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 a square input and an asymmetric kernel.

    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 (int or tuple, optional): Padding applied to the input. Defaults to 0.
        dilation (int or tuple, optional): Spacing between kernel elements. Defaults to 1.
        groups (int, optional): Number of blocked connections from input channels to output channels. Defaults to 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: int = 0, dilation: int = 1, groups: int = 1, bias: bool = False):
        super(Model, self).__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:
        """
        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

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]  # Provide in_channels, out_channels, kernel_size for initialization
    ```
    
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
# 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
from torch.utils.cpp_extension import load_inline


def _pair(v):
    if isinstance(v, (tuple, list)):
        return int(v[0]), int(v[1])
    return int(v), int(v)


_CPP_SRC = "torch::Tensor conv2d_forward(torch::Tensor x, torch::Tensor w, torch::Tensor bias);"

_TEMPLATE = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>
#include <stdint.h>

#define IN_C {IN_C}
#define KH {KH}
#define KW {KW}
#define SH {SH}
#define SW {SW}
#define DH {DH}
#define DW {DW}

#define KDIM (IN_C * KH * KW)
#define BK 32
#define NCHUNK (KDIM / BK)
#define BM 128
#define BN 64
#define NTHREADS 256
#define APITCH (BM + 8)
#define BPITCH (BK + 4)

#define SM_A (2 * BK * APITCH)
#define SM_B (2 * BN * BPITCH)
#define SM_FLOATS (2 * SM_A + SM_B + KDIM)
#define SM_BYTES (SM_FLOATS * 4)

__device__ __forceinline__ unsigned cvt_tf32(float x) {
    unsigned r;
    asm volatile("cvt.rna.tf32.f32 %0, %1;\n" : "=r"(r) : "f"(x));
    return r;
}

__device__ __forceinline__ void split_tf32(float x, unsigned &hi, unsigned &lo) {
    hi = cvt_tf32(x);
    lo = cvt_tf32(x - __uint_as_float(hi));
}

__device__ __forceinline__ void mma_tf32(float &c0, float &c1, float &c2, float &c3,
                                         unsigned a0, unsigned a1, unsigned a2, unsigned a3,
                                         unsigned b0, unsigned b1) {
    asm volatile(
        "mma.sync.aligned.m16n8k8.row.col.f32.tf32.tf32.f32 "
        "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%0,%1,%2,%3};\n"
        : "+f"(c0), "+f"(c1), "+f"(c2), "+f"(c3)
        : "r"(a0), "r"(a1), "r"(a2), "r"(a3), "r"(b0), "r"(b1));
}

template <bool HAS_BIAS, bool NOK>
__global__ void __launch_bounds__(NTHREADS, 1)
igemm3x_kernel(const float* __restrict__ x,
               const float* __restrict__ w,
               const float* __restrict__ bias,
               float* __restrict__ y,
               const int H, const int W,
               const int Ho, const int Wo, const long M,
               const int OC)
{
    extern __shared__ float smem[];
    float* sAhi = smem;                  // [2][BK][APITCH]
    float* sAlo = smem + SM_A;           // [2][BK][APITCH]
    float* sB   = smem + 2 * SM_A;       // [2][BN][BPITCH]
    int*   sK   = (int*)(smem + 2 * SM_A + SM_B);  // [KDIM]

    const int tid  = threadIdx.x;
    const int lane = tid & 31;
    const int warp = tid >> 5;
    const int lg   = lane >> 2;
    const int lt   = lane & 3;
    const int wm   = warp >> 1;   // 0..3, M direction (32 rows each)
    const int wn   = warp & 1;    // 0..1, N direction (32 cols each)

    const long m_tile = (long)blockIdx.x * BM;
    const int  n_blk  = blockIdx.y * BN;
    const long HoWo   = (long)Ho * (long)Wo;
    const long HW     = (long)H * (long)W;

    // ---- shared k offsets: k = ic*(KH*KW) + kh*KW + kw ----
    for (int k = tid; k < KDIM; k += NTHREADS) {
        const int kw = k % KW;
        const int t  = k / KW;
        const int kh = t % KH;
        const int ic = t / KH;
        sK[k] = (int)((long)ic * HW + (long)kh * DH * W + (long)kw * DW);
    }
    __syncthreads();   // make sK visible before any staging reads it

