correct
19_PairwiseDistanceMatrix.py
started
2026-05-11T11:59:46Z
timingkernelbench.timing
kernel mean / median / std
0.01 / — / 0.00 μs
ref mean / median / std
0.08 / — / 0.00 μs
numerical precisioneval_kernel_against_ref
gpu memoryextended_metrics.measure_memory
kernel launches / fusiontorch.profiler
fusion ratio (ref / kernel)
12.00x
SOL (speed-of-light)nsight_hardware_counters
roofline / occupancynsight_hardware_counters
dram bandwidth
619.85 GB/s
warp stalls (top 5)nsight
reference PyTorch source (the prompt the agent sees)
import torch
import torch.nn as nn
class Model(nn.Module):
"""
Compute all-pairs Euclidean distance matrix from a 3-D point cloud.
A core primitive in molecular dynamics simulations, docking, and
distance-geometry-based structure prediction.
"""
def __init__(self):
super().__init__()
def forward(self, coords: torch.Tensor) -> torch.Tensor:
"""
Args:
coords: (B, N, 3) – 3-D coordinates of N atoms / residues
Returns:
dist: (B, N, N) – pairwise Euclidean distance matrix
"""
diff = coords.unsqueeze(2) - coords.unsqueeze(1) # (B, N, N, 3)
dist = torch.sqrt((diff ** 2).sum(dim=-1) + 1e-8)
return dist
num_atoms = 512
batch_size = 8
def get_inputs():
p = popcorn_pri
return [torch.randn(p.jitter_int(batch_size), p.jitter_int(num_atoms), 3)]
def get_init_inputs():
return []
turn 0276.7s turn · 2.6s LLM · 274.0s tools · tokens in=1,460 · out=174 · total=1,634
reasoning
Let me understand the task:
1. I need to replace a PyTorch model that computes all-pairs Euclidean distance matrix from a 3-D point cloud
2. The input is `coords: (B, N, 3)` and output is `dist: (B, N, N)` - pairwise Euclidean distance matrix
3. The computation is:
- `diff = coords.unsqueeze(2) - coords.unsqueeze(1)` -> (B, N, N, 3)
- `dist = torch.sqrt((diff ** 2).sum(dim=-1) + 1e-8)` -> (B, N, N)
So for each batch element, we compute all pairwise distances between N points in 3D space.
Let me first get GPU specs to understand the hardware.
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 1 · 1 tool call(s) · 452.6s turn · 19.8s LLM · tokens in=1,708 · out=1,921 · total=3,629 · 7,888 chars (click to expand)
turn 1452.6s turn · 19.8s LLM · 432.9s tools · tokens in=1,708 · out=1,921 · total=3,629
reasoning
Now let me understand the problem:
- Input: coords of shape (B, N, 3) where B=8, N=512
- Output: dist of shape (B, N, N) - pairwise Euclidean distance matrix
For each batch element, we compute:
dist[i, j] = sqrt((coords[i] - coords[j])^2) for all i, j
This is essentially computing sqrt(sum_k(x_ik - x_jk)^2 + eps) for all pairs (i, j).
A naive approach would have O(N^2 * B) threads, each computing one distance.
Let me write an optimized kernel:
- Each thread block handles one batch element
- Within a block, we compute all pairwise distances for that batch
- We can use shared memory to load the coordinates once and reuse them
Actually, for B=8 batch elements, we could:
1. Have each block handle one batch element
2. Within each block, have threads compute different (i,j) pairs
Since N=512, we have 512*512 = 262144 pairs per batch. With a block of 1024 threads, we need 256 blocks per batch element. Total blocks = 8 * 256 = 2048.
But wait, on H100 with 132 SMs, we can run many blocks in parallel.
Let me think about memory access:
- Each pair (i,j) needs coords[i] and coords[j] (3 floats each)
- We can load coords into shared memory to avoid repeated global memory access
Strategy:
1. Each thread handles one (i, j) pair
2. Load the entire coord matrix for a batch into shared memory (512 * 3 * 4 = 6144 bytes, very small)
3. Each thread reads from shared memory
Actually, let me reconsider. With 512 atoms and 3 coordinates, we need 512 * 3 * 4 = 6144 bytes in shared memory per batch. That's tiny!
We could:
- One thread block per batch element
- 512*512 = 262144 threads needed
- But max threads per block is 1024
So we need multiple blocks per batch element. Let me think...
Alternative approach:
- Each thread handles multiple (i,j) pairs
- Grid stride loop pattern
Or we could:
- Each block handles one row of the output (one value of i)
- 512 threads per block, each computing dist[i, j] for a different j
- 512 blocks per batch element
With this approach:
- Load coords[i] into registers (or shared as a single vector)
- Load all coords into shared memory
- Each thread j computes dist[i, j]
Let me try this approach:
Block configuration:
- Grid: (N, B) = (512, 8) blocks
- Block: N = 512 threads
Wait, actually we need to be careful. If we have 512 blocks per batch and 8 batches, that's 4096 blocks total. That's fine.
But we also need to consider that each block will need the full coords array for that batch in shared memory.
