reasoning
Let me analyze the task:
1. We have a simple model: Conv2d -> GELU -> Global Average Pooling -> Squeeze
2. Input shape: (128, 8, 256, 256)
3. Conv: 8 -> 64 channels, kernel 3x3
4. Output shape: (128, 64)
The operations are:
- Conv2d: 128 * 8 * 64 * 256 * 256 * 3 * 3 ≈ 36.7B multiply-adds
- GELU: element-wise, 128 * 64 * 256 * 256 ≈ 536M
- AdaptiveAvgPool2d(1): 128 * 64 * 256 * 256 ≈ 536M adds / 65536
Given the H100's massive compute (1979 TFLOPS bf16 TC, 67 TFLOPS fp32), this should be compute bound on the convolution. But since it's a relatively small model, we need to think about fusion.
We can fuse the entire pipeline into a single kernel if we want, but Conv2d is best handled by CuDNN/CUTLASS. However, we can fuse:
1. GELU + AdaptiveAvgPool2d (fuse activation into pooling)
2. Or write a custom conv kernel that does it all
Actually, for a 3x3 conv with 8->64 channels, there might be some benefit to a custom kernel that does Conv + GELU + AvgPool. But implementing a high-performance 3x3 conv is very hard to beat CuDNN.
Alternative: Use CuDNN for conv, then fuse GELU + global_avg_pool into one kernel.
Wait, but PyTorch already fuses conv + gelu in some cases via CuDNN. And adaptive_avg_pool2d likely becomes a mean over dimensions.
Let me think about optimization strategies:
1. PyTorch reference does Conv2d -> GELU -> adaptive_avg_pool2d -> squeeze
2. We can try to use cuDNN for conv, then write a fused kernel for GELU + reduce_mean
3. Or we can try to use torch.compile-like approaches
Actually, looking more carefully: PyTorch's Conv2d might not fuse with GELU automatically in eager mode. So we have:
- Conv2d (CuDNN, fast)
- GELU (elementwise kernel)
- adaptive_avg_pool2d (reduction kernel)
- squeeze (view)
The main win would be fusing GELU and adaptive_avg_pool2d into one kernel. But we might also get a win by doing a custom implementation.
Wait - is CuDNN's conv with GELU fusion available through PyTorch? In PyTorch eager mode, `self.conv(x)` followed by `F.gelu(x)` is two separate operations. PyTorch 2.x has CuDNN fusion for conv+activation in some cases but not sure about eager mode.
Actually, we could also try using `torch.nn.functional.conv2d` directly and then fuse everything. But CuDNN is hard to beat for conv.
Let me think: The global average pool reduces each 256x256 feature map to 1 value. So the output is quite small.
Strategy: Use implicit GEMM or direct conv, and since the spatial output is pooled, we could accumulate directly into the pooled output during convolution. This would mean:
- For each output channel and each input channel
- For each output spatial position (but we pool it)
- Actually, we can do: for each output pixel, compute conv + gelu, accumulate to global average
But that's harder because GELU is non-linear, so we can't accumulate before GELU.
So the pipeline must be:
1. Conv (produces 256x256 spatial)
2. GELU (pointwise on 256x256)
3. Average pool (reduce 256x256 to 1)
Since we can't skip intermediate steps due to GELU, best approach:
- Use torch.nn.functional.conv2d for conv (CuDNN)
- Fuse GELU + mean into custom kernel
This saves one memory round-trip (reading/writing the 256x256 tensor for gelu, then reading it again for pool).
The tensor after conv is (128, 64, 256, 256). In fp32, that's 128 * 64 * 256 * 256 * 4 = 2 GB. Actually wait: 128*64*256*256 = 536,870,912 elements. * 4 bytes = 2.147 GB. That's significant!
Memory bandwidth of H100 is 3.35 TB/s, so reading 2GB and writing 2GB takes about 1.2ms. The conv itself is probably a few ms.
So fusing GELU + pool could save ~2ms or more.
Let me write a kernel that:
1. Takes the conv output (or we can even consider fusing conv too...)
2. Applies GELU and averages each channel
Actually, we can do even better: the Conv2d can be done with CuDNN, and then our kernel fuses GELU + adaptive_avg_pool2d. Alternatively, if CuDNN conv is the bottleneck, fusing won't help that much. But avoiding 2GB of memory traffic is significant.
Let's also consider: can we use Tensor Cores? The conv is fp32. H100 has 67 TFLOPS fp32 and 989 TFLOPS TF32. But getting Tensor Cores working in a custom kernel is very complex.
I think the safest bet is:
1. Keep conv as PyTorch's conv2d (CuDNN)
2. Write a fused kernel for GELU + global_avg_pool2d
Wait, but can we beat the reference by just doing this? Maybe. Let me also consider using grouped conv or other optimizations.
