Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

John,
> On 10 Sep 2009, at 12:25, Arnold Neumaier wrote:
> > Dan Zuras Intervals wrote:
> > >     If we are to pursue this at this time, please include accurate
> > >     versions of all of sum, dot product, sum of squares, & sum of
> > >     absolute values for all supported precisions.
> > ...
> > I think only interval-valued results for noninterval inputs should be 
> > provided by the standard. Then there are no problems.
> >
> > If some element is NaN or two terms in the sum are +inf and -inf,
> > the result should be the empty set; otherwise the tightest enclosing
> > interval of the exact result should be returned.
>
> Am I missing something? Suppose we implement as you say, 
> "interval-valued results for noninterval inputs", and just ONE term of 
> the sum is, say, +inf, the rest being finite numbers. Then the result is 
> +inf, but since P1788 is based on the reals, there is no interval that 
> encloses this. What to do?

In the spirit of the Vienna proposal, the (possibly decorated) empty
set. I didn't notice that before; this makes things even simpler.

In any case, if the vector has length 1, the result should be the same 
as for converting a float datum to an interval. Whatever the result of 
converting a single inf or NaN will be decided upon, that must be the 
result of a sum that evaluates exactly to NaN or inf.


Arnold Neumaier