FW-GLM-5-1 · popcorn · pop_l123_all_gpt
correct 32_argmax_tiebreak_smallest_rank.py
model
FW-GLM-5-1
turns / max
14 / 15
tool calls
14
tokens (total)
121702
wall clock
486.5s
truncated
no
backend
cuda fp32
variant
popcorn
runtime
0.01 μs
ref runtime
0.19 μs
speedup
33.16x
started
2026-05-11T22:07:28Z
timingkernelbench.timing
kernel runtime
0.01 μs
ref runtime
0.19 μs
speedup
33.16x
kernel mean / median / std
0.01 / — / 8.07e-05 μs
ref mean / median / std
0.19 / — / 0.01 μs
numerical precisioneval_kernel_against_ref
max abs error
0.00
mean abs error
0.00
max rel error
0.00
mean rel error
0.00
gpu memoryextended_metrics.measure_memory
kernel peak
33.01 MB
ref peak
33.01 MB
kernel / ref
1.00x
kernel launches / fusiontorch.profiler
kernel launches
1
ref launches
94
fusion ratio (ref / kernel)
94.00x
total cuda time
26 μs
SOL (speed-of-light)nsight_hardware_counters
SOL score (0–1)
6.000e-04
dram util %
0.1%
compute util %
0.0%
bottleneck
unknown
dominant pipe
None
arithmetic intensity
—
ridge point
20.00
roofline / occupancynsight_hardware_counters
dram bandwidth
1.96 GB/s
dram util %
0.1%
fp32 tflops
—
fp32 util %
—
fp16 tflops
—
occupancy %
11.5%
bottleneck
unknown
dominant pipe %
—
arithmetic intensity
—
ridge point
20.00
L1 hit %
—
L2 hit %
99.1%
ld sectors / req
4.00
st sectors / req
—
regs / thread
18
smem / block
1024 B
block size
256
peak bw
3350.00 GB/s
peak fp32 tflops
67.00
peak fp16 tflops
1979.00
warp stalls (top 5)nsight
long_scoreboard
2375.4%
short_scoreboard
1096.8%
flagssubmit_kernel guard
excessive speedup
flagged
reference PyTorch source (the prompt the agent sees)
"""
Over virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.

Output (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.
"""

import torch
import torch.nn as nn

from kernelbench.distributed_collectives import default_device

R = 4
B = 8
C = 28


class Model(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # x: (R, B, C)
        best_val = x[0].clone()
        best_idx = torch.zeros(B, C, dtype=torch.long, device=x.device)
        for r in range(1, R):
            xv = x[r]
            improved = xv > best_val
            tied = (xv == best_val) & ~improved
            best_idx = torch.where(
                improved,
                torch.full_like(best_idx, r),
                torch.where(
                    tied,
                    torch.minimum(best_idx, torch.full_like(best_idx, r)),
                    best_idx,
                ),
            )
            best_val = torch.where(improved, xv, best_val)
        stacked = torch.stack([best_val, best_idx.to(best_val.dtype)], dim=-1)
        return stacked


def get_inputs():
    dev = default_device()
    p = popcorn_pri
    return [torch.randn(R, p.jitter_int(B), p.jitter_int(C), device=dev)]


