reasoning
Let me analyze the problem:
1. We have a model with: Linear (GEMM) -> GroupNorm -> HardTanh
2. Input shape: (batch_size=1024, in_features=8192)
3. Output shape: (batch_size=1024, out_features=8192)
4. num_groups = 16
The forward pass:
1. Linear: y = x @ W^T + b, where x is (1024, 8192), W is (8192, 8192)
- This is a large GEMM: 1024 * 8192 * 8192 * 2 ≈ 137 GFLOPs
2. GroupNorm: normalize each group of channels
- For GN on (1024, 8192) with 16 groups: each group has 8192/16 = 512 channels
- We compute mean and variance per group per sample
3. HardTanh: clamp(min_val, max_val)
Since the GEMM is the dominant operation (137 GFLOPs), the main question is whether we can fuse the GroupNorm and HardTanh into a custom kernel that runs after the GEMM, or if we should try to fuse everything into one kernel.
Actually, let me think about this more carefully. The linear layer involves a large GEMM which PyTorch likely dispatches to cuBLAS. Since 137 GFLOPs at 67 TFLOPS = ~2ms compute bound. Memory bandwidth bound for just reading inputs/writing outputs: ~1024*8192*4*3 ≈ 100MB, at 3.35 TB/s = ~0.03ms, so it's definitely compute bound.
PyTorch's linear → group_norm → hardtanh sequence:
- Linear: cuBLAS, works well
- GroupNorm: cuDNN or PyTorch native, probably not bad
- HardTanh: element-wise, memory bound
The overhead might be in:
1. Not fusing GroupNorm + HardTanh (extra memory round-trip)
2. PyTorch's GroupNorm might have overhead
We can write a fused kernel that does GroupNorm + HardTanh in one pass after the GEMM. Or maybe even fuse the bias addition into the GroupNorm kernel.
Actually, looking at it more, PyTorch might already fuse some of this. Let me think about what we can optimize:
- We could do the GEMM with torch.matmul and then fuse group_norm + hardtanh into a custom CUDA kernel
- Or we could try using Tensor Cores for the GEMM, but PyTorch already does that
Wait, since this is fp32 and we need to match PyTorch exactly, there might be precision considerations.
Let me think about the GroupNorm computation:
For each sample n and each group g:
1. Compute mean over channels in group: μ = mean(y[n, g*C/G:(g+1)*C/G])
2. Compute variance: σ² = mean((y - μ)²)
3. Normalize: (y - μ) / sqrt(σ² + ε)
4. Scale and shift: γ * normalized + β
PyTorch's default epsilon for group norm is 1e-5.
A custom fused kernel would:
1. First compute the linear output into a temporary tensor
2. Then launch a kernel that computes group statistics, normalizes, applies scale/shift, and hardtanh
Since batch_size=1024 and num_groups=16, we have 1024*16 = 16384 groups. Each group has 512 elements.
For the reduction (mean/variance), each group spans 512 consecutive channels. For a sample row, there are 16 groups of 512 channels.
A natural kernel design:
- Each thread block handles one or more (sample, group) pairs
- Threads within a block cooperatively reduce 512 elements to mean and variance
- Then apply normalization, weight/bias, and hardtanh
Actually, we can be smarter. Since 8192 channels per sample and groups of 512, we could:
- Launch 1024 blocks (one per sample), each block handles 16 groups
- Or launch 1024*16 = 16384 blocks, each handling 1 group
For a single group of 512 elements, we need to read 512 elements, compute mean and variance. With 128 threads per block, each thread handles 4 elements. That's quite efficient.
For 16384 blocks at 128 threads each = ~2M threads total. We have 132 SMs on H100, so that's plenty of parallelism.
Let me think about the algorithm more precisely:
```cuda
// For each sample n (0..1023) and group g (0..15)
// blockIdx.x could be n * num_groups + g
const int ng = blockIdx.x; // which (sample, group) pair
const int n = ng / num_groups;
const int g = ng % num_groups;
const int group_size = out_features / num_groups; // 512
// Load elements for this group
// x = gemm_output[n, g*group_size + local_idx]
// compute mean
// compute variance
// normalize, apply gamma/beta, hardtanh
// store result
```
For mean and variance, we can do a two-pass or Welford's algorithm. But for numerical equivalence to PyTorch, we need to be careful.
PyTorch's GroupNorm computation:
```python
mean = x.mean(dim=[-1], keepdim=True)
var = x.var(dim=[1], unbiased=False, keepdim=True)
std = torch.sqrt(var + eps)
y = (x - mean) / std
y = y * gamma + beta
```
Wait, PyTorch's GroupNorm works on input of shape (N, C, *). For 2D input (N, C), it computes mean and var over C for each group? No, let me check...
Actually, for GroupNorm with num_groups groups on input (N, C), the input is viewed as (N, num_groups, C/num_groups). Then it computes mean and variance over the last dimension (C/num_groups) for each (N, num_group) pair.
So yes, per sample, per group, over the group_size channels.
For numerical equivalence, let me check what PyTorch does internally. It likely does a two-pass approach or Welford. For matching exactly, I'll need to be careful about the order of operations.
Actually, for fp32 precision with tolerance 1e-4, small differences in reduction order might be okay, but let me try to match PyTorch as closely as possible.
One approach: do linear + bias with torch.matmul/addmm, then call our custom kernel.
Wait, we can also fuse the bias addition into our GroupNorm kernel! After GEMM, we add bias (broadcast over batch). Then our kernel does group norm + hardtanh.
For numerical precision, let me think about what PyTorch does:
1. `nn.Linear` does `x @ W.T + b`
2. `nn.GroupNorm` takes the result, views as (N, G, C/G), computes mean over C/G, var over C/G, normalizes
3. `nn.HardTanh` clamps
If we write a custom kernel, we need to handle the weight and bias of GroupNorm as well.
Wait - the reference uses `nn.GroupNorm`, which has learnable `weight` and `bias` parameters. But in the reference code, the default initialization is `weight=ones, bias=zeros`. The evaluation might initialize with whatever defaults PyTorch uses.
Looking at PyTorch's GroupNorm:
```python
self.weight = Parameter(torch.empty(num_channels))
self.bias = Parameter(torch.empty(num_channels))
```
Default initialization is uniform distribution for weight and bias? No, actually nn.GroupNorm in PyTorch 1.9+ initializes weight to 1 and bias to 0 by default. Let me check...
Actually, PyTorch's GroupNorm does:
```python
def reset_parameters(self):
if self.affine:
init.ones_(self.weight)
init.zeros_(self.bias)
```
So weight=1, bias=0 by default. But the evaluation might train or not... The prompt says "Replace the forward computation" and "get_init_inputs" returns the constructor args. Since the reference is a nn.Module, the evaluation will likely use `ModelNew(*get_init_inputs())` and then compare outputs on `get_inputs()`.
Since the model may or may not have trained parameters, our kernel needs to handle the actual learned parameters. But looking at the task more carefully - it says "Replace the forward computation of the PyTorch model below with a custom CUDA kernel" and "Your ModelNew class must accept the same constructor arguments as Model."
So ModelNew needs to have gemm, group_norm, and hardtanh parameters, or at least handle them. But since we want to use a custom kernel, we could:
1. Keep the nn.Linear layer as-is and use its weight/bias
2. Keep the nn.GroupNorm parameters
3. Fuse the group_norm + hardtanh into a kernel
Actually, a simpler approach: keep all the PyTorch nn modules for parameter storage, but fuse the forward pass into a custom kernel.
```python
class ModelNew(nn.Module):
def __init__(self, ...):
super().__init__()
self.gemm = nn.Linear(...)
self.group_norm = nn.GroupNorm(...)
self.hardtanh = nn.Hardtanh(...)
def forward(self, x):
y = F.linear(x, self.gemm.weight, self.gemm.bias)
# call custom fused kernel with gn weight, gn bias, eps
return fused_gn_hardtanh(y, self.group_norm.weight, self.group_norm.bias,
self.group_norm.num_groups, self.group_norm.eps,
hardtanh_min, hardtanh_max)
```
But we can also just do: `y = torch.mm(x, self.gemm.weight.t())` and add bias in the custom kernel.
For maximum efficiency, let's:
1. Compute `y = x @ W.T` using torch.matmul (which goes to cuBLAS)
2. In our kernel, add bias, compute group norm, apply hardtanh
Wait, actually if we use `torch.addmm` or `F.linear`, PyTorch will dispatch to cuBLAS and already use Tensor Cores (TF32). That's probably optimal for the GEMM.
For the custom kernel, I'll write a CUDA kernel that:
1. Takes the GEMM output (before bias addition? or after?)
2. Adds bias (broadcast over batch)
3. Computes per-group mean and variance
4. Normalizes
5. Applies GroupNorm weight and bias
6. Applies HardTanh
Actually, looking at the problem again. For maximum performance, I should try to fuse as much as possible. But the main bottleneck is likely the GEMM itself. Can I beat PyTorch's end-to-end time?
PyTorch might not fuse GroupNorm + HardTanh, causing an extra memory pass. Also, GroupNorm in PyTorch might be implemented in a way that's not optimal for this specific size.
Let me design the kernel:
Input: `input` of shape (N, C) where N=1024, C=8192
Parameters:
- `bias` of shape (C,) - linear bias
- `gn_weight` of shape (C,)
- `gn_bias` of shape (C,)
Kernel configuration:
- One block per (sample, group) pair: 1024 * 16 = 16384 blocks
- Each block has 128 or 256 threads
- Each group has C/G = 512 elements
Let me think about the reduction more carefully.
For mean and variance over 512 elements:
- With 128 threads, each thread reads 4 elements
- Use shared memory for reduction
- Compute mean using warp shuffle or shared memory reduction
- Compute variance similarly
Algorithm for a block handling one group:
```cuda
__shared__ float sh_mean[...];
__shared__ float sh_var[...];
// Load 4 elements per thread
float sum = 0.0f;
for (i = 0; i < 4; i++) {
float val = input[n, group_start + threadIdx.x + i*128] + bias[group_start + threadIdx.x + i*128];
sum += val;
}
// reduce sum to mean
mean = blockReduceSum(sum) / 512.0f;
// compute variance
float sq_sum = 0.0f;
for (i = 0; i < 4; i++) {
float val = input[...] + bias[...];
float diff = val - mean;
sq_sum += diff * diff;
}
var = blockReduceSum(sq_sum) / 512.0f;
std = sqrtf(var + eps);
// normalize and write back
for (i = 0; i < 4; i++) {
int c = group_start + threadIdx.x + i*128;
float val = input[n, c] + bias[c];
float norm = (val - mean) / std;
norm = norm * gn_weight[c] + gn_bias[c];
norm = fminf(fmaxf(norm, min_val), max_val);
output[n, c] = norm;
}
```
Wait, I don't need to re-read input + bias. I can store the loaded values in registers, but 512 elements per group with 128 threads at 4 elements each = 512. Each thread keeps 4 floats, which is fine.
Actually, I can restructure to minimize register usage and shared memory:
```cuda
// Step 1: compute mean
float local[4];
#pragma unroll
for (int i = 0; i < 4; i++) {
int idx = threadIdx.x + i * blockDim.x;
if (idx < 512) {
local[i] = input[n * 8192 + group_start + idx] + bias[group_start + idx];
}
}
float sum = 0;
#pragma unroll
for (int i = 0; i < 4; i++) sum += local[i];
float mean = blockReduceSum(sum) / 512.0f;
// Step 2: compute variance
float sq_sum = 0;
#pragma unroll
for (int i = 0; i < 4; i++) {
float diff = local[i] - mean;
sq_sum += diff * diff;
}
float var = blockReduceSum(sq_sum) / 512.0f;
float rstd = 1.0f / sqrtf(var + eps);
// Step 3: normalize, apply affine, hardtanh, write
#pragma unroll
for (int i = 0; i < 4; i++) {
int idx = threadIdx.x + i * blockDim.x;
if (idx < 512) {
int c = group_start + idx;
float norm = (local[i] - mean) * rstd;
norm = norm * gn_weight[c] + gn_bias[c];
norm = fminf(fmaxf(norm, min_val), max_val);
output[n * 8192 + c] = norm;
}
}
```
Wait, but there's a precision concern. If I load everything into registers, compute mean, then compute variance using the same values, it should be close to PyTorch but the order of operations in reduction might differ.
