Re: Motion 8: Exception Handling for Interval Arithmetic
Arnold Neumaier wrote:
> Nate Hayes wrote:
>
>>> Or is there an interval portion of an NaI?
>>
>> Only if it is a decorated interval. For a bare decoration, it is
>> implied the interval portion is the empty set.
>
> The motion text says so. But in fact, this may give unwanted results,
> for example if the decoration implies isEntire or notBounded.
> I hadn't notice that before, so the caveat in 2.4 applies.
> Correct is the following formulation:
>
> 2.3. An operation on bare decorations returns the decoration of the
> possible results of the operation on consistently decorated
> intervals with the same input decorations if this is unique, and 0
> otherwise.
>
> We don't know which interval it came from, and don't need to know
> since for semantical consistency we must always return the worst
> possible interpretation.
> (Possibly things would work correctly if the interval portion
> would be Entire, except in case the decoration implies isEmpty.
> But this would need thorough checking.)
>
> I think there should not be a conversion from bare decoration to
> decorated interval. But the conversion from bare interval to decorated
> interval by adding the all-0 decoration (used in 2.4) is semantically
> valid, since all-0 always gives the worst case.
>
>
> In any case, it is clear that careful attention to the details is
> needed. I hope that some of the readers will check the semantical
> consistency of the motion.
I agree. I hope people will discuss and check, too.
Nate