L2 P9 · popcorn

correct 9_MetropolisHastingsStep.py

model

FW-GLM-5-1

turns / max

15 / 15

tool calls

tokens (total)

211357

wall clock

825.8s

truncated

backend

cuda fp32

variant

popcorn

runtime

0.06 μs

ref runtime

0.14 μs

speedup

2.28x

started

2026-05-11T20:06:53Z

timingkernelbench.timing

kernel runtime

0.06 μs

ref runtime

0.14 μs

speedup

2.28x

kernel mean / median / std

0.06 / — / 6.17e-04 μs

ref mean / median / std

0.14 / — / 0.06 μs

numerical precisioneval_kernel_against_ref

max abs error

2.38e-07

mean abs error

1.81e-09

max rel error

3.57e-04

mean rel error

1.23e-08

gpu memoryextended_metrics.measure_memory

kernel peak

36.02 MB

ref peak

37.02 MB

kernel / ref

0.97x

kernel launches / fusiontorch.profiler

kernel launches

ref launches

fusion ratio (ref / kernel)

3.50x

total cuda time

287 μs

SOL (speed-of-light)nsight_hardware_counters

SOL score (0–1)

0.492

dram util %

1.4%

compute util %

49.2%

bottleneck

compute-bound

dominant pipe

FP32

arithmetic intensity

—

ridge point

20.00

roofline / occupancynsight_hardware_counters

dram bandwidth

45.94 GB/s

dram util %

1.4%

fp32 tflops

—

fp32 util %

—

fp16 tflops

—

occupancy %

75.7%

bottleneck

compute-bound

dominant pipe %

49.2%

arithmetic intensity

—

ridge point

20.00

L1 hit %

—

L2 hit %

286.6%

ld sectors / req

13.71

st sectors / req

—

regs / thread

128

smem / block

3072 B

block size

768

peak bw

3350.00 GB/s

peak fp32 tflops

67.00

peak fp16 tflops

1979.00

warp stalls (top 5)nsight

long_scoreboard

4366.9%

short_scoreboard

112.0%

mio_throttle

54.1%

reference PyTorch source (the prompt the agent sees)

import torch
import torch.nn as nn
import math


class Model(nn.Module):
    """
    Batched Metropolis-Hastings MCMC step.  Given a current state and a
    log-probability function (here a Gaussian target for benchmarking),
    proposes a new state via a Gaussian random walk, computes the
    acceptance ratio, and stochastically accepts or rejects.
    """

    def __init__(self, dim, step_size=0.1):
        super().__init__()
        self.dim = dim
        self.step_size = step_size
        # Target: N(mu, sigma^2 I)
        self.register_buffer("mu", torch.zeros(dim))
        self.register_buffer("sigma", torch.ones(dim))

    def _log_prob(self, x: torch.Tensor) -> torch.Tensor:
        return -0.5 * (((x - self.mu) / self.sigma) ** 2).sum(dim=-1)

    def forward(self, x: torch.Tensor) -> tuple:
        """
        Args:
            x: (B, dim) – current chain states
        Returns:
            (x_new, accepted):
                x_new:    (B, dim) – states after accept/reject
                accepted: (B,)    – boolean mask of accepted proposals
        """
        proposal = x + self.step_size * torch.randn_like(x)
        log_alpha = self._log_prob(proposal) - self._log_prob(x)
        log_u = torch.log(torch.rand(x.shape[0], device=x.device).clamp(min=1e-10))
        accepted = log_u < log_alpha
        x_new = torch.where(accepted.unsqueeze(-1), proposal, x)
        return x_new, accepted


dim = 64
batch_size = 4096


def get_inputs():
    return [torch.randn(popcorn_pri.jitter_int(batch_size), dim)]


def get_init_inputs():
    return [dim]

turn 0 · 1 tool call(s) · 21.3s turn · 21.3s LLM · tokens in=2,203 · out=1,776 · total=3,979 · 9,964 chars (click to expand)

turn 021.3s turn · 21.3s LLM · 0.0s tools · tokens in=2,203 · out=1,776 · total=3,979

reasoning

Let me understand the task: 1. I need to implement a batched Metropolis-Hastings MCMC step in CUDA 2. The forward function takes a state `x` of shape (B, dim) and returns: - `x_new`: the new state after accept/reject - `accepted`: boolean mask of accepted proposals The computation involves: 1. Generating random noise for proposals: `proposal = x + step_size * randn_like(x)` 2. Computing log probability of proposal and current state 3. Computing acceptance ratio: `log_alpha = log_prob(proposal) - log_prob(x)` 4. Generating uniform random numbers and taking log 5. Accept/reject based on comparison The log probability for a Gaussian target is: ``` log_prob(x) = -0.5 * sum(((x - mu) / sigma)^2) ``` This is a simple computation but involves random number generation which needs to be done on GPU. Let me start by writing a basic CUDA kernel for this: ```python import torch from torch.utils.cpp_extension import load_inline cuda_source = """ #include <torch/extension.h> #include <cuda.h> #include <cuda_runtime.h> #include <curand_kernel.h> __global__ void mcmc_step_kernel( const float* __restrict__ x, const float* __restrict__ mu, const float* __restrict__ sigma, float* __restrict__ x_new, bool* __restrict__ accepted, float step_size, int batch_size, int dim, unsigned long long seed ) { int batch_idx = blockIdx.x * blockDim.x + threadIdx.x; if (batch_idx >= batch_size) return; // Initialize random number generator curandState state; curand_init(seed, batch_idx, 0, &state); // Compute log_prob(x) float log_prob_x = 0.0f; for (int d = 0; d < dim; d++) { float diff = x[batch_idx * dim + d] - mu[d]; float scaled = diff / sigma[d]; log_prob_x -= 0.5f * scaled * scaled; } // Generate proposal and compute its log_prob float log_prob_proposal = 0.0f; for (int d = 0; d < dim; d++) { float noise = curand_normal(&state); float proposal_d = x[batch_idx * dim + d] + step_size * noise; float diff = proposal_d - mu[d]; float scaled = diff / sigma[d]; log_prob_proposal -= 0.5f * scaled * scaled; x_new[batch_idx * dim + d] = proposal_d; } // Compute acceptance probability float log_alpha = log_prob_proposal - log_prob_x; float log_u = log(curand_uniform(&state)); accepted[batch_idx] = (log_u < log_alpha); } ``` I'm iterating through each dimension to compute log probabilities for both the current state and proposal, generating Gaussian noise for the random walk, then deciding whether to accept based on the Metropolis-Hastings criterion. }; return mcmc_step_cuda(x, mu, sigma, step_size); } """ I need to structure this with a proper `ModelNew` class that holds the dimension, step size, and distribution parameters. The class will initialize buffers for the mean and standard deviation, then provide a forward method that applies the MCMC step to input states. The forward pass takes a batch of states and returns updated states along with an acceptance mask. It uses the compiled CUDA extension to perform the actual MCMC transition on GPU, assuming the input resides on CUDA memory and invoking the kernel with the distribution parameters. However, there's a subtle issue with the acceptance logic. The current implementation writes the proposed state to `x_new` before checking if it should be accepted, which means rejected proposals still get written. I need to ensure that `x_new` only contains the accepted states or the original states for rejected proposals. The approach should be: compute the proposal first, then evaluate its log probability, determine acceptance based on the Metropolis-Hastings criterion, and conditionally write either the proposal or the original state. I'll need separate kernel launches to handle the random number generation and the acceptance logic properly. A cleaner design uses two kernels—one for generating proposals and another for applying the acceptance decision. The proposal kernel generates candidates and stores them separately, while the acceptance kernel reads the original states, proposals, and random numbers to make the final update. This avoids the complexity of managing state within a single kernel and keeps the logic clearer. Actually, a single kernel can handle all of this efficiently: each thread processes one batch element, initializes a random state, computes the log probability of the current position, generates a proposal by sampling from the Gaussian, calculates the proposal's log probability, then accepts or rejects based on the ratio. The key is storing both the original and proposal states so the acceptance step can choose between them. Let me set up the PyTorch extension with the CUDA kernel. I need to include the necessary headers for torch and CUDA runtime. The mcmc_step_kernel will handle the random state initialization using curand for each thread, computing the log probability of the current position, generating proposals via Gaussian noise, and then calculating acceptance probabilities. Each thread processes one sample in the batch, so I'll need to handle the dimension parameter to stride through the data correctly. The kernel iterates through each dimension to accumulate the log probability of the current state, then generates a new proposal by adding scaled Gaussian noise. For each proposed dimension, it computes the corresponding contribution to the log probability of the proposal state. After computing both log probabilities, it draws a uniform random number and compares the log acceptance ratio against a threshold to determine whether to accept or reject the move, updating the state accordingly. The acceptance logic needs to be inverted—accepting when `log_u < log_alpha` rather than the other way around. Once the batch index is validated against batch_size, the function launches the kernel with the provided inputs and returns the updated state along with an acceptance indicator. After calling the CUDA kernel, the output tensors are reshaped to match expected dimensions, and a check confirms CUDA availability before proceeding with the extension loading. The kernel itself requires careful attention to grid and block dimensions to ensure proper parallelization across the batch and dimension axes. For the log probability calculation, I need to accumulate the squared differences between each dimension's value and its mean, scaled by the standard deviation. The curand normal distribution function should provide the random noise needed for the Metropolis-Hastings proposal step. Setting up the kernel configuration with 256 threads per block and calculating the required number of blocks based on batch size. I need to allocate the output tensors for the new state and acceptance flags, then launch the kernel with the input data, mean, standard deviation, and step size parameters. The kernel should handle random number generation for proposals and the acceptance logic. I need to set up the kernel parameters carefully - the input is (B, dim), mu and sigma are 1D vectors of length dim, and x_new will be (B, dim) while accepted is (B,). The indexing needs to account for the tensor layout correctly: for x and x_new I'm accessing [batch_idx, d] as batch_idx * dim + d, while mu and sigma are indexed directly as [d]. The accepted array uses [batch_idx] for the acceptance decisions. The output indexing follows a similar pattern - x_new_out uses batch_idx * dim + d for the tensor values, and accepted_out uses batch_idx for the boolean flags. I'll add asserts to validate tensor dimensions and ensure the kernel launch parameters are set up properly with a block size of 256 threads and enough blocks to cover the batch size. I should also clamp the uniform random values to prevent numerical issues with log(0), matching the reference implementation's use of `clamp(min=1e-10)`. Now I can move forward with testing.

assistantLooking at this task, I need to implement a batched Metropolis-Hastings MCMC step in CUDA. The computation involves: 1. Generating Gaussian random noise for proposals 2. Computing log probabilities (Gaussian target distribution) 3. Computing acceptance ratio and deciding accept/reject 4. Returning new states and acceptance mask Let me start by getting GPU specs and then implementing a CUDA kernel using cuRAND for random number generation.

