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18_Matmul_with_transposed_both • 18_matmul_transposed_block32_base

Level 1 • Task 18
import torch
import torch.nn as nn
import torch.nn.functional as F


def module_fn(A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
    """
    Performs a single matrix multiplication with transposed A and B (C = A.T * B.T).

    Args:
        A: Input tensor of shape (K, M).
        B: Input tensor of shape (N, K).

    Returns:
        Output tensor of shape (M, N).
    """
    return torch.matmul(A.T, B.T)


class Model(nn.Module):
    """
    Simple model that performs a single matrix multiplication (C = A * B)
    """

    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 = 1024
K = 4096
N = 2048


def get_inputs():
    A = torch.randn(K, M)
    B = torch.randn(N, K)
    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)
    """
    def __init__(self):
        super(Model, self).__init__()
    
    def forward(self, A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
        """
        Performs matrix multiplication.

        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.T, B.T)

M = 1024
K = 4096
N = 2048

def get_inputs():
    A = torch.randn(K, M)
    B = torch.randn(N, K)
    return [A, B]

def get_init_inputs():
    return []  # No special initialization inputs needed
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Kernel Information

Operation Name 18_Matmul_with_transposed_both
Level ID 1
Task ID 18
Kernel Name 18_matmul_transposed_block32_base
CUDA Speedup (Native) 0.186x
CUDA Speedup (Compile) 0.211x
CUDA Runtime 1.956 ms
PyTorch Runtime (Native) 0.365 ms
PyTorch Runtime (Compile) 0.413 ms
Correct True
Max Diff (vs. Reference) 0.001000
Model o3-mini-2025-01-31
Temperature 1.00
View Experiment Progress Details

Related Kernels (Level 1, Task 18 • 18_Matmul_with_transposed_both)

Rank Kernel Name Runtime (ms) Speedup Native Speedup Compile
🥇 optimized_matmul_transpose_base 1.87 0.19 0.22
🥈 matmul_transpose_ldg_128bit_align_base 1.90 0.19 0.22
🥉 matmul_transpose_ldg_optimization_base 1.91 0.19 0.22
🥉 optimized_matmul_transpose_base 1.91 0.19 0.22
5 optimized_matmul_transpose_base 1.91 0.19 0.22
6 stride_loop_matmul_transpose_base 1.91 0.19 0.22
6 warp_divergence_optimized_matmul_base 1.91 0.19 0.22
8 optimized_matmul_transpose_base 1.91 0.19 0.22
9 18_matmul_transposed_block32_base 1.96 0.19 0.21
10 combined_matmul_transpose_base 1.97 0.19 0.21
11 optimized_matmul_transpose_base 1.99 0.18 0.21
11 reduced_sync_matmul_transposed_edit_1 1.99 0.18 0.21
13 reduced_sync_matmul_transposed_base 1.99 0.18 0.21
13 optimized_matmul_transpose_edit_1 1.99 0.18 0.21
15 combined_matmul_transpose_edit_1 2.04 0.18 0.20
16 18_Matmul_transposed_coalesced_base 2.15 0.17 0.19
17 modular_matmul_transposed_base 2.15 0.17 0.19
18 18_Matmul_transposed_coalesced_edit_1 2.16 0.17 0.19
19 matmul_transpose_modular_base 2.23 0.16 0.18
20 modular_vectorized_matmul_transposed_base_base 2.24 0.16 0.18 
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>

#define BLOCK_SIZE 32  // You can experiment with 32, 64, 128, etc. to find the optimal block size

// CUDA kernel for matrix multiplication with transposed inputs using shared memory tiling
// and a configurable block size
template <typename scalar_t>
__global__ void matmul_transpose_kernel(
    const scalar_t* __restrict__ A,
    const scalar_t* __restrict__ B,
    scalar_t* __restrict__ C,
    const int M,
    const int N,
    const int K) {
    
    // Each thread computes one element of C
    // Compute global row and column indices
    const int row = blockIdx.x * BLOCK_SIZE + threadIdx.x;
    const int col = blockIdx.y * BLOCK_SIZE + threadIdx.y;

    // Shared memory tiles for A and B
    __shared__ scalar_t tileA[BLOCK_SIZE][BLOCK_SIZE];
    __shared__ scalar_t tileB[BLOCK_SIZE][BLOCK_SIZE];

    scalar_t sum = 0;
    
    // Loop over tiles of the input matrices along the K dimension
    const int numTiles = (K + BLOCK_SIZE - 1) / BLOCK_SIZE;
    for (int t = 0; t < numTiles; ++t) {
        // Load tile from A
        int k_index = t * BLOCK_SIZE + threadIdx.y;
        if (k_index < K && row < M) {
            // A is stored in transposed form: A[k, row] is at A[k * M + row]
            tileA[threadIdx.y][threadIdx.x] = A[k_index * M + row];
        } else {
            tileA[threadIdx.y][threadIdx.x] = 0.0;
        }