Actually, another idea: since the output is just global average pool after GELU, and the conv kernel is 3x3, maybe we can use Winograd or FFT? Probably not worth it for 3x3.
Let me design the fused kernel:
For each batch element b and output channel c:
- Iterate over h=0..255, w=0..255
- Read x[b, c, h, w]
- Compute gelu(x)
- Accumulate sum
- Divide by 256*256 = 65536
That's very simple and memory bound. We can parallelize across (batch, channels) = 128 * 64 = 8192 blocks, each handling one (b, c) feature map.
For better memory throughput, we should use vectorized loads. Each block can process all 65536 elements. With 256 threads per block, that's 256 elements per thread.
Actually, with 65536 elements per (b,c), and we have 8192 such (b,c) pairs, total elements = 536M. Best approach:
- Grid: (128, 64) blocks
- Each block: 256 threads
- Each thread processes 256 consecutive elements (or use a grid-stride loop)
For better memory coalescing, consecutive threads should read consecutive elements. So within a feature map, we should have threads read along the flattened h*w dimension.
Actually, since output channels are independent, and batch elements are independent, a 2D grid of (batch, out_channels) makes sense.
Let me write a simple kernel:
```cuda
__global__ void gelu_avgpool_kernel(const float* input, float* output, int N, int C, int H, int W) {
int b = blockIdx.x;
int c = blockIdx.y;
int tid = threadIdx.x;
int idx = b * C * H * W + c * H * W;
float sum = 0.0f;
int total = H * W;
for (int i = tid; i < total; i += blockDim.x) {
float x = input[idx + i];
// GELU
float c1 = 0.7978845608f; // sqrt(2/pi)
float c2 = 0.044715f;
float x3 = x * x * x;
float t = c1 * (x + c2 * x3);
float gelu_x = 0.5f * x * (1.0f + tanhf(t));
sum += gelu_x;
}
// warp reduction
#pragma unroll
for (int offset = 16; offset > 0; offset /= 2) {
sum += __shfl_down_sync(0xffffffff, sum, offset);
}
if (tid == 0) {
output[b * C + c] = sum / (float)total;
}
}
```
Wait, should we use shared memory for reduction? For 256 threads, warp shuffle is fine. But if we use more threads, we'd need multiple warps. Let's use 256 threads = 8 warps. Then we need either shared memory or more shuffles across warps.
Actually, let's use shared memory reduction since it's straightforward:
```cuda
__shared__ float sdata[256];
// each thread computes partial sum
sdata[tid] = sum;
__syncthreads();
// reduction in shared memory
for (int s = 128; s > 0; s >>= 1) {
if (tid < s) sdata[tid] += sdata[tid + s];
__syncthreads();
}
if (tid == 0) output[b * C + c] = sdata[0] / total;
```
But wait - the inputs are in NCHW format. We need to make sure about memory access patterns. In NCHW, the spatial dimensions are innermost, so consecutive elements along W are contiguous. For H dimension, each row is contiguous. So if threads read consecutive elements in the flattened H*W, that's good coalescing.
Actually, a better approach might be to vectorize loads. Use float4 to read 4 elements at a time. Then the grid can be smaller.
Let me think about vectorization:
- H*W = 65536, divisible by 4
- Each thread can process 4 elements using float4
Let me refine the kernel to use float4 for better bandwidth:
```cuda
__global__ void gelu_avgpool_kernel(const float* __restrict__ input, float* __restrict__ output,
int N, int C, int H, int W) {
int n = blockIdx.x;
int c = blockIdx.y;
int tid = threadIdx.x;
int spatial = H * W;
int base = n * C * spatial + c * spatial;
const float4* in_vec = reinterpret_cast<const float4*>(input + base);
float sum = 0.0f;
int vec_len = spatial / 4;
for (int i = tid; i < vec_len; i += blockDim.x) {
float4 v = __ldg(&in_vec[i]);
// Process each element with GELU
#pragma unroll
for (int j = 0; j < 4; j++) {
float x = (&v.x)[j];
float t = 0.7978845608f * x * (1.0f + 0.044715f * x * x);
float gelu_x = 0.5f * x * (1.0f + tanhf(t));
sum += gelu_x;
}
}
// Handle remaining elements
// ...
// Reduction
__shared__ float smem[256];
smem[tid] = sum;
__syncthreads();
for (int s = 128; s > 0; s >>= 1) {
if (tid < s) smem[tid] += smem[tid + s];
__syncthreads();
}
if (tid == 0) {
output[n * C + c] = smem[0] / (float)spatial;
}
}
```
Wait, `__ldg` is useful for read-only data. We should use it.
