Exact Dot Product Methods

[David Hough]

At the September NCEG meeting in Cupertino I distributed a proposal from
Knoefel and Kulisch to extend IEEE 754 to encompass exact dot product 
methods, as well as an opposing argument from Demmel.   Today I sent the 
following to Knoefel:


                                        PO Box 20370
                                        San Jose, CA 95160
                                        20 October 1991


Dipl. A. Knoefel
Universitaet Karlsruhe
Kaiserstrasse 12
7500 Karlsruhe 1
GERMANY

Dear Mr. Knoefel:

     Thanks for your letter of 12 August summarizing various
points of view about how computer arithmetic should evolve.

     As you know some critics of exact dot  product  methods
question  whether  they  are  the most cost-effective way of
obtaining satisfactory computational error bounds for scien-
tific  computations.   Typical  open questions among various
approaches include

*    Which approaches have the largest domains  of  applica-
     bility?

*    Which approaches produce acceptable results fastest for
     a given level of hardware investment?

     Theoretical considerations lead to arguments  in  favor
of  one approach or another that may sound plausible but are
not ultimately conclusive.  It would be  better  to  compare
the  results  of  implementations  with  comparable hardware
investment, comparable compiler and library technology,  and
comparable algorithmic development effort.

     The approach I favor in this respect is to  incorporate
compiler  extensions  into  widely  available compiler bases
such as GCC.   These can be  relatively  readily  ported  to
different  hardware platforms.  Because GCC is freely avail-
able, extensions make good projects for university students,
and  their  effort is not lost as it can be when they extend
proprietary compilers.

     True  standardization  of  an  interface  results  from
widespread  implementation  and use.  Sometimes this process
is helped along by standards organizations.  As you may know
the  Numerical  C Extensions Group is working on a technical
report (rather  than  a  standard)  proposing  a  number  of
mostly-orthogonal  extensions  to C to make it better suited
to numeric programming.  Each  of  the  extension  areas  is
being  defined  by  small  groups  of interested people.  If
several proponents of exact  dot  product  methods  were  to
prepare a draft of C extensions for those methods, that were
consistent with other proposed NCEG extensions,  that  draft
could be discussed and possibly adopted as part of the final
NCEG technical report.  I don't believe any of  the  current
NCEG  members  are  interested in exact dot product methods,
but neither are most opposed a-priori.  The NCEG chairman is

        Rex Jaeschke
        2051 Swans Neck Way
        Reston, VA  22091


     I think it may be more fruitful  to  define  exact  dot
product  methods  in terms of specific languages rather than
to specify them as part of IEEE 754, whose  full  acceptance
has  been inhibited precisely because many features were not
bound to a specific programming language interface.