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Re: Motion 6

Paul Zimmermann wrote:

       Dear Arnold,


How about a different motion that would generalize Motion 6 to
support midrad and other interval sets? (But some concepts, such
as the tightest FF-interval, would no longer exist.)

I'd prefer a motion to exclude midrad from consideration.
We have more than enough to do for infsup, and most considerations for midrad are completely different than those for infsup, so that virtually everything done for infsup would need to be reconsidered carefully. 
As a result, the work load would nearly double.

Nobody in practice uses midrad as a basic representation,
except for input/output, where only the conversion behavior
needs to be specified, but not the arithmetic.


this is wrong. The iRRAM package (http://www.informatik.uni-trier.de/iRRAM/)
uses the midrad representation with 'mid' in arbitrary precision and 'rad'
in fixed precision. See Section 5 (Simplified Interval Representation) from
http://www.informatik.uni-trier.de/iRRAM/irram.ps.
OK. I was thinking of midrad intervals made from floats when I made this statement. So far, 1788 was only concerned with 758-compatible represntations (though formally more general), and I think this restriction is very appropriate. 



Midrad arithmeitc is used only (in Intlab) as a speedup mechanism
on the BLAS3 level, and doesn't need special standardization.
Moreover, putting BLAS2 and BLAS3 considerations into the standard
seems to me inappropriate.


I agree that in fixed (say double) precision, midrad might not be superior.
But in arbitrary precision, you get a speedup >1 by using different precisions
for 'mid' and 'rad'. Thus excluding midrad from P1788 might exclude de facto
efficient applications using arbitrary precision arithmetic.


For rigorous multiple precision calculations, a triplex representation
is far superior in this respect, as - unlike a midrad representation -
it degrades gracefully when the interval gets wide, and allows the representation of intervals like [1,inf], which the midrad 
representation doesn't.


Arnold Neumaier