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

## Advanced CUDA Features
- **Warp reduction**: Custom `warpReduceMinMax()` using `__shfl_down_sync()`
- **Dual reduction**: Simultaneous min and max computation
- **Block-level parallelism**: One CUDA block per row
- **Dynamic block sizing**: Adaptive thread block size
- **Fused multiply-add**: `fmaf()` for scale+shift operation

## Mathematical Operations
- **Min/Max detection**: Find per-row minimum and maximum
- **Min-Max normalization**: `(x - min) / (max - min + eps)`
- **Scaling**: Multiply by user-defined scale factor
- **Shifting**: Add user-defined shift value
- **Reciprocal computation**: `rsqrtf()²` trick for `1/(range+eps)`

## Parallel Patterns
- **Two-pass algorithm**: First find min/max, then normalize
- **Row-wise processing**: Each block processes one row
- **Dual-value reduction**: Efficient min and max reduction together
- **Grid-stride loops**: Threads process multiple columns per row

## Optimization Techniques
- **Fused operations**: Normalization + scaling + shifting in single kernel
- **Warp-aware reduction**: Optimized for 32-thread warps
- **Numerical stability**: Epsilon prevents division by zero
- **FMA usage**: `fmaf()` for precise scale+shift computation
- **Adaptive block size**: Dynamically adjusted for column count

## Performance Features
- **Massive parallelism**: Row-level and column-level parallelism
- **Efficient reduction**: Custom min/max reduction using warp shuffles
- **Memory coalescing**: Row-major access patterns
- **Numerical optimization**: Reciprocal via rsqrtf()² for speed

## Unique Aspects
- **Dual reduction**: Simultaneous min and max finding
- **Complete normalization pipeline**: Detect range → normalize → scale → shift
- **Parameterized transformation**: User-defined scale and shift
- **Row-wise adaptation**: Each row normalized based on its own statistics

## Numerical Considerations
- **Epsilon protection**: Prevents division by (max-min) ≈ 0
- **Range invariance**: Handles constant rows (max = min)
- **INFINITY constants**: Using CUDA's INFINITY for initial min/max
- **Reciprocal trick**: `rsqrtf(x)*rsqrtf(x)` ≈ `1/x` (fast approximation)




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, scale, shift, eps=1e-5):
        super(Model, self).__init__()
        self.scale = scale
        self.shift = shift
        self.eps = eps

    def forward(self, x):
        min_x = x.min(dim=-1, keepdim=True).values
        max_x = x.max(dim=-1, keepdim=True).values

        range_x = max_x - min_x

        # MinMax Normalization
        norm = (x - min_x) / (range_x + self.eps)

        # Scale and Shift
        return norm * self.scale + self.shift


batch_size = 16
dim = 256


def get_inputs():
    x = torch.randn(batch_size, dim) * 10.0
    return [x]


def get_init_inputs():
    return [2.0, 1.0]