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):
    """
    Simple model that performs a matrix multiplication of a diagonal matrix with another matrix.
    C = diag(A) * B
    """
    def __init__(self):
        super(Model, self).__init__()
    
    def forward(self, A, B):
        """
        Performs the matrix multiplication.

        Args:
            A (torch.Tensor): A 1D tensor representing the diagonal of the diagonal matrix. Shape: (N,).
            B (torch.Tensor): A 2D tensor representing the second matrix. Shape: (N, M).

        Returns:
            torch.Tensor: The result of the matrix multiplication. Shape: (N, M).
        """
        return torch.diag(A) @ B

M = 4096
N = 4096

def get_inputs():
    A = torch.rand(N)
    B = torch.rand(N, M)
    return [A, B]

def get_init_inputs():
    return []  # No special initialization inputs needed
    ```
    
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 3 of 6 for this task. Your previous solution (turn 2) 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

# Custom CUDA kernel for C = diag(A) @ B.
# Mathematically this is row-wise scaling: C[i, j] = A[i] * B[i, j].
# The kernel is purely memory-bandwidth bound: it reads B once (64 MB),
# writes C once (64 MB) and reads A (16 KB, cached). The implementation is
# optimized to reach peak DRAM bandwidth:
#   * 2D grid: blockIdx.x selects the row, so no integer division is needed
#     to recover the row index (the previous version used a costly 64-bit
#     division per thread).
#   * 128-bit vectorized loads/stores (float4) with 4x unrolling so each
#     thread issues 4 independent 16-byte transactions (64 B in flight),
#     which saturates memory bandwidth with high memory-level parallelism.
#   * Streaming cache hints (__ldg / __stcs) since B and C are touched once.
#   * A templated "even" path removes bounds checks when the row length is
#     an exact multiple of the block tile.
diag_matmul_source = """
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

#define BLOCK_SIZE 256
#define UNROLL 4

// Vectorized kernel: requires M % 4 == 0. One block-row per matrix row.
template <bool EVEN>
__global__ void diag_matmul_vec4_kernel(const float* __restrict__ A,
                                        const float* __restrict__ B,
                                        float* __restrict__ C,
                                        int vecM) {
    const long row = blockIdx.x;
    const float a = __ldg(A + row);
    const long offset = row * (long)vecM;
    const float4* Brow = reinterpret_cast<const float4*>(B) + offset;
    float4* Crow = reinterpret_cast<float4*>(C) + offset;

    const int base = blockIdx.y * (BLOCK_SIZE * UNROLL) + threadIdx.x;
    #pragma unroll
    for (int k = 0; k < UNROLL; ++k) {
        const int i = base + k * BLOCK_SIZE;
        if (EVEN || i < vecM) {
            const float4 b = __ldg(Brow + i);
            float4 c;
            c.x = a * b.x;
            c.y = a * b.y;
            c.z = a * b.z;
            c.w = a * b.w;
            __stcs(Crow + i, c);
        }
    }
}

// Scalar fallback kernel (handles any M).
__global__ void diag_matmul_scalar_kernel(const float* __restrict__ A,
                                          const float* __restrict__ B,
                                          float* __restrict__ C,
                                          long M) {
    const long row = blockIdx.x;
    const float a = __ldg(A + row);
    const long offset = row * M;
    const float* Brow = B + offset;
    float* Crow = C + offset;
    const long i = (long)blockIdx.y * blockDim.x + threadIdx.x;
    if (i < M) {
        __stcs(Crow + i, __ldg(Brow + i) * a);
    }
}

torch::Tensor diag_matmul_cuda(torch::Tensor A, torch::Tensor B) {
    TORCH_CHECK(A.is_cuda() && B.is_cuda(), "Inputs must be CUDA tensors");
    TORCH_CHECK(A.scalar_type() == at::kFloat && B.scalar_type() == at::kFloat,
                "Inputs must be float32");
    TORCH_CHECK(B.dim() == 2, "B must be a 2D tensor");

    auto A_c = A.contiguous();
    auto B_c = B.contiguous();

    const long N = A_c.numel();
    const long M = B_c.size(1);

    auto C = at::empty_like(B_c);
    if (N == 0 || M == 0) {
        return C;
    }

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();
    const dim3 block(BLOCK_SIZE);

    if ((M & 3) == 0) {
        const long vecM = M >> 2;
        const long tiles = (vecM + BLOCK_SIZE * UNROLL - 1) / (BLOCK_SIZE * UNROLL);
        const dim3 grid((unsigned)N, (unsigned)tiles);
        if (tiles * (BLOCK_SIZE * UNROLL) == vecM) {
            diag_matmul_vec4_kernel<true><<<grid, block, 0, stream>>>(
                A_c.data_ptr<float>(), B_c.data_ptr<float>(), C.data_ptr<float>(), (int)vecM);
        } else {
            diag_matmul_vec4_kernel<false><<<grid, block, 0, stream>>>(
                A_c.data_ptr<float>(), B_c.data_ptr<float>(), C.data_ptr<float>(), (int)vecM);
        }
    } else {
        const dim3 grid((unsigned)N, (unsigned)((M + BLOCK_SIZE - 1) / BLOCK_SIZE));
        diag_matmul_scalar_kernel<<<grid, block, 0, stream>>>(
            A_c.data_ptr<float>(), B_c.data_ptr<float>(), C.data_ptr<float>(), M);
    }
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return C;
}
"""

diag_matmul_cpp_source = (
    "torch::Tensor diag_matmul_cuda(torch::Tensor A, torch::Tensor B);"
)

