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# Adapted from https://github.com/ELS-RD/kernl/blob/main/src/kernl/implementations/linear_layer.py
# and https://github.com/openai/triton/blob/master/python/triton/ops/matmul.py
from typing import Optional
import torch
import triton
import triton.language as tl
from triton.ops.matmul_perf_model import early_config_prune, estimate_matmul_time
from flash_attn.ops.triton.k_activations import (
gelu,
gelu_approx,
gelu_approx_grad,
gelu_grad,
squared_relu,
squared_relu_grad,
)
# CREDITS: Initially inspired by the Triton tutorial on matrix multiplications
def init_to_zero(name):
return lambda nargs: nargs[name].zero_()
def get_configs_io_bound():
configs = []
for num_stages in [2, 3, 4, 5, 6]:
for block_m in [16, 32]:
for block_k in [32, 64]:
for block_n in [32, 64, 128, 256]:
num_warps = 2 if block_n <= 64 else 4
configs.append(
triton.Config(
{
"BLOCK_M": block_m,
"BLOCK_N": block_n,
"BLOCK_K": block_k,
"SPLIT_K": 1,
},
num_stages=num_stages,
num_warps=num_warps,
)
)
# split_k not used
# for split_k in [2, 4, 8, 16]:
# configs.append(triton.Config(
# {'BLOCK_M': block_m, 'BLOCK_N': block_n, 'BLOCK_K': block_k, 'SPLIT_K': split_k},
# num_stages=num_stages, num_warps=num_warps, pre_hook=init_to_zero('C')))
return configs
@triton.autotune(
configs=[
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 256, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=3, num_warps=8
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 128, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=3, num_warps=8
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 64, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 256, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 128, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 64, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 128, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 32, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 32, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=5, num_warps=2
),
# good for int8
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 256, "BLOCK_K": 128, "SPLIT_K": 1},
num_stages=3,
num_warps=8,
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 128, "BLOCK_K": 128, "SPLIT_K": 1},
num_stages=3,
num_warps=8,
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 64, "BLOCK_K": 128, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 256, "BLOCK_K": 128, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 128, "BLOCK_K": 128, "SPLIT_K": 1},
num_stages=4,
num_warps=4,
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 64, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 128, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 32, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 32, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=5, num_warps=2
),
]
+ get_configs_io_bound(),
key=["CACHE_KEY_M", "CACHE_KEY_N", "CACHE_KEY_K"],
prune_configs_by={
"early_config_prune": early_config_prune,
"perf_model": estimate_matmul_time,
"top_k": 10,
},
)
@triton.heuristics(
{
"EVEN_K": lambda args: args["K"] % (args["BLOCK_K"] * args["SPLIT_K"]) == 0,
}
)
@triton.jit
def kernel_fwd(
C, # Pointers to matrices
ACT_INPUT,
A,
B,
bias,
# Matrix dimensions
M,
N,
K,
CACHE_KEY_M,
CACHE_KEY_N,
CACHE_KEY_K,
# The stride variables represent how much to increase the ptr by when moving by 1
# element in a particular dimension. E.g. stride_am is how much to increase a_ptr
# by to get the element one row down (A has M rows)
stride_cm,
# stride_cn, # Assume that stride_cn == 1
stride_am,
stride_ak,
stride_bn,
stride_bk,
# Meta-parameters
BLOCK_M: tl.constexpr,
GROUP_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
# split k not used, not performant with activation, kept because early_config_prune is expecting it
SPLIT_K: tl.constexpr,
EVEN_K: tl.constexpr,
A_ROWMAJOR: tl.constexpr,
B_COLMAJOR: tl.constexpr,
BIAS: tl.constexpr,
SAVE_ACT_INPUT: tl.constexpr,
ACTIVATION: tl.constexpr,
):
"""
Kernel for computing Out = activation(A x W + C)
- Input has shape (M, K)
- Weight has shape (K, N)
- Bias has shape (N,)
