Re: midrad representation
Since there is no one second this motion, I am withdrawing the motion to avoid any possible confusion.
Chenyi Hu
>>> Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> 2/26/2009 10:30 AM >>>
Chenyi Hu wrote on 2009-02-10 in ''the "set paradigm" is harmful''
> Yes, as Baker suggested, I would like to make the motion as the follow:
>
> An interval can be represented in two ways in the IEEE-1788 standard. One of them is its lower and upper bounds as [inf, sup]. The other is its midpoint and radius as {M, R}. When the rounding error is ignored, the transformation between these two representations are: M = (inf + sup)/2, and R = (sup - inf)/2; and inf = M - R. and sup = M + R. To ensure enclosure property in the [inf, sup] form, transformation from {M, R} form to [inf, sup] form must consider rounding mode properly in implementation.
>
> ==============
>
> The rationales for this motion have been discussed lately and in Baker's comments.
I think it is poor style, potentially causing difficulties, if
votes on such important basic decisions are done without a
document specifying at least one reasonable version of what is
the proposed alternative.
Otherwise, the voters will have to buy a pig in a poke since they
don't know the effect of their voting yes.
So far, none of the promotors of midrad arithmetic has given a
definition of what is meant by it.
The only widespread practical use is for speed in Intlab's matrix
computations, but he converts each time from the infsup representation,
and back after the operation is done. The scalar mode is always
performed in infsup arithmetic. Since we do not discuss matrix
operations in the standard, this use has no consequences for the
standard itself.
Moreover, in the Intlab implementation, the _centered_ midrad arithmetic
is used, _not_ the version I can see in the publications of Markov,
and in my book on interval analysis.
The Vianna proposal supports conversion to and from midrad
representation but does not support operations with midrad intervals.
Just to caution you of what to expect if you decide otherwise:
With midrad arithmetic allowed as a second representation on equal
footing with the infsup representation, a lot of extra work is needed
to make all definitions unambiguous. It will almost double the size
of the standard, since most issues need a separate formulation
for midrad and for infsup.
Arnold Neumaier