You write custom CUDA kernels to replace the pytorch operators in the given architecture to get speedups. 

    You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining matmul+relu), or algorithmic changes (such as online softmax). You are only limited by your imagination.


        Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is: 

        ``` 

        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self) -> None:
        super().__init__()

    def forward(self, a, b):
        return a + b


def get_inputs():
    # randomly generate input tensors based on the model architecture
    a = torch.randn(1, 128).cuda()
    b = torch.randn(1, 128).cuda()
    return [a, b]


def get_init_inputs():
    # randomly generate tensors required for initialization based on the model architecture
    return []

        ``` 

        The example new arch with custom CUDA kernels looks like this:
        ```
        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline

# Define the custom CUDA kernel for element-wise addition
elementwise_add_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>

__global__ void elementwise_add_kernel(const float* a, const float* b, float* out, int size) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) {
        out[idx] = a[idx] + b[idx];
    }
}

torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b) {
    auto size = a.numel();
    auto out = torch::zeros_like(a);

    const int block_size = 256;
    const int num_blocks = (size + block_size - 1) / block_size;

    elementwise_add_kernel<<<num_blocks, block_size>>>(a.data_ptr<float>(), b.data_ptr<float>(), out.data_ptr<float>(), size);

    return out;
}
"""

elementwise_add_cpp_source = (
    "torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b);"
)

# Compile the inline CUDA code for element-wise addition
elementwise_add = load_inline(
    name="elementwise_add",
    cpp_sources=elementwise_add_cpp_source,
    cuda_sources=elementwise_add_source,
    functions=["elementwise_add_cuda"],
    verbose=True,
    extra_cflags=[""],
    extra_ldflags=[""],
)


class ModelNew(nn.Module):
    def __init__(self) -> None:
        super().__init__()
        self.elementwise_add = elementwise_add

    def forward(self, a, b):
        return self.elementwise_add.elementwise_add_cuda(a, b)

        ``` 

        
    You are given the following architecture: 

    ```
    # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn

class Model(nn.Module):
    """
    Performs a depthwise 2D convolution with asymmetric input and square kernel.

    Args:
        in_channels (int): Number of channels in the input tensor.
        out_channels (int): Number of channels produced by the convolution.
        kernel_size (int): Size of the square convolution kernel.
        stride (int, optional): Stride of the convolution. Defaults to 1.
        padding (int, optional): Padding applied to the input. Defaults to 0.
        bias (bool, optional): If `True`, adds a learnable bias to the output. Defaults to `False`.
    """
    def __init__(self, in_channels: int, out_channels: int, kernel_size: int, stride: int = 1, padding: int = 0, bias: bool = False):
        super(Model, self).__init__()
        self.conv2d = nn.Conv2d(in_channels, out_channels, kernel_size=(kernel_size, kernel_size), stride=stride, padding=padding, groups=in_channels, bias=bias)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Performs the depthwise 2D convolution.

        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, in_channels, height_in, width_in).

        Returns:
            torch.Tensor: Output tensor of shape (batch_size, out_channels, height_out, width_out).
        """
        return self.conv2d(x)

# Test code
batch_size = 64
in_channels = 128
out_channels = 128
kernel_size = 3
width_in = 512
height_in = 256
stride = 1
padding = 0

def get_inputs():
    x = torch.rand(batch_size, in_channels, height_in, width_in)
    return [x]

def get_init_inputs():
    return [in_channels, out_channels, kernel_size, stride, padding]
    ```
    
Optimize the architecture named Model with custom CUDA operators! Name your optimized output architecture ModelNew. Output the new code in codeblocks. Please generate real code, NOT pseudocode, make sure the code compiles and is fully functional. Just output the new model code, no other text, and NO testing code! 