- Output has shape (M, N)
- ActInputs (optional) has shape (M, N)
'ActInputs' optionally saves the A x W + C intermediate for backward computations
This kernel will consolidate over K
"""
pid = tl.program_id(axis=0)
grid_m = (M + BLOCK_M - 1) // BLOCK_M
grid_n = (N + BLOCK_N - 1) // BLOCK_N
# re-order program ID for better L2 performance
width = GROUP_M * grid_n
group_id = pid // width
group_size = min(grid_m - group_id * GROUP_M, GROUP_M)
pid_m = group_id * GROUP_M + (pid % group_size)
pid_n = (pid % width) // (group_size)
# now compute the block that each program will go through
# rm (resp. rn) denotes a range of indices
# for rows (resp. col) of C
rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
# trick to avoid masking on M and N axis
ram = tl.max_contiguous(tl.multiple_of(rm % M, BLOCK_M), BLOCK_M)
rbn = tl.max_contiguous(tl.multiple_of(rn % N, BLOCK_N), BLOCK_N)
rk = tl.arange(0, BLOCK_K)
if A_ROWMAJOR:
A = A + (ram[:, None] * stride_am + rk[None, :])
else:
A = A + (ram[:, None] * stride_am + rk[None, :] * stride_ak)
if B_COLMAJOR:
B = B + (rk[:, None] + rbn[None, :] * stride_bn)
else:
B = B + (rk[:, None] * stride_bk + rbn[None, :] * stride_bn)
acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)
for k in range(K, 0, -BLOCK_K):
if EVEN_K:
a = tl.load(A)
b = tl.load(B)
else:
a = tl.load(A, mask=rk[None, :] < k, other=0.0)
b = tl.load(B, mask=rk[:, None] < k, other=0.0)
acc += tl.dot(a, b)
if A_ROWMAJOR:
A += BLOCK_K
else:
A += BLOCK_K * stride_ak
if B_COLMAJOR:
B += BLOCK_K
else:
B += BLOCK_K * stride_bk
# Putting bias after the matmul (instead of before) is faster, idk why
if BIAS:
bias = tl.load(bias + rn, mask=rn < N, other=0.0).to(tl.float32)
acc += bias[None, :]
# optional: save the activation inputs
if SAVE_ACT_INPUT:
# act_in_ptrs = ACT_INPUT + ram[:, None] * stride_cm + rbn[None, :] * stride_cn
act_in_ptrs = ACT_INPUT + ram[:, None] * stride_cm + rbn[None, :]
tl.store(act_in_ptrs, acc)
# optional: fused activation (while the data is in shared memory)
if ACTIVATION == "gelu":
acc = gelu(acc)
elif ACTIVATION == "gelu_approx":
acc = gelu_approx(acc)
elif ACTIVATION == "squared_relu":
acc = squared_relu(acc)
# rematerialize rm and rn to save registers
rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
# write back result
# C = C + rm[:, None] * stride_cm + rn[None, :] * stride_cn
C = C + rm[:, None] * stride_cm + rn[None, :]
mask = (rm < M)[:, None] & (rn < N)[None, :]
tl.store(C, acc)
def triton_linear_act(
x: torch.Tensor,
weight: torch.Tensor,
bias: Optional[torch.Tensor] = None,
activation: str = "id",
save_act_input: bool = False,
) -> torch.Tensor:
"""
Compute e = activation(x @ weight.T + bias).
This wrapper kicks the `kernel_fwd` Triton kernel
:param x: input tensor
:param weight: weight matrix
:param bias: an optional bias tensor
:param activation: Activation name. Needs to be a Triton kernel.
:param act_input: an optional tensor to save the activation inputs (for backward)
:return: result tensor
"""
# if torch.is_autocast_enabled():
# dtype = torch.get_autocast_gpu_dtype()
# x, weight, bias = [a.to(dtype=dtype) for a in [x, weight, bias]]
assert activation in ["id", "gelu", "gelu_approx", "squared_relu"]
batch_shape, n = x.shape[:-1], x.shape[-1]
batch_dim = batch_shape.numel()
x_reshaped = x.reshape(batch_dim, n)
if x_reshaped.stride(0) > 1 and x_reshaped.stride(1) > 1:
x_reshaped = x_reshaped.contiguous()
if weight.stride(0) > 1 and weight.stride(1) > 1:
weight = weight.contiguous()
bias = bias.contiguous() if bias is not None else None
assert (
x.dtype == weight.dtype
), f"Input and weight must have the same dtype, got {x.dtype} and {weight.dtype}"
if bias is not None:
assert (
x.dtype == bias.dtype
), f"Input and bias must have the same dtype, got {x.dtype} and {bias.dtype}"
assert (
x_reshaped.shape[1] == weight.shape[1]
), f"Incompatible dimensions: {x_reshaped.shape} - {weight.shape}"
assert (
bias is None or bias.shape[0] == weight.shape[0]
), "Incompatible dimensions in between weight and bias"
M, K = x_reshaped.shape
N, K = weight.shape
output = torch.empty((M, N), device=x.device, dtype=x.dtype)
