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Jim: Thank you
for sending the paper Hardware
Accelerator for Exact Dot Products written by your
two grad students David Biancolin and Jack Koenig. Let me
congratulate you and your students for these wonderful
results. I very much enjoyed
reading the paper and I hope its contents will be published
soon. I also hope to
get a chance meeting these colleagues once personally. The paper
shows that the authors have made themselves familiar with
all details of
Chapter 8: Scalar
Products and Complete
Arithmetic of my book Computer
Arithmetic and Validity. With your mail of Oct. 10
last year you asked me to
provide some advice for your students how to proceed on the
matter. In my
answer among others I predicted for a hardware
implementation a speed increase
by a factor between 3 and 4 compared with a conventional
computation of the dot
product in floating-point arithmetic. This was based on
experience with our XPA
chip 3233 in 1993/94. With design tools developed at I am also
very pleased that your students mention again that what they
implement is an
electronic version of the operation the
running total which was available on many old mechanic
calculators. The
technique even can be traced back to the old mechanic
calculator by G. W.
Leibniz, 1685. When I recently mentioned this in a mail to
IEEE P1788 a
colleague answered: We
are no longer in
the 17th century. …. the knowledge (new
algorithms …) has evolved. Fig. 1 of
the paper is showing a picture (chest of drawers) taken from
my book. Let me
suggest replacing it by the more detailed picture which can
be taken from the
attached (still unpublished) paper. The new picture also
shows the adder which
eases the understanding.. You know
that I am offering the relevant ideas since 1980. They were
never picked up and
realized by somebody outside of my immediate sphere of
influence. Several times
after talks at international conferences (Computer
Arithmetic meetings at Urbana
1985, at Como 1987, and others) I was publicly attacked and
treated by
colleagues as being a charlatan. Via e-mails this situation
still continues
until today. Without studying details colleagues are
obviously not willing to accept
that computing a dot product exactly can be considerably
simpler and faster
than computing it in conventional floating-point arithmetic.
Computing a correctly
rounded result even would be slower than the latter by at
least a factor of
two. By pipelining the exact dot product can be computed in
the time the
processor needs to read the data, i.e., there cannot be a
faster method. I hope Jim
that you can protect your students from mockery and scorn
and I hope that their
paper will help breaking an old barrier! With best
regards Ulrich Am 19.06.2015 um 16:02 schrieb James Demmel: You might find the attached class project report interesting. Two grad students here, David Biancolin and Jack Koenig (cc-ed) used the hardware design tools being designed at Berkeley to design a long accumulator, and measure its chip area and power requirements at a fairly deep level of detail. Please contact them if you have further questions. Jim Demmel -- Karlsruher Institut für Technologie (KIT) Institut für Angewandte und Numerische Mathematik D-76128 Karlsruhe, Germany Prof. Ulrich Kulisch KIT Distinguished Senior Fellow Telefon: +49 721 608-42680 Fax: +49 721 608-46679 E-Mail: ulrich.kulisch@xxxxxxx www.kit.edu www.math.kit.edu/ianm2/~kulisch/ KIT - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gesellschaft |
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