Note
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Group GEMMΒΆ
This group gemm kernel launches a fixed number of CTA to compute a group of gemms. The scheduling is static and we do it on device.
group-gemm-performance:
N cuBLAS Triton
0 128.0 0.021504 0.013312
1 256.0 0.023552 0.015360
2 512.0 0.033792 0.019456
3 1024.0 0.071680 0.074752
group-gemm-performance-m-8192-k-8192:
M cuBLAS Triton
0 128.0 0.461824 0.505856
1 256.0 0.734208 0.880640
2 512.0 1.725440 1.713152
3 1024.0 2.668544 3.430400
# Copyright (c) 2023 - 2025 NVIDIA Corporation & Affiliates. All rights reserved.
#
# Permission is hereby granted, free of charge, to any person obtaining
# a copy of this software and associated documentation files
# (the "Software"), to deal in the Software without restriction,
# including without limitation the rights to use, copy, modify, merge,
# publish, distribute, sublicense, and/or sell copies of the Software,
# and to permit persons to whom the Software is furnished to do so,
# subject to the following conditions:
#
# The above copyright notice and this permission notice shall be
# included in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
from typing import Optional
import torch
import triton
import triton.language as tl
DEVICE = triton.runtime.driver.active.get_active_torch_device()
def is_cuda():
return triton.runtime.driver.active.get_current_target().backend == "cuda"
def supports_tma():
return is_cuda() and torch.cuda.get_device_capability()[0] >= 9
def num_sms():
if is_cuda():
return torch.cuda.get_device_properties("cuda").multi_processor_count
return 148
@triton.autotune(
configs=[
triton.Config({
'BLOCK_SIZE_M': 128,
'BLOCK_SIZE_N': 128,
'BLOCK_SIZE_K': 32,
'NUM_SM': 84,
}),
triton.Config({
'BLOCK_SIZE_M': 128,
'BLOCK_SIZE_N': 128,
'BLOCK_SIZE_K': 32,
'NUM_SM': 128,
}),
triton.Config({
'BLOCK_SIZE_M': 64,
'BLOCK_SIZE_N': 64,
'BLOCK_SIZE_K': 32,
'NUM_SM': 84,
}),
triton.Config({
'BLOCK_SIZE_M': 64,
'BLOCK_SIZE_N': 64,
'BLOCK_SIZE_K': 32,
'NUM_SM': 128,
}),
triton.Config({
'BLOCK_SIZE_M': 128,
'BLOCK_SIZE_N': 128,
'BLOCK_SIZE_K': 64,
'NUM_SM': num_sms(),
}),
triton.Config({
'BLOCK_SIZE_M': 64,
'BLOCK_SIZE_N': 128,
'BLOCK_SIZE_K': 64,
'NUM_SM': num_sms(),
}),
],
key=['group_size'],
)
@triton.jit
def grouped_matmul_kernel(
# device tensor of matrices pointers
group_a_ptrs,
group_b_ptrs,
group_c_ptrs,
# device tensor of gemm sizes. its shape is [group_size, 3]
# dim 0 is group_size, dim 1 is the values of <M, N, K> of each gemm
group_gemm_sizes,
# device tensor of leading dimension sizes. its shape is [group_size, 3]
# dim 0 is group_size, dim 1 is the values of <lda, ldb, ldc> of each gemm
g_lds,
# number of gemms
group_size,
# number of virtual SM
NUM_SM: tl.constexpr,
# tile sizes
BLOCK_SIZE_M: tl.constexpr,
BLOCK_SIZE_N: tl.constexpr,
BLOCK_SIZE_K: tl.constexpr,
):
tile_idx = tl.program_id(0)
last_problem_end = 0
for g in range(group_size):
# get the gemm size of the current problem
gm = tl.load(group_gemm_sizes + g * 3)
gn = tl.load(group_gemm_sizes + g * 3 + 1)
gk = tl.load(group_gemm_sizes + g * 3 + 2)
num_m_tiles = tl.cdiv(gm, BLOCK_SIZE_M)
num_n_tiles = tl.cdiv(gn, BLOCK_SIZE_N)
num_tiles = num_m_tiles * num_n_tiles
# iterate through the tiles in the current gemm problem
while (tile_idx >= last_problem_end and tile_idx < last_problem_end + num_tiles):
# pick up a tile from the current gemm problem
k = gk
lda = tl.load(g_lds + g * 3)
ldb = tl.load(g_lds + g * 3 + 1)
ldc = tl.load(g_lds + g * 3 + 2)
a_ptr = tl.load(group_a_ptrs + g).to(tl.pointer_type(tl.float16))