Let me write the kernel:
```cuda
__global__ void distance_kernel(const float* __restrict__ coords, float* __restrict__ dist, int N, int B) {
int i = blockIdx.x; // which row (i value)
int b = blockIdx.y; // which batch
int j = threadIdx.x; // which column (j value)
// Each block handles row i of batch b
// Shared memory for coordinates
extern __shared__ float shared_coords[]; // N * 3 floats
// Cooperative load of coordinates into shared memory
for (int k = threadIdx.x; k < N * 3; k += blockDim.x) {
shared_coords[k] = coords[b * N * 3 + k];
}
__syncthreads();
// Now compute distance
float xi = shared_coords[i * 3 + 0];
float yi = shared_coords[i * 3 + 1];
float zi = shared_coords[i * 3 + 2];
float xj = shared_coords[j * 3 + 0];
float yj = shared_coords[j * 3 + 1];
float zj = shared_coords[j * 3 + 2];
float dx = xi - xj;
float dy = yi - yj;
float dz = zi - zj;
float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);
// Write result
dist[b * N * N + i * N + j] = dist_val;
}
```
This should work! Let me refine it.
Shared memory: N * 3 * 4 = 6144 bytes per block, very small.
Block size: 512 threads (covers all j values for one i)
Grid size: (N, B) = (512, 8) blocks
Total threads: 512 * 512 * 8 = 2,097,152
Let me implement this in Python:
assistantLooking at this problem:
- Input: coords (B, N, 3) where B=8, N=512
- Output: dist (B, N, N) - pairwise Euclidean distance matrix
- Each element dist[b,i,j] = sqrt(sum_k(coords[b,i,k] - coords[b,j,k])^2 + eps)
Key optimization opportunities:
1. Load coordinates into shared memory for reuse
2. One block per row (i value), 512 threads for j values
3. Each thread computes one distance value
Let me write and test the kernel:
call → compile_kernel
callcompile_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Define the CUDA kernel\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n__global__ void distance_kernel(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which row (i value), 0 to N-1\n // blockIdx.y: which batch, 0 to B-1 \n // threadIdx.x: which column (j value), 0 to N-1\n \n int i = blockIdx.x;\n int b = blockIdx.y;\n int j = threadIdx.x;\n \n // Shared memory for coordinates of this batch\n extern __shared__ float shared_coords[]; // N * 3 floats\n \n // Cooperative load of coordinates into shared memory\n int tid = threadIdx.x;\n int total = N * 3;\n for (int k = tid; k < total; k += blockDim.x) {\n shared_coords[k] = coords[b * total + k];\n }\n __syncthreads();\n \n // Load coords[i] into registers\n float xi = shared_coords[i * 3 + 0];\n float yi = shared_coords[i * 3 + 1];\n float zi = shared_coords[i * 3 + 2];\n \n // Load coords[j] - could be from shared memory or compute directly\n float xj = shared_coords[j * 3 + 0];\n float yj = shared_coords[j * 3 + 1];\n float zj = shared_coords[j * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n dist[b * N * N + i * N + j] = dist_val;\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n dim3 grid(N, B); // N blocks for rows, B blocks for batches\n dim3 block(N); // N threads per block (one per column)\n \n size_t shared_mem_size = N * 3 * sizeof(float);\n \n distance_kernel<<<grid, block, shared_mem_size>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← compile_kernel (ok)
okcompile_kernel
compile_kernel PASSED: kernel compiled without errors.
turn 2190.4s turn · 6.2s LLM · 184.1s tools · tokens in=2,543 · out=716 · total=3,259
reasoning
Good, the kernel compiled. Let me run the correctness check.
call → run_correctness
callrun_correctness
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Define the CUDA kernel\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n__global__ void distance_kernel(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which row (i value), 0 to N-1\n // blockIdx.y: which batch, 0 to B-1 \n // threadIdx.x: which column (j value), 0 to N-1\n \n int i = blockIdx.x;\n int b = blockIdx.y;\n int j = threadIdx.x;\n \n // Shared memory for coordinates of this batch\n extern __shared__ float shared_coords[]; // N * 3 floats\n \n // Cooperative load of coordinates into shared memory\n int tid = threadIdx.x;\n int total = N * 3;\n for (int k = tid; k < total; k += blockDim.x) {\n shared_coords[k] = coords[b * total + k];\n }\n __syncthreads();\n \n // Load coords[i] into registers\n float xi = shared_coords[i * 3 + 0];\n float yi = shared_coords[i * 3 + 1];\n float zi = shared_coords[i * 3 + 2];\n \n // Load coords[j] - could be from shared memory or compute directly\n float xj = shared_coords[j * 3 + 0];\n float yj = shared_coords[j * 3 + 1];\n float zj = shared_coords[j * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n dist[b * N * N + i * N + j] = dist_val;\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n dim3 grid(N, B); // N blocks for rows, B blocks for batches\n dim3 block(N); // N threads per block (one per column)\n \n size_t shared_mem_size = N * 3 * sizeof(float);\n \n distance_kernel<<<grid, block, shared_mem_size>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← run_correctness (ok)
okrun_correctness
run_correctness PASSED: (5 / 5) trials all matched the reference.
Numerical precision: max_abs_err=4.77e-07 mean_abs_err=2.82e-08 max_rel_err=1.65e-07
turn 3 · 1 tool call(s) · 263.0s turn · 14.0s LLM · tokens in=3,303 · out=1,363 · total=4,666 · 6,320 chars (click to expand)
turn 3263.0s turn · 14.0s LLM · 249.0s tools · tokens in=3,303 · out=1,363 · total=4,666
reasoning
The correctness test passed. The kernel produces numerically equivalent outputs.