def get_init_inputs():
    return []
turn 03.7s turn · 3.7s LLM · 0.0s tools · tokens in=2,148 · out=239 · total=2,387
reasoning
Let me analyze this task: 1. We have a model that takes a tensor `x` of shape `(R, B, C)` where R=4, B=8, C=28 2. For each `(B, C)` position, we find the maximum value across the R dimension 3. On ties, we choose the smallest rank index 4. Output is `(B, C, 2)` where `[:,:,0]` is the best value and `[:,:,1]` is the winning rank as float32 The reference implementation loops through R ranks and updates the best value and index based on comparisons. Let me first get the GPU specs to understand the hardware, then write an initial CUDA kernel. The key operations: - Compare values across R dimension - Track maximum value and minimum index for ties - Output (B, C, 2) tensor A simple CUDA kernel could: 1. Each thread handles one (b, c) position 2. Load all R values for that position 3. Find max and min index for ties Let me start by getting GPU specs and then writing the kernel.
call → get_gpu_specs
callget_gpu_specs {}
result ← get_gpu_specs (ok)
okget_gpu_specs GPU specs for NVIDIA H100 80GB HBM3: total memory (runtime): 79.1 GB spec entry: H100 GPU Architecture: Hopper GPU Memory: 80GB Memory Bandwidth: 3.35 TB/s FP64 TFLOPS: 34 FP64 Tensor Core TFLOPS: 67 FP32 TFLOPS: 67 TF32 Tensor Core TFLOPS: 989 with sparsity BFLOAT16 Tensore Core TFLOPS: 1979 with sparsity FP16 Tensor Core TFLOPS: 1979 with sparsity FP8 Tensor Core TFLOPS: 3958 with sparsity INT8 Tensor Core TOPS: 3958 with sparsity Register File Size: 64K 32-bit registers per SM Maximum number of registers per thread: 255 Maximum number of thread blocks per SM: 32 Shared memory capacity per SM: 228 KB Maximum shared memory per thread block: 227 KB
turn 187.1s turn · 8.3s LLM · 78.8s tools · tokens in=2,396 · out=872 · total=3,268
reasoning
Now let me understand the problem: - Input: (R, B, C) = (4, 8, 28) tensor - For each (B, C) position, find the maximum value across R dimension - On ties, choose the smallest rank index - Output: (B, C, 2) where [:,:,0] = best value, [:,:,1] = winning rank The total elements processed is B*C = 8*28 = 224, which is quite small. This is a simple operation that should be parallelized across the (B, C) dimensions. Let me write a custom CUDA kernel:
assistantLet me understand the problem better and write an optimized CUDA kernel. The task is to find the max value across R ranks for each (B, C) position, and on ties, pick the smallest rank index.
call → compile_kernel
callcompile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int R, int B, int C) {\n \n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n float best_val = x[0 * B * C + b * C + c]; // x[0][b][c]\n int best_idx = 0;\n \n for (int r = 1; r < R; r++) {\n float val = x[r * B * C + b * C + c]; // x[r][b][c]\n if (val > best_val) {\n best_val = val;\n best_idx = r;\n }\n // On ties (val == best_val), keep smallest idx (already have it)\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n \n int R = x.size(0);\n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n R, B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 26.4s turn · 6.4s LLM · 0.0s tools · tokens in=3,147 · out=706 · total=3,853
reasoning
The kernel compiled. Let me now check correctness.
call → run_correctness
callrun_correctness { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int R, int B, int C) {\n \n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n float best_val = x[0 * B * C + b * C + c]; // x[0][b][c]\n int best_idx = 0;\n \n for (int r = 1; r < R; r++) {\n float val = x[r * B * C + b * C + c]; // x[r][b][c]\n if (val > best_val) {\n best_val = val;\n best_idx = r;\n }\n // On ties (val == best_val), keep smallest idx (already have it)\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n \n int R = x.size(0);\n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n R, B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=0.00e+00 mean_abs_err=0.00e+00 max_rel_err=0.00e+00
turn 318.3s turn · 6.6s LLM · 11.7s tools · tokens in=3,900 · out=731 · total=4,631
reasoning
The kernel is correct. Now let me profile it to see if there are any optimization opportunities.
assistantThe kernel is correct. Let me profile it to understand performance and optimize if needed:
call → profile_kernel
callprofile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int R, int B, int C) {\n \n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n float best_val = x[0 * B * C + b * C + c]; // x[0][b][c]\n int best_idx = 0;\n \n for (int r = 1; r < R; r++) {\n float val = x[r * B * C + b * C + c]; // x[r][b][c]\n if (val > best_val) {\n best_val = val;\n best_idx = r;\n }\n // On ties (val == best_val), keep smallest idx (already have it)\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n \n int R = x.size(0);\n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n R, B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty 40.0μs (100%) calls=1 --- Timing --- GPU time: 4.13 μs --- Memory Bandwidth --- DRAM BW: 2.5/3350 GB/s (0.1%) read=2.5 write=0.0 GB/s Hit rates: L2=98.4% --- Compute Throughput --- Pipe util: FMA=1.7%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 10.3% Eligible warps/cycle: 0.04 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=32, smem/blk=1024B, block=256, grid=1 --- Memory Access Quality --- Global ld coalescing: 4.00 sectors/req (4.0x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 2546.3% #################### short_scoreboard 93.1% ################## --- Optimization Hints --- -> 2546% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=4.0 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=4.0x (ideal=1.0) -> 4x wasted DRAM BW. Make per-warp accesses contiguous. -> Low occupancy (10%). Consider __launch_bounds__ or reducing register pressure. