=0)
# [BK,]
b_kj = tl.load(p_kj, boundary_check=(0,)).to(tl.float32)
# [BC, BK]
m_i = o_i[:, None] >= j
# [BC, BK]
b_dq += tl.where(m_i, b_dA[:, None] * tl.exp(b_kj[None, :] - b_z), 0.)
p_dq = tl.make_block_ptr(dq + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
tl.debug_barrier()
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_k_h, (T*K,), (s_k_d,), ((i_t * BT + i_i * BC + BC - 1) * K + i_k * BK,), (BK,), (0,))
# [BK,]
b_zn = tl.load(p_zn, boundary_check=(0,))
# [BC, BK]
b_k = tl.load(p_k, boundary_check=(0, 1))
b_kz = tl.exp(b_k - b_zn[None, :])
b_dk = tl.zeros([BC, BK], dtype=tl.float32)
for i_j in range(i_i + 1, NC):
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0))
p_z = tl.make_block_ptr(z + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0))
p_dA = tl.make_block_ptr(dA + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT + i_j * BC, i_i * BC), (BC, BC), (1, 0))
# [BC, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_z = tl.load(p_z, boundary_check=(0, 1))
b_qz = (b_q * tl.exp(b_zn[None, :] - b_z)).to(b_q.dtype)
# [BC, BC]
b_dA = tl.load(p_dA, boundary_check=(0, 1))
# [BC, BK]
b_dk += tl.dot(tl.trans(b_dA), b_qz, allow_tf32=False)
b_dk *= b_kz
o_dA = i_bh * T * BT + (i_t * BT + i_i * BC) * BT + i_i * BC + tl.arange(0, BC)
for j in range(0, BC):
p_qj = tl.make_block_ptr(q + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i * BC + j) * K + i_k * BK,), (BK,), (0,))
p_zj = tl.make_block_ptr(z + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i * BC + j) * K + i_k * BK,), (BK,), (0,))
# [BC,]
b_dA = tl.load(dA + o_dA + j * BT, mask=(i_t * BT + i_i * BC + j < T), other=0)
# [BK,]
b_qj = tl.load(p_qj, boundary_check=(0,)).to(tl.float32)
b_zj = tl.load(p_zj, boundary_check=(0,)).to(tl.float32)
# [BC, BK]
m_i = o_i[:, None] <= j
b_dk += tl.where(m_i, b_dA[:, None] * b_qj[None, :] * tl.exp(b_k - b_zj[None, :]), 0.)
p_dk = tl.make_block_ptr(dk + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0))
tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_bwd_kernel_intra_K(
v,
z,
do,
dA,
s_v_h,
s_v_t,
s_v_d,
scale,
T: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BC: tl.constexpr,
BV: tl.constexpr,
NC: tl.constexpr
):
i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_t, i_i, i_j = i_c // (NC * NC), (i_c % (NC * NC)) // NC, (i_c % (NC * NC)) % NC
n_bh = tl.num_programs(2)
if i_i > i_j:
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (V, T), (s_v_d, s_v_t), (i_v * BV, i_t * BT + i_j * BC), (BV, BC), (0, 1))
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), ((i_t * BT + i_i * BC) * V + i_v * BV,), (BV,), (0,))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
p_dA = tl.make_block_ptr(dA+(i_bh+i_v*n_bh)*T*BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0))
# [BV,]
b_zn = tl.load(p_zn, boundary_check=(0,))
# [BC, BV]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_do = tl.load(p_do, boundary_check=(0, 1))
b_do = (b_do * tl.exp(b_zn[None, :] - b_z) * scale).to(b_do.dtype)
# [BV, BC]
b_v = tl.load(p_v, boundary_check=(0, 1))
b_v = tl.exp(b_v - b_zn[:, None]).to(b_v.dtype)
# [BC, BC]
b_dA = tl.dot(b_do, b_v, allow_tf32=False)
tl.store(p_dA, b_dA.to(dA.dtype.element_ty), boundary_check=(0, 1))
elif i_i == i_j:
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T * V,), (s_v_d,), ((i_t * BT + i_j * BC) * V + i_v * BV,), (BV,), (0,))
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
# [BC, BV]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_do = tl.load(p_do, boundary_check=(0, 1)) * scale
o_i = tl.arange(0, BC)