For numerical equivalence with PyTorch within 1e-4, differences from reduction order should be minimal since we're using fp32.
Actually, let me think about whether we can avoid the second memory read of input. We need the linear output. If we use `torch.nn.functional.linear` first, then the linear output is in GPU memory, and our kernel reads it.
For performance, we could also compute the linear layer ourselves in the kernel using shared memory tiling... but 8192x8192 GEMM is best left to cuBLAS.
Let me consider fusing the bias addition. Yes, we can add bias when we first read the GEMM output in our custom kernel. That saves a separate kernel launch for bias addition.
Actually, `F.linear` already fuses the GEMM + bias addition in PyTorch (using cuBLAS). So if we call `F.linear`, we get the output with bias already. Then our kernel just needs to do GroupNorm + HardTanh.
Hmm, but we could call `torch.mm(x, weight.t())` without bias, and add bias ourselves. Does that matter? Probably not much, since cuBLAS fusion of bias is already efficient. But if we do our own bias add, we can combine it with reading for GroupNorm, saving a memory write + read of the biased output. Actually, `torch.nn.functional.linear` might launch one fused kernel, so the output is already biased. Then our custom kernel reads it. That's one read of the GEMM output.
If we use `torch.mm(x, weight.t())` and then our kernel adds bias + does GN + hardtanh, we save writing bias to memory and re-reading it. But wait - `torch.addmm` writes the result to memory, so either way we read from memory in our custom kernel. The question is whether the bias is already in that memory.
If `F.linear` writes bias to memory, then our kernel reads it from memory. That's optimal (one read of GEMM output). If we use `torch.mm` without bias, we'd read the GEMM output, add bias in registers, compute GN, and write. That's also one read of GEMM output. Same number of memory reads.
But using `F.linear` is closer to the reference and likely optimal.
Wait, `F.linear` on H100 with TF32 Tensor Cores should be very fast. Let me check:
- 1024 * 8192 * 8192 * 2 = 137 GFLOPs
- At 989 TFLOPS (TF32 Tensor Core) = ~0.14ms
- At 67 TFLOPS (FP32) = ~2ms
TF32 gives 1e-3 precision which should be within our 1e-4 tolerance? Hmm, PyTorch reference uses fp32 by default. If we use `torch.mm` it might use TF32 by default on H100. Actually, PyTorch enables TF32 by default on Ampere/Hopper. The reference also runs on the same GPU, so it would also use TF32 for the GEMM.
For the custom kernel, if we call `F.linear`, we'll get the same TF32 GEMM as the reference, which is good for correctness.
Then our custom kernel just needs to do GroupNorm + HardTanh.
Let me estimate the time for a fused GN+HardTanh kernel:
- Read: 1024 * 8192 * 4 = 32 MB
- Write: 32 MB
- Total memory: ~64 MB at 3.35 TB/s = ~0.019ms
- Plus some compute for reductions.
Actually, if PyTorch's reference does Linear → GroupNorm → HardTanh as three separate operations, there might be extra memory traffic:
- Linear: reads x, W, writes y1. Memory ~ (1024*8192*4 + 8192*8192*4 + 1024*8192*4) ≈ 300MB read + 32MB write
- GroupNorm: reads y1, gn_weight, gn_bias, writes y2. Memory ~ 32MB + 32KB + 32KB read + 32MB write
- HardTanh: reads y2, writes y3. Memory ~ 32MB read + 32MB write
If we fuse GN + HardTanh: we save one round-trip of 32MB read + 32MB write ≈ 64MB of memory traffic.
But since the GEMM is compute-bound at ~0.14ms with TF32, the total time might be dominated by the GEMM. Let's see:
- Linear: ~0.14ms (with TF32)
- GroupNorm: ~0.02ms (memory bound)
- HardTanh: ~0.02ms (memory bound)
Total reference: ~0.18ms
Fused version: ~0.14ms + ~0.02ms = ~0.16ms
Speedup: ~1.12x. Not huge, but might be enough.
Actually, can we do better? What about fusing everything into one kernel?
Let me think about doing the GEMM + GN + HardTanh all in one kernel. For a large GEMM, this doesn't make sense because the GEMM itself should use Tensor Cores via cuBLAS.
But wait - for (1024, 8192) @ (8192, 8192), the output is only 1024*8192 = 8M elements. Each row is 8192 elements. We could process one row in a thread block, computing the linear combination using shared memory for tiling, then do the GN on the result, then write out.
However, doing a full matmul in CUDA without Tensor Cores would be much slower than cuBLAS with Tensor Cores. Let's verify:
- Manual matmul: 137 GFLOPs at ~10-20 TFLOPS (SIMT) = ~7-14ms
- cuBLAS TF32: ~0.14ms
So definitely we should use cuBLAS for the GEMM.
Alternative idea: can we use CUTLASS or some other approach? Not easily with `load_inline`.
So the strategy is:
1. Use `F.linear` or `torch.mm` for GEMM
2. Fuse GroupNorm + HardTanh in a custom kernel
Let me think about whether there's additional optimization. Could we use a more efficient reduction for GroupNorm?
For 512 elements per group and 128 threads:
- We can use warp shuffle for reduction
- 4 warps of 32 threads
- Each thread loads 4 elements
- Warp-level reduction, then final reduction across warps in shared memory
Let me write out the CUDA kernel more carefully:
```cuda
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <cmath>
#define BLOCK_SIZE 128
__device__ __forceinline__ float warp_reduce_sum(float val) {
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
val += __shfl_down_sync(0xFFFFFFFF, val, offset);
return val;
}
__global__ void fused_group_norm_hardtanh_kernel(
const float* __restrict__ input,
const float* __restrict__ weight,
const float* __restrict__ bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
int tid = threadIdx.x;
int ng = blockIdx.x; // which (sample, group) pair
int n = ng / num_groups;
int g = ng % num_groups;
int group_size = C / num_groups;
int c_start = g * group_size;
int row_offset = n * C;
float local_vals[4];
int elems_per_thread = (group_size + BLOCK_SIZE - 1) / BLOCK_SIZE;
// Load and compute mean
float sum = 0.0f;
#pragma unroll
for (int i = 0; i < elems_per_thread; i++) {
int idx = tid + i * BLOCK_SIZE;
if (idx < group_size) {
float val = input[row_offset + c_start + idx];
local_vals[i] = val;
sum += val;
} else {
local_vals[i] = 0.0f;
}
}
// Warp reduce
sum = warp_reduce_sum(sum);
__shared__ float s_mean[BLOCK_SIZE / 32];
int warp_id = tid / 32;
int lane_id = tid % 32;
if (lane_id == 0) s_mean[warp_id] = sum;
__syncthreads();
// Final reduction across warps
if (warp_id == 0) {
float mean = (lane_id < BLOCK_SIZE / 32) ? s_mean[lane_id] : 0.0f;
mean = warp_reduce_sum(mean) / group_size;
if (lane_id == 0) s_mean[0] = mean;
}
__syncthreads();
float mean = s_mean[0];
// Compute variance
float sq_sum = 0.0f;
#pragma unroll
for (int i = 0; i < elems_per_thread; i++) {
int idx = tid + i * BLOCK_SIZE;
if (idx < group_size) {
float diff = local_vals[i] - mean;
sq_sum += diff * diff;
}
}
sq_sum = warp_reduce_sum(sq_sum);
if (lane_id == 0) s_mean[warp_id] = sq_sum;
__syncthreads();
if (warp_id == 0) {
float var = (lane_id < BLOCK_SIZE / 32) ? s_mean[lane_id] : 0.0f;
var = warp_reduce_sum(var) / group_size;
if (lane_id == 0) s_mean[0] = 1.0f / sqrtf(var + eps);
}
__syncthreads();
float rstd = s_mean[0];
// Normalize, apply affine, hardtanh, write
#pragma unroll
for (int i = 0; i < elems_per_thread; i++) {
int idx = tid + i * BLOCK_SIZE;
if (idx < group_size) {
int c = c_start + idx;
float norm = (local_vals[i] - mean) * rstd;
norm = norm * weight[c] + bias[c];
norm = fminf(fmaxf(norm, min_val), max_val);
output[row_offset + c] = norm;
}
}
}
```
Wait, there's an issue. The `s_mean` array is declared as `__shared__ float s_mean[BLOCK_SIZE / 32]`. If BLOCK_SIZE is 128, then it's `float s_mean[4]`. But then when warp_id == 0 does the final reduction, `lane_id` can be up to 31, but we only have 4 elements. So we need `lane_id < (BLOCK_SIZE / 32)` check, which is there. But we also need the shared memory to be big enough. `BLOCK_SIZE / 32 = 4` for 128 threads. That's fine.
Actually, I should make `s_mean` size at least the number of warps. Let me fix the code to be cleaner:
```cuda
__shared__ float s_scratch[BLOCK_SIZE / 32];
```
And in the first reduction:
- Each warp reduces its own sum
- Lane 0 writes to s_scratch[warp_id]
- Then warp 0 reads s_scratch[lane_id] and reduces
For the variance reduction, reuse s_scratch.
This should work.
But wait - if `group_size = 512` and `BLOCK_SIZE = 128`, then `elems_per_thread = 4`. The `#pragma unroll` for `i < elems_per_thread` only works if `elems_per_thread` is a compile-time constant. Since `group_size` is passed at runtime, `elems_per_thread` is computed at runtime. So the compiler can't unroll the loop.
Since 512/128 = 4 exactly, we can just hardcode 4 inside the kernel using a template parameter or by making the compile-time assumption. For this specific problem, C=8192 and num_groups=16, so group_size=512 always. But to be general, let me keep it as a runtime loop - the compiler might still optimize it. Actually, for known `BLOCK_SIZE = 128` and typical `group_size = 512`, we can just write `for (int i = 0; i < 4; i++)` with a guard `if (idx < group_size)`.
Wait, if we always have 512 elements and 128 threads, each thread handles exactly 4 elements, so `idx = tid + i*128` where i=0,1,2,3, and idx is always < 512. We can drop the guard if we know it's exactly 512.
But to be safe and general, let me write it properly.
Actually, for performance, since we're on H100, even a runtime loop should be fine given the small number of iterations. Let me just use a constant template parameter for block size.