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching).
turn 4 · 1 tool call(s) · 94.6s turn · 18.3s LLM · tokens in=5,063 · out=1,850 · total=6,913 · 7,534 chars (click to expand)
turn 494.6s turn · 18.3s LLM · 76.3s tools · tokens in=5,063 · out=1,850 · total=6,913
reasoning
Interesting. The profile shows the kernel is latency-bound with: - Only 10% occupancy - Poor global load coalescing (4x wasted bandwidth) - Long scoreboard stalls (waiting for memory) The issue is that my memory access pattern isn't coalesced properly. Each thread reads from positions separated by C elements in the inner dimension, but when R varies, we're jumping around memory. Actually, looking more carefully at the memory layout: - Input x is (R, B, C) = (4, 8, 28) - For thread i, b = i / C, c = i % C - Reading x[r][b][c] = x[r * B * C + b * C + c] Since C = 28, consecutive threads read consecutive c values within the same b. So: - Thread 0 reads c=0, b=0 - Thread 1 reads c=1, b=0 - ... - Thread 27 reads c=27, b=0 - Thread 28 reads c=0, b=1 (different b!) So actually within a block of 256 threads and B*C = 224, we should have good coalescing. But the issue is that when we loop over R (r from 1 to 3), we're reading from memory locations: - r=0: x[0 * 224 + b*28 + c] = x[b*28 + c] - r=1: x[1 * 224 + b*28 + c] = x[224 + b*28 + c] - r=2: x[2 * 224 + b*28 + c] = x[448 + b*28 + c] - r=3: x[3 * 224 + b*28 + c] = x[672 + b*28 + c] So for consecutive threads (same b, consecutive c), the addresses are consecutive for each r iteration. That should be coalesced... Let me think about this more carefully. The profile shows "Global load coalescing: 4.00 sectors/req" which is 4x wasted. On H100, each transaction is 128 bytes (32 threads × 4 bytes each for float). If threads access consecutive floats, we get perfect coalescing. Actually, I think the issue might be the small problem size. With only 224 threads total, we have just 1 block with 256 threads. This is extremely small - not enough to keep the GPU busy. Let me try optimizing by: 1. Vectorized loads - load 4 floats at once to reduce instruction count 2. Loop unrolling 3. Using float4 for better memory access Actually, wait - looking at the memory pattern again: - x has shape (R, B, C) = (4, 8, 28) - Total elements: 896 floats = 3584 bytes This is extremely small. The entire input fits in cache. The issue is likely just kernel launch overhead. Let me try a different approach - since the problem is so small, maybe using thrust or cub would help, but actually the latency might be dominated by kernel launch time. Let me try optimizing the kernel anyway: 1. Use vectorized loads to read across R dimension (since R=4, we can use float4) 2. Better memory access pattern Actually, I realize the memory layout might be better exploited. The input x[R][B][C] means for the same (b,c), the R values are at positions offset by B*C from each other. For a given (b,c), the 4 values across R are: - x[0][b][c] at offset b*C + c - x[1][b][c] at offset B*C + b*C + c = B*C + b*C + c - x[2][b][c] at offset 2*B*C + b*C + c - x[3][b][c] at offset 3*B*C + b*C + c These are NOT contiguous in memory (they're B*C elements apart). But we could restructure the access pattern. What if each thread handles multiple outputs and we use shared memory? Actually for such a small problem, the simplest optimization is probably just to: 1. Increase threads per block to maximize occupancy within the single block 2. Use float4 to vectorize Let me try a vectorized approach where we load all R values at once using a different indexing strategy.
assistantThe profile shows the kernel is latency-bound with poor coalescing. The problem size is very small (only 224 threads = 1 block), causing low occupancy. Let me optimize by vectorizing loads across the R dimension:
call → compile_kernel
