```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
from torch.utils.cpp_extension import load_inline

# Custom CUDA kernel for matrix-scalar multiplication (C = A * s).
# The op is memory-bandwidth bound, so the kernel uses 128-bit vectorized
# (float4) loads/stores with a 4x unroll to saturate DRAM bandwidth.
scalar_mul_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <cstdint>

#define UNROLL 4

__global__ void scalar_mul_vec4_kernel(const float4* __restrict__ A,
                                       float4* __restrict__ C,
                                       float s,
                                       int64_t n4) {
    int64_t base = ((int64_t)blockIdx.x * blockDim.x) * UNROLL + threadIdx.x;
    #pragma unroll
    for (int j = 0; j < UNROLL; ++j) {
        int64_t i = base + (int64_t)j * blockDim.x;
        if (i < n4) {
            float4 v = A[i];
            v.x *= s;
            v.y *= s;
            v.z *= s;
            v.w *= s;
            C[i] = v;
        }
    }
}

__global__ void scalar_mul_tail_kernel(const float* __restrict__ A,
                                       float* __restrict__ C,
                                       float s,
                                       int64_t start,
                                       int64_t n) {
    int64_t idx = start + (int64_t)blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < n) {
        C[idx] = A[idx] * s;
    }
}

torch::Tensor scalar_mul_cuda(torch::Tensor A, double s) {
    TORCH_CHECK(A.is_cuda(), "A must be a CUDA tensor");
    TORCH_CHECK(A.scalar_type() == at::kFloat, "A must be float32");

    auto Ac = A.contiguous();
    auto C = torch::empty_like(Ac);

    const int64_t n = Ac.numel();
    if (n == 0) {
        return C;
    }

    const float sf = static_cast<float>(s);
    const int block = 256;

    const int64_t n4 = n >> 2;
    const int64_t rem = n & 3;

    if (n4 > 0) {
        const int64_t items_per_block = (int64_t)block * UNROLL;
        const int64_t blocks = (n4 + items_per_block - 1) / items_per_block;
        scalar_mul_vec4_kernel<<<(unsigned int)blocks, block>>>(
            reinterpret_cast<const float4*>(Ac.data_ptr<float>()),
            reinterpret_cast<float4*>(C.data_ptr<float>()),
            sf, n4);
    }

    if (rem > 0) {
        const int64_t start = n4 << 2;
        const int blocks = (int)((rem + block - 1) / block);
        scalar_mul_tail_kernel<<<blocks, block>>>(
            Ac.data_ptr<float>(), C.data_ptr<float>(), sf, start, n);
    }

    return C;
}
"""

scalar_mul_cpp_source = (
    "torch::Tensor scalar_mul_cuda(torch::Tensor A, double s);"
)

# Compile the inline CUDA extension
scalar_mul_ext = load_inline(
    name="scalar_mul_ext",
    cpp_sources=scalar_mul_cpp_source,
    cuda_sources=scalar_mul_source,
    functions=["scalar_mul_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    extra_ldflags=[""],
)


class ModelNew(nn.Module):
    """
    Optimized model that performs matrix-scalar multiplication (C = A * s)
    using a custom vectorized CUDA kernel.
    """
    def __init__(self):
        super(ModelNew, self).__init__()
        self._ext = scalar_mul_ext

    def forward(self, A: torch.Tensor, s: float) -> torch.Tensor:
        if A.is_cuda and A.dtype == torch.float32:
            return self._ext.scalar_mul_cuda(A, float(s))
        # Fallback for non-CUDA / non-FP32 inputs
        return A * s
```