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 standard 2D convolution operation with square input and asymmetric kernel, with dilation and padding.

    Args:
        in_channels (int): Number of channels in the input tensor.
        out_channels (int): Number of channels produced by the convolution.
        kernel_size (tuple): Size of the convolution kernel (height, width). 
        stride (int, optional): Stride of the convolution. Defaults to 1.
        padding (tuple, optional): Padding applied to the input (top/bottom, left/right). Defaults to (0, 0).
        dilation (tuple, optional): Spacing between kernel elements (height, width). Defaults to (1, 1).
        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: tuple, stride: int = 1, padding: tuple = (0, 0), dilation: tuple = (1, 1), bias: bool = False):
        super(Model, self).__init__()
        self.conv2d = nn.Conv2d(in_channels, out_channels, kernel_size, stride=stride, padding=padding, dilation=dilation, bias=bias)
        
    def forward(self, x: torch.Tensor) -> torch.Tensor:
        """
        Performs the 2D convolution.

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

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

# Test code
batch_size = 8
in_channels = 32
out_channels = 64
kernel_size = (5, 9)
width = 512
height = 512
stride = 1
padding = (2, 4)
dilation = (2, 3)

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

def get_init_inputs():
    return [in_channels, out_channels, kernel_size, stride, padding, dilation]
    ```
    
