[IEEE P1788 er subgroup]: Empty set and NaI (not-an-interval)
Nate Hayes wrote:
> The reason this question matters is because, depending on
> if sqrt([-2,-1]) is treated as "empty" or undefined, one
> may obtain two different results in the context of a larger
> interval expression:
> ...
As Dan pointed out, using NaI here conflicts with another rule,
namely that input intervals should be deemed intersected with
a function's domain. What should sqrt([-1,4]) be? What about
sqrt([-eps,+something]) where the argument was computed, and
is essentially positive, except that the lower bound is slightly
negative due to rounding error accumulation?
In the Vienna proposal, the PossiblyUndefined flag can be used to
distinguish Empty due to a completely negative sqrt argument
from an explicit Empty intersection -- if you can stomach flags.
(Ideally the flags should be attributes attached to the result,
but that is a whole other issue which I hinted at in some earlier
posting. It makes sense when intervals are already complicated
structures, e.g. in a variable-precision context, but probably not
for run-of-the-mill intervals that one wants to store compactly.)
Michel.
Sent: 2009-03-22 02:13:20 UTC