    // ---- A staging coordinates: 2 threads per row ----
    const int arow_s = tid & (BM - 1);       // 0..127
    const int akoff  = (tid >> 7) * 16;      // 0 or 16

    const long mg = m_tile + arow_s;
    long abase;
    if (mg < M) {
        const long nb = mg / HoWo;
        const long r  = mg - nb * HoWo;
        const int oh  = (int)(r / Wo);
        const int ow  = (int)(r - (long)oh * Wo);
        abase = nb * ((long)IN_C * HW) + (long)oh * SH * W + (long)ow * SW;
    } else {
        abase = 0;
    }

    // ---- B staging coordinates ----
    const int bn  = tid >> 2;           // 0..63
    const int bk8 = (tid & 3) * 8;      // 0,8,16,24
    const int gn  = n_blk + bn;
    const bool nvalid = NOK || (gn < OC);

    float ast[16];
    float bst[8];

    auto load_stage = [&](int kn0) {
        if (nvalid) {
            const float4 p0 = *reinterpret_cast<const float4*>(w + (long)gn * KDIM + kn0 + bk8);
            const float4 p1 = *reinterpret_cast<const float4*>(w + (long)gn * KDIM + kn0 + bk8 + 4);
            bst[0] = p0.x; bst[1] = p0.y; bst[2] = p0.z; bst[3] = p0.w;
            bst[4] = p1.x; bst[5] = p1.y; bst[6] = p1.z; bst[7] = p1.w;
        } else {
#pragma unroll
            for (int i = 0; i < 8; ++i) bst[i] = 0.f;
        }
#pragma unroll
        for (int i = 0; i < 16; ++i) {
            ast[i] = x[abase + (long)sK[kn0 + akoff + i]];
        }
    };

    auto store_stage = [&](int buf) {
        unsigned* ah = reinterpret_cast<unsigned*>(sAhi + buf * (BK * APITCH));
        unsigned* al = reinterpret_cast<unsigned*>(sAlo + buf * (BK * APITCH));
#pragma unroll
        for (int i = 0; i < 16; ++i) {
            unsigned hi, lo;
            split_tf32(ast[i], hi, lo);
            ah[(akoff + i) * APITCH + arow_s] = hi;
            al[(akoff + i) * APITCH + arow_s] = lo;
        }
        float* sb = sB + buf * (BN * BPITCH) + bn * BPITCH + bk8;
#pragma unroll
        for (int i = 0; i < 8; ++i) sb[i] = bst[i];
    };

    load_stage(0);
    store_stage(0);
    __syncthreads();

    float acc[2][4][4];
#pragma unroll
    for (int mt = 0; mt < 2; ++mt)
#pragma unroll
        for (int nt = 0; nt < 4; ++nt)
#pragma unroll
            for (int i = 0; i < 4; ++i) acc[mt][nt][i] = 0.f;

    const int arow = wm * 32 + lg;
    const int bcol = wn * 32 + lg;

    int buf = 0;
#pragma unroll 1
    for (int c = 0; c < NCHUNK; ++c) {
        const bool has_next = (c + 1) < NCHUNK;
        if (has_next) load_stage((c + 1) * BK);

        const float* sah = sAhi + buf * (BK * APITCH);
        const float* sal = sAlo + buf * (BK * APITCH);
        const float* sb  = sB   + buf * (BN * BPITCH);

