Calculates digits of pi using the Gauss-Legendre Algorithm

digits_of_pi.py

__author__ = "wasi0013"

'''
Calculates digits of pi using the Gauss-Legendre Algorithm
Link: https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorithm
'''

import decimal
import requests, bs4

url = 'http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html'
dec = decimal.Decimal
#set precision
decimal.getcontext().prec = 2000

# Retrieves 10000 digits of pi from the website : http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
def get_pi():

    response = requests.get(url)
    soup = bs4.BeautifulSoup(response.text)
    for i in soup.findAll(['p', 'center', 'h1', 'br', 'hr', 'a']):
        i.extract()
    return "".join(str(soup.body.getText()).strip().split())  

# Implementation of the Gauss Legendre Algorithm
def make_pi(pi = None):
    a, b = 1, 1/dec(2).sqrt()
    p, t = 1, 1/dec(4)
    while True:
        an, b = (a+b)/2, (a*b).sqrt()
        t -= (a-an)*(a-an) * p
        a, p = an, p*2
        
        old_pi = pi
        pi = (a+b)*(a+b) / (4*t)
    
        if old_pi == pi: return pi

def test_pi(value=None):

    correct_digit_count = 0
    pi_value = get_pi()
    if value:
        try:
            for i,digit in enumerate(value):
                if digit==pi_value[i]: correct_digit_count+=1
                else: 
                    break
        except:
            pass    
    return correct_digit_count

calculated_pi = str(make_pi())

#prints correct digit counts (including the dot)
print(test_pi(calculated_pi))