Write a custom CUDA kernel to optimize the Logish activation function.

The mathematical definition is:
f(x) = x * log(1 + sigmoid(x))

Problem Analysis:
The standard PyTorch implementation is memory-bound because it involves a chain of element-wise operations: sigmoid, addition, log, and multiplication.
1. sigmoid(x) creates an intermediate tensor.
2. 1 + temp adds overhead.
3. log(temp) creates another intermediate tensor.
4. x * temp creates the final output.
This results in multiple read/write passes over the GPU global memory, creating a bandwidth bottleneck.

Optimization Strategy: Fused Element-wise Kernel with Vectorized Access

1. Operator Fusion: Create a single CUDA kernel that performs the entire mathematical calculation in registers for each element. This reduces global memory access to just one read and one write per element.

2. Vectorized Memory Access: Since this is a memory-bound operation, maximizing bandwidth is critical. We will use float4 data types to load and store 128 bits (4 floats) per instruction. This reduces the number of memory instructions and improves bus utilization.

3. Grid-Stride Loop: Implement the kernel using a grid-stride loop pattern to handle input tensors of arbitrary size efficiently, regardless of the grid dimension.

4. Numerical Implementation: Use fast hardware intrinsics where appropriate (e.g., expf, logf) to ensure the computation throughput matches the optimized memory bandwidth. The calculation will be performed as: s = 1 / (1 + exp(-x)); result = x * log(1 + s).

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
DIM = 4096
SHAPE = (BATCH_SIZE, DIM)

class Logish(nn.Module):
    """
    公式: f(x) = x * log(1 + sigmoid(x))
    """
    def __init__(self):
        super(Logish, self).__init__()

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return x * torch.log(1 + torch.sigmoid(x))

class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.logish = Logish()
    
    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return self.logish(x)

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

def get_init_inputs():
    return []