Gauss Legendre iterative algorithm This repeats the given calculation a number of times until it converges at the desired output. This is faster than infinitive series algorithm although consume more memory like in our solution. The size of the list

Gauss_Legendre_iterative_algorithm

#!/usr/bin/python
import math
import decimal


def calculatePi (num_of_iteration):
    """
     Gauss Legendre iterative algorithm 
     This repeats the given calculation a number of times until it converges at the desired output. This is faster than infinitive series algorithm although consume more memory like in our solution. The size of the list increases and that affect space complexity.
    """
    list_a, list_b, list_t, list_p = [], [], [], []
    a_0, b_0, t_0, p_0 = 1.0, (1 / math.sqrt(2.0)), 0.25, 1.0
    list_a.append(a_0)
    list_b.append(b_0)
    list_t.append(t_0)
    list_p.append(p_0)
    for pos in range(0, num_of_iteration):
        a_next = (list_a[pos] + list_b[pos] ) / 2.0
        list_a.append(a_next)
        b_next = math.sqrt(list_a[pos] * list_b[pos] )
        list_b.append(b_next)
        t_next = list_t[pos] - (list_p[pos] * (list_a[pos] - a_next)**2 )
        list_t.append(t_next)
        p_next = 2 * list_p[pos]
        list_p.append(p_next)
    pi = ((list_a[-1] + list_b[-1])**2) / (4 * list_t[-1] )
    d = decimal.Decimal(pi)
    return '%.50f' % d

if __name__ == '__main__':
    num_of_iteration = 50
    piValue = calculatePi (num_of_iteration)
    print piValue