Now let me think about optimizations to improve performance:
1. **Shared memory**: Already using shared memory to load all coordinates for a batch
2. **Memory access pattern**: The current approach has good shared memory access for loading coordinates
3. **Thread coarsening**: Could compute multiple j values per thread to amortize overhead
4. **Vectorized loads**: Could use float4 or float3 to load coordinates more efficiently
5. **Restrict qualifier**: Already using __restrict__
6. **Block size**: Using 512 threads per block, which is good for H100
Let me try a few optimizations:
1. Use vectorized loads (float4 for better memory coalescing, though we have 3 floats per point)
2. Try using multiple threads per row or coarsening
3. Consider using block for both dimensions of the output matrix differently
Actually, let me think more carefully about the current approach:
- We have N=512 atoms per batch
- Each block handles one row (i) of one batch
- 512 threads per block, each computing one distance dist[i,j]
The shared memory usage is N*3*4 = 512*12 = 6144 bytes per block, well within the 227KB limit.
One issue: loading coords[j] from shared memory for each thread - but since each thread has a different j, this is scattered access. However, since we're loading x,y,z sequentially from the same j, we have good locality.
Let me try a different approach - tiled computation where threads cooperate more:
- Each block handles a TILE of the output matrix
- Threads load tiles of coordinates into shared memory
- This can reduce redundant loads
But for now, let me try simpler optimizations first:
1. Use float3 or vectorized loads where possible
2. Ensure we're using the right number of threads (256 might be better than 512)
Let me try with 256 threads per block and have each thread compute 2 output elements:
assistantLet me optimize the kernel further. I'll try using vectorized loads and adjusting the thread/block configuration:
call → compile_kernel
callcompile_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Optimized CUDA kernel with float4 vectorized loads and 256-thread blocks\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n__global__ void distance_kernel(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which row (i value), 0 to N-1\n // blockIdx.y: which batch, 0 to B-1 \n // threadIdx.x: which column base (j value), 0 to N/2-1, each thread computes 2 outputs\n \n int i = blockIdx.x;\n int b = blockIdx.y;\n int tid = threadIdx.x;\n int j0 = tid;\n int j1 = tid + blockDim.x; // Second element per thread\n \n // Shared memory for coordinates of this batch\n extern __shared__ float shared_coords[]; // N * 3 floats\n \n // Cooperative load of coordinates into shared memory using float4\n const float4* coords4 = reinterpret_cast<const float4*>(coords + b * N * 3);\n float4* shared4 = reinterpret_cast<float4*>(shared_coords);\n \n int num_float4 = (N * 3 + 3) / 4; // Number of float4 elements needed\n for (int k = tid; k < num_float4; k += blockDim.x) {\n shared4[k] = coords4[k];\n }\n __syncthreads();\n \n // Load coords[i] into registers\n float xi = shared_coords[i * 3 + 0];\n float yi = shared_coords[i * 3 + 1];\n float zi = shared_coords[i * 3 + 2];\n \n // Compute first distance (j0)\n {\n float xj = shared_coords[j0 * 3 + 0];\n float yj = shared_coords[j0 * 3 + 1];\n float zj = shared_coords[j0 * 3 + 2];\n \n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n dist[b * N * N + i * N + j0] = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n }\n \n // Compute second distance (j1)\n {\n float xj = shared_coords[j1 * 3 + 0];\n float yj = shared_coords[j1 * 3 + 1];\n float zj = shared_coords[j1 * 3 + 2];\n \n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n dist[b * N * N + i * N + j1] = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n dim3 grid(N, B); // N blocks for rows, B blocks for batches\n dim3 block(N / 2); // N/2 threads per block, each computes 2 outputs\n \n size_t shared_mem_size = N * 3 * sizeof(float);\n \n distance_kernel<<<grid, block, shared_mem_size>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← compile_kernel (ok)
okcompile_kernel
compile_kernel PASSED: kernel compiled without errors.
turn 4619.9s turn · 9.5s LLM · 610.5s tools · tokens in=4,253 · out=958 · total=5,211
reasoning
Wait, I realize there's a potential issue - if N is not evenly divisible by 2, my second element computation could be out of bounds. Let me check correctness first, then optimize if needed.
call → run_correctness
callrun_correctness
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Optimized CUDA kernel with float4 vectorized loads and 256-thread blocks\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n__global__ void distance_kernel(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which row (i value), 0 to N-1\n // blockIdx.y: which batch, 0 to B-1 \n // threadIdx.x: which column base (j value), 0 to N/2-1, each thread computes 2 outputs\n \n int i = blockIdx.x;\n int b = blockIdx.y;\n int tid = threadIdx.x;\n int j0 = tid;\n int j1 = tid + blockDim.x; // Second element per thread\n \n // Shared memory for coordinates of this batch\n extern __shared__ float shared_coords[]; // N * 3 floats\n \n // Cooperative load of coordinates into shared memory using float4\n const float4* coords4 = reinterpret_cast<const float4*>(coords + b * N * 3);\n float4* shared4 = reinterpret_cast<float4*>(shared_coords);\n \n int num_float4 = (N * 3 + 3) / 4; // Number of float4 elements needed\n for (int k = tid; k < num_float4; k += blockDim.x) {\n shared4[k] = coords4[k];\n }\n __syncthreads();\n \n // Load coords[i] into registers\n float xi = shared_coords[i * 3 + 0];\n float yi = shared_coords[i * 3 + 1];\n float zi = shared_coords[i * 3 + 2];\n \n // Compute first distance (j0)\n {\n float xj = shared_coords[j0 * 3 + 0];\n float yj = shared_coords[j0 * 3 + 1];\n float zj = shared_coords[j0 * 3 + 2];\n \n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n dist[b * N * N + i * N + j0] = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n }\n \n // Compute second distance (j1)\n {\n float xj = shared_coords[j1 * 3 + 0];\n float yj = shared_coords[j1 * 3 + 1];\n float zj = shared_coords[j1 * 3 + 2];\n \n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n dist[b * N * N + i * N + j1] = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n dim3 grid(N, B); // N blocks for rows, B blocks for batches\n dim3 block(N / 2); // N/2 threads per block, each computes 2 outputs\n \n size_t shared_mem_size = N * 3 * sizeof(float);\n \n distance_kernel<<<grid, block, shared_mem_size>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← run_correctness (ok)
okrun_correctness
run_correctness PASSED: (5 / 5) trials all matched the reference.
