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 6 of 6 for this task. Your previous solution (turn 5) 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:
#   * TF32 tensor cores via raw mma.sync.m16n8k8 PTX with cvt.rna.tf32.f32
#     (no slow wmma smem path), accumulator fragments kept resident in
#     registers across the whole K-chunk.
#   * Multi-stage cp.async pipeline (stage count chosen at runtime from the
#     device's max opt-in shared memory, so it runs on sm_80/86/90) with an
#     L2 evict_last hint for the small activation matrix.
#   * Persistent grid + split-K: (n-tile, k-chunk) work items are distributed
#     over a grid sized to the SM count, so there is no wave quantization tail.
#   * Partials are written fully coalesced (float4, via a smem staging tile),
#     and a fused reduction applies bias/min/subtract while streaming the
#     partials at HBM speed.
# ---------------------------------------------------------------------------
gemm_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>
#include <algorithm>

#define BM 128
#define BN 128
#define BK 32
#define LDS 40
#define NTHREADS 256
#define STAGE_FLOATS ((BM + BN) * LDS)
#define CPLDS (BK / 4)

__device__ __forceinline__ void cp_async16_pol(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_async16(void* smem_ptr, const void* gmem_ptr) {
    unsigned saddr = static_cast<unsigned>(__cvta_generic_to_shared(smem_ptr));
    asm volatile("cp.async.cg.shared.global [%0], [%1], 16;\n"
                 :: "r"(saddr), "l"(gmem_ptr));
}
__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));
}

__device__ __forceinline__ float to_tf32(float x) {
    unsigned u;
    asm volatile("cvt.rna.tf32.f32 %0, %1;\n" : "=r"(u) : "f"(x));
    return __uint_as_float(u);
}

__device__ __forceinline__ void mma_tf32(float& d0, float& d1, float& d2, float& d3,
                                         float a0, float a1, float a2, float a3,
                                         float b0, float b1) {
    asm volatile(
        "mma.sync.aligned.m16n8k8.row.col.f32.tf32.tf32.f32 "
        "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%0,%1,%2,%3};\n"
        : "+f"(d0), "+f"(d1), "+f"(d2), "+f"(d3)
        : "r"(__float_as_uint(a0)), "r"(__float_as_uint(a1)),
          "r"(__float_as_uint(a2)), "r"(__float_as_uint(a3)),
          "r"(__float_as_uint(b0)), "r"(__float_as_uint(b1)));
}

// Each block handles a strided range of work items; each item computes a
// 128x128 output tile over a K/S chunk and writes raw partials to ws[s].
template <int STAGES>
__global__ void __launch_bounds__(NTHREADS)
gemm_tf32_splitk_kernel(const float* __restrict__ A,
                        const float* __restrict__ W,
                        float* __restrict__ ws,
                        const int gridN, const int K, const int N,
                        const int kiters_per, const int total_items) {
    unsigned long long pol_a;
    asm volatile("createpolicy.fractional.L2::evict_last.b64 %0, 1.0;\n" : "=l"(pol_a));

    extern __shared__ float smem[];

    const int tid  = threadIdx.x;
    const int warp = tid >> 5;
    const int lane = tid & 31;
    const int g  = lane >> 2;   // fragment row group 0..7
    const int tg = lane & 3;    // fragment col group 0..3
    const int warpM = warp >> 2;   // 0..1 -> 64 rows each
    const int warpN = warp & 3;    // 0..3 -> 32 cols each

    const int stage_loads = (BM + BN) * CPLDS;   // float4 chunks per stage
    const long Kstride = K;

    for (int item = blockIdx.x; item < total_items; item += gridDim.x) {
        const int s  = item / gridN;
        const int nt = item - s * gridN;
        const int n0 = nt * BN;
        const int k_iter0 = s * kiters_per;
        const int iters = kiters_per;

        float acc[4][4][4];
        #pragma unroll
        for (int mi = 0; mi < 4; ++mi)
            #pragma unroll
            for (int ni = 0; ni < 4; ++ni)
                #pragma unroll
                for (int e = 0; e < 4; ++e) acc[mi][ni][e] = 0.0f;

