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3_Batched_matrix_multiplication • bmm_warp_uniform_base_base

Level 1 • Task 3
import torch
import torch.nn as nn
import torch.nn.functional as F


def module_fn(A: torch.Tensor, B: torch.Tensor):
    """
    Performs batched matrix multiplication (C = A * B) where A, B, and C have the same batch dimension.

    Args:
        A: Input tensor of shape (batch_size, m, k).
        B: Input tensor of shape (batch_size, k, n).

    Returns:
        C: Output tensor of shape (batch_size, m, n).
    """
    return torch.bmm(A, B)


class Model(nn.Module):
    """
    Performs batched matrix multiplication (C = A * B) where A, B, and C have the same batch 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)


batch_size = 128
m = 128
k = 256
n = 512


def get_inputs():
    A = torch.randn(batch_size, m, k)
    B = torch.randn(batch_size, 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):
    """
    Performs batched matrix multiplication (C = A * B) where A, B, and C have the same batch dimension.
    """
    def __init__(self):
        super(Model, self).__init__()
    
    def forward(self, A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
        """
        Performs batched matrix multiplication.

        Args:
            A: Input tensor of shape (batch_size, m, k).
            B: Input tensor of shape (batch_size, k, n).

        Returns:
            C: Output tensor of shape (batch_size, m, n).
        """
        return torch.bmm(A, B)

batch_size = 128
m = 128
k = 256
n = 512

def get_inputs():
    A = torch.randn(batch_size, m, k)
    B = torch.randn(batch_size, k, n)
    return [A, B]

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

Operation Name 3_Batched_matrix_multiplication
Level ID 1
Task ID 3
Kernel Name bmm_warp_uniform_base_base
CUDA Speedup (Native) 0.246x
CUDA Speedup (Compile) 0.347x
CUDA Runtime 0.522 ms
PyTorch Runtime (Native) 0.129 ms
PyTorch Runtime (Compile) 0.181 ms
Correct True
Max Diff (vs. Reference) 0.000000
Model bedrock/anthropic.claude-3-5-sonnet-20241022-v2:0
Temperature 0.00
View Experiment Progress Details

Related Kernels (Level 1, Task 3 • 3_Batched_matrix_multiplication)

Rank Kernel Name Runtime (ms) Speedup Native Speedup Compile
🥇 bmm_tiled_shared_memory_optimized_edit_1 0.51 0.25 0.35
🥈 bmm_optimized_sync_reduction_base 0.51 0.25 0.35
🥈 optimized_bmm_kernel_base 0.51 0.25 0.35
🥈 optimized_bmm_kernel_base 0.51 0.25 0.35
🥈 bmm_warp_divergence_reduction_base 0.51 0.25 0.35
🥈 bmm_manual_unroll_base 0.51 0.25 0.35
🥈 bmm_unroll_pragma_optimized_base 0.51 0.25 0.35
8 bmm_optimized_tiling_base 0.51 0.25 0.35
8 bmm_thread_block_optimization_base 0.51 0.25 0.35
10 bmm_double_buffer_min_sync_base 0.52 0.25 0.35
11 bmm_cuda_streams_pipelining_base 0.52 0.25 0.35
12 aligned_ldg_bmm_opt_base 0.52 0.25 0.35
12 bmm_ldg_aligned_base 0.52 0.25 0.35
14 bmm_warp_uniform_base_base 0.52 0.25 0.35
14 bmm_shared_memory_optimized_base 0.52 0.25 0.35
16 bmm_thread_block_optimization_base 0.52 0.25 0.35
16 tiled_bmm_optimal_config_edit_1 0.52 0.25 0.35
16 bmm_warp_uniform_base 0.52 0.25 0.35
16 tiled_batchptr_unroll_base 0.52 0.25 0.35
16 warp_divergence_reduction_edit_1 0.52 0.25 0.35 
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>

#define TILE_SIZE 32
#define WARP_SIZE 32

__global__ void bmm_warp_uniform_kernel(
    const float* __restrict__ A,
    const float* __restrict__ B,
    float* __restrict__ C,
    int batch_size,
    int M,
    int K,
    int N
) {
    __shared__ float As[TILE_SIZE][TILE_SIZE];
    __shared__ float Bs[TILE_SIZE][TILE_SIZE];
    
    const int b = blockIdx.z;
    const int row = blockIdx.y * TILE_SIZE + threadIdx.y;
    const int col = blockIdx.x * TILE_SIZE + threadIdx.x;
    