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 111.3s turn · 10.3s LLM · 1.0s tools · tokens in=2,540 · out=1,018 · total=3,558

reasoning

Now let me write the kernel. The key aspects: 1. Need to generate random numbers using cuRAND 2. Each thread handles one batch element for the MCMC step 3. Compute log-prob for proposal and current state 4. Generate uniform random number for acceptance decision Let me write the initial implementation:

assistantNow let me write the initial CUDA 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# Compile the CUDA kernel\nmcmc_cuda = load_inline(\n name='mcmc_cuda',\n cpp_sources='''\n#include <torch/extension.h>\n#include <curand_kernel.h>\n\n// Kernel for MCMC step\n__global__ void mcmc_step_kernel(\n const float* __restrict__ x,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n float* __restrict__ x_new,\n bool* __restrict__ accepted,\n float step_size,\n int batch_size,\n int dim,\n unsigned long long seed\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Initialize cuRAND state\n curandState state;\n curand_init(seed, batch_idx, 0, &state);\n \n // Compute log_prob(x) - Gaussian target distribution\n float log_prob_x = 0.0f;\n for (int d = 0; d < dim; d++) {\n float diff = (x[batch_idx * dim + d] - mu[d]) / sigma[d];\n log_prob_x += diff * diff;\n }\n log_prob_x = -0.5f * log_prob_x;\n \n // Generate proposal and compute log_prob(proposal)\n float log_prob_proposal = 0.0f;\n for (int d = 0; d < dim; d++) {\n float noise = curand_normal(&state);\n float proposal_d = x[batch_idx * dim + d] + step_size * noise;\n float diff = (proposal_d - mu[d]) / sigma[d];\n log_prob_proposal += diff * diff;\n x_new[batch_idx * dim + d] = proposal_d;\n }\n log_prob_proposal = -0.5f * log_prob_proposal;\n \n // Compute acceptance ratio\n float log_alpha = log_prob_proposal - log_prob_x;\n \n // Generate uniform random number and compute log_u\n float u = curand_uniform(&state);\n u = fmaxf(u, 1e-10f); // clamp to avoid log(0)\n float log_u = logf(u);\n \n // Accept or reject\n bool accept = log_u < log_alpha;\n accepted[batch_idx] = accept;\n \n // If rejected, copy x to x_new\n if (!accept) {\n for (int d = 0; d < dim; d++) {\n x_new[batch_idx * dim + d] = x[batch_idx * dim + d];\n }\n }\n}\n\n// Host function wrapper\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x,\n torch::Tensor mu,\n torch::Tensor sigma,\n float step_size\n) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n unsigned long long seed = 12345ULL; // Fixed seed for reproducibility in testing\n \n mcmc_step_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n mu.data_ptr<float>(),\n sigma.data_ptr<float>(),\n x_new.data_ptr<float>(),\n accepted.data_ptr<bool>(),\n step_size,\n batch_size,\n dim,\n seed\n );\n \n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['mcmc_step_cuda'],\n extra_cuda_cflags=['-lcurand'],\n extra_ldflags=['-lcurand'],\n verbose=True\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n return mcmc_cuda.mcmc_step_cuda(x, self.mu, self.sigma, self.step_size)" }

result ← compile_kernel (fail)

failcompile_kernel compile_kernel FAILED: RuntimeError. RuntimeError: Error building extension 'mcmc_cuda'

turn 220.6s turn · 10.3s LLM · 10.2s tools · tokens in=3,512 · out=1,162 · total=4,674

reasoning

The compilation failed. The error message is not very informative, but the issue could be with how I'm linking cuRAND. Let me try a different approach - I'll generate random numbers on the CPU side and pass them to the kernel, or use a different linking method. Actually, let me try using PyTorch's built-in random number generation for the proposals and then just compute the rest in CUDA. This would be simpler and avoid cuRAND linking issues.

assistantLet me try a different approach - generate random numbers using PyTorch and compute the rest in CUDA:

call → compile_kernel

callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Compile the CUDA kernel\nmcmc_cuda = load_inline(\n name='mcmc_cuda',\n cpp_sources='''\n#include <torch/extension.h>\n\n// Kernel for computing log probability of Gaussian target\n__global__ void log_prob_kernel(\n const float* __restrict__ x,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n float* __restrict__ log_prob,\n int batch_size,\n int dim\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n float sum_sq = 0.0f;\n for (int d = 0; d < dim; d++) {\n float diff = (x[batch_idx * dim + d] - mu[d]) / sigma[d];\n sum_sq += diff * diff;\n }\n log_prob[batch_idx] = -0.5f * sum_sq;\n}\n\n// Kernel for accepting/rejecting proposals\n__global__ void accept_reject_kernel(\n const float* __restrict__ x,\n const float* __restrict__ proposal,\n const float* __restrict__ log_alpha,\n const float* __restrict__ log_u,\n float* __restrict__ x_new,\n bool* __restrict__ accepted,\n int batch_size,\n int dim\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n bool accept = log_u[batch_idx] < log_alpha[batch_idx];\n accepted[batch_idx] = accept;\n \n for (int d = 0; d < dim; d++) {\n if (accept) {\n x_new[batch_idx * dim + d] = proposal[batch_idx * dim + d];\n } else {\n x_new[batch_idx * dim + d] = x[batch_idx * dim + d];\n }\n }\n}\n\n// Host function wrappers\ntorch::Tensor log_prob_cuda(\n torch::Tensor x,\n torch::Tensor mu,\n torch::Tensor sigma\n) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto log_prob = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kFloat32).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n log_prob_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n mu.data_ptr<float>(),\n sigma.data_ptr<float>(),\n log_prob.data_ptr<float>(),\n batch_size,\n dim\n );\n \n return log_prob;\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> accept_reject_cuda(\n torch::Tensor x,\n torch::Tensor proposal,\n torch::Tensor log_alpha,\n torch::Tensor log_u\n) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n accept_reject_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n proposal.data_ptr<float>(),\n log_alpha.data_ptr<float>(),\n log_u.data_ptr<float>(),\n x_new.data_ptr<float>(),\n accepted.data_ptr<bool>(),\n batch_size,\n dim\n );\n \n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['log_prob_cuda', 'accept_reject_cuda'],\n verbose=True\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n # Generate proposal using PyTorch random\n proposal = x + self.step_size * torch.randn_like(x)\n \n # Compute log probabilities in CUDA\n log_prob_x = mcmc_cuda.log_prob_cuda(x, self.mu, self.sigma)\n log_prob_proposal = mcmc_cuda.log_prob_cuda(proposal, self.mu, self.sigma)\n \n # Compute acceptance ratio\n log_alpha = log_prob_proposal - log_prob_x\n \n # Generate uniform random and compute log\n log_u = torch.log(torch.rand(x.shape[0], device=x.device).clamp(min=1e-10))\n \n # Accept/reject in CUDA\n return mcmc_cuda.accept_reject_cuda(x, proposal, log_alpha, log_u)" }

result ← compile_kernel (fail)

failcompile_kernel compile_kernel FAILED: RuntimeError. RuntimeError: Error building extension 'mcmc_cuda_v1'

turn 3 · 1 tool call(s) · 18.8s turn · 7.8s LLM · tokens in=4,603 · out=874 · total=5,477 · 8,791 chars (click to expand)

turn 318.8s turn · 7.8s LLM · 11.0s tools · tokens in=4,603 · out=874 · total=5,477

reasoning

Let me try with less verbose output and see if there's a more specific error message. Maybe I need to handle the compilation differently.

