Re: Discussion about accuracy modes
Sorry, this is a bit old, but I've now had some time to think
about that...
On 2010-08-24 16:36:26 -0700, Dan Zuras Intervals wrote:
> > From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> > To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
> > Cc: "P-1788" <stds-1788@xxxxxxxxxxxxxxxxx>
> > Subject: Re: Discussion about accuracy modes
> > Date: Tue, 24 Aug 2010 14:46:32 -0500
>
> Vincent,
>
> Care to join us for a swim?
>
> The waters are friendly today.
>
> Specifically, would you care to opine on how we might
> specify the behavior of potentially infinite interval
> datatypes?
Well, if the precision of the output is determined dynamically,
"tightest" or "accurate" modes don't make sense.
Note also that even with a fixed precision (or if the target
precision is specified by the user, such as in MPFR), then
"tightest" or "accurate" modes may not be practically possible:
if the range is huge (such as in MPFR or in DPE), trig functions
can't be evaluated on very large arguments in a reasonable time
and with a reasonable amount of memory.
So, I think that there is a class of applications where only the
valid mode would be useful for practical reasons.
Now, assuming that the internal representation is unspecified or
implementation-defined, the standard doesn't have to talk about
mid-rad or similar formats, as such a format could be seen as
a particular implementation of an inf-sup format in valid mode
with a sufficiently high precision (except that the internal
representation would typically use a smaller precision). Note
that with such a format, a function to retrieve the bounds
exactly could be implemented, but may be useless in practice,
as the bounds could require a huge precision; or such a function
could be called after another function that reduces the precision
(typically a conversion function).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)