min / max and empty intervals (was: Friendly amendment to Motion 25)
On 2011-05-28 17:44:36 -0700, Dan Zuras Intervals wrote:
> > From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> > To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
> > Subject: Re: Friendly amendment to Motion 25
> > Date: Sat, 28 May 2011 18:25:23 -0500
[...]
> > From discussions I've witnessed between you and Nick, I gather
> > that in IEEE 754 the correctness of such a result is topic of a
> > longstanding debate. I'm not taking sides as it pertains to IEEE
> > 754. In regards to IEEE 1788, though, this would certainly lead to
> > failure of certain important interval algorithms. So just to be
> > clear: the description given in Motion 25 is really designed to
> > ensure the result of interval min and max is empty if at least one
> > operand is empty, just as it is for addition.
>
> I understand but disagree.
>
> Still, that might not be a problem. Given that it has
> no relation to the rest of your motion, may I suggest you
> remove references to min & max so that we may have this
> discussion at some later date & avoid needless conflict
> with the rest of your motion.
I completely agree with Nate here. I think that min and max should
first be seen as functions over the real numbers (thus necessarily
2-ary, at least with a fixed ariness). On sets of numbers, this
would mean:
min(X,Y) = { min(x,y) | x in X, y in Y }
Thus if X and/or Y is empty, min(X,Y) is empty.
One could define min and max on lists of intervals, but this would
be out of the scope of the standard because there would be too many
generalizations.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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