assistantLet me try with a simpler setup and check for specific errors:

call → compile_kernel

callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda',\n cpp_sources='''\n#include <torch/extension.h>\n\n__global__ void log_prob_kernel(\n const float* x, const float* mu, const float* sigma,\n float* log_prob, int batch_size, int dim) {\n int idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (idx >= batch_size) return;\n \n float sum_sq = 0.0f;\n for (int d = 0; d < dim; d++) {\n float diff = (x[idx * dim + d] - mu[d]) / sigma[d];\n sum_sq += diff * diff;\n }\n log_prob[idx] = -0.5f * sum_sq;\n}\n\ntorch::Tensor log_prob_cuda(torch::Tensor x, torch::Tensor mu, torch::Tensor sigma) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n auto log_prob = torch::empty({batch_size}, x.options());\n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n log_prob_kernel<<<blocks, threads>>>(x.data_ptr<float>(), mu.data_ptr<float>(),\n sigma.data_ptr<float>(), log_prob.data_ptr<float>(), batch_size, dim);\n return log_prob;\n}\n\n__global__ void accept_kernel(const float* x, const float* proposal,\n const float* log_alpha, const float* log_u,\n float* x_new, bool* accepted, int batch_size, int dim) {\n int idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (idx >= batch_size) return;\n \n bool acc = log_u[idx] < log_alpha[idx];\n accepted[idx] = acc;\n for (int d = 0; d < dim; d++) {\n x_new[idx * dim + d] = acc ? proposal[idx * dim + d] : x[idx * dim + d];\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> accept_cuda(\n torch::Tensor x, torch::Tensor proposal, torch::Tensor log_alpha, torch::Tensor log_u) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, x.options().dtype(torch::kBool));\n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n accept_kernel<<<blocks, threads>>>(x.data_ptr<float>(), proposal.data_ptr<float>(),\n log_alpha.data_ptr<float>(), log_u.data_ptr<float>(),\n x_new.data_ptr<float>(), accepted.data_ptr<bool>(), batch_size, dim);\n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['log_prob_cuda', 'accept_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n proposal = x + self.step_size * torch.randn_like(x)\n log_prob_x = mcmc_cuda.log_prob_cuda(x, self.mu, self.sigma)\n log_prob_proposal = mcmc_cuda.log_prob_cuda(proposal, self.mu, self.sigma)\n log_alpha = log_prob_proposal - log_prob_x\n log_u = torch.log(torch.rand(x.shape[0], device=x.device).clamp(min=1e-10))\n return mcmc_cuda.accept_cuda(x, proposal, log_alpha, log_u)" }

result ← compile_kernel (fail)

failcompile_kernel compile_kernel FAILED: RuntimeError. RuntimeError: Error building extension 'mcmc_cuda_v2': [1/2] /opt/conda/bin/x86_64-conda-linux-gnu-c++ -MMD -MF main.o.d -DTORCH_EXTENSION_NAME=mcmc_cuda_v2 -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /opt/conda/include/python3.10 -fPIC -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp -o main.o FAILED: [code=1] main.o /opt/conda/bin/x86_64-conda-linux-gnu-c++ -MMD -MF main.o.d -DTORCH_EXTENSION_NAME=mcmc_cuda_v2 -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /opt/conda/include/python3.10 -fPIC -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp -o main.o /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:5:1: error: '__global__' does not name a type 5 | __global__ void log_prob_kernel( | ^~~~~~~~~~ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp: In function 'at::Tensor log_prob_cuda(at::Tensor, at::Tensor, at::Tensor)': /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:25:5: error: 'log_prob_kernel' was not declared in this scope 25 | log_prob_kernel<<<blocks, threads>>>(x.data_ptr<float>(), mu.data_ptr<float>(), | ^~~~~~~~~~~~~~~ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:25:22: error: expected primary-expression before '<' token 25 | log_prob_kernel<<<blocks, threads>>>(x.data_ptr<float>(), mu.data_ptr<float>(), | ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:25:40: error: expected primary-expression before '>' token 25 | log_prob_kernel<<<blocks, threads>>>(x.data_ptr<float>(), mu.data_ptr<float>(), | ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp: At global scope: /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:30:1: error: '__global__' does not name a type 30 | __global__ void accept_kernel(const float* x, const float* proposal, | ^~~~~~~~~~ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp: In function 'std::tuple<at::Tensor, at::Tensor> accept_cuda(at::Tensor, at::Tensor, at::Tensor, at::Tensor)': /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:51:5: error: 'accept_kernel' was not declared in this scope 51 | accept_kernel<<<blocks, threads>>>(x.data_ptr<float>(), proposal.data_ptr<float>(), | ^~~~~~~~~~~~~ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:51:20: error: expected primary-expression before '<' token 51 | accept_kernel<<<blocks, threads>>>(x.data_ptr<float>(), proposal.data_ptr<float>(), | ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_66090e9f8925/mcmc_cuda/main.cpp:51:38: error: expected primary-expression before '>' token 51 | accept_kernel<<<blocks, threads>>>(x.data_ptr<float>(), proposal.data_ptr<float>(), | ^ ninja: build stopped: subcommand failed.

turn 47.8s turn · 7.8s LLM · 0.0s tools · tokens in=6,822 · out=902 · total=7,724

reasoning

I see the problem. The CUDA kernel code is being passed as C++ source. I need to separate the CUDA code into `cuda_sources` and C++ code into `cpp_sources`. Let me fix this.

assistantI see the issue - I need to separate CUDA code into `cuda_sources` and C++ wrappers into `cpp_sources`:

call → compile_kernel

callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda',\n cuda_sources='''\n#include <torch/extension.h>\n\n__global__ void log_prob_kernel(\n const float* x, const float* mu, const float* sigma,\n float* log_prob, int batch_size, int dim) {\n int idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (idx >= batch_size) return;\n \n float sum_sq = 0.0f;\n for (int d = 0; d < dim; d++) {\n float diff = (x[idx * dim + d] - mu[d]) / sigma[d];\n sum_sq += diff * diff;\n }\n log_prob[idx] = -0.5f * sum_sq;\n}\n\ntorch::Tensor log_prob_cuda(torch::Tensor x, torch::Tensor mu, torch::Tensor sigma) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n auto log_prob = torch::empty({batch_size}, x.options());\n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n log_prob_kernel<<<blocks, threads>>>(x.data_ptr<float>(), mu.data_ptr<float>(),\n sigma.data_ptr<float>(), log_prob.data_ptr<float>(), batch_size, dim);\n return log_prob;\n}\n\n__global__ void accept_kernel(const float* x, const float* proposal,\n const float* log_alpha, const float* log_u,\n float* x_new, bool* accepted, int batch_size, int dim) {\n int idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (idx >= batch_size) return;\n \n bool acc = log_u[idx] < log_alpha[idx];\n accepted[idx] = acc;\n for (int d = 0; d < dim; d++) {\n x_new[idx * dim + d] = acc ? proposal[idx * dim + d] : x[idx * dim + d];\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> accept_cuda(\n torch::Tensor x, torch::Tensor proposal, torch::Tensor log_alpha, torch::Tensor log_u) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, x.options().dtype(torch::kBool));\n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n accept_kernel<<<blocks, threads>>>(x.data_ptr<float>(), proposal.data_ptr<float>(),\n log_alpha.data_ptr<float>(), log_u.data_ptr<float>(),\n x_new.data_ptr<float>(), accepted.data_ptr<bool>(), batch_size, dim);\n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['log_prob_cuda', 'accept_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n proposal = x + self.step_size * torch.randn_like(x)\n log_prob_x = mcmc_cuda.log_prob_cuda(x, self.mu, self.sigma)\n log_prob_proposal = mcmc_cuda.log_prob_cuda(proposal, self.mu, self.sigma)\n log_alpha = log_prob_proposal - log_prob_x\n log_u = torch.log(torch.rand(x.shape[0], device=x.device).clamp(min=1e-10))\n return mcmc_cuda.accept_cuda(x, proposal, log_alpha, log_u)" }

result ← compile_kernel (fail)

failcompile_kernel compile_kernel FAILED: TypeError. TypeError: load_inline() missing 1 required positional argument: 'cpp_sources'

turn 583.9s turn · 8.3s LLM · 75.6s tools · tokens in=7,706 · out=945 · total=8,651

reasoning

I need both cpp_sources and cuda_sources. Let me use cpp_sources for the C++ wrapper functions and cuda_sources for the CUDA kernels.

assistantI need to provide both cpp_sources and cuda_sources properly:

call → compile_kernel

result ← compile_kernel (ok)

okcompile_kernel compile_kernel PASSED: kernel compiled without errors.

turn 68.4s turn · 8.3s LLM · 0.1s tools · tokens in=8,636 · out=928 · total=9,564

reasoning

Good, it compiled! Now let me check correctness.

assistantThe kernel compiled successfully. Now let me check correctness:

call → run_correctness

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 7 · 1 tool call(s) · 113.9s turn · 9.3s LLM · tokens in=9,610 · out=999 · total=10,609 · 6,544 chars (click to expand)

turn 7113.9s turn · 9.3s LLM · 104.6s tools · tokens in=9,610 · out=999 · total=10,609

reasoning

Correctness passed. But my current implementation just offloads the log probability computation and the accept/reject step to CUDA, while the random number generation and proposal creation is done in PyTorch. This might not provide the best speedup. Let me now profile the kernel to understand the performance characteristics and see how much of the computation time is being spent in the CUDA kernels vs. the PyTorch operations.

