Re: more patents on interval arithmetic implementations

[Ulrich Kulisch <Ulrich.Kulisch@xxxxxxxxxxx>]

Arnold Neumaier schrieb:
> 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
As far as I understand the matter all these patents provide hardware 
circuitries to compute sums and dot procducts of  floating-point numbers 
exactly. They have been filed more than 20 years ago and thus should all 
be expired. The most relevant techniques are discussed in a more 
colloquial English in my book: Computer Arithmetic and Validity, De 
Gruyter, 2008. I am convinced that these are the fastest techniques to 
compute sums and dot products exactly.

In contrast to these techniques the following and other papers present 
fast algorithms to compute approximations of hight quality of the sum 
and the dot product of floating-point numbers.
> 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

Best regards
Ulrich Kulisch