        // Prologue: fill STAGES-1 pipeline stages (commit every stage so the
        // group accounting stays uniform even past the chunk end).
        #pragma unroll
        for (int st = 0; st < STAGES - 1; ++st) {
            if (st < iters) {
                const int k0 = (k_iter0 + st) * BK;
                float* smA = smem + st * STAGE_FLOATS;
                float* smW = smA + BM * LDS;
                #pragma unroll
                for (int t = tid; t < stage_loads; t += NTHREADS) {
                    const int row = t / CPLDS;
                    const int ch  = t - row * CPLDS;
                    if (row < BM)
                        cp_async16_pol(smA + row * LDS + ch * 4, A + (long)row * Kstride + k0 + ch * 4, pol_a);
                    else
                        cp_async16(smW + (row - BM) * LDS + ch * 4, W + (long)(n0 + (row - BM)) * Kstride + k0 + ch * 4);
                }
            }
            cp_async_commit();
        }

        // Mainloop in blocks of STAGES so the buffer index is compile-time.
        int i = 0;
        for (; i + STAGES <= iters; i += STAGES) {
            #pragma unroll
            for (int st = 0; st < STAGES; ++st) {
                cp_async_wait<STAGES - 2>();
                __syncthreads();

                const float* smA = smem + st * STAGE_FLOATS;
                const float* smW = smA + BM * LDS;
                const float* a_base = smA + warpM * 64 * LDS + g * LDS + tg * 2;
                const float* b_base = smW + warpN * 32 * LDS + g * LDS + tg * 2;

                float fa[2][4][4];
                float fb[2][4][2];

                #pragma unroll
                for (int mi = 0; mi < 4; ++mi) {
                    const float* p = a_base + mi * 16 * LDS;
                    float2 v01 = *reinterpret_cast<const float2*>(p);
                    float2 v23 = *reinterpret_cast<const float2*>(p + 8 * LDS);
                    fa[0][mi][0] = to_tf32(v01.x); fa[0][mi][1] = to_tf32(v23.x);
                    fa[0][mi][2] = to_tf32(v01.y); fa[0][mi][3] = to_tf32(v23.y);
                }
                #pragma unroll
                for (int ni = 0; ni < 4; ++ni) {
                    float2 v01 = *reinterpret_cast<const float2*>(b_base + ni * 8 * LDS);
                    fb[0][ni][0] = to_tf32(v01.x); fb[0][ni][1] = to_tf32(v01.y);
                }

                #pragma unroll
                for (int kk = 0; kk < BK / 8; ++kk) {
                    if (kk < BK / 8 - 1) {
                        #pragma unroll
                        for (int mi = 0; mi < 4; ++mi) {
                            const float* p = a_base + (kk + 1) * 8 + mi * 16 * LDS;
                            float2 v01 = *reinterpret_cast<const float2*>(p);
                            float2 v23 = *reinterpret_cast<const float2*>(p + 8 * LDS);
                            fa[(kk + 1) & 1][mi][0] = to_tf32(v01.x); fa[(kk + 1) & 1][mi][1] = to_tf32(v23.x);
                            fa[(kk + 1) & 1][mi][2] = to_tf32(v01.y); fa[(kk + 1) & 1][mi][3] = to_tf32(v23.y);
                        }
                        #pragma unroll
                        for (int ni = 0; ni < 4; ++ni) {
                            float2 v01 = *reinterpret_cast<const float2*>(b_base + (kk + 1) * 8 + ni * 8 * LDS);
                            fb[(kk + 1) & 1][ni][0] = to_tf32(v01.x); fb[(kk + 1) & 1][ni][1] = to_tf32(v01.y);
                        }
                    }
                    const int buf = kk & 1;
                    #pragma unroll
                    for (int mi = 0; mi < 4; ++mi)
                        #pragma unroll
                        for (int ni = 0; ni < 4; ++ni)
                            mma_tf32(acc[mi][ni][0], acc[mi][ni][1], acc[mi][ni][2], acc[mi][ni][3],
                                     fa[buf][mi][0], fa[buf][mi][1], fa[buf][mi][2], fa[buf][mi][3],
                                     fb[buf][ni][0], fb[buf][ni][1]);
                }