Also, GELU formula: `0.5 * x * (1 + tanh(sqrt(2/pi) * (x + 0.044715 * x^3)))`
Let me write it more accurately and see if it matches PyTorch.
PyTorch GELU: `0.5 * x * (1 + erf(x / sqrt(2)))`
Approximation with tanh: `0.5 * x * (1 + tanh(sqrt(2/pi) * (x + 0.044715 * x^3)))`
This is the approximation PyTorch uses for the fast path? Actually, PyTorch's gelu uses the exact formula for the default `approximate='none'`. Let me check...
PyTorch's `torch.nn.functional.gelu` by default uses `approximate='none'` which computes `x * 0.5 * (1.0 + torch.erf(x / math.sqrt(2)))`. But they also support `approximate='tanh'`.
Wait, we need to match the reference exactly! The reference uses `torch.nn.functional.gelu(x)` without the approximate argument, so it's the exact erf-based GELU.
Hmm, but erf is expensive in CUDA. However, we need numerical equivalence. Let me check the tolerance: fp32 uses atol=rtol=1e-4.
If PyTorch uses exact erf, and we use tanh approximation, will we pass? Probably not within 1e-4 for all inputs.
What does PyTorch actually compute for `F.gelu`? Let me think... PyTorch's GELU implementation delegates to ATen, which uses Intel TBB/MKL on CPU and CuDNN or a custom CUDA kernel on GPU. On GPU, it likely uses `erf` from libdevice.
Actually, I can check by looking at PyTorch CUDA implementation. The `gelu` kernel in ATen uses:
```cuda
scalar_t cdf = c10::cuda::compat::normcdf(v);
y[i] = v * cdf;
```
Where `normcdf` is `0.5 * (1 + erf(x / sqrt(2)))`.
So yes, it uses `erf`. For numerical matching, we need `erf`. But `erf` in CUDA (from libdevice) might be slow.
Wait, there might be a way to call `erff` from CUDA code.
Actually, CUDA has `erff` in `math.h` for device code. We can use `erff(x)`.
Let me write the GELU as:
```cuda
float gelu(float x) {
return 0.5f * x * (1.0f + erff(x * 0.70710678118f));
}
```
Where `0.70710678118f = 1/sqrt(2)`.
Actually, let me verify: is PyTorch's gelu using erf or the tanh approximation? Looking at recent PyTorch versions, `torch.nn.functional.gelu` default is `approximate='none'`. So it uses `erf`. Let me make sure our kernel matches.
Now, about the conv layer: we're using `self.conv = nn.Conv2d(...)`. In eager mode, `self.conv(x)` calls CuDNN. We should keep this.
So our ModelNew would be:
```python
class ModelNew(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size):
super().__init__()
self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)
def forward(self, x):
x = self.conv(x)
x = fused_gelu_avgpool2d(x) # our custom kernel
return x
```
Wait, the squeeze is not needed because our kernel outputs the right shape.
Let me write the complete kernel code. But first, let me think if there's a better approach.
Alternative: Can we fuse conv + gelu + avgpool into one kernel? This would avoid writing the 2GB intermediate. But implementing a high-performance 3x3 conv from scratch that beats CuDNN is very difficult.
However, the intermediate is 2GB and the conv compute is:
FLOPs = 128 * 8 * 64 * 256 * 256 * 3 * 3 * 2 (multiply-add) ≈ 73.4B FLOPs
At 67 TFLOPS, that's ~1.1ms. At 989 TFLOPS TF32, it's ~0.074ms.
Memory bandwidth: 2GB read (input) + 2GB write (output) = 4GB. At 3.35 TB/s = ~1.2ms.
So conv is roughly at the roofline, probably memory bound or slightly compute bound.
For the gelu+avgpool kernel, we read 2GB and write 32KB (128*64*4). This is pure memory bandwidth bound. Time = 2GB / 3.35TB/s = 0.6ms. But with fusion, we save the 2GB write from conv and 2GB read for gelu+pool.
If conv takes ~1.2ms and gelu+pool takes ~0.6ms, total would be ~1.8ms.
With fused gelu+pool, we save ~0.6ms of the gelu+pool time (since we still need to read conv output).
Actually, conv MUST write its output, and our kernel reads it. So we can't save the conv write or our kernel read. What we save is:
- Not writing after gelu
- Not reading for pool separately
But since gelu+pool is a single pass, we only read once and write once (small output).
Vs reference: conv writes 2GB, gelu reads 2GB and writes 2GB, pool reads 2GB and writes small.
Reference memory traffic: ~6GB read/write for the memory-bound parts.
Our approach: conv writes 2GB, our kernel reads 2GB, writes small. So ~2GB + small.
The reference likely fuses some of this (e.g., CuDNN conv + gelu might already be fused in newer PyTorch), and adaptive_avg_pool2d might also be optimized.
