12_Matmul_with_diagonal_matrices_ • unified_diag_matmul_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>
// Unified kernel that selects between vectorized and row-based scalar approaches
__global__ void unified_diag_matmul_kernel(
const float* __restrict__ A,
const float* __restrict__ B,
float* __restrict__ C,
const int64_t N,
const int64_t M,
const bool use_vectorized
) {
if (use_vectorized) {
// Vectorized branch: works when each row's length M is divisible by 4
int idx = blockIdx.x * blockDim.x + threadIdx.x;
int stride = blockDim.x * gridDim.x;
// Total number of elements in C
int64_t total = N * M;
// Each float4 covers 4 consecutive floats
int64_t vec_total = total / 4;
// Cast B and C pointers to float4
const float4* B_vec = reinterpret_cast<const float4*>(B);
float4* C_vec = reinterpret_cast<float4*>(C);
for (; idx < vec_total; idx += stride) {
int base_idx = idx * 4; // Corresponding starting index in the original array
int row = base_idx / M; // Determine the row based on the flat index
float a_val = A[row];
float4 b_val = B_vec[idx];
float4 c_val;
c_val.x = a_val * b_val.x;
c_val.y = a_val * b_val.y;
c_val.z = a_val * b_val.z;
c_val.w = a_val * b_val.w;
C_vec[idx] = c_val;
}
} else {
// Scalar row-based branch using grid-stride loop over rows.
// Each block will iterate over rows, and threads in the block will collaborate on processing
// columns within a row for improved memory coalescing.
for (int row = blockIdx.x; row < N; row += gridDim.x) {
float a_val = A[row];
int row_offset = row * M;
for (int col = threadIdx.x; col < M; col += blockDim.x) {
int idx = row_offset + col;
C[idx] = a_val * B[idx];
}
}
}
}
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)");
A = A.contiguous();
B = B.contiguous();
const int64_t N = A.size(0);
const int64_t M = B.size(1);
auto C = torch::empty({N, M}, B.options());
// Decide which approach to use:
// Use the vectorized method if M is divisible by 4 and sufficiently large (e.g., M >= 512)
// to better harness memory throughput.
bool use_vectorized = (M % 4 == 0) && (M >= 512);
if (use_vectorized) {
const int threads = 256;
int64_t total = N * M;
int64_t vec_total = total / 4;
int blocks = (vec_total + threads - 1) / threads;
// Clamp grid dimension to hardware limits (max 65535 in x dimension)
blocks = (blocks > 65535) ? 65535 : blocks;
unified_diag_matmul_kernel<<<blocks, threads>>>(
A.data_ptr<float>(), B.data_ptr<float>(), C.data_ptr<float>(),
N, M, true);
} else {
// For the scalar branch, use a grid-stride loop over rows for improved coalescing
int threads = (M < 256) ? (((M + 31) / 32) * 32) : 256;
int blocks = (N < 256) ? N : 256;
unified_diag_matmul_kernel<<<blocks, threads>>>(
A.data_ptr<float>(), B.data_ptr<float>(), C.data_ptr<float>(),
N, M, false);
}
return C;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
m.def("forward", &forward, "Unified diagonal matrix multiplication using vectorized and row-based kernels");
}
| Metric | Value | Unit | Variance | Samples |
|---|---|---|---|---|
| Executed Ipc Active | 1.354 | inst/cycle | 0.000 | 5 |
| Executed Ipc Elapsed | 1.246 | inst/cycle | 0.000 | 5 |
| Issue Slots Busy | 33.932 | % | 0.094 | 5 |
| Issued Ipc Active | 1.354 | inst/cycle | 0.000 | 5 |
| SM Busy | 33.932 | % | 0.094 | 5 |
| Memory Throughput | 2674143214459.126 | byte/second | 194593542367397838848.000 | 5 |
| Mem Busy | 46.738 | % | 0.057 | 5 |
| Max Bandwidth | 79.844 | % | 0.173 | 5 |
| L1/TEX Hit Rate | 2.700 | % | 0.000 | 5 |
| L2 Hit Rate | 49.920 | % | 0.017 | 5 |
| Mem Pipes Busy | 8.882 | % | 0.002 | 5 |
| Warp Cycles Per Issued Instruction | 37.760 | cycle | 0.237 | 5 |
| Warp Cycles Per Executed Instruction | 37.862 | cycle | 0.237 | 5 |
| Avg. Active Threads Per Warp | 32.000 | 0.000 | 5 | |
| Avg. Not Predicated Off Threads Per Warp | 29.370 | 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 | 10.000 | block | 0.000 | 5 |
| Block Limit Shared Mem | 32.000 | 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 | 80.638 | % | 0.029 | 5 |
| Achieved Active Warps Per SM | 51.608 | warp | 0.012 | 5 |
| Rule | Description |
|---|---|
| INF HighPipeUtilization | ALU is the highest-utilized pipeline (20.8%) based on active cycles, taking into account the rates of its different instructions. It executes integer and logic operations. It is well-utilized, but should not be a bottleneck. |
| 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 (80.3%) 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 | 473288.72 | μs |
| Device Time | 7231.42 | μs |
| Self CPU Time | 47.16 | 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 | 473241.56 | μs |
| Device Time | 7231.42 | μs |
| Self CPU Time | 114.22 | 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 | 465631.61 | μs |
| Device Time | 0.00 | μs |
| Self CPU Time | 97.57 | 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 |
| cudaDeviceGetStreamPriorityRange | ||
| CPU Time | 465167.36 | μs |
| Device Time | 0.00 | μs |
| Self CPU Time | 465167.36 | 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 | 690512.52 | μs |
| Device Time | 17762.41 | μs |
| Self CPU Time | 690512.52 | μs |
| Self Device Time | 17762.41 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
| unified_diag_matmul_kernel(float const*, float const*, float*, long, long, bool) | ||
| CPU Time | 0.00 | μs |
| Device Time | 321922.47 | μs |
| Self CPU Time | 0.00 | μs |
| Self Device Time | 321922.47 | 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 | 18557.60 | μs |
| Device Time | 35286.99 | μs |
| Self CPU Time | 18557.60 | μs |
| Self Device Time | 35286.99 | 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 | 280597.46 | μs |
| Device Time | 530774.87 | μs |
| Self CPU Time | 11239.04 | 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 | 269360.23 | μs |
| Device Time | 530774.87 | μs |
| Self CPU Time | 13561.14 | μs |
| Self Device Time | 530774.87 | 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 | 530774.87 | μs |
| Self CPU Time | 0.00 | μs |
| Self Device Time | 530774.87 | μs |
| CPU Memory Usage | 0 | B |
| Device Memory Usage | 0 | B |
| Self CPU Memory Usage | 0 | B |
| Self Device Memory Usage | 0 | B |
45287 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.