b_ptr = tl.load(group_b_ptrs + g).to(tl.pointer_type(tl.float16))
c_ptr = tl.load(group_c_ptrs + g).to(tl.pointer_type(tl.float16))
# figure out tile coordinates
tile_idx_in_gemm = tile_idx - last_problem_end
tile_m_idx = tile_idx_in_gemm // num_n_tiles
tile_n_idx = tile_idx_in_gemm % num_n_tiles
# do regular gemm here
offs_am = tile_m_idx * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
offs_bn = tile_n_idx * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
offs_k = tl.arange(0, BLOCK_SIZE_K)
a_ptrs = a_ptr + offs_am[:, None] * lda + offs_k[None, :]
b_ptrs = b_ptr + offs_k[:, None] * ldb + offs_bn[None, :]
accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
for kk in range(0, tl.cdiv(k, BLOCK_SIZE_K)):
# hint to Triton compiler to do proper loop pipelining
tl.multiple_of(a_ptrs, [16, 16])
tl.multiple_of(b_ptrs, [16, 16])
# assume full tile for now
a = tl.load(a_ptrs)
b = tl.load(b_ptrs)
accumulator += tl.dot(a, b)
a_ptrs += BLOCK_SIZE_K
b_ptrs += BLOCK_SIZE_K * ldb
c = accumulator.to(tl.float16)
offs_cm = tile_m_idx * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
offs_cn = tile_n_idx * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
c_ptrs = c_ptr + ldc * offs_cm[:, None] + offs_cn[None, :]
# assumes full tile for now
tl.store(c_ptrs, c)
# go to the next tile by advancing NUM_SM
tile_idx += NUM_SM
# get ready to go to the next gemm problem
last_problem_end = last_problem_end + num_tiles
def group_gemm_fn(group_A, group_B):
assert len(group_A) == len(group_B)
group_size = len(group_A)
A_addrs = []
B_addrs = []
C_addrs = []
g_sizes = []
g_lds = []
group_C = []
for i in range(group_size):
A = group_A[i]
B = group_B[i]
assert A.shape[1] == B.shape[0]
M, K = A.shape
K, N = B.shape
C = torch.empty((M, N), device=DEVICE, dtype=A.dtype)
group_C.append(C)
A_addrs.append(A.data_ptr())
B_addrs.append(B.data_ptr())
C_addrs.append(C.data_ptr())
g_sizes += [M, N, K]
g_lds += [A.stride(0), B.stride(0), C.stride(0)]
# note these are device tensors
d_a_ptrs = torch.tensor(A_addrs, device=DEVICE)
d_b_ptrs = torch.tensor(B_addrs, device=DEVICE)
d_c_ptrs = torch.tensor(C_addrs, device=DEVICE)
d_g_sizes = torch.tensor(g_sizes, dtype=torch.int32, device=DEVICE)
d_g_lds = torch.tensor(g_lds, dtype=torch.int32, device=DEVICE)
# we use a fixed number of CTA, and it's auto-tunable
grid = lambda META: (META['NUM_SM'], )
grouped_matmul_kernel[grid](
d_a_ptrs,
d_b_ptrs,
d_c_ptrs,
d_g_sizes,
d_g_lds,
group_size,
)
return group_C
tma_configs = [
triton.Config({'BLOCK_SIZE_M': BM, 'BLOCK_SIZE_N': BN, 'BLOCK_SIZE_K' : BK}, num_stages=s, num_warps=w) \
for BM in [128]\
for BN in [128, 256]\
for BK in [64, 128]\
for s in ([3, 4])\
for w in [4, 8]\
]
@triton.autotune(
tma_configs,
key=['group_a_ptrs', 'group_b_ptrs', 'gropup_c_ptrs', 'group_size'],
)
@triton.jit
def grouped_matmul_tma_kernel(
# device tensor of matrices pointers
group_a_ptrs,
group_b_ptrs,
group_c_ptrs,
# device tensor of gemm sizes. its shape is [group_size, 3]
# dim 0 is group_size, dim 1 is the values of <M, N, K> of each gemm
group_gemm_sizes,
# device tensor of leading dimension sizes. its shape is [group_size, 3]
# dim 0 is group_size, dim 1 is the values of <lda, ldb, ldc> of each gemm
g_lds,
# number of gemms
group_size,
# number of virtual SM
NUM_SM: tl.constexpr,
# tile sizes
BLOCK_SIZE_M: tl.constexpr,
BLOCK_SIZE_N: tl.constexpr,
BLOCK_SIZE_K: tl.constexpr,
# is the output FP8 or FP16
FP8: tl.constexpr,
):
dtype = tl.float8e4nv if FP8 else tl.float16
tile_idx = tl.program_id(0)
last_problem_end = 0
