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 6 of 6 for this task. Your previous solution (turn 5) 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 <cublasLt.h>
#include <algorithm>
#include <cstdint>
#include <map>
#include <memory>
#include <tuple>

static void check_lt(cublasStatus_t status) {
    TORCH_CHECK(status == CUBLAS_STATUS_SUCCESS,
                "cuBLASLt error: ", static_cast<int>(status));
}

__global__ void pack_weight_kernel(
    const float* __restrict__ src,
    half* __restrict__ dst,
    int64_t vectors
) {
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < vectors;
         i += int64_t(blockDim.x) * gridDim.x) {
        float4 v = reinterpret_cast<const float4*>(src)[i];
        half2* d = reinterpret_cast<half2*>(dst) + 2 * i;
        d[0] = __floats2half2_rn(v.x * 256.0f, v.y * 256.0f);
        d[1] = __floats2half2_rn(v.z * 256.0f, v.w * 256.0f);
    }
}

__global__ void pack_input_bias_kernel(
    const float* __restrict__ src,
    half* __restrict__ dst,
    const float* __restrict__ bias,
    float* __restrict__ adjusted_bias,
    int64_t vectors,
    int bias_vectors,
    float sub,
    float mul
) {
    const int64_t first =
        int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
    const int64_t step = int64_t(blockDim.x) * gridDim.x;

    for (int64_t i = first; i < vectors; i += step) {
        float4 v = reinterpret_cast<const float4*>(src)[i];
        half2* d = reinterpret_cast<half2*>(dst) + 2 * i;
        d[0] = __floats2half2_rn(v.x, v.y);
        d[1] = __floats2half2_rn(v.z, v.w);
    }

    for (int64_t i = first; i < bias_vectors; i += step) {
        float4 b = reinterpret_cast<const float4*>(bias)[i];
        b.x = __fmul_rn(__fsub_rn(b.x, sub), mul);
        b.y = __fmul_rn(__fsub_rn(b.y, sub), mul);
        b.z = __fmul_rn(__fsub_rn(b.z, sub), mul);
        b.w = __fmul_rn(__fsub_rn(b.w, sub), mul);
        reinterpret_cast<float4*>(adjusted_bias)[i] = b;
    }
}

torch::Tensor pack_weight_cuda(torch::Tensor weight) {
    const c10::cuda::CUDAGuard guard(weight.device());
    weight = weight.contiguous();

    auto packed = torch::empty(
        weight.sizes(), weight.options().dtype(at::kHalf));
    const int64_t vectors = weight.numel() / 4;
    const int blocks = static_cast<int>(
        std::min<int64_t>((vectors + 255) / 256, 8192));

    pack_weight_kernel<<<blocks, 256, 0,
                         at::cuda::getCurrentCUDAStream()>>>(
        weight.data_ptr<float>(),
        reinterpret_cast<half*>(packed.data_ptr<at::Half>()),
        vectors);
    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return packed;
}

struct MatmulPlan {
    cublasLtMatmulDesc_t operation = nullptr;
    cublasLtMatrixLayout_t a = nullptr;
    cublasLtMatrixLayout_t b = nullptr;
    cublasLtMatrixLayout_t c = nullptr;
    cublasLtMatmulAlgo_t algorithm{};
    size_t workspace_bytes = 0;

    ~MatmulPlan() {
        if (operation) cublasLtMatmulDescDestroy(operation);
        if (a) cublasLtMatrixLayoutDestroy(a);
        if (b) cublasLtMatrixLayoutDestroy(b);
        if (c) cublasLtMatrixLayoutDestroy(c);
    }
};

struct ThreadContext {
    cublasLtHandle_t handle = nullptr;
    std::map<std::tuple<int, int, int, int>,
             std::unique_ptr<MatmulPlan>> plans;

    ThreadContext() {
        check_lt(cublasLtCreate(&handle));
    }

    ~ThreadContext() {
        plans.clear();
        if (handle) cublasLtDestroy(handle);
    }

