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39_L2Norm_l2norm_stride_optimized_base

Level 1 • Task 39
import torch
import torch.nn as nn
import torch.nn.functional as F


def module_fn(x: torch.Tensor) -> torch.Tensor:
    """
    Applies L2 normalization to the input tensor.

    Args:
        x (torch.Tensor): Input tensor of shape (*, dim, *).

    Returns:
        torch.Tensor: Output tensor with L2 normalization applied, same shape as input.
    """
    return F.normalize(x, p=2, dim=1)


class Model(nn.Module):
    """
    Simple model that performs L2 normalization.
    """

    def __init__(self):
        """
        Initializes the L2Norm layer.
        """
        super(Model, self).__init__()

    def forward(self, x: torch.Tensor, fn=module_fn) -> torch.Tensor:
        """
        Applies L2 normalization to the input tensor.

        Args:
            x (torch.Tensor): Input tensor of shape (*, dim, *).

        Returns:
            torch.Tensor: Output tensor with L2 normalization applied, same shape as input.
        """
        return fn(x)


batch_size = 16
dim = 16384


def get_inputs():
    x = torch.randn(batch_size, dim)
    return [x]


def get_init_inputs():
    return []
import torch
import torch.nn as nn

class Model(nn.Module):
    """
    Simple model that performs L2 normalization.
    """
    def __init__(self):
        """
        Initializes the L2Norm layer.

        Args:
            dim (int): Dimension along which to normalize.
        """
        super(Model, self).__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Applies L2 normalization to the input tensor.

        Args:
            x (torch.Tensor): Input tensor of shape (*, dim, *).

        Returns:
            torch.Tensor: Output tensor with L2 normalization applied, same shape as input.
        """
        return x / torch.norm(x, p=2, dim=1, keepdim=True)

batch_size = 16
dim = 16384

def get_inputs():
    x = torch.randn(batch_size, dim)
    return [x]

def get_init_inputs():
    return []

Kernel Information

Related Kernels (Level 1, Task 39 • 39_L2Norm_)

Rank Kernel Name Runtime (ms) Speedup Native Speedup Compile
🥇 l2norm_strided_optimized_base_base 0.01 1.89 5.60
🥈 l2_norm_combined_base 0.01 1.55 4.58
🥉 l2_norm_unroll_optimized_base 0.01 1.42 4.20
🥉 39_l2norm_modular_edit_1 0.01 1.42 4.20
🥉 39_l2norm_blocksize_experiment_base 0.01 1.42 4.20
6 39_l2norm_atomic_opt_base 0.01 1.31 3.87
6 l2norm_block_tuned_base 0.01 1.31 3.87
6 l2_norm_block_size_tuning_base 0.01 1.31 3.87
6 l2_norm_atomic_minimized_base_base 0.01 1.31 3.87
6 l2norm_stride_optimized_base 0.01 1.31 3.87
6 39_l2norm_coalesced_base 0.01 1.31 3.87
6 39_l2norm_memory_coalescing_base 0.01 1.31 3.87
6 39_l2norm_modular_refactored_edit_1 0.01 1.31 3.87
6 39_l2norm_optimized_indexing_edit_1 0.01 1.31 3.87
6 39_l2norm_sync_optimized_edit_1 0.01 1.31 3.87
6 39_l2norm_blocksize_experiment_edit_1 0.01 1.31 3.87
6 39_l2norm_memory_coalescing_edit_1 0.01 1.31 3.87
6 39_l2norm_modular_refactored_base 0.01 1.31 3.87
6 l2norm_even_workload_base 0.01 1.31 3.87
6 39_l2norm_atomic_edit_1 0.01 1.31 3.87
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <math.h>

// Define the segment size to determine the workload per block per vector segment
#define SEGMENT_SIZE 1024

// Stage 1: Compute the partial squared sum for each vector segment using stride loops
template <typename scalar_t>
__global__ void l2_normalize_stage1_kernel(
    const scalar_t* __restrict__ input,
    scalar_t* __restrict__ partial_sums,
    const int C,
    const int total_vectors,
    const int stride_C,
    const int outer_stride,
    const int blocks_per_vector) {

    // Determine which vector and segment this block is responsible for
    int vector_idx = blockIdx.x / blocks_per_vector;
    int seg_idx = blockIdx.x % blocks_per_vector;
    if (vector_idx >= total_vectors) return;

    int base_offset = vector_idx * outer_stride;
    int seg_start = seg_idx * SEGMENT_SIZE;
    int seg_end = seg_start + SEGMENT_SIZE;
    if (seg_end > C) seg_end = C;

    scalar_t sum = 0;

    // Use a stride loop to cover all elements in the segment
    // Each thread processes multiple elements spaced by blockDim.x
    for (int i = seg_start + threadIdx.x; i < seg_end; i += blockDim.x) {
        scalar_t val = input[base_offset + i * stride_C];
        sum += val * val;
    }