o_A = (i_bh + i_v * n_bh) * T * BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_j * BC
m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T
for j in range(0, BC):
# [BV,]
b_v = tl.load(p_v, boundary_check=(0,)).to(tl.float32)
# [BC,]
b_dA = tl.sum(b_do * tl.exp(b_v[None, :] - b_z), 1)
b_dA = tl.where(o_i >= j, b_dA, 0)
tl.store(dA + o_A + j, b_dA.to(b_do.dtype), mask=m_A)
p_v = tl.advance(p_v, (V,))
@triton.jit
def chunk_abc_bwd_kernel_K(
q,
k,
v,
z,
h,
A,
do,
dh,
dq,
dk,
dv,
dA,
s_k_h,
s_k_t,
s_k_d,
s_v_h,
s_v_t,
s_v_d,
s_h_h,
s_h_t,
s_h_d,
scale,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BK: tl.constexpr,
BV: tl.constexpr
):
i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_p = tl.maximum(i_t * BT - 1, 0)
n_bh = tl.num_programs(2)
o_i = tl.arange(0, BT)
m_s = o_i[:, None] >= o_i[None, :]
p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_A = tl.make_block_ptr(A + (i_k*n_bh+i_bh) * T * BT, (T, BT, ), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
# [BT, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_k = tl.load(p_k, boundary_check=(0, 1))
# [BT, BT]
b_A = tl.dot((b_q * scale).to(b_q.dtype), tl.trans(b_k), allow_tf32=False)
b_A = tl.where(m_s, b_A, 0.)
tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1))
b_dq = tl.zeros([BT, BK], dtype=tl.float32)
b_dk = tl.zeros([BT, BK], dtype=tl.float32)
for i_v in range(tl.cdiv(V, BV)):
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_zp = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), (i_p * V + i_v * BV,), (BV,), (0,))
p_zc = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (s_v_d,), ((i_t * BT + BT - 1) * V + i_v * BV,), (BV,), (0,))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K*V, (V, K), (s_h_d, s_h_t), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K*V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_dv = tl.make_block_ptr(dv + (i_k*n_bh+i_bh) * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
# [BV,]
b_zp = tl.load(p_zp, boundary_check=(0,))
b_zc = tl.load(p_zc, boundary_check=(0,))
# [BT, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
b_v = tl.exp(b_v - b_zc[None, :]).to(b_v.dtype)
b_z = tl.load(p_z, boundary_check=(0, 1))
b_z = tl.exp(b_zp[None, :] - b_z)
# [BV, BK]
b_h = tl.load(p_h, boundary_check=(0, 1))
# [BT, BV]
b_do = tl.load(p_do, boundary_check=(0, 1))
b_do = (b_do * b_z * scale).to(b_do.dtype)
# [BK, BV]
b_dh = tl.load(p_dh, boundary_check=(0, 1))
# [BT, BK]
b_dq += tl.dot(b_do, b_h, allow_tf32=False)
b_dk += tl.dot(b_v, tl.trans(b_dh), allow_tf32=False)
# [BT, BV]
b_dv = b_v * tl.dot(b_k, b_dh, allow_tf32=False)
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
p_dA = tl.make_block_ptr(dA + i_bh * T * BT, (T, BT, ), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
# [BT, BT]
b_dA = tl.load(p_dA, boundary_check=(0, 1))
# [BT, BK]
b_dq += tl.dot(b_dA, b_k, allow_tf32=False)
b_dk += tl.dot(tl.trans(b_dA).to(b_k.dtype), b_q, allow_tf32=False)
p_dq = tl.make_block_ptr(dq + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dk = tl.make_block_ptr(dk + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_bwd_kernel_intra_KV(
v,
z,
A,
do,
dv,
s_v_h,
s_v_t,
s_v_d,
T: tl.constexpr,
V: tl.constexpr,
BT: tl.constexpr,
BC: tl.constexpr,
BV: tl.constexpr,
NC: tl.constexpr
):
i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_t, i_i = i_c // NC, i_c % NC
p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_v_h, (T*V,), (s_v_d,), ((i_t * BT + i_i * BC + BC - 1) * V + i_v * BV,), (BV,), (0,))
