Ruby script to compute pi with BBP formula.

pi_bbp.rb

#!/usr/local/bin/ruby
#=======================================
# Computation of pi by BBP algorithm.
#=======================================
require 'benchmark'

class PiBbp
  EPS = 1.0e-17  # Loop-exit accuration of the right summation

  def comp_pi(d)
    d -= 1
    pi = (4 * s(1, d) - 2 * s(4, d) - s(5, d) - s(6, d)) % 1.0
    printf("FRACTION  : %.15f\n", pi)
    printf("HEX DIGITS: %10x\n", (pi * 16 ** 10).truncate)
  end

  def s(j, d)
    # Left sum
    s = 0.0
    k = 0
    while k <= d
      r = 8 * k + j
      t = mod_exp(16, d - k, r)
      t /= r.to_f
      s += t % 1.0
      s %= 1.0
      k += 1
    end

    # Right sum
    loop do
      r = 8 * k + j
      t = 16.0 ** (d - k) / r
      break if t < EPS
      s += t
      s %= 1.0
      k += 1
    end

    return s
  end

  def mod_exp(b, e, m)
    return 1 if e == 0
    ans = mod_exp(b, e / 2, m)
    ans = (ans * ans) % m
    ans = (ans * b) % m if e % 2 == 1
    return ans
  end
end

exit unless __FILE__ == $0
exit unless ARGV[0]
obj = PiBbp.new
res = Benchmark.realtime do
  obj.comp_pi(ARGV[0].to_i)
end
puts "TIME: #{res} seconds"