Gauss-Legendre Algorithm

gauss_legendre_alg.py

# Zach Champion
# Calculus II - Honors Calculus Project

# A script in Python that returns a decimal expansion of pi using the
# Gauss-Legendre algorithm.


from __future__ import with_statement

# Used the decimal module for increased accuracy that the standard float
# type doesn't offer.
import decimal

def pi_gauss_legendre():
    D = decimal.Decimal
    with decimal.localcontext() as ctx:
        ctx.prec += 2
        a, b, t, p = 1, 1/D(2).sqrt(), 1/D(4), 1
        pi = None
        while 1:
            an    = (a + b) / 2
            b     = (a * b).sqrt()
            t    -=  p * (a - an) * (a - an)
            a, p  = an, 2*p
            piold = pi
            pi    = (a + b) * (a + b) / (4 * t)
            if pi == piold:
                break
    return +pi

# Requests user input for how many decimal places you want an expansion to.

x = int(raw_input("Enter an integer to indicate how far to expand pi: "))

# The variable x is later used to dictate how many times the function defined
# above loops through the algorithm. Each time it loops it gives another decimal
# position
decimal.getcontext().prec = x
print pi_gauss_legendre()