# [BV,]
b_zn = tl.load(p_zn, boundary_check=(0,))
# [BC, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
b_dv = tl.zeros([BC, BV], dtype=tl.float32)
for i_j in range(i_i + 1, NC):
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0))
p_A = tl.make_block_ptr(A + i_bh * T * BT, (BT, T), (1, BT), (i_i * BC, i_t * BT + i_j * BC), (BC, BC), (0, 1))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0))
# [BC, BV]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_do = tl.load(p_do, boundary_check=(0, 1))
b_do = (b_do * tl.exp(b_zn[None, :] - b_z)).to(b_do.dtype)
# [BC, BC]
b_A = tl.load(p_A, boundary_check=(0, 1))
b_dv += tl.dot(b_A, b_do, allow_tf32=False)
b_dv *= tl.exp(b_v - b_zn[None, :])
o_i = tl.arange(0, BC)
for j in range(0, BC):
p_z = tl.make_block_ptr(z + i_bh * s_v_h, (T * V,), (1,), ((i_t * BT + i_i * BC + j) * V + i_v * BV,), (BV,), (0,))
p_A = tl.make_block_ptr(A + i_bh * T * BT, (T * BT,), (1,), ((i_t * BT + i_i * BC + j) * BT + i_i * BC,), (BC,), (0,))
p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T * V,), (1,), ((i_t * BT + i_i * BC + j) * V + i_v * BV,), (BV,), (0,))
# [BC,]
b_A = tl.load(p_A, boundary_check=(0,))
# [BV,]
b_z = tl.load(p_z, boundary_check=(0,))
b_do = tl.load(p_do, boundary_check=(0,))
# [BC, BV]
m_i = o_i[:, None] <= j
b_dv += tl.where(m_i, tl.exp(b_v - b_z[None, :]) * b_A[:, None] * b_do[None, :], 0.)
p_dv = tl.make_block_ptr(dv + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0))
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
@triton.jit
def chunk_abc_bwd_kernel_rcum_inter(
s,
z,
ss,
doo,
s_s_h,
s_s_t,
s_s_d,
T: tl.constexpr,
S: tl.constexpr,
BT: tl.constexpr,
BS: tl.constexpr,
NT: tl.constexpr
):
i_m, i_bh = tl.program_id(0), tl.program_id(1)
b_sp = tl.zeros([BS,], dtype=tl.float32)
b_zp = tl.full([BS,], float('inf'), dtype=tl.float32)
for i_t in range(NT - 1, -1, -1):
p_s = tl.make_block_ptr(s + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT, i_m * BS), (BT, BS), (1, 0))
p_z = tl.make_block_ptr(z + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT, i_m * BS), (BT, BS), (1, 0))
p_zc = tl.make_block_ptr(z + i_bh * s_s_h, (T * S,), (s_s_d,), ((i_t * BT) * S + i_m * BS,), (BS,), (0,))
p_ss = tl.make_block_ptr(ss + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT, i_m * BS), (BT, BS), (1, 0))
p_doo = tl.make_block_ptr(doo + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT, i_m * BS), (BT, BS), (1, 0))
# [BS,]
b_zc = tl.load(p_zc, boundary_check=(0,))
# [BT, BS]
b_s = tl.load(p_s, boundary_check=(0, 1))
b_z = tl.load(p_z, boundary_check=(0, 1))
b_ss = tl.load(p_ss, boundary_check=(0, 1))
b_doo = tl.exp(b_s - b_zp[None, :]) * b_sp[None, :]
tl.store(p_doo, b_doo.to(p_doo.dtype.element_ty), boundary_check=(0, 1))
# [BS,]
b_sp = b_sp * tl.exp(b_zc - b_zp) + tl.sum(b_ss * tl.exp(b_zc[None, :] - b_z), 0)
b_zp = b_zc
@triton.jit
def chunk_abc_bwd_kernel_rcum_intra(
s,
z,
ss,
doo,
s_s_h,
s_s_t,
s_s_d,
T: tl.constexpr,
S: tl.constexpr,
BT: tl.constexpr,
BC: tl.constexpr,
BS: tl.constexpr,
NC: tl.constexpr
):
i_s, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
i_t, i_i = i_c // NC, i_c % NC
o_i = tl.arange(0, BC)
m_o = tl.full([BC, BC], 1., dtype=tl.float32)
p_s = tl.make_block_ptr(s + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT + i_i * BC, i_s * BS), (BC, BS), (1, 0))
p_zn = tl.make_block_ptr(z + i_bh * s_s_h, (T*S,), (s_s_d,), ((i_t * BT + i_i * BC + BC - 1) * S + i_s * BS,), (BS,), (0,))
p_doo = tl.make_block_ptr(doo + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT + i_i * BC, i_s * BS), (BC, BS), (1, 0))