Let me restructure more carefully:
```cuda
template <int BLOCK_THREADS>
__global__ void fused_gn_hardtanh_kernel(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int group_size = C / num_groups; // Should be 512 for our config
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
const int NUM_LOADS = (group_size + BLOCK_THREADS - 1) / BLOCK_THREADS;
// Cooperative loading and mean computation
float thread_sum = 0.0f;
float vals[NUM_LOADS];
#pragma unroll
for (int i = 0; i < NUM_LOADS; i++) {
int idx = tid + i * BLOCK_THREADS;
if (idx < group_size) {
float v = input[base_idx + idx];
vals[i] = v;
thread_sum += v;
} else {
vals[i] = 0.0f;
}
}
// Warp reduce sum
unsigned mask = 0xFFFFFFFF;
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
thread_sum += __shfl_down_sync(mask, thread_sum, offset);
__shared__ float shared[BLOCK_THREADS / 32];
int lane = tid & 31;
int warp = tid >> 5;
if (lane == 0) shared[warp] = thread_sum;
__syncthreads();
// Reduce across warps
if (warp == 0) {
float val = (lane < (BLOCK_THREADS >> 5)) ? shared[lane] : 0.0f;
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
val += __shfl_down_sync(mask, val, offset);
if (lane == 0) shared[0] = val / (float)group_size;
}
__syncthreads();
float mean = shared[0];
// Variance
float thread_sq = 0.0f;
#pragma unroll
for (int i = 0; i < NUM_LOADS; i++) {
int idx = tid + i * BLOCK_THREADS;
if (idx < group_size) {
float diff = vals[i] - mean;
thread_sq += diff * diff;
}
}
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
thread_sq += __shfl_down_sync(mask, thread_sq, offset);
if (lane == 0) shared[warp] = thread_sq;
__syncthreads();
if (warp == 0) {
float val = (lane < (BLOCK_THREADS >> 5)) ? shared[lane] : 0.0f;
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
val += __shfl_down_sync(mask, val, offset);
if (lane == 0) shared[0] = 1.0f / sqrtf(val / (float)group_size + eps);
}
__syncthreads();
float rstd = shared[0];
// Write output
#pragma unroll
for (int i = 0; i < NUM_LOADS; i++) {
int idx = tid + i * BLOCK_THREADS;
if (idx < group_size) {
int c = base_c + idx;
float v = (vals[i] - mean) * rstd;
v = v * gn_weight[c] + gn_bias[c];
v = fminf(fmaxf(v, min_val), max_val);
output[base_idx + idx] = v;
}
}
}
```
For `BLOCK_THREADS = 128` and `group_size = 512`, `NUM_LOADS = 4` which the compiler can unroll since `BLOCK_THREADS` is a template parameter... Actually, wait. `group_size` is a runtime variable (even though it's `C / num_groups`). So `NUM_LOADS = (group_size + BLOCK_THREADS - 1) / BLOCK_THREADS` requires runtime computation. But since `BLOCK_THREADS` is a template parameter and `group_size` is known to be a constant expression in some contexts... actually no, `group_size = C / num_groups` where C and num_groups are kernel parameters. So it's computed at runtime.
Wait, but if C=8192 and num_groups=16, then group_size=512. However, since these are passed as arguments, the compiler doesn't know at compile time. But we can pass them as template parameters or just unroll manually.
For maximum performance, let me just use a dedicated kernel that assumes 128 threads and handles exactly 4 loads with `#pragma unroll 4` or just write the 4 loads manually.
Actually, if I write `const int NUM_LOADS = 4;` inside the kernel and know it's always 4, the compiler will unroll it. But since `group_size` could vary, let me make the kernel generic.
Hmm, for this problem, since the shapes are fixed, I can also just import those constants into the CUDA code or pass them as constants from Python. But it's cleaner to make it generic.
Actually, for performance, I think a loop with 4 iterations is fine even without unrolling. The compiler will optimize it well.
One concern: `__shfl_down_sync` with dynamic offset? No, the offsets in the reduction loop are constants due to `#pragma unroll`.
Wait, I used `for (int offset = 16; offset > 0; offset /= 2)` which should unroll with constant offsets.
Let me think about whether using `float` is sufficient for numerical precision. PyTorch's GroupNorm uses `float` internally even for fp16 input. For fp32 input, it uses fp32. So matching with float should be fine.
One concern: PyTorch's mean and variance computation order. PyTorch's native CUDA kernels likely use a tree reduction. Our warp shuffle + shared memory reduction should produce similar results, but there might be slight differences in floating point accumulation order.
For matching within 1e-4, this should be fine since we're summing only 512 elements and using fp32.
Now let me think about the Python wrapper:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
...kernel code...
"""
cpp_source = """
torch::Tensor fused_gn_hardtanh(torch::Tensor input, torch::Tensor weight, torch::Tensor bias,
int num_groups, float eps, float min_val, float max_val) {
int N = input.size(0);
int C = input.size(1);
auto output = torch::empty_like(input);
const int threads = 128;
int num_blocks = N * num_groups;
fused_gn_hardtanh_kernel<threads><<<num_blocks, threads>>>(
input.data_ptr<float>(),
weight.data_ptr<float>(),
bias.data_ptr<float>(),
output.data_ptr<float>(),
N, C, num_groups, eps, min_val, max_val
);
return output;
}
"""
fused_gn_hardtanh_op = load_inline(
name="fused_gn_hardtanh",
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=["fused_gn_hardtanh"],
extra_cuda_cflags=["-O3", "--use_fast_math"],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self, in_features, out_features, num_groups, hardtanh_min, hardtanh_max):
super().__init__()
self.gemm = nn.Linear(in_features, out_features)
self.group_norm = nn.GroupNorm(num_groups, out_features)
self.hardtanh = nn.Hardtanh(min_val=hardtanh_min, max_val=hardtanh_max)
self.hardtanh_min = hardtanh_min
self.hardtanh_max = hardtanh_max
def forward(self, x):
x = self.gemm(x)
x = fused_gn_hardtanh_op.fused_gn_hardtanh(
x, self.group_norm.weight, self.group_norm.bias,
self.group_norm.num_groups, self.group_norm.eps,
self.hardtanh_min, self.hardtanh_max
)
return x
```
Wait, there's a subtle issue. PyTorch's `nn.HardTanh` operates in-place if possible, but by default it returns a new tensor. Our kernel writes to a new tensor, which matches.
Also, PyTorch's `nn.Linear` includes bias. So `self.gemm(x)` returns `x @ W.T + b`. Then our kernel takes this as input and applies GroupNorm + HardTanh.
But actually, I want to double check: does PyTorch's `GroupNorm` have `affine=True` by default? Let me check the constructor:
```python
nn.GroupNorm(num_groups, num_channels, eps=1e-5, affine=True)
```
Yes, `affine=True` by default, which means it has `weight` and `bias` parameters of shape `(num_channels,)`.
Another subtlety: the reference uses `self.group_norm` which is an `nn.Module`, and in evaluation our `ModelNew.group_norm` should have the same parameters. Since we construct it with the same constructor arguments, and PyTorch initializes weight=1, bias=0 by default, it matches.
But wait - what if the evaluation code initializes the weights differently or does some training? Our approach still works because we use the actual parameters from `self.group_norm.weight` and `self.group_norm.bias`.
One more thing: the `eps` parameter. In PyTorch, `nn.GroupNorm` defaults to `eps=1e-5`. We should use `self.group_norm.eps`.
Let me also consider whether we should transpose the input or handle non-contiguous tensors. The output of `nn.Linear` is contiguous. We can add `.contiguous()` if needed, but it's probably not necessary.
Now, another optimization idea: what if we also handle the bias addition in our custom kernel, and call `torch.mm(x, self.gemm.weight.t())` instead of `F.linear`? That way we avoid one fused kernel and just do `torch.mm` + our custom kernel. But `torch.addmm` (used by `F.linear`) is highly optimized by cuBLAS. Using `torch.mm` separately and then adding bias in our kernel might be slightly slower or about the same.
Actually, if we call `torch.mm(x, self.gemm.weight.t())`, the result goes to memory. Then our kernel reads it, adds bias, computes GN + HardTanh, and writes to output. That's one read of the GEMM output.
If we call `F.linear(x, self.gemm.weight, self.gemm.bias)`, the cuBLAS kernel writes the biased output to memory. Then our kernel reads it. Also one read of the GEMM output.
So the number of memory operations is the same. The difference is that cuBLAS's addmm might be slightly more efficient than manual mm + our bias add, but probably negligible.
Let me just use `F.linear` to match the reference's computation order more closely.
Wait, there's another thought. What if we use `torch.mm` with `out=x.new_empty(...)` to avoid allocating an intermediate? Actually, `F.linear` already allocates the output. We can use `torch.addmm(self.gemm.bias, x, self.gemm.weight.t(), out=preallocated)` if we preallocate, but that's an optimization for the PyTorch side that's probably not worth it.
Let me write the code and try it.
Actually, I need to be more careful about numerical equivalence. Let me trace through PyTorch's GroupNorm implementation to understand exactly how it computes mean and variance.
PyTorch's native CUDA GroupNorm (from `aten/src/ATen/native/cuda/group_norm_kernel.cu`):
- It computes mean and variance using a reduction over the group dimension
- The reduction is likely done using shared memory / warp shuffle
- For the forward pass, it computes mean and inv_std and stores them, then applies normalization in a second kernel or fused
Actually, I think PyTorch's implementation might launch multiple kernels:
1. A kernel to compute mean and inv_std (reduction)
2. A kernel to apply normalization, weight, bias
If we fuse all of that plus HardTanh into one kernel, we save kernel launch overhead and memory round-trips.
Let me also check if there's any possibility of using Tensor Cores for the GroupNorm part. Probably not necessary since it's memory bound.
Now, an important question: can we launch enough blocks to keep the GPU busy? 16384 blocks of 128 threads each = ~2M threads. H100 has ~132 SMs, each can handle up to 2048 threads, so ~270K threads concurrently. With 16384 blocks, that's plenty of blocks to keep all SMs busy (~124 blocks per SM).
But wait, our kernel only reads 512 * 4 bytes = 2KB per block and writes 2KB. The arithmetic intensity is very low. The kernel is memory bandwidth bound. Since H100 has high bandwidth, it should still be fast.
Let me think about whether we should increase occupancy. With 128 threads and small shared memory usage (4 floats = 16 bytes), we can have many blocks per SM. Register usage is probably low (~32 registers per thread), so we could have 64 warps per SM (2048 threads / 32 = 64 warps). With 128 threads = 4 warps per block, that's 16 blocks per SM concurrently. Total blocks = 16384, so 16384 / 132 / 16 ≈ 7.8 waves. That's plenty.
Now, one potential issue is memory access pattern. For a given block (sample n, group g), threads access elements `n*C + g*group_size + tid + i*BLOCK_THREADS`. Since `group_size = 512`, `BLOCK_THREADS = 128`, consecutive threads access consecutive elements in memory, which is a coalesced access pattern. Good!
Another optimization: use vectorized loads/stores. With float4, we could load 4 floats per thread in one instruction. But since 512 is divisible by 128, each thread handles exactly 4 floats. Using `float4` would help:
```cuda
const float4* input4 = reinterpret_cast<const float4*>(input + base_idx);
float4 val4 = input4[tid];
```
This loads 4 consecutive floats in one instruction. This is very efficient on H100.
Let me rewrite the kernel with float4 loads:
```cuda
__global__ void fused_gn_hardtanh_kernel(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
// Load using float4 (group_size must be divisible by 4)
// Each thread loads 1 float4 = 4 floats
// 128 threads * 4 = 512 floats per group
const float4* input4 = reinterpret_cast<const float4*>(input + base_idx);
const float4* weight4 = reinterpret_cast<const float4*>(gn_weight + base_c);
const float4* bias4 = reinterpret_cast<const float4*>(gn_bias + base_c);
float4* output4 = reinterpret_cast<float4*>(output + base_idx);
float4 in4 = input4[tid];
float v0 = in4.x;
float v1 = in4.y;
float v2 = in4.z;
float v3 = in4.w;
float thread_sum = v0 + v1 + v2 + v3;
// Warp reduce
// ... same as before ...
float mean = ...;
// Variance
float thread_sq = (v0-mean)*(v0-mean) + (v1-mean)*(v1-mean) + (v2-mean)*(v2-mean) + (v3-mean)*(v3-mean);
// ... reduce ...
float rstd = ...;
// Normalize, apply affine, hardtanh
float w0 = weight4[tid].x; // Wait, we need per-element weight/bias
// ...
float4 out4;
out4.x = fminf(fmaxf((v0 - mean) * rstd * w0 + b0, min_val), max_val);
// ...
output4[tid] = out4;
}
```
Using `float4` requires that `base_idx` and `base_c` are aligned to 16 bytes. Since `C = 8192` and `base_c = g * 512`, `base_c` is always a multiple of 512, so it's divisible by 16 (512/4 = 128 float4s). And `n * C` where C=8192 is also divisible by 16. So alignment is guaranteed.
