from math import factorial, pow
import numpy as np

def taylor_series(x, n_max=5):
    res = 0.0
    for n in range(n_max):
        res += ((pow(-1, n)*factorial(2*n))/((1-2*n)*pow(factorial(n), 2)*(pow(4, n))))*pow(x, n)
    return res

def f_my_sqrt_sqr(x, n=52, output=True):
    alpha = x
    if x > 1:
        alpha = alpha - 1

    for k in range(n):
        if alpha > 1:
            alpha = np.sqrt(alpha + 1) - 1
        else:
            alpha = taylor_series(alpha) - 1
        if output:
            print(alpha, k)

    if output:
        print("------")

    for k in range(n):
        alpha = 2 * alpha + alpha * alpha
        if output:
            print(alpha, k)

    if x > 1:
        alpha = alpha + 1

    return alpha


pi = 33.1415;
print(pi)
print(f_my_sqrt_sqr(pi))