assistantThe correctness passed. Now let me profile to understand performance:

call → profile_kernel

callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda',\n cpp_sources='''\n#include <torch/extension.h>\n\ntorch::Tensor log_prob_cuda(torch::Tensor x, torch::Tensor mu, torch::Tensor sigma);\nstd::tuple<torch::Tensor, torch::Tensor> accept_cuda(torch::Tensor x, torch::Tensor proposal, torch::Tensor log_alpha, torch::Tensor log_u);\n''',\n cuda_sources='''\n#include <torch/extension.h>\n\n__global__ void log_prob_kernel(\n const float* x, const float* mu, const float* sigma,\n float* log_prob, int batch_size, int dim) {\n int idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (idx >= batch_size) return;\n \n float sum_sq = 0.0f;\n for (int d = 0; d < dim; d++) {\n float diff = (x[idx * dim + d] - mu[d]) / sigma[d];\n sum_sq += diff * diff;\n }\n log_prob[idx] = -0.5f * sum_sq;\n}\n\ntorch::Tensor log_prob_cuda(torch::Tensor x, torch::Tensor mu, torch::Tensor sigma) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n auto log_prob = torch::empty({batch_size}, x.options());\n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n log_prob_kernel<<<blocks, threads>>>(x.data_ptr<float>(), mu.data_ptr<float>(),\n sigma.data_ptr<float>(), log_prob.data_ptr<float>(), batch_size, dim);\n return log_prob;\n}\n\n__global__ void accept_kernel(const float* x, const float* proposal,\n const float* log_alpha, const float* log_u,\n float* x_new, bool* accepted, int batch_size, int dim) {\n int idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (idx >= batch_size) return;\n \n bool acc = log_u[idx] < log_alpha[idx];\n accepted[idx] = acc;\n for (int d = 0; d < dim; d++) {\n x_new[idx * dim + d] = acc ? proposal[idx * dim + d] : x[idx * dim + d];\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> accept_cuda(\n torch::Tensor x, torch::Tensor proposal, torch::Tensor log_alpha, torch::Tensor log_u) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, x.options().dtype(torch::kBool));\n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n accept_kernel<<<blocks, threads>>>(x.data_ptr<float>(), proposal.data_ptr<float>(),\n log_alpha.data_ptr<float>(), log_u.data_ptr<float>(),\n x_new.data_ptr<float>(), accepted.data_ptr<bool>(), batch_size, dim);\n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['log_prob_cuda', 'accept_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n proposal = x + self.step_size * torch.randn_like(x)\n log_prob_x = mcmc_cuda.log_prob_cuda(x, self.mu, self.sigma)\n log_prob_proposal = mcmc_cuda.log_prob_cuda(proposal, self.mu, self.sigma)\n log_alpha = log_prob_proposal - log_prob_x\n log_u = torch.log(torch.rand(x.shape[0], device=x.device).clamp(min=1e-10))\n return mcmc_cuda.accept_cuda(x, proposal, log_alpha, log_u)" }

result ← profile_kernel (ok)

okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::mul 57772.0μs (61%) calls=1 #2: aten::clamp 11306.0μs (12%) calls=1 #3: aten::add 7939.0μs (8%) calls=1 #4: aten::log 5125.0μs (5%) calls=1 #5: aten::randn_like 4472.0μs (5%) calls=1 ... +13 more kernels --- Timing --- GPU time: 76.83 μs --- Memory Bandwidth --- DRAM BW: 1085.8/3350 GB/s (32.4%) read=1085.8 write=0.0 GB/s Hit rates: L2=823.8% --- Compute Throughput --- Dominant pipe: FP32 util=66.4% Pipe util: FMA=66.4%, Tensor=1.6% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: COMPUTE-BOUND --- Occupancy --- Achieved: 140.0% Eligible warps/cycle: 3.54 Launch: regs/thread=322, smem/blk=10240B, block=1920, grid=1612 --- Memory Access Quality --- Global ld coalescing: 133.82 sectors/req (133.8x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 31896.2% #################### short_scoreboard 1437.3% #################### mio_throttle 54.5% ########## --- Optimization Hints --- -> 31896% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=133.8 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=133.8x (ideal=1.0) -> 134x wasted DRAM BW. Make per-warp accesses contiguous. -> Compute-bound but NOT using tensor cores. If applicable, use FP16/BF16 with torch.matmul or WMMA intrinsics.

turn 8 · 1 tool call(s) · 46.2s turn · 13.8s LLM · tokens in=11,077 · out=1,358 · total=12,435 · 32,509 chars (click to expand)

turn 846.2s turn · 13.8s LLM · 32.4s tools · tokens in=11,077 · out=1,358 · total=12,435

reasoning

The profile shows that most time is spent in PyTorch operations (mul, clamp, add, log, randn_like). The CUDA kernels are fast but the overhead from multiple PyTorch operations is significant. Let me try to fuse more operations into the CUDA kernel. Specifically: 1. Fuse proposal generation into the kernel 2. Fuse the log probability computation for both x and proposal in one kernel 3. Fuse the acceptance decision But there's a problem - I need random numbers. The profile shows randn_like takes significant time. Actually, looking more carefully - the current implementation already works, but the profiling is showing overhead from PyTorch operations. Let me try a more fused kernel that generates random numbers on the fly. The issue is that I need Philox-based RNG to match PyTorch's random number generation exactly... but for the MCMC task, we just need to be correct relative to the reference computation flow. Wait - the correctness passed! So the question is whether the kernel is faster than the reference. Let me try to create a more fused kernel that does everything in CUDA including generating random numbers. For Philox RNG, I can use PyTorch's RNG state directly. Let me try to use ATen's RNG functions within CUDA.

assistantThe profile shows significant time in PyTorch operations like `mul`, `clamp`, `add`, and `log`. Let me create a more fused kernel that handles all computations including random number generation:

call → compile_kernel

result ← compile_kernel (fail)

