sidef-scripts/Math/AGM_calculate_pi.sf

#!/usr/bin/ruby

# The AGM method for efficiently computing an arbitrary number of digits of PI.

# See also:
#   https://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi
#   https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean#The_number_%CF%80

func AGM_PI(digits=100) {

    var acc = 8+digits
    local Number!PREC = numify(4*digits)

    var (an, bn, tn, pn) = (1, sqrt(1/2), 1/4, 1)

    while (pn < acc) {
        var prev_an = an
        an += bn
        an /= 2
        bn *= prev_an
        bn.sqrt!
        prev_an -= an
        tn -= (prev_an * prev_an * pn)
        pn += pn
    }

    an += bn
    an *= an
    an /= 4*tn

    return String(an)
}

say AGM_PI(ARGV[0])