Peter Shenkin wrote:

>I'm not up on all the requirements of interval arithmetic
>(though I know what it is :-) ).  Nevertheless, I'd like to make
>the following observations, which are along the lines of Clive's
>note.

I am of a similar persuasion.

>1.  Interval arithmetic is of interest to a tiny part of the Fortran
>    community.  Incorporating interval arithmetic, per se, into the 
>    standard would be a waste of time for compiler implementers and 
>    probably has already been such for the standards committee.

Very much agreed.  BLAs, LAPACK, etc. are being provided as optimised algorithms 
by vendors.  Many of the BLAs 1 routines are now part of F95, but possibly 
accidentally because of the array notation.  Interval arithmetic could be part 
of such a vendor library, but **NOT** part of the Fortran standard.  We are 
moving the vendors into *iffy* areas of maths which are not always required.  My 
field does not require it.  To me it is a spurious academic area and I prefer to 
follow academicians who are involved in my field within maths of sparse 
techniques.

Someone might prove otherwise, but I see little application of interval 
arithmetic for me, possibly many other people in industry or government, so why 
make it part of the standard?

Use of interval arithmetic implies to me that the inputs are accurate -- not 
very often the case.  In electricity transmission planning problems we are 
conjecturing the demand at various substations several years hence.  The 
accuracy implied by interval arithmetic is nonsensical.

>2.  However, facilities that are lacking in Fortran that would be
>    useful for interval arithmetic as well as other things should be
>    seriously considered.  One is support for the required rounding
>    modes.  But this should be done in a general way, not in the
>    context of a special interval arithmetic facility.

The point I pick here is that rounding modes should be portable -- a la IEEE.  
They would be of use for interval arithmetic, but more useful for the general 
problems that many of us experience.

>3.  I disagree strongly with Keith's assertion that one needs to be
>    able to provide "the desired syntax".  Fortran should continue to
>    determine syntax based on broad utility for lots of things.  A
>    special syntax for interval arithmetic would be a waste of time
>    to specify and implement for any but the tiny community for whom
>    this is an issue.

Yes, and for something that is less than useful for our community, a syntax was 
withheld for a potential (but useless) feature.  I think it was Jan Vorbrouggen 
(sp., I apologise) who raised the issue of a current better usage in a recent 
thread on comp.lang.fortran.

>4.  OTOH, optimization (per Keith) is another question.  Like rounding
>    modes, careful consideration should be given to *general* facilities
>    which could be added to Fortran to allow useful packages like
>    interval arithmetic to be efficiently implemented as modules, or 
>    classes, or whatever the hell we're going to have in the next standard.

For the small, probably academic cases where interval arithmetic will help write 
papers, is optimisation really an issue?  Sparse arithmetic is a damned sight 
more important issue regarding efficiency to me.

Regards, Paddy

Paddy O'Brien,
System Planning,
TransGrid,
PO Box A1000, Sydney South, 
NSW 2000, Australia

Tel:   +61 2 9284-3063
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