This is turn 6 of 6 for this task. Your previous solution (turn 5) was:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor depthwise3x3_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <cstdint>

template<int StaticHeight, int StaticWidth, bool HasBias>
__global__ __launch_bounds__(256)
void depthwise3x3_kernel(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int channels,
    int dynamic_height,
    int dynamic_width,
    int64_t planes)
{
    constexpr int Rows = 8;
    const int height = StaticHeight ? StaticHeight : dynamic_height;
    const int width = StaticWidth ? StaticWidth : dynamic_width;
    const int oh = height - 2;
    const int ow = width - 2;
    const int x = (int(blockIdx.x) * 256 + int(threadIdx.x)) * 2;
    const int y = int(blockIdx.y) * Rows;

    if (x >= ow)
        return;

    for (int64_t plane = blockIdx.z; plane < planes; plane += gridDim.z) {
        const int channel = plane % channels;
        const float* w = weight + int64_t(channel) * 9;

        const float w00 = w[0], w01 = w[1], w02 = w[2];
        const float w10 = w[3], w11 = w[4], w12 = w[5];
        const float w20 = w[6], w21 = w[7], w22 = w[8];
        const float b = HasBias ? bias[channel] : 0.0f;

        const float* src =
            input + plane * int64_t(height) * width + int64_t(y) * width + x;
        float* dst =
            output + plane * int64_t(oh) * ow + int64_t(y) * ow + x;

        float2 r0a = *reinterpret_cast<const float2*>(src);
        float2 r0b = *reinterpret_cast<const float2*>(src + 2);
        float2 r1a = *reinterpret_cast<const float2*>(src + width);
        float2 r1b = *reinterpret_cast<const float2*>(src + width + 2);

        #pragma unroll
        for (int row = 0; row < Rows; ++row) {
            if (y + row < oh) {
                const float* next = src + int64_t(row + 2) * width;
                const float2 r2a = *reinterpret_cast<const float2*>(next);
                const float2 r2b = *reinterpret_cast<const float2*>(next + 2);

                float a0 = r0a.x * w00;
                float a1 = r0a.y * w00;

                a0 = fmaf(r0a.y, w01, a0);
                a1 = fmaf(r0b.x, w01, a1);
                a0 = fmaf(r0b.x, w02, a0);
                a1 = fmaf(r0b.y, w02, a1);

                a0 = fmaf(r1a.x, w10, a0);
                a1 = fmaf(r1a.y, w10, a1);
                a0 = fmaf(r1a.y, w11, a0);
                a1 = fmaf(r1b.x, w11, a1);
                a0 = fmaf(r1b.x, w12, a0);
                a1 = fmaf(r1b.y, w12, a1);

                a0 = fmaf(r2a.x, w20, a0);
                a1 = fmaf(r2a.y, w20, a1);
                a0 = fmaf(r2a.y, w21, a0);
                a1 = fmaf(r2b.x, w21, a1);
                a0 = fmaf(r2b.x, w22, a0);
                a1 = fmaf(r2b.y, w22, a1);

                if (HasBias) {
                    a0 += b;
                    a1 += b;
                }

                *reinterpret_cast<float2*>(dst + int64_t(row) * ow) =
                    make_float2(a0, a1);

                r0a = r1a;
                r0b = r1b;
                r1a = r2a;
                r1b = r2b;
            }
        }
    }
}

template<int H, int W>
void launch_depthwise(
    const torch::Tensor& input,
    const torch::Tensor& weight,
    const c10::optional<torch::Tensor>& bias,
    torch::Tensor& output,
    dim3 grid,
    cudaStream_t stream)
{
    const int channels = input.size(1);
    const int height = input.size(2);
    const int width = input.size(3);
    const int64_t planes = input.size(0) * int64_t(channels);

    if (bias.has_value()) {
        depthwise3x3_kernel<H, W, true><<<grid, 256, 0, stream>>>(
            input.data_ptr<float>(),
            weight.data_ptr<float>(),
            bias.value().data_ptr<float>(),
            output.data_ptr<float>(),
            channels, height, width, planes);
    } else {
        depthwise3x3_kernel<H, W, false><<<grid, 256, 0, stream>>>(
            input.data_ptr<float>(),
            weight.data_ptr<float>(),
            nullptr,
            output.data_ptr<float>(),
            channels, height, width, planes);
    }
}

torch::Tensor depthwise3x3_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias)
{
    const c10::cuda::CUDAGuard device_guard(input.device());