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 2 of 6 for this task. Your previous solution (turn 1) was:
```python
import functools

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


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

torch::Tensor asymmetric_conv_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias,
    int64_t sh, int64_t sw,
    int64_t ph, int64_t pw,
    int64_t dh, int64_t dw);
"""


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

namespace {

constexpr int BM = 64;
constexpr int BN = 64;
constexpr int BK = 32;

union __align__(32) SharedStorage {
    struct {
        float ah[BM * BK];
        float al[BM * BK];
        float bh[BK * BN];
        float bl[BK * BN];
    } operands;
    float result[BM * BN];
};

__global__ void convolution_kernel(
    const float* __restrict__ x,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int channels, int height, int width,
    int out_channels, int kh, int kw,
    int out_height, int out_width,
    int sh, int sw, int ph, int pw, int dh, int dw)
{
#if __CUDA_ARCH__ >= 800
    using namespace nvcuda;

    __shared__ SharedStorage storage;

    const int tid = threadIdx.x;
    const int warp = tid / 32;
    const int tile_m = blockIdx.y * BM;
    const int tile_n = blockIdx.x * BN;
    const int batch = blockIdx.z;
    const int spatial = out_height * out_width;
    const int kernel_area = kh * kw;
    const int reduction = channels * kernel_area;

    const int warp_m = (warp / 2) * 16;
    const int warp_n = (warp % 2) * 16;

    wmma::fragment<wmma::accumulator, 16, 16, 8, float> acc0, acc1;
    wmma::fill_fragment(acc0, 0.0f);
    wmma::fill_fragment(acc1, 0.0f);

    const int input_col = tid % BN;
    const int output_position = tile_n + input_col;
    const int base_h = (output_position / out_width) * sh - ph;
    const int base_w = (output_position % out_width) * sw - pw;

    const float* batch_input =
        x + static_cast<int64_t>(batch) * channels * height * width;

    for (int k_base = 0; k_base < reduction; k_base += BK) {
        #pragma unroll
        for (int i = tid; i < BM * BK; i += 256) {
            const int row = i / BK;
            const int k = k_base + i % BK;
            float value = 0.0f;

            if (tile_m + row < out_channels && k < reduction) {
                value = weight[
                    static_cast<int64_t>(tile_m + row) * reduction + k];
            }

            const float high = __float_to_tf32(value);
            storage.operands.ah[i] = high;
            storage.operands.al[i] = __float_to_tf32(value - high);
        }

        #pragma unroll
        for (int i = tid; i < BK * BN; i += 256) {
            const int k = k_base + i / BN;
            float value = 0.0f;

            if (k < reduction && output_position < spatial) {
                const int channel = k / kernel_area;
                const int kernel_position = k % kernel_area;
                const int input_h = base_h + (kernel_position / kw) * dh;
                const int input_w = base_w + (kernel_position % kw) * dw;

                if (static_cast<unsigned>(input_h) <
                        static_cast<unsigned>(height) &&
                    static_cast<unsigned>(input_w) <
                        static_cast<unsigned>(width)) {
                    value = batch_input[
                        (static_cast<int64_t>(channel) * height + input_h)
                        * width + input_w];
                }
            }

            const float high = __float_to_tf32(value);
            storage.operands.bh[i] = high;
            storage.operands.bl[i] = __float_to_tf32(value - high);
        }

        __syncthreads();

        #pragma unroll
        for (int kk = 0; kk < BK; kk += 8) {
            wmma::fragment<
                wmma::matrix_a, 16, 16, 8,
                wmma::precision::tf32, wmma::row_major> ah, al;

            wmma::fragment<
                wmma::matrix_b, 16, 16, 8,
                wmma::precision::tf32, wmma::row_major> bh, bl;

            wmma::load_matrix_sync(
                ah, storage.operands.ah + warp_m * BK + kk, BK);
            wmma::load_matrix_sync(
                al, storage.operands.al + warp_m * BK + kk, BK);

            wmma::load_matrix_sync(
                bh, storage.operands.bh + kk * BN + warp_n, BN);
            wmma::load_matrix_sync(
                bl, storage.operands.bl + kk * BN + warp_n, BN);

            wmma::mma_sync(acc0, ah, bl, acc0);
            wmma::mma_sync(acc0, al, bh, acc0);
            wmma::mma_sync(acc0, ah, bh, acc0);

            wmma::load_matrix_sync(
                bh, storage.operands.bh + kk * BN + warp_n + 32, BN);
            wmma::load_matrix_sync(
                bl, storage.operands.bl + kk * BN + warp_n + 32, BN);

            wmma::mma_sync(acc1, ah, bl, acc1);
            wmma::mma_sync(acc1, al, bh, acc1);
            wmma::mma_sync(acc1, ah, bh, acc1);
        }

        __syncthreads();
    }

    wmma::store_matrix_sync(
        storage.result + warp_m * BN + warp_n,
        acc0, BN, wmma::mem_row_major);
    wmma::store_matrix_sync(
        storage.result + warp_m * BN + warp_n + 32,
        acc1, BN, wmma::mem_row_major);

    __syncthreads();

    #pragma unroll
    for (int i = tid; i < BM * BN; i += 256) {
        const int channel = tile_m + i / BN;
        const int position = tile_n + i % BN;

        if (channel < out_channels && position < spatial) {
            float value = storage.result[i];
            if (bias != nullptr) {
                value += bias[channel];
            }
            output[
                (static_cast<int64_t>(batch) * out_channels + channel)
                * spatial + position] = value;
        }
    }
#endif
}

}  // namespace

torch::Tensor asymmetric_conv_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias,
    int64_t sh, int64_t sw,
    int64_t ph, int64_t pw,
    int64_t dh, int64_t dw)
{
    TORCH_CHECK(x.is_cuda() && weight.is_cuda(), "Expected CUDA tensors");
    TORCH_CHECK(x.scalar_type() == torch::kFloat32 &&
                weight.scalar_type() == torch::kFloat32,
                "Expected float32 tensors");
    TORCH_CHECK(x.dim() == 4 && weight.dim() == 4,
                "Expected four-dimensional tensors");
    TORCH_CHECK(x.is_contiguous() && weight.is_contiguous(),
                "Expected contiguous tensors");
    TORCH_CHECK(x.device() == weight.device(), "Device mismatch");
    TORCH_CHECK(x.size(1) == weight.size(1), "Channel mismatch");

    const c10::cuda::CUDAGuard device_guard(x.device());
    TORCH_CHECK(
        at::cuda::getCurrentDeviceProperties()->major >= 8,
        "This kernel requires an Ampere or newer GPU");

    const int64_t oh =
        (x.size(2) + 2 * ph - dh * (weight.size(2) - 1) - 1) / sh + 1;
    const int64_t ow =
        (x.size(3) + 2 * pw - dw * (weight.size(3) - 1) - 1) / sw + 1;
    TORCH_CHECK(oh > 0 && ow > 0, "Invalid convolution output size");

    const float* bias_ptr = nullptr;
    if (bias.has_value()) {
        TORCH_CHECK(
            bias->device() == x.device() &&
            bias->scalar_type() == torch::kFloat32 &&
            bias->is_contiguous() &&
            bias->numel() == weight.size(0),
            "Invalid bias");
        bias_ptr = bias->data_ptr<float>();
    }

    auto output = torch::empty(
        {x.size(0), weight.size(0), oh, ow}, x.options());
    if (output.numel() == 0) {
        return output;
    }

    const dim3 grid(
        (oh * ow + BN - 1) / BN,
        (weight.size(0) + BM - 1) / BM,
        x.size(0));

    convolution_kernel<<<
        grid, 256, 0, at::cuda::getCurrentCUDAStream()>>>(
        x.data_ptr<float>(),
        weight.data_ptr<float>(),
        bias_ptr,
        output.data_ptr<float>(),
        x.size(1), x.size(2), x.size(3),
        weight.size(0), weight.size(2), weight.size(3),
        oh, ow, sh, sw, ph, pw, dh, dw);

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""


@functools.lru_cache(maxsize=1)
def _extension():
    return load_inline(
        name="asymmetric_dilated_conv_tf32_split_v1",
        cpp_sources=_CPP_SOURCE,
        cuda_sources=_CUDA_SOURCE,
        functions=["asymmetric_conv_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: tuple,
        stride: int = 1,
        padding: tuple = (0, 0),
        dilation: tuple = (1, 1),
        bias: bool = False,
    ):
        super().__init__()
        self.conv2d = nn.Conv2d(
            in_channels,
            out_channels,
            kernel_size,
            stride=stride,
            padding=padding,
            dilation=dilation,
            bias=bias,
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv2d
        if (
            not x.is_cuda
            or x.ndim != 4
            or x.dtype != torch.float32
            or conv.weight.dtype != torch.float32
            or torch.is_autocast_enabled()
            or isinstance(conv.padding, str)
        ):
            return conv(x)

        if torch.cuda.get_device_capability(x.device)[0] < 8:
            return conv(x)

        return _extension().asymmetric_conv_cuda(
            x.contiguous(),
            conv.weight.contiguous(),
            conv.bias,
            conv.stride[0],
            conv.stride[1],
            conv.padding[0],
            conv.padding[1],
            conv.dilation[0],
            conv.dilation[1],
        )
```
Result of evaluating it:
The solution compiled but failed at run time. Error output:
```
Error building extension 'asymmetric_dilated_conv_tf32_split_v1': [1/3] c++ -MMD -MF main.o.d -DTORCH_EXTENSION_NAME=asymmetric_dilated_conv_tf32_split_v1 -DTORCH_API_INCLUDE_EXTENSION_H -isystem /...
```

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.