callcompile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int R, int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n // Load all R values for this (b, c) position\n // x[r][b][c] = x[r * B * C + b * C + c]\n // Since R is typically 4 and contiguous in outermost dimension, \n // we load values strided by B*C\n \n int base_offset = b * C + c; // offset within one rank\n int stride = B * C; // stride between ranks\n \n float vals[4];\n vals[0] = x[base_offset];\n vals[1] = x[base_offset + stride];\n vals[2] = x[base_offset + stride * 2];\n vals[3] = x[base_offset + stride * 3];\n \n // Find max with smallest index on ties\n float best_val = vals[0];\n int best_idx = 0;\n \n #pragma unroll\n for (int r = 1; r < 4; r++) {\n if (vals[r] > best_val) {\n best_val = vals[r];\n best_idx = r;\n }\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int R = x.size(0);\n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n R, B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 58.3s turn · 8.2s LLM · 0.0s tools · tokens in=5,970 · out=858 · total=6,828
reasoning
Good, let me check correctness of this version.
call → run_correctness
callrun_correctness { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int R, int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n // Load all R values for this (b, c) position\n // x[r][b][c] = x[r * B * C + b * C + c]\n // Since R is typically 4 and contiguous in outermost dimension, \n // we load values strided by B*C\n \n int base_offset = b * C + c; // offset within one rank\n int stride = B * C; // stride between ranks\n \n float vals[4];\n vals[0] = x[base_offset];\n vals[1] = x[base_offset + stride];\n vals[2] = x[base_offset + stride * 2];\n vals[3] = x[base_offset + stride * 3];\n \n // Find max with smallest index on ties\n float best_val = vals[0];\n int best_idx = 0;\n \n #pragma unroll\n for (int r = 1; r < 4; r++) {\n if (vals[r] > best_val) {\n best_val = vals[r];\n best_idx = r;\n }\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int R = x.size(0);\n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n R, B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=0.00e+00 mean_abs_err=0.00e+00 max_rel_err=0.00e+00
turn 626.8s turn · 7.6s LLM · 19.2s tools · tokens in=6,875 · out=862 · total=7,737
reasoning
Correctness passes. Let me profile this version to see if it improved.
call → profile_kernel
callprofile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int R, int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n // Load all R values for this (b, c) position\n // x[r][b][c] = x[r * B * C + b * C + c]\n // Since R is typically 4 and contiguous in outermost dimension, \n // we load values strided by B*C\n \n int base_offset = b * C + c; // offset within one rank\n int stride = B * C; // stride between ranks\n \n float vals[4];\n vals[0] = x[base_offset];\n vals[1] = x[base_offset + stride];\n vals[2] = x[base_offset + stride * 2];\n vals[3] = x[base_offset + stride * 3];\n \n // Find max with smallest index on ties\n float best_val = vals[0];\n int best_idx = 0;\n \n #pragma unroll\n for (int r = 1; r < 4; r++) {\n if (vals[r] > best_val) {\n best_val = vals[r];\n best_idx = r;\n }\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int R = x.size(0);\n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n R, B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty 40.0μs (100%) calls=1 --- Timing --- GPU time: 3.10 μs [↓1.0μs ok] --- Memory Bandwidth --- DRAM BW: 2.1/3350 GB/s (0.1%) [↓0.0% REGRESSED] read=2.1 write=0.0 GB/s Hit rates: L2=97.6% --- Compute Throughput --- Pipe util: FMA=1.1%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 11.6% [↑1.3% ok] Eligible warps/cycle: 0.04 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=16, smem/blk=1024B, block=256, grid=1 --- Memory Access Quality --- Global ld coalescing: 4.00 sectors/req (4.0x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 2409.7% #################### short_scoreboard 130.1% #################### --- Optimization Hints --- -> 2410% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=4.0 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=4.0x (ideal=1.0) -> 4x wasted DRAM BW. Make per-warp accesses contiguous. -> Low occupancy (12%). Consider __launch_bounds__ or reducing register pressure. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching). --- Delta vs Previous Iteration --- GPU time: 4.13→3.10μs (↓1.02) ok DRAM BW%: 0.07→0.06% (↓0.01) REGRESSED Occupancy: 10.31→11.64% (↑1.32) ok L2 hit%: 98.37→97.56% (↓0.80) REGRESSED
turn 7 · 1 tool call(s) · 90.0s turn · 13.2s LLM · tokens in=8,297 · out=1,352 · total=9,649 · 6,293 chars (click to expand)
turn 790.0s turn · 13.2s LLM · 76.8s tools · tokens in=8,297 · out=1,352 · total=9,649
reasoning
The kernel is slightly faster (4.13 -> 3.10 us). The coalescing issue remains because we're reading values that are B*C apart. However, for such a small problem size, the overhead of kernel launch dominates. Let me try a different approach - using a single thread to handle everything since B*C = 224 is tiny. Actually that won't be faster. Let me try to improve memory access by reorganizing how we read the data. The issue is that threads in a warp access different (b, c) positions, so they access strided memory. Actually, the problem is fundamental - for small problem sizes like 224 elements, the overhead of CUDA kernels dominates. But we need to be faster than PyTorch which has even more overhead. Let me try a different approach - use float4 to load values for all 4 ranks at once if possible. The data layout is (R, B, C), so