Re: Motion P1788/M0012.01:InnerAdditionAndSubtraction
Jürgen Wolff v Gudenberg wrote:
Nate, P1788
the inner operations are proposed in the Vienna proposal and are
supported by Baker.
Nevertheless I would like to get more information about their
application. I am not convinced by the examples given in the rationale.
We have found them important for efficient constraint propagation
in solving global optimization problems, and use them in COCONUT and
in GloptLab. Our use is explained in Proposition 14.2 of my survey paper
Complete Search in Continuous Global Optimization and Constraint
Satisfaction
http://www.mat.univie.ac.at/~neum/ms/glopt03.pdf
Is it correct that they are the first step of Kaucher or modal arithmetic?
They happen to coincide with Kaucher addition and subtraction in exact
arithmetic, but must have the opposite rounding behavior (than what is
advocated in the modal arithmetic literature) when executed with
interval arithmetic, to be useful for the above applications in
optimization. Thus they are not mnaturally part of a Kaucher arithmetic.
The required rounding behavior is specified in the Vienna Proposal,
Section 5.7.3. (I haven't checked whether this coincides with the
proposal in the motion. I have currently very little time for
following the discussion of the 1788 standard.)
Arnold Neumaier