Re: Re-submission of motion 5: multiple-format arithmetic.

[Ulrich Kulisch <Ulrich.Kulisch@xxxxxxxxxxx>]

Dominique Lohez schrieb:
> Ulrich Kulisch a écrit :
> > Dominique Lohez schrieb:
> > > Ralph Baker Kearfott a écrit :
> > > > Arnold Neumaier wrote:
> > > > > Nate Hayes schrieb:
> > > > > > John Pryce wrote:
> > > > .
> > > > .
> > > > .
> > > > > > > I believe nothing in this motion and rationale hinders the
> > > > > > > implementation of various forms of non-standard intervals -- Kahan,
> > > > > > > modal, etc. -- as discussed at the end of Vienna/1.2.
> > > > > >
> > > > > > I've mentioned before this is simply not true. If traps or flags 
> > > > > > are only
> > > > > > way to obtain NaI result from an interval operation such as 
> > > > > > 1/[-2,3], this
> > > > > > is hinderance to efficient modal interval implementations.
> > > > >
> > > > > This is another eason why modal intervals should not be part of
> > > > > the standard. It makes the latter unnecessarily complicated,
> > > > > only to introduce an error-prone technique that can be safely handled
> > > > > only by a tiny minority of users.
> > > > >
> > > > > Not deciding this issue (modal or not) very soon will constitute a
> > > > > major quarrel in each issue to be decided.
> > > >
> > > > Does someone wish to formulate and formally put forward a
> > > > simple motion to decide whether or not the standard should
> > > > explicitly contain specifications for modal arithmetic?
> > > >
> > > > Baker
> > > My opinion is that a decision in favor or against the inclusion of a 
> > > explicit mention of modal intervals should be delayed
> > >  until the following points are elucidated
> > >
> > >             1) The motion 3 states that
> > >                                     - the intended number set is R 
> > > and not R*
> > >                                      - the intervals are the 
> > > connected  closed subset of R
> > >                     However no method was given to handle  
> > > calculation with infinite bound intervals.
> > This is the reason why I supplied the proposal "Atithmetic operations 
> > for floating-point intervals". I attach it again, although it will be 
> > reformulated due to arguments by Arnold Neumaier.
>
> Ok . This is a fine answer  to some of my questions.
> It explain clearly how starting from  an arithmetic over IR on can 
> reach an arithmetic over IF and finally (IF)
> However th path from IR to (IR) and consequently (IF) is missing.
The formulas for the operations in IR and (IR) are the same as those 
shown in the tables. The operations are just performed without the 
rounding symbels 'nabla' and 'delta'.
Best wishes
Ulrich Kulisch

> I think that considering this point carrefully  may of crucial 
> importance to allow significative improvement of the performances of  
> interval algorithmS
>
>
> > >                      IMHO searching for such methods would provide 
> > > a  natural way to introduce modal intervals simply as a feature of 
> > > the the mathematical required background.
> > >                      This could obviate the otherwise meaningful 
> > > argument of  Arnold Neumaier.
> > >                       I intended to propose a position in two weeks. 
> > >                       However , owing to the evolution of the the 
> > > discussion , I feel the need to send this summary of my position.
> > >
> > >
> > >           2)From a mathematical point going from uncountable sets of 
> > > numbers and  intervals to finite such sets is a dramatic change.
> > >               This change should be   carefully studied before 
> > > detailed considerations of    some specific  computer representations.
> > >               Further arguments in favor of  modal intervals might  
> > > arise from this study.
> > >
> > > Dominique LOHEZ
> >
> > Best wishes
> > Ulrich Kulisch