import os
from typing import Optional
import torch
import triton
import triton.language as tl
from .utils import prepare_chunk_indices, make_tensor_descriptor, input_guard, is_amd
def _ensure_slice_ops() -> bool:
"""Probe and attach tl.extract_slice / insert_slice if missing; return success."""
if hasattr(tl, "extract_slice") and hasattr(tl, "insert_slice"):
return True
try:
from triton.language.extra.cann.extension import extract_slice, insert_slice
tl.extract_slice = extract_slice
tl.insert_slice = insert_slice
return True
except ImportError:
return False
_TRITON_SLICE_AVAILABLE: bool = _ensure_slice_ops()
FLA_TRIL_PRECISION = os.environ.get('FLA_TRIL_PRECISION', 'ieee')
@triton.heuristics({"IS_VARLEN": lambda args: args["cu_seqlens"] is not None})
@triton.jit(do_not_specialize=["T"])
def solve_tril_16x16_loop_kernel_paral_v3(
A_ptr,
Ad_ptr,
cu_seqlens,
chunk_indices,
T,
H: tl.constexpr,
BT: tl.constexpr,
IS_VARLEN: tl.constexpr,
LARGE_BLOCK_T: tl.constexpr,
NT: tl.constexpr,
BH: tl.constexpr,
):
worker_id = tl.program_id(0)
total_tasks = NT * BH
num_tasks = total_tasks // 48
remainder = total_tasks - num_tasks * 48
upper_bound = min(total_tasks, num_tasks * (worker_id + 1) + min(worker_id + 1, remainder))
lower_bound = num_tasks * worker_id + min(worker_id, remainder)
for task_id in range(lower_bound, upper_bound):
i_t = task_id // BH
i_bh = task_id % BH
i_b, i_h = i_bh // H, i_bh % H
if IS_VARLEN:
i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(
chunk_indices + i_t * 2 + 1
).to(tl.int32)
bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(
cu_seqlens + i_n + 1
).to(tl.int32)
T = eos - bos
else:
bos, eos = i_b * T, i_b * T + T
A = A_ptr + (bos * H + i_h) * BT
Ad = Ad_ptr + (bos * H + i_h) * 16
base_t = i_t * LARGE_BLOCK_T
NTASKS: tl.constexpr = 2
N_BLOCKS: tl.constexpr = LARGE_BLOCK_T // 16 // NTASKS
for taskid in range(0, NTASKS):
base_t += taskid * (LARGE_BLOCK_T // NTASKS)
b_A = tl.zeros((N_BLOCKS, 16, 16), dtype=tl.float32)
for blkid in range(0, N_BLOCKS):
row_start_o = base_t + blkid * 16
col_start_o = row_start_o % BT
offs_rows_in_block = tl.arange(0, 16)
offs_cols_in_block = tl.arange(0, 16)
ptr_A_subrec16 = (
A
+ row_start_o * H * BT
+ col_start_o
+ offs_rows_in_block[:, None] * H * BT
+ offs_cols_in_block[None, :]
)
global_rows = row_start_o + offs_rows_in_block[:, None]
global_cols = col_start_o + offs_cols_in_block[None, :]
load_mask = (global_rows < T) & (global_cols < BT)
b_A_subrec16 = tl.load(ptr_A_subrec16, mask=load_mask, other=0.0).to(
tl.float32
)
b_A = tl.insert_slice(
ful=b_A,
sub=b_A_subrec16[None, :, :],
offsets=[blkid, 0, 0],
sizes=[1, 16, 16],
strides=[1, 1, 1],
)
local_ori_A = tl.trans(b_A, (1, 0, 2))
local_ori_A = tl.reshape(local_ori_A, (16, 16 * N_BLOCKS))
tmp = tl.arange(0, 16).to(tl.float32)
rows = tmp[:, None]
cols = tmp[None, :]
is_lower = (rows > cols).to(b_A.dtype)
b_A = -b_A * is_lower
for i in range(1, 16):
nblks_vec16 = -tl.extract_slice(
local_ori_A, (i, 0), (1, 16 * N_BLOCKS), (16 * N_BLOCKS, 1)
)
b_a = tl.reshape(nblks_vec16, (N_BLOCKS, 16))
dot_tmp = tl.trans(b_a[:, :, None] * b_A, (1, 0, 2))
dot_product = tl.sum(dot_tmp, 0)
b_a = b_a + dot_product
b_a_new_expanded = b_a[:, None, :]
b_A = tl.insert_slice(
ful=b_A,
