reasoning
reasoning (truncated 33460 chars): Let me analyze this task. I need to implement a fused GroupNorm + SiLU kernel in CUDA that's faster than the PyTorch reference.
The reference model:
1. Applies GroupNorm to normalize channels
2. Applies SiLU activation (x * sigmoid(x))
GroupNorm details:
- Divides channels into groups
- Normalizes within each group independently
- Has learnable affine parameters (weight, bias) if affine=True
For a fused kernel, I need to:
1. Compute mean and variance for each group across (C/G, H, W) for each sample in batch
2. Normalize: x_norm = (x - mean) / sqrt(var + eps)
3. Apply affine: out = weight * x_norm + bias
4. Apply SiLU: out = out * sigmoid(out)
Key considerations:
- GroupNorm computes statistics over (C/G * H * W) elements per group per sample
- This is a reduction operation, then an elementwise operation
- I should fuse the entire pipeline to avoid multiple kernel launches
Let me design the CUDA kernel:
Option 1: Single kernel with shared memory reduction
- Each block handles one group of one sample
- Threads collaborate to compute mean, then variance, then normalize+silu
- Need two passes or compute mean and variance in one pass using Welford's algorithm
Option 2: Two kernels
- Kernel 1: Compute mean and variance per group
- Kernel 2: Normalize and apply SiLU
For best performance, Option 1 with a single kernel per group is ideal. I'll use Welford's online algorithm or compute mean then variance.
Actually, let me think about the memory access pattern. Each block handles one (batch, group) pair. The elements for that group span channels [g * C/G, (g+1) * C/G) and all H, W.
For H=24, W=24, C/G = 256/32 = 8, so each group has 8 * 24 * 24 = 4608 elements.
I'll use a block with enough threads to cover this, with each thread handling multiple elements if needed.
Let me write the kernel:
```cpp
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cmath>
template <typename scalar_t>
__global__ void groupnorm_silu_kernel(
const scalar_t* __restrict__ x,
const scalar_t* __restrict__ weight,
const scalar_t* __restrict__ bias,
scalar_t* __restrict__ out,
int N, int C, int H, int W, int G,
int channels_per_group, int elements_per_group,
scalar_t eps) {
int batch_idx = blockIdx.x / G;
int group_idx = blockIdx.x % G;
int group_start_channel = group_idx * channels_per_group;
// Thread index
int tid = threadIdx.x;
int block_size = blockDim.x;
// Compute mean and variance using Welford's algorithm
// Each thread processes elements with stride
scalar_t mean = 0;
scalar_t var = 0;
int count = 0;
for (int i = tid; i < elements_per_group; i += block_size) {
int c_local = i / (H * W);
int hw = i % (H * W);
int h = hw / W;
int w = hw % W;
int c = group_start_channel + c_local;
int idx = batch_idx * C * H * W + c * H * W + h * W + w;
scalar_t val = x[idx];
// Welford's online algorithm
count++;
scalar_t delta = val - mean;
mean += delta / count;
scalar_t delta2 = val - mean;
var += delta * delta2;
}
// Reduce within block
// Using shared memory
__shared__ scalar_t s_mean[32]; // Assuming max 32 warps
__shared__ scalar_t s_var[32];
__shared__ int s_count[32];
int warp_id = tid / 32;
int lane_id = tid % 32;
// Warp reduce
for (int offset = 16; offset > 0; offset /= 2) {
scalar_t other_mean = __shfl_down_sync(0xffffffff, mean, offset);
scalar_t other_var = __shfl_down_sync(0xffffffff, var, offset);
int other_count = __shfl_down_sync(0xffffffff, count, offset);
if (lane_id < offset) {
// Combine statistics
scalar_t combined_mean = (mean * count + other_mean * other_count) / (count + other_count);
var = var + other_var + (mean - other_mean) * (mean - other_mean) * count * other_count / (count + other_count);
mean = combined_mean;
count = count + other_count;
}
}
if (lane_id == 0) {
s_mean[warp_id] = mean;
s_var[warp_id] = var;
s_count[warp_id] = count;
