Rich Comparisons Gotcha

[Robert Kern]

Rhamphoryncus wrote:
> On Dec 7, 4:20 pm, Steven D'Aprano <st... at REMOVE-THIS-
> cybersource.com.au> wrote:
>> On Sun, 07 Dec 2008 15:32:53 -0600, Robert Kern wrote:
>>> Rasmus Fogh wrote:
>>>> Current behaviour is both inconsistent and counterintuitive, as these
>>>> examples show.
>>>>>>> x = float('NaN')
>>>>>>> x == x
>>>> False
>>> Blame IEEE for that one. Rich comparisons have nothing to do with that
>>> one.
>> There is nothing to blame them for. This is the correct behaviour. NaNs
>> should *not* compare equal to themselves, that's mathematically
>> incoherent.
> 
> Mathematically, NaNs shouldn't be comparable at all.  They should
> raise an exception when compared.  In fact, they should raise an
> exception when *created*.  But that's not what we want.  What we want
> is a dummy value that silently plods through our calculations.  For a
> dummy value it seems a lot more sense to pick an arbitrary yet
> consistent sort order (I suggest just above -Inf), rather than quietly
> screwing up the sort.

Well, there are explicitly two kinds of NaNs: signalling NaNs and quiet NaNs, to 
accommodate both requirements. Additionally, there is significant flexibility in 
trapping the signals.

> Regarding the mythical IEEE 754, although it's extremely rare to find
> quotations, I have one on just this subject.  And it does NOT say "x
> == NaN gives false".  It says it gives *unordered*.  It is C and
> probably most other languages that turn that into false (as they want
> a dummy value, not an error.)
> 
> http://groups.google.ca/group/sci.math.num-analysis/browse_thread/thread/ead0392e646b7cc0/a5bc354cd46f2c49?lnk=st&q=why+does+NaN+not+equal+itself%3F&rnum=3&hl=en&pli=1

Table 4 on page 9 of the standard is pretty clear on the subject. When the two 
operands are unordered, the operator == returns False. The standard defines how 
to do comparisons notionally; two operands can be "greater than", "less than", 
"equal" or "unordered". It then goes on to map these notional concepts to 
programming language boolean predicates.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco