square_root_arithmetic-harmonic_mean.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 17 March 2018
# https://github.com/trizen

# A new algorithm for computing the square root of a given number at arbitrary precision.

# Based on the arithmetic-harmonic mean (AHM).

func square_root (n, p=50) {

    var a = 1

    loop {
        var t = (a + n)
        var u = (t / 2)
        var v = (2*a*n / t)

        if (
            (u.round(-p) == a.round(-p)) &&
            (v.round(-p) == n.round(-p))
        ) {
            return a
        }

        (a, n) = (u,  v)
    }
}

say square_root(2)          #=> 1.41421356237309504880168872420969807856967187538
say square_root(1234.567)   #=> 35.13640562152025248047681253395668334052672496563