Wait, but `gn_weight` and `gn_bias` start at index `base_c`. Since `base_c` is a multiple of 512, `gn_weight + base_c` is also 16-byte aligned.
For the float4 loads of weight and bias:
```cuda
const float4* weight4 = reinterpret_cast<const float4*>(gn_weight + base_c);
const float4* bias4 = reinterpret_cast<const float4*>(gn_bias + base_c);
```
Then `weight4[tid]` loads the correct float4.
This float4 approach is very efficient and should saturate memory bandwidth.
But wait - PyTorch tensor alignment... PyTorch ensures tensors are at least 256-byte aligned for the start of the tensor. But are they 16-byte aligned for all offsets? Yes, because the alignment of the start is typically at least 64 bytes or more, and `base_c` adds `base_c * sizeof(float) = base_c * 4` bytes. Since `base_c` is a multiple of 512, the offset is a multiple of 2048 bytes, which is more than 16.
So float4 access is safe and aligned.
Actually, let me double check: PyTorch tensors are allocated with a certain alignment. The base pointer is aligned. Accessing `tensor + offset` with `float4` requires `offset * sizeof(float)` to be a multiple of 16. `offset = base_idx = n * C + g * group_size`. With C=8192, group_size=512:
- `n * 8192` is always a multiple of 16 since 8192 is divisible by 4.
- `g * 512` is always a multiple of 16 since 512 is divisible by 4.
So yes, aligned float4 access is safe.
Let me write the full kernel with float4:
```cuda
#include <torch/extension.h>
#include <cuda_runtime.h>
__device__ __forceinline__ float warp_reduce_sum(float val) {
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
val += __shfl_down_sync(0xFFFFFFFF, val, offset);
return val;
}
__global__ void fused_gn_hardtanh_kernel(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int group_size = C / num_groups; // 512
const int tid = threadIdx.x; // 0..127
const int ng = blockIdx.x; // 0..(N*num_groups-1)
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
const float4* input4 = reinterpret_cast<const float4*>(input + base_idx);
const float4* weight4 = reinterpret_cast<const float4*>(gn_weight + base_c);
const float4* bias4 = reinterpret_cast<const float4*>(gn_bias + base_c);
float4* output4 = reinterpret_cast<float4*>(output + base_idx);
// tid goes from 0 to 127, so we load 128 float4 = 512 floats
float4 in4 = input4[tid];
float4 w4 = weight4[tid];
float4 b4 = bias4[tid];
float v0 = in4.x, v1 = in4.y, v2 = in4.z, v3 = in4.w;
float thread_sum = v0 + v1 + v2 + v3;
// Mean reduction
thread_sum = warp_reduce_sum(thread_sum);
__shared__ float shared[4]; // 4 warps for 128 threads
int lane = tid & 31;
int warp = tid >> 5;
if (lane == 0) shared[warp] = thread_sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? shared[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) shared[0] = val / (float)group_size;
}
__syncthreads();
float mean = shared[0];
// Variance reduction
float d0 = v0 - mean, d1 = v1 - mean, d2 = v2 - mean, d3 = v3 - mean;
float thread_sq = d0*d0 + d1*d1 + d2*d2 + d3*d3;
thread_sq = warp_reduce_sum(thread_sq);
if (lane == 0) shared[warp] = thread_sq;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? shared[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) shared[0] = 1.0f / sqrtf(val / (float)group_size + eps);
}
__syncthreads();
float rstd = shared[0];
// Normalize, affine, hardtanh
float4 out4;
out4.x = fminf(fmaxf(((v0 - mean) * rstd) * w4.x + b4.x, min_val), max_val);
out4.y = fminf(fmaxf(((v1 - mean) * rstd) * w4.y + b4.y, min_val), max_val);
out4.z = fminf(fmaxf(((v2 - mean) * rstd) * w4.z + b4.z, min_val), max_val);
out4.w = fminf(fmaxf(((v3 - mean) * rstd) * w4.w + b4.w, min_val), max_val);
output4[tid] = out4;
}
```
Wait, I need to be careful about the launch configuration. `blockIdx.x` goes from 0 to `N * num_groups - 1`. For N=1024 and num_groups=16, that's 16384 blocks. Each block has 128 threads. Each thread loads one `float4`. 128 threads * 4 floats = 512 floats per block. That's exactly one group.
Wait, is `tid` always less than `group_size / 4`? Yes, `group_size / 4 = 512 / 4 = 128`, which matches `BLOCK_SIZE = 128`.
But what if the problem sizes change? The prompt says fixed sizes for batch_size, in_features, etc., but `ModelNew` should accept the same constructor arguments and work for different sizes. However, the evaluation likely uses the exact sizes specified.
To be safe, I should handle cases where `group_size` is not exactly 512 or not divisible by 4. Let me add a fallback path or make sure the kernel handles it.
Actually, for a robust implementation, I should ensure:
1. If `group_size % 4 == 0` and `group_size / 4 <= 1024`, use the optimized float4 path
2. Otherwise, use a generic loop-based path
But since GroupNorm with num_groups dividing num_channels is typical, and our specific case has group_size=512 (divisible by 4), let me add a check in the Python code.
Actually, a cleaner approach is to just assert or check in the Python wrapper and use the template/generic version. But for simplicity, since this is a benchmark with fixed params, I'll optimize for exactly 128 threads and assume group_size is a multiple of 4. Let me also add a generic check to handle edge cases.
Wait, but looking at the kernel more carefully, `tid` ranges from 0 to `blockDim.x - 1`. If I launch with 128 threads but `group_size / 4 > 128` (e.g., group_size = 2048), then `tid` will range to 127 but we'd need to load 512 float4s. That doesn't work.
For a generic kernel, I'd need `blockDim.x = group_size / 4` if using float4, but CUDA limits block size to 1024. So group_size > 4096 wouldn't work with this approach.
For our case, group_size = 512, so 128 threads is perfect. Let me create a generic version that handles the full range:
```cuda
template <int BLOCK_THREADS>
__global__ void fused_gn_hardtanh_kernel(...) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
const int num_iters = (group_size + BLOCK_THREADS - 1) / BLOCK_THREADS;
float vals[16]; // max elements per thread: 4096/256 = 16, but we can use dynamic
// Actually, for a robust implementation...
}
```
You know what, let me just write two paths: one for the specific case (float4, 128 threads, group_size divisible by 4) and a generic fallback. Or better yet, let me just write a generic but efficient kernel using loops, and add a special case for float4 when the alignment permits.
Actually, for this competition, the exact sizes matter most. Let me check if I should just hardcode for the given problem sizes.
The problem states exact sizes. But `ModelNew` should accept constructor arguments just like `Model`. So it needs to work for any valid inputs. The evaluation might test with different sizes.
Let me write a robust kernel. I'll use a generic loop with `float4` when possible:
```cuda
__global__ void fused_gn_hardtanh_kernel(...) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
// Each thread processes elements starting at tid, stepping by blockDim.x
float thread_sum = 0.0f;
float thread_sq = 0.0f;
// First pass: compute mean
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float v = input[base_idx + idx];
// We can't easily store all values without dynamic allocation
// For small group_size (up to ~1024), we could store in registers
}
}
```
Hmm, storing values in registers for a generic kernel is tricky because `group_size / blockDim.x` is not known at compile time.
Let me rethink. For our specific problem, group_size = 512. With block_size = 128, each thread handles 4 elements. Using a fixed-size array of 4 is easy. For generic sizes, I could allocate shared memory to store the entire group's values, but that uses 512*4 = 2KB per block for group_size=512, which fits easily in shared memory. For larger group sizes, shared memory might still work up to 48KB or 227KB on H100.
Wait, let me think about a shared-memory-based approach:
1. Load all elements for the group into shared memory
2. Compute mean via reduction on shared memory
3. Compute variance via reduction on shared memory
4. Normalize, apply affine, hardtanh, write back
For group_size=512, shared memory = 512 * 4 bytes = 2KB. That's tiny! We have 227KB per block available. Even for group_size=8192, that's 32KB.
Actually, loading into shared memory first means we read from global memory once, then do all computations using shared memory. Then write back once. This is very efficient.
But wait, if we load into shared memory and then write back to shared memory before writing to global memory, that adds extra shared memory traffic. Alternatively, we can keep the data in registers as much as possible.
Actually, for our case, a register-based approach with manual unrolling for 4 elements per thread is cleaner and faster. Let me just do that.
For a generic approach, I can use a template for the number of elements per thread. Or I can have the generic kernel use shared memory for loading and then use the generic two-pass approach.
Actually, looking at this more carefully, let me check if PyTorch's GroupNorm has any specific epsilon value I need to match. Default is 1e-5, but I should use `self.group_norm.eps` anyway.
Let me now think about whether I need to handle non-contiguous tensors. The output of `nn.Linear` is contiguous. Our kernel assumes contiguous layout (N, C) with N being the outer dimension, C being the inner dimension.
Actually, one more thing: does the reference use channels-last or channels-first? For 2D input (N, C), there's no difference. So we're fine.
Let me also think about whether we can use half-precision internally. The reference is fp32, and we need to match fp32 output. So we must use fp32.
What if the evaluation sets `torch.backends.cuda.matmul.allow_tf32 = False` or `True`? The reference would use whatever the default is. Our `F.linear` call would also use the same default. So that's fine.
Let me write the code now. I'll make a robust generic kernel that can handle different sizes, but I'll optimize it for the common case.
Actually, for maximum performance on the given problem, let me create a specialized path when `C / num_groups == 512` and `blockDim.x == 128` by using the float4 approach. I can check this in the host code and call the appropriate kernel.
Here is my plan:
1. Write a generic kernel using loops (works for any size)
2. Write a specialized `float4` kernel for when `group_size` is divisible by 4 and `group_size / 4 <= 1024`
3. In the C++ wrapper, check conditions and dispatch to the appropriate kernel
For this problem, the specialized kernel will be used.
Actually, simpler: just write one generic kernel that uses float4 when the pointer is aligned and group_size is divisible by 4. We can do this with a branch in the host code. Or even simpler: since the evaluation tests with `group_size=512` and `C=8192`, let me write a robust generic kernel but make sure it's efficient.
For the generic kernel, I'll use a loop but unroll the inner part manually when possible. Since 512/128 = 4, and I know the evaluation uses these sizes, let me write it as a template on BLOCK_THREADS with a compile-time loop if I know the number of loads.
Actually, let me just write a kernel that works for the specific sizes and has a fallback. Here's what I'll do - write a single kernel with template parameter `BLOCK_THREADS` and handle `group_size` generically with a `#pragma unroll` loop. Even if `group_size` is a runtime value, `for (int i = 0; i < 4; i++)` with the guard `if (idx < group_size)` inside is fine because the compiler sees the loop bound is a compile-time constant (after constant propagation if group_size expression is simple enough... but it's not because it's a runtime parameter).
OK, let me stop overthinking this. Let me write a clean kernel with `BLOCK_SIZE = 128` and a loop of up to 4 iterations (since max we'd support is 512 group_size / 128 threads = 4). If `group_size` is smaller, the guard handles it.
Actually, to be safe and generic, I'll just allocate a small shared memory buffer, load all values into it cooperatively, then compute mean/variance from shared memory, then write back. This handles any group_size up to `BLOCK_SIZE * MAX_LOADS`.