    // Pre-calculate batch offsets
    const float* batch_A = A + b * M * K;
    const float* batch_B = B + b * K * N;
    float* batch_C = C + b * M * N;
    
    // Pre-calculate validity masks for boundary conditions
    const bool valid_row = row < M;
    const bool valid_col = col < N;
    const bool valid_thread = valid_row && valid_col;
    
    float sum = 0.0f;
    
    // Calculate number of tiles and handle the K dimension uniformly
    const int num_tiles = (K + TILE_SIZE - 1) / TILE_SIZE;
    
    #pragma unroll 1
    for (int t = 0; t < num_tiles; t++) {
        const int k_base = t * TILE_SIZE;
        
        // Load tiles using predicated writes to avoid divergent branches
        const int k_idx = k_base + threadIdx.x;
        const int k_idy = k_base + threadIdx.y;
        
        // Predicated loads for A
        float a_val = 0.0f;
        if (valid_row && k_idx < K) {
            a_val = batch_A[row * K + k_idx];
        }
        As[threadIdx.y][threadIdx.x] = a_val;
        
        // Predicated loads for B
        float b_val = 0.0f;
        if (k_idy < K && valid_col) {
            b_val = batch_B[k_idy * N + col];
        }
        Bs[threadIdx.y][threadIdx.x] = b_val;
        
        __syncthreads();
        
        // Compute partial results - all threads perform the same operations
        #pragma unroll
        for (int k = 0; k < TILE_SIZE; k++) {
            sum += As[threadIdx.y][k] * Bs[k][threadIdx.x];
        }
        
        __syncthreads();
    }
    
    // Predicated write to global memory
    if (valid_thread) {
        batch_C[row * N + col] = sum;
    }
}

torch::Tensor forward_bmm(torch::Tensor A, torch::Tensor B) {
    TORCH_CHECK(A.is_cuda(), "A must be a CUDA tensor");
    TORCH_CHECK(B.is_cuda(), "B must be a CUDA tensor");
    TORCH_CHECK(A.dim() == 3, "A must be 3D");
    TORCH_CHECK(B.dim() == 3, "B must be 3D");
    TORCH_CHECK(A.size(0) == B.size(0), "Batch sizes must match");
    TORCH_CHECK(A.size(2) == B.size(1), "Inner dimensions (K) must match");

    int batch_size = A.size(0);
    int M = A.size(1);
    int K = A.size(2);
    int N = B.size(2);

    auto options = torch::TensorOptions().dtype(A.dtype()).device(A.device());
    auto C = torch::zeros({batch_size, M, N}, options);

    // Ensure grid dimensions are multiples of warp size where possible
    dim3 block(TILE_SIZE, TILE_SIZE);
    dim3 grid((N + TILE_SIZE - 1) / TILE_SIZE,
              (M + TILE_SIZE - 1) / TILE_SIZE,
              batch_size);

    bmm_warp_uniform_kernel<<<grid, block>>>(
        A.data_ptr<float>(),
        B.data_ptr<float>(),
        C.data_ptr<float>(),
        batch_size, M, K, N
    );

