Re: Multi-precision (was...Please give me advice)
This discussion again suffers from the one-sided view that intervals
represent uncertain numbers.
When intervals are used to express ranges of values, the concept of a
midpoint frequently doesn't even make sense. Why should the arithmetic
mean of the endpoints be significant? In many applications (e.g. large
ranges of physical values) the geometric mean makes more sense. If the
computation involves both logarithmic and linear transformations, the
point of view changes within one sequence. And when the bounds are
themselves uncertain, the absolute uncertainty is likely to be very
different for the two bounds.
So the inability of mid-rad to express a semibounded domain is only ONE
of the tripping points.
I see issues even when talking about uncertain numbers, when mid-rad is
used in a finite-precision setting. Should the radius be relative or
absolute? If absolute, and one wants to take advantage of lesser
precision in the radius, should the exponent range of the midpoint be
artificially restricted to that of the radius? (With most FP formats
the exponent range shrinks with precision.) It is the fact that there
are multiple different but equally reasonable alternatives that are an
obstacle to premature standardization, in my opinion. (Note that these
issues are much more tractable at the level of text intervals, which is
why the Vienna Proposal has no difficulty in supporting both absolute
and relative mid-rad text formats.)
Michel.
---Sent: 2010-10-15 10:59:52 UTC