reasoning
Now I need to write a custom CUDA kernel for sigmoid activation. Let me analyze the problem:
1. Input shape: batch_size=4096, dim=393216
2. Total elements: 4096 * 393216 = 1,610,612,736 ≈ 1.61B elements
3. At fp32, that's about 6.44 GB of data
4. Sigmoid is bandwidth-bound: read x, compute exp, write output
The operation is: sigmoid(x) = 1 / (1 + exp(-x))
For an H100 with 3.35 TB/s bandwidth:
- Memory bandwidth bound kernel: 6.44 GB read + 6.44 GB write = ~12.88 GB total memory traffic
- Minimum time = 12.88 GB / 3.35 TB/s ≈ 3.84 ms
But actually, sigmoid reads input and writes output, so 2 * 6.44 GB = 12.88 GB total.
Wait, in practice we might only count one read plus one write for non-coalesced or coalesced cases.
For such a large tensor, a simple elementwise kernel should be close to bandwidth-bound. Let me write an efficient vectorized kernel.
For large contiguous arrays, I should use vectorized loads/stores (float4) and enough threads.
Let me write the kernel code:
```python
import torch
from torch.utils.cpp_extension import load_inline
# Let me think about the optimal kernel
# Total elements: 4096 * 393216 = 1,610,612,736
# This is divisible by many powers of 2
# 393216 = 2^17 * 3 = 131072 * 3
# 4096 = 2^12
# Total = 2^29 * 3
#
# A vectorized kernel using float4 would process 4 elements per thread
# Total threads needed = 1,610,612,736 / 4 = 402,653,184
# With 256 threads per block: 1,572,864 blocks
# With 128 threads per block: 3,145,728 blocks
#
# Actually, I should check if we can use float4, float2, etc.
```
Let me write a simple and efficient kernel. I'll use float4 vectorization if possible.
Actually, for the H100, a very simple kernel with enough threads should be close to optimal. Let me use a grid-stride loop with vectorized memory accesses.
```python
import torch
from torch.utils.cpp_extension import load_inline
cuda_source = '''
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <cmath>
__global__ void sigmoid_kernel(const float* __restrict__ input, float* __restrict__ output, int64_t n) {
int64_t idx = blockIdx.x * blockDim.x + threadIdx.x;
int64_t stride = blockDim.x * gridDim.x;
for (int64_t i = idx; i < n; i += stride) {
float x = input[i];
output[i] = 1.0f / (1.0f + expf(-x));
}
}
torch::Tensor sigmoid_cuda(torch::Tensor input) {
auto output = torch::empty_like(input);
int64_t n = input.numel();
const int threads = 256;
const int blocks = (n + threads - 1) / threads;
// Cap blocks to avoid launching too many
const int max_blocks = 65535 * 256; // large enough
const int actual_blocks = min(blocks, max_blocks);
sigmoid_kernel<<<actual_blocks, threads>>>(input.data_ptr<float>(), output.data_ptr<float>(), n);
return output;
}
'''
cpp_source = "torch::Tensor sigmoid_cuda(torch::Tensor input);"
```
Wait, but we can do better with vectorization. Let me write a float4 version:
Actually, let me first try a simple version and see how it performs. But I also want to consider using `__ldg` for read-only cached loads and vectorized memory access.
For H100, memory bandwidth is the key. Let me try using float4:
```cuda
__global__ void sigmoid_kernel_float4(const float* __restrict__ input, float* __restrict__ output, int64_t n) {
int64_t idx = (blockIdx.x * blockDim.x + threadIdx.x) * 4;
int64_t stride = blockDim.x * gridDim.x * 4;
for (int64_t i = idx; i < n; i += stride) {
if (i + 3 < n) {
float4 x = reinterpret_cast<const float4*>(input)[i / 4];
x.x = 1.0f / (1.0f + expf(-x.x));
x.y = 1.0f / (1.0f + expf(-x.y));
x.z = 1.0f / (1.0f + expf(-x.z));
x.w = 1.0f / (1.0f + expf(-x.w));
reinterpret_cast<float4*>(output)[i / 4] = x;
} else {
for (int64_t j = i; j < n; ++j) {
output[j] = 1.0f / (1.0f + expf(-input[j]));
}
}
}
}
```
Actually, I need to be careful about alignment for float4. The tensor might be aligned, but I should use a scalar tail loop.
Let me write a cleaner version. For 1.61B elements, the tail won't matter much.
Let me also consider using a larger block size and more blocks. On H100, we want to saturate all SMs.
Actually, let me think about what PyTorch's native sigmoid does. PyTorch likely uses its elementwise kernel system which is already quite optimized. But we might be able to beat it by:
1. Reducing launch overhead
2. Better occupancy
3. Vectorized loads
Actually, PyTorch uses ATen's `sigmoid_kernel` which likely uses TensorIterator and is quite efficient. But a custom kernel that does a single monolithic launch might have less overhead, especially for huge tensors.
Let me try a float4 vectorized kernel.
One issue: `393216 = 3 * 131072`, so `4096 * 393216 = 12288 * 131072 = 1610612736`. This is divisible by 4 (and much more), so float4 should work well.
Let me write the kernel.
call → compile_kernel
callcompile_kernel
{
"kernel_code": "import torch\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = '''\n#include <torch/extension.h>\n#include <cuda_runtime.h>\n\n__global__ void sigmoid_kernel_float4(const float* __restrict__ input, float* __restrict__ output, int64_t n) {\n int64_t idx = (blockIdx.x * blockDim.x + threadIdx.x);\n int64_t num_vec = n / 4;\n int64_t stride = blockDim.x * gridDim.x;\n \n // Process 4 elements at a time using float4\n for (int64_t i = idx; i < num_vec; i += stride) {\n float4 x = reinterpret_cast<const float4*>(input)[i];\n x.x = 1.0f / (1.0f + expf(-x.x));\n x.y = 1.0f / (1.0f + expf(-x.y));\n x.z = 1.0f / (1.0f + expf(-x.z));\n x.w = 1.0f / (1.0f + expf(-x.w));\n reinterpret_cast<float4*>(output)[i] = x;\n }\n \n // Handle remaining elements\n int64_t remainder_start = num_vec * 4;\n for (int64_t i = remainder_start + idx; i < n; i += stride) {\n float x = input[i];\n output[i] = 1.0f / (1.0f + expf(-x));\n }\n}\n\ntorch::Tensor sigmoid_cuda(torch::Tensor input) {\n auto output = torch::empty_like(input);\n int64_t n = input.numel();\n \n const int threads = 256;\n const int blocks = 8192; // Enough to saturate H100\n \n sigmoid_kernel_float4<<<blocks, threads>>>(input.data_ptr<float>(), output.data_ptr<float>(), n);\n return output;\n}\n'''\n\ncpp_source = '''\ntorch::Tensor sigmoid_cuda(torch::Tensor input);\n'''\n\n# Compile the extension\nsigmoid_ext = load_inline(\n name=\"sigmoid_ext\",\n cpp_sources=[cpp_source],\n cuda_sources=[cuda_source],\n functions=[\"sigmoid_cuda\"],\n extra_cuda_cflags=[\"-O3\", \"--use_fast_math\"],\n verbose=False\n)\n\nclass ModelNew(torch.nn.Module):\n def __init__(self):\n super(ModelNew, self).__init__()\n \n def forward(self, x: torch.Tensor) -> torch.Tensor:\n return sigmoid_ext.sigmoid_cuda(x)\n"
}