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
# 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

# Fully fused operator:
#   out = relu( mul * (x @ weight^T + bias - sub) )
#       = relu( mul * (x @ weight^T) + mul * (bias - sub) )
# A tiny kernel builds bias_eff = mul * (bias - sub); a single cublasLt GEMM
# with TF32 tensor-core math (explicitly allowed for this task) and the fused
# RELU_BIAS epilogue computes everything else (alpha = mul). On the first
# call for a given (M, N, K) the top cublasLt heuristics are micro-benchmarked
# and the fastest algorithm is cached.
_cpp_src = """
torch::Tensor linear_sub_mul_relu(torch::Tensor x, torch::Tensor weight,
                                  torch::Tensor bias, double sub, double mul);
torch::Tensor sub_mul_relu(torch::Tensor y, double sub, double mul);
"""

_cuda_src = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cublasLt.h>
#include <cuda_runtime.h>
#include <map>
#include <tuple>

#define CUBLASLT_CHECK(expr)                                                   \
  do {                                                                         \
    cublasStatus_t _status = (expr);                                           \
    TORCH_CHECK(_status == CUBLAS_STATUS_SUCCESS, "cublasLt call failed: ",    \
                #expr, " status=", (int)_status);                              \
  } while (0)

namespace {

cublasLtHandle_t getLtHandle() {
  static cublasLtHandle_t handle = nullptr;
  if (handle == nullptr) {
    CUBLASLT_CHECK(cublasLtCreate(&handle));
  }
  return handle;
}

// TF32 tensor-core math is explicitly allowed for this task (sm_80+).
bool tf32Supported() {
  static int supported = -1;
  if (supported < 0) {
    int dev = 0;
    supported = 0;
    if (cudaGetDevice(&dev) == cudaSuccess) {
      int major = 0;
      if (cudaDeviceGetAttribute(&major, cudaDevAttrComputeCapabilityMajor,
                                 dev) == cudaSuccess &&
          major >= 8) {
        supported = 1;
      }
    }
  }
  return supported == 1;
}

__global__ void bias_transform_kernel(const float* __restrict__ bias,
                                      float* __restrict__ out, int n,
                                      float sub, float mul) {
  int i = blockIdx.x * blockDim.x + threadIdx.x;
  if (i < n) {
    out[i] = (bias[i] - sub) * mul;
  }
}

__global__ void sub_mul_relu_vec4_kernel(const float4* __restrict__ in,
                                         float4* __restrict__ out, long n4,
                                         float sub, float mul) {
  const long stride = (long)gridDim.x * blockDim.x;
  for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < n4;
       i += stride) {
    float4 v = in[i];
    v.x = fmaxf((v.x - sub) * mul, 0.0f);
    v.y = fmaxf((v.y - sub) * mul, 0.0f);
    v.z = fmaxf((v.z - sub) * mul, 0.0f);
    v.w = fmaxf((v.w - sub) * mul, 0.0f);
    out[i] = v;
  }
}

__global__ void sub_mul_relu_kernel(const float* __restrict__ in,
                                    float* __restrict__ out, long n, float sub,
                                    float mul) {
  const long stride = (long)gridDim.x * blockDim.x;
  for (long i = (long)blockIdx.x * blockDim.x + threadIdx.x; i < n;
       i += stride) {
    out[i] = fmaxf((in[i] - sub) * mul, 0.0f);
  }
}

}  // namespace

torch::Tensor linear_sub_mul_relu(torch::Tensor x, torch::Tensor weight,
                                  torch::Tensor bias, double sub, double mul) {
  TORCH_CHECK(x.is_cuda() && weight.is_cuda() && bias.is_cuda(),
              "CUDA tensors required");
  TORCH_CHECK(x.scalar_type() == at::kFloat &&
                  weight.scalar_type() == at::kFloat &&
                  bias.scalar_type() == at::kFloat,
              "FP32 tensors required");
  TORCH_CHECK(x.dim() >= 2, "x must have at least 2 dims");
  TORCH_CHECK(weight.dim() == 2, "weight must be 2D");