Actually, wait. In PyTorch eager mode, does CuDNN fuse conv+gelu? It depends on the PyTorch version. Recent versions (2.0+) may have automatic fusion through CuDNN, but I'm not sure if it happens in standard nn.Module forward without torch.compile.
Given that we're on H100 with very fast memory, the difference might be smaller. But a well-written kernel should help.
Let me also consider another optimization: using TF32 for the conv. PyTorch likely already uses TF32 by default with CuDNN. We don't need to change that.
Actually, let me reconsider fusing conv. For such a small conv (8->64, 3x3), maybe a custom implicit GEMM or direct conv + gelu + pool kernel could be competitive with CuDNN because:
1. We avoid the 2GB intermediate write entirely
2. The conv is relatively small in terms of channels but large spatially
Let me estimate: Input is 128*8*256*256 = 67M elements = 268MB.
If we do direct convolution: for each output pixel, we load 3*3*8 = 72 input values, compute 64 output channels.
Total input reads: 128*64*256*256*3*3*8 = 36.7B floats = 147GB.
This is way more than reading the input once (0.268GB) or the output once (2GB).
CuDNN minimizes this through tiling and shared memory caching. A custom kernel might not beat it unless we do a really good job.
But actually, since we pool the output, we might be able to do things differently. Wait, no - GELU is applied before pooling, so we can't accumulate across the convolution and then apply GELU.
What about fusing just conv + gelu? PyTorch might already do this if we use `torch.nn.Conv2d` + `F.gelu` in newer versions.
Let me just write the fused GELU + adaptive_avg_pool2d kernel. This is safe and should give some speedup.
Actually, I realize something: the output of conv is (128, 64, 254, 254) not (128, 64, 256, 256)! Because kernel_size=3 with default padding=0 and stride=1, so H_out = 256 - 3 + 1 = 254.
Let me recalculate: Output size = (batch_size, out_channels, 254, 254).
254*254 = 64516 elements per channel.
Total elements = 128*64*64516 = 528,075,264 ≈ 2.01 GB in fp32.
For adaptive_avg_pool2d with output size 1, it just averages all elements in each channel. So the exact spatial size doesn't matter to our kernel - we just average all elements.
Let me write the fused kernel using float4 vectorized loads.
Grid dimensions: (128, 64) blocks, 256 threads each.
Spatial size = 254 * 254 = 64516. Not divisible by 4! 64516 / 4 = 16129.
Actually, 64516 / 4 = 16129 exactly? Let me check: 16129 * 4 = 64516. Yes!
Great, so we can use float4.
Wait, but the output of conv is NCHW, and 64516 / 4 = 16129 exactly. So float4 works perfectly if the starting address is aligned.
But nn.Conv2d output might not be 16-byte aligned for each channel! In NCHW, each channel has C*H*W offset. For the first channel of each batch, base address is aligned. But consecutive channels differ by H*W = 64516 elements, and 64516 * 4 = 258064 bytes, which is not divisible by 16!
So float4 loads would be misaligned for most channels!
We need to handle alignment or not use float4. Actually, we can use float4 for the first channel if we ensure the tensor is aligned properly. But for offset 64516 floats = 258064 bytes, the remainder mod 16 is 258064 % 16 = 0? Let me check: 258064 / 16 = 16129. Yes! 258064 = 16 * 16129. So it IS divisible by 16!
Wait: 64516 * 4 = 258064. 258064 / 16 = 16129. Yes! So each channel starts at a 16-byte boundary! Great.
64516 % 4 = 0, and 64516 * 4 % 16 = 0. So float4 works for all channels.
Let me double check: in a tensor allocated with PyTorch, the base address is 512-byte aligned typically. And the stride between channels is H*W elements = 64516. 64516 * 4 bytes = 258064 bytes. The offset of channel c is c * 258064. Since 258064 is divisible by 16, all channels are 16-byte aligned. Excellent.
So float4 is safe.
