Moores

#!/usr/bin/env python
#coding=utf-8
# piByChudnovskyAlgorithm2.py
# same as piByChudnovskyAlgorithm.py but with a loop
# see The Chudnovsky algorithm at http://en.wikipedia.org/wiki/Chudnovsky

from mpmath import mp, mpf, pi
import time

cached_factorials = [mpf(1)]

def f(n):
    n = int(n)
    if n < len(cached_factorials):
        return cached_factorials[n]
    p = cached_factorials[-1]
    for i in range(len(cached_factorials), n+1):
        p *= i
        cached_factorials.append(p)
    return p

print
while True:
    print \
    """
    Enter a positive integer to set precision.
    Close program by entering a zero.
    """

    precision = int(raw_input("integer: "))
    if precision == 0:
        print "Bye"
        time.sleep(1)
        break
    timeStart = time.time()
    mp.dps = precision
    k = mpf(0)
    term = 0
    sum = 0
    sumPrevious = 0
    i = 0
    while True:
        i += 1
        nom = (((-1)**k) * f(6*k) * (13591409+545140134*k))
        denom = (f(3*k) * ((f(k))**3) * (640320**(3*k)))
        term = nom/denom
        sum += term
        if sum == sumPrevious:
            timeEnd = time.time()
            print "The result calculated from the first %d terms of the series is:" % (i-1)
            print 1/(12*sum/640320**(mpf(3)/2))
            print
            print "pi to %d digits is:" % precision
            print pi
            break
        sumPrevious = sum
        k += 1

    print "Time was %.4g seconds" % (timeEnd - timeStart)
    print