                // Prefetch stage i + STAGES - 1 into buffer st - 1 (mod STAGES).
                const int nxt = i + st + STAGES - 1;
                if (nxt < iters) {
                    const int k0 = (k_iter0 + nxt) * BK;
                    const int pb = (st == 0) ? (STAGES - 1) : (st - 1);
                    float* pA = smem + pb * STAGE_FLOATS;
                    float* pW = pA + BM * LDS;
                    #pragma unroll
                    for (int t = tid; t < stage_loads; t += NTHREADS) {
                        const int row = t / CPLDS;
                        const int ch  = t - row * CPLDS;
                        if (row < BM)
                            cp_async16_pol(pA + row * LDS + ch * 4, A + (long)row * Kstride + k0 + ch * 4, pol_a);
                        else
                            cp_async16(pW + (row - BM) * LDS + ch * 4, W + (long)(n0 + (row - BM)) * Kstride + k0 + ch * 4);
                    }
                }
                cp_async_commit();
            }
        }
        // Drain remaining iterations (compile-time buffer indices).
        {
            #pragma unroll
            for (int st = 0; st < STAGES; ++st) {
                if (i + st >= iters) break;
                cp_async_wait<STAGES - 2>();
                __syncthreads();
                const float* smA = smem + st * STAGE_FLOATS;
                const float* smW = smA + BM * LDS;
                const float* a_base = smA + warpM * 64 * LDS + g * LDS + tg * 2;
                const float* b_base = smW + warpN * 32 * LDS + g * LDS + tg * 2;
                #pragma unroll
                for (int kk = 0; kk < BK / 8; ++kk) {
                    float fa[4][4];
                    float fb[4][2];
                    #pragma unroll
                    for (int mi = 0; mi < 4; ++mi) {
                        const float* p = a_base + kk * 8 + mi * 16 * LDS;
                        float2 v01 = *reinterpret_cast<const float2*>(p);
                        float2 v23 = *reinterpret_cast<const float2*>(p + 8 * LDS);
                        fa[mi][0] = to_tf32(v01.x); fa[mi][1] = to_tf32(v23.x);
                        fa[mi][2] = to_tf32(v01.y); fa[mi][3] = to_tf32(v23.y);
                    }
                    #pragma unroll
                    for (int ni = 0; ni < 4; ++ni) {
                        float2 v01 = *reinterpret_cast<const float2*>(b_base + kk * 8 + ni * 8 * LDS);
                        fb[ni][0] = to_tf32(v01.x); fb[ni][1] = to_tf32(v01.y);
                    }
                    #pragma unroll
                    for (int mi = 0; mi < 4; ++mi)
                        #pragma unroll
                        for (int ni = 0; ni < 4; ++ni)
                            mma_tf32(acc[mi][ni][0], acc[mi][ni][1], acc[mi][ni][2], acc[mi][ni][3],
                                     fa[mi][0], fa[mi][1], fa[mi][2], fa[mi][3],
                                     fb[ni][0], fb[ni][1]);
                }
                cp_async_commit();
            }
        }

        cp_async_wait<0>();
        __syncthreads();

        // Stage the 128x128 partial tile through smem for coalesced float4
        // global writes.
        float* smC = smem;
        #pragma unroll
        for (int mi = 0; mi < 4; ++mi) {
            const int r0 = warpM * 64 + mi * 16;
            #pragma unroll
            for (int ni = 0; ni < 4; ++ni) {
                const int c0 = warpN * 32 + ni * 8;
                float* dst0 = smC + (r0 + g) * (BN + 4) + c0 + tg * 2;
                float* dst1 = smC + (r0 + g + 8) * (BN + 4) + c0 + tg * 2;
                *reinterpret_cast<float2*>(dst0) = make_float2(acc[mi][ni][0], acc[mi][ni][1]);
                *reinterpret_cast<float2*>(dst1) = make_float2(acc[mi][ni][2], acc[mi][ni][3]);
            }
        }
        __syncthreads();

        float* ws_base = ws + ((long)s * BM) * N + n0;
        #pragma unroll 8
        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 * (BN + 4) + c4 * 4);
        }
        __syncthreads();
    }
}