for a fixed (b, c), values across R are strided by B*C. This isn't contiguous. However, let me think about this differently. The coalescing hint says 4 sectors per request, which means we're accessing memory in a suboptimal pattern. Each warp of 32 threads accesses 32 different (b, c) positions, so 32 * 4 = 128 floats spread across the input. Let me try using shared memory to prefetch and reorganize the data, which might help with coalescing. Or better, let me try a block-level approach where each block handles a subset of (b, c) and uses shared memory. Actually, for such a tiny problem (224 elements), a better approach might be to have fewer threads with more work per thread. Let me try having each thread handle multiple (b, c) positions to increase the work per thread and hide latency. Actually, the simplest optimization is to reduce block size to maximize occupancy. With 224 total threads, using 256 threads per block means only 1 block. If we use 32 threads per block, we get 7 blocks which might help a bit. Let me try a different strategy - process multiple elements per thread:
assistantThe kernel is still latency-bound due to the tiny problem size (224 elements). Let me try processing multiple elements per thread to hide latency better:
call → compile_kernel
callcompile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\ntemplate<int VEC_SIZE>\n__global__ void max_over_ranks_kernel_vec(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles VEC_SIZE consecutive (b, c) positions\n int tid = blockIdx.x * blockDim.x + threadIdx.x;\n int start_bc = tid * VEC_SIZE;\n \n if (start_bc >= B * C) return;\n \n int end_bc = min(start_bc + VEC_SIZE, B * C);\n int stride = B * C;\n \n for (int bc_idx = start_bc; bc_idx < end_bc; bc_idx++) {\n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int base_offset = b * C + c;\n \n // Load all R values\n float vals[4];\n vals[0] = x[base_offset];\n vals[1] = x[base_offset + stride];\n vals[2] = x[base_offset + stride * 2];\n vals[3] = x[base_offset + stride * 3];\n \n // Find max with smallest index on ties\n float best_val = vals[0];\n int best_idx = 0;\n \n #pragma unroll\n for (int r = 1; r < 4; r++) {\n if (vals[r] > best_val) {\n best_val = vals[r];\n best_idx = r;\n }\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n }\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n const int VEC_SIZE = 4; // Each thread handles 4 elements\n int total_threads = (B * C + VEC_SIZE - 1) / VEC_SIZE;\n int threads_per_block = 64; // Smaller block for better occupancy\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel_vec<VEC_SIZE><<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 87.4s turn · 7.4s LLM · 0.0s tools · tokens in=9,210 · out=876 · total=10,086
reasoning
Let me test correctness.
call → run_correctness
callrun_correctness { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\ntemplate<int VEC_SIZE>\n__global__ void max_over_ranks_kernel_vec(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles VEC_SIZE consecutive (b, c) positions\n int tid = blockIdx.x * blockDim.x + threadIdx.x;\n int start_bc = tid * VEC_SIZE;\n \n if (start_bc >= B * C) return;\n \n int end_bc = min(start_bc + VEC_SIZE, B * C);\n int stride = B * C;\n \n for (int bc_idx = start_bc; bc_idx < end_bc; bc_idx++) {\n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int base_offset = b * C + c;\n \n // Load all R values\n float vals[4];\n vals[0] = x[base_offset];\n vals[1] = x[base_offset + stride];\n vals[2] = x[base_offset + stride * 2];\n vals[3] = x[base_offset + stride * 3];\n \n // Find max with smallest index on ties\n float best_val = vals[0];\n int best_idx = 0;\n \n #pragma unroll\n for (int r = 1; r < 4; r++) {\n if (vals[r] > best_val) {\n best_val = vals[r];\n best_idx = r;\n }\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n }\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n const int VEC_SIZE = 4; // Each thread handles 4 elements\n int total_threads = (B * C + VEC_SIZE - 1) / VEC_SIZE;\n int threads_per_block = 64; // Smaller block for better occupancy\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel_vec<VEC_SIZE><<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=0.00e+00 mean_abs_err=0.00e+00 max_rel_err=0.00e+00
turn 920.8s turn · 7.6s LLM · 13.2s tools · tokens in=10,138 · out=884 · total=11,022
reasoning
The kernel works. Let me profile it to see if performance improved.
call → profile_kernel
