6_Matmul_with_large_K_dimension_ • 6_matmul_no_divergence_baseimport torch
import torch.nn as nn
import torch.nn.functional as F
def module_fn(A, B):
"""
Performs a single matrix multiplication (C = A * B) with a large K dimension.
Args:
A: Input tensor of shape (M, K)
B: Input tensor of shape (K, N)
Returns:
Output tensor of shape (M, N)
"""
return torch.matmul(A, B)
class Model(nn.Module):
"""
Simple model that performs a single matrix multiplication (C = A * B) with a large K dimension
"""
def __init__(self):
super(Model, self).__init__()
def forward(self, A: torch.Tensor, B: torch.Tensor, fn=module_fn) -> torch.Tensor:
return fn(A, B)
M = 256
N = 256
K = 131072
def get_inputs():
A = torch.randn(M, K)
B = torch.randn(K, N)
return [A, B]
def get_init_inputs():
return [] # No special initialization inputs needed
import torch
import torch.nn as nn
class Model(nn.Module):
"""
Simple model that performs a single matrix multiplication (C = A * B) with a large K dimension
"""
def __init__(self):
super(Model, self).__init__()
def forward(self, A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
"""
Performs matrix multiplication of A and B.
Args:
A: Input tensor of shape (M, K)
B: Input tensor of shape (K, N)
Returns:
Output tensor of shape (M, N)
"""
return torch.matmul(A, B)
M = 256
N = 256
K = 131072
def get_inputs():
A = torch.randn(M, K)
B = torch.randn(K, N)
return [A, B]
def get_init_inputs():
return [] # No special initialization inputs needed#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#define TILE_WIDTH 16
// CUDA kernel for matrix multiplication with minimized warp divergence
// The kernel distinguishes between interior blocks (fully within matrix bounds) and boundary blocks.
// For interior blocks, bounds checks are omitted to ensure uniform control flow and avoid divergent branching.
template <typename scalar_t>
__global__ void matmul_cuda_kernel(const scalar_t* __restrict__ A,
const scalar_t* __restrict__ B,
scalar_t* __restrict__ C,
int M, int K, int N) {
// Compute global row and column indices
int row = blockIdx.y * TILE_WIDTH + threadIdx.y;
int col = blockIdx.x * TILE_WIDTH + threadIdx.x;
scalar_t value = 0;
// Determine if this block is completely interior (i.e. no boundary checks needed).
// If (blockIdx.x+1)*TILE_WIDTH <= N and (blockIdx.y+1)*TILE_WIDTH <= M, the entire tile is within bounds.
bool interior_block = ((blockIdx.x + 1) * TILE_WIDTH <= N) && ((blockIdx.y + 1) * TILE_WIDTH <= M);
__shared__ scalar_t sA[TILE_WIDTH][TILE_WIDTH];
__shared__ scalar_t sB[TILE_WIDTH][TILE_WIDTH];
int num_tiles = (K + TILE_WIDTH - 1) / TILE_WIDTH;
for (int t = 0; t < num_tiles; ++t) {
int tiledA_col = t * TILE_WIDTH + threadIdx.x;
int tiledB_row = t * TILE_WIDTH + threadIdx.y;
// For interior blocks, all accesses are within bounds so we avoid conditional checks.
if (interior_block) {
sA[threadIdx.y][threadIdx.x] = __ldg(&A[row * K + tiledA_col]);
sB[threadIdx.y][threadIdx.x] = __ldg(&B[tiledB_row * N + col]);
} else {
// For boundary blocks, use a ternary operator for a branchless-like selection
sA[threadIdx.y][threadIdx.x] = (row < M && tiledA_col < K) ? __ldg(&A[row * K + tiledA_col]) : static_cast<scalar_t>(0);
sB[threadIdx.y][threadIdx.x] = (col < N && tiledB_row < K) ? __ldg(&B[tiledB_row * N + col]) : static_cast<scalar_t>(0);
}
__syncthreads();
#pragma unroll
for (int i = 0; i < TILE_WIDTH; ++i) {
value += sA[threadIdx.y][i] * sB[i][threadIdx.x];
}
__syncthreads();
}
// Write the computed result if within output bounds
if (row < M && col < N) {
C[row * N + col] = value;
}
}
// Forward function called from Python
torch::Tensor module_fn(torch::Tensor A, torch::Tensor B) {
TORCH_CHECK(A.is_cuda(), "Input tensor A must be a CUDA tensor");
TORCH_CHECK(B.is_cuda(), "Input tensor B must be a CUDA tensor");
int M = A.size(0);
int K = A.size(1);
int N = B.size(1);
TORCH_CHECK(K == B.size(0), "Inner dimensions of A and B must match");
auto C = torch::empty({M, N}, A.options());
dim3 threads(TILE_WIDTH, TILE_WIDTH);
dim3 blocks((N + TILE_WIDTH - 1) / TILE_WIDTH, (M + TILE_WIDTH - 1) / TILE_WIDTH);
AT_DISPATCH_FLOATING_TYPES(A.scalar_type(), "matmul_cuda_kernel", ([&] {
matmul_cuda_kernel<scalar_t><<<blocks, threads>>>(
A.data_ptr<scalar_t>(),
B.data_ptr<scalar_t>(),
C.data_ptr<scalar_t>(),
M, K, N);
}));
cudaDeviceSynchronize();
return C;
}
// Pybind11 module binding
PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
m.def("forward", &module_fn, "Matrix multiplication with minimized warp divergence");
}
| Metric | Value | Unit | Variance | Samples |
|---|---|---|---|---|
| Executed Ipc Active | 0.760 | inst/cycle | 0.000 | 5 |
| Executed Ipc Elapsed | 0.740 | inst/cycle | 0.000 | 5 |
| Issue Slots Busy | 18.884 | % | 0.000 | 5 |
