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 with math.h

## CUDA Components
- **CUDA kernel**: `real_imag_hypot_kernel`
- **CUDA math function**: `hypotf()` for hypotenuse calculation
- **Complex number processing**: Interleaved real/imaginary pairs
- **Reduction operation**: 2 floats → 1 float per complex number

## Mathematical Operation
- **Complex magnitude**: Compute |z| = sqrt(real² + imag²)
- **Hypotenuse function**: `hypotf(X, Y)` = sqrt(X² + Y²)
- **Magnitude calculation**: Euclidean norm of complex number
- **Dimension reduction**: From [N, 2] to [N]

## Architecture
- **2-to-1 reduction**: Each thread processes 2 floats, outputs 1 float
- **Standard 1D grid**: Simple block/grid configuration
- **Memory pattern**: Coalesced access to interleaved complex data
- **Tensor shape change**: Input [N, 2] → Output [N]

## CUDA Optimization
- **hypotf() function**: Optimized hypotenuse calculation (avoids overflow)
- **Numerical stability**: Better than sqrt(x² + y²) for extreme values
- **Single operation**: Efficient magnitude computation

## Performance Features
- **GPU acceleration**: Parallel magnitude computation
- **Memory reduction**: Output half the size of input
- **Efficient math**: Hardware-optimized hypotf() function
- **Simple kernel**: Low computational overhead

## Numerical Considerations
- **Overflow/underflow**: hypotf() handles extreme values better than manual sqrt
- **Precision**: Single-precision floating point
- **Input format**: Expects interleaved [real, imag, real, imag, ...]
- **Non-negative output**: Always ≥ 0

## Use Case Applications
- **Complex number processing**: Magnitude extraction
- **Signal processing**: Amplitude calculation
- **Computer vision**: Distance/magnitude computations
- **Physics simulations**: Vector magnitude calculations

## Implementation Details
- **Tensor reshaping**: Explicit output tensor creation with size [N]
- **Complex representation**: Assumes last dimension is size 2 (real/imag)
- **Batch dimension**: N represents batch size of complex numbers
- **Dimension reduction**: Collapses complex dimension to magnitude

## Mathematical Properties
- **Non-negative**: Output always ≥ 0
- **Scale preserving**: |αz| = |α||z|
- **Triangle inequality**: |z1 + z2| ≤ |z1| + |z2|
- **Complex norm**: Satisfies norm properties

## Comparison
- **Similar to previous**: Simpler version of `complex_abs_angle_polar_cuda.py`
- **Focused operation**: Only magnitude, no angle computation
- **Memory efficient**: Half the output size
- **Simpler kernel**: Single math function call




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):
        # Interpret input [N, 2] as complex Z = X + iY
        z = torch.complex(x[..., 0], x[..., 1])

        # Calculate Magnitude |Z|
        return torch.abs(z)


batch_size = 1024
dim = 2


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


def get_init_inputs():
    return []