#!/usr/bin/env python

import sys
import random
import math

"""
Theory:
The chance of two random integers being coprime is 6/pi**2
So try and generate pi using two parameters:
 
 * the maximum number (randint(1,N))
 * the number of random pairs generated

Ref:
https://en.wikipedia.org/wiki/Coprime_integers

Usage:
./random_vals_pi.py <max rand value> <number of random pair samples>

"""

def calc_pi(max_rand, samples):
  coprime_count = 0
  for _ in range(0, samples):
    if gcd(random.randint(1,max_rand), random.randint(1,  max_rand)) == 1:
      coprime_count += 1
  return math.sqrt( 6 / (coprime_count/float(samples)) )

def recursive_gcd(a,b):
  """
  gcd calculated by Euclid's Algorithm
  https://en.wikipedia.org/wiki/Greatest_common_divisor#Using_Euclid.27s_algorithm
  """
  if a == b:
    return a
  elif a > b:
    return gcd(a - b, b)
  else:
    return gcd(a, b - a)

def gcd(a,b):
  """
  gcd calculated by Euclid's Algorithm
  non-recursive to work on larger numbers
  https://en.wikipedia.org/wiki/Greatest_common_divisor#Using_Euclid.27s_algorithm
  """
  while a != b:
    if a > b:
      a = a - b
    else:
      b = b - a
  return a

if __name__ == "__main__":
  print( calc_pi(*[int(x) for x in sys.argv[1:3]]) )