using System;

namespace StatsSuite
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("rounded index " + Linearize(416, 65536));
        }

        public static double Linearize(double ct, int N, int dx = 1024)
        {
            Console.WriteLine("Ct " + ct);
            double zx = ct / Math.Sqrt(N);
            Console.WriteLine("z-score " + zx);
            return (int)Math.Round(dx * Phi(zx));
        }

        public static double Phi(double x)
        {
            // constants
            double c1 = 2.506628275;
            double c2 = 0.31938153;
            double c3 = -0.356563782;
            double c4 = 1.781477937;
            double c5 = -1.821255978;
            double c6 = 1.330274429;
            double c7 = 0.2316419;

            // Save the sign of x
            int sign = 1;
            if (x < 0)
                sign = -1;

            double t = 1 + c7 * sign * x;
            double y = 1 / t;
            double cdf = 0.5 + sign * (0.5 - (c2 + (c6 + c5 * t + c4 * Math.Pow(t, 2) + c3 * Math.Pow(t, 3)) / Math.Pow(t, 4)) / (c1 * Math.Exp(0.5 * x * x) * t));
            Console.WriteLine("linearized cdf " + cdf);
            return cdf;
        }
    }
}