Write a custom CUDA kernel to optimize `Gish` using `float64` (double) precision.

Formula: f(x) = x * log(2 - exp(-exp(x)))

Problem Analysis:
1. Precision Issues with float32: The double exponential `exp(-exp(x))` is highly sensitive to floating-point errors. Minor inaccuracies in the inner `exp(x)` are amplified by the outer `exp`, leading to significant deviations. Using `double` precision is necessary for accuracy alignment.
2. Memory Bottleneck: The operation is memory-bound, now with 8 bytes per element.

Optimization Strategy: Fused Element-wise Kernel with Double Precision

1. Data Type: All computations are performed in `double`.

2. Vectorized Loads (double2): Use `double2` to load 128 bits (2 double elements) per memory transaction.

3. Fused Stable Math (in double):
   - Clamp input to a safe range for `double` precision `exp` (e.g., 700).
   - Use standard `double` precision math functions (`exp`, `log`).

4. One-Pass: Fuse all logic 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)

DTYPE = torch.float64

class Gish(nn.Module):
    def __init__(self):
        super(Gish, self).__init__()
        # Clamp value for double precision exp
        self.exp_clamp = 700.0

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        clamped_x = torch.clamp(x, max=self.exp_clamp)
        inner_exp = torch.exp(clamped_x)
        outer_exp = torch.exp(-inner_exp)
        log_val = torch.log(2.0 - outer_exp)
        return x * log_val

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

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

def get_init_inputs():
    return []