Re: The current proposal
On Sun, 22 Feb 2009 18:22:00 -0100, Michel Hack <hack@xxxxxxxxxxxxxx>
wrote:
Siegfried Rump wrote, concerning whether intervals
should or should not contain Infinity as a number:
Imagine the question "What is the result of -0==0" is at stake.
NO, whether intervals should contain Infinity as a member is NOT the point!
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.
and
(2) [a,b] = hull(interval(a),interval(b)).
Both is very natural in interval computations.
My point is to START with PROPERTIES we wish to maintain, not
with solutions.
Such properties are (1) and (2), and also
(3) 0*A=0 under any circumstances.
This is a very nice property and an argument against Infinity
being a member of intervals. Another property is
(4) xx=interval(x) implies xx.inf==xx.sup.
This is also nice property and an argument against
interval(Infinity)=[realmax,Infinity].
IMHO, the properties (1), (2) are mandatory, (3) is important,
(4) is nice to have. Note that I am mainly speaking as a potential
USER of the interval arithmetic standard, not as an implementer.
If there is no acceptable way to maintain all properties (1..4)
we may think about workarounds and look for the best compromise.
Of course, the speed is important as well.
I would like to hear opinions from people working with interval
arithmetic what properties for them are mandatory, important or
nice to have.
Best wishes
Siegfried M. Rump
Imagine the question "What is the result of -0==0" is at stake.
Good example. There are indeed two ways to look at this, and each
is convenient for some things and inconvenient for others. So 754
picked the one that seems most convenient for most cases -- but ALSO
provides the totalOrder() predicate to accomodate the other cases.
Incidentally, if they/we had made the other choice (-0 != +0), there
would have been a branchless way to compute (x==y) in the (-0==+0)
sense -- i.e. without undue performance penalty: ((x+(+0))==(y+(+0)).
So, with respect to IA, when the decision to chose whether or not
standard intervals can contain infinities comes up for a vote, we
should try to make sure that there are viable constructs to deal
with cases that would have preferred the other approach.
Michel.
Sent: 2009-02-22 19:39:22 UTC
--
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
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and
Visiting Professor at Waseda University
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