# Copyright (c) Huawei Technologies Co., Ltd. 2025. All rights reserved.
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# THE SOFTWARE.
"""
Matrix Multiplication
===============
"""
import triton
import triton.language as tl
import torch
import torch_npu
import triton.language.extra.cann.extension as extension
DEV = "npu"
def get_autotune_config():
return [
triton.Config({"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 128}),
triton.Config({"BLOCK_SIZE_M": 64, "BLOCK_SIZE_N": 64, "BLOCK_SIZE_K": 64}),
]
@triton.autotune(
configs=get_autotune_config(),
key=["M", "N", "K"],
)
@triton.jit
def matmul_kernel(
# Pointers to matrices
a_ptr,
b_ptr,
c_ptr,
# Matrix dimensions
M,
N,
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_am,
stride_ak, #
stride_bk,
stride_bn, #
stride_cm,
stride_cn,
# Meta-parameters
BLOCK_SIZE_M: tl.constexpr,
BLOCK_SIZE_N: tl.constexpr,
BLOCK_SIZE_K: tl.constexpr, #
ACTIVATION: tl.constexpr, #
):
"""Kernel for computing the matmul C = A x B.
A has shape (M, K), B has shape (K, N) and C has shape (M, N)
"""
GROUP_SIZE_M: tl.constexpr = 1
# -----------------------------------------------------------
# Map program ids `pid` to the block of C it should compute.
# This is done in a grouped ordering to promote L2 data reuse.
# See above `L2 Cache Optimizations` section for details.
pid = tl.program_id(axis=0)
num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
num_pid_in_group = GROUP_SIZE_M * num_pid_n
group_id = pid // num_pid_in_group
first_pid_m = group_id * GROUP_SIZE_M
group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M)
pid_m = first_pid_m + ((pid % num_pid_in_group) % group_size_m)
pid_n = (pid % num_pid_in_group) // group_size_m
# ----------------------------------------------------------
# Create pointers for the first blocks of A and B.
# We will advance this pointer as we move in the K direction
# and accumulate
# `a_ptrs` is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers
# `b_ptrs` is a block of [BLOCK_SIZE_K, BLOCK_SIZE_N] pointers
# See above `Pointer Arithmetic` section for details
offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
offs_k = tl.arange(0, BLOCK_SIZE_K)
a_ptrs_base = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak)
b_ptrs_base = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn)
msk_m = offs_am < M
msk_n = offs_bn < N
# -----------------------------------------------------------
# Iterate to compute a block of the C matrix.
# We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block
# of fp32 values for higher accuracy.
# `accumulator` will be converted back to fp16 after the loop.
accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
# Load the next block of A and B, generate a mask by checking the K dimension.
# If it is out of bounds, set it to 0.
a_ptrs = a_ptrs_base + k * BLOCK_SIZE_K * stride_ak
b_ptrs = b_ptrs_base + k * BLOCK_SIZE_K * stride_bk
a = tl.load(
a_ptrs,
mask=msk_m[:, None] and (offs_k[None, :] < K - k * BLOCK_SIZE_K),
other=0.0,
)
b = tl.load(
b_ptrs,
mask=msk_n[None, :] and (offs_k[:, None] < K - k * BLOCK_SIZE_K),
other=0.0,
)
# We accumulate along the K dimension.
accumulator = tl.dot(a, b, accumulator)
# You can fuse arbitrary activation functions here
# while the accumulator is still in FP32!
# Original vector operations
# # -----------------------------------------------------------
# # Write back the block of the output matrix C with masks.
# Comment out the following lines to enable split the workload to two vector cores
SUB_BLK_M: tl.constexpr = BLOCK_SIZE_M // 2
for s in extension.parallel(0, 2, bind_sub_block=True):
vec_sub_blk = extension.extract_slice(
accumulator, (s * SUB_BLK_M, 0), (SUB_BLK_M, BLOCK_SIZE_N), (1, 1)
)
if ACTIVATION == "leaky_relu_custom":
vec_sub_blk = leaky_relu_custom(vec_sub_blk)
c_sub_blk = vec_sub_blk.to(tl.float16)
# -----------------------------------------------------------
# Write back the block of the output matrix C with masks.
offs_cm = pid_m * BLOCK_SIZE_M + s * SUB_BLK_M + tl.arange(0, SUB_BLK_M)
offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :]
c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
tl.store(c_ptrs, c_sub_blk, mask=c_mask)
# We can fuse `leaky_relu_custom` by providing it as an `ACTIVATION` meta-parameter in `matmul_kernel`.
@triton.jit
def leaky_relu_custom(x):
return tl.where(x >= 0, x, 0.01 * x) + 1.0
def torch_matmul(a, b, activation=""):
c = torch.matmul(a, b)
if activation == "leaky_relu_custom":
c = torch.where(c >= 0, c, 0.01 * c) + 1.0
return c
# %%
# We can now create a convenience wrapper function that only takes two input tensors,
# and (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel.
def matmul(a, b, activation=""):
# Check constraints.
assert a.shape[1] == b.shape[0], "Incompatible dimensions"
assert a.is_contiguous(), "Matrix A must be contiguous"
M, K = a.shape
K, N = b.shape
# Allocates output.
c = torch.empty((M, N), device=a.device, dtype=torch.float16)
# 1D launch kernel where each block gets its own program.
def grid(META):
return (triton.cdiv(M, META["BLOCK_SIZE_M"]) * triton.cdiv(N, META["BLOCK_SIZE_N"]), )
matmul_kernel[grid](
a,
b,
c, #
M,
N,
K, #
a.stride(0),
a.stride(1), #
b.stride(0),
b.stride(1), #
c.stride(0),
c.stride(1), #
ACTIVATION=activation, #
)
return c
# %%
# Unit Test
# ---------
#
# We can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS).
def test():
activation = "leaky_relu_custom"
torch.manual_seed(0)
a = torch.randn((512, 512), device=DEV, dtype=torch.float16)
b = torch.randn((512, 512), device=DEV, dtype=torch.float16)
triton_output = matmul(a, b, activation)
torch_output = torch_matmul(a, b, activation)
print(f"triton_output_with_fp16_inputs={triton_output}")
print(f"torch_output_with_fp16_inputs={torch_output}")
torch.testing.assert_close(triton_output, torch_output, atol=1e-3, rtol=1e-3)
print("Passed")
if __name__ == "__main__":
test()