| Issued Ipc Active | 0.760 | inst/cycle | 0.000 | 5 |
| SM Busy | 18.884 | % | 0.000 | 5 |
| Memory Throughput | 46664206040.824 | byte/second | 1142340236746573.500 | 5 |
| Mem Busy | 42.086 | % | 0.001 | 5 |
| Max Bandwidth | 35.802 | % | 0.001 | 5 |
| L1/TEX Hit Rate | 0.308 | % | 0.001 | 5 |
| L2 Hit Rate | 83.106 | % | 0.023 | 5 |
| Mem Pipes Busy | 33.044 | % | 0.001 | 5 |
| Warp Cycles Per Issued Instruction | 20.428 | cycle | 0.000 | 5 |
| Warp Cycles Per Executed Instruction | 20.428 | cycle | 0.000 | 5 |
| Avg. Active Threads Per Warp | 32.000 | 0.000 | 5 | |
| Avg. Not Predicated Off Threads Per Warp | 32.000 | 0.000 | 5 | |
| Max Active Clusters | 0.000 | cluster | 0.000 | 5 |
| Max Cluster Size | 8.000 | block | 0.000 | 5 |
| Overall GPU Occupancy | 0.000 | % | 0.000 | 5 |
| Cluster Occupancy | 0.000 | % | 0.000 | 5 |
| Block Limit SM | 32.000 | block | 0.000 | 5 |
| Block Limit Registers | 8.000 | block | 0.000 | 5 |
| Block Limit Shared Mem | 21.000 | block | 0.000 | 5 |
| Block Limit Warps | 8.000 | block | 0.000 | 5 |
| Theoretical Active Warps per SM | 64.000 | warp | 0.000 | 5 |
| Theoretical Occupancy | 100.000 | % | 0.000 | 5 |
| Achieved Occupancy | 24.104 | % | 0.000 | 5 |
| Achieved Active Warps Per SM | 15.426 | warp | 0.000 | 5 |
| Rule | Description |
|---|---|
| WRN HighPipeUtilization | All compute pipelines are under-utilized. Either this kernel is very small or it doesn't issue enough warps per scheduler. Check the Launch Statistics and Scheduler Statistics sections for further details. |
| INF CPIStall | Check the Warp Stall Sampling (All Cycles) table for the top stall locations in your source based on sampling data. The Kernel Profiling Guide (https://docs.nvidia.com/nsight-compute/ProfilingGuide/index.html#metrics-reference) provides more details on each stall reason. |
| WRN Occupancy | This kernel's theoretical occupancy is not impacted by any block limit. The difference between calculated theoretical (100.0%) and measured achieved occupancy (24.1%) can be the result of warp scheduling overheads or workload imbalances during the kernel execution. Load imbalances can occur between warps within a block as well as across blocks of the same kernel. See the CUDA Best Practices Guide (https://docs.nvidia.com/cuda/cuda-c-best-practices-guide/index.html#occupancy) for more details on optimizing occupancy. |
| Operation / Metric | Value | Unit |
|---|---|---|
| aten::to | ||
| CPU Time | 358802.59 | μs |
| Device Time | 28271.38 | μs |
| Self CPU Time | 55.39 | μs |
| Self Device Time | 0.00 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| aten::_to_copy | ||
| CPU Time | 358747.19 | μs |
| Device Time | 28271.38 | μs |
| Self CPU Time | 116.86 | μs |
| Self Device Time | 0.00 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| aten::empty_strided | ||
| CPU Time | 329993.74 | μs |
| Device Time | 0.00 | μs |
| Self CPU Time | 97.88 | μs |
| Self Device Time | 0.00 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| cudaDeviceGetStreamPriorityRange | ||
| CPU Time | 329416.51 | μs |
| Device Time | 0.00 | μs |
| Self CPU Time | 329416.51 | μs |
| Self Device Time | 0.00 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| cudaDeviceSynchronize | ||
| CPU Time | 8096521.66 | μs |
| Device Time | 10157.28 | μs |
| Self CPU Time | 8096521.66 | μs |
| Self Device Time | 10157.28 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| void matmul_cuda_kernel<float>(float const*, float const*, float*, int, int, int) | ||
| CPU Time | 0.00 | μs |
| Device Time | 8003557.13 | μs |
| Self CPU Time | 0.00 | μs |
| Self Device Time | 8003557.13 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| aten::zero_ | ||
| CPU Time | 32175.87 | μs |
| Device Time | 116703.42 | μs |
| Self CPU Time | 5253.13 | μs |
| Self Device Time | 0.00 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| aten::fill_ | ||
| CPU Time | 26924.75 | μs |
| Device Time | 116703.42 | μs |
| Self CPU Time | 8375.00 | μs |
| Self Device Time | 116703.42 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| void at::native::vectorized_elementwise_kernel<4, at::native::FillFunctor<int>, at::detail::Array<char*, 1> >(int, at::native::FillFunctor<int>, at::detail::Array<char*, 1>) | ||
| CPU Time | 0.00 | μs |
| Device Time | 116703.42 | μs |
| Self CPU Time | 0.00 | μs |
| Self Device Time | 116703.42 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
45286 warnings generated when compiling for host. Suppressed 45322 warnings (45275 in non-user code, 47 NOLINT). Use -header-filter=.* to display errors from all non-system headers. Use -system-headers to display errors from system headers as well.