// Split-K reduction with fused epilogue:
// out = min(sum_s ws[s] + bias, c) - c   (vectorized float4; bias read
// through L2/L1 cache, no dynamic smem so no opt-in attribute is needed)
__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;
    }
}

template <int STAGES>
static void launch_gemm(const float* A, const float* W, float* ws,
                        int grid, int gridN, int K, int N,
                        int kiters_per, int total_items, cudaStream_t stream) {
    static bool attr_set = false;
    if (!attr_set) {
        cudaFuncSetAttribute(gemm_tf32_splitk_kernel<STAGES>,
                             cudaFuncAttributeMaxDynamicSharedMemorySize,
                             STAGES * STAGE_FLOATS * 4);
        attr_set = true;
    }
    gemm_tf32_splitk_kernel<STAGES><<<grid, NTHREADS, STAGES * STAGE_FLOATS * 4, stream>>>(
        A, W, ws, gridN, K, N, kiters_per, total_items);
}

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;
    int max_smem = 0;
    cudaDeviceGetAttribute(&max_smem, cudaDevAttrMaxSharedMemoryPerBlockOptin, dev);

    // Cost model over split-K factor S (divisors of total_iters only).
    const double hbm_bw   = 1.8e12;
    const double l2_bw    = 5.0e12;
    const double flop_sm  = 1.0e12;   // sustained TF32 per SM (fraction of peak)
    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) {
        if (total_iters % s != 0) continue;
        const long items = (long)gridN * s;
        const double kiters = (double)total_iters / s;
        const double flop_item = 2.0 * BM * BN * (kiters * BK);
        const double t_comp = flop_item / flop_sm;
        const double t_w = (kiters * BK * BN * 4.0) / (hbm_bw / sms);
        const double t_a = (kiters * BK * BM * 4.0) / (l2_bw / sms);
        double t_item = std::max(t_comp, std::max(t_w, t_a)) + 20e-6;
        const double t = ((double)(items + sms - 1) / sms) * t_item
                         + (s > 1 ? (double)s * tile_mb * 2.0 / hbm_bw : 0.0);
        if (t < bestT - 1e-12) { bestT = t; bestS = s; }
    }
    const int S = bestS;
    const int kiters_per = total_iters / S;
    const long total_items = (long)gridN * S;

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

    cudaStream_t stream = at::cuda::getCurrentCUDAStream();
    const int ggrid = (int)std::min<long>((long)sms, total_items);

    int stages = max_smem / (STAGE_FLOATS * 4);
    if (stages > 5) stages = 5;
    TORCH_CHECK(stages >= 2, "insufficient shared memory for pipelined kernel");
    switch (stages) {
        case 5: launch_gemm<5>(xc.data_ptr<float>(), wc.data_ptr<float>(), ws_ptr,
                               ggrid, gridN, (int)K, (int)N, kiters_per, (int)total_items, stream); break;
        case 4: launch_gemm<4>(xc.data_ptr<float>(), wc.data_ptr<float>(), ws_ptr,
                               ggrid, gridN, (int)K, (int)N, kiters_per, (int)total_items, stream); break;
        case 3: launch_gemm<3>(xc.data_ptr<float>(), wc.data_ptr<float>(), ws_ptr,
                               ggrid, gridN, (int)K, (int)N, kiters_per, (int)total_items, stream); break;
        default: launch_gemm<2>(xc.data_ptr<float>(), wc.data_ptr<float>(), ws_ptr,
                                ggrid, gridN, (int)K, (int)N, kiters_per, (int)total_items, stream); break;
    }

    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, 4096L);
    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_v4",
    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.

    For the benchmark shape everything (GEMM + bias + min + subtract) runs on
    a custom persistent split-K TF32 tensor-core kernel:
      * the 1 GiB FP32 weight matrix is streamed from HBM exactly once via a
        multi-stage cp.async pipeline (stage count adapts to the device's
        shared-memory size),
      * the 8 MiB activation matrix is pinned in L2 (evict_last) and served
        to all blocks from cache,
      * mma.sync.m16n8k8 with register-resident accumulators and register
        double-buffered fragments,
      * the epilogue (bias add, torch.min, subtract) is fused into the split-K
        reduction so the final output is written exactly once.

    Falls back to the standard PyTorch path (TF32 cuBLAS) 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.weight.is_cuda
                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 1.3 ms; the PyTorch reference (with TF32 enabled) takes 0.918 ms; speedup 0.706x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| void gemm_tf32_splitk_kernel<4>(float const*, float const*, float*, int, int, int, int, in | 1249.0 | 1 |
| reduce_min_sub_kernel(float4 const*, float4 const*, float4*, int, long, long, float) | 29.1 | 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().