callprofile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\ntemplate<int VEC_SIZE>\n__global__ void max_over_ranks_kernel_vec(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles VEC_SIZE consecutive (b, c) positions\n int tid = blockIdx.x * blockDim.x + threadIdx.x;\n int start_bc = tid * VEC_SIZE;\n \n if (start_bc >= B * C) return;\n \n int end_bc = min(start_bc + VEC_SIZE, B * C);\n int stride = B * C;\n \n for (int bc_idx = start_bc; bc_idx < end_bc; bc_idx++) {\n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int base_offset = b * C + c;\n \n // Load all R values\n float vals[4];\n vals[0] = x[base_offset];\n vals[1] = x[base_offset + stride];\n vals[2] = x[base_offset + stride * 2];\n vals[3] = x[base_offset + stride * 3];\n \n // Find max with smallest index on ties\n float best_val = vals[0];\n int best_idx = 0;\n \n #pragma unroll\n for (int r = 1; r < 4; r++) {\n if (vals[r] > best_val) {\n best_val = vals[r];\n best_idx = r;\n }\n }\n \n // Output is (B, C, 2)\n int out_base = b * C * 2 + c * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n }\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n const int VEC_SIZE = 4; // Each thread handles 4 elements\n int total_threads = (B * C + VEC_SIZE - 1) / VEC_SIZE;\n int threads_per_block = 64; // Smaller block for better occupancy\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel_vec<VEC_SIZE><<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty 41.0μs (100%) calls=1 --- Timing --- GPU time: 3.26 μs [↑0.2μs REGRESSED] --- Memory Bandwidth --- DRAM BW: 2.7/3350 GB/s (0.1%) [↑0.0% ok] read=2.7 write=0.0 GB/s Hit rates: L2=98.8% --- Compute Throughput --- Pipe util: FMA=0.5%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 3.1% [↓8.5% REGRESSED] Eligible warps/cycle: 0.04 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=32, smem/blk=1024B, block=64, grid=1 --- Memory Access Quality --- Global ld coalescing: 14.00 sectors/req (14.0x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 752.6% #################### short_scoreboard 303.9% #################### --- Optimization Hints --- -> 753% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=14.0 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=14.0x (ideal=1.0) -> 14x wasted DRAM BW. Make per-warp accesses contiguous. -> Low occupancy (3%) limited by small block (64). Consider __launch_bounds__ or reducing register pressure. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching). --- Delta vs Previous Iteration --- GPU time: 3.10→3.26μs (↑0.16) REGRESSED DRAM BW%: 0.06→0.08% (↑0.02) ok Occupancy: 11.64→3.10% (↓8.54) REGRESSED Ld sectors/req: 4.00→14.00 (↑10.00) REGRESSED L2 hit%: 97.56→98.80% (↑1.23) ok
turn 1088.4s turn · 12.4s LLM · 76.0s tools · tokens in=11,614 · out=1,288 · total=12,902
reasoning
That made it worse - occupancy dropped to 3% and coalescing got much worse. The issue is the small block size and the strided access pattern. Let me try a different approach - use float4 to load contiguous values, and transpose the problem. Actually, the key insight is: - x has shape (R, B, C) = (4, 8, 28) - Total elements = 896 floats - We need 224 outputs The memory layout is: x[0][0][0], x[0][0][1], ..., x[0][0][27], x[0][1][0], ..., x[0][7][27], x[1][0][0], ... So for each (b, c), the R values are at positions: - r=0: b*C + c - r=1: B*C + b*C + c - r=2: 2*B*C + b*C + c - r=3: 3*B*C + b*C + c The stride between consecutive ranks is B*C = 224 floats = 896 bytes. For coalescing, threads in a warp should access consecutive memory. If thread t handles bc_idx = t, then: - Thread 0 accesses offset 0 (for r=0) - Thread 1 accesses offset 1 (for r=0) - ... - Thread 31 accesses offset 31 (for r=0) That's actually coalesced! The issue is that the next load (for r=1) jumps to offset 224, 225, ..., 255 which are also coalesced. So the problem isn't coalescing per se - the problem is the strided accesses mean we can't use L1 cache efficiently. Let me try loading all 4 values at once using a custom structure or just optimizing the kernel differently. Actually, for small problems like this, the overhead of kernel launch might dominate. Let me try a different approach: use CUDA's __ldg intrinsic for read-only cache, and ensure we have enough threads. Actually, let me just try a simpler optimization - keep the 256 threads per block but use launch_bounds to help the compiler:
assistantLet me try a simpler approach - focus on better memory access with float4 loads where possible:
call → compile_kernel
callcompile_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void __launch_bounds__(256) max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int stride = B * C;\n int base_offset = b * C + c;\n \n // Load all R=4 values using __ldg for read-only cache\n float v0 = __ldg(&x[base_offset]);\n float v1 = __ldg(&x[base_offset + stride]);\n float v2 = __ldg(&x[base_offset + stride * 2]);\n float v3 = __ldg(&x[base_offset + stride * 3]);\n \n // Find max with smallest index on ties\n float best_val = v0;\n int best_idx = 0;\n \n if (v1 > best_val) { best_val = v1; best_idx = 1; }\n if (v2 > best_val) { best_val = v2; best_idx = 2; }\n if (v3 > best_val) { best_val = v3; best_idx = 3; }\n \n // Output is (B, C, 2)\n int out_base = bc_idx * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v4',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 117.5s turn · 7.5s LLM · 0.0s tools · tokens in=12,448 · out=812 · total=13,260
reasoning
Let me check correctness and profile this version.
call → run_correctness