Numerical precision: max_abs_err=4.77e-07 mean_abs_err=2.82e-08 max_rel_err=1.65e-07
turn 5 · 1 tool call(s) · 602.6s turn · 16.2s LLM · tokens in=5,227 · out=1,604 · total=6,831 · 6,986 chars (click to expand)
turn 5602.6s turn · 16.2s LLM · 586.4s tools · tokens in=5,227 · out=1,604 · total=6,831
reasoning
Good, the vectorized version also passes correctness. Let me now think about the memory access patterns and optimizations more carefully.
The output matrix is (B, N, N) = (8, 512, 512) = 8 * 512 * 512 * 4 = 8 MB per batch
Current approach: each block handles one row of the output matrix, with N/2 threads each computing 2 values.
Memory access pattern for output: each thread writes 2 values to adjacent addresses in the same row - this should be coalesced since threads with consecutive IDs write to consecutive addresses.
However, I'm using shared memory extensively which might be good for reusing input data, but the shared memory usage is 512 * 3 * 4 = 6144 bytes per block, which fits easily.
Let me try an alternative approach that might be faster:
1. Use larger thread blocks with more cooperative work
2. Optimize for memory bandwidth by using float4 stores
Actually, let me reconsider the algorithm. The key insight is:
- For each (i, j) pair, we compute distance between coords[i] and coords[j]
- coords[i] and coords[j] each have 3 values
Since we're computing N*N distances per batch, and each distance computation involves:
- 6 loads (xi, yi, zi, xj, yj, zj) = 24 bytes from coords
- 6 FLOPs (3 subs, 3 muls, 2 adds, 1 sqrt) ≈ 12 FLOPs (sqrt is expensive)
- 4 bytes store to dist
Total data: 8 * 512 * 512 * (24 + 4) = 8 * 262144 * 28 = ~59 MB
Total FLOPs: 8 * 512 * 512 * ~15 = ~31 MFLOPs
This is memory-bound since 31 MFLOPs / 59 MB ≈ 0.5 FLOPs/byte, much less than the GPU's compute intensity.
Let me focus on memory bandwidth optimization. The shared memory approach should help because each coordinate is loaded once per block, rather than potentially multiple times.
But wait - in the current kernel, each coordinate value is loaded N times (once for each row i). The shared memory helps within a row but not across rows.
Let me think about a tiled approach where we load a tile of coordinates into shared memory and compute all pairs within that tile.
Actually, let me try a different approach: launch blocks where each block computes a tile of the output matrix, say 16x16 or 32x32. This way, we can reuse coordinate loads more effectively.
Let me try a 2D tiled approach:
assistantLet me try a tiled 2D block approach for better memory reuse:
call → compile_kernel
callcompile_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Tiled 2D block approach: each block computes a 16x16 tile of the output matrix\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n#define TILE_SIZE 32\n\n__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which tile column (j direction)\n // blockIdx.y: which tile row (i direction)\n // blockIdx.z: which batch\n \n int tile_i = blockIdx.y;\n int tile_j = blockIdx.x;\n int b = blockIdx.z;\n \n int tx = threadIdx.x; // 0 to TILE_SIZE-1\n int ty = threadIdx.y; // 0 to TILE_SIZE-1\n \n int i = tile_i * TILE_SIZE + ty; // Global row index\n int j = tile_j * TILE_SIZE + tx; // Global col index\n \n // Shared memory for the two tiles of coordinates\n // Tile_i coords: TILE_SIZE * 3 floats\n // Tile_j coords: TILE_SIZE * 3 floats\n __shared__ float s_coords_i[TILE_SIZE * 3];\n __shared__ float s_coords_j[TILE_SIZE * 3];\n \n // Cooperative load of tile_i coordinates\n // Each thread loads one float, we need TILE_SIZE*3 floats per tile\n int load_idx = ty * TILE_SIZE + tx; // Linear thread index\n \n // Load tile_i coordinates (the rows we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int row = load_idx / 3;\n int comp = load_idx % 3;\n int global_row = tile_i * TILE_SIZE + row;\n if (global_row < N) {\n s_coords_i[load_idx] = coords[b * N * 3 + global_row * 3 + comp];\n }\n }\n \n // Load tile_j coordinates (the columns we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int col = load_idx / 3;\n int comp = load_idx % 3;\n int global_col = tile_j * TILE_SIZE + col;\n if (global_col < N) {\n s_coords_j[load_idx] = coords[b * N * 3 + global_col * 3 + comp];\n }\n }\n \n __syncthreads();\n \n // Load the i-th coordinate into registers\n float xi = s_coords_i[ty * 3 + 0];\n float yi = s_coords_i[ty * 3 + 1];\n float zi = s_coords_i[ty * 3 + 2];\n \n // Load the j-th coordinate into registers\n float xj = s_coords_j[tx * 3 + 0];\n float yj = s_coords_j[tx * 3 + 1];\n float zj = s_coords_j[tx * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n if (i < N && j < N) {\n dist[b * N * N + i * N + j] = dist_val;\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;\n \n dim3 grid(num_tiles, num_tiles, B);\n dim3 block(TILE_SIZE, TILE_SIZE);\n \n distance_kernel_tiled<<<grid, block>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_tiled',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← compile_kernel (ok)
okcompile_kernel
compile_kernel PASSED: kernel compiled without errors.
