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Concerning accurate dot product and summation there are yet more and very fast alternatives: http://www.ti3.tu-harburg.de/paper/rump/RuOgOi07I.pdf http://www.ti3.tu-harburg.de/paper/rump/RuOgOi07II.pdf http://www.ti3.tu-harburg.de/paper/rump/Ru08b.pdf Since dot products are transformed into summation, all summation routines can be used to compute dot products. Best wishes for the New Year Siegfried M. RumpOn Fri, 26 Dec 2008 18:03:02 -0100, Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> wrote:
Arnold Neumaier schrieb:
more patents, not yet mentioned in my previous two mails:
Several old patents, two by Kulisch, one by Miranker, and one by Rump,
are related to items 2 and 3 (accurate sum and inner product) in
Section 5.1 of the Vienna proposal:
- Circuitry for generating sums, especially scalar products
http://www.patentstorm.us/patents/4866653/fulltext.html
- Circuitry for generating scalar products and sums of floating point
numbers with maximum accuracy
http://www.patentstorm.us/patents/4622650/fulltext.html
- Systolic super summation device
http://www.patentstorm.us/patents/4751665/fulltext.html
- Method and circuit arrangement for adding floating point numbers
http://www.patentstorm.us/patents/4866651/fulltext.html
There are, however, recent alternative (public and better)
implementation techniques by
Ogita, Rump, and Oishhi
Accurate sum and dot product
http://www.ti3.tu-harburg.de/paper/rump/OgRuOi05.pdf
Arnold Neumaier
-- ===================================================== Prof. Dr. Siegfried M. Rump Institute for Reliable Computing Hamburg University of Technology Schwarzenbergstr. 95 21071 Hamburg Germany phone +49 40 42878 3027 fax +49 40 42878 2489 http://www.ti3.tu-harburg.de and Visiting Professor at Waseda University Faculty of Science and Engineering Shinjuku Lambdax Bldg. 902 2-4-12 Okubo, Shinjuku-ku Tokyo 169-0072 Japan phone/fax in Japan +81 3 5286 3414