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18_Matmul_with_transposed_both • optimized_matmul_transpose_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 optimized_matmul_transpose_base
CUDA Speedup (Native) 0.183x
CUDA Speedup (Compile) 0.208x
CUDA Runtime 1.988 ms
PyTorch Runtime (Native) 0.365 ms
PyTorch Runtime (Compile) 0.413 ms
Correct True
Max Diff (vs. Reference) 0.001000
Model bedrock/anthropic.claude-3-5-sonnet-20241022-v2:0
Temperature 0.50
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>

template <typename scalar_t, int TILE_SIZE=32>
__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) {
    
    __shared__ scalar_t tileA[TILE_SIZE][TILE_SIZE];
    __shared__ scalar_t tileB[TILE_SIZE][TILE_SIZE];
    
    const int row = blockIdx.x * TILE_SIZE + threadIdx.x;
    const int col = blockIdx.y * TILE_SIZE + threadIdx.y;
    
    scalar_t sum = 0;
    const int numTiles = (K + TILE_SIZE - 1) / TILE_SIZE;
    
    for (int t = 0; t < numTiles; ++t) {
        const int k_offset = t * TILE_SIZE;
        
        if (k_offset + threadIdx.y < K && row < M) {
            tileA[threadIdx.y][threadIdx.x] = A[(k_offset + threadIdx.y) * M + row];
        } else {
            tileA[threadIdx.y][threadIdx.x] = 0.0;
        }
        
        if (k_offset + threadIdx.x < K && col < N) {
            tileB[threadIdx.y][threadIdx.x] = B[col * K + k_offset + threadIdx.x];
        } else {
            tileB[threadIdx.y][threadIdx.x] = 0.0;
        }
        
        __syncthreads();
        
        #pragma unroll
        for (int k = 0; k < TILE_SIZE; ++k) {
            sum = fma(tileA[k][threadIdx.x], tileB[threadIdx.y][k], sum);
        }
        
        if (t < numTiles - 1) {
            __syncthreads();
        }
    }
    
    if (row < M && col < N) {
        C[row * N + col] = sum;
    }
}

torch::Tensor matmul_transpose_cuda(torch::Tensor A, torch::Tensor B) {
    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());
    
    constexpr int TILE_SIZE = 32;
    dim3 threads(TILE_SIZE, TILE_SIZE);
    dim3 blocks((M + TILE_SIZE - 1) / TILE_SIZE,
                (N + TILE_SIZE - 1) / TILE_SIZE);
    
    AT_DISPATCH_FLOATING_TYPES(A.type(), "matmul_transpose_kernel", ([&] {
        matmul_transpose_kernel<scalar_t, TILE_SIZE><<<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, "Optimized matrix multiplication with transpose (CUDA)");
}
Performance Metrics
Metric Value Unit Variance Samples
Executed Ipc Active 1.630 inst/cycle 0.000 5
Executed Ipc Elapsed 1.580 inst/cycle 0.000 5
Issue Slots Busy 40.740 % 0.001 5
Issued Ipc Active 1.630 inst/cycle 0.000 5
SM Busy 40.740 % 0.001 5
Memory Throughput 25246950700.464 byte/second 16794110212959654.000 5
Mem Busy 86.504 % 0.004 5
Max Bandwidth 81.940 % 0.004 5
L1/TEX Hit Rate 0.092 % 0.000 5
L2 Hit Rate 94.404 % 0.272 5
Mem Pipes Busy 72.126 % 0.002 5
Warp Cycles Per Issued Instruction 37.990 cycle 0.000 5
Warp Cycles Per Executed Instruction 37.990 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 96.706 % 0.000 5
Achieved Active Warps Per SM 61.894 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 342223.63 μs
Device Time 5102.49 μs
Self CPU Time 44.70 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 5766150.16 μs
Device Time 7832.26 μs
Self CPU Time 5766150.16 μs
Self Device Time 7832.26 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, 32>(float const*, float const*, float*, int, int, int)
CPU Time 0.00 μs
Device Time 6151057.58 μs
Self CPU Time 0.00 μs
Self Device Time 6151057.58 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 542104.29 μs
Device Time 77.66 μs
Self CPU Time 542104.29 μs
Self Device Time 77.66 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 12702.18 μs
Device Time 15275.89 μs
Self CPU Time 12702.18 μs
Self Device Time 15275.89 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 5606025.71 μs
Device Time 239630.15 μs
Self CPU Time 6686.52 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 5599340.86 μs
Device Time 239630.15 μs
Self CPU Time 9484.06 μs
Self Device Time 239630.15 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 239630.15 μs
Self CPU Time 0.00 μs
Self Device Time 239630.15 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 
45284 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/b4_s1_optimized_matmul_transpose/base/base.cu:7:5 bugprone-easily-swappable-parameters
7 | const scalar_t* __restrict__ A,
| ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
8 | const scalar_t* __restrict__ B,
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b4_s1_optimized_matmul_transpose/base/base.cu:7:34: note: the first parameter in the range is 'A'
7 | const scalar_t* __restrict__ A,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b4_s1_optimized_matmul_transpose/base/base.cu:8:34: note: the last parameter in the range is 'B'
8 | const scalar_t* __restrict__ B,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b4_s1_optimized_matmul_transpose/base/base.cu:56:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
56 | const int K = A.size(0);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b4_s1_optimized_matmul_transpose/base/base.cu:57:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
57 | const int M = A.size(1);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b4_s1_optimized_matmul_transpose/base/base.cu:58:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
58 | const int N = B.size(0);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250207_optimize_b5_s4_e1_sweep/level_1/task_18/b4_s1_optimized_matmul_transpose/base/base.cu:67:5: 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]
67 | 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/b4_s1_optimized_matmul_transpose/base/base.cu:67:5: warning: 'scalar_type' is deprecated: passing at::DeprecatedTypeProperties to an AT_DISPATCH macro is deprecated, pass an at::ScalarType instead [clang-diagnostic-deprecated-declarations]
67 | 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/b4_s1_optimized_matmul_transpose/base/base.cu:67:34: 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]
67 | 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)]]
| ^