    return C;
}

PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
    m.def("forward", &forward_bmm, "Batched matrix multiplication with uniform warp execution (CUDA)");
}
Performance Metrics
Metric Value Unit Variance Samples
Executed Ipc Active 1.764 inst/cycle 0.000 5
Executed Ipc Elapsed 1.740 inst/cycle 0.000 5
Issue Slots Busy 44.122 % 0.000 5
Issued Ipc Active 1.764 inst/cycle 0.000 5
SM Busy 44.122 % 0.000 5
Memory Throughput 181887277956.030 byte/second 132275818804217296.000 5
Mem Busy 86.304 % 0.003 5
Max Bandwidth 81.860 % 0.003 5
L1/TEX Hit Rate 0.024 % 0.000 5
L2 Hit Rate 72.562 % 0.492 5
Mem Pipes Busy 72.340 % 0.002 5
Warp Cycles Per Issued Instruction 35.608 cycle 0.000 5
Warp Cycles Per Executed Instruction 35.610 cycle 0.000 5
Avg. Active Threads Per Warp 32.000 0.000 5
Avg. Not Predicated Off Threads Per Warp 31.890 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 98.266 % 0.000 5
Achieved Active Warps Per SM 62.888 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 598461.38 μs
Device Time 9132.45 μs
Self CPU Time 48.70 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
aten::zeros
CPU Time 1122158.49 μs
Device Time 189928.00 μs
Self CPU Time 28584.56 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::zero_
CPU Time 9193319.79 μs
Device Time 1442796.95 μs
Self CPU Time 56340.79 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 9136980.80 μs
Device Time 1442796.95 μs
Self CPU Time 77413.94 μs
Self Device Time 1442796.95 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 9123495.61 μs
Device Time 207271.04 μs
Self CPU Time 9123495.61 μs
Self Device Time 207271.04 μs
CPU Memory Usage 0 B
Device Memory Usage 0 B
Self CPU Memory Usage 0 B
Self Device Memory Usage 0 B
bmm_warp_uniform_kernel(float const*, float const*, float*, int, int, int, int)
CPU Time 0.00 μs
Device Time 8255417.86 μs
Self CPU Time 0.00 μs
Self Device Time 8255417.86 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 1252868.95 μs
Self CPU Time 0.00 μs
Self Device Time 1252868.95 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 
45291 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/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:9:5 bugprone-easily-swappable-parameters
9 | const float* __restrict__ A,
| ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
10 | const float* __restrict__ B,
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:9:31: note: the first parameter in the range is 'A'
9 | const float* __restrict__ A,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:10:31: note: the last parameter in the range is 'B'
10 | const float* __restrict__ B,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:12:5: warning: 2 adjacent parameters of 'bmm_warp_uniform_kernel' of similar type ('int') are easily swapped by mistake [bugprone-easily-swappable-parameters]
12 | int batch_size,
| ^~~~~~~~~~~~~~~
13 | int M,
| ~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:12:9: note: the first parameter in the range is 'batch_size'
12 | int batch_size,
| ^~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:13:9: note: the last parameter in the range is 'M'
13 | int M,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:20:19: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
20 | const int b = blockIdx.z;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:21:21: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
21 | const int row = blockIdx.y * TILE_SIZE + threadIdx.y;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:22:21: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
22 | const int col = blockIdx.x * TILE_SIZE + threadIdx.x;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:25:28: warning: result of multiplication in type 'int' is used as a pointer offset after an implicit widening conversion to type 'ptrdiff_t' [bugprone-implicit-widening-of-multiplication-result]
25 | const float* batch_A = A + b * M * K;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:25:32: note: make conversion explicit to silence this warning
4 | const float* batch_A = A + b * M * K;
| ^~~~~~~~~
| static_cast<ptrdiff_t>( )
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:25:32: note: perform multiplication in a wider type
25 | const float* batch_A = A + b * M * K;
| ^~~~~
| static_cast<ptrdiff_t>( )
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:26:28: warning: result of multiplication in type 'int' is used as a pointer offset after an implicit widening conversion to type 'ptrdiff_t' [bugprone-implicit-widening-of-multiplication-result]
26 | const float* batch_B = B + b * K * N;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:26:32: note: make conversion explicit to silence this warning
26 | const float* batch_B = B + b * K * N;
| ^~~~~~~~~
| static_cast<ptrdiff_t>( )
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:26:32: note: perform multiplication in a wider type
26 | const float* batch_B = B + b * K * N;
| ^~~~~
| static_cast<ptrdiff_t>( )
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:27:22: warning: result of multiplication in type 'int' is used as a pointer offset after an implicit widening conversion to type 'ptrdiff_t' [bugprone-implicit-widening-of-multiplication-result]
27 | float* batch_C = C + b * M * N;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:27:26: note: make conversion explicit to silence this warning
27 | float* batch_C = C + b * M * N;
| ^~~~~~~~~
| static_cast<ptrdiff_t>( )
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:27:26: note: perform multiplication in a wider type
27 | float* batch_C = C + b * M * N;
| ^~~~~
| static_cast<ptrdiff_t>( )
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:44:27: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
44 | const int k_idx = k_base + threadIdx.x;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:45:27: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
45 | const int k_idy = k_base + threadIdx.y;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:78:41: warning: the parameter 'A' is copied for each invocation but only used as a const reference; consider making it a const reference [performance-unnecessary-value-param]
78 | torch::Tensor forward_bmm(torch::Tensor A, torch::Tensor B) {
| ^
| const &
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:78:58: warning: the parameter 'B' is copied for each invocation but only used as a const reference; consider making it a const reference [performance-unnecessary-value-param]
78 | torch::Tensor forward_bmm(torch::Tensor A, torch::Tensor B) {
| ^
| const &
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:86:22: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
86 | int batch_size = A.size(0);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:87:13: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
87 | int M = A.size(1);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:88:13: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
88 | int K = A.size(2);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250202_optimize_b10_s4_e0_sweep/level_1/task_3/b7_s2_bmm_warp_uniform_base/base/base.cu:89:13: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
89 | int N = B.size(2);
| ^