D Math

DMath.d

// https://de.wikipedia.org/wiki/Bin%C3%A4re_Exponentiation#Pseudocode_(Algorithmus)
double powi(double v, int pow) {
    double res = 1;

    // we just use the 8 bit
    for(int i=7;i>=0;i--) {
        res = res*res;

        //if( pow & (1 << i) )
        //    res = res * v;

        // jump free version of the above code
        int a = (pow >> i) & 1;
        res *= ((a*v) + ((1-a)*1));
    }
    
    return res;
}

// see https://en.wikipedia.org/wiki/Nth_root_algorithm
double nthRoot(double v, int n, double epsilon = 0.000001) {
    import std.math : abs, sqrt;
    
    double x = sqrt(v);
    
    for(;;) {
        double delta = (1.0/n) * (powi(x, n-1) - x);
        x += delta;

        if( abs(delta) < epsilon )  break;
    }

    return x;
}