    MatmulPlan& get_plan(
        int device, int m, int n, int k, const float* bias
    ) {
        auto key = std::make_tuple(device, m, n, k);
        auto found = plans.find(key);
        if (found != plans.end())
            return *found->second;

        auto plan = std::make_unique<MatmulPlan>();
        check_lt(cublasLtMatmulDescCreate(
            &plan->operation, CUBLAS_COMPUTE_32F, CUDA_R_32F));

        cublasOperation_t trans_a = CUBLAS_OP_T;
        cublasOperation_t trans_b = CUBLAS_OP_N;
        cublasLtEpilogue_t epilogue = CUBLASLT_EPILOGUE_RELU_BIAS;

        check_lt(cublasLtMatmulDescSetAttribute(
            plan->operation, CUBLASLT_MATMUL_DESC_TRANSA,
            &trans_a, sizeof(trans_a)));
        check_lt(cublasLtMatmulDescSetAttribute(
            plan->operation, CUBLASLT_MATMUL_DESC_TRANSB,
            &trans_b, sizeof(trans_b)));
        check_lt(cublasLtMatmulDescSetAttribute(
            plan->operation, CUBLASLT_MATMUL_DESC_EPILOGUE,
            &epilogue, sizeof(epilogue)));
        check_lt(cublasLtMatmulDescSetAttribute(
            plan->operation, CUBLASLT_MATMUL_DESC_BIAS_POINTER,
            &bias, sizeof(bias)));

        // Column-major interpretation gives output = weight @ input.T.
        check_lt(cublasLtMatrixLayoutCreate(
            &plan->a, CUDA_R_16F, k, n, k));
        check_lt(cublasLtMatrixLayoutCreate(
            &plan->b, CUDA_R_16F, k, m, k));
        check_lt(cublasLtMatrixLayoutCreate(
            &plan->c, CUDA_R_32F, n, m, n));

        cublasLtMatmulPreference_t preference;
        check_lt(cublasLtMatmulPreferenceCreate(&preference));
        const size_t workspace_limit = 64ULL << 20;
        auto status = cublasLtMatmulPreferenceSetAttribute(
            preference, CUBLASLT_MATMUL_PREF_MAX_WORKSPACE_BYTES,
            &workspace_limit, sizeof(workspace_limit));
        if (status != CUBLAS_STATUS_SUCCESS) {
            cublasLtMatmulPreferenceDestroy(preference);
            check_lt(status);
        }

        cublasLtMatmulHeuristicResult_t result{};
        int count = 0;
        status = cublasLtMatmulAlgoGetHeuristic(
            handle, plan->operation,
            plan->a, plan->b, plan->c, plan->c,
            preference, 1, &result, &count);
        cublasLtMatmulPreferenceDestroy(preference);
        check_lt(status);
        TORCH_CHECK(count > 0, "No compatible cuBLASLt algorithm");
        check_lt(result.state);

        plan->algorithm = result.algo;
        plan->workspace_bytes = result.workspaceSize;

        auto inserted = plans.emplace(key, std::move(plan));
        return *inserted.first->second;
    }
};

torch::Tensor linear_activate_cuda(
    torch::Tensor x,
    torch::Tensor packed_weight,
    torch::Tensor bias,
    double subtract_value,
    double multiply_value
) {
    const c10::cuda::CUDAGuard guard(x.device());

    // clone also handles contiguous tensors with unaligned storage offsets.
    if (!x.is_contiguous() ||
        (reinterpret_cast<uintptr_t>(x.data_ptr()) & 15))
        x = x.clone(at::MemoryFormat::Contiguous);
    if (!bias.is_contiguous() ||
        (reinterpret_cast<uintptr_t>(bias.data_ptr()) & 15))
        bias = bias.clone(at::MemoryFormat::Contiguous);

    const int m = static_cast<int>(x.size(0));
    const int n = static_cast<int>(packed_weight.size(0));
    const int k = static_cast<int>(x.size(1));

    auto output = torch::empty({m, n}, x.options());
    auto xh = torch::empty(x.sizes(), x.options().dtype(at::kHalf));
    auto adjusted_bias = torch::empty({n}, bias.options());

