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**: `complex_abs_angle_polar_kernel`
- **CUDA math functions**: `hypotf()`, `atan2f()`
- **Complex number representation**: Interleaved real/imaginary parts
- **Element-wise parallelism**: One thread per complex number

## Complex Number Operations
- **Magnitude (abs)**: `hypotf(real, imag)` = sqrt(real² + imag²)
- **Angle (argument)**: `atan2f(imag, real)` = arctan(imag/real)
- **Polar conversion**: Cartesian (x,y) → Polar (r,θ)
- **Complex storage**: Interleaved [real0, imag0, real1, imag1, ...]

## Architecture
- **2-element processing**: Each thread handles one complex number (2 floats)
- **Standard 1D grid**: Simple block/grid configuration
- **Memory pattern**: Coalesced access to interleaved complex data
- **Output format**: Same layout as input ([R0, Θ0, R1, Θ1, ...])

## CUDA Math Functions
- **hypotf()**: Single-precision hypotenuse (avoids overflow)
- **atan2f()**: Single-precision arctangent with quadrant handling
- **Numerical stability**: Proper handling of edge cases

## Mathematical Properties
- **Complex transformation**: Cartesian → Polar coordinates
- **Magnitude preservation**: R ≥ 0 always
- **Angle range**: Θ ∈ (-π, π] typically
- **Bijective mapping**: One-to-one correspondence (except origin)

## Performance Features
- **GPU acceleration**: Parallel computation across complex numbers
- **Efficient functions**: `hypotf()` optimized for magnitude calculation
- **Memory efficiency**: In-place style computation pattern
- **Simple operations**: Moderate computational cost

## Numerical Considerations
- **Origin handling**: atan2(0,0) returns 0 (implementation-defined)
- **Overflow avoidance**: hypotf() prevents overflow in sqrt(x²+y²)
- **Precision**: Single-precision floating point
- **Quadrant awareness**: atan2f() correctly handles all four quadrants

## Use Case Applications
- **Signal processing**: Complex number transformations
- **Fourier analysis**: Convert between complex forms
- **Computer graphics**: Polar coordinate conversions
- **Physics simulations**: Complex number manipulations

## Implementation Details
- **Tensor shape**: Expects [N, 2] or similar even-last-dimension shape
- **Memory layout**: Interleaved complex representation
- **Batch processing**: Handles multiple complex numbers in parallel
- **Output format**: Polar coordinates in same interleaved format



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):
        z = torch.complex(x[..., 0], x[..., 1])

        R = torch.abs(z)
        Theta = torch.angle(z)

        return torch.stack([R, Theta], dim=-1)


batch_size = 1024
dim = 2


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


def get_init_inputs():
    return []