pi2.py

from __future__ import division
import decimal

decimal.getcontext().prec = 100
dd=decimal.Decimal

def newton(x):
	xn=dd(0)
	while True:
		xn+=1
		if xn**2>x:
			break
	while True:
		ss=xn
		xn=(xn+x/xn)/2
		if ss-xn<((dd(1)/10)**100):
			break
	return xn

def pi2(x):
    a=dd(1)
    b=newton(dd("0.5"))
    t=dd("0.25")
    p=dd(1)
    for sq in range(x):
            X=(a+b)/dd(2)
            t=t-p*((a-X)**2)
            b=newton(a*b)
            a=X
            p*=2
    return  ((a+b)**2)/(4*t)