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):
    """
    Model that performs a matrix multiplication, subtraction, multiplication, and ReLU activation.
    """
    def __init__(self, in_features, out_features, subtract_value, multiply_value):
        super(Model, self).__init__()
        self.linear = nn.Linear(in_features, out_features)
        self.subtract_value = subtract_value
        self.multiply_value = multiply_value

    def forward(self, x):
        x = self.linear(x)
        x = x - self.subtract_value
        x = x * self.multiply_value
        x = torch.relu(x)
        return x

batch_size = 1024
in_features = 8192
out_features = 8192
subtract_value = 2.0
multiply_value = 1.5

def get_inputs():
    return [torch.rand(batch_size, in_features)]

def get_init_inputs():
    return [in_features, out_features, subtract_value, multiply_value]
    ```
    
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 4 of 6 for this task. Your previous solution (turn 3) was:
```python
import math
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline


_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 <cuda_fp16.h>
#include <cublas_v2.h>
#include <algorithm>
#include <climits>
#include <cstdint>

__global__ void pack_matrices(
    const float* __restrict__ x,
    const float* __restrict__ w,
    half* __restrict__ xh,
    half* __restrict__ wh,
    int64_t nx,
    int64_t nw
) {
    const int64_t xv = (nx + 3) / 4;
    const int64_t wv = (nw + 3) / 4;

    for (int64_t t = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         t < xv + wv;
         t += int64_t(blockDim.x) * gridDim.x) {
        const bool is_weight = t >= xv;
        const int64_t i = (is_weight ? t - xv : t) * 4;
        const int64_t size = is_weight ? nw : nx;
        const float* src = is_weight ? w : x;
        half* dst = is_weight ? wh : xh;
        // Power-of-two scaling preserves small initialized weights in FP16.
        const float scale = is_weight ? 256.0f : 1.0f;

        if (i + 3 < size &&
            (reinterpret_cast<uintptr_t>(src + i) & 15) == 0) {
            const float4 v = *reinterpret_cast<const float4*>(src + i);
            half2* out = reinterpret_cast<half2*>(dst + i);
            out[0] = __floats2half2_rn(v.x * scale, v.y * scale);
            out[1] = __floats2half2_rn(v.z * scale, v.w * scale);
        } else {
            for (int j = 0; j < 4 && i + j < size; ++j) {
                dst[i + j] = __float2half_rn(src[i + j] * scale);
            }
        }
    }
}

__device__ __forceinline__ float activate(
    float value, float bias, float subtract_value, float multiply_value
) {
    value = __fadd_rn(value, bias);
    value = __fsub_rn(value, subtract_value);
    value = __fmul_rn(value, multiply_value);
    return value < 0.0f ? 0.0f : value;
}

__global__ void epilogue4(
    float4* __restrict__ output,
    const float4* __restrict__ bias,
    int64_t count,
    int columns,
    float subtract_value,
    float multiply_value
) {
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count;
         i += int64_t(blockDim.x) * gridDim.x) {
        float4 v = output[i];
        const float4 b = bias[i % columns];
        v.x = activate(v.x, b.x, subtract_value, multiply_value);
        v.y = activate(v.y, b.y, subtract_value, multiply_value);
        v.z = activate(v.z, b.z, subtract_value, multiply_value);
        v.w = activate(v.w, b.w, subtract_value, multiply_value);
        output[i] = v;
    }
}

__global__ void epilogue1(
    float* __restrict__ output,
    const float* __restrict__ bias,
    int64_t count,
    int columns,
    float subtract_value,
    float multiply_value
) {
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count;
         i += int64_t(blockDim.x) * gridDim.x) {
        output[i] = activate(
            output[i], bias[i % columns], subtract_value, multiply_value
        );
    }
}

torch::Tensor linear_activate_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    double subtract_value,
    double multiply_value
) {
    TORCH_CHECK(x.is_cuda() && weight.is_cuda() && bias.is_cuda(),
                "Expected CUDA tensors");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                weight.scalar_type() == at::kFloat &&
                bias.scalar_type() == at::kFloat,
                "Expected float32 tensors");
    TORCH_CHECK(x.device() == weight.device() &&
                x.device() == bias.device(), "Device mismatch");
    TORCH_CHECK(x.dim() == 2 && weight.dim() == 2 && bias.dim() == 1 &&
                x.size(1) == weight.size(1) &&
                bias.numel() == weight.size(0), "Invalid shapes");
    TORCH_CHECK(x.size(0) <= INT_MAX &&
                weight.size(0) <= INT_MAX &&
                x.size(1) <= INT_MAX, "Matrix dimensions are too large");

    const c10::cuda::CUDAGuard guard(x.device());
    x = x.contiguous();
    weight = weight.contiguous();
    bias = bias.contiguous();

    const int m = static_cast<int>(x.size(0));
    const int n = static_cast<int>(weight.size(0));
    const int k = static_cast<int>(x.size(1));
    auto output = torch::empty({m, n}, x.options());
    if (m == 0 || n == 0) {
        return output;
    }

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();
    constexpr int threads = 256;

    if (k == 0) {
        C10_CUDA_CHECK(cudaMemsetAsync(
            output.data_ptr<float>(), 0,
            output.numel() * sizeof(float), stream
        ));
    } else {
        auto xh = torch::empty(x.sizes(), x.options().dtype(at::kHalf));
        auto wh = torch::empty(
            weight.sizes(), weight.options().dtype(at::kHalf)
        );

        const int64_t pack_count =
