```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.
# The operation is purely memory-bound, so the kernel is optimized for
# maximum memory bandwidth:
#   * 128-bit vectorized loads/stores via float4 (4 floats per thread)
#   * __restrict__ pointers to enable read-only cache loads
#   * tail kernel to handle any remainder elements
scalar_mul_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <ATen/cuda/CUDAContext.h>

__global__ void scalar_mul_vec4_kernel(const float4* __restrict__ A,
                                       float4* __restrict__ C,
                                       float s,
                                       long n4) {
    long idx = (long)blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < n4) {
        float4 a = A[idx];
        C[idx] = make_float4(a.x * s, a.y * s, a.z * s, a.w * s);
    }
}

__global__ void scalar_mul_tail_kernel(const float* __restrict__ A,
                                       float* __restrict__ C,
                                       float s,
                                       long start,
                                       long n) {
    long idx = start + (long)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 A_contig = A.contiguous();
    auto C = torch::empty_like(A_contig);

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

    const float fs = static_cast<float>(s);
    const float* a_ptr = A_contig.data_ptr<float>();
    float* c_ptr = C.data_ptr<float>();

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

    const int block_size = 256;

    // Main body: process 4 elements per thread with float4 vectorized I/O.
    const long n4 = n / 4;
    if (n4 > 0) {
        const long blocks = (n4 + block_size - 1) / block_size;
        scalar_mul_vec4_kernel<<<(unsigned int)blocks, block_size, 0, stream>>>(
            reinterpret_cast<const float4*>(a_ptr),
            reinterpret_cast<float4*>(c_ptr),
            fs, n4);
    }

    // Tail: remaining (n % 4) elements, if any.
    const long rem = n - n4 * 4;
    if (rem > 0) {
        const long blocks = (rem + block_size - 1) / block_size;
        scalar_mul_tail_kernel<<<(unsigned int)blocks, block_size, 0, stream>>>(
            a_ptr, c_ptr, fs, 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"],
)


class ModelNew(nn.Module):
    """
    Optimized model that performs a matrix-scalar multiplication (C = A * s)
    using a custom CUDA kernel with vectorized float4 memory accesses to
    saturate memory bandwidth.
    """
    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))
        # Fallback for CPU tensors or non-float32 dtypes
        return A * s
```