Programming Assignment: Here is a loop that starts with an initial estimate of the square root of a, x, and improves it until it stops changing: while True: y = (x + a / x) / 2 if abs(y - x) < epsilon: break x = y where epsilon has a value like 0.0000001 that determines how close is close enough. Encapsulate this loop in a function called square_root that takes a as a parameter, chooses a reasonable value of x, and returns an estimate of the square root of a. To test the square root algorithm in this chapter, you could compare it with math.sqrt. Write a function named test_square_root that prints a table like this: 1.0 1.0 1.0 0.0 2.0 1.41421356237 1.41421356237 2.22044604925e-16 3.0 1.73205080757 1.73205080757 0.0 4.0 2.0 2.0 0.0 5.0 2.2360679775 2.2360679775 0.0 6.0 2.44948974278 2.44948974278 0.0 7.0 2.64575131106 2.64575131106 0.0 8.0 2.82842712475 2.82842712475 4.4408920985e-16 9.0 3.0 3.0 0.0 The first column is a number, a; the second column is the square root of a computed with the [your function]; the third column is the square root computed by math.sqrt; the fourth column is the absolute value of the difference between the two estimates.
Programming Assignment:
Here is a loop that starts with an initial estimate of the square root of a, x, and improves it until it
stops changing:
while True:
y = (x + a / x) / 2
if abs(y - x) < epsilon:
break
x = y
where epsilon has a value like 0.0000001 that determines how close is close enough.
Encapsulate this loop in a function called square_root that takes a as a parameter, chooses a
reasonable value of x, and returns an estimate of the square root of a.
To test the square root
function named test_square_root that prints a table like this:
1.0 1.0 1.0 0.0
2.0 1.41421356237 1.41421356237 2.22044604925e-16
3.0 1.73205080757 1.73205080757 0.0
4.0 2.0 2.0 0.0
5.0 2.2360679775 2.2360679775 0.0
6.0 2.44948974278 2.44948974278 0.0
7.0 2.64575131106 2.64575131106 0.0
8.0 2.82842712475 2.82842712475 4.4408920985e-16
9.0 3.0 3.0 0.0
The first column is a number, a; the second column is the square root of a computed with the
[your function]; the third column is the square root computed by math.sqrt; the fourth column
is the absolute value of the difference between the two estimates.
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