reasoning
reasoning (truncated 31402 chars): Let me analyze this task. I need to replace a PyTorch model that performs a Metropolis-Hastings MCMC step with a custom CUDA kernel.
The reference model:
1. Takes input `x` of shape (B, dim) - current chain states
2. Proposes a new state: `proposal = x + step_size * randn_like(x)`
3. Computes log probability difference: `log_alpha = log_prob(proposal) - log_prob(x)`
4. Accepts if `log(rand()) < log_alpha`
5. Returns `(x_new, accepted)` where `x_new = proposal` if accepted else `x`
The log probability is for a Gaussian target: `log_prob(x) = -0.5 * sum(((x - mu) / sigma)^2)`
So the computation involves:
1. Generating random noise for proposals
2. Computing proposals = x + step_size * noise
3. Computing log_prob for proposal and x
4. Generating uniform random numbers
5. Comparing and selecting
Let me write a custom CUDA kernel for this. I'll use cuRAND for random number generation.
Here's my plan:
1. Initialize cuRAND states for each thread
2. For each sample in the batch, generate the proposal and compute acceptance
3. Use XORWOW or Philox generator for random numbers
Let me write the kernel:
```cpp
#include <cuda.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#include <torch/extension.h>
// Kernel to initialize cuRAND states
__global__ void init_curand_state(curandState* states, unsigned long long seed, int n) {
int idx = blockIdx.x * blockDim.x + threadIdx.x;
if (idx < n) {
curand_init(seed, idx, 0, &states[idx]);
}
}
// Main MCMC kernel
__global__ void mcmc_step_kernel(
const float* __restrict__ x, // (B, dim)
float* __restrict__ x_new, // (B, dim)
bool* __restrict__ accepted, // (B,)
const float* __restrict__ mu, // (dim,)
const float* __restrict__ sigma, // (dim,)
curandState* states, // (B,)
int B, int dim, float step_size
) {
int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
if (batch_idx >= B) return;
curandState local_state = states[batch_idx];
// 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 normalized = diff / sigma[d];
log_prob_x += normalized * normalized;
}
log_prob_x = -0.5f * log_prob_x;
// Generate proposal and compute log_prob(proposal)
float log_prob_proposal = 0.0f;
for (int d = 0; d < dim; d++) {
float noise = curand_normal(&local_state);
float proposal_d = x[batch_idx * dim + d] + step_size * noise;
float diff = proposal_d - mu[d];
float normalized = diff / sigma[d];
log_prob_proposal += normalized * normalized;
x_new[batch_idx * dim + d] = proposal_d;
}
log_prob_proposal = -0.5f * log_prob_proposal;
// Compute acceptance ratio
float log_alpha = log_prob_proposal - log_prob_x;
// Generate uniform random and check acceptance
float u = curand_uniform(&local_state);
float log_u = logf(max(u, 1e-10f));
bool accept = log_u < log_alpha;
accepted[batch_idx] = accept;
// If rejected, copy x to x_new
if (!accept) {
for (int d = 0; d < dim; d++) {
x_new[batch_idx * dim + d] = x[batch_idx * dim + d];
}
}
states[batch_idx] = local_state;
}
```
Wait, this approach has a problem - we need to store the cuRAND states persistently. Let me think about how to handle this in PyTorch's cpp_extension.
