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 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

# Allow TF32 tensor-core math for FP32 matmuls (explicitly permitted by the
# precision rule). Storage and compute type stay FP32.
torch.backends.cuda.matmul.allow_tf32 = True
try:
    torch.set_float32_matmul_precision("high")
except Exception:
    pass

# ---------------------------------------------------------------------------
# Fully fused implementation of:  out = min(x @ W.T + bias, c) - c
#
# For the benchmark shape (M=128, K=N=16384) the op is dominated by streaming
# the 1 GiB FP32 weight matrix from HBM exactly once. This kernel is built to
# be HBM-bandwidth-bound:
#   * TF32 tensor-core GEMM (wmma) on a 128x128 tile, BK=32.
#   * 4-stage cp.async pipeline (~96 KiB in flight per SM) so even a partial
#     wave of blocks can saturate HBM.
#   * L2 eviction policies: the tiny activation matrix (8 MiB) is marked
#     evict_last (read once from HBM, then served from L2 by all blocks) while
#     the streamed weights are marked evict_first (no L2 thrash).
#   * A runtime cost model picks the split-K factor S; for the target shape it
#     picks S=1 so the epilogue (bias add, min, subtract) is fused directly
#     into the GEMM with zero extra passes over the output. For S>1 a fused
#     reduction kernel applies the epilogue.
# ---------------------------------------------------------------------------
gemm_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>
#include <mma.h>
#include <algorithm>
#include <cmath>

using namespace nvcuda;

#define BM 128
#define BN 128
#define BK 32
#define STAGES 4
#define LDS (BK + 4)
#define NTHREADS 256
#define SMEM_BYTES (STAGES * (BM + BN) * LDS * 4)

__device__ __forceinline__ void cp_async16(void* smem_ptr, const void* gmem_ptr,
                                           unsigned long long policy) {
    unsigned saddr = static_cast<unsigned>(__cvta_generic_to_shared(smem_ptr));
    asm volatile("cp.async.cg.shared.global.L2::cache_hint [%0], [%1], 16, %2;\n"
                 :: "r"(saddr), "l"(gmem_ptr), "l"(policy));
}
__device__ __forceinline__ void cp_async_commit() {
    asm volatile("cp.async.commit_group;\n");
}
template <int N>
__device__ __forceinline__ void cp_async_wait() {
    asm volatile("cp.async.wait_group %0;\n" :: "n"(N));
}

// Computes a 128x128 output tile of C = A[128,K] @ W[N,K]^T over a K-chunk.
// If S == 1 the epilogue is fused: out = min(C + bias, c) - c.
// Otherwise the raw partial sums are written to ws[s].
__global__ void __launch_bounds__(NTHREADS)
gemm_tf32_fused_kernel(const float* __restrict__ A,
                       const float* __restrict__ W,
                       const float* __restrict__ bias,
                       float* __restrict__ out,
                       float* __restrict__ ws,
                       const int gridN, const int K, const int N,
                       const int base_iters, const int rem,
                       const int S, const float c) {
    unsigned long long pol_a, pol_w;
    asm volatile("createpolicy.fractional.L2::evict_last.b64 %0, 1.0;\n" : "=l"(pol_a));
    asm volatile("createpolicy.fractional.L2::evict_first.b64 %0, 1.0;\n" : "=l"(pol_w));

    const int s  = blockIdx.x / gridN;
    const int nt = blockIdx.x % gridN;
    const int n0 = nt * BN;

    const int kiters = base_iters + (s < rem ? 1 : 0);
    const int kstart = s * base_iters + min(s, rem);

    extern __shared__ float smem[];
    float* As[STAGES];
    float* Ws[STAGES];
    #pragma unroll
    for (int st = 0; st < STAGES; ++st) {
        As[st] = smem + st * (BM + BN) * LDS;
        Ws[st] = As[st] + BM * LDS;
    }

    const int tid  = threadIdx.x;
    const int warp = tid >> 5;
    const int warpM = warp >> 2;   // 0..1  -> 64 rows each
    const int warpN = warp & 3;    // 0..3  -> 32 cols each