Let me write the CUDA kernel:
```cuda
#include <cuda_runtime.h>
#include <math.h>
__device__ __forceinline__ float gelu_exact(float x) {
const float sqrt_2_inv = 0.7071067811865475f;
return 0.5f * x * (1.0f + erff(x * sqrt_2_inv));
}
__global__ void gelu_avgpool_kernel(const float* __restrict__ input, float* __restrict__ output,
int N, int C, int H, int W) {
int n = blockIdx.x;
int c = blockIdx.y;
int tid = threadIdx.x;
int spatial = H * W;
int base = n * C * spatial + c * spatial;
const float4* in_vec = reinterpret_cast<const float4*>(input + base);
float sum = 0.0f;
int vec_count = spatial / 4;
for (int i = tid; i < vec_count; i += blockDim.x) {
float4 v = in_vec[i];
float x0 = v.x;
float x1 = v.y;
float x2 = v.z;
float x3 = v.w;
sum += gelu_exact(x0);
sum += gelu_exact(x1);
sum += gelu_exact(x2);
sum += gelu_exact(x3);
}
__shared__ float smem[256];
smem[tid] = sum;
__syncthreads();
#pragma unroll
for (int stride = 128; stride > 0; stride >>= 1) {
if (tid < stride) {
smem[tid] += smem[tid + stride];
}
__syncthreads();
}
if (tid == 0) {
output[n * C + c] = smem[0] / (float)spatial;
}
}
```
Wait, `blockDim.x` is 256. The loop `for (int i = tid; i < vec_count; i += blockDim.x)` will process all 16129 float4s. 16129 / 256 ≈ 63 iterations per thread.
Reduction: I have `__syncthreads()` inside the unrolled loop, which is fine. But I need to make sure the loop handles the case correctly.
Actually, blockDim.x should be a power of 2 for the reduction to work cleanly. 256 is fine.
Let me also think about register pressure. With 256 threads, we have 256 * registers_per_thread. And shared memory is 256 * 4 = 1KB per block. Very light.
Occupancy should be very high.
Now, the host wrapper function:
```cpp
torch::Tensor gelu_avgpool_forward(torch::Tensor input) {
int N = input.size(0);
int C = input.size(1);
int H = input.size(2);
int W = input.size(3);
auto output = torch::empty({N, C}, input.options());
dim3 blocks(N, C);
dim3 threads(256);
gelu_avgpool_kernel<<<blocks, threads>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
N, C, H, W
);
return output;
}
```
And the Python side:
```python
class ModelNew(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size):
super(ModelNew, self).__init__()
self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)
def forward(self, x):
x = self.conv(x)
x = gelu_avgpool_forward(x)
return x
```
Wait, but the reference does adaptive_avg_pool2d with output_size=1, which for any input spatial size would produce 1x1. PyTorch's adaptive_avg_pool2d handles this correctly. Our kernel assumes we know H and W, but since we read them from the tensor, it's equivalent.
One issue: does the kernel compile? Let's check if we need to include torch headers.
```cpp
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <math.h>
```
Yes.
Wait, but can we do even better? What if the conv is the main bottleneck and we can't beat it?
Let me think about another approach. Maybe we can use torch.compile or a custom CUDA kernel for the conv itself.
Actually, for a 3x3 conv with 8 input channels and 64 output channels on 254x254 spatial, the arithmetic intensity is:
FLOPs = N * C_out * C_in * H * W * K * K * 2 = 128 * 64 * 8 * 254 * 254 * 3 * 3 * 2 = 72.2B FLOPs
Memory for weights = 64 * 8 * 3 * 3 * 4 = 18.4KB
Memory for input = 128 * 8 * 256 * 256 * 4 = 268MB
Memory for output = 128 * 64 * 254 * 254 * 4 = 2.01GB
Total memory = 2.28GB
Arithmetic intensity = 72.2B / 2.28GB = 31.7 FLOPs/byte
At 3.35 TB/s, compute roofline is at 31.7 * 3.35e12 = 106 TFLOPS
H100 fp32 is 67 TFLOPS, so with fp32 this is compute bound!
With TF32 tensor cores (989 TFLOPS), it's well below compute roofline.
So actually, PyTorch's CuDNN conv in TF32 should be very fast for this problem. And since it's compute bound, the memory savings from fusing gelu+pool might not help conv speed.
But the gelu+pool part might cause non-trivial overhead. Let's estimate:
Reference after conv:
1. GELU: read 2GB, write 2GB, some compute (erf)
2. Pool: read 2GB, write 32KB
Total: ~4GB memory traffic at ~3.35 TB/s = 1.2ms, plus some kernel launch overhead.
Our approach:
1. GELU+Pool: read 2GB, write 32KB, compute (erf)
Total: ~2GB at ~3.35 TB/s = 0.6ms
So we save about 0.6ms. The conv might take ~1ms (TF32). So total is ~1.6ms vs ~2.2ms, about 1.37x speedup. That's decent.
Can we do better? What about avoiding the conv output write entirely?
If we could fuse conv + gelu + pool, we save the 2GB conv write and 2GB fused kernel read. That's 4GB of memory traffic saved. But implementing this kernel is very hard.
What about using CUTLASS or CUTLASS-like epilogue fusion? CuDNN supports arbitrary epilogue functions? Actually, CuDNN 8+ has "operation graphs" and "pointwise" operations that can be fused with conv. But PyTorch eager mode might not use this for GELU+pool.