No wait, shared memory for 512 floats is 2KB, which is fine. But if I load into shared memory, I then need to read from it for the reduction, which adds extra latency compared to keeping values in registers.
For our case with 4 elements per thread, registers are perfect. Let me just assume `group_size <= BLOCK_SIZE * 4` for the generic case and use registers.
Actually, let me write a kernel with a template parameter for `MAX_ELEMS_PER_THREAD` and unroll the loop. But since `#pragma unroll` needs a compile-time constant, I can just unroll manually for a maximum of, say, 8 loads per thread. For group_size=512 and 128 threads, that's 4, which fits.
Hmm, but the problem says `ModelNew` must accept the same constructor arguments. If someone passes `num_groups=1`, then `group_size=8192`, and with 128 threads, each thread needs 64 loads. That would require a much bigger register array.
For robustness, let me use shared memory:
```cuda
// Shared memory holds the entire group's values
// For group_size elements, need group_size * sizeof(float) bytes
// Plus small space for reductions
extern __shared__ float s_mem[]; // Dynamically sized: group_size + BLOCK_SIZE/32
// Load into shared memory
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
s_mem[idx] = input[base_idx + idx];
}
__syncthreads();
// Compute mean: sum all s_mem[0..group_size-1]
// Each thread sums a portion
float thread_sum = 0.0f;
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
thread_sum += s_mem[idx];
}
// ... reduce to mean ...
// Compute variance
float thread_sq = 0.0f;
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
float diff = s_mem[idx] - mean;
thread_sq += diff * diff;
}
// ... reduce to var ...
// Normalize and write back
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
float v = (s_mem[idx] - mean) * rstd;
v = v * gn_weight[base_c + idx] + gn_bias[base_c + idx];
v = fminf(fmaxf(v, min_val), max_val);
output[base_idx + idx] = v;
}
```
With shared memory:
- We need `group_size * sizeof(float)` bytes for data + maybe `BLOCK_SIZE/32 * sizeof(float)` for reduction
- For group_size=512: 512*4 + 4*4 = 2064 bytes per block
- We can launch up to 64 blocks per SM (with 128 threads), shared memory is 227KB per SM
- 64 blocks * 2KB = 128KB, which fits!
Wait, can we really launch 64 blocks per SM? With 128 threads per block, and max 2048 threads per SM, that's 16 blocks per SM max. 16 blocks * 2KB = 32KB. That easily fits.
The shared memory approach is very clean and generic. But it has more shared memory traffic: load from global to shared, read from shared for reduction, read again for variance, read again for writing output. That's 4 passes over shared memory per group.
With registers, we load once from global, keep in registers, compute mean + variance + normalize, then write once. Less total data movement.
For group_size=512, each thread handles 4 elements. Keeping 4 floats in registers is very natural. Let me do the register approach but make it generic with a dynamic maximum. I'll template on a max loads per thread, say 8. That handles group_size up to 128 * 8 = 1024. For larger group sizes, I can increase the template parameter or fall back to a different approach.
Actually, for a fully generic solution, let me just use a `#pragma unroll` on a loop with a known upper bound, and put the loop body in a helper lambda. The compiler might be smart enough to optimize it.
Or I can simply write the generic loop without register storage:
```cuda
// Pass 1: mean
float thread_sum = 0.0f;
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
thread_sum += input[base_idx + idx];
}
// reduce to mean
// Pass 2: variance
float thread_sq = 0.0f;
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
float diff = input[base_idx + idx] - mean;
thread_sq += diff * diff;
}
// reduce to var
// Pass 3: normalize and write
for (int idx = tid; idx < group_size; idx += BLOCK_SIZE) {
float v = input[base_idx + idx];
v = (v - mean) * rstd;
v = v * gn_weight[base_c + idx] + gn_bias[base_c + idx];
v = fminf(fmaxf(v, min_val), max_val);
output[base_idx + idx] = v;
}
```
This reads the input 3 times from global memory. For group_size=512 and N=1024, total input reads = 3 * 1024 * 8192 * 4 bytes = 96MB. But the memory reads are coalesced. At 3.35 TB/s, that's ~0.029ms. The writes are 32MB, ~0.0096ms. Total memory traffic: ~0.039ms. That's still very fast!
And it's completely generic - works for any group_size and any BLOCK_SIZE. The downside is 3x reads, but memory bandwidth is high.
For comparison, the register-based approach does 1 read + 1 write, so ~0.013ms. The difference is small (0.026ms).
PyTorch's reference probably does: Linear (reads input+weight, writes output) → GroupNorm (reads output+gn_weight+gn_bias, writes normalized) → HardTanh (reads normalized, writes final). That's also multiple reads. If we use 3-pass generic in our kernel, it's still fewer total memory operations than the reference because we fuse GroupNorm+HardTanh.
Wait, actually: if we call `F.linear` first, that writes the linear output to memory. Then our 3-pass kernel reads it 3 times and writes once. Total global memory traffic after linear:
- Reads: 3 * 32MB = 96MB
- Writes: 32MB
- Total: 128MB
Reference after linear:
- GroupNorm reads: 32MB (input) + 0.032MB (weight) + 0.032MB (bias), writes 32MB = ~64MB
- HardTanh reads 32MB, writes 32MB = 64MB
- Total after linear: 128MB
So our 3-pass kernel has the same memory traffic as the reference's separate ops. The speedup comes entirely from eliminating kernel launch overhead and the fact that the reads might have better cache behavior.
Wait, but if PyTorch's GroupNorm does an intermediate computation (like computing mean/var in one kernel and applying in another), there might be extra writes. Actually, PyTorch's native GroupNorm likely writes the mean/rstd to temporary buffers, and then the normalization kernel reads them. So there might be more memory traffic in the reference.
Let me look more carefully at what PyTorch's GroupNorm does. I believe it:
1. Computes mean and variance per group, writes to intermediate buffers (N*num_groups*2 floats)
2. Launches a second kernel that reads the input, mean, var, weight, bias, and writes the normalized output
For N=1024, num_groups=16, intermediate is ~131KB. Negligible.
So the main win from our fused kernel is:
1. Fewer kernel launches
2. No intermediate buffers
3. HardTanh fused into the same kernel
For maximum speedup, the 1-pass register-based approach is better. Let me try to write both and see which is more practical.
For the 1-pass register approach, I need to know the max elements per thread. I'll use a template parameter:
```cuda
template <int BLOCK_THREADS, int MAX_LOADS>
__global__ void fused_gn_hardtanh_kernel(...) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
float vals[MAX_LOADS];
int num_loads = (group_size + BLOCK_THREADS - 1) / BLOCK_THREADS;
if (num_loads > MAX_LOADS) {
// Fallback: shouldn't happen for known configs
return;
}
float thread_sum = 0.0f;
#pragma unroll
for (int i = 0; i < MAX_LOADS; i++) {
int idx = tid + i * BLOCK_THREADS;
if (idx < group_size) {
float v = input[base_idx + idx];
vals[i] = v;
thread_sum += v;
} else {
vals[i] = 0.0f;
}
}
// ... reductions ...
#pragma unroll
for (int i = 0; i < MAX_LOADS; i++) {
int idx = tid + i * BLOCK_THREADS;
if (idx < group_size) {
// normalize and write
}
}
}
```
For `MAX_LOADS = 4`, `BLOCK_THREADS = 128`, this handles up to `group_size = 512` perfectly.
For larger group sizes, I can launch with more threads (e.g., 256 or 512) or use a larger MAX_LOADS. But for the evaluation, 4 should be sufficient.
Wait, `num_groups` might be different. If `num_groups=1`, then `group_size=8192`, `num_loads=64`. That's way more than 4.
For robustness, I'll make sure the code handles arbitrary sizes. I'll use the 3-pass generic loop for the fallback when `num_loads` exceeds a threshold.
Actually, let me write a smarter dispatcher in C++:
```cpp
torch::Tensor fused_gn_hardtanh(...) {
int N = input.size(0);
int C = input.size(1);
int group_size = C / num_groups;
auto output = torch::empty_like(input);
const int threads = 128;
int blocks = N * num_groups;
if (group_size % 4 == 0 && group_size / 4 <= 1024) {
// Use float4, single pass
int block_size = group_size / 4;
if (block_size < 64) block_size = 64;
// wait, this gets complicated
}
// Generic 3-pass
fused_gn_hardtanh_generic<<<blocks, threads>>>(...);
return output;
}
```
Ahhhh. Let me simplify. I'll write a single kernel that's efficient for our specific workload. The task is about replacing the forward computation for this specific model and sizes. Let me make it work well for the given configuration.
For the given config: `group_size = 512`. I'll write a kernel where `BLOCK_SIZE` is a template parameter and each thread handles `ELEMS_PER_THREAD` elements. I'll instantiate it for `(128, 4)` which covers 512 exactly.
For other sizes, I'll add a generic fallback kernel. The C++ wrapper will dispatch based on `group_size`.
Let me write both kernels:
```cuda
// Specialized kernel for when group_size is exactly BLOCK_THREADS * ELEMS_PER_THREAD
template <int BLOCK_THREADS, int ELEMS_PER_THREAD>
__global__ void fused_gn_hardtanh_fast(...) {
// ...
}
// Generic kernel
__global__ void fused_gn_hardtanh_generic(...) {
// 3-pass approach with dynamic loop
// ...
}
```
In the C++ wrapper:
```cpp
if (group_size == 512) {
fused_gn_hardtanh_fast<128, 4><<<blocks, 128>>>(...);
} else {
fused_gn_hardtanh_generic<<<blocks, 128>>>(...);
}
```
This is clean and efficient.
Wait, I should also consider if `C` might not equal `out_features` in some cases. In the reference, `out_features` is the number of output channels, and `GroupNorm` operates on that. So `C = out_features`. In our kernel, `C` comes from `input.size(1)` which is correct.
Let me now write the actual code. I'll create the specialized kernel for maximum performance and a generic fallback.
One more thing: for the specialized kernel, I can use float4 loads. Let me try to make it even faster.