}
__syncthreads();
// First warp reduces across warps
if (warp_id == 0) {
mean = (lane_id < blockDim.x / 32) ? s_mean[lane_id] : 0;
var = (lane_id < blockDim.x / 32) ? s_var[lane_id] : 0;
count = (lane_id < blockDim.x / 32) ? s_count[lane_id] : 0;
for (int offset = 16; offset > 0; offset /= 2) {
scalar_t other_mean = __shfl_down_sync(0xffffffff, mean, offset);
scalar_t other_var = __shfl_down_sync(0xffffffff, var, offset);
int other_count = __shfl_down_sync(0xffffffff, count, offset);
if (lane_id < offset) {
scalar_t combined_mean = (mean * count + other_mean * other_count) / (count + other_count);
var = var + other_var + (mean - other_mean) * (mean - other_mean) * count * other_count / (count + other_count);
mean = combined_mean;
count = count + other_count;
}
}
if (lane_id == 0) {
s_mean[0] = mean;
s_var[0] = var;
}
}
__syncthreads();
mean = s_mean[0];
var = s_var[0] / elements_per_group; // Convert sum of squared differences to variance
scalar_t inv_std = rsqrt(var + eps);
// Apply normalization, affine, and SiLU
for (int i = tid; i < elements_per_group; i += block_size) {
int c_local = i / (H * W);
int hw = i % (H * W);
int h = hw / W;
int w = hw % W;
int c = group_start_channel + c_local;
int idx = batch_idx * C * H * W + c * H * W + h * W + w;
scalar_t val = x[idx];
scalar_t normalized = (val - mean) * inv_std;
scalar_t affine_val = normalized;
if (weight != nullptr) {
affine_val = weight[c] * normalized;
}
if (bias != nullptr) {
affine_val = affine_val + bias[c];
}
// SiLU: x * sigmoid(x)
scalar_t sigmoid_val = 1.0 / (1.0 + exp(-affine_val));
out[idx] = affine_val * sigmoid_val;
}
}
torch::Tensor groupnorm_silu_cuda(
torch::Tensor x,
torch::Tensor weight,
torch::Tensor bias,
int num_groups,
double eps) {
int N = x.size(0);
int C = x.size(1);
int H = x.size(2);
int W = x.size(3);
int G = num_groups;
int channels_per_group = C / G;
int elements_per_group = channels_per_group * H * W;
auto out = torch::empty_like(x);
int blocks = N * G;
int threads = min(1024, elements_per_group);
AT_DISPATCH_FLOATING_TYPES(x.scalar_type(), "groupnorm_silu_kernel", ([&] {
groupnorm_silu_kernel<scalar_t><<<blocks, threads>>>(
x.data_ptr<scalar_t>(),
weight.defined() ? weight.data_ptr<scalar_t>() : nullptr,
bias.defined() ? bias.data_ptr<scalar_t>() : nullptr,
out.data_ptr<scalar_t>(),
N, C, H, W, G,
channels_per_group, elements_per_group,
static_cast<scalar_t>(eps)
);
}));
return out;
}
```
Wait, this is getting complex. Let me simplify using two-pass approach (mean first, then variance), which is more straightforward:
Actually, let me think about the reduction more carefully. For 4608 elements with 256 threads per block:
- Each thread handles ~18 elements
- First pass: compute sum, reduce, broadcast mean
- Second pass: compute sum of squared differences, reduce, broadcast
- Third pass: normalize and apply SiLU
But this requires multiple passes through memory. Better to use single pass with Welford.
Actually, let me try a simpler approach: use CUDA's atomic operations or just compute sum and
...[ omitted 33460 characters ]...
down_sync(0xffffffff, sum_sq, offset);
}
// Shared memory for cross-warp reduction
__shared__ scalar_t s_sum[32];
__shared__ scalar_t s_sum_sq[32];
if (lane_id == 0) {
s_sum[warp_id] = sum;
s_sum_sq[warp_id] = sum_sq;
}
__syncthreads();
// First warp reduces across warps
if (warp_id == 0) {
sum = (lane_id < num_warps) ? s_sum[lane_id] : scalar_t(0);
sum_sq = (lane_id < num_warps) ? s_sum_sq[lane_id] : scalar_t(0);
#pragma unroll
for (int offset = 16; offset > 0; offset >>= 1) {
sum += __shfl_down_sync(0xffffffff, sum, offset);
sum_sq += __shfl_down_sync(0xffffffff, sum_sq, offset);
}
if (lane_id == 0) {
scalar_t mean = sum / static_cast<scalar_t>(elements_per_group);
scalar_t var = sum_sq / static_cast<scalar_t>(elements_per_group) - mean * mean;