            (x.numel() + 3) / 4 + (weight.numel() + 3) / 4;
        const int pack_blocks = static_cast<int>(std::min<int64_t>(
            (pack_count + threads - 1) / threads, 8192
        ));

        pack_matrices<<<pack_blocks, threads, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(),
            reinterpret_cast<half*>(xh.data_ptr<at::Half>()),
            reinterpret_cast<half*>(wh.data_ptr<at::Half>()),
            x.numel(), weight.numel()
        );
        C10_CUDA_KERNEL_LAUNCH_CHECK();

        cublasHandle_t handle = at::cuda::getCurrentCUDABlasHandle();
        cublasMath_t old_math;
        cublasPointerMode_t old_pointer_mode;
        TORCH_CHECK(cublasGetMathMode(handle, &old_math) ==
                    CUBLAS_STATUS_SUCCESS, "Cannot read cuBLAS math mode");
        TORCH_CHECK(cublasGetPointerMode(handle, &old_pointer_mode) ==
                    CUBLAS_STATUS_SUCCESS, "Cannot read cuBLAS pointer mode");

        const cublasMath_t math_mode = static_cast<cublasMath_t>(
            CUBLAS_DEFAULT_MATH |
            CUBLAS_MATH_DISALLOW_REDUCED_PRECISION_REDUCTION
        );
        TORCH_CHECK(cublasSetMathMode(handle, math_mode) ==
                    CUBLAS_STATUS_SUCCESS, "Cannot set cuBLAS math mode");

        const auto pointer_status =
            cublasSetPointerMode(handle, CUBLAS_POINTER_MODE_HOST);
        if (pointer_status != CUBLAS_STATUS_SUCCESS) {
            cublasSetMathMode(handle, old_math);
            TORCH_CHECK(false, "Cannot set cuBLAS pointer mode");
        }

        const float alpha = 1.0f / 256.0f;
        const float beta = 0.0f;
        const auto status = cublasGemmEx(
            handle, CUBLAS_OP_T, CUBLAS_OP_N,
            n, m, k,
            &alpha,
            wh.data_ptr<at::Half>(), CUDA_R_16F, k,
            xh.data_ptr<at::Half>(), CUDA_R_16F, k,
            &beta,
            output.data_ptr<float>(), CUDA_R_32F, n,
            CUBLAS_COMPUTE_32F,
            CUBLAS_GEMM_DEFAULT_TENSOR_OP
        );

        const auto restore_pointer =
            cublasSetPointerMode(handle, old_pointer_mode);
        const auto restore_math = cublasSetMathMode(handle, old_math);

        TORCH_CHECK(status == CUBLAS_STATUS_SUCCESS,
                    "cuBLAS GEMM failed: ", static_cast<int>(status));
        TORCH_CHECK(restore_pointer == CUBLAS_STATUS_SUCCESS &&
                    restore_math == CUBLAS_STATUS_SUCCESS,
                    "Cannot restore cuBLAS state");
    }

    const int64_t count = output.numel();
    if (n % 4 == 0 &&
        (reinterpret_cast<uintptr_t>(bias.data_ptr<float>()) & 15) == 0) {
        const int64_t vectors = count / 4;
        const int blocks = static_cast<int>(std::min<int64_t>(
            (vectors + threads - 1) / threads, 4096
        ));
        epilogue4<<<blocks, threads, 0, stream>>>(
            reinterpret_cast<float4*>(output.data_ptr<float>()),
            reinterpret_cast<const float4*>(bias.data_ptr<float>()),
            vectors, n / 4,
            static_cast<float>(subtract_value),
            static_cast<float>(multiply_value)
        );
    } else {
        const int blocks = static_cast<int>(std::min<int64_t>(
            (count + threads - 1) / threads, 4096
        ));
        epilogue1<<<blocks, threads, 0, stream>>>(
            output.data_ptr<float>(), bias.data_ptr<float>(),
            count, n,
            static_cast<float>(subtract_value),
            static_cast<float>(multiply_value)
        );
    }
    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_extension = load_inline(
    name="linear_packed_tensorcore_activation_v3",
    cpp_sources=r"""
torch::Tensor linear_activate_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    torch::Tensor bias,
    double subtract_value,
    double multiply_value
);
""",
    cuda_sources=_cuda_source,
    functions=["linear_activate_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    extra_ldflags=["-lcublas"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self, in_features, out_features, subtract_value, multiply_value
    ):
        super().__init__()
        self.linear = nn.Linear(in_features, out_features)
        self.subtract_value = subtract_value
        self.multiply_value = multiply_value

    def forward(self, x):
        if (
            not x.is_cuda
            or x.dtype != torch.float32
            or self.linear.weight.dtype != torch.float32
            or self.linear.bias.dtype != torch.float32
            or torch.is_autocast_enabled()
        ):
            y = F.linear(x, self.linear.weight, self.linear.bias)
            return torch.relu(
                (y - self.subtract_value) * self.multiply_value
            )

        if x.ndim == 0 or x.shape[-1] != self.linear.in_features:
            raise ValueError("Input's last dimension must match in_features")

        shape = (*x.shape[:-1], self.linear.out_features)
        rows = math.prod(x.shape[:-1])
        return _extension.linear_activate_cuda(
            x.reshape(rows, self.linear.in_features),
            self.linear.weight,
            self.linear.bias,
            float(self.subtract_value),
            float(self.multiply_value),
        ).view(shape)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 0.981 ms; the PyTorch reference (with TF32 enabled) takes 1.27 ms; speedup 1.295x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void cutlass::Kernel2<cutlass_80_tensorop_s16816gemm_f16_128x128_32x4_tn_align8>(cutlass_8 | 558.4 | 1 |
| pack_matrices(float const*, float const*, __half*, __half*, long, long) | 337.0 | 1 |
| epilogue4(float4*, float4 const*, long, int, float, float) | 38.0 | 1 |
| Memset (Device) | 1.2 | 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.
