import sys
import math
from decimal import *

def main(argv):

	if len(argv) != 1:
		sys.exit('Usage: calc_pi.py <n>')

	print '\nComputing Pi v.01\n'
	
	a = Decimal(1.0)
	b = Decimal(1.0/math.sqrt(2))
	t = Decimal(1.0)/Decimal(4.0)
	p = Decimal(1.0)
		
	for i in range(int(sys.argv[1])):
		at = Decimal((a+b)/2)
		bt = Decimal(math.sqrt(a*b))
		tt = Decimal(t - p*(a-at)**2)
		pt = Decimal(2*p)
		
		a = at;b = bt;t = tt;p = pt
		
	my_pi = (a+b)**2/(4*t)
	accuracy = 100*(Decimal(math.pi)-my_pi)/my_pi
		
	print "Pi is approximately: " + str(my_pi)
	print "Accuracy with math.pi: " + str(accuracy)
	
if __name__ == "__main__":
	main(sys.argv[1:])