scalar_t inv_std = rsqrt(var + eps);
s_sum[0] = mean;
s_sum_sq[0] = inv_std;
}
}
__syncthreads();
scalar_t mean = s_sum[0];
scalar_t inv_std = s_sum_sq[0];
// Apply normalization, affine, and SiLU
for (int i = tid; i < elements_per_group; i += block_size) {
int c_local = i / (H * W);
int c = group_start_channel + c_local;
int idx = base_idx + i;
scalar_t val = x[idx];
scalar_t normalized = (val - mean) * inv_std;
scalar_t affine_val = normalized;
if (weight != nullptr) {
affine_val = affine_val * weight[c];
}
if (bias != nullptr) {
affine_val = affine_val + bias[c];
}
// SiLU: x * sigmoid(x)
scalar_t sigmoid_val = scalar_t(1) / (scalar_t(1) + exp(-affine_val));
out[idx] = affine_val * sigmoid_val;
}
}
torch::Tensor groupnorm_silu_cuda(
torch::Tensor x,
c10::optional<torch::Tensor> weight_opt,
c10::optional<torch::Tensor> bias_opt,
int64_t num_groups,
double eps) {
TORCH_CHECK(x.is_cuda(), "Input must be a CUDA tensor");
TORCH_CHECK(x.dim() == 4, "Input must be 4D (NCHW)");
int N = static_cast<int>(x.size(0));
int C = static_cast<int>(x.size(1));
int H = static_cast<int>(x.size(2));
int W = static_cast<int>(x.size(3));
int G = static_cast<int>(num_groups);
int channels_per_group = C / G;
int elements_per_group = channels_per_group * H * W;
auto out = torch::empty_like(x);
int blocks = N * G;
int threads = std::min(1024, elements_per_group);
// Round down to power of 2
threads = 1 << (31 - __builtin_clz(threads));
threads = std::max(threads, 32); // At least one warp
cudaStream_t stream = at::cuda::getCurrentCUDAStream();
AT_DISPATCH_FLOATING_TYPES(x.scalar_type(), "groupnorm_silu_kernel", ([&] {
const scalar_t* weight_ptr = weight_opt.has_value() ? weight_opt.value().data_ptr<scalar_t>() : nullptr;
const scalar_t* bias_ptr = bias_opt.has_value() ? bias_opt.value().data_ptr<scalar_t>() : nullptr;
groupnorm_silu_kernel<scalar_t><<<blocks, threads, 0, stream>>>(
x.data_ptr<scalar_t>(),
weight_ptr,
bias_ptr,
out.data_ptr<scalar_t>(),
N, C, H, W, G,
channels_per_group, elements_per_group,
static_cast<scalar_t>(eps)
);
}));
return out;
}
"""
cpp_source = r"""
torch::Tensor groupnorm_silu_cuda(
torch::Tensor x,
c10::optional<torch::Tensor> weight_opt,
c10::optional<torch::Tensor> bias_opt,
int64_t num_groups,
double eps);
"""
# Load the extension at module level
module = load_inline(
name='groupnorm_silu_ext',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['groupnorm_silu_cuda'],
verbose=False,
extra_cuda_cflags=['-O3'],
)
class ModelNew(nn.Module):
def __init__(
self,
num_channels: int,
num_groups: int,
eps: float = 1e-5,
affine: bool = True,
):
super().__init__()
self.num_channels = num_channels
self.num_groups = num_groups
self.eps = eps
self.affine = affine
if affine:
self.weight = nn.Parameter(torch.ones(num_channels))
self.bias = nn.Parameter(torch.zeros(num_channels))
else:
self.register_parameter('weight', None)
self.register_parameter('bias', None)
def forward(self, x: torch.Tensor) -> torch.Tensor:
return module.groupnorm_silu_cuda(
x,
self.weight,
self.bias,
self.num_groups,
self.eps
)
```
Wait, I just realized there's a potential issue. When `threads = 1 << (31 - __builtin_clz(threads))`, if threads is already a power of 2, this gives the correct result. Let me verify:
If threads = 1024 = 2^10:
- __builtin_clz(1024) = 31 - 10 = 21
- 31 - 21 = 10
- 1 << 10 = 1024 ✓
If threads = 100:
- __builtin_clz(100) = 31 - 7 = 24 (since 100 requires 7 bits)
- Wait, let me check. 100 in binary is 1100100, which is 7 bits.
- In 32-bit representation: 0000...01100100 (25 leading zeros)
- __builtin_clz(100) = 25
- 31 - 25 = 6
- 1 << 6 = 64 ✓
Actually, I think __builtin_clz counts leading zeros in a 32-bit int:
- 1024 in binary: 00000000000000000000010000000000 (21 leading zeros)
- __builtin_clz(1024) = 21
- 31 - 21 = 10
- 1 << 10 = 1024 ✓
Good, the logic is correct.
