Re: Vienna proposal for interval standardization, final version
Bob Davis wrote:
A question on the patents.
Is it possible to perform calculation in interval arithmetic, although
possibly slower, without requiring a patent license from the Marcel
Gavriliu, Eldon Hansen, Nathan Hayes, and William Walster?
The policy has been to design standards to not use patented material
wherever a possible alternate solution is available.
I am not a lawyer, so what I say are just my subjective impressions.
Many of the relevant patents can be found by typing in turn each one
of the above authors (the patents are not jointly by these) into the
top left search line of
http://www.patentstorm.us/
(begin with William Walster to get the most relevant list).
Most of these patents seem to cover various specific things to be done
with interval arithmetic, not the arithmetic per se; though from the
legal formulations employed it is not clear to me whether the pure
arithmetic really remains untouched. The arithmetic itself is the
main contents for the patents mentioned below (among those I am
aware of); the complete list of interval analysis related patents
is too large to be discussed in this mail.
In any case, there is lots of prior art in frequently-used public
software implementations of interval arithmetic of various sorts,
so that the parts of the patents covering software realizations of
interval arithmetic should be vacuous according to my naive
understanding. (I am less sure about the impact of the patents
on hardware implementations.)
It seems that patent offices check prior art only as far as patent
literature is concerned; otherwise it is not understandable how
well-known practices could have been patented long after
well-documented use.
A standard along the Vienna Proposal might be affected by the patents
under 1.-4. below, although the proposal took care to specify only
the semantics of each operation and not the precise way to perform
the computations leading to the conforming results.
A standard along the Vienna Proposal would not be affected by the
patents under 5. below, I believe, since the proposal does not
explicitly support modal arithmetic. The minimal amount of support
for nonstandard intervals required in the Vienna Proposal makes
the latter compatible with a modal interval arithmetic implementation;
but it can be implemented without making use of anything that hadn't
be done often before.
Arnold Neumaier
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Patents directly related to interval arithmetic and its generalizations:
1. The 2003 patent
http://www.patentstorm.us/patents/6658443/fulltext.html
seems to have patented the well-known and always used representation
of an interval by means of the end points.
2. A particular, well-known formula for standard interval multiplication
and division seems to have been patented in the 2004/5/7 patents
http://www.patentstorm.us/patents/6751638/fulltext.html
http://www.patentstorm.us/patents/6842764/fulltext.html
http://www.patentstorm.us/patents/7219117/fulltext.html
many years after these formulas had been in use in various
implementations and. The 2003 patents
http://www.patentstorm.us/patents/6629120/fulltext.html
http://www.patentstorm.us/patents/6658444/fulltext.html
are about a hardware implementation of some interval multiplication and
division formula.
3. Inner subtraction (Secxtion 5.6.3) seems to have been patented
in the 2003 patent
http://www.patentstorm.us/patents/6668268/fulltext.html
But the procedure had been in use at least since 1988; see p. 11
of the scanned copy at http://www.mat.univie.ac.at/~neum/ms/moore.pdf of
A. Neumaier, The enclosure of solutions of parameter-dependent
systems of equations. In: Reliability in Computing (ed. by R.E.
Moore). Acad. Press, San Diego 1988, pp. 269-286.
4. The 2007 patent
http://www.patentstorm.us/patents/7222146/fulltext.html
is also about interval arithmetic itself. Its contents is not clear
to me.
5. Some of the patents by Nathan Hayes refer to modal arithmetic,
an extension of interval arithmetic using nonstandard intervals:
- Representation of Modal Intervals within a Computer,
http://www.faqs.org/patents/app/20080263335
- Reliable and Efficient Computation of Modal Interval Arithmetic
Operations,
http://www.faqs.org/patents/app/20080256156
- Modal interval processor,
http://www.wipo.int/pctdb/en/wo.jsp?wo=2006107996
The last item is at present only a patent application.
Nate Hayes is among the subscribers of the 1788 mailing list,
and will surely present his own understanding of the matter.
See also my paper
http://www.mat.univie.ac.at/~neum/papers.html#nonstandard
(which is now available online)