Re: Bare decorations (was ...level 2 datums)
On 2010-11-02 02:16:24 -0700, Dan Zuras Intervals wrote:
> Vincent,
>
> While I do not agree with this approach to bare
> intervals & bare decorations, I think Nate is
> generally going in the right direction to treat
> bare decorations as a flavor of NaI that is
> generally NaI preserving.
>
> You are also correct in that there will be some
> minor exceptions. Some hypot cases are one.
> Some selection functions are another. We may
> have max([al,au],<bare_decoration>) want to be
> the interval or we may want it to be [al,+inf].
> Just as we may want max(interval,empty) to be
> the interval. I'm not sure yet. There may be
> some subtlties I'm missing.
With intervals, we would have both Empty/Entire and NaI, while IEEE 754
just has NaN. So I think it would make more sense and would be safer if
we had no exceptions concerning the NaI propagation. Now, I don't know
the implications on practical applications.
If there were an analogy we could make, I'd say that Empty and Entire
would be close to qNaN and NaI would be close to sNaN. Indeed a qNaN
can occur:
* [Empty] when one writes something that doesn't make sense,
e.g. sqrt(-1.0), i.e. something that could be seen as having
no solutions;
* [Entire] due to a succession of rounding errors on a mathematical
expression that makes sense (one gets a NaN and doesn't know
anything about the real value).
(Note: this is not exhaustive, Empty and Entire can have their own
meaning...)
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)