6.3: Numerical Error

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Consider the following python statement when answering the questions below:

0.1 + 0.2 == 0.3

False

Question

Why does Python return False even though the above statement is clearly true?

Do This

Let’s consider another example. Run the following code which should return true.

import numpy as np
J = np.array([20])
L = [20]

pow(L[0],8) == pow(J[0],8)

True

If you have an older version of numpy installed (like 1.18.5) then the results of running the above cell may be false (did anyone get this result?). This is because numpy changed how it handles something called “roundoff error”. here is another cell that may help you see better what is going on:

import numpy as np
J = np.array([20])
L = [20]
print(pow(20,8))
print(pow(L[0],8))
print(pow(J[0],8))

25600000000
25600000000
25600000000

The older version of numpy would return the following:

25600000000
25600000000
-169803776

We could say to always upgrade to the latest stable version (generally a good idea). But some other libraries that depend on numpy may not be up to date so sometimes python will install an older version to maintain compatibility. For example, one really popular program is tensorflow, which often requires an older version of numpy.

Question

If Python is sometimes wrong, why do we use it?

Question

What are ways you can do to watch out for these types of errors?

Question

Modify the following program to return True if the values are within some small number (e) of each other.

def checktrue(a,b,e=0.001):
    return a == b

#Test function
checktrue(0.1+0.2, 0.3)

False

Question

What is a good value to set for e and why?

Question

The errors seen in this example seem like they would be fairly common in Python. See if you can find a function in Numpy that has the same purpose as checktrue:

The class answercheck program will take into consideration round off error. For example, the checkanswer.float command would consider both of the above correct:

from urllib.request import urlretrieve
urlretrieve('https://raw.githubusercontent.com/colbrydi/jupytercheck/master/answercheck.py', 
            'answercheck.py');

from answercheck import checkanswer

checkanswer.float(0.300,'e85b79abfd76b7c13b1334d8d8c194a5');

Testing 0.3
Answer seems to be correct

checkanswer.float(0.1+0.2,'e85b79abfd76b7c13b1334d8d8c194a5')

Testing 0.3
Answer seems to be correct