Calculate sqrt using newton iteration method

newton_sqrt.py

##
# Calculate sqrt using newton iteration method
# @autor Lukáš Plevač <lukas@plevac.eu>
# @date 6.8.2021
# Under CC0
#

import math

#
# Theory on: https://en.wikipedia.org/wiki/Newton%27s_method
#

##
# Calculate sqrt using newton iteration method
# @param x0 number for sqrt
# @param accuracy accuracy of output (default 0.001)
# @return sqrt(x0) with accuracy of accuracy
def newton_sqrt(x0, accuracy = 0.001):
    x = x0 / 2 # initial estimate

    while True:
        cur_acc = x ** 2 - x0

        if abs(cur_acc) <= accuracy:
            break
        else:
            x = x - cur_acc / (2 * x) # calculation of a new x (refinement of the estimate)

    return x

print(newton_sqrt(3))
print(math.sqrt(3))