.NET Framework 4.8下用SIMD优化double点积及ChainRule函数性能

我希望用SIMD加速以下双精度点积计算：

[MethodImpl(MethodImplOptions.AggressiveInlining)]
static double Dot(double x1, double x2, double y1, double y2)
{
    return x1 * y1 + x2 * y2;
}

已知Vector2.Dot仅支持float类型，且无法切换到.NET Core，因此不能使用Vector128.Create(double e0, double e1)来实现双精度SIMD点积。

上述Dot方法用于计算两个有序ID列表的并集，核心逻辑在以下ChainRule函数中：

static void ChainRule(int x_n, int[] x_id, double[] x_jacobi, double x_diff,
                      int y_n, int[] y_id, double[] y_jacobi, double y_diff,
                      out int z_n, out int[] z_id, out double[] z_jacobi)
{
    int n = x_n + y_n;
    z_id = new int[n];
    z_jacobi = new double[n];
    int i = 0, ix = 0, iy = 0;
    while (ix < x_n && iy < y_n)
    {
        if (x_id[ix] < y_id[iy])
        {
            z_id[i] = x_id[ix];
            z_jacobi[i++] = x_diff * x_jacobi[ix++];
        }
        else if (y_id[iy] < x_id[ix])
        {
            z_id[i] = y_id[iy];
            z_jacobi[i++] = y_diff * y_jacobi[iy++];
        }
        else
        {
            z_id[i] = x_id[ix];
            z_jacobi[i++] = Dot(x_diff, y_diff, x_jacobi[ix++],  y_jacobi[iy++]);
        }
    }
    while (ix < x_n)
    {
        z_id[i] = x_id[ix];
        z_jacobi[i++] = x_diff * x_jacobi[ix++];
    }
    while (iy < y_n)
    {
        z_id[i] = y_id[iy];
        z_jacobi[i++] = y_diff * y_jacobi[iy++];
    }
    z_n = i;
}

我曾尝试预计算x_diff与x_jacobi、y_diff与y_jacobi的乘积，代码如下：

double[] x_diff_jacobi = new double[x_n];
for (int i0 = 0; i0 < x_n; i0++)
    x_diff_jacobi[i0] = x_diff * x_jacobi[i0];
double[] y_diff_jacobi = new double[y_n];
for (int i0 = 0; i0 < y_n; i0++)
    y_diff_jacobi[i0] = y_diff * y_jacobi[i0];

这样可以将交集处的计算简化为z_jacobi[i++] = x_diff_jacobi[ix++] + y_diff_jacobi[iy++]，但实际运行速度比原代码更慢，推测是额外数组的初始化和内存分配带来了开销。

请问还有其他优化这段代码的思路吗？

内容的提问来源于stack exchange，提问作者Wollmich