pi_digits.rb

#! /usr/bin/env ruby

# see: https://en.wikipedia.org/wiki/BaileyBorwein-Plouffe_formula
require 'bigdecimal'

NUMERATOR     = ->(k) do
  BigDecimal.new('120')*(k**2) + BigDecimal.new('151')*k + BigDecimal.new('47')
end

DENOMINATOR_1 = ->(k) do
  BigDecimal.new('512')*(k**4) + BigDecimal.new('1024')*(k**3) + BigDecimal.new('712')*(k**2) + BigDecimal.new('194')*k + BigDecimal.new('15')
end

DENOMINATOR_2 = ->(k) do
  BigDecimal.new('16')**k
end

sum = BigDecimal.new('0.0')
k   = BigDecimal.new('0.0')

until k > 100
  sum += (NUMERATOR.(k)/(DENOMINATOR_1.(k) * DENOMINATOR_2.(k)))
  k += 1.0

  puts "\n\tk: #{k}\n\tsum: #{sum}" 
end

puts "\nfinal value: #{sum}"

^ looses accuracy after 19 digits