# Compile the inline CUDA extension.
diag_matmul = load_inline(
    name="diag_matmul_v2",
    cpp_sources=diag_matmul_cpp_source,
    cuda_sources=diag_matmul_source,
    functions=["diag_matmul_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized version of Model that computes C = diag(A) @ B as a fused
    row-scaling CUDA kernel (C[i, j] = A[i] * B[i, j]) in FP32.
    """
    def __init__(self):
        super(ModelNew, self).__init__()
        self.diag_matmul = diag_matmul

    def forward(self, A, B):
        if (A.is_cuda and B.is_cuda and A.dtype == torch.float32
                and B.dtype == torch.float32):
            return self.diag_matmul.diag_matmul_cuda(A, B)
        # Fallback (e.g. CPU tensors): mathematically equivalent row scaling.
        return A.unsqueeze(-1) * B
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 0.12 ms; the PyTorch reference (with TF32 enabled) takes 1.08 ms; speedup 9.000x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void diag_matmul_vec4_kernel<true>(float const*, float const*, float*, int) | 100.1 | 1 |

The fastest correct solution so far (9.076x speedup) is:
```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

# Custom CUDA kernel for C = diag(A) @ B.
# Mathematically this is just a row-wise scaling: C[i, j] = A[i] * B[i, j].
# This avoids materializing the N x N diagonal matrix and the O(N^2 * M) matmul,
# reducing the work to a single memory-bandwidth-bound elementwise pass (O(N*M)).
diag_matmul_source = """
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

// Scalar fallback kernel (handles any M).
__global__ void diag_matmul_scalar_kernel(const float* __restrict__ A,
                                          const float* __restrict__ B,
                                          float* __restrict__ C,
                                          long N, long M) {
    long idx = (long)blockIdx.x * blockDim.x + threadIdx.x;
    long total = N * M;
    if (idx < total) {
        long row = idx / M;
        C[idx] = __ldg(A + row) * B[idx];
    }
}

// Vectorized kernel using 128-bit loads/stores (requires M % 4 == 0).
__global__ void diag_matmul_vec4_kernel(const float* __restrict__ A,
                                        const float* __restrict__ B,
                                        float* __restrict__ C,
                                        long N, long vecM) {
    long idx = (long)blockIdx.x * blockDim.x + threadIdx.x;
    long total = N * vecM;
    if (idx < total) {
        long row = idx / vecM;
        float a = __ldg(A + row);
        float4 b = reinterpret_cast<const float4*>(B)[idx];
        float4 c;
        c.x = a * b.x;
        c.y = a * b.y;
        c.z = a * b.z;
        c.w = a * b.w;
        reinterpret_cast<float4*>(C)[idx] = c;
    }
}

torch::Tensor diag_matmul_cuda(torch::Tensor A, torch::Tensor B) {
    TORCH_CHECK(A.is_cuda() && B.is_cuda(), "Inputs must be CUDA tensors");
    TORCH_CHECK(A.scalar_type() == at::kFloat && B.scalar_type() == at::kFloat,
                "Inputs must be float32");
    TORCH_CHECK(B.dim() == 2, "B must be a 2D tensor");

    auto A_c = A.contiguous();
    auto B_c = B.contiguous();

    const long N = A_c.numel();
    const long M = B_c.size(1);

    auto C = at::empty_like(B_c);
    if (N == 0 || M == 0) {
        return C;
    }

    const int block_size = 256;
    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    if ((M & 3) == 0) {
        const long vecM = M >> 2;
        const long total = N * vecM;
        const long num_blocks = (total + block_size - 1) / block_size;
        diag_matmul_vec4_kernel<<<num_blocks, block_size, 0, stream>>>(
            A_c.data_ptr<float>(), B_c.data_ptr<float>(), C.data_ptr<float>(), N, vecM);
    } else {
        const long total = N * M;
        const long num_blocks = (total + block_size - 1) / block_size;
        diag_matmul_scalar_kernel<<<num_blocks, block_size, 0, stream>>>(
            A_c.data_ptr<float>(), B_c.data_ptr<float>(), C.data_ptr<float>(), N, M);
    }
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return C;
}
"""

diag_matmul_cpp_source = (
    "torch::Tensor diag_matmul_cuda(torch::Tensor A, torch::Tensor B);"
)

# Compile the inline CUDA extension.
diag_matmul = load_inline(
    name="diag_matmul",
    cpp_sources=diag_matmul_cpp_source,
    cuda_sources=diag_matmul_source,
    functions=["diag_matmul_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Optimized version of Model that computes C = diag(A) @ B as a fused
    row-scaling CUDA kernel (C[i, j] = A[i] * B[i, j]) in FP32.
    """
    def __init__(self):
        super(ModelNew, self).__init__()
        self.diag_matmul = diag_matmul

    def forward(self, A, B):
        if (A.is_cuda and B.is_cuda and A.dtype == torch.float32
                and B.dtype == torch.float32):
            return self.diag_matmul.diag_matmul_cuda(A, B)
        # Fallback (e.g. CPU tensors): mathematically equivalent row scaling.
        return A.unsqueeze(-1) * B
```

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.


Precision rule: the timed forward must compute in FP32 (TF32 tensor-core math is allowed, as in the PyTorch reference). Do not cast inputs, weights or intermediate results to float16 or bfloat16 and do not call half-precision kernels in forward().
