(j3.2006) Liaison to IFIP WG 2.5
Tue Aug 21 11:43:33 EDT 2007
Van Snyder wrote:
> IFIP WG 2.5 are very interested in interval arithmetic. They plan to
> send a letter to IEEE to complain that support for interval arithmetic
> in 754r is inadequate.
Inadequate?? That's a value judgment. I think "non-existent' more
factual. Most people, evidently, think that is adequate. Otherwise,
SUN would have put the rest of us out of business by now.
> I pointed out that if IEEE committees are anything like ANSI and ISO
> standards committees, it is very difficult to get something specific and
> significant into a standard unless somebody actually comes to meetings
> and writes words for the standard -- especially if those who come
> otherwise don't consider themselves experts or enthusiasts for the
> proposal. Ulrich Kulisch (Wolfgang Walter's mentor) has given me a
> manuscript of a book (which he has asked me not to circulate in
> electronic form) that explains how simple it would be to support
> interval arithmetic in hardware, with not many more transistors (est. 1%
> more), and only a very small number of gate delays. Upper and lower
> bounds could in principle be computed in parallel, so interval
> arithmetic might be almost as fast as point arithmetic if appropriate
> hardware were provided.
Maybe, but it you are doubling the number of functional units (for
parallel execution), and doubling the number of registers to be able to
hold the same number of 'values', I think you are looking at way more
than a 1% increase in transistors.
> Doing it in software at the source level, with
> Intel 80x86 processors and the Fortran IEEE support, imposes about 100x
> (not %) penalty.
SUN has a software implementation, and I can't imagine the performance
is that bad. I suspect this 100X estimate is way off base. I'd guess
more like 2X.
> Interval arithmetic is very attractive mathematically. In addition to
> pointing out that IEEE is unlikely to move on interval arithmetic
> without a champion who actually attends meetings, I pointed out that J3
> and WG5 are equally unlikely to move. If WG 2.5 want interval
> arithmetic, either in Fortran or IEEE 754r, an expert(s) needs to come
> to both kinds of meetings.
> J3 and WG5 should ponder whether interval arithmetic in Fortran is
> hopeless even if an expert, willing to work, shows up at our meetings,
> and advise me what to tell IFIP WG 2.5.
We already have a great facility for intervals build into Fortran -
modules. I think there would need to be two preconditions satisfied
before it was interesting to go beyond that:
1) There would have to be significant customer demand (so far I've seen
exactly zero such demand), and
2) Hardware support needs to be widespread to make something beyond a
module worthwhile from a performance point of view. That means, at a
minimum, that IEEE 754r++ specify a standard.
Bill Long longb at cray.com
Fortran Technical Support & voice: 651-605-9024
Bioinformatics Software Development fax: 651-605-9142
Cray Inc., 1340 Mendota Heights Rd., Mendota Heights, MN, 55120
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