# [BC, BS]
b_s = tl.load(p_s, boundary_check=(0, 1))
# [BS,]
b_zn = tl.load(p_zn, boundary_check=(0,))
b_doo = tl.zeros([BC, BS], dtype=tl.float32)
for i_j in range(i_i + 1, NC):
p_z = tl.make_block_ptr(z + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT + i_j * BC, i_s * BS), (BC, BS), (1, 0))
p_ss = tl.make_block_ptr(ss + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT + i_j * BC, i_s * BS), (BC, BS), (1, 0))
# [BC, BS]
b_z = tl.load(p_z, boundary_check=(0, 1))
b_ss = tl.load(p_ss, boundary_check=(0, 1))
# [BC, BS]
b_doo += b_ss * tl.exp(b_zn[None, :] - b_z)
b_doo = tl.exp(b_s - b_zn[None, :]) * tl.dot(m_o.to(b_s.dtype), b_doo.to(b_s.dtype), allow_tf32=False)
for j in range(0, BC):
p_z = tl.make_block_ptr(z + i_bh * s_s_h, (T * S,), (1,), ((i_t * BT + i_i * BC + j) * S + i_s * BS,), (BS,), (0,))
p_ss = tl.make_block_ptr(ss + i_bh * s_s_h, (T * S,), (1,), ((i_t * BT + i_i * BC + j) * S + i_s * BS,), (BS,), (0,))
# [BS,]
b_z = tl.load(p_z, boundary_check=(0,))
b_ss = tl.load(p_ss, boundary_check=(0,))
# [BC, BS]
m_i = o_i[:, None] <= j
b_doo += tl.where(m_i, tl.exp(b_s - b_z[None, :]) * b_ss[None, :], 0.)
b_doo += tl.load(p_doo, boundary_check=(0, 1))
tl.store(p_doo, b_doo.to(p_doo.dtype.element_ty), boundary_check=(0, 1))
class ChunkABCFunction(torch.autograd.Function):
@staticmethod
@contiguous
def forward(ctx, q, k, v, s, initial_state, output_final_state):
B, H, T, K, V, M = *q.shape, v.shape[-1], s.shape[-1]
BT, BC = 64, 16
BK = min(64, triton.next_power_of_2(K))
BV = min(64, triton.next_power_of_2(V))
BM = min(64, triton.next_power_of_2(M))
NT, NC = triton.cdiv(T, BT), triton.cdiv(BT, BC)
NV, NM = triton.cdiv(V, BV), triton.cdiv(M, BM)
num_warps = 4 if BK == 64 else 2
num_stages = 1
def fwd_pre(s, B, H, T, S):
# keep cummulative normalizer in fp32
z = torch.empty_like(s, dtype=torch.float)
grid = (B * H,)
logcumsumexp_fwd_kernel[grid](
s, z,
s.stride(1), s.stride(2), s.stride(3),
T=T, S=S
)
return z
def fwd_inner(q, k, v, z, B, H, T, K, V, BT, BK, BV, NT, normk=False, h0=None, ht=None):
NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV)
h = q.new_empty(B, H, NT * K, V)
grid = (NV, NK, B * H)
chunk_abc_fwd_kernel_h[grid](
k, v, z, h, h0, ht,
k.stride(1), k.stride(2), k.stride(3),
v.stride(1), v.stride(2), v.stride(3),
h.stride(1), h.stride(2), h.stride(3),
T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
NORMK=normk,
USE_INITIAL_STATE=h0 is not None,
STORE_FINAL_STATE=ht is not None,
num_warps=num_warps,
num_stages=num_stages
)
return h
final_state = None
if output_final_state:
final_state = (q.new_empty(B, H, K, M, dtype=torch.float),
q.new_empty(B, H, M, V, dtype=torch.float))
z = fwd_pre(s, B, H, T, M)
scale = K ** -0.5
hk = fwd_inner(
q=q, k=k, v=s, z=z,
B=B, H=H, T=T, K=K, V=M, BT=BT, BK=BK, BV=BM, NT=NT,
normk=False,
h0=initial_state[0] if initial_state is not None else None,
ht=final_state[0] if final_state is not None else None
)
ok1 = torch.empty_like(s)
Ak = q.new_empty(B, H, T, BT)
grid = (NM, NT, B * H)
chunk_abc_fwd_kernel_K[grid](
q, k, z, hk, ok1, Ak,
k.stride(1), k.stride(2), k.stride(3),
s.stride(1), s.stride(2), s.stride(3),
hk.stride(1), hk.stride(2), hk.stride(3),
scale=scale,
T=T, K=K, V=M, BT=BT, BK=BK, BV=BM,
num_warps=num_warps,
num_stages=num_stages
)
ok0 = torch.empty_like(s)
grid = (NM, NT * NC, B * H)
chunk_abc_fwd_kernel_intra_K[grid](
s, z, ok0, Ak,
s.stride(1), s.stride(2), s.stride(3),
T=T, V=M, BT=BT, BC=BC, BV=BM, NC=NC,
num_warps=2,
num_stages=num_stages
)
ok = ok0.add_(ok1)
scale = 1.
