Re: Proposal for a new structure of the standard
Nice work. A few comments:
* Does IDBar have to be a finite set? This doesn't seem to be really
useful and that would rule out some implementations, such as
intervals of GMP integers, for instance.
* IMHO, the definition of the hull should not be required. It seems
to be useful only for the tighest arithmetic, and the standard
shouldn't require things that are not used. One question is: do
we wish to allow arbitrary precision, where the precision would
be determined more or less dynamically? That would make sense
with the "valid" version.
* Should there be a notion of internal and interchange idatatypes?
* I don't think reproducibility is necessarily important (at least
for all applications). The standard should not require it, only
recommend it. If one really wants a good (but somewhat slower)
implementation with the best properties, one should use the
tightest arithmetic, and reproducibility would be implied.
Note: Interval arithmetic is not designed to detect bugs in the
processors. And if the goal is to check the results because of
possible bugs somewhere, there may be other (better) ways to check
them than rerunning the same program on a different platform.
Indeed, by doing that, one will not detect bugs in the program
itself. So, one may want to run a different algorithm on a
different platform, and since the algorithm is different,
reproducibility no longer matters.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)