```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 asymmetric_conv_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    bool has_bias);
"""

_CUDA_SOURCE = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAStream.h>
#include <c10/cuda/CUDAException.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cuda_fp16.h>
#include <mma.h>

namespace {

constexpr int IC = 32;
constexpr int OC = 64;
constexpr int IH = 512;
constexpr int IW = 512;
constexpr int KH = 5;
constexpr int KW = 9;
constexpr int OH = 508;
constexpr int OW = 504;
constexpr int SPATIAL = OH * OW;
constexpr int REDUCTION = IC * KH * KW;

constexpr int TM = 64;
constexpr int TN = 128;
constexpr int TK = 32;

union __align__(32) SharedStorage {
    struct {
        half ah[TM * TK];
        half al[TM * TK];
        half bh[TK * TN];
        half bl[TK * TN];
    } operands;
    float result[TM * TN];
};

__global__ void asymmetric_conv_kernel(
    const float* __restrict__ x,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    bool has_bias)
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 700
    using namespace nvcuda;

    __shared__ SharedStorage shared;

    const int tid = threadIdx.x;
    const int warp = tid / 32;
    const int row_start = (warp / 4) * 32;
    const int col_start = (warp % 4) * 32;
    const int position_start = blockIdx.x * TN;
    const int batch = blockIdx.y;

    const float* batch_x =
        x + static_cast<int64_t>(batch) * IC * IH * IW;

    wmma::fragment<
        wmma::accumulator, 16, 16, 16, float
    > main_acc[2][2], correction_acc[2][2];

    #pragma unroll
    for (int i = 0; i < 2; ++i) {
        #pragma unroll
        for (int j = 0; j < 2; ++j) {
            wmma::fill_fragment(main_acc[i][j], 0.0f);
            wmma::fill_fragment(correction_acc[i][j], 0.0f);
        }
    }

    for (int reduction_start = 0;
         reduction_start < REDUCTION;
         reduction_start += TK) {

        for (int index = tid; index < TM * TK; index += 256) {
            const int channel = index / TK;
            const int reduction = reduction_start + index % TK;

            const float value = weight[channel * REDUCTION + reduction];
            const half high = __float2half_rn(value);
            const half low = __float2half_rn(
                (value - __half2float(high)) * 4096.0f);

            shared.operands.ah[index] = high;
            shared.operands.al[index] = low;
        }

        for (int index = tid; index < TK * TN; index += 256) {
            const int reduction = reduction_start + index / TN;
            const int position = position_start + index % TN;

            const int input_channel = reduction / (KH * KW);
            const int kernel_position = reduction % (KH * KW);
            const int kernel_h = kernel_position / KW;
            const int kernel_w = kernel_position % KW;

            float value = 0.0f;
            if (position < SPATIAL) {
                const int input_h = position / OW + kernel_h;
                const int input_w = position % OW + kernel_w;
                value = batch_x[
                    (input_channel * IH + input_h) * IW + input_w];
            }

            const half high = __float2half_rn(value);
            const half low = __float2half_rn(
                (value - __half2float(high)) * 4096.0f);

            shared.operands.bh[index] = high;
            shared.operands.bl[index] = low;
        }

        __syncthreads();

        #pragma unroll
        for (int reduction_tile = 0;
             reduction_tile < TK;
             reduction_tile += 16) {

            wmma::fragment<
                wmma::matrix_a, 16, 16, 16, half, wmma::row_major
            > ah[2], al[2];

            wmma::fragment<
                wmma::matrix_b, 16, 16, 16, half, wmma::row_major
            > bh[2], bl[2];

            #pragma unroll
            for (int i = 0; i < 2; ++i) {
                const int offset =
                    (row_start + i * 16) * TK + reduction_tile;
                wmma::load_matrix_sync(
                    ah[i], shared.operands.ah + offset, TK);
                wmma::load_matrix_sync(
                    al[i], shared.operands.al + offset, TK);
            }

            #pragma unroll
            for (int j = 0; j < 2; ++j) {
                const int offset =
                    reduction_tile * TN + col_start + j * 16;
                wmma::load_matrix_sync(
                    bh[j], shared.operands.bh + offset, TN);
                wmma::load_matrix_sync(
                    bl[j], shared.operands.bl + offset, TN);
            }

            #pragma unroll
            for (int i = 0; i < 2; ++i) {
                #pragma unroll
                for (int j = 0; j < 2; ++j) {
                    wmma::mma_sync(
                        main_acc[i][j],
                        ah[i], bh[j], main_acc[i][j]);
                    wmma::mma_sync(
                        correction_acc[i][j],
                        ah[i], bl[j], correction_acc[i][j]);
                    wmma::mma_sync(
                        correction_acc[i][j],