#pragma unroll
        for (int ks = 0; ks < BK; ks += 8) {
            unsigned afh[2][4], afl[2][4];
#pragma unroll
            for (int mt = 0; mt < 2; ++mt) {
                const int r = arow + mt * 16;
                const float* p0h = sah + (ks + lt) * APITCH + r;
                const float* p1h = sah + (ks + lt + 4) * APITCH + r;
                const float* p0l = sal + (ks + lt) * APITCH + r;
                const float* p1l = sal + (ks + lt + 4) * APITCH + r;
                afh[mt][0] = __float_as_uint(p0h[0]);
                afh[mt][1] = __float_as_uint(p0h[8]);
                afh[mt][2] = __float_as_uint(p1h[0]);
                afh[mt][3] = __float_as_uint(p1h[8]);
                afl[mt][0] = __float_as_uint(p0l[0]);
                afl[mt][1] = __float_as_uint(p0l[8]);
                afl[mt][2] = __float_as_uint(p1l[0]);
                afl[mt][3] = __float_as_uint(p1l[8]);
            }
            unsigned bfh[4][2], bfl[4][2];
#pragma unroll
            for (int nt = 0; nt < 4; ++nt) {
                const float* p = sb + (bcol + nt * 8) * BPITCH + ks + lt;
                const float bv0 = p[0];
                const float bv1 = p[4];
                split_tf32(bv0, bfh[nt][0], bfl[nt][0]);
                split_tf32(bv1, bfh[nt][1], bfl[nt][1]);
            }
#pragma unroll
            for (int mt = 0; mt < 2; ++mt) {
#pragma unroll
                for (int nt = 0; nt < 4; ++nt) {
                    float* c = acc[mt][nt];
                    mma_tf32(c[0], c[1], c[2], c[3],
                             afh[mt][0], afh[mt][1], afh[mt][2], afh[mt][3],
                             bfh[nt][0], bfh[nt][1]);
                    mma_tf32(c[0], c[1], c[2], c[3],
                             afh[mt][0], afh[mt][1], afh[mt][2], afh[mt][3],
                             bfl[nt][0], bfl[nt][1]);
                    mma_tf32(c[0], c[1], c[2], c[3],
                             afl[mt][0], afl[mt][1], afl[mt][2], afl[mt][3],
                             bfh[nt][0], bfh[nt][1]);
                }
            }
        }

        if (has_next) store_stage(buf ^ 1);
        __syncthreads();
        buf ^= 1;
    }

    // ---- epilogue: write directly in NCHW layout ----
    const long ocoff = (long)(OC - 1) * HoWo;
#pragma unroll
    for (int mt = 0; mt < 2; ++mt) {
#pragma unroll
        for (int h = 0; h < 2; ++h) {
            const long row = m_tile + wm * 32 + mt * 16 + h * 8 + lg;
            if (row < M) {
                const long nb = row / HoWo;
                float* yb = y + row + nb * ocoff;
#pragma unroll
                for (int nt = 0; nt < 4; ++nt) {
                    const int col = n_blk + wn * 32 + nt * 8 + lt * 2;
                    float v0 = acc[mt][nt][2 * h];
                    float v1 = acc[mt][nt][2 * h + 1];
                    if (HAS_BIAS) {
                        v0 += bias[col];
                        v1 += bias[col + 1];
                    }
                    float* p = yb + (long)col * HoWo;
                    if (NOK) {
                        p[0] = v0;
                        p[HoWo] = v1;
                    } else {
                        if (col < OC) p[0] = v0;
                        if (col + 1 < OC) p[HoWo] = v1;
                    }
                }
            }
        }
    }
}

template <bool HAS_BIAS, bool NOK>
static void launch_igemm(const float* x, const float* w, const float* bias, float* y,
                         int H, int W, int Ho, int Wo, long M, int OC,
                         unsigned gx, unsigned gy, cudaStream_t stream) {
    static bool configured = false;
    if (!configured) {
        cudaFuncSetAttribute(igemm3x_kernel<HAS_BIAS, NOK>,
                             cudaFuncAttributeMaxDynamicSharedMemorySize, SM_BYTES);
        configured = true;
    }
    igemm3x_kernel<HAS_BIAS, NOK><<<dim3(gx, gy), NTHREADS, SM_BYTES, stream>>>(
        x, w, bias, y, H, W, Ho, Wo, M, OC);
}

torch::Tensor conv2d_forward(torch::Tensor x, torch::Tensor w, torch::Tensor bias) {
    TORCH_CHECK(x.is_cuda() && w.is_cuda(), "inputs must be CUDA tensors");
    TORCH_CHECK(x.scalar_type() == at::kFloat && w.scalar_type() == at::kFloat,
                "only fp32 supported");
    TORCH_CHECK(w.size(1) == IN_C && w.size(2) == KH && w.size(3) == KW,
                "weight shape mismatch");
    TORCH_CHECK(x.size(1) == IN_C, "input channel mismatch");

    auto xc = x.contiguous();
    auto wc = w.contiguous();

    const long N  = xc.size(0);
    const long H  = xc.size(2);
    const long W  = xc.size(3);
    const long OC = wc.size(0);
    const long Ho = (H - DH * (KH - 1) - 1) / SH + 1;
    const long Wo = (W - DW * (KW - 1) - 1) / SW + 1;
    const long M  = N * Ho * Wo;

    auto y = torch::empty({N, OC, Ho, Wo}, xc.options());
    if (M == 0 || OC == 0) return y;