# equivalent to:
# p = ok.softmax(-1, torch.float)
# p is kept in fp32 for safe softmax backward
p = torch.empty_like(ok, dtype=torch.float)
grid = (NT, B * H)
softmax_fwd_kernel[grid](
ok, p,
s.stride(1), s.stride(2), s.stride(3),
T=T, S=M, BT=BT
)
qv = p.to(q.dtype)
scale = 1.
hv = fwd_inner(
q=qv, k=s, v=v, z=z,
B=B, H=H, T=T, K=M, V=V, BT=BT, BK=BM, BV=BV, NT=NT,
normk=True,
h0=initial_state[1] if initial_state is not None else None,
ht=final_state[1] if final_state is not None else None
)
Av = q.new_zeros(NM, B, H, T, BT)
grid = (NM, NT * NC * NC, B * H)
chunk_abc_fwd_kernel_intra_V[grid](
qv, s, z, Av,
s.stride(1), s.stride(2), s.stride(3),
scale=scale,
T=T, K=M, BT=BT, BC=BC, BK=BM, NC=NC,
num_warps=2,
num_stages=num_stages
)
Av = Av.sum(0)
ov = torch.empty_like(v)
grid = (NV, NT, B * H)
chunk_abc_fwd_kernel_V[grid](
qv, v, z, hv, ov, Av,
s.stride(1), s.stride(2), s.stride(3),
v.stride(1), v.stride(2), v.stride(3),
hv.stride(1), hv.stride(2), hv.stride(3),
scale=scale,
T=T, K=M, V=V, BT=BT, BK=BM, BV=BV,
num_warps=num_warps,
num_stages=num_stages
)
ctx.save_for_backward(q, k, v, s, z, ok, p, hk, hv, Av)
ctx.BT = BT
return ov, final_state
@staticmethod
@contiguous
def backward(ctx, dov, dht=None):
q, k, v, s, z, ok, p, hk, hv, Av = ctx.saved_tensors
B, H, T, K, V, M = *q.shape, v.shape[-1], s.shape[-1]
BT, BC = ctx.BT, 16
BK = min(64, triton.next_power_of_2(K))
BV = min(64, triton.next_power_of_2(V))
BM = min(64, triton.next_power_of_2(M))
NT, NC = triton.cdiv(T, BT), triton.cdiv(BT, BC)
NK, NM = triton.cdiv(K, BK), triton.cdiv(M, BM)
num_warps = 4 if BK == 64 else 2
num_stages = 1
def bwd_inner(q, z, do, B, H, T, K, V, BT, BK, BV, NT, scale, normk=False):
NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV)
dh = q.new_empty(B, H, NT * K, V)
grid = (NK, NV, B * H)
chunk_abc_bwd_kernel_dh[grid](
q, z, do, dh,
q.stride(1), q.stride(2), q.stride(3),
do.stride(1), do.stride(2), do.stride(3),
dh.stride(1), dh.stride(2), dh.stride(3),
scale=scale,
T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
NORMK=normk,
num_warps=num_warps,
num_stages=num_stages
)
return dh
def bwd_post(s, z, ss, B, H, T, S, BT, BC, BS, NT, NC, NS):
doo = torch.empty_like(s)
grid = (NS, B * H)
chunk_abc_bwd_kernel_rcum_inter[grid](
s, z, ss, doo,
s.stride(1), s.stride(2), s.stride(3),
T=T, S=S, BT=BT, BS=BS, NT=NT,
num_warps=num_warps,
num_stages=num_stages
)
grid = (NS, NT * NC, B * H)
chunk_abc_bwd_kernel_rcum_intra[grid](
s, z, ss, doo,
s.stride(1), s.stride(2), s.stride(3),
T=T, S=S, BT=BT, BC=BC, BS=BS, NC=NC,
num_warps=num_warps,
num_stages=num_stages
)
return doo
scale = 1.