  auto xc = x.contiguous();
  auto wc = weight.contiguous();
  auto bc = bias.contiguous();

  const int64_t K = xc.size(-1);
  const int64_t N = wc.size(0);
  TORCH_CHECK(wc.size(1) == K, "weight shape mismatch");
  TORCH_CHECK(bc.numel() == N, "bias shape mismatch");

  auto x2 = xc.reshape({-1, K});
  const int64_t M = x2.size(0);

  auto out_sizes = xc.sizes().vec();
  out_sizes.back() = N;
  auto out = at::empty({M, N}, xc.options());
  if (M == 0 || N == 0) {
    return out.reshape(out_sizes);
  }
  TORCH_CHECK(K > 0 && K <= INT32_MAX && M <= INT32_MAX && N <= INT32_MAX,
              "unsupported dims");

  cudaStream_t stream = at::cuda::getCurrentCUDAStream();

  // bias_eff = (bias - sub) * mul   (one entry per output feature)
  auto bias_eff = at::empty({N}, xc.options());
  {
    const int threads = 256;
    const int blocks = (int)((N + threads - 1) / threads);
    bias_transform_kernel<<<blocks, threads, 0, stream>>>(
        bc.data_ptr<float>(), bias_eff.data_ptr<float>(), (int)N, (float)sub,
        (float)mul);
  }

  const int use_tf32 = tf32Supported() ? 1 : 0;
  const cublasComputeType_t compute_type =
      use_tf32 ? CUBLAS_COMPUTE_32F_FAST_TF32 : CUBLAS_COMPUTE_32F;

  cublasLtMatmulDesc_t op_desc = nullptr;
  CUBLASLT_CHECK(cublasLtMatmulDescCreate(&op_desc, compute_type, CUDA_R_32F));

  // Row-major C(M,N) = X(M,K) * W^T(K,N) is computed as the equivalent
  // column-major problem C^T(N,M) = W(N,K) * X^T(K,M):
  //   A = weight buffer viewed as col-major (K,N), op(A) = A^T = W (N,K)
  //   B = x buffer      viewed as col-major (K,M), op(B) = X^T (K,M)
  cublasOperation_t transa = CUBLAS_OP_T;
  cublasOperation_t transb = CUBLAS_OP_N;
  CUBLASLT_CHECK(cublasLtMatmulDescSetAttribute(
      op_desc, CUBLASLT_MATMUL_DESC_TRANSA, &transa, sizeof(transa)));
  CUBLASLT_CHECK(cublasLtMatmulDescSetAttribute(
      op_desc, CUBLASLT_MATMUL_DESC_TRANSB, &transb, sizeof(transb)));

  cublasLtEpilogue_t epilogue = CUBLASLT_EPILOGUE_RELU_BIAS;
  CUBLASLT_CHECK(cublasLtMatmulDescSetAttribute(
      op_desc, CUBLASLT_MATMUL_DESC_EPILOGUE, &epilogue, sizeof(epilogue)));
  float* bias_ptr = bias_eff.data_ptr<float>();
  CUBLASLT_CHECK(cublasLtMatmulDescSetAttribute(
      op_desc, CUBLASLT_MATMUL_DESC_BIAS_POINTER, &bias_ptr, sizeof(bias_ptr)));

  cublasLtMatrixLayout_t a_desc = nullptr, b_desc = nullptr, c_desc = nullptr;
  CUBLASLT_CHECK(cublasLtMatrixLayoutCreate(&a_desc, CUDA_R_32F, K, N, K));
  CUBLASLT_CHECK(cublasLtMatrixLayoutCreate(&b_desc, CUDA_R_32F, K, M, K));
  CUBLASLT_CHECK(cublasLtMatrixLayoutCreate(&c_desc, CUDA_R_32F, N, M, N));

  const float alpha = (float)mul;
  const float beta = 0.0f;

  typedef std::tuple<int64_t, int64_t, int64_t, int> Key;
  static std::map<Key, cublasLtMatmulHeuristicResult_t> algo_cache;
  const Key key = std::make_tuple(M, N, K, use_tf32);