        // Load tile from B
        int k_index_B = t * BLOCK_SIZE + threadIdx.x;
        if (k_index_B < K && col < N) {
            // B is stored in transposed form: B[col, k] is at B[col * K + k]
            tileB[threadIdx.y][threadIdx.x] = B[col * K + k_index_B];
        } else {
            tileB[threadIdx.y][threadIdx.x] = 0.0;
        }

        __syncthreads();

        // Compute partial product for this tile
        #pragma unroll
        for (int k = 0; k < BLOCK_SIZE; ++k) {
            sum += tileA[k][threadIdx.x] * tileB[threadIdx.y][k];
        }

        __syncthreads();
    }

    // Write the computed value to C
    if (row < M && col < N) {
        C[row * N + col] = sum;
    }
}

// Entry point for the CUDA extension
torch::Tensor matmul_transpose_cuda(torch::Tensor A, torch::Tensor B) {
    // Dimensions: A is (K, M) and B is (N, K), computing C = A^T*B^T, resulting in C of shape (M, N)
    const int K = A.size(0);
    const int M = A.size(1);
    const int N = B.size(0);

    auto C = torch::empty({M, N}, A.options());

    // Configure grid and block dimensions based on BLOCK_SIZE
    dim3 threads(BLOCK_SIZE, BLOCK_SIZE);
    dim3 blocks((M + BLOCK_SIZE - 1) / BLOCK_SIZE, (N + BLOCK_SIZE - 1) / BLOCK_SIZE);

    AT_DISPATCH_FLOATING_TYPES(A.type(), "matmul_transpose_kernel", ([&] {
        matmul_transpose_kernel<scalar_t><<<blocks, threads>>>(
            A.data_ptr<scalar_t>(),
            B.data_ptr<scalar_t>(),
            C.data_ptr<scalar_t>(),
            M, N, K
        );
    }));

