Re: RoundToZero(+Inf) and Mid(semi-bounded interval)
On 2012-03-01 11:17:33 -0500, Michel Hack wrote:
> Vincent Lef?vre replied to me:
> > No, roundToZero does not apply to entire operations (this makes no
> > sense), but to unrounded results. Here the unrounded result mid(X)
> > is +inf, because at Level 1: ...
>
> Well, IEEE 754 rounding DOES apply to entire operations. FormatOf()
> operations and elementary functions are supposed to round only at the
> end, when coercing a result to the target format.
What I mean is that IEEE 754 rounding gives a specification on
a Level 1 value, not on an operation. What operations are used
before rounding doesn't matter. Based on this fact, see my other
answer on Mon, 5 Mar 2012 16:27:11 +0100, where I explain why it
is not possible to get rid of Fmax_F or any equivalent expression
related to Level 2 (without changing Level 1).
> Now -- how can we rephrase Dan's mid() definition to reflect our intent?
> Of course, if we follow Arnold Neumaier's approach instead this issue
> would not arise. (For Arnold the unbounded intervals have NO midpoint,
> or rather, no unique midpoint, so he suggests returning NaN.)
I would be OK with Arnold's proposal as well (which was also mine
initially, BTW).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)