[std-interval] More on interval computations as proofs

Lawrence Crowl Lawrence at Crowl.org
Thu Oct 5 12:08:40 PDT 2006

On 10/5/06, Guillaume Melquiond <guillaume.melquiond at ens-lyon.fr> wrote:
> Le mercredi 04 octobre 2006 à 16:29 -0700, Lawrence Crowl a écrit :
> > My understanding is that interval computations tend to require
> > some rewriting anyway.  That is, straightforward translations of
> > plain floating-point computations tend to have wide intervals.
> > Am I mistaken?
> So, to qualify your point on straightforward translation, I would say
> that you are right for resolution algorithms (finding roots, solving
> differential equations, and so on), as they simply won't work. But for
> evaluation functions, you don't have to rewrite them. Just change
> "double" to "interval<double>", and the interval resolution algorithms
> will take care of these evaluation functions.

That is good news.

The question still remains though whether adding and explicit
bool ref parameter to the division operations (et.al.) will be a
significant additional burden in changing an evaluation function
from float to interval.  If the burden will be significant, and
these functions are defined to modify some thread-local state,
then compilers will do less optimization around them.  It is up
to the interval experts to make that choice, so having stated the
consequences, I will abstain.

Lawrence Crowl

More information about the Std-interval mailing list