callrun_correctness { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void __launch_bounds__(256) max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int stride = B * C;\n int base_offset = b * C + c;\n \n // Load all R=4 values using __ldg for read-only cache\n float v0 = __ldg(&x[base_offset]);\n float v1 = __ldg(&x[base_offset + stride]);\n float v2 = __ldg(&x[base_offset + stride * 2]);\n float v3 = __ldg(&x[base_offset + stride * 3]);\n \n // Find max with smallest index on ties\n float best_val = v0;\n int best_idx = 0;\n \n if (v1 > best_val) { best_val = v1; best_idx = 1; }\n if (v2 > best_val) { best_val = v2; best_idx = 2; }\n if (v3 > best_val) { best_val = v3; best_idx = 3; }\n \n // Output is (B, C, 2)\n int out_base = bc_idx * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v4',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=0.00e+00 mean_abs_err=0.00e+00 max_rel_err=0.00e+00
turn 127.4s turn · 7.4s LLM · 0.0s tools · tokens in=13,340 · out=818 · total=14,158
reasoning
The kernel is correct. Let me check the static analysis and then submit it.
call → static_check
callstatic_check { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void __launch_bounds__(256) max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int stride = B * C;\n int base_offset = b * C + c;\n \n // Load all R=4 values using __ldg for read-only cache\n float v0 = __ldg(&x[base_offset]);\n float v1 = __ldg(&x[base_offset + stride]);\n float v2 = __ldg(&x[base_offset + stride * 2]);\n float v3 = __ldg(&x[base_offset + stride * 3]);\n \n // Find max with smallest index on ties\n float best_val = v0;\n int best_idx = 0;\n \n if (v1 > best_val) { best_val = v1; best_idx = 1; }\n if (v2 > best_val) { best_val = v2; best_idx = 2; }\n if (v3 > best_val) { best_val = v3; best_idx = 3; }\n \n // Output is (B, C, 2)\n int out_base = bc_idx * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v4',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← static_check (ok)
okstatic_check static_check PASSED: no violations or warnings detected.
turn 1319.8s turn · 7.3s LLM · 12.5s tools · tokens in=14,188 · out=820 · total=15,008 · FINAL
reasoning
The kernel is correct, passes static check, and is optimized. Let me submit it.
call → submit_kernel
callsubmit_kernel { "kernel_code": "\"\"\"\nOver virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.\n\nOutput (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.\n\"\"\"\n\nimport torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\nimport os\n\nR = 4\nB = 8\nC = 28\n\n# Compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void __launch_bounds__(256) max_over_ranks_kernel(\n const float* __restrict__ x,\n float* __restrict__ output,\n int B, int C) {\n \n // Each thread handles one (b, c) position\n int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (bc_idx >= B * C) return;\n \n int b = bc_idx / C;\n int c = bc_idx % C;\n \n int stride = B * C;\n int base_offset = b * C + c;\n \n // Load all R=4 values using __ldg for read-only cache\n float v0 = __ldg(&x[base_offset]);\n float v1 = __ldg(&x[base_offset + stride]);\n float v2 = __ldg(&x[base_offset + stride * 2]);\n float v3 = __ldg(&x[base_offset + stride * 3]);\n \n // Find max with smallest index on ties\n float best_val = v0;\n int best_idx = 0;\n \n if (v1 > best_val) { best_val = v1; best_idx = 1; }\n if (v2 > best_val) { best_val = v2; best_idx = 2; }\n if (v3 > best_val) { best_val = v3; best_idx = 3; }\n \n // Output is (B, C, 2)\n int out_base = bc_idx * 2;\n output[out_base + 0] = best_val;\n output[out_base + 1] = (float)best_idx;\n}\n\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x) {\n TORCH_CHECK(x.dim() == 3, \"Input must be 3D\");\n TORCH_CHECK(x.scalar_type() == torch::kFloat32, \"Input must be float\");\n TORCH_CHECK(x.size(0) == 4, \"R dimension must be 4\");\n \n int B = x.size(1);\n int C = x.size(2);\n \n auto output = torch::empty({B, C, 2}, x.options());\n \n int total_threads = B * C;\n int threads_per_block = 256;\n int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;\n \n max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(\n x.data_ptr<float>(),\n output.data_ptr<float>(),\n B, C\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor max_over_ranks_cuda(torch::Tensor x);\n\"\"\"\n\nmodule = load_inline(\n name='max_over_ranks_ext_v4',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['max_over_ranks_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=True\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n\n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.max_over_ranks_cuda(x)" }
result ← submit_kernel (ok)
oksubmit_kernel submit_kernel PASSED: (3 / 3) correctness trials all passed. Kernel runtime: 0.01 μs Runtime stats: mean=0.01μs median=?μs std=0.00μs Numerical precision: max_abs_err=0.00e+00 mean_abs_err=0.00e+00 max_rel_err=0.00e+00 Memory: 33.01 MB peak (ref: 33.01 MB, ratio: 0.9998x) Kernel launches: 1 (ref: 94, fusion ratio: 94.0) SOL score: 0.0006 Flagged for excessive speedup — this submission may have been rejected by automated review.
final submitted kernel (101 lines, 2,667 chars) — full source, untruncated
"""
Over virtual ranks R, for each (B, C) position take the maximum value; on ties choose the smallest rank index.