Actually, I think a better approach is to:
1. Store the cuRAND states as a member variable in ModelNew
2. Initialize them once
3. Use them in each forward call
Let me write the complete solution:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <cuda.h>
#include <cuda_runtime.h>
#include <curand_kernel.h>
#include <torch/extension.h>
// Kernel to initialize cuRAND states
__global__ void init_curand_state(curandState* states, unsigned long long seed, int n) {
int idx = blockIdx.x * blockDim.x + threadIdx.x;
if (idx < n) {
curand_init(seed, idx, 0, &states[idx]);
}
}
// Main MCMC kernel
__global__ void mcmc_step_kernel(
const float* __restrict__ x,
float* __restrict__ x_new,
bool* __restrict__ accepted,
const float* __restrict__ mu,
const float* __restrict__ sigma,
curandState* states,
int B, int dim, float step_size
) {
int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
if (batch_idx >= B) return;
curandState local_state = states[batch_idx];
// 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 normalized = diff / sigma[d];
log_prob_x += normalized * normalized;
}
log_prob_x = -0.5f * log_prob_x;
// Generate proposal and compute log_prob(proposal)
float log_prob_proposal = 0.0f;
for (int d = 0; d < dim; d++) {
float noise = curand_normal(&local_state);
float proposal_d = x[batch_idx * dim + d] + step_size * noise;
float diff = proposal_d - mu[d];
float normalized = diff / sigma[d];
log_prob_proposal += normalized * normalized;
x_new[batch_idx * dim + d] = proposal_d;
}
log_prob_proposal = -0.5f * log_prob_proposal;
// Compute acceptance ratio
float log_alpha = log_prob_proposal - log_prob_x;
// Generate uniform random and check acceptance
float u = curand_uniform(&local_state);
float log_u = logf(max(u, 1e-10f));
bool accept = log_u < log_alpha;
accepted[batch_idx] = accept;
// If rejected, copy x to x_new
if (!accept) {
for (int d = 0; d < dim; d++) {
x_new[batch_idx * dim + d] = x[batch_idx * dim + d];
}
}
states[batch_idx] = local_state;
}
// Host function wrappers
void init_curand_wrapper(curandState* states, unsigned long long seed, int n) {
int threads = 256;
int blocks = (n + threads - 1) / threads;
init_curand_state<<<blocks, threads>>>(states, seed, n);
}
void mcmc_step_wrapper(
const float* x, float* x_new, bool* accepted,
const float* mu, const float* sigma,
curandState* states,
int B, int dim, float step_size
) {
int threads = 256;
int blocks = (B + threads - 1) / threads;
mcmc_step_kernel<<<blocks, threads>>>(
x, x_new, accepted, mu, sigma, states, B, dim, step_size
);
}
"""
cpp_source = """
#include <torch/extension.h>
// Forward declarations
struct curandState;
void init_curand_wrapper(curandState* states, unsigned long long seed, int n);
void mcmc_step_wrapper(
const float* x, float* x_new, bool* accepted,
const float* mu, const float* sigma,
curandState* states,
int B, int dim, float step_size
);
// PyTorch wrapper functions
void init_curand(torch::Tensor states, unsigned long long seed, int n) {
init_curand_wrapper((curandState*)states.data_ptr(), seed, n);
}
void mcmc_step(
torch::Tensor x, torch::Tensor x_new, torch::Tensor accepted,
torch::Tensor mu, torch::Tensor sigma,
torch::Tensor states,
int B, int dim, float step_size
) {
mcmc_step_wrapper(
x.data_ptr<float>(), x_new.data_ptr<float>(), accepted.data_ptr<bool>(),
mu.data_ptr<float>(), sigma.data_ptr<float>(),
(curandState*)states.data_ptr(),
B, dim, step_size
);
}
"""
mcmc_module = load_inline(
name='mcmc_cuda',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['init_curand', 'mcmc_step'],
extra_cuda_cflags=['-lcurand'],
verbose=True
)
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))
self._states = None
self._batch_size = None
...[ omitted 31402 characters ]...
+= diff_x * diff_x;
const float noise = curand_normal(&state);
const float prop_d = x_d + step_size * noise;
x_new_ptr[d] = prop_d;
const float diff_p = (prop_d - mu_d) * inv_sigma_d;
sum_sq_p += diff_p * diff_p;
}
const float log_prob_x = -0.5f * sum_sq_x;
const float log_prob_p = -0.5f * sum_sq_p;
const float log_alpha = log_prob_p - log_prob_x;
const float u = curand_uniform(&state);
const float log_u = logf(max(u, 1e-10f));
const bool accept = log_u < log_alpha;
accepted[batch_idx] = accept ? 1 : 0;
if (!accept) {
for (int d = 0; d < dim; d++) {
x_new_ptr[d] = __ldg(&x_ptr[d]);
}
}
}
void mcmc_step_cuda(
const float* x, float* x_new, uint8_t* accepted,
const float* mu, const float* sigma,
int B, int dim, float step_size, unsigned long long seed
) {
const int threads = 256;
const int blocks = (B + threads - 1) / threads;
mcmc_step_kernel<<<blocks, threads>>>(
x, x_new, accepted, mu, sigma, B, dim, step_size, seed
);
}
"""
cpp_source = r"""
#include <torch/extension.h>
void mcmc_step_cuda(
const float* x, float* x_new, uint8_t* accepted,
const float* mu, const float* sigma,
int B, int dim, float step_size, unsigned long long seed
);
void mcmc_step(
torch::Tensor x, torch::Tensor x_new, torch::Tensor accepted,
torch::Tensor mu, torch::Tensor sigma,
int64_t B, int64_t dim, float step_size, unsigned long long seed
) {
mcmc_step_cuda(
x.data_ptr<float>(), x_new.data_ptr<float>(), accepted.data_ptr<uint8_t>(),
mu.data_ptr<float>(), sigma.data_ptr<float>(),
static_cast<int>(B), static_cast<int>(dim), step_size, seed
);
}
"""
mcmc_module = load_inline(
name='mcmc_cuda',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['mcmc_step'],
extra_cuda_cflags=['-lcurand'],
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))
self._call_count = 0
def forward(self, x):
B, dim = x.shape
assert dim == self.dim
x_new = torch.empty_like(x)
accepted = torch.empty(B, dtype=torch.uint8, device=x.device)
# Use a different seed for each call
seed = (self._call_count * 2654435761 + 12345) & 0xFFFFFFFFFFFFFFFF
self._call_count += 1
mcmc_module.mcmc_step(
x, x_new, accepted,
self.mu, self.sigma,
B, dim, self.step_size, seed
)
return x_new, accepted.to(torch.bool)
```
Wait, I think I need to be careful with the linking of curand. Let me check the compilation flags.
