Answer to Question #167319 in Python for Paul Carpenter

Question

Part 1

Encapsulate the following Python code from Section 7.5 in a function named my_sqrt that takes a as a parameter, chooses a starting value for x, and returns an estimate of the square root of a.

while True:

y = (x + a/x) / 2.0

if y == x:

break

x = y

Part 2

Write a function named test_sqrt that prints a table like the following using a while loop, where "diff" is the absolute value of the difference between my_sqrt(a) and math.sqrt(a).

a = 1 | my_sqrt(a) = 1 | math.sqrt(a) = 1.0 | diff = 0.0

a = 2 | my_sqrt(a) = 1.41421356237 | math.sqrt(a) = 1.41421356237 | diff = 2.22044604925e-16

a = 3 | my_sqrt(a) = 1.73205080757 | math.sqrt(a) = 1.73205080757 | diff = 0.0

a = 4 | my_sqrt(a) = 2.0 | math.sqrt(a) = 2.0 | diff = 0.0

a = 5 | my_sqrt(a) = 2.2360679775 | math.sqrt(a) = 2.2360679775 | diff = 0.0

a = 6 | my_sqrt(a) = 2.44948974278 | math.sqrt(a) = 2.44948974278 | diff = 0.0

a = 7 | my_sqrt(a) = 2.64575131106 | math.sqrt(a) = 2.64575131106 | diff = 0.0

a = 8 | my_sqrt(a) = 2.82842712475 | math.sqrt(a) = 2.82842712475 | diff = 4.4408920985e-16

a = 9 | my_sqrt(a) = 3.0 | math.sqrt(a) = 3.0 | diff = 0.0

Answer 1

import math


def my_sqrt(a):
    x = 1
    while True:
        y = (x + a / x) / 2.0
        if y == x:
            break
        x = y

    return x


def test_sqrt():
    a = 1
    while a < 10:
        my = my_sqrt(a)
        math_sqrt = math.sqrt(a)
        diff = math.fabs(my - math_sqrt)
        print("a = {a} | my_sqrt(a) = {my} | math.sqrt(a) = {math} | diff = {diff}".format(
            a=a,
            my=my,
            math=math_sqrt,
            diff=diff
        ))

        a += 1


if __name__ == "__main__":
    test_sqrt()