    const int64_t batch = input.size(0);
    const int channels = input.size(1);
    const int height = input.size(2);
    const int width = input.size(3);
    const int oh = height - 2;
    const int ow = width - 2;
    const int64_t planes = batch * channels;

    auto output = torch::empty(
        {batch, int64_t(channels), int64_t(oh), int64_t(ow)},
        input.options());

    if (output.numel() == 0)
        return output;

    const dim3 grid(
        (ow + 511) / 512,
        (oh + 7) / 8,
        static_cast<unsigned int>(planes < 65535 ? planes : 65535));

    const cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    if (height == 256 && width == 512) {
        launch_depthwise<256, 512>(
            input, weight, bias, output, grid, stream);
    } else {
        launch_depthwise<0, 0>(
            input, weight, bias, output, grid, stream);
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_depthwise_extension = load_inline(
    name="depthwise3x3_pair_rows8_v5",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["depthwise3x3_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        kernel_size: int,
        stride: int = 1,
        padding: int = 0,
        bias: bool = False,
    ):
        super().__init__()
        self.conv2d = nn.Conv2d(
            in_channels,
            out_channels,
            kernel_size=(kernel_size, kernel_size),
            stride=stride,
            padding=padding,
            groups=in_channels,
            bias=bias,
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv2d
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 4
            and x.is_contiguous()
            and x.size(1) == conv.in_channels
            and x.size(2) >= 3
            and x.size(3) >= 4
            and x.size(3) % 2 == 0
            and (x.size(2) + 5) // 8 <= 65535
            and x.size(3) <= 2147483136
            and x.data_ptr() % 8 == 0
            and conv.in_channels == conv.out_channels
            and conv.kernel_size == (3, 3)
            and conv.stride == (1, 1)
            and conv.padding == (0, 0)
            and conv.dilation == (1, 1)
            and conv.weight.dtype == torch.float32
            and conv.weight.device == x.device
            and conv.weight.is_contiguous()
            and (
                conv.bias is None
                or (
                    conv.bias.dtype == torch.float32
                    and conv.bias.device == x.device
                    and conv.bias.is_contiguous()
                )
            )
            and not torch.is_autocast_enabled()
        ):
            return _depthwise_extension.depthwise3x3_cuda(
                x, conv.weight, conv.bias
            )
        return conv(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 6.66 ms; the PyTorch reference (with TF32 enabled) takes 15.2 ms; speedup 2.282x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void depthwise3x3_kernel<256, 512, false>(float const*, float const*, float const*, float* | 6629.2 | 1 |

The fastest correct solution so far (2.346x speedup) is:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor depthwise3x3_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <cstdint>

__global__ void depthwise3x3_kernel(
    const float* __restrict__ input,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int channels,
    int height,
    int width,
    int output_height,
    int output_width,
    int64_t planes)
{
    const int x = (blockIdx.x * blockDim.x + threadIdx.x) * 2;
    const int y = blockIdx.y * 4;

    if (x >= output_width)
        return;

    for (int64_t plane = blockIdx.z; plane < planes; plane += gridDim.z) {
        const int channel = plane % channels;
        const float* w = weight + channel * 9;

        const float w00 = w[0], w01 = w[1], w02 = w[2];
        const float w10 = w[3], w11 = w[4], w12 = w[5];
        const float w20 = w[6], w21 = w[7], w22 = w[8];
        const float b = bias ? bias[channel] : 0.0f;

        const float* src =
            input + plane * height * width + int64_t(y) * width + x;
        float* dst =
            output + plane * output_height * output_width
            + int64_t(y) * output_width + x;

        float2 r0a = *reinterpret_cast<const float2*>(src);
        float2 r0b = *reinterpret_cast<const float2*>(src + 2);
        float2 r1a = *reinterpret_cast<const float2*>(src + width);
        float2 r1b = *reinterpret_cast<const float2*>(src + width + 2);