act_input = torch.empty_like(output) if save_act_input else None
# 1D launch kernel where each block gets its own program.
grid = lambda META: (triton.cdiv(M, META["BLOCK_M"]) * triton.cdiv(N, META["BLOCK_N"]),) # noqa
kernel_fwd[grid](
output,
act_input,
x_reshaped,
weight, # data ptrs
bias if bias is not None else x, # auto skip bias if not present
M, # shapes
N,
K,
M // 32, # key for triton cache (limit number of compilations)
N // 32,
K // 32,
stride_cm=output.stride(0), # strides
# stride_cn=output.stride(1),
stride_am=x_reshaped.stride(0),
stride_ak=x_reshaped.stride(1),
stride_bk=weight.stride(1),
stride_bn=weight.stride(0),
BIAS=bias is not None, # optional fused bias
SAVE_ACT_INPUT=save_act_input, # optional save activation inputs
ACTIVATION=activation, # optional fused activation
A_ROWMAJOR=x_reshaped.stride(1) == 1,
B_COLMAJOR=weight.stride(1) == 1,
GROUP_M=8, # speed optimization: group the programs
)
if not save_act_input:
return output.reshape(*batch_shape, output.shape[-1])
else:
return (
output.reshape(*batch_shape, output.shape[-1]),
act_input.reshape(*batch_shape, act_input.shape[-1]),
)
@triton.autotune(
configs=[
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 256, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=3, num_warps=8
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 128, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=3, num_warps=8
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 64, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 256, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 128, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 64, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 128, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 32, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 32, "BLOCK_K": 32, "SPLIT_K": 1}, num_stages=5, num_warps=2
),
# good for int8
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 256, "BLOCK_K": 128, "SPLIT_K": 1},
num_stages=3,
num_warps=8,
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 128, "BLOCK_K": 128, "SPLIT_K": 1},
num_stages=3,
num_warps=8,
),
triton.Config(
{"BLOCK_M": 256, "BLOCK_N": 64, "BLOCK_K": 128, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 256, "BLOCK_K": 128, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 128, "BLOCK_K": 128, "SPLIT_K": 1},
num_stages=4,
num_warps=4,
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 64, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 128, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 128, "BLOCK_N": 32, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=4, num_warps=4
),
triton.Config(
{"BLOCK_M": 64, "BLOCK_N": 32, "BLOCK_K": 64, "SPLIT_K": 1}, num_stages=5, num_warps=2
),
]
+ get_configs_io_bound(),
key=["CACHE_KEY_M", "CACHE_KEY_N", "CACHE_KEY_K"],
prune_configs_by={
"early_config_prune": early_config_prune,
"perf_model": estimate_matmul_time,
"top_k": 10,
},
)
@triton.heuristics(
{
"EVEN_K": lambda args: args["K"] % (args["BLOCK_K"] * args["SPLIT_K"]) == 0,
}
)
@triton.jit
def kernel_bwd(
C, # Pointers to matrices
ACT_INPUT,
A,
B,
# Matrix dimensions
M,
N,
K,
CACHE_KEY_M,
CACHE_KEY_N,
CACHE_KEY_K,
# The stride variables represent how much to increase the ptr by when moving by 1
# element in a particular dimension. E.g. stride_am is how much to increase a_ptr
# by to get the element one row down (A has M rows)
stride_cm,
# stride_cn, # Assume that stride_cn == 1
stride_am,
stride_ak,
stride_bk,
stride_bn,
# Meta-parameters
BLOCK_M: tl.constexpr,
GROUP_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
# split k not used, not performant with activation, kept because early_config_prune is expecting it
SPLIT_K: tl.constexpr,
EVEN_K: tl.constexpr,
ACTIVATION: tl.constexpr,
):
"""
Kernel for computing Out = activation(A x W + C)
- Input has shape (M, K)
- Weight has shape (K, N)
- Output has shape (M, N)
- ActInputs (optional) has shape (M, N)
'ActInputs' optionally saves the A x W + C intermediate for backward computations
This kernel will consolidate over K
"""