    wmma::fragment<wmma::accumulator, 16, 16, 8, float> acc[4][2];
    #pragma unroll
    for (int mi = 0; mi < 4; ++mi)
        #pragma unroll
        for (int ni = 0; ni < 2; ++ni)
            wmma::fill_fragment(acc[mi][ni], 0.0f);

    const long Kstride = K;

    auto prefetch = [&](int iter, int buf) {
        const int k0 = (kstart + iter) * BK;
        // A tile: 128 rows x BK floats (8 float4 per row) -> 1024 chunks
        #pragma unroll
        for (int t = tid; t < BM * (BK / 4); t += NTHREADS) {
            const int row = t >> 3;
            const int ch  = t & 7;
            cp_async16(As[buf] + row * LDS + ch * 4,
                       A + (long)row * Kstride + k0 + ch * 4, pol_a);
        }
        // W tile: rows n0..n0+127 (streamed, evict_first)
        #pragma unroll
        for (int t = tid; t < BN * (BK / 4); t += NTHREADS) {
            const int row = t >> 3;
            const int ch  = t & 7;
            cp_async16(Ws[buf] + row * LDS + ch * 4,
                       W + (long)(n0 + row) * Kstride + k0 + ch * 4, pol_w);
        }
        cp_async_commit();
    };

    // Prologue: fill the first STAGES-1 pipeline stages.
    #pragma unroll
    for (int st = 0; st < STAGES - 1; ++st) {
        if (st < kiters) prefetch(st, st);
        else cp_async_commit();
    }

    for (int i = 0; i < kiters; ++i) {
        cp_async_wait<STAGES - 2>();
        __syncthreads();

        const int nxt = i + STAGES - 1;
        if (nxt < kiters) prefetch(nxt, nxt & (STAGES - 1));
        else cp_async_commit();

        const float* a = As[i & (STAGES - 1)];
        const float* w = Ws[i & (STAGES - 1)];
        #pragma unroll
        for (int kk = 0; kk < BK / 8; ++kk) {
            wmma::fragment<wmma::matrix_a, 16, 16, 8, wmma::precision::tf32, wmma::row_major> fa[4];
            wmma::fragment<wmma::matrix_b, 16, 16, 8, wmma::precision::tf32, wmma::col_major> fb[2];
            #pragma unroll
            for (int mi = 0; mi < 4; ++mi) {
                wmma::load_matrix_sync(fa[mi], a + (warpM * 64 + mi * 16) * LDS + kk * 8, LDS);
                #pragma unroll
                for (int e = 0; e < fa[mi].num_elements; ++e)
                    fa[mi].x[e] = wmma::__float_to_tf32(fa[mi].x[e]);
            }
            #pragma unroll
            for (int ni = 0; ni < 2; ++ni) {
                wmma::load_matrix_sync(fb[ni], w + (warpN * 32 + ni * 16) * LDS + kk * 8, LDS);
                #pragma unroll
                for (int e = 0; e < fb[ni].num_elements; ++e)
                    fb[ni].x[e] = wmma::__float_to_tf32(fb[ni].x[e]);
            }
            #pragma unroll
            for (int mi = 0; mi < 4; ++mi)
                #pragma unroll
                for (int ni = 0; ni < 2; ++ni)
                    wmma::mma_sync(acc[mi][ni], fa[mi], fb[ni], acc[mi][ni]);
        }
    }

    cp_async_wait<0>();
    __syncthreads();

    // Stage the accumulator tile through shared memory for fully coalesced
    // vectorized global accesses.
    float* smC = smem;  // >= 128*132 floats available
    #pragma unroll
    for (int mi = 0; mi < 4; ++mi)
        #pragma unroll
        for (int ni = 0; ni < 2; ++ni)
            wmma::store_matrix_sync(
                smC + (warpM * 64 + mi * 16) * 132 + warpN * 32 + ni * 16,
                acc[mi][ni], 132, wmma::mem_row_major);
    __syncthreads();

