Re: A proposal for the next motion
On 2009-05-13 13:18:27 -0400, Nate Hayes wrote:
> > - Example. With these definitions
> > xx*{0} = {0} and xx/{0} = Empty for any nonempty interval xx.
> > - All interval functions used here are automatically defined for all
> > arguments (e.g. sqrt([-1,4]) = [0,2], sqrt([-2,-1]) = Empty). It is left
> > open what exceptional action may be taken by an implementation on
> > evaluating ff(ss), when ff is an extension of a point function f, and
> > ss is not a subset of D_f.
>
> These interpretations are not compatible with modal intervals.
>
> By default, they should be:
>
> sqrt([-1,4]) = NaI
> sqrt([-2,-1]) = NaI
>
> where NaI simply means "undefined" or "invalid operation," so that the NaI
> will be guaranteed to propagate through the remainder of a lengthy
> computation.
I disagree that one should get NaI in such cases. There may be a
"possibly-invalid" flag either associated with the returned interval
or global (to a block or whatever) to propagate this information if
need be.
> If users are interested in the c-set conventions, they can explicitly
> intersect the interval argument with the natural domain of the function,
> i.e.:
>
> sqrt([-1,4]&[0,+oo)) = sqrt([0,4]) = [0,2]
> sqrt([-2,-1]&[0,+oo)) = sqrt({empty}) = {empty}
This is not acceptable. In particular, what would you do if the natural
domain of the function is not an interval or is an interval having an
endpoint that is not an exactly representable number?
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)