Re: mid-rad representation

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Paul Zimmermann schrieb:
> I have read with interest the latest discussions on inf-sup vs mid-rad
> representation.
>
> Although I strongly agree that P1788 would fail if it would standardize
> too many different representations or encodings of intervals, I see one
> argument in favor of mid-rad representation which has not been mentioned
> before.
>
> When working with variable precision and narrow intervals, inf-sup
> requires two values of large precision, 

See the remarks on variable precision interval arithmetic in Section 1.6
of the Vienna proposal. The recipe given there preserves the advantages 
you describe below without restricting the use of such an arithmetic to 
very narrow intervals.


> whereas with mid-rad the
> radius might have a very small precision (typically a few bits).
> This will give a speedup of a factor 2 to 4 depending on the operation.

Only for very low precision, which is probably inferior in speed to 
using ordinary double interval arithmetic.

Once the precision is high (say 50 decimal digits or more), the
cost of handling the interval part is small compared to the cost
of the precision part.


Thus there is no need for a separate midrad arithmetic.


Arnold Neumaier