sidef-scripts/Math/geometric-harmonic_mean.sf

#!/usr/bin/ruby

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

# Geometric-harmonic mean (GHM).

# If AGM(x,y) is the arithmetic-geometric mean, then GHM(x,y) is equivalent with:
#
#   GHM(x,y) = 1/AGM(1/x, 1/y)
#

func GHM(g, h, p=100) {
    loop {
        var g1 = sqrt(g*h)
        var h1 = (2 / (1/g + 1/h))

        if (
            (g1.round(-p) == g.round(-p)) &&
            (h1.round(-p) == h.round(-p))
        ) {
            return g
        }

        (g, h) = (g1, h1)
    }
}

say GHM(1, 2)             #=> 1.37288050061835016469763757500780605809453862535
say GHM(1, 1/2)           #=> 0.686440250309175082348818787503903029047269312674
say GHM(3, 1/sqrt(2))     #=> 1.28640254813473954856043309974567498549916997311