Specialized fast kernel with float4:
```cuda
template <int BLOCK_THREADS>
__global__ void fused_gn_hardtanh_fast_512(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
// Assumes group_size == 512 and BLOCK_THREADS == 128
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * 512;
const int base_idx = n * C + base_c;
const float4* in4 = reinterpret_cast<const float4*>(input + base_idx);
const float4* w4 = reinterpret_cast<const float4*>(gn_weight + base_c);
const float4* b4 = reinterpret_cast<const float4*>(gn_bias + base_c);
float4* out4 = reinterpret_cast<float4*>(output + base_idx);
float4 inv = in4[tid];
float4 wv = w4[tid];
float4 bv = b4[tid];
float v0 = inv.x, v1 = inv.y, v2 = inv.z, v3 = inv.w;
float sum = v0 + v1 + v2 + v3;
// reduce sum to mean
sum = warp_reduce_sum(sum);
__shared__ float s[4];
int lane = tid & 31;
int warp = tid >> 5;
if (lane == 0) s[warp] = sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = val / 512.0f;
}
__syncthreads();
float mean = s[0];
float d0 = v0 - mean, d1 = v1 - mean, d2 = v2 - mean, d3 = v3 - mean;
sum = d0*d0 + d1*d1 + d2*d2 + d3*d3;
sum = warp_reduce_sum(sum);
if (lane == 0) s[warp] = sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = 1.0f / sqrtf(val / 512.0f + eps);
}
__syncthreads();
float rstd = s[0];
float4 o;
o.x = fminf(fmaxf((v0 - mean) * rstd * wv.x + bv.x, min_val), max_val);
o.y = fminf(fmaxf((v1 - mean) * rstd * wv.y + bv.y, min_val), max_val);
o.z = fminf(fmaxf((v2 - mean) * rstd * wv.z + bv.z, min_val), max_val);
o.w = fminf(fmaxf((v3 - mean) * rstd * wv.w + bv.w, min_val), max_val);
out4[tid] = o;
}
```
For the generic fallback:
```cuda
__global__ void fused_gn_hardtanh_generic(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
// Mean
float thread_sum = 0.0f;
for (int idx = tid; idx < group_size; idx += blockDim.x) {
thread_sum += input[base_idx + idx];
}
thread_sum = warp_reduce_sum(thread_sum);
__shared__ float s[32];
int lane = tid & 31;
int warp = tid >> 5;
int num_warps = blockDim.x >> 5;
if (lane == 0) s[warp] = thread_sum;
__syncthreads();
if (warp == 0) {
float val = (lane < num_warps) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = val / (float)group_size;
}
__syncthreads();
float mean = s[0];
// Variance
float thread_sq = 0.0f;
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float d = input[base_idx + idx] - mean;
thread_sq += d * d;
}
thread_sq = warp_reduce_sum(thread_sq);
if (lane == 0) s[warp] = thread_sq;
__syncthreads();
if (warp == 0) {
float val = (lane < num_warps) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = 1.0f / sqrtf(val / (float)group_size + eps);
}
__syncthreads();
float rstd = s[0];
// Write
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float v = input[base_idx + idx];
v = (v - mean) * rstd;
v = v * gn_weight[base_c + idx] + gn_bias[base_c + idx];
v = fminf(fmaxf(v, min_val), max_val);
output[base_idx + idx] = v;
}
}
```
Note that `s` shared memory array needs to be big enough for `num_warps`. If `blockDim.x <= 1024`, then `num_warps <= 32`, so `s[32]` is enough.
In the C++ wrapper:
```cpp
torch::Tensor fused_gn_hardtanh(torch::Tensor input, torch::Tensor weight, torch::Tensor bias,
int num_groups, float eps, float min_val, float max_val) {
int N = input.size(0);
int C = input.size(1);
auto output = torch::empty_like(input);
int blocks = N * num_groups;
if (C / num_groups == 512) {
fused_gn_hardtanh_fast_512<128><<<blocks, 128>>>(
input.data_ptr<float>(), weight.data_ptr<float>(), bias.data_ptr<float>(),
output.data_ptr<float>(), N, C, num_groups, eps, min_val, max_val);
} else {
fused_gn_hardtanh_generic<<<blocks, 128>>>(
input.data_ptr<float>(), weight.data_ptr<float>(), bias.data_ptr<float>(),
output.data_ptr<float>(), N, C, num_groups, eps, min_val, max_val);
}
return output;
}
```
Wait, I need to make sure the shared memory size for the warp reduction in the generic kernel is declared correctly. The generic kernel uses `__shared__ float s[32];` which is 128 bytes. That's fine.
One more thing: I should check if the input tensor is contiguous and on CUDA. For the evaluation, it will be. But to be safe, I can add `.contiguous()`. Actually, since `torch.empty_like(input)` preserves layout, and `nn.Linear` output is contiguous, everything should be contiguous. I'll just assume that.
Now, there's another potential optimization: what if `gn_weight` is all ones and `gn_bias` is all zeros (PyTorch default)? Can we skip the multiplication and addition? But since the model might have trained parameters, we can't make that assumption.
Actually, wait. Looking at the task description again: "Replace the forward computation of the PyTorch model below with a custom CUDA kernel." The evaluation likely compares outputs. The `get_init_inputs()` just returns the constructor args. The evaluation might instantiate `ModelNew` and then call forward on `get_inputs()`. It does not mention training. So the parameters are initialized to PyTorch defaults.
For `nn.Linear`: weight is initialized with `kaiming_uniform_`, bias is initialized with `uniform_` if `bias=True`.
For `nn.GroupNorm`: weight is initialized to ones, bias to zeros.
For `nn.HardTanh`: no parameters.
However, we cannot rely on GroupNorm weight being ones and bias being zeros. The evaluation code might compare a trained model or might initialize differently. We should handle the actual parameters.
But actually, looking at the setup: `get_init_inputs()` returns args for `__init__`. The evaluation probably does something like `model = ModelNew(*get_init_inputs())` and then compares `model(get_inputs()[0])` with `Model(*get_init_inputs())(get_inputs()[0])`. The initialization should be the same since we use the same `nn.Linear` and `nn.GroupNorm` modules. So the parameters will match.
Let me write the full Python code.
One issue with `load_inline`: I need to make sure the CUDA source is a string and the compilation works. I should test it first.
Let me draft the full code:
```python
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline
cuda_source = r'''
#include <torch/extension.h>
#include <cuda_runtime.h>
__device__ __forceinline__ float warp_reduce_sum(float val) {
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
val += __shfl_down_sync(0xFFFFFFFF, val, offset);
return val;
}
__global__ void fused_gn_hardtanh_fast_512(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * 512;
const int base_idx = n * C + base_c;
const float4* in4 = reinterpret_cast<const float4*>(input + base_idx);
const float4* w4 = reinterpret_cast<const float4*>(gn_weight + base_c);
const float4* b4 = reinterpret_cast<const float4*>(gn_bias + base_c);
float4* out4 = reinterpret_cast<float4*>(output + base_idx);
float4 inv = in4[tid];
float4 wv = w4[tid];
float4 bv = b4[tid];
float v0 = inv.x, v1 = inv.y, v2 = inv.z, v3 = inv.w;
float sum = v0 + v1 + v2 + v3;
sum = warp_reduce_sum(sum);
__shared__ float s[4];
int lane = tid & 31;
int warp = tid >> 5;
if (lane == 0) s[warp] = sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = val / 512.0f;
}
__syncthreads();
float mean = s[0];
float d0 = v0 - mean, d1 = v1 - mean, d2 = v2 - mean, d3 = v3 - mean;
sum = d0 * d0 + d1 * d1 + d2 * d2 + d3 * d3;
sum = warp_reduce_sum(sum);
if (lane == 0) s[warp] = sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = 1.0f / sqrtf(val / 512.0f + eps);
}
__syncthreads();
float rstd = s[0];
float4 o;
o.x = fminf(fmaxf((v0 - mean) * rstd * wv.x + bv.x, min_val), max_val);
o.y = fminf(fmaxf((v1 - mean) * rstd * wv.y + bv.y, min_val), max_val);
o.z = fminf(fmaxf((v2 - mean) * rstd * wv.z + bv.z, min_val), max_val);
o.w = fminf(fmaxf((v3 - mean) * rstd * wv.w + bv.w, min_val), max_val);
out4[tid] = o;
}
__global__ void fused_gn_hardtanh_generic(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
float thread_sum = 0.0f;
for (int idx = tid; idx < group_size; idx += blockDim.x) {
thread_sum += input[base_idx + idx];
}
thread_sum = warp_reduce_sum(thread_sum);
__shared__ float s[32];
int lane = tid & 31;
int warp = tid >> 5;
int num_warps = blockDim.x >> 5;
if (lane == 0) s[warp] = thread_sum;
__syncthreads();
if (warp == 0) {
float val = (lane < num_warps) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = val / (float)group_size;
}
__syncthreads();
float mean = s[0];
float thread_sq = 0.0f;
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float d = input[base_idx + idx] - mean;
thread_sq += d * d;
}
thread_sq = warp_reduce_sum(thread_sq);
if (lane == 0) s[warp] = thread_sq;
__syncthreads();
if (warp == 0) {
float val = (lane < num_warps) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = 1.0f / sqrtf(val / (float)group_size + eps);
}
__syncthreads();
float rstd = s[0];
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float v = input[base_idx + idx];
v = (v - mean) * rstd;
v = v * gn_weight[base_c + idx] + gn_bias[base_c + idx];
v = fminf(fmaxf(v, min_val), max_val);
output[base_idx + idx] = v;
}
}
'''
cpp_source = r'''
torch::Tensor fused_gn_hardtanh(torch::Tensor input, torch::Tensor weight, torch::Tensor bias,
int num_groups, float eps, float min_val, float max_val) {
int N = input.size(0);
int C = input.size(1);
auto output = torch::empty_like(input);
int blocks = N * num_groups;
if (C / num_groups == 512) {
fused_gn_hardtanh_fast_512<<<blocks, 128>>>(
input.data_ptr<float>(), weight.data_ptr<float>(), bias.data_ptr<float>(),
output.data_ptr<float>(), N, C, num_groups, eps, min_val, max_val);
} else {
fused_gn_hardtanh_generic<<<blocks, 128>>>(
input.data_ptr<float>(), weight.data_ptr<float>(), bias.data_ptr<float>(),
output.data_ptr<float>(), N, C, num_groups, eps, min_val, max_val);
}
return output;
}
'''
fused_gn_hardtanh_op = load_inline(
name="fused_gn_hardtanh",
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=["fused_gn_hardtanh"],
extra_cuda_cflags=["-O3", "--use_fast_math"],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self, in_features, out_features, num_groups, hardtanh_min, hardtanh_max):
super(ModelNew, self).__init__()
self.gemm = nn.Linear(in_features, out_features)
self.group_norm = nn.GroupNorm(num_groups, out_features)
self.hardtanh = nn.Hardtanh(min_val=hardtanh_min, max_val=hardtanh_max)
self.hardtanh_min = hardtanh_min
self.hardtanh_max = hardtanh_max
def forward(self, x):
x = self.gemm(x)
x = fused_gn_hardtanh_op.fused_gn_hardtanh(
x, self.group_norm.weight, self.group_norm.bias,
self.group_norm.num_groups, self.group_norm.eps,
self.hardtanh_min, self.hardtanh_max
)
return x
```
Wait, there's a subtle issue. The `fused_gn_hardtanh_op` is defined at module load time. It's accessible globally. Inside `ModelNew.__init__`, we store `hardtanh_min` and `hardtanh_max`.
One more thought: can we also fuse the linear layer bias addition into the kernel by using `torch.mm(x, self.gemm.weight.t())` instead of `self.gemm(x)`? In this case, we'd pass the linear bias to the kernel too. But this might cause precision differences because `torch.mm` + manual bias addition might be slightly different from `F.linear` (which uses cuBLAS addmm). Since we need numerical equivalence within 1e-4, and both are fp32, they should be very close. But to be safe and match exactly, using `self.gemm(x)` is better because it ensures the GEMM part is identical.
Actually, I just realized: `nn.Linear` uses `F.linear` or `torch.addmm` internally. If we use `self.gemm(x)`, we get exactly the same GEMM behavior as the reference. Perfect.
But what about the `nn.GroupNorm` inside our `ModelNew.__init__`? We create it but never call it in forward. We just use its `weight`, `bias`, `num_groups`, and `eps`. That's fine. The parameters will be initialized the same way.
Wait, but does `nn.GroupNorm`'s forward modify anything or handle affine differently? No, `weight` and `bias` are straightforward Parameters. And `eps` is a scalar. Our kernel implements the same math.
One potential issue: PyTorch's `GroupNorm` might handle the channel dimension differently when `out_features % num_groups != 0`. For our case, 8192 % 16 = 0, so it's fine. For the generic kernel, we should probably assert that `C % num_groups == 0`. Let me add a `TORCH_CHECK` in the C++ wrapper. Actually, standard GroupNorm requires `num_channels % num_groups == 0`, and PyTorch raises an error if not. So our generic kernel can assume it.
```cpp
TORCH_CHECK(C % num_groups == 0, "num_channels must be divisible by num_groups");
```
Actually, our C++ wrapper doesn't have access to TORCH_CHECK unless we include the right header. But since `torch/extension.h` includes everything, it should be fine.
Let me add the check.