    if (S == 1) {
        // Fused epilogue: out = min(C + bias, c) - c
        float* out_base = out + n0;
        const float4* bias4 = reinterpret_cast<const float4*>(bias + n0);
        #pragma unroll 4
        for (int t = tid; t < BM * (BN / 4); t += NTHREADS) {
            const int row = t >> 5;
            const int c4  = t & 31;
            float4 v = *reinterpret_cast<const float4*>(smC + row * 132 + c4 * 4);
            float4 bv = bias4[c4];
            v.x = fminf(v.x + bv.x, c) - c;
            v.y = fminf(v.y + bv.y, c) - c;
            v.z = fminf(v.z + bv.z, c) - c;
            v.w = fminf(v.w + bv.w, c) - c;
            *reinterpret_cast<float4*>(out_base + (long)row * N + c4 * 4) = v;
        }
    } else {
        float* ws_base = ws + ((long)s * BM) * N + n0;
        #pragma unroll 4
        for (int t = tid; t < BM * (BN / 4); t += NTHREADS) {
            const int row = t >> 5;
            const int c4  = t & 31;
            *reinterpret_cast<float4*>(ws_base + (long)row * N + c4 * 4) =
                *reinterpret_cast<const float4*>(smC + row * 132 + c4 * 4);
        }
    }
}

// Split-K reduction with fused epilogue:
// out = min(sum_s ws[s] + bias, c) - c   (vectorized float4)
__global__ void reduce_min_sub_kernel(const float4* __restrict__ ws,
                                      const float4* __restrict__ bias,
                                      float4* __restrict__ out,
                                      const int S,
                                      const long n4,
                                      const long biasN4,
                                      const float c) {
    const long stride = (long)gridDim.x * blockDim.x;
    for (long i = blockIdx.x * (long)blockDim.x + threadIdx.x; i < n4; i += stride) {
        float4 acc = bias[i % biasN4];
        const float4* p = ws + i;
        for (int sp = 0; sp < S; ++sp) {
            float4 v = p[(long)sp * n4];
            acc.x += v.x; acc.y += v.y; acc.z += v.z; acc.w += v.w;
        }
        acc.x = fminf(acc.x, c) - c;
        acc.y = fminf(acc.y, c) - c;
        acc.z = fminf(acc.z, c) - c;
        acc.w = fminf(acc.w, c) - c;
        out[i] = acc;
    }
}

torch::Tensor gemm_min_sub_cuda(torch::Tensor x, torch::Tensor w, torch::Tensor b, double c) {
    TORCH_CHECK(x.is_cuda() && w.is_cuda() && b.is_cuda(), "tensors must be CUDA");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "x must be float32");

    const long M = x.size(0);
    const long K = x.size(1);
    const long N = w.size(0);
    TORCH_CHECK(M == BM, "M must be 128");
    TORCH_CHECK(K % BK == 0, "K must be a multiple of 32");
    TORCH_CHECK(N % BN == 0, "N must be a multiple of 128");

    auto xc = x.contiguous();
    auto wc = w.contiguous();
    auto bc = b.contiguous();

    const int gridN = (int)(N / BN);
    const int total_iters = (int)(K / BK);

    int dev = 0;
    cudaGetDevice(&dev);
    int sms = 0;
    cudaDeviceGetAttribute(&sms, cudaDevAttrMultiProcessorCount, dev);
    if (sms <= 0) sms = 108;

    // Split-K cost model. Each block streams W through cp.async with ~96 KiB
    // in flight, so even a partially filled wave can sustain close to peak
    // HBM bandwidth; model the GEMM as pure bandwidth time per wave with a
    // per-SM bandwidth cap, plus the split-K reduction traffic.
    const double hbm_bw  = 1.8e12;    // effective HBM bytes/s
    const double persm_bw = 110e9;    // sustainable bytes/s per SM
    const double w_bytes  = (double)N * (double)K * 4.0;
    const double tile_mb  = (double)M * (double)N * 4.0;