        #pragma unroll
        for (int row = 0; row < 4; ++row) {
            if (y + row < output_height) {
                const float* next = src + int64_t(row + 2) * width;
                const float2 r2a =
                    *reinterpret_cast<const float2*>(next);
                const float2 r2b =
                    *reinterpret_cast<const float2*>(next + 2);

                float a0 = r0a.x * w00;
                float a1 = r0a.y * w00;

                a0 = fmaf(r0a.y, w01, a0);
                a1 = fmaf(r0b.x, w01, a1);
                a0 = fmaf(r0b.x, w02, a0);
                a1 = fmaf(r0b.y, w02, a1);

                a0 = fmaf(r1a.x, w10, a0);
                a1 = fmaf(r1a.y, w10, a1);
                a0 = fmaf(r1a.y, w11, a0);
                a1 = fmaf(r1b.x, w11, a1);
                a0 = fmaf(r1b.x, w12, a0);
                a1 = fmaf(r1b.y, w12, a1);

                a0 = fmaf(r2a.x, w20, a0);
                a1 = fmaf(r2a.y, w20, a1);
                a0 = fmaf(r2a.y, w21, a0);
                a1 = fmaf(r2b.x, w21, a1);
                a0 = fmaf(r2b.x, w22, a0);
                a1 = fmaf(r2b.y, w22, a1);

                *reinterpret_cast<float2*>(
                    dst + int64_t(row) * output_width
                ) = make_float2(a0 + b, a1 + b);

                r0a = r1a;
                r0b = r1b;
                r1a = r2a;
                r1b = r2b;
            }
        }
    }
}

torch::Tensor depthwise3x3_cuda(
    torch::Tensor input,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias)
{
    const c10::cuda::CUDAGuard device_guard(input.device());

    const int64_t batch = input.size(0);
    const int channels = input.size(1);
    const int height = input.size(2);
    const int width = input.size(3);
    const int output_height = height - 2;
    const int output_width = width - 2;
    const int64_t planes = batch * channels;

    auto output = torch::empty(
        {batch, channels, output_height, output_width},
        input.options());

    if (output.numel() == 0)
        return output;

    const float* bias_ptr = bias.has_value()
        ? bias.value().data_ptr<float>()
        : nullptr;

    constexpr int threads = 256;
    const dim3 grid(
        (output_width + threads * 2 - 1) / (threads * 2),
        (output_height + 3) / 4,
        static_cast<unsigned int>(planes < 65535 ? planes : 65535));

    depthwise3x3_kernel<<<
        grid, threads, 0, at::cuda::getCurrentCUDAStream()
    >>>(
        input.data_ptr<float>(),
        weight.data_ptr<float>(),
        bias_ptr,
        output.data_ptr<float>(),
        channels,
        height,
        width,
        output_height,
        output_width,
        planes);

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_depthwise_extension = load_inline(
    name="depthwise3x3_pair_rows_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["depthwise3x3_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        kernel_size: int,
        stride: int = 1,
        padding: int = 0,
        bias: bool = False,
    ):
        super().__init__()
        self.conv2d = nn.Conv2d(
            in_channels,
            out_channels,
            kernel_size=(kernel_size, kernel_size),
            stride=stride,
            padding=padding,
            groups=in_channels,
            bias=bias,
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv2d
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 4
            and x.is_contiguous()
            and x.size(1) == conv.in_channels
            and x.size(2) >= 3
            and x.size(3) >= 4
            and x.size(3) % 2 == 0
            and (x.size(2) + 1) // 4 <= 65535
            and conv.in_channels == conv.out_channels
            and conv.kernel_size == (3, 3)
            and conv.stride == (1, 1)
            and conv.padding == (0, 0)
            and conv.dilation == (1, 1)
            and conv.weight.dtype == torch.float32
            and conv.weight.device == x.device
            and conv.weight.is_contiguous()
            and (
                conv.bias is None
                or (
                    conv.bias.dtype == torch.float32
                    and conv.bias.device == x.device
                    and conv.bias.is_contiguous()
                )
            )
            and not torch.is_autocast_enabled()
        ):
            return _depthwise_extension.depthwise3x3_cuda(
                x, conv.weight, conv.bias
            )
        return conv(x)
```

Write an improved complete ModelNew: fix any error, and if the solution is already correct, make it faster. Output the new code in one ```python codeblock. Just the model code, no other text, and NO testing code.