for g in range(group_size):
# get the gemm size of the current problem
gm = tl.load(group_gemm_sizes + g * 3)
gn = tl.load(group_gemm_sizes + g * 3 + 1)
gk = tl.load(group_gemm_sizes + g * 3 + 2)
num_m_tiles = tl.cdiv(gm, BLOCK_SIZE_M)
num_n_tiles = tl.cdiv(gn, BLOCK_SIZE_N)
num_tiles = num_m_tiles * num_n_tiles
if tile_idx >= last_problem_end and tile_idx < last_problem_end + num_tiles:
# pick up a tile from the current gemm problem
lda = tl.load(g_lds + g * 3)
ldb = tl.load(g_lds + g * 3 + 1)
ldc = tl.load(g_lds + g * 3 + 2)
a_ptr = tl.load(group_a_ptrs + g).to(tl.pointer_type(dtype))
b_ptr = tl.load(group_b_ptrs + g).to(tl.pointer_type(dtype))
c_ptr = tl.load(group_c_ptrs + g).to(tl.pointer_type(dtype))
a_desc = tl.make_tensor_descriptor(
a_ptr,
shape=[gm, gk],
strides=[lda, 1],
block_shape=[BLOCK_SIZE_M, BLOCK_SIZE_K],
)
b_desc = tl.make_tensor_descriptor(
b_ptr,
shape=[gn, gk],
strides=[ldb, 1],
block_shape=[BLOCK_SIZE_N, BLOCK_SIZE_K],
)
c_desc = tl.make_tensor_descriptor(
c_ptr,
shape=[gm, gn],
strides=[ldc, 1],
block_shape=[BLOCK_SIZE_M, BLOCK_SIZE_N],
)
# iterate through the tiles in the current gemm problem
while (tile_idx >= last_problem_end and tile_idx < last_problem_end + num_tiles):
k = gk
# figure out tile coordinates
tile_idx_in_gemm = tile_idx - last_problem_end
tile_m_idx = tile_idx_in_gemm // num_n_tiles
tile_n_idx = tile_idx_in_gemm % num_n_tiles
# do regular gemm here
offs_am = tile_m_idx * BLOCK_SIZE_M
offs_bn = tile_n_idx * BLOCK_SIZE_N
accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
for kk in range(0, tl.cdiv(k, BLOCK_SIZE_K)):
a = a_desc.load([offs_am, kk * BLOCK_SIZE_K])
b = b_desc.load([offs_bn, kk * BLOCK_SIZE_K])
accumulator += tl.dot(a, b.T)
offs_cm = tile_m_idx * BLOCK_SIZE_M
offs_cn = tile_n_idx * BLOCK_SIZE_N
c = accumulator.to(dtype)
c_desc.store([offs_cm, offs_cn], c)
# go to the next tile by advancing NUM_SM
tile_idx += NUM_SM
# get ready to go to the next gemm problem
last_problem_end = last_problem_end + num_tiles
def group_gemm_tma_fn(group_A, group_B):
assert supports_tma()
assert len(group_A) == len(group_B)
group_size = len(group_A)
A_addrs = []
B_addrs = []
C_addrs = []
g_sizes = []
g_lds = []
group_C = []
for i in range(group_size):
A = group_A[i]
B = group_B[i]
assert A.shape[1] == B.shape[1]
M, K = A.shape
N, K = B.shape
C = torch.empty((M, N), device=DEVICE, dtype=A.dtype)
group_C.append(C)
A_addrs.append(A.data_ptr())
B_addrs.append(B.data_ptr())
C_addrs.append(C.data_ptr())
g_sizes += [M, N, K]
g_lds += [A.stride(0), B.stride(0), C.stride(0)]
# note these are device tensors
d_a_ptrs = torch.tensor(A_addrs, device=DEVICE)
d_b_ptrs = torch.tensor(B_addrs, device=DEVICE)
d_c_ptrs = torch.tensor(C_addrs, device=DEVICE)
d_g_sizes = torch.tensor(g_sizes, dtype=torch.int32, device=DEVICE)
d_g_lds = torch.tensor(g_lds, dtype=torch.int32, device=DEVICE)
# we use a fixed number of CTA, and it's auto-tunable
# TMA descriptors require a global memory allocation
def alloc_fn(size: int, alignment: int, stream: Optional[int]):
return torch.empty(size, device="cuda", dtype=torch.int8)
triton.set_allocator(alloc_fn)
grid = lambda META: (META['NUM_SM'], )
grouped_matmul_tma_kernel[grid](d_a_ptrs, d_b_ptrs, d_c_ptrs, d_g_sizes, d_g_lds, group_size,
FP8=torch.float8_e4m3fn == group_A[0].dtype, NUM_SM=num_sms())
return group_C
group_m = [1024, 512, 256, 128]
group_n = [1024, 512, 256, 128]
group_k = [1024, 512, 256, 128]
group_A = []
group_B = []
group_B_T = []
assert len(group_m) == len(group_n)
assert len(group_n) == len(group_k)