Actually, looking at other CUDA projects, for curand we might need:
- `-lcurand` for the library
- But `extra_cuda_cflags` is for nvcc flags, not linker flags
Let me try using `extra_ldflags` instead:
```python
mcmc_module = load_inline(
name='mcmc_cuda',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['mcmc_step'],
extra_cuda_cflags=['-O3'],
extra_ldflags=['-lcurand'],
verbose=False
)
```
Actually, I realize curand is a device library, so it should be linked differently. Let me check...
For CUDA device code that uses curand, you need to link against curand. In PyTorch's cpp_extension, you can use `libraries=['curand']` or `extra_ldflags=['-lcurand']`.
Let me try:
```python
mcmc_module = load_inline(
name='mcmc_cuda',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['mcmc_step'],
extra_cuda_cflags=['-O3'],
libraries=['curand'],
verbose=False
)
```
Actually, I just realized that curand_kernel.h is the device API and doesn't require linking to a library for the device code. The host-side curand library (libcurand.so) is for host functions, not device functions.
For device-side curand (curand_kernel.h), the random number generation is implemented inline in the kernel code, so we don't need to link against libcurand.
Let me verify this by removing the library linking and just having:
```python
mcmc_module = load_inline(
name='mcmc_cuda',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['mcmc_step'],
extra_cuda_cflags=['-O3'],
verbose=False
)
```
Actually, I think you do need to link to curand even for the device API because the header includes some library code. Let me include the library to be safe.
Let me also think about potential issues:
1. The `accepted` tensor - I'm using `uint8_t` but PyTorch's `torch.bool` might have a different representation. Let me check... PyTorch's bool tensors are typically 1 byte per element, so uint8_t should work.
2. The seed - I'm using a simple counter-based seed. This should give different random sequences for each call.
3. Numerical precision - I'm using `float` (fp32) throughout, which should match the reference.
Let me also add some safety checks and ensure the code compiles correctly.
Actually, let me simplify the kernel a bit and make sure it works first:
```cpp
__global__ void mcmc_step_kernel(
const float* __restrict__ x,
float* __restrict__ x_new,
uint8_t* __restrict__ accepted,
const float* __restrict__ mu,
const float* __restrict__ sigma,
int B, int dim, float step_size,
unsigned long long seed
) {
const int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
if (batch_idx >= B) return;
curandState state;
curand_init(seed, batch_idx, 0, &state);
float sum_sq_x = 0.0f;
float sum_sq_p = 0.0f;
for (int d = 0; d < dim; d++) {
const float x_d = x[batch_idx * dim + d];
const float mu_d = mu[d];
const float inv_sigma_d = 1.0f / sigma[d];
const float diff_x = (x_d - mu_d) * inv_sigma_d;
sum_sq_x += diff_x * diff_x;
const float noise = curand_normal(&state);
const float prop_d = x_d + step_size * noise;
x_new[batch_idx * dim + d] = prop_d;
const float diff_p = (prop_d - mu_d) * inv_sigma_d;
sum_sq_p += diff_p * diff_p;
}
const float log_alpha = -0.5f * (sum_sq_p - sum_sq_x);
const float u = curand_uniform(&state);
const float log_u = logf(max(u, 1e-10f));
const bool accept = log_u < log_alpha;
accepted[batch_idx] = accept ? 1 : 0;
if (!accept) {
for (int d = 0; d < dim; d++) {
x_new[batch_idx * dim + d] = x[batch_idx * dim + d];
}
}
}
```
Actually, I made an error in simplification. The log_alpha calculation should be:
```
log_prob_p = -0.5 * sum_sq_p
log_prob_x = -0.5 * sum_sq_x
log_alpha = log_prob_p - log_prob_x = -0.5 * (sum_sq_p - sum_sq_x)
```
Wait, that's not right either:
```
log_alpha = log_prob_p - log_prob_x
= (-0.5 * sum_sq_p) - (-0.5 * sum_sq_x)
= -0.5 * sum_sq_p + 0.5 * sum_sq_x
= 0.5 * (sum_sq_x - sum_sq_p)
```
Let me redo:
```
log_alpha = log_prob_proposal - log_prob_x
= (-0.5 * sum_sq_p) - (-0.5 * sum_sq_x)
= 0.5 * (sum_sq_x - sum_sq_p)
```
So `log_alpha = 0.5f * (sum_sq_x - sum_sq_p)`.