    const bool has_bias = bias.numel() > 0;
    const float* bias_ptr = nullptr;
    torch::Tensor bc;
    if (has_bias) {
        bc = bias.contiguous();
        bias_ptr = bc.data_ptr<float>();
    }

    const unsigned gx = (unsigned)((M + BM - 1) / BM);
    const unsigned gy = (unsigned)((OC + BN - 1) / BN);
    auto stream = at::cuda::getCurrentCUDAStream();

    const bool nok = (OC % BN) == 0;
    if (has_bias) {
        if (nok) launch_igemm<true, true>(xc.data_ptr<float>(), wc.data_ptr<float>(), bias_ptr,
                                          y.data_ptr<float>(), (int)H, (int)W, (int)Ho, (int)Wo,
                                          M, (int)OC, gx, gy, stream.stream());
        else launch_igemm<true, false>(xc.data_ptr<float>(), wc.data_ptr<float>(), bias_ptr,
                                       y.data_ptr<float>(), (int)H, (int)W, (int)Ho, (int)Wo,
                                       M, (int)OC, gx, gy, stream.stream());
    } else {
        if (nok) launch_igemm<false, true>(xc.data_ptr<float>(), wc.data_ptr<float>(), nullptr,
                                           y.data_ptr<float>(), (int)H, (int)W, (int)Ho, (int)Wo,
                                           M, (int)OC, gx, gy, stream.stream());
        else launch_igemm<false, false>(xc.data_ptr<float>(), wc.data_ptr<float>(), nullptr,
                                        y.data_ptr<float>(), (int)H, (int)W, (int)Ho, (int)Wo,
                                        M, (int)OC, gx, gy, stream.stream());
    }

    return y;
}
"""


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(ModelNew, self).__init__()
        self.conv2d = nn.Conv2d(in_channels, out_channels, kernel_size,
                                stride=stride, padding=padding,
                                dilation=dilation, groups=groups, bias=bias)

        kh, kw = _pair(kernel_size)
        st = _pair(stride)
        pd = _pair(padding)
        dl = _pair(dilation)

        kdim = int(in_channels) * kh * kw

        self._native = True
        self._ext = None
        self._fn = None
        self._empty_bias = None

        ok = (
            groups == 1
            and pd == (0, 0)
            and (kdim % 32) == 0
            and (int(out_channels) % 8) == 0
            and int(in_channels) >= 1
        )

        if ok and torch.cuda.is_available():
            try:
                major, minor = torch.cuda.get_device_capability()
                prop = torch.cuda.get_device_properties(torch.cuda.current_device())
                sm_need = (2 * (2 * 32 * 136) + (2 * 64 * 36) + kdim) * 4
                ok = (major >= 8) and (prop.shared_memory_per_block_optin >= sm_need)
            except Exception:
                ok = False
        else:
            ok = False

        if ok:
            macros = {
                "IN_C": int(in_channels),
                "KH": kh,
                "KW": kw,
                "SH": st[0],
                "SW": st[1],
                "DH": dl[0],
                "DW": dl[1],
            }
            src = _TEMPLATE
            for k, v in macros.items():
                src = src.replace("{%s}" % k, str(v))
            name = "igemm3xtf32_c{}_k{}x{}_s{}x{}_d{}x{}_v5".format(
                in_channels, kh, kw, st[0], st[1], dl[0], dl[1])
            self._ext = load_inline(
                name=name,
                cpp_sources=_CPP_SRC,
                cuda_sources=src,
                functions=["conv2d_forward"],
                verbose=False,
                extra_cuda_cflags=["-O3"],
            )
            self._fn = self._ext.conv2d_forward
            self._native = False
            if bias:
                self._empty_bias = None
            else:
                self._empty_bias = torch.empty(0)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        fn = self._fn
        if fn is not None and x.is_cuda and x.dtype == torch.float32 and x.dim() == 4:
            b = self.conv2d.bias
            if b is None:
                b = self._empty_bias
                if b.device != x.device:
                    b = x.new_empty(0)
                    self._empty_bias = b
            return fn(x, self.conv2d.weight, b)
        return self.conv2d(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 15.1 ms; the PyTorch reference (with TF32 enabled) takes 12.5 ms; speedup 0.828x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void igemm3x_kernel<false, true>(float const*, float const*, float const*, float*, int, in | 15141.4 | 1 |

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.
