Re: (forwarded for Michel Hack): Re: complex intervals
thank you Michel for your detailed answer.
> One other minor point (also discussed here recently):
> > whereas the "mid-rad" representation needs only n+1 values
> > (where the "+1" can have lower precision for tiny intervals).
>
> With most floating-point formats (not IBM's old HFP) lower precision
> brings with it a smaller exponent range. That would limit the exponent
> range of the midpoint too: outward rounding would blow up intervals to
> obscene widths, possibly the almost useless Entire. Arnold Neumaier's
> triplex format, with a separate scaling component, is needed to deal
> with this issue. Ok, so it would be n+2 and not n+1...
I did not have in mind a fixed-precision format, but an arbitrary precision
one, where usually there is no tight restriction on the exponent range.
Please make sure the P1788 standard does not forget about variable or
arbitrary precision!
Paul Zimmermann