[Python-Dev] Not-a-Number (was PyObject_RichCompareBool identity shortcut)

[Steven D'Aprano]

Mark Shannon wrote:
> Related to the discussion on "Not a Number" can I point out a few things 
> that have not be explicitly addressed so far.
> 
> The IEEE standard is about hardware and bit patterns, rather than types 
> and values so may not be entirely appropriate for high-level language
> like Python.

I would argue that the implementation of NANs is irrelevant. If NANs are 
useful in hardware floats -- and I think they are -- then they're just 
as equally useful as objects, or as strings in languages like REXX or 
Hypertalk where all data is stored as strings, or as quantum wave 
functions in some future quantum computer.


> NaN is *not* a number (the clue is in the name).
> Python treats it as if it were a number:
> 
>  >>> import numbers
>  >>> isinstance(nan, numbers.Number)
> True
> 
> Can be read as "'Not a Number' is a Number" ;)

I see your wink, but what do you make of these?

class NotAnObject(object):
     pass

nao = NotAnObject()
assert isinstance(nao, object)

class NotAType(object):
     pass

assert type(NotAType) is type



> NaN does not have to be a float or a Decimal.
> Perhaps it should have its own class.

Others have already pointed out this won't make any difference.

Fundamentally, the problem is that some containers bypass equality tests 
for identity tests. There may be good reasons for that shortcut, but it 
leads to problems with *any* object that does not define equality to be 
reflexive, not just NANs.


 >>> class Null:
...     def __eq__(self, other):
...             return False
...
 >>> null = Null()
 >>> null == null
False
 >>> [null] == [null]
True



> The default comparisons will then work as expected for collections.
> (No doubt, making NaN a new class will cause a whole new set of problems)
> 
> As pointed out by Meyer:
> NaN == NaN is False
> is no more logical than
> NaN != NaN is False

I don't agree with this argument. I think Meyer is completely mistaken 
there. The question of NAN equality is that of a vacuous truth, quite 
similar to the Present King of France:

http://en.wikipedia.org/wiki/Present_King_of_France

Meyer would have us accept that:

     The present King of France is a talking horse

and

     The present King of France is not a talking horse

are equally (pun not intended) valid. No, no they're not. I don't know 
much about who the King of France would be if France had a king, but I 
do know that he wouldn't be a talking horse.

Once you accept that NANs aren't equal to anything else, it becomes a 
matter of *practicality beats purity* to accept that they can't be equal 
to themselves either. A NAN doesn't represent a specific thing. It's a 
signal that your calculation has generated an indefinite, undefined, 
undetermined value. NANs aren't equal to anything. The fact that a NAN 
happens to have an existence as a bit-pattern at some location, or as a 
distinct object, is an implementation detail that is irrelevant. If you 
just happen by some fluke to compare a NAN to "itself", that shouldn't 
change the result of the comparison:

     The present King of France is the current male sovereign who
     rules France

is still false, even if you happen to write it like this:

     The present King of France is the present King of France


This might seem surprising to those who are used to reflexivity. Oh 
well. Just because reflexivity holds for actual things, doesn't mean it 
holds for, er, things that aren't things. NANs are things that aren't 
things.





> Although both NaN == NaN and NaN != NaN could arguably be a "maybe" 
> value, the all important reflexivity (x == x is True)  is effectively 
> part of the language.
> All collections rely on it and Python wouldn't be much use without 
> dicts, tuples and lists.

Perhaps they shouldn't rely on it. Identity tests are an implementation 
detail. But in any case, reflexivity is *not* a guarantee of Python. 
With rich comparisons, you can define __eq__ to do anything you like.





-- 
Steven