Re: Midpoint and unbounded intervals
> The radius = width/2 may not work in DFP .
> Suppose precision of two decimal digits.
> width(0.1,10) = 9.9 - can be represented exactly
> width(0.1,10)/2 = 4.95 - can't be represented exactly
True -- but neither must width be exact if the magnitude of one endpoint
is more than double that of the other, in BFP as well as DFP.
You are correct that in DFP width could be exact, but rad inexact.
For BFP that only happens for subnormal endpoints.
> 1) Should midRad(), mid(), rad() be consistent
> midRad(x) = ( mid(x), rad(x) ) ?
Meaningful only if there is a midrad type (an "implicit" type).
The question is, how much should 1788 say about implicit types,
beyond the requirement that they have a well-defined hull operation?
> 2) Should we expect the following containment for bounded intervals:
> x C= [ mid(x) - rad(x), mid(x) + rad(x) ] ?
(I assume that the to-me-unreadable thingy was \subset_or_equal symbol.)
This only works for outer_rad(), i.e. rounded up. For round-to-nearest
radius this could fail for 2-digit DFP [0.3,10] with mid=5.2 and rad=4.8
(rounded to even from 4.85), but outer_rad=4.9 would be ok.
With inner_rad() we could claim the reverse containment.
Michel.
---Sent: 2012-01-25 21:30:03 UTC