Write a custom CUDA kernel to optimize `FPFLU` (Faster Power Function Linear Unit).

Formula:
  f(x) = x                 if x >= 0
  f(x) = x / (1 + x^2)     if x < 0

This is a fast, non-monotonic activation that avoids expensive sqrt operations.

Problem Analysis:
1. Memory Bound: This is a point-wise activation with low arithmetic intensity. Performance is limited by memory bandwidth.
2. Operator Chaining: The PyTorch implementation using `torch.where` creates intermediate tensors.

Optimization Strategy: Fused Element-wise Kernel with Vectorization

1. One-Thread-per-Element: Map each element to a CUDA thread.

2. Vectorized Loads (float4): Use `float4` to process 128 bits per memory transaction.

3. Fused Fast Math:
   - For each element `x`, check `if (x < 0)`.
   - If true, compute `x * (1.0f / (1.0f + x*x))`.
   - If false, result is `x`.
   - Using reciprocal multiplication `x * rcp(1 + x*x)` can be faster.

4. One-Pass: Fuse all steps into a single read-compute-write kernel.
  
Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:   
  
```python
import torch
import torch.nn as nn

BATCH_SIZE = 4096
HIDDEN_DIM = 4096
SHAPE = (BATCH_SIZE, HIDDEN_DIM)

class FPFLU(nn.Module):
    """
    Faster Power Function Linear Unit (FPFLU).
    PFLU and FPFLU: Two novel non-monotonic activation functions in convolutional neural network
    https://doi.org/10.1016/j.neucom.2020.11.068
    """
    def __init__(self):
        super(FPFLU, self).__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # PyTorch 原生实现
        pos_part = x
        neg_part = x / (1.0 + x.pow(2))
        return torch.where(x >= 0, pos_part, neg_part)

class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.act = FPFLU()
    
    def forward(self, x):
        return self.act(x)

def get_inputs():
    input_tensor = torch.randn(SHAPE, dtype=torch.float32) * 5.0
    return [input_tensor.contiguous()]

def get_init_inputs():
    return []