failcompile_kernel compile_kernel FAILED: RuntimeError. RuntimeError: Error building extension 'mcmc_cuda_fused': [1/3] /opt/conda/bin/x86_64-conda-linux-gnu-c++ -MMD -MF main.o.d -DTORCH_EXTENSION_NAME=mcmc_cuda_fused -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /usr/local/cuda/include -isystem /opt/conda/include/python3.10 -fPIC -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/main.cpp -o main.o [2/3] /usr/local/cuda/bin/nvcc -MD -MF cuda.cuda.o.d -ccbin /opt/conda/bin/x86_64-conda-linux-gnu-cc -DTORCH_EXTENSION_NAME=mcmc_cuda_fused -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /usr/local/cuda/include -isystem /opt/conda/include/python3.10 -D__CUDA_NO_HALF_OPERATORS__ -D__CUDA_NO_HALF_CONVERSIONS__ -D__CUDA_NO_BFLOAT16_CONVERSIONS__ -D__CUDA_NO_HALF2_OPERATORS__ --expt-relaxed-constexpr -gencode=arch=compute_90,code=compute_90 -gencode=arch=compute_90,code=sm_90 --compiler-options '-fPIC' -O3 -use_fast_math -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu -o cuda.cuda.o FAILED: [code=2] cuda.cuda.o /usr/local/cuda/bin/nvcc -MD -MF cuda.cuda.o.d -ccbin /opt/conda/bin/x86_64-conda-linux-gnu-cc -DTORCH_EXTENSION_NAME=mcmc_cuda_fused -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /usr/local/cuda/include -isystem /opt/conda/include/python3.10 -D__CUDA_NO_HALF_OPERATORS__ -D__CUDA_NO_HALF_CONVERSIONS__ -D__CUDA_NO_BFLOAT16_CONVERSIONS__ -D__CUDA_NO_HALF2_OPERATORS__ --expt-relaxed-constexpr -gencode=arch=compute_90,code=compute_90 -gencode=arch=compute_90,code=sm_90 --compiler-options '-fPIC' -O3 -use_fast_math -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu -o cuda.cuda.o nvcc warning : incompatible redefinition for option 'compiler-bindir', the last value of this option was used /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(26): error: name followed by "::" must be a class or namespace name auto seeds = at::cuda::philox::unpack(rng_state); ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(28): error: no instance of overloaded function "std::get" matches the argument list argument types are: (<error-type>) curand_init(std::get<0>(seeds), batch_idx, std::get<1>(seeds), &state); ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1180): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::variant<_Types...> &&)" failed get(const variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1170): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::variant<_Types...> &)" failed get(const variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1160): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::variant<_Types...> &&)" failed get(variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1150): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::variant<_Types...> &)" failed get(variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1745): note #3327-D: candidate function template "std::get<_Np,_Types...>(const std::variant<_Types...> &&)" failed deduction get(const variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1734): note #3327-D: candidate function template "std::get<_Np,_Types...>(const std::variant<_Types...> &)" failed deduction get(const variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1723): note #3327-D: candidate function template "std::get<_Np,_Types...>(std::variant<_Types...> &&)" failed deduction get(variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1712): note #3327-D: candidate function template "std::get<_Np,_Types...>(std::variant<_Types...> &)" failed deduction get(variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2515): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::tuple<_Types...> &&) noexcept" failed get(const tuple<_Types...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2503): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::tuple<_Types...> &) noexcept" failed get(const tuple<_Types...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2492): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::tuple<_Types...> &&) noexcept" failed get(tuple<_Types...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2481): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::tuple<_Types...> &) noexcept" failed get(tuple<_Types...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2474): note #3327-D: candidate function template "std::get<__i,_Elements...>(const std::tuple<_Elements...> &)" failed deduction get(const tuple<_Elements...>&) = delete; ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1307): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Up, _Tp> &&) noexcept" failed get(const pair<_Up, _Tp>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1302): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Up, _Tp> &&) noexcept" failed get(pair<_Up, _Tp>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1297): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Up, _Tp> &) noexcept" failed get(const pair<_Up, _Tp>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1292): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Up, _Tp> &) noexcept" failed get(pair<_Up, _Tp>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1287): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Tp, _Up> &&) noexcept" failed get(const pair<_Tp, _Up>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1282): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Tp, _Up> &&) noexcept" failed get(pair<_Tp, _Up>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1277): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Tp, _Up> &) noexcept" failed get(const pair<_Tp, _Up>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1272): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Tp, _Up> &) noexcept" failed get(pair<_Tp, _Up>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(417): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(const std::array<_Tp, _Nm> &&) noexcept" failed deduction get(const array<_Tp, _Nm>&& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(408): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(const std::array<_Tp, _Nm> &) noexcept" failed deduction get(const array<_Tp, _Nm>& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(399): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(std::array<_Tp, _Nm> &&) noexcept" failed deduction get(array<_Tp, _Nm>&& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(390): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(std::array<_Tp, _Nm> &) noexcept" failed deduction get(array<_Tp, _Nm>& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2464): note #3327-D: candidate function template "std::get<__i,_Elements...>(const std::tuple<_Elements...> &&) noexcept" failed deduction get(const tuple<_Elements...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2455): note #3327-D: candidate function template "std::get<__i,_Elements...>(std::tuple<_Elements...> &&) noexcept" failed deduction get(tuple<_Elements...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2449): note #3327-D: candidate function template "std::get<__i,_Elements...>(const std::tuple<_Elements...> &) noexcept" failed deduction get(const tuple<_Elements...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2443): note #3327-D: candidate function template "std::get<__i,_Elements...>(std::tuple<_Elements...> &) noexcept" failed deduction get(tuple<_Elements...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1265): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(const std::pair<_Tp1, _Tp2> &&) noexcept" failed deduction get(const pair<_Tp1, _Tp2>&& __in) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1260): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(const std::pair<_Tp1, _Tp2> &) noexcept" failed deduction get(const pair<_Tp1, _Tp2>& __in) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1255): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(std::pair<_Tp1, _Tp2> &&) noexcept" failed deduction get(pair<_Tp1, _Tp2>&& __in) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1250): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(std::pair<_Tp1, _Tp2> &) noexcept" failed deduction get(pair<_Tp1, _Tp2>& __in) noexcept ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(28): error: no instance of overloaded function "std::get" matches the argument list argument types are: (<error-type>) curand_init(std::get<0>(seeds), batch_idx, std::get<1>(seeds), &state); ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1180): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::variant<_Types...> &&)" failed get(const variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1170): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::variant<_Types...> &)" failed get(const variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1160): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::variant<_Types...> &&)" failed get(variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1150): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::variant<_Types...> &)" failed get(variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1745): note #3327-D: candidate function template "std::get<_Np,_Types...>(const std::variant<_Types...> &&)" failed deduction get(const variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1734): note #3327-D: candidate function template "std::get<_Np,_Types...>(const std::variant<_Types...> &)" failed deduction get(const variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1723): note #3327-D: candidate function template "std::get<_Np,_Types...>(std::variant<_Types...> &&)" failed deduction get(variant<_Types...>&& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/variant(1712): note #3327-D: candidate function template "std::get<_Np,_Types...>(std::variant<_Types...> &)" failed deduction get(variant<_Types...>& __v) ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2515): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::tuple<_Types...> &&) noexcept" failed get(const tuple<_Types...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2503): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(const std::tuple<_Types...> &) noexcept" failed get(const tuple<_Types...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2492): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::tuple<_Types...> &&) noexcept" failed get(tuple<_Types...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2481): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get<_Tp,_Types...>(std::tuple<_Types...> &) noexcept" failed get(tuple<_Types...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2474): note #3327-D: candidate function template "std::get<__i,_Elements...>(const std::tuple<_Elements...> &)" failed deduction get(const tuple<_Elements...>&) = delete; ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1307): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Up, _Tp> &&) noexcept" failed get(const pair<_Up, _Tp>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1302): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Up, _Tp> &&) noexcept" failed get(pair<_Up, _Tp>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1297): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Up, _Tp> &) noexcept" failed get(const pair<_Up, _Tp>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1292): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Up, _Tp> &) noexcept" failed get(pair<_Up, _Tp>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1287): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Tp, _Up> &&) noexcept" failed get(const pair<_Tp, _Up>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1282): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Tp, _Up> &&) noexcept" failed get(pair<_Tp, _Up>&& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1277): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(const std::pair<_Tp, _Up> &) noexcept" failed get(const pair<_Tp, _Up>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1272): note #3323-D: substituting explicit template arguments "<<expression>>" for function template "std::get(std::pair<_Tp, _Up> &) noexcept" failed get(pair<_Tp, _Up>& __p) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(417): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(const std::array<_Tp, _Nm> &&) noexcept" failed deduction get(const array<_Tp, _Nm>&& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(408): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(const std::array<_Tp, _Nm> &) noexcept" failed deduction get(const array<_Tp, _Nm>& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(399): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(std::array<_Tp, _Nm> &&) noexcept" failed deduction get(array<_Tp, _Nm>&& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/array(390): note #3327-D: candidate function template "std::get<_Int,_Tp,_Nm>(std::array<_Tp, _Nm> &) noexcept" failed deduction get(array<_Tp, _Nm>& __arr) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2464): note #3327-D: candidate function template "std::get<__i,_Elements...>(const std::tuple<_Elements...> &&) noexcept" failed deduction get(const tuple<_Elements...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2455): note #3327-D: candidate function template "std::get<__i,_Elements...>(std::tuple<_Elements...> &&) noexcept" failed deduction get(tuple<_Elements...>&& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2449): note #3327-D: candidate function template "std::get<__i,_Elements...>(const std::tuple<_Elements...> &) noexcept" failed deduction get(const tuple<_Elements...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/tuple(2443): note #3327-D: candidate function template "std::get<__i,_Elements...>(std::tuple<_Elements...> &) noexcept" failed deduction get(tuple<_Elements...>& __t) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1265): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(const std::pair<_Tp1, _Tp2> &&) noexcept" failed deduction get(const pair<_Tp1, _Tp2>&& __in) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1260): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(const std::pair<_Tp1, _Tp2> &) noexcept" failed deduction get(const pair<_Tp1, _Tp2>& __in) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1255): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(std::pair<_Tp1, _Tp2> &&) noexcept" failed deduction get(pair<_Tp1, _Tp2>&& __in) noexcept ^ /opt/conda/lib/gcc/x86_64-conda-linux-gnu/14.2.0/include/c++/bits/stl_pair.h(1250): note #3327-D: candidate function template "std::get<_Int,_Tp1,_Tp2>(std::pair<_Tp1, _Tp2> &) noexcept" failed deduction get(pair<_Tp1, _Tp2>& __in) noexcept ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(81): error: name followed by "::" must be a class or namespace name at::PhiloxCudaState rng_state = at::cuda::philox::state_from( ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(82): error: namespace "at::detail" has no member "getDefaultGenerator" at::detail::getDefaultGenerator().get<at::CUDAGeneratorImpl>()); ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(82): error: type name is not allowed at::detail::getDefaultGenerator().get<at::CUDAGeneratorImpl>()); ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu(82): error: expected an expression at::detail::getDefaultGenerator().get<at::CUDAGeneratorImpl>()); ^ 7 errors detected in the compilation of "/scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_2_problem_9_cache/k_0716895e647f/mcmc_cuda_fused/cuda.cu". ninja: build stopped: subcommand failed.

turn 988.3s turn · 9.4s LLM · 78.8s tools · tokens in=19,289 · out=1,060 · total=20,349

reasoning

The PyTorch RNG API is tricky. Let me try a simpler approach - pass the random tensors generated by PyTorch to a fused kernel that handles everything else in one kernel call.

assistantThe RNG API is complex. Let me take a simpler approach - pass random tensors generated by PyTorch to a fully fused kernel:

call → compile_kernel

result ← compile_kernel (ok)

okcompile_kernel compile_kernel PASSED: kernel compiled without errors.

turn 108.6s turn · 8.6s LLM · 0.0s tools · tokens in=20,324 · out=1,005 · total=21,329

reasoning

The kernel compiled. Let me test correctness.

call → run_correctness

result ← run_correctness (ok)

okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.81e-09 max_rel_err=3.57e-04

turn 11 · 1 tool call(s) · 98.1s turn · 8.5s LLM · tokens in=21,377 · out=1,015 · total=22,392 · 6,821 chars (click to expand)

turn 1198.1s turn · 8.5s LLM · 89.5s tools · tokens in=21,377 · out=1,015 · total=22,392

reasoning

Good, correctness passed. Let me profile this to see performance.

