double double (was: Re: Motion 4 ...)
Dan Zuras brought up the strange possibilities raised by the double+double
method of extending precision.
First of all, the format can be used with discipline, where results are
consistently rounded to 106 bits of precision. When that is done, the
issues disappear, or rather, reduce to keeping constructors well-behaved,
a situation we face already with interval constructors.
Second, the uneven-density property is shared with MidRad intervals,
where again it could possibly be kept under control by restricting the
range of a non-zero radius.
The whole thing brings up an interesting philosophical issue about the
meaning of singleton intervals, because those share the property of
being very selective as to which singletons can be represented. The
rationale is of course that this restricted set includes mathematically
meaningful entities such as small integers. With BFP, one may be able
to make a case for dyadic rationals, and with DFP, for numbers that are
of interest to people or financial regulations.
Michel.
---Sent: 2009-04-13 16:07:36 UTC