sub=b_a_new_expanded,
offsets=[0, i, 0],
sizes=[N_BLOCKS, 1, 16],
strides=[1, 1, 1],
)
on_diagonal = rows == cols
b_A = tl.where(on_diagonal, b_A + 1.0, b_A)
b_A = tl.reshape(b_A, (N_BLOCKS * 16, 16))
offs_rows_to_store = tl.arange(0, N_BLOCKS * 16)
offs_cols_to_store = tl.arange(0, 16)
p_Ai = (
Ad
+ base_t * H * 16
+ 0
+ offs_rows_to_store[:, None] * H * 16
+ offs_cols_to_store[None, :]
)
global_store_rows = base_t + offs_rows_to_store[:, None]
store_mask = global_store_rows < T
tl.store(
p_Ai,
b_A.to(p_Ai.dtype.element_ty, fp_downcast_rounding="rtne"),
mask=store_mask,
)
@triton.heuristics({"IS_VARLEN": lambda args: args["cu_seqlens"] is not None})
@triton.jit(do_not_specialize=["T"])
def merge_16x16_to_32x32_loop_inverse_kernel(
A,
Ad,
Ai,
cu_seqlens,
chunk_indices,
T,
H: tl.constexpr,
BT: tl.constexpr,
IS_VARLEN: tl.constexpr,
NT: tl.constexpr,
BH: tl.constexpr,
):
worker_id = tl.program_id(0)
total_tasks = NT * BH
num_tasks = total_tasks // 24
remainder = total_tasks - num_tasks * 24
upper_bound = min(total_tasks, num_tasks * (worker_id + 1) + min(worker_id + 1, remainder))
lower_bound = num_tasks * worker_id + min(worker_id, remainder)
for task_id in range(lower_bound, upper_bound):
i_tt = task_id // BH
i_bh = task_id % BH
i_b, i_h = i_bh // H, i_bh % H
if IS_VARLEN:
i_n, i_t = tl.load(chunk_indices + i_tt * 2).to(tl.int32), tl.load(
chunk_indices + i_tt * 2 + 1
).to(tl.int32)
bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(
cu_seqlens + i_n + 1
).to(tl.int32)
T = eos - bos
else:
bos, eos = i_b * T, i_b * T + T
i_t = i_tt
A_ptr = A + (bos * H + i_h) * BT
Ad_ptr = Ad + (bos * H + i_h) * 16
Ai_ptr = Ai + (bos * H + i_h) * 32
p_A_21 = tl.make_block_ptr(
A_ptr, (T, BT), (H * BT, 1), (i_t * 32 + 16, 0 + i_t % (BT // 32) * 32), (16, 16), (1, 0)
)
p_Ad_11 = tl.make_block_ptr(
Ad_ptr, (T, 16), (H * 16, 1), (i_t * 32, 0), (16, 16), (1, 0)
)
p_Ad_22 = tl.make_block_ptr(
Ad_ptr, (T, 16), (H * 16, 1), (i_t * 32 + 16, 0), (16, 16), (1, 0)
)
p_Ai_11 = tl.make_block_ptr(
Ai_ptr, (T, 32), (H * 32, 1), (i_t * 32, 0), (16, 16), (1, 0)
)
p_Ai_22 = tl.make_block_ptr(
Ai_ptr, (T, 32), (H * 32, 1), (i_t * 32 + 16, 16), (16, 16), (1, 0)
)
p_Ai_21 = tl.make_block_ptr(
Ai_ptr, (T, 32), (H * 32, 1), (i_t * 32 + 16, 0), (16, 16), (1, 0)
)
A_21 = tl.load(p_A_21, boundary_check=(0, 1)).to(tl.float32)
Ai_11 = tl.load(p_Ad_11, boundary_check=(0, 1)).to(tl.float32)
Ai_22 = tl.load(p_Ad_22, boundary_check=(0, 1)).to(tl.float32)
Ai_21 = -tl.dot(
tl.dot(Ai_22, A_21, input_precision="ieee"), Ai_11, input_precision="ieee"
)
tl.store(
p_Ai_11,
Ai_11.to(p_Ai_11.dtype.element_ty, fp_downcast_rounding="rtne"),
boundary_check=(0, 1),
)
tl.store(
p_Ai_22,
Ai_22.to(p_Ai_22.dtype.element_ty, fp_downcast_rounding="rtne"),
boundary_check=(0, 1),
)
tl.store(
p_Ai_21,
Ai_21.to(p_Ai_21.dtype.element_ty, fp_downcast_rounding="rtne"),
boundary_check=(0, 1),
)
@triton.heuristics(
{
"IS_VARLEN": lambda args: args["cu_seqlens"] is not None,
}
)
@triton.jit(do_not_specialize=["T"])
def merge_32x32_to_64x64_loop_inverse_kernel(
A,
Ad,
Ai,
cu_seqlens,
chunk_indices,
T,
H: tl.constexpr,
BT: tl.constexpr,
IS_VARLEN: tl.constexpr,
NT: tl.constexpr,
BH: tl.constexpr,
):
worker_id = tl.program_id(0)
total_tasks = NT * BH