turn 6381.9s turn · 9.3s LLM · 372.6s tools · tokens in=6,272 · out=1,027 · total=7,299
reasoning
Let me test correctness of this tiled approach.
call → run_correctness
callrun_correctness
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Tiled 2D block approach: each block computes a 16x16 tile of the output matrix\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n#define TILE_SIZE 32\n\n__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which tile column (j direction)\n // blockIdx.y: which tile row (i direction)\n // blockIdx.z: which batch\n \n int tile_i = blockIdx.y;\n int tile_j = blockIdx.x;\n int b = blockIdx.z;\n \n int tx = threadIdx.x; // 0 to TILE_SIZE-1\n int ty = threadIdx.y; // 0 to TILE_SIZE-1\n \n int i = tile_i * TILE_SIZE + ty; // Global row index\n int j = tile_j * TILE_SIZE + tx; // Global col index\n \n // Shared memory for the two tiles of coordinates\n // Tile_i coords: TILE_SIZE * 3 floats\n // Tile_j coords: TILE_SIZE * 3 floats\n __shared__ float s_coords_i[TILE_SIZE * 3];\n __shared__ float s_coords_j[TILE_SIZE * 3];\n \n // Cooperative load of tile_i coordinates\n // Each thread loads one float, we need TILE_SIZE*3 floats per tile\n int load_idx = ty * TILE_SIZE + tx; // Linear thread index\n \n // Load tile_i coordinates (the rows we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int row = load_idx / 3;\n int comp = load_idx % 3;\n int global_row = tile_i * TILE_SIZE + row;\n if (global_row < N) {\n s_coords_i[load_idx] = coords[b * N * 3 + global_row * 3 + comp];\n }\n }\n \n // Load tile_j coordinates (the columns we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int col = load_idx / 3;\n int comp = load_idx % 3;\n int global_col = tile_j * TILE_SIZE + col;\n if (global_col < N) {\n s_coords_j[load_idx] = coords[b * N * 3 + global_col * 3 + comp];\n }\n }\n \n __syncthreads();\n \n // Load the i-th coordinate into registers\n float xi = s_coords_i[ty * 3 + 0];\n float yi = s_coords_i[ty * 3 + 1];\n float zi = s_coords_i[ty * 3 + 2];\n \n // Load the j-th coordinate into registers\n float xj = s_coords_j[tx * 3 + 0];\n float yj = s_coords_j[tx * 3 + 1];\n float zj = s_coords_j[tx * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n if (i < N && j < N) {\n dist[b * N * N + i * N + j] = dist_val;\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;\n \n dim3 grid(num_tiles, num_tiles, B);\n dim3 block(TILE_SIZE, TILE_SIZE);\n \n distance_kernel_tiled<<<grid, block>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_tiled',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← run_correctness (ok)
okrun_correctness
run_correctness PASSED: (5 / 5) trials all matched the reference.
Numerical precision: max_abs_err=9.54e-07 mean_abs_err=5.12e-08 max_rel_err=2.23e-07
turn 710.8s turn · 10.8s LLM · 0.0s tools · tokens in=7,347 · out=1,083 · total=8,430
reasoning
The tiled approach also passes correctness. Let me run a static check and then submit the tiled version. But let me also try one more optimization - using a larger tile size and more optimized loading.
Actually, let me first submit the current tiled version to see how it performs. If it's not fast enough, I can iterate.
call → static_check
callstatic_check
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Tiled 2D block approach: each block computes a 16x16 tile of the output matrix\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n#define TILE_SIZE 32\n\n__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which tile column (j direction)\n // blockIdx.y: which tile row (i direction)\n // blockIdx.z: which batch\n \n int tile_i = blockIdx.y;\n int tile_j = blockIdx.x;\n int b = blockIdx.z;\n \n int tx = threadIdx.x; // 0 to TILE_SIZE-1\n int ty = threadIdx.y; // 0 to TILE_SIZE-1\n \n int i = tile_i * TILE_SIZE + ty; // Global row index\n int j = tile_j * TILE_SIZE + tx; // Global col index\n \n // Shared memory for the two tiles of coordinates\n // Tile_i coords: TILE_SIZE * 3 floats\n // Tile_j coords: TILE_SIZE * 3 floats\n __shared__ float s_coords_i[TILE_SIZE * 3];\n __shared__ float s_coords_j[TILE_SIZE * 3];\n \n // Cooperative load of tile_i coordinates\n // Each thread loads one float, we need TILE_SIZE*3 floats per tile\n int load_idx = ty * TILE_SIZE + tx; // Linear thread index\n \n // Load tile_i coordinates (the rows we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int row = load_idx / 3;\n int comp = load_idx % 3;\n int global_row = tile_i * TILE_SIZE + row;\n if (global_row < N) {\n s_coords_i[load_idx] = coords[b * N * 3 + global_row * 3 + comp];\n }\n }\n \n // Load tile_j coordinates (the columns we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int col = load_idx / 3;\n int comp = load_idx % 3;\n int global_col = tile_j * TILE_SIZE + col;\n if (global_col < N) {\n s_coords_j[load_idx] = coords[b * N * 3 + global_col * 3 + comp];\n }\n }\n \n __syncthreads();\n \n // Load the i-th coordinate into registers\n float xi = s_coords_i[ty * 3 + 0];\n float yi = s_coords_i[ty * 3 + 1];\n float zi = s_coords_i[ty * 3 + 2];\n \n // Load the j-th coordinate into registers\n float xj = s_coords_j[tx * 3 + 0];\n float yj = s_coords_j[tx * 3 + 1];\n float zj = s_coords_j[tx * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n if (i < N && j < N) {\n dist[b * N * N + i * N + j] = dist_val;\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;\n \n dim3 grid(num_tiles, num_tiles, B);\n dim3 block(TILE_SIZE, TILE_SIZE);\n \n distance_kernel_tiled<<<grid, block>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_tiled',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← static_check (ok)
okstatic_check
static_check PASSED: no violations or warnings detected.
turn 8284.4s turn · 12.8s LLM · 271.6s tools · tokens in=8,378 · out=1,326 · total=9,704
reasoning
Let me submit this tiled kernel. It uses shared memory efficiently with a 32x32 tile size. Each thread computes one distance value, and coordinates are loaded cooperatively into shared memory. This should be reasonably efficient.