CuDNN 8.1+ supports fusing conv + bias + relu, etc. But GELU is more complex. And pool after GELU is even harder to fuse into the conv.
Let me check if we can use `torch.backends.cudnn.flags` or something... No, we can't assume the reference uses anything but standard PyTorch.
Given the complexity, I think the fused GELU+avgpool kernel is a good approach.
But wait, there's another optimization! For the conv, we could maybe use `groups` or depthwise-separable, but that changes the model architecture. Not allowed.
What if we use channels_last (NHWC) format? The reference uses NCHW. We can convert input to channels_last, do conv in channels_last (which is faster on newer GPUs), then our kernel would need to handle NHWC.
Actually, PyTorch's Conv2d on H100 with CuDNN already picks the fastest format. It might use NHWC internally through CuDNN. So we probably don't need to worry.
Let me try another angle: what if the reference is slower because PyTorch's adaptive_avg_pool2d kernel is not well optimized for output_size=1? It might do a generic reduction that's slower than necessary.
A custom kernel specifically for global average pool + GELU should definitely be faster.
Let me also consider: should we use warp shuffle instead of shared memory? For 256 threads (8 warps), warp shuffle alone isn't enough. We'd need shared memory for inter-warp reduction. Or we could reduce each warp and then one thread does the final sum of 8 warp values.
We can do:
```cuda
// Warp reduction
for (int offset = 16; offset > 0; offset /= 2)
sum += __shfl_down_sync(0xffffffff, sum, offset);
if (tid % 32 == 0) smem[tid / 32] = sum;
__syncthreads();
if (tid < 8) {
sum = smem[tid];
for (int offset = 4; offset > 0; offset /= 2)
sum += __shfl_down_sync(0xffffffff, sum, offset);
}
if (tid == 0) output[...] = sum / spatial;
```
This might be slightly faster than shared memory reduction for all threads. But shared memory reduction is also very fast. Let me stick with shared memory for simplicity.
Actually, for 256 threads, full shared memory reduction has 8 iterations with __syncthreads each. The warp-shuffle approach has fewer iterations overall (4 for warp + 3 for final). Let's use warp shuffle.
Updated kernel:
```cuda
__global__ void gelu_avgpool_kernel(const float* __restrict__ input, float* __restrict__ output,
int N, int C, int H, int W) {
int n = blockIdx.x;
int c = blockIdx.y;
int tid = threadIdx.x;
int lane = tid % 32;
int warp = tid / 32;
int spatial = H * W;
int base = n * C * spatial + c * spatial;
const float4* in_vec = reinterpret_cast<const float4*>(input + base);
int vec_count = spatial / 4;
float sum = 0.0f;
for (int i = tid; i < vec_count; i += blockDim.x) {
float4 v = in_vec[i];
sum += gelu_exact(v.x);
sum += gelu_exact(v.y);
sum += gelu_exact(v.z);
sum += gelu_exact(v.w);
}
// Warp reduction
for (int offset = 16; offset > 0; offset /= 2)
sum += __shfl_down_sync(0xffffffff, sum, offset);
__shared__ float warp_sums[8]; // 256/32 = 8 warps
if (lane == 0) warp_sums[warp] = sum;
__syncthreads();
// Final reduction by warp 0
if (warp == 0) {
sum = (lane < 8) ? warp_sums[lane] : 0.0f;
for (int offset = 4; offset > 0; offset /= 2)
sum += __shfl_down_sync(0xffffffff, sum, offset);
if (lane == 0)
output[n * C + c] = sum / (float)spatial;
}
}
```
I think this is good. But I used `warp_sums` with size 8. If blockDim.x is 256, there are 8 warps. But what if someone calls with fewer threads? We should use `blockDim.x / 32` sized shared memory or at least declare large enough.
Actually, let me use dynamic shared memory or just pass it. For simplicity, what if blockDim.x is always 256? I'll make it a constant, say `threads_per_block = 256`.
Actually, a safer approach: use shared memory reduction but only for the inter-warp step, and make the shared memory array size based on the maximum possible warps. Or just use a fixed-size array of 32 (enough for 1024 threads).
Let me write it more carefully.
Actually, I just realized I could also try using cooperative groups for reduction, but that's overkill.
Let me think about another optimization: can we process multiple (n, c) pairs per block to improve occupancy? With (128, 64) = 8192 blocks, and H100 has ~132 SMs, that's about 62 blocks per SM, which should be plenty to keep all SMs busy. Actually, each block only uses 256 threads and very little shared memory, so we can have many blocks per SM concurrently.
8192 blocks is more than enough. We don't need to fuse across (n, c).
Now, let's code up the full Python module.
I need to be careful about `load_inline`. The `cuda_sources` contains the CUDA code, and `cpp_sources` contains the C++ wrapper.
