Re: Motion 8: Exception Handling for Interval Arithmetic
Nate Hayes wrote:
Or is there an interval portion of an NaI?
Only if it is a decorated interval. For a bare decoration, it is implied the
interval portion is the empty set.
The motion text says so. But in fact, this may give unwanted results,
for example if the decoration implies isEntire or notBounded.
I hadn't notice that before, so the caveat in 2.4 applies.
Correct is the following formulation:
2.3. An operation on bare decorations returns the decoration of the
possible results of the operation on consistently decorated intervals
with the same input decorations if this is unique, and 0 otherwise.
We don't know which interval it came from, and don't need to know
since for semantical consistency we must always return the worst
possible interpretation.
(Possibly things would work correctly if the interval portion
would be Entire, except in case the decoration implies isEmpty.
But this would need thorough checking.)
I think there should not be a conversion from bare decoration to
decorated interval. But the conversion from bare interval to decorated
interval by adding the all-0 decoration (used in 2.4) is semantically
valid, since all-0 always gives the worst case.
In any case, it is clear that careful attention to the details is
needed. I hope that some of the readers will check the semantical
consistency of the motion.
Arnold Neumaier