Let me also try one more optimization - using vectorized loads for the shared memory loading:
call → compile_kernel
callcompile_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Optimized tiled kernel with vectorized loads\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n#define TILE_SIZE 32\n\n__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which tile column (j direction)\n // blockIdx.y: which tile row (i direction)\n // blockIdx.z: which batch\n \n int tile_i = blockIdx.y;\n int tile_j = blockIdx.x;\n int b = blockIdx.z;\n \n int tx = threadIdx.x; // 0 to TILE_SIZE-1\n int ty = threadIdx.y; // 0 to TILE_SIZE-1\n \n int i = tile_i * TILE_SIZE + ty; // Global row index\n int j = tile_j * TILE_SIZE + tx; // Global col index\n \n // Shared memory for the two tiles of coordinates\n __shared__ float s_coords_i[TILE_SIZE * 3];\n __shared__ float s_coords_j[TILE_SIZE * 3];\n \n // Vectorized load using float4\n const float4* coords4 = reinterpret_cast<const float4*>(coords + b * N * 3);\n float4* si4 = reinterpret_cast<float4*>(s_coords_i);\n float4* sj4 = reinterpret_cast<float4*>(s_coords_j);\n \n int num_float4 = (TILE_SIZE * 3 + 3) / 4; // Number of float4 per tile = 24\n int base_i = tile_i * TILE_SIZE * 3 / 4; // Base index for tile_i\n int base_j = tile_j * TILE_SIZE * 3 / 4; // Base index for tile_j\n \n // Linear thread index\n int tid = ty * TILE_SIZE + tx;\n \n // Cooperative vectorized load\n for (int k = tid; k < num_float4; k += TILE_SIZE * TILE_SIZE) {\n int global_idx_i = base_i + k;\n int global_idx_j = base_j + k;\n \n // Calculate actual float position\n int float_pos_i = tile_i * TILE_SIZE * 3 + k * 4;\n int float_pos_j = tile_j * TILE_SIZE * 3 + k * 4;\n \n // Bounds check and load\n if (float_pos_i + 3 < N * 3) {\n si4[k] = coords4[global_idx_i];\n } else {\n // Handle boundary\n for (int c = 0; c < 4; c++) {\n int fp = float_pos_i + c;\n if (fp < N * 3) {\n int row = (fp / 3) % TILE_SIZE;\n int comp = fp % 3;\n s_coords_i[row * 3 + comp] = coords[b * N * 3 + fp];\n }\n }\n }\n \n if (float_pos_j + 3 < N * 3) {\n sj4[k] = coords4[global_idx_j];\n } else {\n for (int c = 0; c < 4; c++) {\n int fp = float_pos_j + c;\n if (fp < N * 3) {\n int row = (fp / 3) % TILE_SIZE;\n int comp = fp % 3;\n s_coords_j[row * 3 + comp] = coords[b * N * 3 + fp];\n }\n }\n }\n }\n \n __syncthreads();\n \n // Load the i-th coordinate into registers\n float xi = s_coords_i[ty * 3 + 0];\n float yi = s_coords_i[ty * 3 + 1];\n float zi = s_coords_i[ty * 3 + 2];\n \n // Load the j-th coordinate into registers\n float xj = s_coords_j[tx * 3 + 0];\n float yj = s_coords_j[tx * 3 + 1];\n float zj = s_coords_j[tx * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n if (i < N && j < N) {\n dist[b * N * N + i * N + j] = dist_val;\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;\n \n dim3 grid(num_tiles, num_tiles, B);\n dim3 block(TILE_SIZE, TILE_SIZE);\n \n distance_kernel_tiled<<<grid, block>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← compile_kernel (ok)
okcompile_kernel
compile_kernel PASSED: kernel compiled without errors.
turn 9234.6s turn · 11.3s LLM · 223.3s tools · tokens in=9,687 · out=1,292 · total=10,979
reasoning
The kernel compiled successfully. Let me check correctness and then submit if it passes. The tiled approach with vectorized loads should be efficient.
