```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 operation is purely memory-bandwidth bound, so we use vectorized
# float4 loads/stores to saturate DRAM bandwidth with minimal overhead.
scalar_mul_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

__global__ void scalar_mul_vec4_kernel(const float4* __restrict__ in,
                                       float4* __restrict__ out,
                                       const float s,
                                       const long n4) {
    const long idx = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < n4) {
        float4 v = in[idx];
        v.x *= s;
        v.y *= s;
        v.z *= s;
        v.w *= s;
        out[idx] = v;
    }
}

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

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

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

    const long n = A_contig.numel();
    if (n == 0) {
        return C;
    }

    const float* in_ptr = A_contig.data_ptr<float>();
    float* out_ptr = C.data_ptr<float>();
    const float sf = static_cast<float>(s);

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

    const long n4 = n / 4;
    const int block = 256;

    if (n4 > 0) {
        const long blocks = (n4 + block - 1) / block;
        scalar_mul_vec4_kernel<<<(unsigned int)blocks, block, 0, stream>>>(
            reinterpret_cast<const float4*>(in_ptr),
            reinterpret_cast<float4*>(out_ptr),
            sf,
            n4);
    }

    const long rem = n - n4 * 4;
    if (rem > 0) {
        scalar_mul_tail_kernel<<<1, (unsigned int)rem, 0, stream>>>(
            in_ptr, out_ptr, sf, n4 * 4, 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_cuda_cflags=["-O3", "--use_fast_math"],
)


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.scalar_mul = scalar_mul_ext

    def forward(self, A: torch.Tensor, s: float) -> torch.Tensor:
        if A.is_cuda and A.dtype == torch.float32:
            return self.scalar_mul.scalar_mul_cuda(A, float(s))
        return A * s
```