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**: `complex_conj_mul_div_kernel`
- **FMA optimization**: `fmaf()` for fused multiply-add operations
- **Complex arithmetic**: Interleaved real/imaginary representation
- **Element-wise parallelism**: One thread per complex number

## Complex Number Operations
1. **Complex conjugate**: conj(A) = Xa - iYa
2. **Complex multiplication**: conj(A) × B
3. **Complex division**: P / C with regularization
- **Three-input operation**: Combines three complex tensors

## Mathematical Formulas
- **Conjugate multiplication**: (XaXb + YaYb) + i(XaYb - YaXb)
- **Complex division**: ( (XpXc + YpYc) + i(YpXc - XpYc) ) / |C|²
- **Denominator**: D = Xc² + Yc² + eps (regularized)
- **Fused operations**: Using `fmaf()` for better precision

## Architecture
- **3-element processing**: Each thread handles 3 complex numbers (6 floats)
- **Standard 1D grid**: Simple block/grid configuration
- **Memory pattern**: Coalesced access to interleaved complex data
- **Numerical stability**: Epsilon (1e-12) prevents division by zero

## CUDA Optimizations
- **FMA usage**: `fmaf()` for multiply-add with single rounding
- **Efficient division**: Precompute reciprocal to avoid multiple divisions
- **Regularization**: Epsilon protects against division by small magnitudes

## Performance Features
- **GPU acceleration**: Parallel computation across complex numbers
- **Precision optimization**: FMA reduces rounding errors
- **Memory efficiency**: Single kernel for three operations
- **Numerical robustness**: Regularized division

## Numerical Considerations
- **Division safety**: Epsilon prevents division by zero/near-zero
- **Precision**: FMA improves accuracy of complex operations
- **Overflow/underflow**: Magnitude squared could overflow for large values
- **Complex representation**: Interleaved format [real, imag, real, imag, ...]

## Use Case Applications
- **Signal processing**: Complex correlation/division operations
- **Communications**: Complex number manipulations
- **Physics simulations**: Complex arithmetic in wave equations
- **Computer vision**: Complex filter operations

## Mathematical Properties
- **Linearity**: Operation is linear in B, conjugate-linear in A
- **Scale invariance**: Division normalizes by |C|²
- **Complex algebra**: Proper handling of complex arithmetic
- **Three-input function**: Unique combination of complex operations

## Implementation Details
- **Tensor shape**: Expects same shape for a, b, c (N complex numbers)
- **Output format**: Same interleaved complex format as input
- **Batch processing**: Handles multiple complex numbers in parallel
- **Fixed epsilon**: Hardcoded 1e-12 for numerical stability



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, a, b, c):
        a_c = torch.complex(a[..., 0], a[..., 1])
        b_c = torch.complex(b[..., 0], b[..., 1])
        c_c = torch.complex(c[..., 0], c[..., 1])

        out_c = (torch.conj(a_c) * b_c) / c_c

        return torch.stack([out_c.real, out_c.imag], dim=-1)


batch_size = 1024


def get_inputs():
    a = torch.randn(batch_size, 2)
    b = torch.randn(batch_size, 2)
    c = torch.randn(batch_size, 2) + 1.0  # Bias away from zero
    return [a, b, c]


def get_init_inputs():
    return []