Output (B, C, 2): [:,:,0] = best value, [:,:,1] = winning rank as float32.
"""

import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
import os

R = 4
B = 8
C = 28

# Compile the CUDA kernel
cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>

__global__ void __launch_bounds__(256) max_over_ranks_kernel(
    const float* __restrict__ x,
    float* __restrict__ output,
    int B, int C) {
    
    // Each thread handles one (b, c) position
    int bc_idx = blockIdx.x * blockDim.x + threadIdx.x;
    
    if (bc_idx >= B * C) return;
    
    int b = bc_idx / C;
    int c = bc_idx % C;
    
    int stride = B * C;
    int base_offset = b * C + c;
    
    // Load all R=4 values using __ldg for read-only cache
    float v0 = __ldg(&x[base_offset]);
    float v1 = __ldg(&x[base_offset + stride]);
    float v2 = __ldg(&x[base_offset + stride * 2]);
    float v3 = __ldg(&x[base_offset + stride * 3]);
    
    // Find max with smallest index on ties
    float best_val = v0;
    int best_idx = 0;
    
    if (v1 > best_val) { best_val = v1; best_idx = 1; }
    if (v2 > best_val) { best_val = v2; best_idx = 2; }
    if (v3 > best_val) { best_val = v3; best_idx = 3; }
    
    // Output is (B, C, 2)
    int out_base = bc_idx * 2;
    output[out_base + 0] = best_val;
    output[out_base + 1] = (float)best_idx;
}

torch::Tensor max_over_ranks_cuda(torch::Tensor x) {
    TORCH_CHECK(x.dim() == 3, "Input must be 3D");
    TORCH_CHECK(x.scalar_type() == torch::kFloat32, "Input must be float");
    TORCH_CHECK(x.size(0) == 4, "R dimension must be 4");
    
    int B = x.size(1);
    int C = x.size(2);
    
    auto output = torch::empty({B, C, 2}, x.options());
    
    int total_threads = B * C;
    int threads_per_block = 256;
    int num_blocks = (total_threads + threads_per_block - 1) / threads_per_block;
    
    max_over_ranks_kernel<<<num_blocks, threads_per_block>>>(
        x.data_ptr<float>(),
        output.data_ptr<float>(),
        B, C
    );
    
    return output;
}
"""

cpp_source = """
torch::Tensor max_over_ranks_cuda(torch::Tensor x);
"""

module = load_inline(
    name='max_over_ranks_ext_v4',
    cpp_sources=cpp_source,
    cuda_sources=cuda_source,
    functions=['max_over_ranks_cuda'],
    extra_cuda_cflags=['-O3', '-use_fast_math'],
    verbose=True
)


class ModelNew(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return module.max_over_ranks_cuda(x)