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();
    const int64_t vectors = x.numel() / 4;
    const int64_t work = std::max<int64_t>(vectors, n / 4);
    const int blocks = static_cast<int>(
        std::min<int64_t>((work + 255) / 256, 4096));

    pack_input_bias_kernel<<<blocks, 256, 0, stream>>>(
        x.data_ptr<float>(),
        reinterpret_cast<half*>(xh.data_ptr<at::Half>()),
        bias.data_ptr<float>(),
        adjusted_bias.data_ptr<float>(),
        vectors, n / 4,
        static_cast<float>(subtract_value),
        static_cast<float>(multiply_value));
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    static thread_local ThreadContext context;
    const float* bias_pointer = adjusted_bias.data_ptr<float>();
    MatmulPlan& plan = context.get_plan(
        x.get_device(), m, n, k, bias_pointer);
    check_lt(cublasLtMatmulDescSetAttribute(
        plan.operation, CUBLASLT_MATMUL_DESC_BIAS_POINTER,
        &bias_pointer, sizeof(bias_pointer)));

    auto workspace = torch::empty(
        {static_cast<int64_t>(plan.workspace_bytes)},
        x.options().dtype(at::kByte));

    const float alpha = static_cast<float>(multiply_value) / 256.0f;
    const float beta = 0.0f;
    check_lt(cublasLtMatmul(
        context.handle, plan.operation,
        &alpha,
        packed_weight.data_ptr<at::Half>(), plan.a,
        xh.data_ptr<at::Half>(), plan.b,
        &beta,
        output.data_ptr<float>(), plan.c,
        output.data_ptr<float>(), plan.c,
        &plan.algorithm,
        workspace.data_ptr(), plan.workspace_bytes,
        stream));

    return output;
}
"""

_extension = load_inline(
    name="linear_packed_lt_fused_v5",
    cpp_sources=r"""
torch::Tensor pack_weight_cuda(torch::Tensor weight);
torch::Tensor linear_activate_cuda(
    torch::Tensor x,
    torch::Tensor packed_weight,
    torch::Tensor bias,
    double subtract_value,
    double multiply_value);
""",
    cuda_sources=_cuda_source,
    functions=["pack_weight_cuda", "linear_activate_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    extra_ldflags=["-lcublasLt"],
    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
        self.register_buffer("_packed_weight", None, persistent=False)
        self._packed_weight_key = None

    def _apply(self, fn, recurse=True):
        self._packed_weight = None
        self._packed_weight_key = None
        return super()._apply(fn, recurse=recurse)

    def forward(self, x):
        weight = self.linear.weight
        bias = self.linear.bias
        if (
            not x.is_cuda
            or x.dtype != torch.float32
            or weight.dtype != torch.float32
            or bias.dtype != torch.float32
            or torch.is_autocast_enabled()
            or self.linear.in_features == 0
            or self.linear.out_features == 0
            or self.linear.in_features % 8 != 0
            or self.linear.out_features % 8 != 0
            or x.numel() == 0
        ):
            return torch.relu(
                (F.linear(x, weight, bias) - 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")
        if x.device != weight.device or x.device != bias.device:
            raise ValueError("Input and parameters must share a device")

        try:
            version = weight._version
        except RuntimeError:
            version = None

        stream = torch.cuda.current_stream(weight.device)
        key = (
            id(weight),
            weight.data_ptr(),
            version,
            tuple(weight.shape),
            tuple(weight.stride()),
            weight.device,
            stream.cuda_stream,
        )

        if (
            version is None
            or self._packed_weight is None
            or self._packed_weight_key != key
        ):
            source = weight
            if not source.is_contiguous() or source.data_ptr() % 16:
                source = source.clone(memory_format=torch.contiguous_format)
            packed_weight = _extension.pack_weight_cuda(source)
            if version is not None:
                self._packed_weight = packed_weight
                self._packed_weight_key = key
        else:
            packed_weight = self._packed_weight

        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),
            packed_weight,
            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 0.666 ms; the PyTorch reference (with TF32 enabled) takes 1.27 ms; speedup 1.907x.
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 | 559.2 | 1 |
| pack_input_bias_kernel(float const*, __half*, float const*, float*, long, int, float, floa | 41.3 | 1 |
| Memset (Device) | 2.3 | 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.