Let me draft it:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <cuda_runtime.h>
#include <math.h>
__device__ __forceinline__ float gelu_exact(float x) {
const float sqrt_2_inv = 0.7071067811865475f;
return 0.5f * x * (1.0f + erff(x * sqrt_2_inv));
}
__global__ void gelu_avgpool_kernel(const float* __restrict__ input, float* __restrict__ output,
int N, int C, int H, int W) {
int n = blockIdx.x;
int c = blockIdx.y;
int tid = threadIdx.x;
int lane = tid % 32;
int warp_id = tid / 32;
int spatial = H * W;
int base = n * C * spatial + c * spatial;
const float4* in_vec = reinterpret_cast<const float4*>(input + base);
int vec_count = spatial / 4;
float sum = 0.0f;
for (int i = tid; i < vec_count; i += blockDim.x) {
float4 v = in_vec[i];
sum += gelu_exact(v.x);
sum += gelu_exact(v.y);
sum += gelu_exact(v.z);
sum += gelu_exact(v.w);
}
#pragma unroll
for (int offset = 16; offset > 0; offset >>= 1) {
sum += __shfl_down_sync(0xffffffff, sum, offset);
}
__shared__ float warp_sums[8];
if (lane == 0) {
warp_sums[warp_id] = sum;
}
__syncthreads();
if (warp_id == 0) {
sum = (lane < 8) ? warp_sums[lane] : 0.0f;
#pragma unroll
for (int offset = 4; offset > 0; offset >>= 1) {
sum += __shfl_down_sync(0xffffffff, sum, offset);
}
if (lane == 0) {
output[n * C + c] = sum / (float)spatial;
}
}
}
"""
cpp_source = """
#include <torch/extension.h>
torch::Tensor gelu_avgpool_forward(torch::Tensor input) {
int N = input.size(0);
int C = input.size(1);
int H = input.size(2);
int W = input.size(3);
auto output = torch::empty({N, C}, input.options());
dim3 blocks(N, C);
dim3 threads(256);
gelu_avgpool_kernel<<<blocks, threads>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
N, C, H, W
);
return output;
}
"""
gelu_avgpool = load_inline(
name="gelu_avgpool",
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=["gelu_avgpool_forward"],
extra_cuda_cflags=["-O3", "--use_fast_math"],
extra_cflags=["-O3"],
)
class ModelNew(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size):
super(ModelNew, self).__init__()
self.conv = nn.Conv2d(in_channels, out_channels, kernel_size)
def forward(self, x):
x = self.conv(x)
x = gelu_avgpool.gelu_avgpool_forward(x)
return x
```
Wait, there's an issue. PyTorch's `Conv2d` output might not have `H*W` divisible by 4! Let me verify.
Input: (128, 8, 256, 256)
Conv: kernel=3, stride=1, padding=0 (default)
Output: (128, 64, 254, 254)
H*W = 254*254 = 64516
64516 / 4 = 16129. Exactly divisible. Good.
But what if the conv had padding? Not in this case. But in general, we should maybe handle non-divisible sizes. I'll add a tail loop to be safe. Actually, since we know the exact problem, and 64516 is divisible by 4, we might skip the tail loop. But for robustness, let's add it.
Actually, even if H*W is divisible by 4, when casting to float4, we need the pointer to be aligned to 16 bytes. Since 64516 * 4 bytes = 258064 bytes, which is divisible by 16, all channels are aligned. BUT what about the last few float4s? The total size is exactly divisible, so no issue.
However, to be safe, let me use `__ldg` for the loads? That requires read-only data and can help with cache. Let me add it.
Also, I should make sure `erff` is available. Yes, in CUDA math API.
One more thing: `--use_fast_math` might make `erff` less accurate. We need accuracy within 1e-4. PyTorch uses a precise `erf` via `normcdf`. With `--use_fast_math`, `erff` might use a faster, less accurate approximation. Let me not use `--use_fast_math` to be safe. Actually, let me check... The tolerance for fp32 is `atol=rtol=1e-4`, which is relatively loose. But `erff` with fast math might be fine.
Actually, I'll remove `--use_fast_math` to be safe and keep `-O3`.
Let me also think about another issue: the float4 cast. We need to make sure the pointer is aligned. PyTorch tensors are typically aligned to 512 bytes or more for the base pointer. But is `input + base` always aligned to 16 bytes?
As I calculated, `base` in elements is `n * C * spatial + c * spatial`. `spatial = 64516`.
`spatial * sizeof(float) = 64516 * 4 = 258064 bytes`.
258064 / 16 = 16129. So yes, the offset in bytes is always a multiple of 16.
Therefore `input + base` is always 16-byte aligned. Perfect.