But wait, there's an edge case: if threads = 1, then:
- __builtin_clz(1) = 31
- 31 - 31 = 0
- 1 << 0 = 1 ✓
If threads = 0 (which shouldn't happen, but just in case):
- __builtin_clz(0) is undefined behavior!
So I need to make sure threads >= 1 before this line. Since elements_per_group should always be >= 1 (C/G >= 1 and H*W >= 1), threads should be at least 1.
Actually, let me add a safety check:
```cpp
int threads = std::min(1024, elements_per_group);
threads = std::max(threads, 32);
threads = 1 << (31 - __builtin_clz(threads));
```
This ensures threads is at least 32 (one warp).
OK let me finalize the code. I'll also add a comment that the sigmoid computation might cause numerical issues for very large positive/negative values, but for typical neural network values, this should be fine.
One more thing - I should check that the indexing for c_local is correct. If i is the flat index within a group:
- c_local = i / (H * W) gives the local channel index within the group
- This works because within each group, elements are stored channel-major (first H*W elements for first channel, etc.)
Actually, let me trace through an example:
- N=1, C=256, H=24, W=24, G=32
- channels_per_group = 8
- elements_per_group = 8 * 24 * 24 = 4608
- For group 0, base_idx = 0 * 256 * 24 * 24 + 0 * 8 * 24 * 24 = 0
- For group 1, base_idx = 0 * 256 * 24 * 24 + 1 * 8 * 24 * 24 = 8 * 24 * 24 = 4608
- Within group 0:
- i=0: c_local = 0/(24*24) = 0, c = 0+0 = 0, idx = 0 + 0 = 0
- i=575 (just before H*W=576): c_local = 575/576 = 0, idx = 0 + 575 = 575
- i=576: c_local = 576/576 = 1, c = 0+1 = 1, idx = 0 + 576 = 576
- This corresponds to:
- idx 0-575: batch 0, channel 0, all H*W positions
- idx 576-1151: batch 0, channel 1, all H*W positions
- etc.
The indexing is correct!
Alright, let me finalize and submit the kernel. I'll also make sure to handle the case when the module is loaded multiple times (by giving it a unique name).
Actually, I just realized that `__builtin_clz` is a GCC/Clang builtin and might not work with all compilers. But since we're using nvcc which is based on GCC/Clang, it should work.
Let me also make sure the shared memory is correctly declared. I'm using scalar_t for s_sum and s_sum_sq, which should work.
One more consideration: the warp reduction assumes the warp size is 32, which is true for all current NVIDIA GPUs.
Alright, I think the kernel is ready. Let me submit it.
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 <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\ntemplate <typename scalar_t>\n__global__ void groupnorm_silu_kernel(\n const scalar_t* __restrict__ x,\n const scalar_t* __restrict__ weight,\n const scalar_t* __restrict__ bias,\n scalar_t* __restrict__ out,\n int N, int C, int H, int W, int G,\n int channels_per_group, int elements_per_group,\n scalar_t eps) {\n \n int batch_idx = blockIdx.x / G;\n int group_idx = blockIdx.x % G;\n \n int group_start_channel = group_idx * channels_per_group;\n int base_idx = batch_idx * C * H * W + group_start_channel * H * W;\n \n int tid = threadIdx.x;\n int lane_id = tid & 31;\n int warp_id = tid >> 5;\n int block_size = blockDim.x;\n int num_warps = (block_size + 31) >> 5;\n \n // Compute sum and sum of squares\n scalar_t sum = scalar_t(0);\n scalar_t sum_sq = scalar_t(0);\n \n for (int i = tid; i < elements_per_group; i += block_size) {\n scalar_t val = x[base_idx + i];\n sum += val;\n sum_sq += val * val;\n }\n \n // Warp-level reduction using shuffle\n #pragma unroll\n for (int offset = 16; offset > 0; offset >>= 1) {\n sum += __shfl_down_sync(0xffffffff, sum, offset);\n sum_sq += __shfl_down_sync(0xffffffff, sum_sq, offset);\n }\n \n // Shared memory for cross-warp reduction\n __shared__ scalar_t s_sum[32];\n __shared__ scalar_t s_sum_sq[32];\n \n if (lane_id == 0) {\n s_sum[warp_id] = sum;\n s_sum_sq[warp_id] = sum_sq;\n }\n __syncthreads();\n \n // First warp reduces across warps\n if (warp_id == 0) {\n sum = (lane_id < num_warps) ? s_sum[lane_id] : scalar_t(0);\n sum_sq = (lane_id < num_warps) ? s_sum_sq[lane_id] : scalar_t(0);\n \n #pragma unroll\n for (int offset = 16; offset > 0; offset >>= 1) {\n sum += __shfl_down_sync(0xffffffff, sum, offset);\n sum_sq += __shfl_down_sync(0xffffffff, sum_sq, offset);\n }\n \n if (lane_id == 0) {\n scalar_t mean = sum / static_cast<scalar_t>(elements_per_group);\n scalar_t var = sum_sq / static_cast<scalar_t>(elements_per_group) - mean * mean;\n scalar_t inv_std = rsqrt(var + eps);\n s_sum[0] = mean;\n s_sum_sq[0] = inv_std;\n }\n }\n __syncthreads();\n \n scalar_t mean = s_sum[0];\n scalar_t inv_std = s_sum_sq[0];\n \n // Apply normalization, affine, and SiLU\n for (int i = tid; i < elements_per_group; i += block_size) {\n int c_local = i / (H * W);\n int c = group_start_channel + c_local;\n int idx = base_idx + i;\n \n scalar_t val = x[idx];\n scalar_t normalized = (val - mean) * inv_std;\n \n scalar_t affine_val = normalized;\n if (weight != nullptr) {\n affine_val = affine_val * weight[c];\n }\n if (bias != nullptr) {\n affine_val = affine_val + bias[c];\n }\n \n // SiLU: x * sigmoid(x)\n scalar_t sigmoid_val = scalar_t(1) / (scalar_t(1) + exp(-affine_val));\n out[idx] = affine_val * sigmoid_val;\n }\n}\n\ntorch::Tensor groupnorm_silu_cuda(\n torch::Tensor x,\n c10::optional<torch::Tensor> weight_opt,\n c10::optional<torch::Tensor> bias_opt,\n int64_t num_groups,\n double eps) {\n \n TORCH_CHECK(x.is_cuda(), \"Input must be a CUDA tensor\");\n TORCH_CHECK(x.dim() == 4, \"Input must be 4D (NCHW)\");\n \n int N = static_cast<int>(x.size(0));\n int C = static_cast<int>(x.size(1));\n int H = static_cast<int>(x.size(2));\n int W = static_cast<int>(x.size(3));\n int G = static_cast<int>(num_groups);\n int channels_per_group = C / G;\n int elements_per_group = channels_per_group * H * W;\n \n auto out = torch::empty_like(x);\n \n int blocks = N * G;\n int threads = std::min(1024, elements_per_group);\n threads = std::max(threads, 32);\n threads = 1 << (31 - __builtin_clz(threads));\n \n cudaStream_t stream = at::cuda::getCurrentCUDAStream();\n \n AT_DISPATCH_FLOATING_TYPES(x.scalar_type(), \"groupnorm_silu_kernel\", ([&] {\n const scalar_t* weight_ptr = weight_opt.has_value() ? weight_opt.value().data_ptr<scalar_t>() : nullptr;\n const scalar_t* bias_ptr = bias_opt.has_value() ? bias_opt.value().data_ptr<scalar_t>() : nullptr;\n \n groupnorm_silu_kernel<scalar_t><<<blocks, threads, 0, stream>>>(\n x.data_ptr<scalar_t>(),\n weight_ptr,\n bias_ptr,\n out.data_ptr<scalar_t>(),\n N, C, H, W, G,\n channels_per_group, elements_per_group,\n static_cast<scalar_t>(eps)\n );\n }));\n \n return out;\n}\n\"\"\"\n\ncpp_source = r\"\"\"\ntorch::Tensor groupnorm_silu_cuda(\n torch::Tensor x,\n c10::optional<torch::Tensor> weight_opt,\n c10::optional<torch::Tensor> bias_opt,\n int64_t num_groups,\n double eps);\n\"\"\"\n\n# Load the extension at module level\nmodule = load_inline(\n name='groupnorm_silu_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['groupnorm_silu_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3'],\n)\n\nclass ModelNew(nn.Module):\n def __init__(\n self,\n num_channels: int,\n num_groups: int,\n eps: float = 1e-5,\n affine: bool = True,\n ):\n super().__init__()\n self.num_channels = num_channels\n self.num_groups = num_groups\n self.eps = eps\n self.affine = affine\n \n if affine:\n self.weight = nn.Parameter(torch.ones(num_channels))\n self.bias = nn.Parameter(torch.zeros(num_channels))\n else:\n self.register_parameter('weight', None)\n self.register_parameter('bias', None)\n \n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return module.groupnorm_silu_cuda(\n x,\n self.weight,\n self.bias,\n self.num_groups,\n self.eps\n )"
}