Also, I should think about whether `input` might be half-precision or something. The evaluation uses `fp32 precision`. So we can assume `input.dtype() == torch.float32`.
But to be robust, I can add a check or cast. Since the spec says fp32, I'll assume float tensors.
Another consideration: `load_inline` caches compiled extensions by the source code hash. If I change the code and reload, it might use the cached version. That's handled by the tool, but for debugging I should be aware of it. The tool probably cleans the cache between runs.
Now let me think about the total speedup. PyTorch reference:
1. `self.gemm(x)`: ~0.14ms (TF32 Tensor Core) or ~2ms (FP32 cuBLAS)
2. `self.group_norm(x)`: ?
3. `self.hardtanh(x)`: ~0.02ms
Actually, I should consider whether PyTorch uses TF32 by default. On H100, `torch.backends.cuda.matmul.allow_tf32` defaults to True. So `nn.Linear` uses TF32 Tensor Cores. The GEMM time for 1024x8192x8192 in TF32:
- M=1024, N=8192, K=8192
- FLOPs = 1024 * 8192 * 8192 * 2 = 137 GFLOPs
- TF32 Tensor Core peak: ~494 TFLOPS (without sparsity)
- Time = 137 / 494 = 0.277ms
Actually, 989 TFLOPS is with sparsity. Without sparsity, it's about half, so ~494 TFLOPS. 137/494 ≈ 0.28ms. But real efficiency might be 30-50% of peak, so maybe 0.5-1ms.
Wait, even at 50% efficiency, it's ~0.55ms. That's still very fast.
For the entire reference model:
- Linear: ~0.55ms
- GroupNorm: let's say ~0.1ms
- HardTanh: ~0.02ms
- Total: ~0.67ms
Our fused version:
- Linear: ~0.55ms (same)
- Fused GN+HardTanh: ~0.03ms
- Total: ~0.58ms
- Speedup: ~1.15x
Hmm, that's not a huge speedup. But maybe PyTorch's GroupNorm is slower than I estimated.
Actually, let me reconsider. PyTorch's native GroupNorm for large channels might be non-trivial. And kernel launch overhead for 3 separate operations vs 2 might matter.
Also, I might be underestimating the fused kernel time. With the float4 single-pass approach, for 16384 blocks:
- Each block loads 512 floats, computes, writes 512 floats
- Total memory: 16384 * 512 * 4 * 2 = ~64MB
- Bandwidth utilization might not be 100% due to reduction overhead
- Maybe ~0.05ms to 0.1ms
Reference GroupNorm + HardTanh might be 0.2ms together. So speedup from fusion might be ~0.1ms out of 0.7ms = ~14%. Not amazing, but still a speedup.
Is there a way to do better? One idea: instead of using `nn.Linear` + our fused kernel, can we write a custom kernel that usesCUTLASS or our own shared-memory GEMM tile + on-the-fly GroupNorm + HardTanh?
For M=1024, N=8192, K=8192, doing the entire fused GEMM+GN+HardTanh in one kernel would save reading/writing the large intermediate GEMM output. The GEMM output is 32MB. Saving that write + read is significant.
If we can compute tiles of the GEMM output, accumulate in registers/shared memory, and then apply GN and HardTanh before writing to global memory, we eliminate the 32MB intermediate entirely!
This is more complex but potentially much faster. Let me think about how to do this.
For a simple approach: each thread block computes one or more complete output rows (since M=1024, each row is 8192 floats).
For one row (8192 floats):
- We need to compute `x[n, :] @ W.T` where x[n, :] is 8192 elements, W.T is 8192x8192
- Naive row computation: each thread computes one output element by doing a dot product of 8192 elements
- Dot product of 8192 elements: 8192 multiply-adds
- For 8192 output elements per row: 8192 threads running in parallel, each doing 8192 FMAs
- Total FMAs per row: 8192 * 8192 = 67M
- Total rows: 1024
- Total FMAs: 67B ≈ 134 GFLOPs
If each thread block handles one row with 256 threads:
- Each thread computes 32 output elements (8192/256 = 32)
- For each output element, a dot product of 8192 input elements
- We can tile the K dimension (8192) into chunks that fit in shared memory
Actually, let me think about a more realistic tiling strategy:
- Block size: 256 threads
- Tile K into chunks of, say, 64 or 128
- Each block computes a portion of the output row
Wait, if we compute one full row per block:
- Load a chunk of K (say 64) values from x[n, :] into shared memory
- Load a chunk of K (64) x N_chunk values from W.T into shared memory
- Each thread computes partial sums for its assigned output channels
- Accumulate across K chunks
For N_output = 8192 and 256 threads, each thread handles 32 output channels.
- For K_chunk = 64, we load 64 floats of x (256 bytes) and 64*32 = 2048 floats of W (8KB) per thread? No wait...
Actually, let me think about this more carefully. If a block computes a full row:
- The row output is 8192 floats
- With 256 threads, each thread computes 32 outputs
- For K_chunk = 64:
- Load x[n, k:k+64] into smem: 64 floats
- Load W.T[k:k+64, c:c+32] for each thread's outputs... but W is 8192x8192 and stored as (out_features, in_features). W.T is (in_features, out_features).
- Wait, `nn.Linear` does `y = x @ W.T + b`. W is (out_features, in_features). W.T is (in_features, out_features).
- So W.T is stored in column-major effectively if W is row-major... Actually, PyTorch tensors are row-major. W[i, j] is `W[i * in_features + j]`.
- W.T[k, c] = W[c, k]. So accessing W.T[k:k+64, c] for fixed c and varying k is contiguous in W: `W[c, k]` for k=k_start..k_start+63. That's contiguous!
So for thread computing output channel c, to compute dot(x[n, :], W[c, :]), we can load W[c, k:k+64] contiguously. But each of 256 threads needs a different c, so the accesses to W are strided by `in_features` (8192 floats = 32KB). That's not contiguous across threads, but each thread can load its own contiguous chunk.
Actually, for coalesced access, threads in a warp should access adjacent memory. If thread i loads `W[c_i, k]`, and `c_{i+1} = c_i + 1`, then thread i+1 loads `W[c_i+1, k]`, which is `base + (c_i+1)*in_features + k`. The stride between threads is 8192 floats = 32KB. That's not coalesced at all!
To get coalesced access, we need threads in a warp to load adjacent elements. So for W access, we should have threads load adjacent W.T[k, c] values, i.e., for fixed k and adjacent c. But then each thread would need to accumulate dot products for different c values, which is the natural output assignment.
So if thread `tid` handles output channels `tid * 32 + j` for `j=0..31`, and we tile K:
- For each k in K_tile:
- Load x[n, k] (broadcast to all threads, or better, into a shared memory register)
- Load W.T[k, c_start:c_start+32] for each thread, i.e., W[c_start:c_start+32, k]
- Since W is stored as W[c, k], for fixed k, W[:, k] is strided by `in_features`. Not contiguous.
Wait, W.T[k, c] = W[c, k]. For fixed k, varying c, the memory access pattern is strided by `in_features`. On H100, L2 cache handles strided access reasonably well if the stride is not too large, but global memory coalescing requires contiguous access. So each thread would issue a separate cache line request, which is very inefficient.
For the GEMM, cuBLAS handles this perfectly by using sophisticated tiling and reordering. A naive CUDA implementation would be much slower. So it's best to use cuBLAS for the GEMM.
But what if we still want to avoid the intermediate memory write? One approach is to use CUTLASS's epilogue fusion, but that's not easily accessible through `load_inline`.
Another idea: use `torch.mm` with a custom epilogue. PyTorch exposes `torch._scaled_mm` and similar, but not general epilogue fusion.
What about using Triton? Not available through `load_inline` in a standard way, and the task specifically asks for `load_inline` with CUDA C++.
So I'll stick with the fusion of GroupNorm + HardTanh, which is a safe and reasonable optimization.
Let me reconsider whether there are other optimizations. One thing I noticed: in PyTorch, `nn.HardTanh(min_val, max_val)` might be implemented as `torch.clamp(x, min_val, max_val)`, which is just one operation. Fusing it with GroupNorm is still worthwhile.
Another idea: since `nn.Linear` can be replaced with `F.linear`, and we know the output shape, can we compute the GEMM using the CUTLASS-wrapped operation `torch.ops.aten._efficient_attention_forward`? No, that's for attention.
Can we use the `torch.backends.cuda.matmul.allow_tf32` flag to ensure matching behavior? Not necessary since both reference and our implementation use the same PyTorch layers.
Let me think about whether we can do the `nn.Linear` computation in fp16 or bf16 to be faster. The spec says "Produce numerically equivalent outputs at fp32 precision." But the reference model operates in fp32 if the input is fp32. PyTorch's `nn.Linear` with fp32 input and fp32 weights produces fp32 output. We can't change the precision.
If the reference model uses TF32 for the GEMM internally (which it does by default on Ampere/Hopper), the actual numerical precision is about 1e-3 for the GEMM. The tolerance for correctness is 1e-4 for fp32... wait, 1e-4 is quite tight if TF32 is used!
Wait, TF32 has 10 mantissa bits vs fp32's 23. That's about 3 decimal digits of precision. A GEMM of size 8192 involves summing 8192 products, each with ~1e-3 relative error. The total error could be around 1e-3 * sqrt(8192) ≈ 0.09 relative to the output magnitude? Actually, error analysis for GEMM is more nuanced.
But the important thing is: PyTorch reference uses TF32 by default. Our `self.gemm(x)` also uses TF32. So we match the reference GEMM exactly.
For the GroupNorm and HardTanh, we do them in fp32, which is also what PyTorch does (the normalization is done in fp32 even for fp16 inputs). So we should match.
I need to be careful about one thing: does our kernel match PyTorch's GroupNorm exactly? PyTorch's native CUDA GroupNorm likely does the reduction using a specific algorithm. For fp32 with 1e-4 tolerance, small differences in reduction order should be fine for groups of 512 elements. The maximum difference from different reduction order for summing 512 floats is on the order of machine epsilon times the number of operations, which is ~1e-7 * 512 ≈ 5e-5. That's within 1e-4.
Wait, if some values are large and some are small, catastrophic cancellation could cause larger relative errors. But GroupNorm computes mean and variance of activations, which for a well-behaved neural network are usually within a reasonable range. And with fp32, the absolute tolerance of 1e-4 should be achievable.
One more thing: in our kernel, the reduction order is:
1. Each thread sums 4 values locally
2. Warp shuffle reduction (tree reduction within warp)
3. Warp 0 reduces the 4 warp sums
PyTorch might do:
1. Each thread loads values
2. Shared memory reduction (tree reduction)
3. Or atomicAdd to global memory
The exact order of floating-point additions differs, but for 512 elements in fp32, the difference should be well under 1e-4.
Actually, I just realized something about the float4 loads. We load `in4[tid]` which is at offset `tid * 4` from `base_idx`. Then:
- `inv.x` = element at `base_idx + tid*4 + 0`
- `inv.y` = element at `base_idx + tid*4 + 1`
- `inv.z` = element at `base_idx + tid*4 + 2`
- `inv.w` = element at `base_idx + tid*4 + 3`
Thread `tid` handles these 4 elements. Thread `tid+1` handles the next 4. This gives perfect coalescing for the float4 loads.
The elements we compute the mean over are:
- Thread 0: elements 0, 1, 2, 3
- Thread 1: elements 4, 5, 6, 7
- ...
- Thread 127: elements 508, 509, 510, 511
Then the warp shuffle reduction adds them in a specific order within the warp. The final order is different from a simple sequential sum, but the difference is small.
Let me write out the exact warp shuffle reduction:
```
thread 0 gets: sum0 + sum16
thread 0 gets: (sum0 + sum16) + (sum8 + sum24)
...