num_tasks = total_tasks // 24
remainder = total_tasks - num_tasks * 24
upper_bound = min(total_tasks, num_tasks * (worker_id + 1) + min(worker_id + 1, remainder))
lower_bound = num_tasks * worker_id + min(worker_id, remainder)
for task_id in range(lower_bound, upper_bound):
i_tt = task_id // BH
i_bh = task_id % BH
i_b, i_h = i_bh // H, i_bh % H
if IS_VARLEN:
i_n, i_t = tl.load(chunk_indices + i_tt * 2).to(tl.int32), tl.load(
chunk_indices + i_tt * 2 + 1
).to(tl.int32)
bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(
cu_seqlens + i_n + 1
).to(tl.int32)
T = eos - bos
else:
bos, eos = i_b * T, i_b * T + T
i_t = i_tt
A_ptr = A + (bos * H + i_h) * BT
Ad_ptr = Ad + (bos * H + i_h) * 32
Ai_ptr = Ai + (bos * H + i_h) * 64
p_A_21 = tl.make_block_ptr(
A_ptr, (T, BT), (H * BT, 1), (i_t * 64 + 32, 0 + i_t % (BT // 64) * 64), (32, 32), (1, 0)
)
p_Ad_11 = tl.make_block_ptr(
Ad_ptr, (T, 32), (H * 32, 1), (i_t * 64, 0), (32, 32), (1, 0)
)
p_Ad_22 = tl.make_block_ptr(
Ad_ptr, (T, 32), (H * 32, 1), (i_t * 64 + 32, 0), (32, 32), (1, 0)
)
p_Ai_11 = tl.make_block_ptr(
Ai_ptr, (T, 64), (H * 64, 1), (i_t * 64, 0), (32, 32), (1, 0)
)
p_Ai_22 = tl.make_block_ptr(
Ai_ptr, (T, 64), (H * 64, 1), (i_t * 64 + 32, 32), (32, 32), (1, 0)
)
p_Ai_21 = tl.make_block_ptr(
Ai_ptr, (T, 64), (H * 64, 1), (i_t * 64 + 32, 0), (32, 32), (1, 0)
)
A_21 = tl.load(p_A_21, boundary_check=(0, 1)).to(tl.float32)
Ai_11 = tl.load(p_Ad_11, boundary_check=(0, 1)).to(tl.float32)
Ai_22 = tl.load(p_Ad_22, boundary_check=(0, 1)).to(tl.float32)
Ai_21 = -tl.dot(
tl.dot(Ai_22, A_21, input_precision="ieee"), Ai_11, input_precision="ieee"
)
tl.store(
p_Ai_11,
Ai_11.to(p_Ai_11.dtype.element_ty, fp_downcast_rounding="rtne"),
boundary_check=(0, 1),
)
tl.store(
p_Ai_22,
Ai_22.to(p_Ai_22.dtype.element_ty, fp_downcast_rounding="rtne"),
boundary_check=(0, 1),
)
tl.store(
p_Ai_21,
Ai_21.to(p_Ai_21.dtype.element_ty, fp_downcast_rounding="rtne"),
boundary_check=(0, 1),
)
@triton.heuristics({"IS_VARLEN": lambda args: args["cu_seqlens"] is not None})
@triton.jit(do_not_specialize=['T'])
def solve_tril_64x64_kernel(
A,
Ai,
cu_seqlens,
chunk_indices,
T,
H: tl.constexpr,
BT: tl.constexpr,
USE_TMA: tl.constexpr,
IS_VARLEN: tl.constexpr,
DOT_PRECISION: 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 IS_VARLEN:
i_n, i_t = tl.load(chunk_indices + i_t * 2).to(tl.int32), tl.load(chunk_indices + i_t * 2 + 1).to(tl.int32)
bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
T = eos - bos
else:
bos, eos = i_b * T, i_b * T + T
o_i = tl.arange(0, 64)
m_I = o_i[:, None] == o_i[None, :]
A = A + (bos * H + i_h) * BT
Ai = Ai + (bos * H + i_h) * 64
offset = (i_t * 64) % BT
if not USE_TMA:
p_A = tl.make_block_ptr(A, (T, BT), (H * BT, 1), (i_t * 64, offset), (64, 64), (1, 0))
b_A = -tl.load(p_A, boundary_check=(0, 1)).to(tl.float32)
else:
desc = make_tensor_descriptor(A, [T, BT], [H * BT, 1], [64, 64])
desc_o = make_tensor_descriptor(Ai, [T, 64], [H * 64, 1], [64, 64])
b_A = -desc.load([i_t * 64, offset]).to(tl.float32)
for i in range(2, min(64, T - i_t * 64)):
b_a = -tl.load(A + (i_t * 64 + i) * H * BT + o_i + offset)
b_a = b_a + tl.sum(b_a[:, None] * b_A, 0)
b_A = tl.where((o_i == i)[:, None], b_a, b_A)
b_A += m_I
if not USE_TMA:
