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, applies minimum, and subtracts a constant.
    """
    def __init__(self, in_features, out_features, constant):
        super(Model, self).__init__()
        self.linear = nn.Linear(in_features, out_features)
        self.constant = nn.Parameter(torch.tensor(constant))

    def forward(self, x):
        x = self.linear(x)
        x = torch.min(x, self.constant)
        x = x - self.constant
        return x

batch_size = 128
in_features = 16384
out_features = 16384
constant = 2.0

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

def get_init_inputs():
    return [in_features, out_features, constant]
    ```
    
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 2 of 6 for this task. Your previous solution (turn 1) 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

# Allow TF32 tensor-core math for FP32 matmuls (explicitly permitted by the
# precision rule). This keeps FP32 storage/semantics while using tensor cores.
torch.backends.cuda.matmul.allow_tf32 = True
try:
    torch.set_float32_matmul_precision("high")
except Exception:
    pass

# Custom CUDA kernel that fuses the two elementwise epilogue ops:
#     out = min(x, c) - c
# into a single pass over the GEMM output (halves the epilogue memory traffic
# and kernel launches compared to two separate PyTorch ops).
min_sub_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>
#include <algorithm>

__global__ void min_sub_const_vec4_kernel(const float4* __restrict__ in,
                                          float4* __restrict__ out,
                                          const float c,
                                          const long n4) {
    long i = blockIdx.x * (long)blockDim.x + threadIdx.x;
    const long stride = (long)gridDim.x * blockDim.x;
    for (; i < n4; i += stride) {
        float4 v = in[i];
        v.x = fminf(v.x, c) - c;
        v.y = fminf(v.y, c) - c;
        v.z = fminf(v.z, c) - c;
        v.w = fminf(v.w, c) - c;
        out[i] = v;
    }
}

__global__ void min_sub_const_kernel(const float* __restrict__ in,
                                     float* __restrict__ out,
                                     const float c,
                                     const long n) {
    long i = blockIdx.x * (long)blockDim.x + threadIdx.x;
    const long stride = (long)gridDim.x * blockDim.x;
    for (; i < n; i += stride) {
        out[i] = fminf(in[i], c) - c;
    }
}

torch::Tensor min_sub_const_cuda(torch::Tensor x, double c) {
    TORCH_CHECK(x.is_cuda(), "x must be a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "x must be float32");

    auto xc = x.contiguous();
    auto out = at::empty_like(xc);
    const long n = xc.numel();
    if (n == 0) {
        return out;
    }

    const float cf = static_cast<float>(c);
    const int block = 256;
    cudaStream_t stream = at::cuda::getCurrentCUDAStream();

    if ((n & 3) == 0) {
        const long n4 = n >> 2;
        const long blocks_needed = (n4 + block - 1) / block;
        const int grid = (int)std::min<long>(blocks_needed, 524288L);
        min_sub_const_vec4_kernel<<<grid, block, 0, stream>>>(
            reinterpret_cast<const float4*>(xc.data_ptr<float>()),
            reinterpret_cast<float4*>(out.data_ptr<float>()),
            cf, n4);
    } else {
        const long blocks_needed = (n + block - 1) / block;
        const int grid = (int)std::min<long>(blocks_needed, 524288L);
        min_sub_const_kernel<<<grid, block, 0, stream>>>(
            xc.data_ptr<float>(), out.data_ptr<float>(), cf, n);
    }
    return out;
}
"""

min_sub_cpp_source = "torch::Tensor min_sub_const_cuda(torch::Tensor x, double c);"

fused_min_sub = load_inline(
    name="fused_min_sub_const",
    cpp_sources=min_sub_cpp_source,
    cuda_sources=min_sub_source,
    functions=["min_sub_const_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3", "--use_fast_math"],
)


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

    - The linear layer (GEMM + fused bias epilogue) runs through cuBLAS with
      TF32 tensor cores enabled (allowed by the precision rule; tensors stay
      in FP32).
    - The `torch.min(x, constant)` and `x - constant` ops are fused into a
      single custom CUDA kernel, cutting the epilogue memory passes in half.
    """
    def __init__(self, in_features, out_features, constant):
        super(ModelNew, self).__init__()
        self.linear = nn.Linear(in_features, out_features)
        self.constant = nn.Parameter(torch.tensor(constant))
        self._const_val = float(constant)

    def forward(self, x):
        x = F.linear(x, self.linear.weight, self.linear.bias)
        if x.is_cuda and x.dtype == torch.float32:
            return fused_min_sub.min_sub_const_cuda(x, self._const_val)
        # Fallback for non-CUDA execution.
        return torch.min(x, self.constant) - self.constant
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 0.908 ms; the PyTorch reference (with TF32 enabled) takes 0.918 ms; speedup 1.011x.
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 | 847.3 | 1 |
| min_sub_const_vec4_kernel(float4 const*, float4*, float, long) | 7.6 | 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().
