Question

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

Modify your program so that it outputs lines for a values from 1 to 25 instead of just 1 to 9.

You should submit a script file and a plain text output file (.txt) that contains the test output. Multiple file uploads are permitted.

Answer 1

Python code:

import math

def my_sqrt(a): # Same as given in question
x = a
while True:
y = (x + a / x) / 2.0
if y == x:
break
x = y
return x

def test_sqrt():
for a in range(1, 26): # Loop over the values of a
my, lib = my_sqrt(a), math.sqrt(a) # Calculate and store to avoid repetition
print(f"a = {a} | my_sqrt(a) = {my} | math.sqrt(a) = {lib} | diff = {abs(my - lib)}") # Print result line

test_sqrt()

Output:

a = 1 | my_sqrt(a) = 1 | math.sqrt(a) = 1.0 | diff = 0.0
a = 2 | my_sqrt(a) = 1.414213562373095 | math.sqrt(a) = 1.4142135623730951 | diff = 2.220446049250313e-16
a = 3 | my_sqrt(a) = 1.7320508075688772 | math.sqrt(a) = 1.7320508075688772 | diff = 0.0
a = 4 | my_sqrt(a) = 2.0 | math.sqrt(a) = 2.0 | diff = 0.0
a = 5 | my_sqrt(a) = 2.23606797749979 | math.sqrt(a) = 2.23606797749979 | diff = 0.0
a = 6 | my_sqrt(a) = 2.449489742783178 | math.sqrt(a) = 2.449489742783178 | diff = 0.0
a = 7 | my_sqrt(a) = 2.6457513110645907 | math.sqrt(a) = 2.6457513110645907 | diff = 0.0
a = 8 | my_sqrt(a) = 2.82842712474619 | math.sqrt(a) = 2.8284271247461903 | diff = 4.440892098500626e-16
a = 9 | my_sqrt(a) = 3.0 | math.sqrt(a) = 3.0 | diff = 0.0
a = 10 | my_sqrt(a) = 3.162277660168379 | math.sqrt(a) = 3.1622776601683795 | diff = 4.440892098500626e-16
a = 11 | my_sqrt(a) = 3.3166247903554 | math.sqrt(a) = 3.3166247903554 | diff = 0.0
a = 12 | my_sqrt(a) = 3.4641016151377544 | math.sqrt(a) = 3.4641016151377544 | diff = 0.0
a = 13 | my_sqrt(a) = 3.6055512754639896 | math.sqrt(a) = 3.605551275463989 | diff = 4.440892098500626e-16
a = 14 | my_sqrt(a) = 3.7416573867739413 | math.sqrt(a) = 3.7416573867739413 | diff = 0.0
a = 15 | my_sqrt(a) = 3.872983346207417 | math.sqrt(a) = 3.872983346207417 | diff = 0.0
a = 16 | my_sqrt(a) = 4.0 | math.sqrt(a) = 4.0 | diff = 0.0
a = 17 | my_sqrt(a) = 4.123105625617661 | math.sqrt(a) = 4.123105625617661 | diff = 0.0
a = 18 | my_sqrt(a) = 4.242640687119286 | math.sqrt(a) = 4.242640687119285 | diff = 8.881784197001252e-16
a = 19 | my_sqrt(a) = 4.358898943540673 | math.sqrt(a) = 4.358898943540674 | diff = 8.881784197001252e-16
a = 20 | my_sqrt(a) = 4.47213595499958 | math.sqrt(a) = 4.47213595499958 | diff = 0.0
a = 21 | my_sqrt(a) = 4.58257569495584 | math.sqrt(a) = 4.58257569495584 | diff = 0.0
a = 22 | my_sqrt(a) = 4.69041575982343 | math.sqrt(a) = 4.69041575982343 | diff = 0.0
a = 23 | my_sqrt(a) = 4.795831523312719 | math.sqrt(a) = 4.795831523312719 | diff = 0.0
a = 24 | my_sqrt(a) = 4.898979485566356 | math.sqrt(a) = 4.898979485566356 | diff = 0.0
a = 25 | my_sqrt(a) = 5.0 | math.sqrt(a) = 5.0 | diff = 0.0