You write custom CUDA kernels to replace the pytorch operators in the given GeGLU architecture to get speedups.

You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining chunk+gelu+elementwise_mul), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.

This CUDA kernel implements a custom activation function (SSU - Shifted Sinc Unit) with the following optimizations:
Grid-Stride Loop: Uses strided indexing to handle arbitrary tensor sizes efficiently, ensuring good GPU utilization regardless of input dimensions.
Memory Access Optimization: Employs __restrict__qualifiers and contiguous memory tensors to enable better compiler optimizations and reduce memory bank conflicts.
Numerical Stability: Includes special case handling in sinc_opwhen y ≈ 0using fabsf(y) < 1e-6fto avoid division by zero and ensure numerical stability.
Mathematical Function: Implements a complex activation function based on shifted sinc functions: (π/2) * [sinc(x-π) - sinc(x+π)].
Compiler Optimizations: Enabled with -O3flag for aggressive performance optimization of the generated code.
Occupancy Optimization: Configures 256 threads per block and dynamically calculates grid size (up to 65535 blocks) to maximize GPU occupancy.
Inlined Device Functions: Both the core mathematical operation (ssu_op) and helper function (sinc_op) are marked with __forceinline__to eliminate function call overhead within the kernel.


Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:
import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        term1 = torch.sinc(x - torch.pi)
        term2 = torch.sinc(x + torch.pi)
        return torch.pi / 2 * (term1 - term2)


batch_size = 128
feature_dim = 512


def get_inputs():
    x = torch.randn(batch_size, feature_dim, dtype=torch.float32)
    return [x]


def get_init_inputs():
    return []