Wait, let me verify: `n * C * spatial * 4` is also a multiple of 16 because `C * spatial * 4 = 64 * 64516 * 4 = 16,595,584` which is divisible by 16. So each batch offset is also a multiple of 16.
Great.
Now, another optimization idea: instead of processing one (n, c) per block, what if we process multiple (n, c) pairs? With 8192 blocks, that's already a lot. But maybe we can improve cache locality by having a block process a contiguous range of channels for the same batch?
Actually, for memory bandwidth, it doesn't matter much. The reads are fully coalesced.
One potential issue: the kernel uses 8192 blocks. For a grid of (128, 64), CUDA maps the first dimension to x and second to y. So blockIdx.x ranges from 0 to 127, blockIdx.y from 0 to 63. This is fine.
But wait, can we launch 8192 blocks on H100? Yes, max is much higher.
Let me think about another approach: what if we use a single block to process multiple channels to better utilize the SMs? Actually, 8192 blocks is plenty for 132 SMs.
Here's another idea: the conv output is in NCHW format. The float4 loads read 4 consecutive floats along W. But the spatial size is 254x254 = 64516. Access is linear along the flattened spatial dimension, which corresponds to W then H. So consecutive float4s read 16 consecutive floats along W. Since W=254, every 254/4 = 63.5 float4s, we cross a row boundary. But since the entire spatial dimension is contiguous in memory (NCHW), this is fine.
Wait, in NCHW, the memory layout is: batch -> channel -> H -> W. So within a channel, all H*W elements are contiguous. Reading linearly is perfectly fine and maximally coalesced.
Good.
One more optimization: should we use `float2` or `float4`? `float4` gives 128-bit loads, which is good for H100 memory bandwidth.
Actually, I just realized we might want to try another approach: write a kernel for the entire pipeline but use CUTLASS or implicit GEMM for the conv. But that's much more complex. Let me first try the simple fusion approach and see the results.
Let me compile and test the kernel.
Wait, I need to be more careful about matching PyTorch's numerical behavior. PyTorch's `F.gelu` computes `0.5 * x * (1 + erf(x / sqrt(2)))` using double precision for the constants? Actually, it probably uses float32 constants and the `erf` function which might have slightly different behavior than `erff` in CUDA.
CUDA's `erff` is the float version of `erf`. PyTorch's `erf` on CUDA calls `std::erf` from `c10::cuda::compat::erf`, which maps to the CUDA `erf` function (which for float arguments calls `erff`).
Actually, wait. PyTorch's gelu uses `erf(scalar_t(x) * scalar_t(M_SQRT1_2))`. For float, this is `float` precision. And on CUDA, `erf(float)` calls `erff`. So it should match.
But there's a subtlety: PyTorch might compute `M_SQRT1_2` as a double constant and then cast to float. This could give slightly different results than our hardcoded float constant.
Let me check: `M_SQRT1_2` is typically defined as `0.70710678118654752440` (double). When cast to float, it becomes `0.70710677` or similar. Our constant `0.7071067811865475f` as a float literal will be rounded to the nearest float, which is the same.
Actually, let me verify by checking if `0.7071067811865475f` as a float is exactly equal to `(float)M_SQRT1_2`. Yes, both round to the same 32-bit float.
So our GELU should match.
But what about the exact formula? Our kernel computes `0.5f * x * (1.0f + erff(x * sqrt_2_inv))`. PyTorch computes `x * 0.5 * (1 + erf(x * M_SQRT1_2))`. These are algebraically identical, but order of operations might differ slightly. The difference should be well within 1e-4.
One more thing: adaptive_avg_pool2d. Our kernel divides by the total number of elements. PyTorch's adaptive_avg_pool2d with output_size=1 computes the mean over the entire spatial dimension. For integer sizes, this is just sum / (H*W). No issue there.
But wait: PyTorch uses a specific algorithm for adaptive_avg_pool2d which might not be a simple mean in all cases. But when output_size=1 and the stride equals the input size, it's exactly the mean.
Actually, let me double check. `torch.nn.functional.adaptive_avg_pool2d(x, (1, 1))` computes the average of each channel's spatial grid. Yes, it's `x.mean(dim=(2, 3))`. Our kernel does the exact same thing.
Great.
Let me compile and run correctness check.
Actually, before that, let me also consider another optimization: what if we use a larger block size? 512 threads instead of 256? With 64516 elements per (n,c), that's 16129 float4s. 256 threads give ~63 iterations per thread. 512 threads give ~32 iterations per thread. Both are fine. 256 is a good balance.
What about 1024 threads? That's only ~16 iterations. But then we'd have fewer blocks overall (still 8192 blocks for everything). Let me stick with 256.
Another idea: grid-stride loop with vectorization and multiple elements per thread. Already doing that.
Let me write the complete code and test it.