Re: position paper on comparisons

[Jürgen Wolff von Gudenberg <wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx>]

P1788
  please find attached our position paper extended by Tables that 
calculate the Fortran 95 interval relations with the help of our 
overlapping relation.
Although we like our approach with the 14-valued result type, we will 
support a more traditional interface. We think the best choice are the
7 interval comparisons (brought into discussion by  Nate Hayes)
=, interior, \subseteq, pred , \predeq , less , \leq
together with the 4 lattice operatons from motion 13.
These can be efficiently implemented in hardware and are somehow basic 
for the others.
Perhaps we can use operation names for the strict comparisons and 
operation symbols for those including equality to avoid problems with 
familiar relations that do not hold here
Juergen

Jürgen Wolff von Gudenberg schrieb:
> Baker, Svetoslav, P1788
> When we started work on this position paper, we tried to single out 
> interval relations that play a fundamental role in generating all the 
> many interval comparisons. Our goal was a minimal set of independent 
> floating-point comparisons, that can be executed in parallel. We further 
> wanted to separate all 13 cases in table 2.
> table 2 displays the relative positions of 2 intervals with respect to 
> overlapping. In English I call that the interval overlapping relation, 
> you are right, however, in mathematics it is a mapping.
>
>
>
> Svetoslav Markov schrieb:
> > 2. It seems to me that your position paper concerns
> > implementation layers 3 and 4, is this correct? If so,
> > your position paper has little or no impact on Motion 13, is this so?
> This is correct. Our approach describes an alternative implementation of 
> the operations listed in motion 13
> > I think that  your position paper would become more useful, if it 
> > includes:
> >
> > i)  a presentation of all order relations enlisted in
> > Table 2 by means of the four basic order relations as
> > given in Motion 13 (improved by remarks made by Nate
> > Hayes and Michel Hack);
> more interesting will be to show that the comparisons of motion 13 and 
> those added by Nate in his  comment, can easily be computed with our 
> mapping
> > ii) an alternative approach for implementation that is based on 
> > Kulisch's four basic order relations;
> and more than that we can implement the Fortran 95 comparisons
> > iii) a comparison beween the two approaches  w.r.t. effective 
> > implementation.
> Since dependent comparisons are very common in applications we think 
> that we'll have an advantage here. That has to be checked
> >
>
> To conclude
>  -  the position paper presents a way of implementation of interval 
> comparisons and lattice operations.
>  -  it provides appropriate building blocks
>  -  the API , however, is new and different from the usual
>  - the impact on motion 13 is marginal
>  - It gives a good overview of relations between various sets of 
> comparisons.
> - We will prepare a version with explicit tables to improve the last point.
>
> regards
> Jürgen

Attachment: overlapping.pdf
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