Re: mid-rad, inf-sup, a caution...
Svetoslav's defense of mid-rad is written entirely from the
point of view of "imprecise numbers", and not the more general
one of intervals (which, as I keep saying, have TWO DIFFERENT
mental models behind them). Indeed, he says so explicitly:
> - the FP standard for midpoint is available, it only needs
> to be extended and completed so that the concept of an
> FP-number is extended to the concept approximate number
> (which is actually an interval).
This affects the types of operation to be supported, and their
precise definition, as Arnold has pointed out already.
The really nasty part here is that there is no obvious cutoff
between narrow intervals (which might represent imprecise numbers)
and wide intervals (which frequently represent subdomains).
In the case of infsup, all operations, including reverse and set
types, and be defined precisely and uniquely. Some may only be
appropriate for one or the other of the two mental images I've
been talking about, but that does not affect their definition.
If midrad were a primary interval type of the same nature as BFP
vs DFP in 754, nearly *every* operation would have to be defined
for both in a logically-uniform manner. There is an escape, in
that 754-2008 does define certain operations explicitly for DFP
only, and that DFP brings one additional concept to the table
that is not applicable to BFP, namely "preferred quantum" or
"preferred exponent" (and the notion of "cohort"). I'm not
sure however that this approach would work for midrad vs infsup.
The issue of midrad interchange formats is separate from that of
first-class support, and can be decided independently either way.
The basis for this decision would be usefulness and agreement on
a well-defined set of representations, perhaps tied to the format
used to represent the midpoint.
One word of caution with respect to using a lower-precision format
for the radius: lower precision usually brings with it a smaller
exponent range -- and that can be a problem, because it would
effectively limit the exponent range of the midpoint too. The
triplex format avoids this by effectively specifying a third and
effectively unrestricted exponent.
Michel.
---Sent: 2010-05-11 13:41:45 UTC