  cublasLtMatmulHeuristicResult_t heuristic;
  std::map<Key, cublasLtMatmulHeuristicResult_t>::iterator it =
      algo_cache.find(key);
  if (it != algo_cache.end()) {
    heuristic = it->second;
  } else {
    cublasLtMatmulPreference_t pref = nullptr;
    CUBLASLT_CHECK(cublasLtMatmulPreferenceCreate(&pref));
    size_t max_workspace = 64ull * 1024ull * 1024ull;
    CUBLASLT_CHECK(cublasLtMatmulPreferenceSetAttribute(
        pref, CUBLASLT_MATMUL_PREF_MAX_WORKSPACE_BYTES, &max_workspace,
        sizeof(max_workspace)));

    const int max_results = 8;
    cublasLtMatmulHeuristicResult_t results[8];
    int returned = 0;
    CUBLASLT_CHECK(cublasLtMatmulAlgoGetHeuristic(
        getLtHandle(), op_desc, a_desc, b_desc, c_desc, c_desc, pref,
        max_results, results, &returned));
    cublasLtMatmulPreferenceDestroy(pref);
    TORCH_CHECK(returned > 0, "cublasLt found no suitable algorithm");

    size_t ws = 1;
    for (int i = 0; i < returned; ++i) {
      if (results[i].workspaceSize > ws) {
        ws = results[i].workspaceSize;
      }
    }
    auto workspace = at::empty({(int64_t)ws}, xc.options().dtype(at::kByte));

    // One-time micro autotune over the candidate algorithms.
    cudaEvent_t ev0, ev1;
    cudaEventCreate(&ev0);
    cudaEventCreate(&ev1);
    float best_ms = 1e30f;
    int best = -1;
    for (int i = 0; i < returned; ++i) {
      cublasStatus_t st = cublasLtMatmul(
          getLtHandle(), op_desc, &alpha,
          wc.data_ptr<float>(), a_desc,
          x2.data_ptr<float>(), b_desc,
          &beta,
          out.data_ptr<float>(), c_desc,
          out.data_ptr<float>(), c_desc,
          &results[i].algo, workspace.data_ptr(), results[i].workspaceSize,
          stream);
      if (st != CUBLAS_STATUS_SUCCESS) {
        continue;
      }
      cudaEventRecord(ev0, stream);
      for (int r = 0; r < 5; ++r) {
        cublasLtMatmul(getLtHandle(), op_desc, &alpha,
                       wc.data_ptr<float>(), a_desc,
                       x2.data_ptr<float>(), b_desc,
                       &beta,
                       out.data_ptr<float>(), c_desc,
                       out.data_ptr<float>(), c_desc,
                       &results[i].algo, workspace.data_ptr(),
                       results[i].workspaceSize, stream);
      }
      cudaEventRecord(ev1, stream);
      cudaEventSynchronize(ev1);
      float ms = 0.0f;
      cudaEventElapsedTime(&ms, ev0, ev1);
      if (ms < best_ms) {
        best_ms = ms;
        best = i;
      }
    }
    cudaEventDestroy(ev0);
    cudaEventDestroy(ev1);
    TORCH_CHECK(best >= 0, "no runnable cublasLt algorithm found");
    heuristic = results[best];
    algo_cache.emplace(key, heuristic);
  }

  const size_t ws_bytes =
      heuristic.workspaceSize > 0 ? heuristic.workspaceSize : (size_t)1;
  auto workspace =
      at::empty({(int64_t)ws_bytes}, xc.options().dtype(at::kByte));

