ISO/IEC JTC1/SC22/WG5 N1736

                             LIAISON REPORT
                     IFIP WG 2.5 (Numerical Software)
                    Presented to ISO/IEC JTC1/SC22/WG5
                  Meeting in Tokyo, Japan, 16-21 Nov 2008

At the 2007 IFIP WG 2.5 meeting in Uppsala, Sweden, immediately
following the SC22/WG5 meeting in London, WG 2.5 proposed to send a
letter to IEEE P754 to urge that support for interval arithmetic and
complete arithmetic be incorporated into the revision of the
floating-point arithmetic standard.  Complete arithmetic is
high-precision fixed-point accumulation of floating-point results, such
that no precision is lost due to rounding or truncation.  It turns out
that complete dot product is adequate for all purposes.

I remarked that the letter was too vague, that somebody had to write
the precise words that ought to be incorporated into the standard, and
that the proposed addition should be integrated with the standard --
use the same terminology, etc.  I also expressed a belief that it was
unlikely that anybody on the IEEE P754 committee would do that,
especially from such vague specifications as were contained in the
proposed letter.

I was asked whether I was willing to prepare a more detailed proposal,
and agreed to so so provided I got support and cooperation from those
who actually understood the topic.

During the next six weeks or so, I and Ulrich Kulisch and Bo Einarsson
prepared precise editorial instructions to incorporate interval
arithmetic and complete arithmetic into draft 1.4.28 of the IEEE
floating-point arithmetic standard.

The IEEE P754 committee studied the proposal, and presumably debated it
at their meetings, but ultimately decided not to incorporate it into
the standard.

Subsequently, a group led by R. Baker Kearfott <rbk@louisiana.edu> (an
old friend of WG5) and Nathalie Revol <Nathalie.Revol@ens-lyon.fr>
approached IEEE with a proposal to form a committee to develop an
independent standard for interval arithmetic and complete arithmetic,
that would be compatible with the floating-point arithmetic standard. 
That group has forwarded a proposal to IEEE; they are awaiting an IEEE
decision whether to form a committee.

Correspondence among volunteers serving that group has revealed that
there are at least two interpretations of "interval arithmetic," each
of which has application to a field of problems.  I'm not expert in
interval arithmetic so I don't know the full problem.  One issue is
whether sqrt(0.0:1.0) is 0.0:1.0 or -1.0:1.0.  I'm sure that either
Baker or Nathalie could explain the full scope of the differences.

This suggests that it might have been a good thing that Fortran did not
incorporate interval arithmetic into the 2003 standard, as it now
appears that support for at least two varieties of several parts of it
is desirable.

Van Snyder
Caltech / Jet Propulsion Laboratory