12_Matmul_with_diagonal_matrices_ • diag_matmul_shared_min_sync_baseimport torch
import torch.nn as nn
import torch.nn.functional as F
def module_fn(A, B):
"""
Performs a matrix multiplication of a diagonal matrix with another matrix.
Args:
A (torch.Tensor): A 1D tensor representing the diagonal of the diagonal matrix. Shape: (N,).
B (torch.Tensor): A 2D tensor representing the second matrix. Shape: (N, M).
Returns:
torch.Tensor: The result of the matrix multiplication. Shape: (N, M).
"""
return torch.diag(A) @ B
class Model(nn.Module):
"""
Simple model that performs a matrix multiplication of a diagonal matrix with another matrix.
C = diag(A) * B
"""
def __init__(self):
super(Model, self).__init__()
def forward(self, A, B, fn=module_fn):
return fn(A, B)
M = 4096
N = 4096
def get_inputs():
A = torch.randn(N)
B = torch.randn(N, M)
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 matrix multiplication of a diagonal matrix with another matrix.
C = diag(A) * B
"""
def __init__(self):
super(Model, self).__init__()
def forward(self, A, B):
"""
Performs the matrix multiplication.
Args:
A (torch.Tensor): A 1D tensor representing the diagonal of the diagonal matrix. Shape: (N,).
B (torch.Tensor): A 2D tensor representing the second matrix. Shape: (N, M).
Returns:
torch.Tensor: The result of the matrix multiplication. Shape: (N, M).
"""
return torch.diag(A) @ B
M = 4096
N = 4096
def get_inputs():
A = torch.randn(N)
B = torch.randn(N, M)
return [A, B]
def get_init_inputs():
return [] # No special initialization inputs needed#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
// Kernel with minimal synchronization and vectorized memory access where possible
__global__ void diag_matmul_shared_kernel(
const float* __restrict__ A,
const float* __restrict__ B,
float* __restrict__ C,
const int64_t N,
const int64_t M
) {
int row = blockIdx.x;
// Use shared memory for the diagonal element
__shared__ float a_val;
// Only one thread loads the diagonal element
if (threadIdx.x == 0) {
a_val = A[row];
}
// Single synchronization point - necessary for shared memory consistency
__syncthreads();
// Process four elements at a time when possible
int col = threadIdx.x;
const int stride = blockDim.x;
const float4* B_vec = reinterpret_cast<const float4*>(B + row * M);
float4* C_vec = reinterpret_cast<float4*>(C + row * M);
// Handle vectorized loads first
const int vec_limit = M / 4;
while (col < vec_limit) {
float4 b4 = B_vec[col];
float4 c4;
c4.x = a_val * b4.x;
c4.y = a_val * b4.y;
c4.z = a_val * b4.z;
c4.w = a_val * b4.w;
C_vec[col] = c4;
col += stride;
}
// Handle remaining elements
col = threadIdx.x + (vec_limit * 4);
while (col < M) {
C[row * M + col] = a_val * B[row * M + col];
col += stride;
}
}
// Forward function wraps the CUDA kernel
at::Tensor forward(at::Tensor A, at::Tensor B) {
TORCH_CHECK(A.dim() == 1, "A must be a 1D tensor");
TORCH_CHECK(B.dim() == 2, "B must be a 2D tensor");
TORCH_CHECK(A.size(0) == B.size(0),
"Dimension mismatch: A.size(0) must match B.size(0)");
// Ensure inputs are contiguous
A = A.contiguous();
B = B.contiguous();
int64_t N = A.size(0);
int64_t M = B.size(1);
// Create output tensor
auto C = torch::empty({N, M}, B.options());
// Launch kernel with one block per row
const int threads = 256;
diag_matmul_shared_kernel<<<N, threads>>>(
A.data_ptr<float>(),
B.data_ptr<float>(),
C.data_ptr<float>(),
N,
M
);
return C;
}
// Pybind11 module definition
PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
m.def("forward", &forward, "Optimized diagonal matrix multiplication with minimal synchronization");
}| Metric | Value | Unit | Variance | Samples |
|---|---|---|---|---|
| Executed Ipc Active | 0.436 | inst/cycle | 0.000 | 5 |
| Executed Ipc Elapsed | 0.398 | inst/cycle | 0.000 | 5 |
| Issue Slots Busy | 11.000 | % | 0.005 | 5 |
| Issued Ipc Active | 0.440 | inst/cycle | 0.000 | 5 |
| SM Busy | 11.000 | % | 0.005 | 5 |
| Memory Throughput | 2628241629826.128 | byte/second | 178384802146014232576.000 | 5 |
| Mem Busy | 46.294 | % | 0.050 | 5 |
| Max Bandwidth | 78.482 | % | 0.146 | 5 |
| L1/TEX Hit Rate | 0.000 | % | 0.000 | 5 |
| L2 Hit Rate | 49.862 | % | 0.002 | 5 |
| Mem Pipes Busy | 5.964 | % | 0.001 | 5 |
| Warp Cycles Per Issued Instruction | 122.580 | cycle | 0.100 | 5 |
| Warp Cycles Per Executed Instruction | 123.672 | cycle | 0.105 | 5 |
| Avg. Active Threads Per Warp | 32.000 | 0.000 | 5 | |
| Avg. Not Predicated Off Threads Per Warp | 27.900 | 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 | 28.000 | 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 | 84.572 | % | 0.270 | 5 |
| Achieved Active Warps Per SM | 54.126 | warp | 0.111 | 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 (84.5%) 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 | 461762.50 | μs |
| Device Time | 7032.67 | μs |
| Self CPU Time | 34.64 | 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 | 461727.86 | μs |
| Device Time | 7032.67 | μs |
| Self CPU Time | 96.92 | 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 | 454363.00 | μs |
| Device Time | 0.00 | μs |
| Self CPU Time | 71.60 | 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 | 453974.38 | μs |
| Device Time | 0.00 | μs |
| Self CPU Time | 453974.38 | 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 |
| cudaLaunchKernel | ||
| CPU Time | 850745.49 | μs |
| Device Time | 23458.44 | μs |
| Self CPU Time | 850745.49 | μs |
| Self Device Time | 23458.44 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| diag_matmul_shared_kernel(float const*, float const*, float*, long, long) | ||
| CPU Time | 0.00 | μs |
| Device Time | 393036.16 | μs |
| Self CPU Time | 0.00 | μs |
| Self Device Time | 393036.16 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| cudaEventRecord | ||
| CPU Time | 23303.09 | μs |
| Device Time | 43542.60 | μs |
| Self CPU Time | 23303.09 | μs |
| Self Device Time | 43542.60 | 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 | 343486.46 | μs |
| Device Time | 649627.54 | μs |
| Self CPU Time | 13728.57 | 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 | 329759.01 | μs |
| Device Time | 649627.54 | μs |
| Self CPU Time | 17654.47 | μs |
| Self Device Time | 649627.54 | 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 | 649627.54 | μs |
| Self CPU Time | 0.00 | μs |
| Self Device Time | 649627.54 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
45282 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.