Why is -0.0 not the same as 0.0?

2024/11/17 14:30:49

I could be missing something fundamental, but consider this interpreter session1:

>>> -0.0 is 0.0
False
>>> 0.0 is 0.0
True
>>> -0.0  # The sign is even retained in the output.  Why?
-0.0
>>>

You would think that the Python interpreter would realize that -0.0 and 0.0 are the same number. In fact, it compares them as being equal:

>>> -0.0 == 0.0
True
>>>

So why is Python differentiating between the two and generating a whole new object for -0.0? It doesn't do this with integers:

>>> -0 is 0
True
>>> -0  # Sign is not retained
0
>>>

Now, I realize that floating point numbers are a huge source of problems with computers, but those problems are always with regard to their accuracy. For example:

>>> 1.3 + 0.1
1.4000000000000001
>>>

But this isn't an accuracy problem, is it? I mean, we are talking about the sign of the number here, not its decimal places.


1I can reproduce this behavior in both Python 2.7 and Python 3.4, so this is not a version-specific question.

Answer

In IEEE754, the format of floating point numbers, the sign is a separate bit. So -0.0 and 0.0 are different by this bit. Integers use the two's complement, to represent negative numbers; that's why there is only one 0.

Use is only of you really want to compare instances of objects. Otherwise, especially for numbers, use ==:

>>> 1999+1 is 2000
False>>> 0.0 == -0.0
True
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