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.

# Technologies Used in This Code

## Core Libraries
- **PyTorch**: Deep learning framework
- **CUDA**: NVIDIA GPU parallel computing
- **C++**: Kernel implementation

## CUDA Components
- **CUDA kernel**: `sin_cos_hypot_kernel`
- **CUDA math functions**: `sinf()`, `cosf()`, `hypotf()`
- **Element-wise parallelism**: One thread per element
- **math.h inclusion**: Standard C math library

## Mathematical Operations
- **Sine function**: `sinf(x)`
- **Cosine function**: `cosf(x)`
- **Hypotenuse function**: `hypotf(sin_x, cos_x)`
- **Trigonometric identity**: hypot(sin(x), cos(x)) = 1 (mathematically)
- **Floating-point computation**: Potential small numerical errors

## Architecture
- **Standard 1D grid**: Simple block/grid configuration
- **Element-wise computation**: Independent processing per element
- **Memory pattern**: Coalesced memory access

## CUDA Math Functions
- **sinf()**: Single-precision sine
- **cosf()**: Single-precision cosine
- **hypotf()**: Single-precision hypotenuse (sqrt(sin² + cos²))

## Mathematical Properties
- **Identity verification**: Computes sqrt(sin²(x) + cos²(x)) = 1
- **Numerical stability**: hypotf() avoids overflow/underflow
- **Trigonometric test**: Can be used to verify trigonometric identities
- **Unit circle**: Result should always be 1 (within floating-point error)

## Performance Features
- **GPU acceleration**: Parallel trigonometric computations
- **Specialized function**: hypotf() optimized for hypotenuse calculation
- **Numerical accuracy**: Potential floating-point rounding errors
- **Simple operations**: Moderate computational cost (trig functions)

## Numerical Considerations
- **Floating-point precision**: Result may not be exactly 1.0
- **Range handling**: Input x can be any real number
- **Error accumulation**: Small numerical errors from sin/cos then hypot
- **Mathematical identity**: Useful for testing numerical accuracy



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

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

    def forward(self, x):
        return torch.hypot(torch.sin(x), torch.cos(x))

batch_size = 1024
dim = 1024

def get_inputs():
    x = torch.randn(batch_size, dim) * 2 * 3.14159
    return [x]

def get_init_inputs():
    return []