Re: Motion 19.02 NO

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Svetoslav Markov wrote:
>  
> My vote to motion 19.02  is "no".
>  
>   I would vote "yes" if either:
>  
>  a) the motion is modified so that an implementation 
> that supports only an implicit type is also conforming
>
>   b) the name of the interval arithmetic standard is 
> modified accordingly.
>
> Svetoslav Markov, IMI-BAS
>  
>   PS. Motion 19.02 makes a significant step towards the
> recognition of the "mid-rad" implementations as auxiliary to
> "inf-sup".  However, I think that "mid-rad only" arithmetic
> should also be conforming. Let me recall  the  two main 
> mathematical arguments  against  "mid-rad only"  support:
>  
>   1.  infinite intervals are not representable in mid-rad, and
>  
>   2.  when the midpoint of a (real) interval is exactly in the middle
>  between  two machine numbers, then mid-rad presentation is not unique.
>
>   I do not find these arguments sufficiently serious.

You grossly distort the argumentation against a mid-rad datatype.

The main argument against it is that there has been _extremely_ little
past use of mid-rad arithmetic on single intervals. (The only serious
use of mid-rad is for vectorized matrix-vector and matrix-matrix
multiply, and this application doesn't make use of a mid-rad interval
format, but does all computations by means of a midpoint matrix and a
radius matrix. So a standard on midrad intwervals would have no bearing
on this.