assistantLet me profile this fused kernel:

call → profile_kernel

callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda_fused',\n cpp_sources='''\n#include <torch/extension.h>\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma, \n torch::Tensor randn, torch::Tensor randu, float step_size);\n''',\n cuda_sources='''\n#include <torch/extension.h>\n\n__global__ void mcmc_step_kernel(\n const float* __restrict__ x,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n const float* __restrict__ randn,\n const float* __restrict__ randu,\n float* __restrict__ x_new,\n bool* __restrict__ accepted,\n float step_size,\n int batch_size,\n int dim\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Compute log_prob(x) - Gaussian target distribution\n float log_prob_x = 0.0f;\n for (int d = 0; d < dim; d++) {\n float diff = (x[batch_idx * dim + d] - mu[d]) / sigma[d];\n log_prob_x += diff * diff;\n }\n log_prob_x = -0.5f * log_prob_x;\n \n // Generate proposal and compute log_prob(proposal)\n float log_prob_proposal = 0.0f;\n for (int d = 0; d < dim; d++) {\n float noise = randn[batch_idx * dim + d];\n float proposal_d = x[batch_idx * dim + d] + step_size * noise;\n float diff = (proposal_d - mu[d]) / sigma[d];\n log_prob_proposal += diff * diff;\n x_new[batch_idx * dim + d] = proposal_d;\n }\n log_prob_proposal = -0.5f * log_prob_proposal;\n \n // Compute acceptance ratio\n float log_alpha = log_prob_proposal - log_prob_x;\n \n // Get uniform random number and compute log_u\n float u = randu[batch_idx];\n u = fmaxf(u, 1e-10f); // clamp to avoid log(0)\n float log_u = logf(u);\n \n // Accept or reject\n bool accept = log_u < log_alpha;\n accepted[batch_idx] = accept;\n \n // If rejected, copy x to x_new\n if (!accept) {\n for (int d = 0; d < dim; d++) {\n x_new[batch_idx * dim + d] = x[batch_idx * dim + d];\n }\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma,\n torch::Tensor randn, torch::Tensor randu, float step_size) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n mcmc_step_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n mu.data_ptr<float>(),\n sigma.data_ptr<float>(),\n randn.data_ptr<float>(),\n randu.data_ptr<float>(),\n x_new.data_ptr<float>(),\n accepted.data_ptr<bool>(),\n step_size,\n batch_size,\n dim\n );\n \n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['mcmc_step_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n randn = torch.randn_like(x)\n randu = torch.rand(x.shape[0], device=x.device)\n return mcmc_cuda.mcmc_step_cuda(x, self.mu, self.sigma, randn, randu, self.step_size)" }

result ← profile_kernel (ok)

okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::randn_like 1508.0μs (29%) calls=1 #2: aten::normal_ 1221.0μs (23%) calls=1 #3: aten::rand 1041.0μs (20%) calls=1 #4: aten::uniform_ 993.0μs (19%) calls=1 #5: aten::empty_like 240.0μs (5%) calls=1 ... +5 more kernels --- Timing --- GPU time: 60.90 μs [↓15.9μs ok] --- Memory Bandwidth --- DRAM BW: 45.7/3350 GB/s (1.4%) [↓31.0% REGRESSED] read=45.7 write=0.0 GB/s Hit rates: L2=285.9% --- Compute Throughput --- Dominant pipe: FP32 util=48.2% [↓18.2% REGRESSED] Pipe util: FMA=48.2%, Tensor=1.4% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: COMPUTE-BOUND --- Occupancy --- Achieved: 75.6% [↓64.4% REGRESSED] Eligible warps/cycle: 3.14 Launch: regs/thread=128, smem/blk=3072B, block=768, grid=1056 --- Memory Access Quality --- Global ld coalescing: 13.71 sectors/req (13.7x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 3354.0% #################### short_scoreboard 95.8% ################### mio_throttle 52.4% ########## --- Optimization Hints --- -> 3354% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=13.7 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=13.7x (ideal=1.0) -> 14x wasted DRAM BW. Make per-warp accesses contiguous. -> Compute-bound but NOT using tensor cores. If applicable, use FP16/BF16 with torch.matmul or WMMA intrinsics. --- Delta vs Previous Iteration --- GPU time: 76.83→60.90μs (↓15.94) ok DRAM BW%: 32.41→1.36% (↓31.05) REGRESSED Compute%: 66.43→48.20% (↓18.23) REGRESSED Occupancy: 139.99→75.58% (↓64.41) REGRESSED Eligible warps/cyc: 3.54→3.14 (↓0.40) REGRESSED Ld sectors/req: 133.82→13.71 (↓120.11) ok L2 hit%: 823.83→285.87% (↓537.96) REGRESSED

turn 12 · 1 tool call(s) · 94.6s turn · 19.2s LLM · tokens in=23,166 · out=2,063 · total=25,229 · 8,471 chars (click to expand)

turn 1294.6s turn · 19.2s LLM · 75.4s tools · tokens in=23,166 · out=2,063 · total=25,229

reasoning

The fused kernel has passed correctness checks and shows some improvement in GPU time (76.83 → 60.90 μs). However, there's still significant time spent in random number generation (randn_like, normal_, rand, uniform_). Let me try to optimize further by improving memory access patterns in the kernel. The profile shows 13.7x wasted bandwidth from uncoalesced loads. I should try using vectorized loads and better memory access patterns. Let me create an optimized version with: 1. Vectorized loads (float4) for better memory coalescing 2. Caching mu/sigma in registers or shared memory Actually, looking at the timing, the kernel itself is fast but the random number generation is taking most of the time. This is expected since random number generation is expensive. Let me try a different approach - use warp-level parallelism and shared memory to optimize the kernel further. But first, let me check if the current version is faster than the reference by submitting it. Actually, let me first try to optimize the memory access pattern in the kernel by using vectorized loads for the dimension loop. Since dim=64, I can process 4 elements at a time.

assistantLet me optimize the kernel with vectorized memory access to improve memory coalescing:

call → compile_kernel

callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda_v2',\n cpp_sources='''\n#include <torch/extension.h>\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma, \n torch::Tensor randn, torch::Tensor randu, float step_size);\n''',\n cuda_sources='''\n#include <torch/extension.h>\n\n__global__ void mcmc_step_kernel(\n const float* __restrict__ x,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n const float* __restrict__ randn,\n const float* __restrict__ randu,\n float* __restrict__ x_new,\n bool* __restrict__ accepted,\n float step_size,\n int batch_size,\n int dim\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Use __ldg for read-only cache optimization\n const float* x_row = x + batch_idx * dim;\n const float* randn_row = randn + batch_idx * dim;\n float* x_new_row = x_new + batch_idx * dim;\n \n // Compute log_prob(x) - Gaussian target distribution\n float log_prob_x = 0.0f;\n \n // Process in chunks of 4 for better memory throughput\n int d = 0;\n for (; d <= dim - 4; d += 4) {\n float x0 = __ldg(&x_row[d]);\n float x1 = __ldg(&x_row[d+1]);\n float x2 = __ldg(&x_row[d+2]);\n float x3 = __ldg(&x_row[d+3]);\n \n float m0 = __ldg(&mu[d]);\n float m1 = __ldg(&mu[d+1]);\n float m2 = __ldg(&mu[d+2]);\n float m3 = __ldg(&mu[d+3]);\n \n float s0 = __ldg(&sigma[d]);\n float s1 = __ldg(&sigma[d+1]);\n float s2 = __ldg(&sigma[d+2]);\n float s3 = __ldg(&sigma[d+3]);\n \n float diff0 = (x0 - m0) / s0;\n float diff1 = (x1 - m1) / s1;\n float diff2 = (x2 - m2) / s2;\n float diff3 = (x3 - m3) / s3;\n \n log_prob_x += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;\n }\n // Handle remaining elements\n for (; d < dim; d++) {\n float diff = (__ldg(&x_row[d]) - __ldg(&mu[d])) / __ldg(&sigma[d]);\n log_prob_x += diff * diff;\n }\n log_prob_x = -0.5f * log_prob_x;\n \n // Generate proposal and compute log_prob(proposal)\n float log_prob_proposal = 0.0f;\n d = 0;\n for (; d <= dim - 4; d += 4) {\n float n0 = __ldg(&randn_row[d]);\n float n1 = __ldg(&randn_row[d+1]);\n float n2 = __ldg(&randn_row[d+2]);\n float n3 = __ldg(&randn_row[d+3]);\n \n float x0 = __ldg(&x_row[d]);\n float x1 = __ldg(&x_row[d+1]);\n float x2 = __ldg(&x_row[d+2]);\n float x3 = __ldg(&x_row[d+3]);\n \n float p0 = x0 + step_size * n0;\n float p1 = x1 + step_size * n1;\n float p2 = x2 + step_size * n2;\n float p3 = x3 + step_size * n3;\n \n float m0 = __ldg(&mu[d]);\n float m1 = __ldg(&mu[d+1]);\n float m2 = __ldg(&mu[d+2]);\n float m3 = __ldg(&mu[d+3]);\n \n float s0 = __ldg(&sigma[d]);\n float s1 = __ldg(&sigma[d+1]);\n float s2 = __ldg(&sigma[d+2]);\n float s3 = __ldg(&sigma[d+3]);\n \n float diff0 = (p0 - m0) / s0;\n float diff1 = (p1 - m1) / s1;\n float diff2 = (p2 - m2) / s2;\n float diff3 = (p3 - m3) / s3;\n \n log_prob_proposal += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;\n \n x_new_row[d] = p0;\n x_new_row[d+1] = p1;\n x_new_row[d+2] = p2;\n x_new_row[d+3] = p3;\n }\n for (; d < dim; d++) {\n float noise = __ldg(&randn_row[d]);\n float proposal_d = __ldg(&x_row[d]) + step_size * noise;\n float diff = (proposal_d - __ldg(&mu[d])) / __ldg(&sigma[d]);\n log_prob_proposal += diff * diff;\n x_new_row[d] = proposal_d;\n }\n log_prob_proposal = -0.5f * log_prob_proposal;\n \n // Compute acceptance ratio\n float log_alpha = log_prob_proposal - log_prob_x;\n \n // Get uniform random number and compute log_u\n float u = __ldg(&randu[batch_idx]);\n u = fmaxf(u, 1e-10f);\n float log_u = logf(u);\n \n // Accept or reject\n bool accept = log_u < log_alpha;\n accepted[batch_idx] = accept;\n \n // If rejected, copy x to x_new\n if (!accept) {\n for (int d = 0; d < dim; d++) {\n x_new_row[d] = __ldg(&x_row[d]);\n }\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma,\n torch::Tensor randn, torch::Tensor randu, float step_size) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n mcmc_step_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n mu.data_ptr<float>(),\n sigma.data_ptr<float>(),\n randn.data_ptr<float>(),\n randu.data_ptr<float>(),\n x_new.data_ptr<float>(),\n accepted.data_ptr<bool>(),\n step_size,\n batch_size,\n dim\n );\n \n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['mcmc_step_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n randn = torch.randn_like(x)\n randu = torch.rand(x.shape[0], device=x.device)\n return mcmc_cuda.mcmc_step_cuda(x, self.mu, self.sigma, randn, randu, self.step_size)" }

result ← compile_kernel (ok)

okcompile_kernel compile_kernel PASSED: kernel compiled without errors.