    // Warp-level reduction using shuffle operations
    for (int offset = warpSize / 2; offset > 0; offset /= 2) {
        sum += __shfl_down_sync(0xffffffff, sum, offset);
    }

    // Use shared memory to reduce across warps in this block
    __shared__ scalar_t shared_mem[32]; // Enough to hold one value per warp
    int warp_id = threadIdx.x / warpSize;
    if ((threadIdx.x % warpSize) == 0) {
        shared_mem[warp_id] = sum;
    }
    __syncthreads();

    // First warp reduces the values in shared memory
    if (warp_id == 0) {
        sum = (threadIdx.x < (blockDim.x + warpSize - 1) / warpSize) ? shared_mem[threadIdx.x] : 0;
        for (int offset = warpSize / 2; offset > 0; offset /= 2) {
            sum += __shfl_down_sync(0xffffffff, sum, offset);
        }
        if (threadIdx.x == 0) {
            // Atomic addition to accumulate the partial sum for the vector
            atomicAdd(&partial_sums[vector_idx], sum);
        }
    }
}

// Stage 2: Normalize the vector using the computed partial sum
// Each block covers a segment of the vector and applies the normalization using stride loops.
template <typename scalar_t>
__global__ void l2_normalize_stage2_kernel(
    const scalar_t* __restrict__ input,
    scalar_t* __restrict__ output,
    const scalar_t* __restrict__ partial_sums,
    const int C,
    const int total_vectors,
    const int stride_C,
    const int outer_stride,
    const int blocks_per_vector) {

    int vector_idx = blockIdx.x / blocks_per_vector;
    int seg_idx = blockIdx.x % blocks_per_vector;
    if (vector_idx >= total_vectors) return;

    int base_offset = vector_idx * outer_stride;
    int seg_start = seg_idx * SEGMENT_SIZE;
    int seg_end = seg_start + SEGMENT_SIZE;
    if (seg_end > C) seg_end = C;

    // Compute the normalization factor from the accumulated squared sum
    scalar_t norm = partial_sums[vector_idx];
    scalar_t inv_norm = 1.0 / (sqrt(norm) + 1e-12);

    // Use a stride loop to normalize each element in the segment
    for (int i = seg_start + threadIdx.x; i < seg_end; i += blockDim.x) {
        output[base_offset + i * stride_C] = input[base_offset + i * stride_C] * inv_norm;
    }
}

// The forward function prepares the kernel execution and launches the two stages
torch::Tensor forward(torch::Tensor input) {
    TORCH_CHECK(input.is_cuda(), "input must be a CUDA tensor");
    TORCH_CHECK(input.dim() >= 1, "Need at least 1 dimension");

    const int C = input.size(1);
    const int total_vectors = input.numel() / C;
    const int stride_C = input.stride(1);
    const int outer_stride = input.stride(0);

    auto output = torch::empty_like(input);
    auto partial_sums = torch::zeros({total_vectors}, input.options());

    const int threads = 256;
    // Calculate the number of blocks per vector based on the segment size
    const int blocks_per_vector = (C + SEGMENT_SIZE - 1) / SEGMENT_SIZE;
    const int total_blocks = total_vectors * blocks_per_vector;

    AT_DISPATCH_FLOATING_TYPES(input.scalar_type(), "l2_normalize_stride", ([&] {
        l2_normalize_stage1_kernel<scalar_t><<<total_blocks, threads>>>(
            input.data_ptr<scalar_t>(),
            partial_sums.data_ptr<scalar_t>(),
            C,
            total_vectors,
            stride_C,
            outer_stride,
            blocks_per_vector
        );

        l2_normalize_stage2_kernel<scalar_t><<<total_blocks, threads>>>(
            input.data_ptr<scalar_t>(),
            output.data_ptr<scalar_t>(),
            partial_sums.data_ptr<scalar_t>(),
            C,
            total_vectors,
            stride_C,
            outer_stride,
            blocks_per_vector
        );
    }));

