Can someone explain this behavior with this function?

Question

>>> def my_max(x,y):
        return ( x + y + abs(x - y)) / 2
>>> my_max(-894,2.3)
2.2999999999999545
>>> my_max(34,77)
77.0
>>> my_max(0.1,0.01)
0.1
>>> my_max(-0.1 , 0.01)
0.009999999999999995

I am just playing around with python and i made this function that it sometimes works and others it just gets close to the awnser

I know it has to do with floating-point errors, but why would work for some inputs and not in others??

Answer 1

Easier to test this out when you separate the function:

def m(x, y):

    first = x + y
    second = abs(x - y)
    third = first + second
    fourth = third / 2

    print("x+y\t\t\t", first)
    print("abs(x-y)\t\t", second)
    print("x+y + abs(x-y)\t\t", third)
    print("(x+y + abs(x-y))/2\t", fourth)

m(-894, 2.3)

You receive the following outputs:

x+y                  -891.7
abs(x-y)             896.3
x+y + abs(x-y)       4.599999999999909
(x+y + abs(x-y))/2   2.2999999999999545

Now looking at x+y + abs(x-y) we have the following:

var = -891.7 + 896.3
print(var)

Which outputs:

4.599999999999909

This should, of course, be 4.6, but what is happening can be referred from Python's documentation here:

Note that this is in the very nature of binary floating-point: this is not a bug in Python, and it is not a bug in your code either. You’ll see the same kind of thing in all languages that support your hardware’s floating-point arithmetic (although some languages may not display the difference by default, or in all output modes).

You can resolve this by utilizing the decimal library that comes with Python:

from decimal import *

getcontext().prec = 10
var = Decimal(-891.7) + Decimal(896.3)
print(var)

outputs:

4.600000000

In this case, your precision can be as large as 13 for it to correctly output a variation of 4.6. Increase it to 14 or larger and you will notice you will once again receive your 4.59.....