turn 13 · 1 tool call(s) · 91.4s turn · 14.7s LLM · tokens in=25,028 · out=1,733 · total=26,761 · 6,951 chars (click to expand)

turn 1391.4s turn · 14.7s LLM · 76.7s tools · tokens in=25,028 · out=1,733 · total=26,761

reasoning

Let me check correctness of the optimized kernel first, then decide if I should submit or make more optimizations.

call → run_correctness

callrun_correctness { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda_v2',\n cpp_sources='''\n#include <torch/extension.h>\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma, \n torch::Tensor randn, torch::Tensor randu, float step_size);\n''',\n cuda_sources='''\n#include <torch/extension.h>\n\n__global__ void mcmc_step_kernel(\n const float* __restrict__ x,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n const float* __restrict__ randn,\n const float* __restrict__ randu,\n float* __restrict__ x_new,\n bool* __restrict__ accepted,\n float step_size,\n int batch_size,\n int dim\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n const float* x_row = x + batch_idx * dim;\n const float* randn_row = randn + batch_idx * dim;\n float* x_new_row = x_new + batch_idx * dim;\n \n float log_prob_x = 0.0f;\n int d = 0;\n for (; d <= dim - 4; d += 4) {\n float x0 = __ldg(&x_row[d]);\n float x1 = __ldg(&x_row[d+1]);\n float x2 = __ldg(&x_row[d+2]);\n float x3 = __ldg(&x_row[d+3]);\n \n float m0 = __ldg(&mu[d]);\n float m1 = __ldg(&mu[d+1]);\n float m2 = __ldg(&mu[d+2]);\n float m3 = __ldg(&mu[d+3]);\n \n float s0 = __ldg(&sigma[d]);\n float s1 = __ldg(&sigma[d+1]);\n float s2 = __ldg(&sigma[d+2]);\n float s3 = __ldg(&sigma[d+3]);\n \n float diff0 = (x0 - m0) / s0;\n float diff1 = (x1 - m1) / s1;\n float diff2 = (x2 - m2) / s2;\n float diff3 = (x3 - m3) / s3;\n \n log_prob_x += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;\n }\n for (; d < dim; d++) {\n float diff = (__ldg(&x_row[d]) - __ldg(&mu[d])) / __ldg(&sigma[d]);\n log_prob_x += diff * diff;\n }\n log_prob_x = -0.5f * log_prob_x;\n \n float log_prob_proposal = 0.0f;\n d = 0;\n for (; d <= dim - 4; d += 4) {\n float n0 = __ldg(&randn_row[d]);\n float n1 = __ldg(&randn_row[d+1]);\n float n2 = __ldg(&randn_row[d+2]);\n float n3 = __ldg(&randn_row[d+3]);\n \n float x0 = __ldg(&x_row[d]);\n float x1 = __ldg(&x_row[d+1]);\n float x2 = __ldg(&x_row[d+2]);\n float x3 = __ldg(&x_row[d+3]);\n \n float p0 = x0 + step_size * n0;\n float p1 = x1 + step_size * n1;\n float p2 = x2 + step_size * n2;\n float p3 = x3 + step_size * n3;\n \n float m0 = __ldg(&mu[d]);\n float m1 = __ldg(&mu[d+1]);\n float m2 = __ldg(&mu[d+2]);\n float m3 = __ldg(&mu[d+3]);\n \n float s0 = __ldg(&sigma[d]);\n float s1 = __ldg(&sigma[d+1]);\n float s2 = __ldg(&sigma[d+2]);\n float s3 = __ldg(&sigma[d+3]);\n \n float diff0 = (p0 - m0) / s0;\n float diff1 = (p1 - m1) / s1;\n float diff2 = (p2 - m2) / s2;\n float diff3 = (p3 - m3) / s3;\n \n log_prob_proposal += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;\n \n x_new_row[d] = p0;\n x_new_row[d+1] = p1;\n x_new_row[d+2] = p2;\n x_new_row[d+3] = p3;\n }\n for (; d < dim; d++) {\n float noise = __ldg(&randn_row[d]);\n float proposal_d = __ldg(&x_row[d]) + step_size * noise;\n float diff = (proposal_d - __ldg(&mu[d])) / __ldg(&sigma[d]);\n log_prob_proposal += diff * diff;\n x_new_row[d] = proposal_d;\n }\n log_prob_proposal = -0.5f * log_prob_proposal;\n \n float log_alpha = log_prob_proposal - log_prob_x;\n \n float u = __ldg(&randu[batch_idx]);\n u = fmaxf(u, 1e-10f);\n float log_u = logf(u);\n \n bool accept = log_u < log_alpha;\n accepted[batch_idx] = accept;\n \n if (!accept) {\n for (int d = 0; d < dim; d++) {\n x_new_row[d] = __ldg(&x_row[d]);\n }\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma,\n torch::Tensor randn, torch::Tensor randu, float step_size) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n mcmc_step_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n mu.data_ptr<float>(),\n sigma.data_ptr<float>(),\n randn.data_ptr<float>(),\n randu.data_ptr<float>(),\n x_new.data_ptr<float>(),\n accepted.data_ptr<bool>(),\n step_size,\n batch_size,\n dim\n );\n \n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['mcmc_step_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n randn = torch.randn_like(x)\n randu = torch.rand(x.shape[0], device=x.device)\n return mcmc_cuda.mcmc_step_cuda(x, self.mu, self.sigma, randn, randu, self.step_size)" }

result ← run_correctness (ok)

okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.81e-09 max_rel_err=3.57e-04

turn 14 · FINAL · 1 tool call(s) · 112.5s turn · 15.1s LLM · tokens in=26,886 · out=1,740 · total=28,626 · 7,176 chars (click to expand)

turn 14112.5s turn · 15.1s LLM · 97.4s tools · tokens in=26,886 · out=1,740 · total=28,626 · FINAL

reasoning

The kernel is correct and has been optimized with vectorized memory access and __ldg for read-only cache optimization. Let me submit it now.

call → submit_kernel

callsubmit_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\nmcmc_cuda = load_inline(\n name='mcmc_cuda_v2',\n cpp_sources='''\n#include <torch/extension.h>\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma, \n torch::Tensor randn, torch::Tensor randu, float step_size);\n''',\n cuda_sources='''\n#include <torch/extension.h>\n\n__global__ void mcmc_step_kernel(\n const float* __restrict__ x,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n const float* __restrict__ randn,\n const float* __restrict__ randu,\n float* __restrict__ x_new,\n bool* __restrict__ accepted,\n float step_size,\n int batch_size,\n int dim\n) {\n int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n const float* x_row = x + batch_idx * dim;\n const float* randn_row = randn + batch_idx * dim;\n float* x_new_row = x_new + batch_idx * dim;\n \n float log_prob_x = 0.0f;\n int d = 0;\n for (; d <= dim - 4; d += 4) {\n float x0 = __ldg(&x_row[d]);\n float x1 = __ldg(&x_row[d+1]);\n float x2 = __ldg(&x_row[d+2]);\n float x3 = __ldg(&x_row[d+3]);\n \n float m0 = __ldg(&mu[d]);\n float m1 = __ldg(&mu[d+1]);\n float m2 = __ldg(&mu[d+2]);\n float m3 = __ldg(&mu[d+3]);\n \n float s0 = __ldg(&sigma[d]);\n float s1 = __ldg(&sigma[d+1]);\n float s2 = __ldg(&sigma[d+2]);\n float s3 = __ldg(&sigma[d+3]);\n \n float diff0 = (x0 - m0) / s0;\n float diff1 = (x1 - m1) / s1;\n float diff2 = (x2 - m2) / s2;\n float diff3 = (x3 - m3) / s3;\n \n log_prob_x += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;\n }\n for (; d < dim; d++) {\n float diff = (__ldg(&x_row[d]) - __ldg(&mu[d])) / __ldg(&sigma[d]);\n log_prob_x += diff * diff;\n }\n log_prob_x = -0.5f * log_prob_x;\n \n float log_prob_proposal = 0.0f;\n d = 0;\n for (; d <= dim - 4; d += 4) {\n float n0 = __ldg(&randn_row[d]);\n float n1 = __ldg(&randn_row[d+1]);\n float n2 = __ldg(&randn_row[d+2]);\n float n3 = __ldg(&randn_row[d+3]);\n \n float x0 = __ldg(&x_row[d]);\n float x1 = __ldg(&x_row[d+1]);\n float x2 = __ldg(&x_row[d+2]);\n float x3 = __ldg(&x_row[d+3]);\n \n float p0 = x0 + step_size * n0;\n float p1 = x1 + step_size * n1;\n float p2 = x2 + step_size * n2;\n float p3 = x3 + step_size * n3;\n \n float m0 = __ldg(&mu[d]);\n float m1 = __ldg(&mu[d+1]);\n float m2 = __ldg(&mu[d+2]);\n float m3 = __ldg(&mu[d+3]);\n \n float s0 = __ldg(&sigma[d]);\n float s1 = __ldg(&sigma[d+1]);\n float s2 = __ldg(&sigma[d+2]);\n float s3 = __ldg(&sigma[d+3]);\n \n float diff0 = (p0 - m0) / s0;\n float diff1 = (p1 - m1) / s1;\n float diff2 = (p2 - m2) / s2;\n float diff3 = (p3 - m3) / s3;\n \n log_prob_proposal += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;\n \n x_new_row[d] = p0;\n x_new_row[d+1] = p1;\n x_new_row[d+2] = p2;\n x_new_row[d+3] = p3;\n }\n for (; d < dim; d++) {\n float noise = __ldg(&randn_row[d]);\n float proposal_d = __ldg(&x_row[d]) + step_size * noise;\n float diff = (proposal_d - __ldg(&mu[d])) / __ldg(&sigma[d]);\n log_prob_proposal += diff * diff;\n x_new_row[d] = proposal_d;\n }\n log_prob_proposal = -0.5f * log_prob_proposal;\n \n float log_alpha = log_prob_proposal - log_prob_x;\n \n float u = __ldg(&randu[batch_idx]);\n u = fmaxf(u, 1e-10f);\n float log_u = logf(u);\n \n bool accept = log_u < log_alpha;\n accepted[batch_idx] = accept;\n \n if (!accept) {\n for (int d = 0; d < dim; d++) {\n x_new_row[d] = __ldg(&x_row[d]);\n }\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(\n torch::Tensor x, torch::Tensor mu, torch::Tensor sigma,\n torch::Tensor randn, torch::Tensor randu, float step_size) {\n int batch_size = x.size(0);\n int dim = x.size(1);\n \n auto x_new = torch::empty_like(x);\n auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));\n \n int threads = 256;\n int blocks = (batch_size + threads - 1) / threads;\n \n mcmc_step_kernel<<<blocks, threads>>>(\n x.data_ptr<float>(),\n mu.data_ptr<float>(),\n sigma.data_ptr<float>(),\n randn.data_ptr<float>(),\n randu.data_ptr<float>(),\n x_new.data_ptr<float>(),\n accepted.data_ptr<bool>(),\n step_size,\n batch_size,\n dim\n );\n \n return std::make_tuple(x_new, accepted);\n}\n''',\n functions=['mcmc_step_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim, step_size=0.1):\n super().__init__()\n self.dim = dim\n self.step_size = step_size\n self.register_buffer(\"mu\", torch.zeros(dim))\n self.register_buffer(\"sigma\", torch.ones(dim))\n\n def forward(self, x: torch.Tensor) -> tuple:\n randn = torch.randn_like(x)\n randu = torch.rand(x.shape[0], device=x.device)\n return mcmc_cuda.mcmc_step_cuda(x, self.mu, self.sigma, randn, randu, self.step_size)" }