group_size = len(group_m)
for i in range(group_size):
M = group_m[i]
N = group_n[i]
K = group_k[i]
A = torch.rand((M, K), device=DEVICE, dtype=torch.float16)
B = torch.rand((K, N), device=DEVICE, dtype=torch.float16)
B_T = B.T.contiguous()
group_A.append(A)
group_B.append(B)
group_B_T.append(B_T)
tri_out = group_gemm_fn(group_A, group_B)
ref_out = [torch.matmul(a, b) for a, b in zip(group_A, group_B)]
for i in range(group_size):
assert torch.allclose(ref_out[i], tri_out[i], atol=1e-2, rtol=1e-2)
if supports_tma():
tri_tma_out = group_gemm_tma_fn(group_A, group_B_T)
for i in range(group_size):
assert torch.allclose(ref_out[i], tri_tma_out[i], atol=1e-2, rtol=1e-2)
# only launch the kernel, no tensor preparation here to remove all overhead
def triton_perf_fn(a_ptrs, b_ptrs, c_ptrs, sizes, lds, group_size):
grid = lambda META: (META['NUM_SM'], )
grouped_matmul_kernel[grid](
a_ptrs,
b_ptrs,
c_ptrs,
sizes,
lds,
group_size,
)
def triton_tma_perf_fn(a_ptrs, b_ptrs, c_ptrs, sizes, lds, group_size, dtype):
grid = lambda META: (META['NUM_SM'], )
grouped_matmul_tma_kernel[grid](a_ptrs, b_ptrs, c_ptrs, sizes, lds, group_size, FP8=torch.float8_e4m3fn == dtype,
NUM_SM=num_sms())
def torch_perf_fn(group_A, group_B):
for a, b in zip(group_A, group_B):
torch.matmul(a, b)
@triton.testing.perf_report(
triton.testing.Benchmark(
# argument names to use as an x-axis for the plot
x_names=['N'],
x_vals=[2**i for i in range(7, 11)], # different possible values for `x_name`
line_arg='provider',
# argument name whose value corresponds to a different line in the plot
# possible values for `line_arg``
line_vals=['cublas', 'triton'] + (['triton-tma'] if supports_tma() else []),
# label name for the lines
line_names=["cuBLAS", "Triton"] + (['Triton + TMA'] if supports_tma() else []),
# line styles
styles=[('green', '-'), ('blue', '-')] + ([('red', '-')] if supports_tma() else []),
ylabel="runtime(ms)", # label name for the y-axis
plot_name="group-gemm-performance",
# name for the plot. Used also as a file name for saving the plot.
args={},
))
def benchmark_square_matrices(N, provider):
group_size = 4
group_A = []
group_B = []
group_B_T = []
A_addrs = []
B_addrs = []
B_T_addrs = []
C_addrs = []
g_sizes = []
g_lds = []
group_C = []
for i in range(group_size):
A = torch.rand((N, N), device=DEVICE, dtype=torch.float16)
B = torch.rand((N, N), device=DEVICE, dtype=torch.float16)
C = torch.empty((N, N), device=DEVICE, dtype=torch.float16)
B_T = B.T.contiguous()
group_A.append(A)
group_B.append(B)
group_B_T.append(B_T)
group_C.append(C)
A_addrs.append(A.data_ptr())
B_addrs.append(B.data_ptr())
B_T_addrs.append(B_T.data_ptr())
C_addrs.append(C.data_ptr())
g_sizes += [N, N, N]
g_lds += [N, N, N]
d_a_ptrs = torch.tensor(A_addrs, device=DEVICE)
d_b_ptrs = torch.tensor(B_addrs, device=DEVICE)
d_b_t_ptrs = torch.tensor(B_T_addrs, device=DEVICE)
d_c_ptrs = torch.tensor(C_addrs, device=DEVICE)
d_g_sizes = torch.tensor(g_sizes, dtype=torch.int32, device=DEVICE)
d_g_lds = torch.tensor(g_lds, dtype=torch.int32, device=DEVICE)
quantiles = [0.5, 0.2, 0.8]
if provider == 'cublas':
ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch_perf_fn(group_A, group_B), quantiles=quantiles)
if provider == 'triton':
ms, min_ms, max_ms = triton.testing.do_bench(
lambda: triton_perf_fn(d_a_ptrs, d_b_ptrs, d_c_ptrs, d_g_sizes, d_g_lds, group_size), quantiles=quantiles)
if provider == 'triton-tma':
ms, min_ms, max_ms = triton.testing.do_bench(
lambda: triton_tma_perf_fn(d_a_ptrs, d_b_t_ptrs, d_c_ptrs, d_g_sizes, d_g_lds, group_size, dtype=torch.