pid = tl.program_id(axis=0)
grid_m = (M + BLOCK_M - 1) // BLOCK_M
grid_n = (N + BLOCK_N - 1) // BLOCK_N
# re-order program ID for better L2 performance
width = GROUP_M * grid_n
group_id = pid // width
group_size = min(grid_m - group_id * GROUP_M, GROUP_M)
pid_m = group_id * GROUP_M + (pid % group_size)
pid_n = (pid % width) // (group_size)
# now compute the block that each program will go through
# rm (resp. rn) denotes a range of indices
# for rows (resp. col) of C
rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
# trick to avoid masking on M and N axis
ram = tl.max_contiguous(tl.multiple_of(rm % M, BLOCK_M), BLOCK_M)
rbn = tl.max_contiguous(tl.multiple_of(rn % N, BLOCK_N), BLOCK_N)
rk = tl.arange(0, BLOCK_K)
A = A + (ram[:, None] * stride_am + rk[None, :] * stride_ak)
B = B + (rk[:, None] * stride_bk + rbn[None, :] * stride_bn)
acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)
for k in range(K, 0, -BLOCK_K):
if EVEN_K:
a = tl.load(A)
b = tl.load(B)
else:
a = tl.load(A, mask=rk[None, :] < k, other=0.0)
b = tl.load(B, mask=rk[:, None] < k, other=0.0)
acc += tl.dot(a, b)
A += BLOCK_K * stride_ak
B += BLOCK_K * stride_bk
# optional: fused activation (while the data is in shared memory)
if ACTIVATION != "id":
act_in_ptrs = ACT_INPUT + ram[:, None] * stride_cm + rbn[None, :]
act_input = tl.load(act_in_ptrs).to(acc.dtype)
if ACTIVATION == "gelu":
acc *= gelu_grad(act_input)
elif ACTIVATION == "gelu_approx":
acc *= gelu_approx_grad(act_input)
elif ACTIVATION == "squared_relu":
acc *= squared_relu_grad(act_input)
# rematerialize rm and rn to save registers
rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
# write back result
C = C + rm[:, None] * stride_cm + rn[None, :]
mask = (rm < M)[:, None] & (rn < N)[None, :]
tl.store(C, acc, mask=mask)
def triton_dgrad_act(
grad_output: torch.Tensor,
weight: torch.Tensor,
activation: str = "id",
act_input: Optional[torch.Tensor] = None,
) -> torch.Tensor:
"""
Compute e = activation(grad_output @ weight + bias).
This wrapper kicks the `kernel_fwd` Triton kernel
:param grad_output: input tensor
:param weight: weight matrix
:param activation: Activation name. Needs to be a Triton kernel.
:param act_input: an optional tensor to save the activation inputs (for backward)
:return: result tensor
"""
assert activation in ["id", "gelu", "gelu_approx", "squared_relu"]
batch_shape, n = grad_output.shape[:-1], grad_output.shape[-1]
batch_dim = batch_shape.numel()
grad_output_reshaped = grad_output.reshape(batch_dim, n)
if grad_output_reshaped.stride(0) > 1 and grad_output_reshaped.stride(1) > 1:
grad_output_reshaped = grad_output_reshaped.contiguous()
if weight.stride(0) > 1 and weight.stride(1) > 1:
weight = weight.contiguous()
assert (
grad_output.dtype == weight.dtype
), f"grad_output and weight must have the same dtype, got {grad_output.dtype} and {weight.dtype}"
assert (
grad_output_reshaped.shape[1] == weight.shape[0]
), f"Incompatible dimensions: {grad_output_reshaped.shape} - {weight.shape}"
if activation != "id":
assert act_input is not None, f"act_input is required for activation {activation}"
# M, N, K in bwd are different from M, N, K in fwd
M, K = grad_output_reshaped.shape
K, N = weight.shape
grad_input = torch.empty((M, N), device=grad_output.device, dtype=grad_output.dtype)
# 1D launch kernel where each block gets its own program.
grid = lambda META: (triton.cdiv(M, META["BLOCK_M"]) * triton.cdiv(N, META["BLOCK_N"]),) # noqa
kernel_bwd[grid](
grad_input,
act_input,
grad_output_reshaped,
weight, # data ptrs
M, # shapes
N,
K,
M // 32, # key for triton cache (limit number of compilations)
N // 32,
K // 32,
stride_cm=grad_input.stride(0), # strides
# stride_cn=grad_input.stride(1),
stride_am=grad_output_reshaped.stride(0),
stride_ak=grad_output_reshaped.stride(1),
stride_bk=weight.stride(0),
stride_bn=weight.stride(1),
ACTIVATION=activation, # optional fused activation
GROUP_M=8, # speed optimization: group the programs
)
return grad_input.reshape(*batch_shape, grad_input.shape[-1])
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