    return output;
}

PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
    m.def("forward", &forward, "L2 normalization along dim=1 using stride loops");
}
Performance Metrics
Metric Value Unit Variance Samples
Executed Ipc Active 0.344 inst/cycle 0.000 5
Executed Ipc Elapsed 0.184 inst/cycle 0.000 5
Issue Slots Busy 8.820 % 0.007 5
Issued Ipc Active 0.354 inst/cycle 0.000 5
SM Busy 8.820 % 0.007 5
Memory Throughput 195688281970.630 byte/second 16597868308642918400.000 5
Mem Busy 9.436 % 0.044 5
Max Bandwidth 8.668 % 0.034 5
L1/TEX Hit Rate 2.650 % 0.000 5
L2 Hit Rate 66.816 % 0.050 5
Mem Pipes Busy 2.926 % 0.004 5
Warp Cycles Per Issued Instruction 41.068 cycle 1.275 5
Warp Cycles Per Executed Instruction 42.276 cycle 1.345 5
Avg. Active Threads Per Warp 32.000 0.000 5
Avg. Not Predicated Off Threads Per Warp 29.820 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 16.000 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 22.470 % 0.005 5
Achieved Active Warps Per SM 14.384 warp 0.002 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.
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 (22.6%) 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::empty_strided
CPU Time 709650.51 μs
Device Time 0.00 μs
Self CPU Time 219419.39 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 5403707.02 μs
Device Time 204229.33 μs
Self CPU Time 116097.33 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 5743492.03 μs
Device Time 7396417.19 μs
Self CPU Time 258803.08 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 5484690.77 μs
Device Time 7396417.19 μs
Self CPU Time 379951.07 μs
Self Device Time 7396417.19 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 5780549.30 μs
Device Time 354264.34 μs
Self CPU Time 5780549.30 μs
Self Device Time 354264.34 μs
CPU Memory Usage 0 B
Device Memory Usage 0 B
Self CPU Memory Usage 0 B
Self Device Memory Usage 0 B
void l2_normalize_stage1_kernel<float>(float const*, float*, int, int, int, int, int)
CPU Time 0.00 μs
Device Time 492395.04 μs
Self CPU Time 0.00 μs
Self Device Time 492395.04 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 7192503.35 μs
Self CPU Time 0.00 μs
Self Device Time 7192503.35 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
45292 warnings generated when compiling for host.
Suppressed 45321 warnings (45274 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/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:14:5 bugprone-easily-swappable-parameters
14 | const int C,
| ^~~~~~~~~~~~
15 | const int total_vectors,
| ~~~~~~~~~~~~~~~~~~~~~~~~
16 | const int stride_C,
| ~~~~~~~~~~~~~~~~~~~
17 | const int outer_stride,
| ~~~~~~~~~~~~~~~~~~~~~~~
18 | const int blocks_per_vector) {
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:14:15: note: the first parameter in the range is 'C'
14 | const int C,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:18:15: note: the last parameter in the range is 'blocks_per_vector'
18 | const int blocks_per_vector) {
| ^~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:21:22: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
21 | int vector_idx = blockIdx.x / blocks_per_vector;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:22:19: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
22 | int seg_idx = blockIdx.x % blocks_per_vector;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:34:18: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
34 | for (int i = seg_start + threadIdx.x; i < seg_end; i += blockDim.x) {
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:34:61: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
34 | for (int i = seg_start + threadIdx.x; i < seg_end; i += blockDim.x) {
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:46:19: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
46 | int warp_id = threadIdx.x / warpSize;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:72:5: warning: 5 adjacent parameters of 'l2_normalize_stage2_kernel' of similar type ('const int') are easily swapped by mistake [bugprone-easily-swappable-parameters]
72 | const int C,
| ^~~~~~~~~~~~
73 | const int total_vectors,
| ~~~~~~~~~~~~~~~~~~~~~~~~
74 | const int stride_C,
| ~~~~~~~~~~~~~~~~~~~
75 | const int outer_stride,
| ~~~~~~~~~~~~~~~~~~~~~~~
76 | const int blocks_per_vector) {
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:72:15: note: the first parameter in the range is 'C'
72 | const int C,
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:76:15: note: the last parameter in the range is 'blocks_per_vector'
76 | const int blocks_per_vector) {
| ^~~~~~~~~~~~~~~~~
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:78:22: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
78 | int vector_idx = blockIdx.x / blocks_per_vector;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:79:19: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
79 | int seg_idx = blockIdx.x % blocks_per_vector;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:92:18: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
92 | for (int i = seg_start + threadIdx.x; i < seg_end; i += blockDim.x) {
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:92:61: warning: narrowing conversion from 'unsigned int' to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
92 | for (int i = seg_start + threadIdx.x; i < seg_end; i += blockDim.x) {
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:102:19: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
102 | const int C = input.size(1);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:103:31: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
103 | const int total_vectors = input.numel() / C;
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:104:26: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
104 | const int stride_C = input.stride(1);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:105:30: warning: narrowing conversion from 'int64_t' (aka 'long') to signed type 'int' is implementation-defined [bugprone-narrowing-conversions]
105 | const int outer_stride = input.stride(0);
| ^
/home/robert_sakana_ai/llm_cuda/experiments/20250208_optimize_b5_s4_e1_sweep/level_1/task_39/b3_s2_l2norm_stride_optimized/base/base.cu:115:5: 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]
115 | AT_DISPATCH_FLOATING_TYPES(input.scalar_type(), "l2_normalize_stride", ([&] {
| ^
/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__, \
| ^