call → run_correctness
callrun_correctness
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Optimized tiled kernel with vectorized loads\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n#define TILE_SIZE 32\n\n__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which tile column (j direction)\n // blockIdx.y: which tile row (i direction)\n // blockIdx.z: which batch\n \n int tile_i = blockIdx.y;\n int tile_j = blockIdx.x;\n int b = blockIdx.z;\n \n int tx = threadIdx.x; // 0 to TILE_SIZE-1\n int ty = threadIdx.y; // 0 to TILE_SIZE-1\n \n int i = tile_i * TILE_SIZE + ty; // Global row index\n int j = tile_j * TILE_SIZE + tx; // Global col index\n \n // Shared memory for the two tiles of coordinates\n __shared__ float s_coords_i[TILE_SIZE * 3];\n __shared__ float s_coords_j[TILE_SIZE * 3];\n \n // Vectorized load using float4\n const float4* coords4 = reinterpret_cast<const float4*>(coords + b * N * 3);\n float4* si4 = reinterpret_cast<float4*>(s_coords_i);\n float4* sj4 = reinterpret_cast<float4*>(s_coords_j);\n \n int num_float4 = (TILE_SIZE * 3 + 3) / 4; // Number of float4 per tile = 24\n int base_i = tile_i * TILE_SIZE * 3 / 4; // Base index for tile_i\n int base_j = tile_j * TILE_SIZE * 3 / 4; // Base index for tile_j\n \n // Linear thread index\n int tid = ty * TILE_SIZE + tx;\n \n // Cooperative vectorized load\n for (int k = tid; k < num_float4; k += TILE_SIZE * TILE_SIZE) {\n int global_idx_i = base_i + k;\n int global_idx_j = base_j + k;\n \n // Calculate actual float position\n int float_pos_i = tile_i * TILE_SIZE * 3 + k * 4;\n int float_pos_j = tile_j * TILE_SIZE * 3 + k * 4;\n \n // Bounds check and load\n if (float_pos_i + 3 < N * 3) {\n si4[k] = coords4[global_idx_i];\n } else {\n // Handle boundary\n for (int c = 0; c < 4; c++) {\n int fp = float_pos_i + c;\n if (fp < N * 3) {\n int row = (fp / 3) % TILE_SIZE;\n int comp = fp % 3;\n s_coords_i[row * 3 + comp] = coords[b * N * 3 + fp];\n }\n }\n }\n \n if (float_pos_j + 3 < N * 3) {\n sj4[k] = coords4[global_idx_j];\n } else {\n for (int c = 0; c < 4; c++) {\n int fp = float_pos_j + c;\n if (fp < N * 3) {\n int row = (fp / 3) % TILE_SIZE;\n int comp = fp % 3;\n s_coords_j[row * 3 + comp] = coords[b * N * 3 + fp];\n }\n }\n }\n }\n \n __syncthreads();\n \n // Load the i-th coordinate into registers\n float xi = s_coords_i[ty * 3 + 0];\n float yi = s_coords_i[ty * 3 + 1];\n float zi = s_coords_i[ty * 3 + 2];\n \n // Load the j-th coordinate into registers\n float xj = s_coords_j[tx * 3 + 0];\n float yj = s_coords_j[tx * 3 + 1];\n float zj = s_coords_j[tx * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n if (i < N && j < N) {\n dist[b * N * N + i * N + j] = dist_val;\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;\n \n dim3 grid(num_tiles, num_tiles, B);\n dim3 block(TILE_SIZE, TILE_SIZE);\n \n distance_kernel_tiled<<<grid, block>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← run_correctness (ok)
okrun_correctness
run_correctness PASSED: (5 / 5) trials all matched the reference.
Numerical precision: max_abs_err=9.54e-07 mean_abs_err=5.12e-08 max_rel_err=2.23e-07
turn 10577.5s turn · 10.5s LLM · 567.0s tools · tokens in=11,041 · out=1,060 · total=12,101 · FINAL
reasoning
I have a correct kernel. Let me submit it now since I have 2 turns remaining and the kernel is passing correctness checks. The tiled approach with 32x32 blocks should provide good memory reuse and performance.
call → submit_kernel
callsubmit_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Tiled 2D block approach: each block computes a 32x32 tile of the output matrix\ncuda_source = \"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n#define TILE_SIZE 32\n\n__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {\n // blockIdx.x: which tile column (j direction)\n // blockIdx.y: which tile row (i direction)\n // blockIdx.z: which batch\n \n int tile_i = blockIdx.y;\n int tile_j = blockIdx.x;\n int b = blockIdx.z;\n \n int tx = threadIdx.x; // 0 to TILE_SIZE-1\n int ty = threadIdx.y; // 0 to TILE_SIZE-1\n \n int i = tile_i * TILE_SIZE + ty; // Global row index\n int j = tile_j * TILE_SIZE + tx; // Global col index\n \n // Shared memory for the two tiles of coordinates\n // Tile_i coords: TILE_SIZE * 3 floats\n // Tile_j coords: TILE_SIZE * 3 floats\n __shared__ float s_coords_i[TILE_SIZE * 3];\n __shared__ float s_coords_j[TILE_SIZE * 3];\n \n // Cooperative load of tile_i coordinates\n // Each thread loads one float, we need TILE_SIZE*3 floats per tile\n int load_idx = ty * TILE_SIZE + tx; // Linear thread index\n \n // Load tile_i coordinates (the rows we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int row = load_idx / 3;\n int comp = load_idx % 3;\n int global_row = tile_i * TILE_SIZE + row;\n if (global_row < N) {\n s_coords_i[load_idx] = coords[b * N * 3 + global_row * 3 + comp];\n }\n }\n \n // Load tile_j coordinates (the columns we're computing)\n if (load_idx < TILE_SIZE * 3) {\n int col = load_idx / 3;\n int comp = load_idx % 3;\n int global_col = tile_j * TILE_SIZE + col;\n if (global_col < N) {\n s_coords_j[load_idx] = coords[b * N * 3 + global_col * 3 + comp];\n }\n }\n \n __syncthreads();\n \n // Load the i-th coordinate into registers\n float xi = s_coords_i[ty * 3 + 0];\n float yi = s_coords_i[ty * 3 + 1];\n float zi = s_coords_i[ty * 3 + 2];\n \n // Load the j-th coordinate into registers\n float xj = s_coords_j[tx * 3 + 0];\n float yj = s_coords_j[tx * 3 + 1];\n float zj = s_coords_j[tx * 3 + 2];\n \n // Compute distance\n float dx = xi - xj;\n float dy = yi - yj;\n float dz = zi - zj;\n \n float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);\n \n // Write result\n if (i < N && j < N) {\n dist[b * N * N + i * N + j] = dist_val;\n }\n}\n\ntorch::Tensor compute_distances(torch::Tensor coords) {\n // coords: (B, N, 3)\n auto B = coords.size(0);\n auto N = coords.size(1);\n \n auto dist = torch::empty({B, N, N}, coords.options());\n \n int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;\n \n dim3 grid(num_tiles, num_tiles, B);\n dim3 block(TILE_SIZE, TILE_SIZE);\n \n distance_kernel_tiled<<<grid, block>>>(\n coords.data_ptr<float>(),\n dist.data_ptr<float>(),\n N\n );\n \n return dist;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor compute_distances(torch::Tensor coords);\n\"\"\"\n\n# Load the extension\ndistance_extension = load_inline(\n name='distance_extension_tiled',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['compute_distances'],\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, coords: torch.Tensor) -> torch.Tensor:\n return distance_extension.compute_distances(coords)"
}
result ← submit_kernel (ok)
oksubmit_kernel
submit_kernel PASSED: (5 / 5) correctness trials all passed.