qv = p.to(q.dtype)
dhv = bwd_inner(
qv, z, dov,
B=B, H=H, T=T, K=M, V=V, BT=BT, BK=BM, BV=BV, NT=NT,
scale=scale,
normk=True
)
dp1 = torch.empty_like(p)
dsv1 = torch.empty_like(s, dtype=torch.float)
dv = v.new_empty(NM, *v.shape)
dAv = q.new_zeros(B, H, T, BT)
grid = (NM, NT, B * H)
chunk_abc_bwd_kernel_V[grid](
s, v, z, hv, Av, dov, dhv, dp1, dsv1, dv, dAv,
s.stride(1), s.stride(2), s.stride(3),
v.stride(1), v.stride(2), v.stride(3),
hv.stride(1), hv.stride(2), hv.stride(3),
scale=scale,
T=T, K=M, V=V, BT=BT, BK=BM, BV=BV,
num_warps=num_warps,
num_stages=num_stages
)
dv = dv.sum(0)
dp0 = torch.empty_like(p)
dsv0 = s.new_zeros(s.shape, dtype=torch.float)
grid = (NM, NT * NC, B * H)
chunk_abc_bwd_kernel_intra_V[grid](
qv, s, z, dAv, dp0, dsv0,
s.stride(1), s.stride(2), s.stride(3),
T=T, K=M, BT=BT, BC=BC, BK=BM, NC=NC,
num_warps=2,
num_stages=num_stages
)
dp = dp1.add_(dp0)
dsv = dsv1.add_(dsv0)
# softmax gradient, equivalent to:
# dok = p * (dp - (p * dp).sum(-1, True))
dok = torch.empty_like(ok)
grid = (NT, B * H)
softmax_bwd_kernel[grid](
p, dp, dok,
s.stride(1), s.stride(2), s.stride(3),
T=T, S=M, BT=BT
)
scale = K ** -0.5
dhk = bwd_inner(
q, z, dok,
B=B, H=H, T=T, K=K, V=M, BT=BT, BK=BK, BV=BM, NT=NT,
scale=scale,
normk=False
)
dAk = q.new_zeros(NM, B, H, T, BT)
grid = (NM, NT * NC * NC, B * H)
chunk_abc_bwd_kernel_intra_K[grid](
s, z, dok, dAk,
s.stride(1), s.stride(2), s.stride(3),
scale=scale,
T=T, V=M, BT=BT, BC=BC, BV=BM, NC=NC,
num_warps=2,
num_stages=num_stages
)
dAk = dAk.sum(0)
Ak = q.new_zeros(NK, B, H, T, BT)
dq = torch.empty_like(q)
dk = torch.empty_like(k)
dsk1 = s.new_empty(NK, *s.shape, dtype=torch.float)
grid = (NK, NT, B * H)
chunk_abc_bwd_kernel_K[grid](
q, k, s, z, hk, Ak, dok, dhk, dq, dk, dsk1, dAk,
q.stride(1), q.stride(2), q.stride(3),
s.stride(1), s.stride(2), s.stride(3),
hk.stride(1), hk.stride(2), hk.stride(3),
scale=scale,
T=T, K=K, V=M, BT=BT, BK=BK, BV=BM,
num_warps=num_warps,
num_stages=num_stages
)
Ak = Ak.sum(0)
dsk1 = dsk1.sum(0)
dsk0 = torch.empty_like(s, dtype=torch.float)
grid = (NM, NT * NC, B * H)
chunk_abc_bwd_kernel_intra_KV[grid](
s, z, Ak, dok, dsk0,
s.stride(1), s.stride(2), s.stride(3),
T=T, V=M, BT=BT, BC=BC, BV=BM, NC=NC,
num_warps=2,
num_stages=num_stages
)
ds = dsv.add_(dsk1.add_(dsk0))
ds -= bwd_post(s, z, ok * dok + p * dp, B, H, T, M, BT, BC, BM, NT, NC, NM)
ds = ds.to(s.dtype)
return dq, dk, dv, ds, None, None
def chunk_abc(
q: torch.Tensor,
k: torch.Tensor,
v: torch.Tensor,
s: torch.Tensor,
initial_state: Optional[Tuple[torch.Tensor]] = None,
output_final_state: Optional[bool] = False
) -> Tuple[torch.Tensor, Tuple[torch.Tensor]]:
if initial_state is not None:
initial_state = tuple(i.detach() for i in initial_state)
ov, final_state = ChunkABCFunction.apply(q, k, v, s, initial_state, output_final_state)
return ov, final_state
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