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
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