    int bestS = 1;
    double bestT = 1e300;
    const int maxS = std::min(16, total_iters);
    for (int s = 1; s <= maxS; ++s) {
        const long blocks = (long)gridN * s;
        const double per_block = w_bytes / (double)blocks;
        double t = 0.0;
        long remaining = blocks;
        while (remaining > 0) {
            const long b = std::min<long>(remaining, sms);
            const double rate = std::min(hbm_bw, persm_bw * (double)b);
            t += per_block * (double)b / rate;
            remaining -= b;
        }
        if (s > 1) t += (double)s * tile_mb * 2.0 / hbm_bw;  // ws write+read
        t += tile_mb / hbm_bw;                               // output write
        if (t < bestT - 1e-12) { bestT = t; bestS = s; }
    }
    const int S = bestS;
    const int base_iters = total_iters / S;
    const int rem = total_iters % S;

    auto out = at::empty({M, N}, x.options());
    torch::Tensor ws;
    float* ws_ptr = nullptr;
    if (S > 1) {
        ws = at::empty({(long)S, M, N}, x.options());
        ws_ptr = ws.data_ptr<float>();
    }

    static bool attr_set = false;
    if (!attr_set) {
        cudaFuncSetAttribute(gemm_tf32_fused_kernel,
                             cudaFuncAttributeMaxDynamicSharedMemorySize,
                             SMEM_BYTES);
        attr_set = true;
    }

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();
    dim3 grid((unsigned)((long)gridN * S));
    gemm_tf32_fused_kernel<<<grid, NTHREADS, SMEM_BYTES, stream>>>(
        xc.data_ptr<float>(), wc.data_ptr<float>(), bc.data_ptr<float>(),
        out.data_ptr<float>(), ws_ptr,
        gridN, (int)K, (int)N, base_iters, rem, S, static_cast<float>(c));

    if (S > 1) {
        const long n4 = (M * N) >> 2;
        const long biasN4 = N >> 2;
        const long blocks_needed = (n4 + NTHREADS - 1) / NTHREADS;
        const int rgrid = (int)std::min<long>(blocks_needed, 8192L);
        reduce_min_sub_kernel<<<rgrid, NTHREADS, 0, stream>>>(
            reinterpret_cast<const float4*>(ws_ptr),
            reinterpret_cast<const float4*>(bc.data_ptr<float>()),
            reinterpret_cast<float4*>(out.data_ptr<float>()),
            S, n4, biasN4, static_cast<float>(c));
    }

    return out;
}
"""

gemm_cpp_source = (
    "torch::Tensor gemm_min_sub_cuda(torch::Tensor x, torch::Tensor w, torch::Tensor b, double c);"
)

fused_gemm = load_inline(
    name="fused_gemm_tf32_min_sub_v2",
    cpp_sources=gemm_cpp_source,
    cuda_sources=gemm_source,
    functions=["gemm_min_sub_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3", "--use_fast_math"],
)


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

    Everything (GEMM + bias + min + subtract) runs in a single custom TF32
    tensor-core CUDA kernel for the benchmark shape:
      * the 1 GiB FP32 weight matrix is streamed from HBM exactly once via a
        4-stage cp.async pipeline (evict_first so it never pollutes L2),
      * the 8 MiB activation matrix is pinned in L2 (evict_last) and served
        to all blocks from cache,
      * the epilogue (bias add, torch.min, subtraction) is fused into the
        GEMM, so the output is written exactly once with no extra passes.

    Falls back to the standard PyTorch path for any other shape/device.
    """
    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):
        if (x.is_cuda and x.dtype == torch.float32 and x.dim() == 2
                and x.size(0) == 128
                and self.linear.in_features % 32 == 0
                and self.linear.out_features % 128 == 0):
            return fused_gemm.gemm_min_sub_cuda(
                x, self.linear.weight, self.linear.bias, self._const_val)
        out = F.linear(x, self.linear.weight, self.linear.bias)
        return torch.min(out, self.constant) - self.constant
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 2.88 ms; the PyTorch reference (with TF32 enabled) takes 0.918 ms; speedup 0.319x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| gemm_tf32_fused_kernel(float const*, float const*, float const*, float*, float*, int, int, | 2854.3 | 1 |

The fastest correct solution so far (1.011x 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
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
```

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().
