Attached is ViennaProposal.pdf, the final version of the
Vienna proposal for interval standardization, in preparation for
the formal discussion of the future IEEE 1788 standard on
interval arithmetic.
Appended below are the abstract of the proposal, and two abstracts
of companion papers, together with links for downloading the papers.
(All links will be active only starting Monday evening CET
since I haven't been able to finish them in time.)
nonstandard.pdf gives background explaining the reasons for some
decisions taken by the proposal, and encl.pdf explains the proper
use of interval arithmetic for getting good range enclosures,
These papers should be read to better understand the Vienna proposal.
Since some of the issues in the standard to be may be related to
a number of patents obtained by Marcel Gavriliu, Eldon Hansen,
Nathan Hayes, and William Walster, I'd also like to draw attention
to the official IEEE slides
http://standards.ieee.org/board/pat/pat-slideset.pdf
containing instructions about the IEEE's patent policy.
Arnold Neumaier
ViennaProposal.pdf
------------------
http://www.mat.univie.ac.at/~neum//papers.html#1788
(The latex source can be obtained from me upon request.)
ViennaProposal.pdf contains a detailed proposal for a future IEEE 1788
standard on interval arithmetic. It is written in a form that should
be not too difficult to transform into a formal, complete and fully
precise document specifying the standard to be.
Part 1 contains a concise summary of the basic assumptions (some of
which may be controversial) upon which the remaining document is
based. The items in Part 1 are grouped such that separate voting on
each issue is meaningful.
Parts 2-5 specify the internal representation of intervals and the
operations defined on them. Part 6 specifies the external
representation of intervals and the conversion between internal and
external representations.
Part 7 is optional and discusses useful modifications of the directed
rounding behavior specified in the IEEE 754-2008 standard that would
simplify an implementation of the proposed standard.
This final version incorporates many suggestions and corrections by
a number of people active on the stds-1788 mailing list; they are
mentioned on p.1 of the document. In particular, comprehensive
discussions with Michel Hack, who read and commented in detail
many intermediate versions, had a strong influence on this proposal.
Compared with the preliminary public version v3.0 of November 21, 2008,
the major changes are the distinction between L-numerals (for
language-provided numbers) and B-numerals (for representing bounds),
the removal of optional dual operations (old Section 5.9),
the addition of many remarks (and the the marking of all remarks),
which explain or justify rather than specify things, a few changes
in the labeling of sections, remarks on NaI, and references to two
companion papers with additional background (to which the remarks
about hardware implementations were moved). In addition, many
small things were fixed or improved.
nonstandard.pdf
---------------
http://www.mat.univie.ac.at/~neum/papers.html#nonstandard
This document is an assessment of the value of optimal linear
interpolation enclosures and of nonstandard intervals,
especially with respect to applications in computer graphics, and of
the extent a future IEEE interval standard should support these.
It turns out that essentially all present applications of nonstandard
intervals to practical problems can be matched by similarly efficient
approaches based on standard intervals only. On the other hand,
a number of applications were inspired by the use of nonstandard
arithmetic.
This suggests the requirement of a minimal support for nonstandard
intervals, allowing implementations of nonstandard interval arithmetic
to be compatible with the standard, while a full support by making one
of the conflicting variants required seems not appropriate.
encl.pdf
--------
http://www.mat.univie.ac.at/~neum/papers.html#encl
This draft of a paper discusses some methods to improve the quality
of interval enclosures of the range of a function over a box,
and the results of a simple interval challenge that I had posed to
the reliable computing mailing list on November 26, 2008.
The draft is provided in the present, incomplete form since it is
referenced in the Vienna Proposal as background information explaining
what is needed in practice to make competent use of the interval
arithmetic provided by an implementation of the standard to be.
But its form is still far from final. A revised version with gaps
(currently denoted by a black bar in the margin) filled, more
complete references and further details on challenge solutions
will be presented in January 2009.