float16), quantiles=quantiles)
return ms, max_ms, min_ms
@triton.testing.perf_report(
triton.testing.Benchmark(
# argument names to use as an x-axis for the plot
x_names=['M'],
x_vals=[2**i for i in range(7, 11)], # different possible values for `x_name`
line_arg='provider',
# argument name whose value corresponds to a different line in the plot
# possible values for `line_arg``
line_vals=['cublas', 'triton'] + (['triton-tma'] if supports_tma() else []),
# label name for the lines
line_names=["cuBLAS", "Triton"] + (['Triton + TMA'] if supports_tma() else []),
# line styles
styles=[('green', '-'), ('blue', '-')] + ([('red', '-')] if supports_tma() else []),
ylabel="runtime(ms)", # label name for the y-axis
plot_name="group-gemm-performance-m-8192-k-8192",
# name for the plot. Used also as a file name for saving the plot.
args={},
))
def benchmark_batches(M, provider):
N = 8192
K = 8192
group_size = 4
group_A = []
group_B = []
group_B_T = []
A_addrs = []
B_addrs = []
B_T_addrs = []
C_addrs = []
g_sizes = []
g_lds = []
g_T_lds = []
group_C = []
for i in range(group_size):
A = torch.rand((M, K), device=DEVICE, dtype=torch.float16)
B = torch.rand((K, N), device=DEVICE, dtype=torch.float16)
C = torch.empty((M, N), device=DEVICE, dtype=torch.float16)
B_T = B.T.contiguous()
group_A.append(A)
group_B.append(B)
group_B_T.append(B_T)
group_C.append(C)
A_addrs.append(A.data_ptr())
B_addrs.append(B.data_ptr())
B_T_addrs.append(B_T.data_ptr())
C_addrs.append(C.data_ptr())
g_sizes += [M, N, K]
g_lds += [A.stride(0), B.stride(0), C.stride(0)]
g_T_lds += [A.stride(0), B_T.stride(0), C.stride(0)]
d_a_ptrs = torch.tensor(A_addrs, device=DEVICE)
d_b_ptrs = torch.tensor(B_addrs, device=DEVICE)
d_b_t_ptrs = torch.tensor(B_T_addrs, device=DEVICE)
d_c_ptrs = torch.tensor(C_addrs, device=DEVICE)
d_g_sizes = torch.tensor(g_sizes, dtype=torch.int32, device=DEVICE)
d_g_lds = torch.tensor(g_lds, dtype=torch.int32, device=DEVICE)
d_g_t_lds = torch.tensor(g_T_lds, dtype=torch.int32, device=DEVICE)
quantiles = [0.5, 0.2, 0.8]
if provider == 'cublas':
ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch_perf_fn(group_A, group_B), quantiles=quantiles)
if provider == 'triton':
ms, min_ms, max_ms = triton.testing.do_bench(
lambda: triton_perf_fn(d_a_ptrs, d_b_ptrs, d_c_ptrs, d_g_sizes, d_g_lds, group_size), quantiles=quantiles)
if provider == 'triton-tma':
ms, min_ms, max_ms = triton.testing.do_bench(
lambda: triton_tma_perf_fn(d_a_ptrs, d_b_t_ptrs, d_c_ptrs, d_g_sizes, d_g_t_lds, group_size, dtype=torch.
float16), quantiles=quantiles)
return ms, max_ms, min_ms
benchmark_square_matrices.run(show_plots=True, print_data=True)
benchmark_batches.run(show_plots=True, print_data=True)
Total running time of the script: (0 minutes 5.473 seconds)