Re: Motion 6
On 2009-09-21 12:41:12 +0200, Arnold Neumaier wrote:
> Vincent Lefevre wrote:
> >On 2009-09-21 10:41:07 +0200, Arnold Neumaier wrote:
> >>The little difference may be decisive, though, for example when
> >>checking algebraic numbers for their sign, using multiprecision
> >>arithmetic. x in 1e-10000 + [0,Inf] encodes sign information,
> >>which is lost when going to midrad.
> >
> >Yes, but such kind of application (where intervals can be very
> >large), you should use infsup. Don't use midrad if your application
> >is not suited for midrad.
>
> I had thought it was you who had been recommending midrad for
> rigorous multipresicion calculations.
No, I'm not recommending midrad for every multiprecision applications.
I'm saying that the standard should *not exclude* midrad. Then the
user could choose the representation (when midrad is available) that
is best for his application, just like the user needs to choose the
floating-point format (radix and precision) that is best for his
application. By default, it could be infsup, because it works in
most cases. The goal of midrad is only for performance in some class
of applications (a factor of almost 2 is quite important IMHO).
See this a bit like the possibility of using a FMA for expressions
like a * b + c in floating-point arithmetic: this can introduce a
difference in the results, even give unexpected results[*], but this
is faster and in general it allows to get more accurate results.
[*] http://www.vinc17.org/research/fptest.en.html#contract2fma
One application is to perform approximate computations in high
precision and get an error bound to validate the approximated results.
I'm currently using infsup for that, not because it is thought as
being better, but because it is the only one available (at least at
the time I searched for an interval arithmetic package).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.org/blog/>
Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)