p_Ai = tl.make_block_ptr(Ai, (T, 64), (H * 64, 1), (i_t * 64, 0), (64, 64), (1, 0))
tl.store(p_Ai, b_A.to(p_Ai.dtype.element_ty, fp_downcast_rounding="rtne"), boundary_check=(0, 1))
else:
desc_o.store([i_t * 64, 0], b_A.to(desc_o.dtype, fp_downcast_rounding="rtne"))
def solve_tril_64(
A: torch.Tensor,
cu_seqlens: Optional[torch.Tensor] = None,
output_dtype: torch.dtype = torch.float,
):
B, T, H, BT = A.shape
chunk_indices = prepare_chunk_indices(cu_seqlens, BT) if cu_seqlens is not None else None
NT = len(chunk_indices) if cu_seqlens is not None else triton.cdiv(T, BT)
Ai = torch.zeros_like(A, dtype=output_dtype)
solve_tril_64x64_kernel[NT, B * H](
A=A,
Ai=Ai,
cu_seqlens=cu_seqlens,
chunk_indices=chunk_indices,
T=T,
H=H,
BT=BT,
USE_TMA=False,
DOT_PRECISION=FLA_TRIL_PRECISION,
)
return Ai
@input_guard
def solve_tril(
A: torch.Tensor,
cu_seqlens: Optional[torch.Tensor] = None,
output_dtype: torch.dtype = torch.float
) -> torch.Tensor:
"""
Compute the inverse of the matrix I + A
A should be strictly lower triangular, i.e., A.triu() == 0.
Args:
A (torch.Tensor):
[B, T, H, BT], where BT should only be 16, 32, or 64.
cu_seqlens (torch.Tensor):
The cumulative sequence lengths of the input tensor. Default: `None`.
output_dtype (torch.dtype):
The dtype of the output tensor. Default: `torch.float`.
If `None`, the output dtype will be the same as the input dtype.
Returns:
(I + A)^-1 with the same shape as A
"""
output_dtype = A.dtype if output_dtype is None else output_dtype
if not _TRITON_SLICE_AVAILABLE:
if A.shape[-1] not in [64]:
raise ValueError(
f"A shape BT should in [64], but current is {A.shape[-1]}"
)
return solve_tril_64(A, cu_seqlens, output_dtype)
if A.shape[-1] not in [16, 32, 64]:
raise ValueError(
f"A shape BT should in [16, 32, 64], but current is {A.shape[-1]}"
)
B, T, H, BT = A.shape
Ad = torch.empty(
B, T, H, 16, device=A.device, dtype=torch.float if BT != 16 else output_dtype
)
LARGE_BLOCK_T = 608 * 2
chunk_indices = (
prepare_chunk_indices(cu_seqlens, LARGE_BLOCK_T)
if cu_seqlens is not None
else None
)
NT = len(chunk_indices) if cu_seqlens is not None else triton.cdiv(T, LARGE_BLOCK_T)
solve_tril_16x16_loop_kernel_paral_v3[(48,)](
A,
Ad,
cu_seqlens=cu_seqlens,
chunk_indices=chunk_indices,
T=T,
H=H,
BT=BT,
LARGE_BLOCK_T=LARGE_BLOCK_T,
NT=NT,
BH=B * H,
)
if BT == 16:
return Ad
Ai = torch.zeros(
B, T, H, 32, device=A.device, dtype=torch.float if BT != 32 else output_dtype
)
chunk_indices = (
prepare_chunk_indices(cu_seqlens, 32) if cu_seqlens is not None else None
)
NT = len(chunk_indices) if cu_seqlens is not None else triton.cdiv(T, 32)
merge_16x16_to_32x32_loop_inverse_kernel[(24,)](
A=A,
Ad=Ad,
Ai=Ai,
cu_seqlens=cu_seqlens,
chunk_indices=chunk_indices,
T=T,
H=H,
BT=BT,
NT=NT,
BH=B * H,
)
if BT == 32:
return Ai
Ad = Ai
Ai = torch.zeros(
B, T, H, 64, device=A.device, dtype=torch.float if BT != 64 else output_dtype
)
chunk_indices = (
prepare_chunk_indices(cu_seqlens, 64) if cu_seqlens is not None else None
)
NT = len(chunk_indices) if cu_seqlens is not None else triton.cdiv(T, 64)
merge_32x32_to_64x64_loop_inverse_kernel[(24,)](
A=A,
Ad=Ad,
Ai=Ai,
cu_seqlens=cu_seqlens,
chunk_indices=chunk_indices,
T=T,
H=H,
BT=BT,
NT=NT,
BH=B * H,
)
if BT == 64:
return Ai
return Ai