                        al[i], bh[j], correction_acc[i][j]);
                }
            }
        }

        __syncthreads();
    }

    #pragma unroll
    for (int i = 0; i < 2; ++i) {
        #pragma unroll
        for (int j = 0; j < 2; ++j) {
            #pragma unroll
            for (int element = 0;
                 element < main_acc[i][j].num_elements;
                 ++element) {
                main_acc[i][j].x[element] = fmaf(
                    correction_acc[i][j].x[element],
                    1.0f / 4096.0f,
                    main_acc[i][j].x[element]);
            }

            wmma::store_matrix_sync(
                shared.result
                    + (row_start + i * 16) * TN
                    + col_start + j * 16,
                main_acc[i][j],
                TN,
                wmma::mem_row_major);
        }
    }

    __syncthreads();

    for (int index = tid; index < TM * TN; index += 256) {
        const int channel = index / TN;
        const int position = position_start + index % TN;

        if (position < SPATIAL) {
            float value = shared.result[index];
            if (has_bias) {
                value += bias[channel];
            }
            output[
                (static_cast<int64_t>(batch) * OC + channel)
                * SPATIAL + position] = value;
        }
    }
#endif
}

} // namespace

torch::Tensor asymmetric_conv_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    bool has_bias)
{
    TORCH_CHECK(x.is_cuda() && weight.is_cuda(),
                "Input and weight must be CUDA tensors");
    TORCH_CHECK(x.scalar_type() == torch::kFloat32 &&
                weight.scalar_type() == torch::kFloat32,
                "Input and weight must have dtype float32");
    TORCH_CHECK(x.is_contiguous() && weight.is_contiguous(),
                "Input and weight must be contiguous");
    TORCH_CHECK(x.device() == weight.device(),
                "Input and weight must be on the same device");
    TORCH_CHECK(
        x.dim() == 4 && x.size(1) == IC &&
        x.size(2) == IH && x.size(3) == IW,
        "Unsupported input shape");
    TORCH_CHECK(
        weight.dim() == 4 &&
        weight.size(0) == OC && weight.size(1) == IC &&
        weight.size(2) == KH && weight.size(3) == KW,
        "Unsupported weight shape");
    TORCH_CHECK(x.size(0) <= 65535, "Batch is too large");

    if (has_bias) {
        TORCH_CHECK(
            bias.is_cuda() && bias.device() == x.device() &&
            bias.scalar_type() == torch::kFloat32 &&
            bias.is_contiguous() && bias.numel() == OC,
            "Invalid bias");
    }

    const c10::cuda::CUDAGuard device_guard(x.device());

    auto output = torch::empty(
        {x.size(0), OC, OH, OW}, x.options());

    if (x.size(0) == 0) {
        return output;
    }

    const dim3 grid(
        (SPATIAL + TN - 1) / TN,
        static_cast<unsigned int>(x.size(0)));
    const auto stream =
        c10::cuda::getCurrentCUDAStream(x.get_device());

    asymmetric_conv_kernel<<<grid, 256, 0, stream.stream()>>>(
        x.data_ptr<float>(),
        weight.data_ptr<float>(),
        has_bias ? bias.data_ptr<float>() : nullptr,
        output.data_ptr<float>(),
        has_bias);

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_extension = None


def _get_extension():
    global _extension
    if _extension is None:
        _extension = load_inline(
            name="asymmetric_conv_wmma_compensated_v4",
            cpp_sources=_CPP_SOURCE,
            cuda_sources=_CUDA_SOURCE,
            functions=["asymmetric_conv_cuda"],
            extra_cflags=["-O3"],
            extra_cuda_cflags=["-O3"],
            verbose=False,
        )
    return _extension


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

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv2d
        weight = conv.weight

        supported = (
            x.is_cuda
            and x.dtype == torch.float32
            and weight.dtype == torch.float32
            and weight.device == x.device
            and x.ndim == 4
            and tuple(x.shape[1:]) == (32, 512, 512)
            and x.shape[0] <= 65535
            and conv.in_channels == 32
            and conv.out_channels == 64
            and conv.kernel_size == (5, 9)
            and conv.stride == (1, 1)
            and conv.padding == (0, 0)
            and conv.dilation == (1, 1)
            and conv.groups == 1
            and not torch.is_autocast_enabled()
        )

        if not supported:
            return conv(x)

        if torch.cuda.get_device_capability(x.device)[0] < 7:
            return conv(x)

        bias = conv.bias
        if bias is not None and (
            bias.dtype != torch.float32 or bias.device != x.device
        ):
            return conv(x)

        with torch.cuda.device(x.device):
            return _get_extension().asymmetric_conv_cuda(
                x.contiguous(),
                weight.contiguous(),
                bias.contiguous() if bias is not None else weight,
                bias is not None,
            )
```