Kernel runtime: 0.01 μs
Runtime stats: mean=0.01μs median=?μs std=0.00μs
Numerical precision: max_abs_err=9.54e-07 mean_abs_err=5.12e-08 max_rel_err=2.23e-07
Memory: 41.05 MB peak (ref: 89.05 MB, ratio: 0.461x)
Kernel launches: 1 (ref: 12, fusion ratio: 12.0)
SOL score: 0.185
final submitted kernel (125 lines, 3,598 chars) — full source, untruncated
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
# Tiled 2D block approach: each block computes a 32x32 tile of the output matrix
cuda_source = """
#include <cuda.h>
#include <cuda_runtime.h>
#include <cmath>
#define TILE_SIZE 32
__global__ void distance_kernel_tiled(const float* __restrict__ coords, float* __restrict__ dist, int N) {
// blockIdx.x: which tile column (j direction)
// blockIdx.y: which tile row (i direction)
// blockIdx.z: which batch
int tile_i = blockIdx.y;
int tile_j = blockIdx.x;
int b = blockIdx.z;
int tx = threadIdx.x; // 0 to TILE_SIZE-1
int ty = threadIdx.y; // 0 to TILE_SIZE-1
int i = tile_i * TILE_SIZE + ty; // Global row index
int j = tile_j * TILE_SIZE + tx; // Global col index
// Shared memory for the two tiles of coordinates
// Tile_i coords: TILE_SIZE * 3 floats
// Tile_j coords: TILE_SIZE * 3 floats
__shared__ float s_coords_i[TILE_SIZE * 3];
__shared__ float s_coords_j[TILE_SIZE * 3];
// Cooperative load of tile_i coordinates
// Each thread loads one float, we need TILE_SIZE*3 floats per tile
int load_idx = ty * TILE_SIZE + tx; // Linear thread index
// Load tile_i coordinates (the rows we're computing)
if (load_idx < TILE_SIZE * 3) {
int row = load_idx / 3;
int comp = load_idx % 3;
int global_row = tile_i * TILE_SIZE + row;
if (global_row < N) {
s_coords_i[load_idx] = coords[b * N * 3 + global_row * 3 + comp];
}
}
// Load tile_j coordinates (the columns we're computing)
if (load_idx < TILE_SIZE * 3) {
int col = load_idx / 3;
int comp = load_idx % 3;
int global_col = tile_j * TILE_SIZE + col;
if (global_col < N) {
s_coords_j[load_idx] = coords[b * N * 3 + global_col * 3 + comp];
}
}
__syncthreads();
// Load the i-th coordinate into registers
float xi = s_coords_i[ty * 3 + 0];
float yi = s_coords_i[ty * 3 + 1];
float zi = s_coords_i[ty * 3 + 2];
// Load the j-th coordinate into registers
float xj = s_coords_j[tx * 3 + 0];
float yj = s_coords_j[tx * 3 + 1];
float zj = s_coords_j[tx * 3 + 2];
// Compute distance
float dx = xi - xj;
float dy = yi - yj;
float dz = zi - zj;
float dist_val = sqrtf(dx*dx + dy*dy + dz*dz + 1e-8f);
// Write result
if (i < N && j < N) {
dist[b * N * N + i * N + j] = dist_val;
}
}
torch::Tensor compute_distances(torch::Tensor coords) {
// coords: (B, N, 3)
auto B = coords.size(0);
auto N = coords.size(1);
auto dist = torch::empty({B, N, N}, coords.options());
int num_tiles = (N + TILE_SIZE - 1) / TILE_SIZE;
dim3 grid(num_tiles, num_tiles, B);
dim3 block(TILE_SIZE, TILE_SIZE);
distance_kernel_tiled<<<grid, block>>>(
coords.data_ptr<float>(),
dist.data_ptr<float>(),
N
);
return dist;
}
"""
cpp_source = """
torch::Tensor compute_distances(torch::Tensor coords);
"""
# Load the extension
distance_extension = load_inline(
name='distance_extension_tiled',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['compute_distances'],
extra_cuda_cflags=['-O3', '--use_fast_math'],
verbose=True
)
class ModelNew(nn.Module):
def __init__(self):
super().__init__()
def forward(self, coords: torch.Tensor) -> torch.Tensor:
return distance_extension.compute_distances(coords)