Re: [IEEE P1788 er subgroup]: Kaucher intervals (Was: Undefined behaviour (Was: ...))
Dear Vladik,
I think the general opinion is NOT to expand our standard to Kaucher
intervals, because this will be too much work.<<
I believe it can actually simplify the standard by reducing the number of "implementation defined" and "undefined behaviours" that would otherwise be required.
Let us therefore not go into expressions with Kaucher intervals. In
contrast to well-defined and well-studied regular interval expressions,
expressions with Kaucher intervals are a subject of ongoing research.
There are some useful applications (Shary etc.), but the topic is still
very far from being ripe for standardization.<<
We find very practical uses for the Kaucher arithmetic in our interval computer graphics rendering software, which we hope will be a commercial product very soon. We are also developing a Kaucher interval processor to accelerate our
computer graphics applications.
I believe (and recommend) the topic of including nonstandard intervals in 1788 can be delayed until the dust settles on other issues. But I hope near the end of the standardization process the P1788 group would consider including the
Kaucher intervals. I do not believe it would be as difficult as some people think.
Sincerely,
Nate Hayes
Sunfish Studio, LLC
-----Original Message-----
From: owner-stds-1788-er@xxxxxxxxxxxxxxxxxxxxx
[mailto:owner-stds-1788-er@xxxxxxxxxxxxxxxxxxxxx] On Behalf Of Michel
Hack
Sent: Tuesday, March 17, 2009 7:56 AM
To: stds-1788; P1788 ER subgroup
Subject: [IEEE P1788 er subgroup]: Kaucher intervals (Was: Undefined
behaviour (Was: ...))
It would have helped if early on we had seen a concise, though perhaps
incomplete, description of Kaucher intervals, as Baker just gave. Not
even the paper that Nate pointed us to was that clear, one had to guess
it from the way they were used.
So: a Kaucher interval is an interval with Lower and Upper bounds,
always non-empty, with an additional flag that directs how the bounds
are to participate in monotonic arithmetic. This is useful in cases
where backwards containment needs to be calculated. (The mode flag is
encoded in the order in which the two bounds are given in the interval
representation, because that leads naturally to the desired effect, at
least in common cases -- or does it always work, obviating the need to
test the "flag"?)
Critical in the context of the Expression-Rearrangement subgroup is
how much knowledge of applicability of Kaucher rules is needed when
expressions are transformed.
Also -- how is Empty handled in Kaucher Arithmetic?
Finally -- is "Infinity as a Member" decided one way or the other in
Kaucher Arithmetic, and if not, are the issues similar?
Michel.
P.S. I started using "KA" -- but that could be misinterpreted as
"Kahan Arithmetic". Would "MA" for "Modal Arithmetic" work,
leaving "IA" as the generic term for Interval Arithmetic?
Sent: 2009-03-17 14:05:27 UTC