#!/usr/bin/env python3

'''This file contains a trivial implementation of Netwon Method
written in python3 for educational purposes.

The related video can be found at the following URL: 

Author: Leonardo Tamiano.
Date: 2021-09-13

'''

import math

# -------------------------
# Global variables
PRECISION = 0.000001

# -------------------------
# General math functions

def my_abs(x):
    if x >= 0:
       return x
    else: # x < 0
        return -x

def square(x):    
    return x**2

def average(x, y):
    return (x + y) / 2 
    
# -------------------------
# Functions for square root

def good_enough(approx, x):
    global PRECISION
    
    if my_abs(square(approx) - x) >= PRECISION:
        return False
    else:
        return True

def improve_approximation(approx, x):
    return average(approx, x / approx)

def square_root(x):
    approx = 1.0

    while not good_enough(approx, x):
        approx = improve_approximation(approx, x)

    return approx

# -------------------------

def test():
    numbers_to_test = list(range(1, 101))

    for number in numbers_to_test:
        our_square_root = square_root(number)
        python_square_root = math.sqrt(number)

        abs_difference = my_abs(our_square_root - python_square_root)

        message = f"number={number}, our_square_root={our_square_root}, python_square_root={python_square_root}, difference={abs_difference}"
        
        if abs_difference > PRECISION:
            print("[ERROR]: " + message)
        else:
            print("[INFO]: " + message)            

# -------------------------

if __name__ == "__main__":
    test()