    return C;
}

PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
    m.def("forward", &matmul_transpose_cuda, "Matrix multiplication with transposed inputs (CUDA) with block size experiment");
}
Performance Metrics
Metric Value Unit Variance Samples
Executed Ipc Active 1.620 inst/cycle 0.000 5
Executed Ipc Elapsed 1.570 inst/cycle 0.000 5
Issue Slots Busy 40.520 % 0.000 5
Issued Ipc Active 1.620 inst/cycle 0.000 5
SM Busy 40.520 % 0.000 5
Memory Throughput 25170739769.612 byte/second 8074006718458872.000 5
Mem Busy 87.570 % 0.005 5
Max Bandwidth 83.174 % 0.004 5
L1/TEX Hit Rate 0.026 % 0.000 5
L2 Hit Rate 94.436 % 0.268 5
Mem Pipes Busy 73.206 % 0.003 5
Warp Cycles Per Issued Instruction 38.192 cycle 0.000 5
Warp Cycles Per Executed Instruction 38.192 cycle 0.000 5
Avg. Active Threads Per Warp 32.000 0.000 5
Avg. Not Predicated Off Threads Per Warp 31.990 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 2.000 block 0.000 5
Block Limit Shared Mem 3.000 block 0.000 5
Block Limit Warps 2.000 block 0.000 5
Theoretical Active Warps per SM 64.000 warp 0.000 5
Theoretical Occupancy 100.000 % 0.000 5
Achieved Occupancy 96.702 % 0.000 5
Achieved Active Warps Per SM 61.892 warp 0.000 5
Analysis Rules
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.
INF Occupancy This kernel's theoretical occupancy is not impacted by any block limit.
Operation / Metric Value Unit
aten::to
CPU Time 385865.99 μs
Device Time 5312.65 μs
Self CPU Time 71.17 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 5512426.01 μs
Device Time 7597.05 μs
Self CPU Time 5512426.01 μs
Self Device Time 7597.05 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_transpose_kernel<float>(float const*, float const*, float*, int, int, int)
CPU Time 0.00 μs
Device Time 5890786.50 μs
Self CPU Time 0.00 μs
Self Device Time 5890786.50 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 533520.31 μs
Device Time 77.57 μs
Self CPU Time 533520.31 μs
Self Device Time 77.57 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 10929.91 μs
Device Time 14811.87 μs
Self CPU Time 10929.91 μs
Self Device Time 14811.87 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 5359566.14 μs
Device Time 233233.37 μs
Self CPU Time 6957.08 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 5352610.67 μs
Device Time 233233.37 μs
Self CPU Time 9381.29 μs
Self Device Time 233233.37 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 233233.37 μs
Self CPU Time 0.00 μs
Self Device Time 233233.37 μs
CPU Memory Usage 0 B
Device Memory Usage 0 B
Self CPU Memory Usage 0 B
Self Device Memory Usage 0 B
Status: Completed 
45288 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.
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:11:5 bugprone-easily-swappable-parameters
11 | const scalar_t* __restrict__ A,
| ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
12 | const scalar_t* __restrict__ B,
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:11:34: note: the first parameter in the range is 'A'
11 | const scalar_t* __restrict__ A,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:12:34: note: the last parameter in the range is 'B'
12 | const scalar_t* __restrict__ B,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:20:21: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
20 | const int row = blockIdx.x * BLOCK_SIZE + threadIdx.x;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:21:21: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
21 | const int col = blockIdx.y * BLOCK_SIZE + threadIdx.y;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:33:23: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
33 | int k_index = t * BLOCK_SIZE + threadIdx.y;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:42:25: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
42 | int k_index_B = t * BLOCK_SIZE + threadIdx.x;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:70:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
70 | const int K = A.size(0);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:71:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
71 | const int M = A.size(1);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:72:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
72 | const int N = B.size(0);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:80:5: warning: inside a lambda, '__func__' expands to the name of the function call operator; consider capturing the name of the enclosing function explicitly [bugprone-lambda-function-name]
80 | AT_DISPATCH_FLOATING_TYPES(A.type(), "matmul_transpose_kernel", ([&] {
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:237:34: note: expanded from macro 'AT_DISPATCH_FLOATING_TYPES'
237 | AT_DISPATCH_SWITCH(TYPE, NAME, AT_DISPATCH_CASE_FLOATING_TYPES(__VA_ARGS__))
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:233:3: note: expanded from macro 'AT_DISPATCH_CASE_FLOATING_TYPES'
233 | AT_DISPATCH_CASE(at::ScalarType::Double, __VA_ARGS__) \
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:74:3: note: expanded from macro 'AT_DISPATCH_CASE'
74 | AT_PRIVATE_CASE_TYPE_USING_HINT(enum_type, scalar_t, __VA_ARGS__)
| ^
note: (skipping 1 expansions in backtrace; use -fmacro-backtrace-limit=0 to see all)
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:58:7: note: expanded from macro 'AT_PRIVATE_CHECK_SELECTIVE_BUILD'
58 | AT_ERROR( \
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/c10/util/Exception.h:711:32: note: expanded from macro 'AT_ERROR'
711 | C10_EXPAND_MSVC_WORKAROUND(TORCH_CHECK(false, ::c10::str(__VA_ARGS__))); \
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/c10/util/Exception.h:536:9: note: expanded from macro 'TORCH_CHECK'
536 | __func__, \
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:80:5: warning: 'scalar_type' is deprecated: passing at::DeprecatedTypeProperties to an AT_DISPATCH macro is deprecated, pass an at::ScalarType instead [clang-diagnostic-deprecated-declarations]
80 | AT_DISPATCH_FLOATING_TYPES(A.type(), "matmul_transpose_kernel", ([&] {
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:237:3: note: expanded from macro 'AT_DISPATCH_FLOATING_TYPES'
237 | AT_DISPATCH_SWITCH(TYPE, NAME, AT_DISPATCH_CASE_FLOATING_TYPES(__VA_ARGS__))
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:218:36: note: expanded from macro 'AT_DISPATCH_SWITCH'
218 | at::ScalarType _st = ::detail::scalar_type(the_type); \
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/Dispatch.h:106:1: note: 'scalar_type' has been explicitly marked deprecated here
106 | C10_DEPRECATED_MESSAGE(
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/c10/util/Deprecated.h:24:43: note: expanded from macro 'C10_DEPRECATED_MESSAGE'
24 | #define C10_DEPRECATED_MESSAGE(message) [[deprecated(message)]]
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b3_s0_18_matmul_transposed_block32/base/base.cu:80:34: warning: 'type' is deprecated: Tensor.type() is deprecated. Instead use Tensor.options(), which in many cases (e.g. in a constructor) is a drop-in replacement. If you were using data from type(), that is now available from Tensor itself, so instead of tensor.type().scalar_type(), use tensor.scalar_type() instead and instead of tensor.type().backend() use tensor.device(). [clang-diagnostic-deprecated-declarations]
80 | AT_DISPATCH_FLOATING_TYPES(A.type(), "matmul_transpose_kernel", ([&] {
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/ATen/core/TensorBody.h:224:3: note: 'type' has been explicitly marked deprecated here
224 | C10_DEPRECATED_MESSAGE("Tensor.type() is deprecated. Instead use Tensor.options(), which in many cases (e.g. in a constructor) is a drop-in replacement. If you were using data from type(), that is now available from Tensor itself, so instead of tensor.type().scalar_type(), use tensor.scalar_type() instead and instead of tensor.type().backend() use tensor.device().")
| ^
/home/robert_sakana_ai/miniconda3/envs/llm2cuda/lib/python3.11/site-packages/torch/include/c10/util/Deprecated.h:24:43: note: expanded from macro 'C10_DEPRECATED_MESSAGE'
24 | #define C10_DEPRECATED_MESSAGE(message) [[deprecated(message)]]
| ^