  CUBLASLT_CHECK(cublasLtMatmul(
      getLtHandle(), op_desc, &alpha,
      wc.data_ptr<float>(), a_desc,
      x2.data_ptr<float>(), b_desc,
      &beta,
      out.data_ptr<float>(), c_desc,
      out.data_ptr<float>(), c_desc,
      &heuristic.algo,
      workspace.data_ptr(), heuristic.workspaceSize,
      stream));

  cublasLtMatrixLayoutDestroy(a_desc);
  cublasLtMatrixLayoutDestroy(b_desc);
  cublasLtMatrixLayoutDestroy(c_desc);
  cublasLtMatmulDescDestroy(op_desc);

  return out.reshape(out_sizes);
}

torch::Tensor sub_mul_relu(torch::Tensor y, double sub, double mul) {
  TORCH_CHECK(y.is_cuda(), "CUDA tensor required");
  TORCH_CHECK(y.scalar_type() == at::kFloat, "FP32 tensor required");
  auto yc = y.contiguous();
  auto out = at::empty_like(yc);
  const long n = (long)yc.numel();
  if (n == 0) {
    return out;
  }
  cudaStream_t stream = at::cuda::getCurrentCUDAStream();
  const float* in_ptr = yc.data_ptr<float>();
  float* out_ptr = out.data_ptr<float>();
  const int threads = 256;
  if ((n & 3) == 0) {
    const long n4 = n >> 2;
    long blocks = (n4 + threads - 1) / threads;
    if (blocks > 16384) blocks = 16384;
    sub_mul_relu_vec4_kernel<<<(int)blocks, threads, 0, stream>>>(
        reinterpret_cast<const float4*>(in_ptr),
        reinterpret_cast<float4*>(out_ptr), n4, (float)sub, (float)mul);
  } else {
    long blocks = (n + threads - 1) / threads;
    if (blocks > 65536) blocks = 65536;
    sub_mul_relu_kernel<<<(int)blocks, threads, 0, stream>>>(
        in_ptr, out_ptr, n, (float)sub, (float)mul);
  }
  return out;
}
"""

_ext = load_inline(
    name="fused_linear_sub_mul_relu_v3",
    cpp_sources=_cpp_src,
    cuda_sources=_cuda_src,
    functions=["linear_sub_mul_relu", "sub_mul_relu"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    extra_ldflags=["-lcublas", "-lcublasLt"],
)


class ModelNew(nn.Module):
    """
    Optimized version of Model.

    The whole forward (matmul + bias + subtract + multiply + ReLU) is fused
    into a single custom cublasLt-based CUDA operator by folding the subtract
    into the bias vector and the multiply into the GEMM alpha, using a TF32
    tensor-core GEMM (explicitly allowed) with a fused ReLU+bias epilogue and
    a one-time algorithm autotune. If the fused path is unavailable, it falls
    back to cuBLAS linear followed by a custom fused subtract-multiply-ReLU
    kernel.
    """

    def __init__(self, in_features, out_features, subtract_value,
                 multiply_value):
        super(ModelNew, self).__init__()
        self.linear = nn.Linear(in_features, out_features)
        self.subtract_value = float(subtract_value)
        self.multiply_value = float(multiply_value)
        self._use_fused = True
        # TF32 tensor-core math is explicitly permitted for this task; make
        # sure the ATen fallback path also benefits from it.
        if torch.cuda.is_available():
            try:
                torch.backends.cuda.matmul.allow_tf32 = True
            except Exception:
                pass

    def forward(self, x):
        if x.is_cuda and x.dtype == torch.float32:
            weight = self.linear.weight
            bias = self.linear.bias
            if self._use_fused and bias is not None:
                try:
                    return _ext.linear_sub_mul_relu(
                        x, weight, bias, self.subtract_value,
                        self.multiply_value)
                except RuntimeError:
                    self._use_fused = False
            y = F.linear(x, weight, bias)
            return _ext.sub_mul_relu(y, self.subtract_value,
                                     self.multiply_value)
        # CPU fallback: reference computation.
        x = self.linear(x)
        x = x - self.subtract_value
        x = x * self.multiply_value
        return torch.relu(x)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 1.11 ms; the PyTorch reference (with TF32 enabled) takes 1.27 ms; speedup 1.144x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void cutlass::Kernel2<cutlass_80_tensorop_s1688gemm_256x128_32x3_tn_align4>(cutlass_80_ten | 1055.9 | 1 |
| (anonymous namespace)::bias_transform_kernel(float const*, float*, int, float, float) | 2.4 | 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.


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().
