Re: float("nan") in set or as key

From	Nobody <nobody@nowhere.com>
Subject	Re: float("nan") in set or as key
Date	2011-06-01 21:41 +0100
Message-Id	<pan.2011.06.01.20.40.18.453000@nowhere.com>
Newsgroups	comp.lang.python
References	(1 earlier) <94dkd3F7k4U1@mid.individual.net> <4de1e3e7$0$2195$742ec2ed@news.sonic.net> <4de22007$0$29996$c3e8da3$5496439d@news.astraweb.com> <pan.2011.05.29.21.19.12.375000@nowhere.com> <4de2d746$0$29996$c3e8da3$5496439d@news.astraweb.com>
Organization	Zen Internet

Show all headers | View raw

On Sun, 29 May 2011 23:31:19 +0000, Steven D'Aprano wrote:

>> That's overstating it. There's a good argument to be made for raising an
>> exception. 
> 
> If so, I've never heard it, and I cannot imagine what such a good 
> argument would be. Please give it.

Exceptions allow you to write more natural code by ignoring the awkward
cases. E.g. writing "x * y + z" rather than first determining whether
"x * y" is even defined then using a conditional.

>> Bear in mind that an exception is not necessarily an error,
>> just an "exceptional" condition.
> 
> True, but what's your point? Testing two floats for equality is not an 
> exceptional condition.

NaN itself is an exceptional condition which arises when a result is
undefined or not representable. When an operation normally returns a
number but a specific case cannot do so, it returns not-a-number.

The usual semantics for NaNs are practically identical to those for
exceptions. If any intermediate result in a floating-point expression is
NaN, the overall result is NaN. Similarly, if any intermediate calculation
throws an exception, the calculation as a whole throws an exception.

If x is NaN, then "x + y" is NaN, "x * y" is NaN, pretty much anything
involving x is NaN. By this reasoning both "x == y" and "x != y" should
also be NaN. But only the floating-point types have a NaN value, while
bool doesn't. However, all types have exceptions.

>>> The correct answer to "nan == nan" is False, they are not equal.
>> 
>> There is no correct answer to "nan == nan". 
> 
> Why on earth not?

Why should there be a correct answer? What does NaN actually mean?

Apart from anything else, defining "NaN == NaN" as False means that
"x == x" is False if x is NaN, which violates one of the fundamental
axioms of an equivalence relation (and, in every other regard, "==" is
normally intended to be an equivalence relation).

The creation of NaN was a pragmatic decision on how to handle exceptional
conditions in hardware. It is not holy writ, and there's no fundamental
reason why a high-level language should export the hardware's behaviour
verbatim.

>> Arguably, "nan != nan" should also be false,
>> but that would violate the invariant "(x != y) == !(x == y)".
> 
> I cannot imagine what that argument would be. Please explain.

A result of NaN means that the result of the calculation is undefined, so
the value is "unknown". If x is unknown and y is unknown, then whether x
is equal to y is itself unknown, and whether x differs from y is also
unknown.

Thread

float("nan") in set or as key MRAB <python@mrabarnett.plus.com> - 2011-05-29 00:41 +0100
  Re: float("nan") in set or as key Erik Max Francis <max@alcyone.com> - 2011-05-28 17:16 -0700
  Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-29 00:26 +0000
  Re: float("nan") in set or as key Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2011-05-29 13:04 +1200
    Re: float("nan") in set or as key John Nagle <nagle@animats.com> - 2011-05-28 23:12 -0700
      Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-29 10:29 +0000
        Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-05-29 22:19 +0100
          Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-05-29 23:31 +0000
            Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-06-01 21:41 +0100
              Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-02 09:54 +0000
                Re: float("nan") in set or as key Grant Edwards <invalid@invalid.invalid> - 2011-06-02 13:05 +0000
                Re: float("nan") in set or as key Robert Kern <robert.kern@gmail.com> - 2011-06-02 12:04 -0500
                Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-06-02 21:47 +0100
                Re: float("nan") in set or as key Grant Edwards <invalid@invalid.invalid> - 2011-06-03 14:52 +0000
                Re: float("nan") in set or as key Chris Torek <nospam@torek.net> - 2011-06-03 17:52 +0000
                Re: float("nan") in set or as key Grant Edwards <invalid@invalid.invalid> - 2011-06-06 13:54 +0000
                Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-06-04 00:29 +0100
                Re: float("nan") in set or as key Chris Angelico <rosuav@gmail.com> - 2011-06-04 09:51 +1000
                Re: float("nan") in set or as key rusi <rustompmody@gmail.com> - 2011-06-04 00:52 -0700
                Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-06-04 20:29 +0100
                Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-05 07:21 +0000
                Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-06-05 19:15 +0100
                Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-06 00:55 +0000
                Re: float("nan") in set or as key Nobody <nobody@nowhere.com> - 2011-06-06 23:14 +0100
                Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-06 23:44 +0000
                Re: float("nan") in set or as key Chris Angelico <rosuav@gmail.com> - 2011-06-07 11:00 +1000
                Re: float("nan") in set or as key Grant Edwards <invalid@invalid.invalid> - 2011-06-06 14:03 +0000
                Re: float("nan") in set or as key Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2011-06-03 11:17 +1200
                Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-03 04:23 +0000
                Re: float("nan") in set or as key Chris Angelico <rosuav@gmail.com> - 2011-06-03 14:35 +1000
                Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-03 05:59 +0000
                Re: float("nan") in set or as key Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2011-06-04 12:14 +1200
                Re: float("nan") in set or as key Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-06-04 02:21 +0000
                Re: float("nan") in set or as key Erik Max Francis <max@alcyone.com> - 2011-06-05 00:27 -0700
          Re: float("nan") in set or as key Grant Edwards <invalid@invalid.invalid> - 2011-06-01 21:01 +0000
      Re: float("nan") in set or as key Chris Torek <nospam@torek.net> - 2011-05-30 00:02 +0000
  Re: float("nan") in set or as key Raymond Hettinger <python@rcn.com> - 2011-05-29 21:49 -0700

csiph-web