#!/usr/bin/python
import math


def preciseAcot(value, scale):
	"""This function calculates the arc cotan of a value scaled by the scale 
	factor. It uses long integer arithmetic to get more precision."""
	n = 1
	term = preciseAcotTerm(value, 1, scale)
	sumTerms = 0
	while (abs(term) >= 1):
		sumTerms += term
		n += 1
		term = preciseAcotTerm(value, n, scale)
	return sumTerms


def preciseAcotTerm(value, n, scale):
	if ( n % 2 ) == 0:
		sign = -1
	else:
		sign = 1	
	numerator = (sign * scale)
	denominator = ((value ** ((2 * n) - 1)) * ((2 * n) - 1))
	retVal = numerator // denominator
	return retVal

	
def evenFibonacci():
	""" An unbounded generator for the even terms (F2, F4, F6, etc.) of the 
	Fibonacci sequence.	Based upon recipe 19.3, by Tom Good and Leandro Mariano 
	Lopez, from the	Python Cookbook. The sequence starts from F2."""
	F_odd, F_even = 1, 2
	while True:
		yield F_even
		F_odd  = F_odd + F_even
		F_even = F_odd + F_even


def sumExpansion(scale):
	# This function sums up the arc cotan function values of the even terms 
	# in the Fibonacci sequence to produce an approximation of pi/4
	evenFiboGen = evenFibonacci()
	Fn = evenFiboGen.next()
	term = preciseAcot(Fn, scale)
	sumTerms = 0L
	while (abs(term) >= 1):
		sumTerms += term
		Fn = evenFiboGen.next()	
		term = preciseAcot(Fn, scale)
	return sumTerms


def calculatePi(precision):
	# Add a couple of extra decimal places to the precision to take rounding 
	# error of terms in the expansion into account. Scale back down for the 
	# output.
	extraDigits = ( long(math.ceil(math.log10(precision * 30))) + 1)
	scale = pow(10, (precision + extraDigits))	
	piDigits = 4 * sumExpansion(scale)
	return piDigits // pow(10, extraDigits)


if __name__ == "__main__":
	import sys
	precision = int(sys.argv[1])
	print "Hello world. Here are", precision,"digits of pi:\n", calculatePi(precision)