Re: position paper on comparisons
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