Write a custom CUDA kernel to optimize `NLReLU` (Natural-Logarithm-Rectified Linear Unit).

Formula:
  f(x) = log(beta * x + 1.0)   if x >= 0
  f(x) = 0                     if x < 0

This is equivalent to `log(beta * max(0, x) + 1.0)`.

Problem Analysis:
1. Memory Bound: As a point-wise activation, its performance is strictly limited by memory bandwidth.
2. Operator Chaining: The PyTorch implementation `torch.log(beta * F.relu(x) + 1.0)` chains multiple kernels (`relu`, `mul`, `add`, `log`), creating high memory traffic.

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 to maximize throughput.

3. Fused Branching Logic:
   - For each element `x`, check `if (x >= 0)`.
   - If true, compute `__logf(beta * x + 1.0f)`.
   - If false, the result is `0.0f`.

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
import torch.nn.functional as F

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

# NLReLU 超参数 beta ，论文中建议范围 0.7-1.1
BETA_VALUE = 1.0

class NLReLU(nn.Module):
    """
    "Natural-Logarithm-Rectified Activation Function in Convolutional Neural Networks"
    Formula:
      f(x) = log(beta * x + 1.0)   if x >= 0
      f(x) = 0                     if x < 0
    """
    def __init__(self, beta=1.0):
        super(NLReLU, self).__init__()
        self.beta = beta

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x_relu = F.relu(x)
        inner = self.beta * x_relu + 1.0
        return torch.log(inner)

class Model(nn.Module):
    def __init__(self, beta=1.0):
        super(Model, self).__init__()
        self.act = NLReLU(beta=beta)
    
    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 [BETA_VALUE]