result ← submit_kernel (ok)

oksubmit_kernel submit_kernel PASSED: (3 / 3) correctness trials all passed. Kernel runtime: 0.06 μs Runtime stats: mean=0.06μs median=?μs std=0.00μs Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.81e-09 max_rel_err=3.57e-04 Memory: 36.02 MB peak (ref: 37.02 MB, ratio: 0.9731x) Kernel launches: 10 (ref: 35, fusion ratio: 3.5) SOL score: 0.4923

final submitted kernel (177 lines, 5,473 chars) — full source, untruncated

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

mcmc_cuda = load_inline(
    name='mcmc_cuda_v2',
    cpp_sources='''
#include <torch/extension.h>

std::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(
    torch::Tensor x, torch::Tensor mu, torch::Tensor sigma, 
    torch::Tensor randn, torch::Tensor randu, float step_size);
''',
    cuda_sources='''
#include <torch/extension.h>

__global__ void mcmc_step_kernel(
    const float* __restrict__ x,
    const float* __restrict__ mu,
    const float* __restrict__ sigma,
    const float* __restrict__ randn,
    const float* __restrict__ randu,
    float* __restrict__ x_new,
    bool* __restrict__ accepted,
    float step_size,
    int batch_size,
    int dim
) {
    int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
    
    if (batch_idx >= batch_size) return;
    
    const float* x_row = x + batch_idx * dim;
    const float* randn_row = randn + batch_idx * dim;
    float* x_new_row = x_new + batch_idx * dim;
    
    float log_prob_x = 0.0f;
    int d = 0;
    for (; d <= dim - 4; d += 4) {
        float x0 = __ldg(&x_row[d]);
        float x1 = __ldg(&x_row[d+1]);
        float x2 = __ldg(&x_row[d+2]);
        float x3 = __ldg(&x_row[d+3]);
        
        float m0 = __ldg(&mu[d]);
        float m1 = __ldg(&mu[d+1]);
        float m2 = __ldg(&mu[d+2]);
        float m3 = __ldg(&mu[d+3]);
        
        float s0 = __ldg(&sigma[d]);
        float s1 = __ldg(&sigma[d+1]);
        float s2 = __ldg(&sigma[d+2]);
        float s3 = __ldg(&sigma[d+3]);
        
        float diff0 = (x0 - m0) / s0;
        float diff1 = (x1 - m1) / s1;
        float diff2 = (x2 - m2) / s2;
        float diff3 = (x3 - m3) / s3;
        
        log_prob_x += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;
    }
    for (; d < dim; d++) {
        float diff = (__ldg(&x_row[d]) - __ldg(&mu[d])) / __ldg(&sigma[d]);
        log_prob_x += diff * diff;
    }
    log_prob_x = -0.5f * log_prob_x;
    
    float log_prob_proposal = 0.0f;
    d = 0;
    for (; d <= dim - 4; d += 4) {
        float n0 = __ldg(&randn_row[d]);
        float n1 = __ldg(&randn_row[d+1]);
        float n2 = __ldg(&randn_row[d+2]);
        float n3 = __ldg(&randn_row[d+3]);
        
        float x0 = __ldg(&x_row[d]);
        float x1 = __ldg(&x_row[d+1]);
        float x2 = __ldg(&x_row[d+2]);
        float x3 = __ldg(&x_row[d+3]);
        
        float p0 = x0 + step_size * n0;
        float p1 = x1 + step_size * n1;
        float p2 = x2 + step_size * n2;
        float p3 = x3 + step_size * n3;
        
        float m0 = __ldg(&mu[d]);
        float m1 = __ldg(&mu[d+1]);
        float m2 = __ldg(&mu[d+2]);
        float m3 = __ldg(&mu[d+3]);
        
        float s0 = __ldg(&sigma[d]);
        float s1 = __ldg(&sigma[d+1]);
        float s2 = __ldg(&sigma[d+2]);
        float s3 = __ldg(&sigma[d+3]);
        
        float diff0 = (p0 - m0) / s0;
        float diff1 = (p1 - m1) / s1;
        float diff2 = (p2 - m2) / s2;
        float diff3 = (p3 - m3) / s3;
        
        log_prob_proposal += diff0 * diff0 + diff1 * diff1 + diff2 * diff2 + diff3 * diff3;
        
        x_new_row[d] = p0;
        x_new_row[d+1] = p1;
        x_new_row[d+2] = p2;
        x_new_row[d+3] = p3;
    }
    for (; d < dim; d++) {
        float noise = __ldg(&randn_row[d]);
        float proposal_d = __ldg(&x_row[d]) + step_size * noise;
        float diff = (proposal_d - __ldg(&mu[d])) / __ldg(&sigma[d]);
        log_prob_proposal += diff * diff;
        x_new_row[d] = proposal_d;
    }
    log_prob_proposal = -0.5f * log_prob_proposal;
    
    float log_alpha = log_prob_proposal - log_prob_x;
    
    float u = __ldg(&randu[batch_idx]);
    u = fmaxf(u, 1e-10f);
    float log_u = logf(u);
    
    bool accept = log_u < log_alpha;
    accepted[batch_idx] = accept;
    
    if (!accept) {
        for (int d = 0; d < dim; d++) {
            x_new_row[d] = __ldg(&x_row[d]);
        }
    }
}

std::tuple<torch::Tensor, torch::Tensor> mcmc_step_cuda(
    torch::Tensor x, torch::Tensor mu, torch::Tensor sigma,
    torch::Tensor randn, torch::Tensor randu, float step_size) {
    int batch_size = x.size(0);
    int dim = x.size(1);
    
    auto x_new = torch::empty_like(x);
    auto accepted = torch::empty({batch_size}, torch::TensorOptions().dtype(torch::kBool).device(x.device()));
    
    int threads = 256;
    int blocks = (batch_size + threads - 1) / threads;
    
    mcmc_step_kernel<<<blocks, threads>>>(
        x.data_ptr<float>(),
        mu.data_ptr<float>(),
        sigma.data_ptr<float>(),
        randn.data_ptr<float>(),
        randu.data_ptr<float>(),
        x_new.data_ptr<float>(),
        accepted.data_ptr<bool>(),
        step_size,
        batch_size,
        dim
    );
    
    return std::make_tuple(x_new, accepted);
}
''',
    functions=['mcmc_step_cuda'],
    extra_cuda_cflags=['-O3', '-use_fast_math'],
    verbose=False
)

class ModelNew(nn.Module):
    def __init__(self, dim, step_size=0.1):
        super().__init__()
        self.dim = dim
        self.step_size = step_size
        self.register_buffer("mu", torch.zeros(dim))
        self.register_buffer("sigma", torch.ones(dim))

    def forward(self, x: torch.Tensor) -> tuple:
        randn = torch.randn_like(x)
        randu = torch.rand(x.shape[0], device=x.device)
        return mcmc_cuda.mcmc_step_cuda(x, self.mu, self.sigma, randn, randu, self.step_size)