```
It's a tree reduction. PyTorch might also use a tree reduction. The difference is just in the shape of the tree.
Let me also think about whether `__shfl_down_sync` with offset 16 means:
- lane 0 gets lane 16's value
- lane 0 adds it to its own
- Then offset 8: lane 0 gets lane 8's value
- etc.
So the final sum for warp 0 is `sum0 + sum16 + sum8 + sum24 + sum4 + sum20 + sum12 + sum28 + sum2 + ...`
That's a specific bit-reversed-ish order. The difference from sequential sum or from a different tree should be very small.
For the cross-warp reduction:
- Lane 0 of warp 0 writes warp_sum to `s[0]`
- Lane 0 of warp 1 writes to `s[1]`
- ...
- Then warp 0's lane i reads `s[i]`
- `lane 0` in warp 0 does the tree reduction: `s[0] + s[2]`, then `+ s[1]`, then `+ s[3]` or something similar depending on the shuffle pattern.
Actually, in the cross-warp reduction:
```cuda
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
}
```
`warp_reduce_sum` on lane 0..3 with lane 0 as the aggregator:
- lane 0 gets val0 + val2
- lane 0 gets (val0 + val2) + val1
- lane 0 gets ((val0 + val2) + val1) + val3
So the final sum for the block is `((s[0] + s[2]) + s[1]) + s[3]`.
This is a particular reduction order. PyTorch's implementation might do `(((s[0] + s[1]) + s[2]) + s[3])` or something else. The difference should be minimal.
I think our numerical precision should be fine.
One more thought: should I use `float` or `double` for intermediate reductions? Using `double` for mean and variance would improve accuracy but PyTorch uses `float` for fp32 input. So we should use `float`.
OK, let me write the final code. I need to be careful about string escaping in Python since both CUDA and C++ source are strings.
Also, I should check: the task says "Do not write your own `PYBIND11_MODULE(...)` block in `cpp_sources`." and "List the host-side wrapper function names in `functions=[...]` instead." So my `cpp_source` should only contain the function declaration/definition, not a pybind module.
Let me also make sure to import `torch.nn.functional as F` if needed, though I'm just using `self.gemm(x)`.
Wait, actually `self.gemm(x)` might do something slightly different from `F.linear(x, self.gemm.weight, self.gemm.bias)` if there are hooks or other things. But for this simple model, it's fine.
One more optimization: instead of doing `self.gemm(x)` which allocates a new tensor, I could preallocate an output buffer in `__init__` and use it. But PyTorch's autograd would still allocate tensors for gradients. Since the evaluation likely doesn't use autograd (just forward), in-place operations might help. But `nn.Linear` doesn't support an `out` parameter directly.
Actually, `torch.addmm(self.gemm.bias, x, self.gemm.weight.t(), out=buf)` would write to a preallocated buffer. Let me see if that's useful. I could create `self.buf` in `__init__` and reuse it. But the buffer size depends on batch size, which could vary. And preallocation for dynamic batch size isn't straightforward.
For simplicity, I'll just use `self.gemm(x)`.
Wait, I should check whether the evaluation might use different batch sizes. The `forward()` signature takes `x` of shape `(batch_size, in_features)`. The `get_inputs()` returns a fixed size, but to be robust, I should handle variable batch sizes. Our kernel already does since `N = input.size(0)`.
Let me now write the complete code. I'll add some safety checks.
Oh, and one more thing. The `load_inline` function might need `extra_include_paths` etc. But for a simple kernel, `extra_cuda_cflags=["-O3", "--use_fast_math"]` should be sufficient.
Actually, `--use_fast_math` replaces `sqrtf` with an approximate version. For matching PyTorch exactly, this might cause issues if PyTorch uses the accurate `sqrt`. PyTorch's `rsqrt` in CUDA might use an intrinsic. To be safe, I'll use `--use_fast_math` for speed but also check if correctness passes. If not, I'll remove it.
PyTorch's GroupNorm uses `rsqrt` (reciprocal square root), which on GPU is typically a hardware intrinsic. `--use_fast_math` also generates `rsqrt.approx` or similar. The difference should be very small for fp32, well under 1e-4. But if correctness fails, I can remove it.
Let me write the code now.
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
__device__ __forceinline__ float warp_reduce_sum(float val) {
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2)
val += __shfl_down_sync(0xFFFFFFFF, val, offset);
return val;
}
__global__ void fused_gn_hardtanh_fast_512(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * 512;
const int base_idx = n * C + base_c;
const float4* in4 = reinterpret_cast<const float4*>(input + base_idx);
const float4* w4 = reinterpret_cast<const float4*>(gn_weight + base_c);
const float4* b4 = reinterpret_cast<const float4*>(gn_bias + base_c);
float4* out4 = reinterpret_cast<float4*>(output + base_idx);
float4 inv = in4[tid];
float4 wv = w4[tid];
float4 bv = b4[tid];
float v0 = inv.x;
float v1 = inv.y;
float v2 = inv.z;
float v3 = inv.w;
float sum = v0 + v1 + v2 + v3;
sum = warp_reduce_sum(sum);
__shared__ float s[4];
int lane = tid & 31;
int warp = tid >> 5;
if (lane == 0) s[warp] = sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = val / 512.0f;
}
__syncthreads();
float mean = s[0];
float d0 = v0 - mean;
float d1 = v1 - mean;
float d2 = v2 - mean;
float d3 = v3 - mean;
sum = d0 * d0 + d1 * d1 + d2 * d2 + d3 * d3;
sum = warp_reduce_sum(sum);
if (lane == 0) s[warp] = sum;
__syncthreads();
if (warp == 0) {
float val = (lane < 4) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = 1.0f / sqrtf(val / 512.0f + eps);
}
__syncthreads();
float rstd = s[0];
float4 o;
o.x = fminf(fmaxf((v0 - mean) * rstd * wv.x + bv.x, min_val), max_val);
o.y = fminf(fmaxf((v1 - mean) * rstd * wv.y + bv.y, min_val), max_val);
o.z = fminf(fmaxf((v2 - mean) * rstd * wv.z + bv.z, min_val), max_val);
o.w = fminf(fmaxf((v3 - mean) * rstd * wv.w + bv.w, min_val), max_val);
out4[tid] = o;
}
__global__ void fused_gn_hardtanh_generic(
const float* __restrict__ input,
const float* __restrict__ gn_weight,
const float* __restrict__ gn_bias,
float* __restrict__ output,
int N, int C, int num_groups, float eps, float min_val, float max_val) {
const int group_size = C / num_groups;
const int tid = threadIdx.x;
const int ng = blockIdx.x;
const int n = ng / num_groups;
const int g = ng % num_groups;
const int base_c = g * group_size;
const int base_idx = n * C + base_c;
float thread_sum = 0.0f;
for (int idx = tid; idx < group_size; idx += blockDim.x) {
thread_sum += input[base_idx + idx];
}
thread_sum = warp_reduce_sum(thread_sum);
__shared__ float s[32];
int lane = tid & 31;
int warp = tid >> 5;
int num_warps = blockDim.x >> 5;
if (lane == 0) s[warp] = thread_sum;
__syncthreads();
if (warp == 0) {
float val = (lane < num_warps) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = val / (float)group_size;
}
__syncthreads();
float mean = s[0];
float thread_sq = 0.0f;
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float d = input[base_idx + idx] - mean;
thread_sq += d * d;
}
thread_sq = warp_reduce_sum(thread_sq);
if (lane == 0) s[warp] = thread_sq;
__syncthreads();
if (warp == 0) {
float val = (lane < num_warps) ? s[lane] : 0.0f;
val = warp_reduce_sum(val);
if (lane == 0) s[0] = 1.0f / sqrtf(val / (float)group_size + eps);
}
__syncthreads();
float rstd = s[0];
for (int idx = tid; idx < group_size; idx += blockDim.x) {
float v = input[base_idx + idx];
v = (v - mean) * rstd;
v = v * gn_weight[base_c + idx] + gn_bias[base_c + idx];
v = fminf(fmaxf(v, min_val), max_val);
output[base_idx + idx] = v;
}
}
"""
cpp_source = """
torch::Tensor fused_gn_hardtanh(torch::Tensor input, torch::Tensor weight, torch::Tensor bias,
int num_groups, float eps, float min_val, float max_val) {
TORCH_CHECK(input.dim() == 2, "input must be 2D");
TORCH_CHECK(input.scalar_type() == torch::kFloat32, "input must be float32");
int N = input.size(0);
int C = input.size(1);
TORCH_CHECK(C % num_groups == 0, "num_channels must be divisible by num_groups");
auto output = torch::empty_like(input);
int blocks = N * num_groups;
if (C / num_groups == 512) {
fused_gn_hardtanh_fast_512<<<blocks, 128>>>(
input.data_ptr<float>(), weight.data_ptr<float>(), bias.data_ptr<float>(),
output.data_ptr<float>(), N, C, num_groups, eps, min_val, max_val);
} else {
fused_gn_hardtanh_generic<<<blocks, 128>>>(
input.data_ptr<float>(), weight.data_ptr<float>(), bias.data_ptr<float>(),
output.data_ptr<float>(), N, C, num_groups, eps, min_val, max_val);
}
return output;
}
"""
fused_gn_hardtanh_op = load_inline(
name="fused_gn_hardtanh",
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=["fused_gn_hardtanh"],
extra_cuda_cflags=["-O3"],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self, in_features, out_features, num_groups, hardtanh_min, hardtanh_max):
super(ModelNew, self).__init__()
self.gemm = nn.Linear(in_features, out_features)
self.group_norm = nn.GroupNorm(num_groups, out_features)
self.hardtanh = nn.Hardtanh(min_val=hardtanh_min, max_val=hardtanh_max)
self.hardtanh_min = hardtanh_min
self.hardtanh_max = hardtanh_max
def forward(self, x):
x = self.gemm(x)
x = fused_gn_hardtanh_op.fused_gn_hardtanh(
x, self.group_norm.weight, self.group_norm.bias,
self.group_norm.num_groups, self.group_norm.eps,
self.hardtanh_min, self.hardtanh_max
)
return x
```
Wait, I need to double check the `TORCH_CHECK`. It requires `#include <torch/extension.h>` which is already included in the CUDA source, but the C++ source might also need it. Actually, `load_inline` includes standard headers automatically, and `torch/extension.h` contains `TORCH_CHECK`. Since I include it in `cuda_sources`, and `cpp_sources` is compiled together with `cuda_sources`, the include should be visible.
Hmm, but for safety, let me add `#include <torch/extension.h>` to `cpp_source` as well, or just rely on the fact that the CUDA sources are included first.
Actually, `load_inline` compiles both sources together, so includes in one are visible in the other. But to be safe, let me make `cpp_source` also include the header.
Wait, I can just include it in `cpp_source`:
```cpp
#include <torch/extension.h>
torch::Tensor fused_gn_hardtanh(...) { ... }
```
Actually, including it in both might cause no harm due to include guards.
Let me also think about whether I should use `.contiguous()` on the inputs. The output of `nn.Linear` is always contiguous. The GroupNorm weight and bias are also contiguous. So no need.
One more thing: the output tensor `output = torch::empty_like(input)` might not be initialized, but we write to all elements in the kernel, so it's fine.
Actually, I want to verify whether the alignment assumptions for `float4` are always valid. PyTorch allocates tensors with 256-byte or 512-byte alignment typically. And our offsets `base_idx` and `base_c` are multiples of 512, which in terms of bytes is 2048, so definitely aligned to 16 bytes. The only potential issue is if `C` is not a multiple of 4. But `C = 8192`, which is a multiple of 4.
For the generic case, we don't use `float4`, so no alignment issues.
OK, I'm going to compile and test this. Let me write the complete Python file as a string.