InstanceNorm CUDA Implementation - Enhanced Optimized Version

Key optimization techniques used in this implementation:

1. **Warp-Level Parallel Reduction**: Implements efficient warp-level reduction for mean and variance
   calculations using warp shuffle operations (__shfl_down_sync) for intra-warp communication

2. **Hierarchical Reduction Strategy**: Employs two-level reduction approach with warp-level reduction
   followed by block-level reduction, minimizing synchronization overhead

3. **Dual-Kernel Optimization**: Provides specialized kernels for different spatial sizes - optimized
   kernel for large feature maps (≥1024 elements) and simplified kernel for small spatial dimensions

4. **Dynamic Thread Configuration**: Automatically selects optimal thread block size (64-256 threads)
   and kernel variant based on spatial dimension size for maximum GPU utilization

5. **Fused Operation Pipeline**: Combines statistics computation (mean/variance calculation) and
   normalization application in a single kernel launch, eliminating intermediate memory transfers

6. **Shared Memory Hierarchy**: Utilizes multi-level shared memory buffers for efficient data sharing
   between warps and within thread blocks

7. **Bank Conflict Avoidance**: Carefully structures shared memory allocation with separate buffers
   for warp sums and warp sum squares to minimize shared memory bank conflicts

8. **Numerical Precision Preservation**: Maintains PyTorch-compatible numerical precision with robust
   variance calculation using fmaxf() for non-negative variance and rsqrtf() for inverse standard deviation

Technical Features:

1. **Warp-Centric Design**: Leverages warp-level primitives for efficient 32-thread parallel reduction
2. **Adaptive Kernel Selection**: Intelligent switching between optimized and simplified kernels based on spatial size
3. **Efficient Synchronization**: Minimized __syncthreads() usage with warp-level synchronization primitives
4. **Memory Access Patterns**: Optimized global memory access with coalesced reading and writing
5. **Resource Optimization**: Dynamic shared memory allocation tailored to each kernel's requirements
6. **Boundary Handling**: Comprehensive out-of-bounds checking for irregular tensor dimensions
7. **PyTorch Compatibility**: Exact mathematical equivalence with PyTorch's InstanceNorm2d implementation

Performance Benefits:

1. **Eliminates Multiple Kernel Launches**: Single kernel computes both statistics and normalization
2. **Reduces Global Memory Traffic**: Intermediate results kept in shared memory and registers
3. **Optimized for Various Spatial Sizes**: Specialized kernels provide optimal performance across different feature map sizes
4. **Maximizes Parallelism**: Efficient utilization of warp-level parallelism across batch and channel dimensions
5. **Minimized Synchronization Overhead**: Strategic use of warp shuffles reduces thread block synchronization needs
6. **Enhanced Occupancy**: Adaptive thread configuration ensures optimal GPU resource utilization
7. **Memory Bandwidth Efficiency**: Coalesced memory access patterns maximize memory throughput

The custom kernel delivers significant performance improvements by processing entire InstanceNorm operation
in optimized fused kernels with hierarchical parallel reduction strategy and intelligent resource management.

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):
    """
    Simple model that performs InstanceNorm operation.
    """

    def __init__(self, num_features=64, eps=1e-5, affine=True, track_running_stats=False):
        super(Model, self).__init__()
        self.num_features = num_features
        self.eps = eps
        self.affine = affine
        self.track_running_stats = track_running_stats

        # 创建InstanceNorm层
        self.instance_norm = nn.InstanceNorm2d(
            num_features=num_features,
            eps=eps,
            affine=affine,
            track_running_stats=track_running_stats
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Applies InstanceNorm to the input tensor.

        Args:
            x (torch.Tensor): Input tensor of shape [batch_size, num_features, height, width]

        Returns:
            torch.Tensor: Output tensor after instance normalization, same shape as input.
        """
        return self.instance_norm(x)


# 参数配置
batch_size = 16
num_features = 64
height = 128
width = 128


def get_inputs():
    """
    生成InstanceNorm的输入张量。

    Returns:
        list: 包含一个形状为 [batch_size, num_features, height, width] 的张量
    """
    x = torch.randn(batch_size, num_features, height, width)
    return [x]


def get_init_inputs():
    """
    获取模型初始化所需的输入（空列表，因为不需要特殊初始化）。

    Returns:
        list: 空列表
    """
    return []  # No special initialization inputs needed