Weird means drill

using Statistics

const tol = 1e-9 # tolerance threshold
const expo = 1/3 # cube root exponent

function agm(x::Real, y::Real)
    while abs(x - y) > tol
        a = (x + y)/2
        b = sqrt(x*y)
        x, y = a, b
    end

    return x
end

function gmdm(x::Array{<:Real})
    a = mean(x)
    g = (prod(x))^(1/length(x))
    m = median(x)
    x = [a, g, m]
    smallest, largest = extrema(x)

    while largest - smallest > tol
        a = mean(x)
        g = (prod(x))^expo
        m = median(x)
        x = [a, g, m]
        smallest, largest = extrema(x)
    end

    return a
end