Re: The current proposal
Siegfried M. Rump schrieb:
The point is that always, without case distinction, the following
should be true:
(1) For a given function F, for example, X=F(interval(A.sup)) should
give an
inclusion of the value of F at the right bound of A.
Always???
This value is not even properly defined in many cases,
such as when F(x)=x-x or F(x)=(x-1)/(x+1) and A=[0,inf].
and
(2) [a,b] = hull(interval(a),interval(b)).
Both is very natural in interval computations.
According to the Vienna Proposal, both desires are essentially
achieved with a slightly different syntax:
(1') X = F(isup(A)) returns for all continuous F an inclusion
of lim_{x->A.sup} F(x).
(2') B = convexHull(iinf(A),isup(A)) always returns B=A
even though interval(inf) = Empty, so that your original
constructions don't work correctly.
But writing (1') and (2') is much nicer anyway, and also avoids
nasty issues for cases when the bound representation and the
float representation differ, and interval(A.sup) may have problems,
for example if A is an interval in midrad representation with
radius less than one ulp.
Arnold Neumaier