float("nan") in set or as key

[Chris Angelico]

On Mon, May 30, 2011 at 10:55 AM, Carl Banks <pavlovevidence at gmail.com> wrote:
> If exceptions had commonly existed in that environment there's no chance they would have chosen that behavior; comparison against NaN (or any operation with NaN) would have signaled a floating point exception.  That is the correct way to handle exceptional conditions.
>
> The only reason to keep NaN's current behavior is to adhere to IEEE, but given that Python has trailblazed a path of correcting arcane mathematical behavior, I definitely see an argument that Python should do the same for NaN, and if it were done Python would be a better language.

If you're going to change behaviour, why have a floating point value
called "nan" at all? Other than being a title for one's grandmother,
what meaning does that string have, and why should it be able to be
cast as floating point?

Lifting from http://en.wikipedia.org/wiki/NaN a list of things that
can return a NaN (I've removed non-ASCII characters from this
snippet):
* Operations with a NaN as at least one operand.
(you need to bootstrap that somehow, so we can ignore this - it just
means that nan+1 = nan)

* The divisions 0/0 and infinity/infinity
* The multiplications 0*infinity and infinity*0
* The additions +inf + (-inf), (-inf) + +inf and equivalent subtractions
* The standard pow function and the integer exponent pown function
define 0**0, 1**inf, and inf**0 as 1.
* The powr function define all three indeterminate forms as invalid
operations and so returns NaN.
* The square root of a negative number.
* The logarithm of a negative number
* The inverse sine or cosine of a number that is less than -1 or
greater than +1.

Rather than having comparisons with NaN trigger exceptions, wouldn't
it be much cleaner to have all these operations trigger exceptions?
And, I would guess that they probably already do.

NaN has an additional use in that it can be used like a "null
pointer"; a floating-point variable can store 1.0, or 0.000000000005,
or "no there's no value that I'm storing in this variable". Since a
Python variable can contain None instead of a float, this use is
unnecessary too.

So, apart from float("nan"), are there actually any places where real
production code has to handle NaN? I was unable to get a nan by any of
the above methods, except for operations involving inf; for instance,
float("inf")-float("inf") == nan. All the others raised an exception
rather than return nan.

Chris Angelico