Let me verify with the reference:
```python
log_alpha = self._log_prob(proposal) - self._log_prob(x)
```
where `_log_prob(x) = -0.5 * sum(((x - mu) / sigma)^2)`.
So if sum_sq_x = sum(((x - mu) / sigma)^2) and sum_sq_p = sum(((proposal - mu) / sigma)^2), then:
```
log_alpha = (-0.5 * sum_sq_p) - (-0.5 * sum_sq_x)
= -0.5 * sum_sq_p + 0.5 * sum_sq_x
= 0.5 * (sum_sq_x - sum_sq_p)
```
Yes, so `log_alpha = 0.5f * (sum_sq_x - sum_sq_p)`.
Let me correct my kernel:
```cpp
const float log_alpha = 0.5f * (sum_sq_x - sum_sq_p);
```
OK let me write the final complete solution:
call → submit_kernel
callsubmit_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = r\"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <curand_kernel.h>\n#include <torch/extension.h>\n\n__global__ void mcmc_step_kernel(\n const float* __restrict__ x,\n float* __restrict__ x_new,\n uint8_t* __restrict__ accepted,\n const float* __restrict__ mu,\n const float* __restrict__ sigma,\n int B, int dim, float step_size,\n unsigned long long seed\n) {\n const int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;\n if (batch_idx >= B) return;\n \n // Initialize RNG state for this thread\n curandState state;\n curand_init(seed, batch_idx, 0, &state);\n \n // Compute log_prob(x) and generate proposal in one pass\n float sum_sq_x = 0.0f; // sum of ((x - mu) / sigma)^2\n float sum_sq_p = 0.0f; // sum of ((proposal - mu) / sigma)^2\n \n // Process elements in pairs using curand_normal2 for efficiency\n const int pairs = dim / 2;\n for (int p = 0; p < pairs; p++) {\n const int d0 = p * 2;\n const int d1 = d0 + 1;\n \n const float x0 = __ldg(&x[batch_idx * dim + d0]);\n const float x1 = __ldg(&x[batch_idx * dim + d1]);\n \n const float mu0 = __ldg(&mu[d0]);\n const float mu1 = __ldg(&mu[d1]);\n \n const float inv_sigma0 = __frcp_rn(__ldg(&sigma[d0]));\n const float inv_sigma1 = __frcp_rn(__ldg(&sigma[d1]));\n \n // Contribution from x\n const float diff_x0 = (x0 - mu0) * inv_sigma0;\n const float diff_x1 = (x1 - mu1) * inv_sigma1;\n sum_sq_x = __fmaf_rn(diff_x0, diff_x0, __fmaf_rn(diff_x1, diff_x1, sum_sq_x));\n \n // Generate proposal using two normal samples at once\n const float2 noise = curand_normal2(&state);\n const float prop0 = __fmaf_rn(step_size, noise.x, x0);\n const float prop1 = __fmaf_rn(step_size, noise.y, x1);\n x_new[batch_idx * dim + d0] = prop0;\n x_new[batch_idx * dim + d1] = prop1;\n \n // Contribution from proposal\n const float diff_p0 = (prop0 - mu0) * inv_sigma0;\n const float diff_p1 = (prop1 - mu1) * inv_sigma1;\n sum_sq_p = __fmaf_rn(diff_p0, diff_p0, __fmaf_rn(diff_p1, diff_p1, sum_sq_p));\n }\n \n // Handle remaining element if dim is odd\n if (dim & 1) {\n const int d = dim - 1;\n const float x_d = __ldg(&x[batch_idx * dim + d]);\n const float mu_d = __ldg(&mu[d]);\n const float inv_sigma_d = __frcp_rn(__ldg(&sigma[d]));\n \n const float diff_x = (x_d - mu_d) * inv_sigma_d;\n sum_sq_x = __fmaf_rn(diff_x, diff_x, sum_sq_x);\n \n const float noise = curand_normal(&state);\n const float prop_d = __fmaf_rn(step_size, noise, x_d);\n x_new[batch_idx * dim + d] = prop_d;\n \n const float diff_p = (prop_d - mu_d) * inv_sigma_d;\n sum_sq_p = __fmaf_rn(diff_p, diff_p, sum_sq_p);\n }\n \n // Compute log acceptance ratio\n // log_alpha = log_prob(proposal) - log_prob(x)\n // = -0.5 * sum_sq_p - (-0.5 * sum_sq_x)\n // = 0.5 * (sum_sq_x - sum_sq_p)\n const float log_alpha = 0.5f * (sum_sq_x - sum_sq_p);\n \n // Generate uniform and check acceptance\n const float u = curand_uniform(&state);\n const float log_u = logf(fmaxf(u, 1e-10f));\n \n const bool accept = log_u < log_alpha;\n accepted[batch_idx] = accept ? uint8_t(1) : uint8_t(0);\n \n // If rejected, restore original x\n if (!accept) {\n for (int d = 0; d < dim; d++) {\n x_new[batch_idx * dim + d] = __ldg(&x[batch_idx * dim + d]);\n }\n }\n}\n\nvoid mcmc_step_cuda(\n const float* x, float* x_new, uint8_t* accepted,\n const float* mu, const float* sigma,\n int B, int dim, float step_size, unsigned long long seed\n) {\n const int threads = 256;\n const int blocks = (B + threads - 1) / threads;\n mcmc_step_kernel<<<blocks, threads>>>(\n x, x_new, accepted, mu, sigma, B, dim, step_size, seed\n );\n}\n\"\"\"\n\ncpp_source = r\"\"\"\n#include <torch/extension.h>\n\nvoid mcmc_step_cuda(\n const float* x, float* x_new, uint8_t* accepted,\n const float* mu, const float* sigma,\n int B, int dim, float step_size, unsigned long long seed\n);\n\nvoid mcmc_step(\n torch::Tensor x, torch::Tensor x_new, torch::Tensor accepted,\n torch::Tensor mu, torch::Tensor sigma,\n int64_t B, int64_t dim, float step_size, unsigned long long seed\n) {\n mcmc_step_cuda(\n x.data_ptr<float>(), x_new.data_ptr<float>(), accepted.data_ptr<uint8_t>(),\n mu.data_ptr<float>(), sigma.data_ptr<float>(),\n static_cast<int>(B), static_cast<int>(dim), step_size, seed\n );\n}\n\"\"\"\n\nmcmc_module = load_inline(\n name='mcmc_cuda_v1',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['mcmc_step'],\n extra_cuda_cflags=['-O3', '--use_fast_math'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n \"\"\"\n Batched Metropolis-Hastings MCMC step with custom CUDA kernel.\n Fuses random number generation, proposal computation, and acceptance\n into a single kernel launch for optimal performance.\n \"\"\"\n \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 self._call_count = 0\n \n def forward(self, x: torch.Tensor) -> tuple:\n \"\"\"\n Args:\n x: (B, dim) - current chain states\n Returns:\n (x_new, accepted):\n x_new: (B, dim) - states after accept/reject\n accepted: (B,) - boolean mask of accepted proposals\n \"\"\"\n B, dim = x.shape\n assert dim == self.dim, f\"Expected dim={self.dim}, got {dim}\"\n assert x.is_cuda, \"Input must be on CUDA device\"\n \n x_new = torch.empty_like(x)\n accepted = torch.empty(B, dtype=torch.uint8, device=x.device)\n \n # Use a different seed for each call to ensure independent samples\n seed = (self._call_count * 2654435761ULL + 12345) & 0xFFFFFFFFFFFFFFFF\n self._call_count += 1\n \n mcmc_module.mcmc_step(\n x.contiguous(), x_new, accepted,\n self.mu.contiguous(), self.sigma.contiguous(),\n B, dim, self.step_size, seed\n )\n \n return x_new, accepted.to(torch.bool)"
}