[Python-Dev] PyObject_RichCompareBool identity shortcut

[Stephen J. Turnbull]

Glenn Linderman writes:
 > On 4/27/2011 6:11 PM, Ethan Furman wrote:

 > > Totally out of my depth, but what if the a NaN object was allowed to 
 > > compare equal to itself, but different NaN objects still compared 
 > > unequal?  If NaN was a singleton then the current behavior makes more 
 > > sense, but since we get a new NaN with each instance creation is there 
 > > really a good reason why the same NaN can't be equal to itself?

Yes.  A NaN is a special object that means "the computation that
produced this object is undefined."  For example, consider the
computation 1/x at x = 0.  If you approach from the left, 1/0
"obviously" means minus infinity, while if you approach from the right
just as obviously it means plus infinity.  So what does the 1/0 that
occurs in [1/x for x in range(-5, 6)] mean?  In what sense is it
"equal to itself"?  How can something which is not a number be
compared for numerical equality?

 >  >>> n1 = float('NaN')
 >  >>> n2 = float('NaN')
 >  >>> n3 = n1
 > 
 >  >>> n1
 > nan
 >  >>> n2
 > nan
 >  >>> n3
 > nan
 > 
 >  >>> [n1] == [n2]
 > False
 >  >>> [n1] == [n3]
 > True
 > 
 > This is the current situation: some NaNs compare equal sometimes, and 
 > some don't.

No, Ethan is asking for "n1 == n3" => True.  As Mark points out, "[n1]
== [n3]" can be interpreted as a containment question, rather than an
equality question, with respect to the NaNs themselves.  In standard
set theory, these are the same question, but that's not necessarily so
in other set-like toposes.  In particular, getting equality and set
membership to behave reasonably with respect to each other one of the
problems faced in developing a workable theory of fuzzy sets.

I don't think it matters what behavior you choose for NaNs, somebody
is going be unhappy sometimes.