Re: Suggestions for hardware implementation

[Ulrich Kulisch <Ulrich.Kulisch@xxxxxxxxxxx>]

Arnold Neumaier schrieb:
> Ulrich Kulisch schrieb:
> > Please have a look at the Kirchner/Kulisch paper. I attach a copy
>
> This is interesting but does not yet address the use of the
> pipelines for both interval arithmetic and real directed operations.
>
> Note that many of the more advanced kinds of rigorous computations
> require a mix of interval computation and real computation with
> directed rounding. Thus the directed rounding pipelines should be
> usable for both kinds of operations.
>
> I had mentioned already
> - the Hansen-Bliek method for solving linear systems with
>   interval coefficients
>   Reliable Computing 5 (1999), 131-136.
>   Erratum, Reliable Computing 6 (2000), 227.
>   http://www.mat.univie.ac.at/~neum/papers.html#ning
> - Barth and Nuding's optimal solution of linear systems with
>   an interval M-matrix
>   Computing 12 (1974), 117-125
> - the linear interpolation algorithms in Section 5.8 of
>   ViennaProposal-v3.0
> but there are further cases including
> - optimal aposteriori bounds in linear progrsmming
>   A. Neumaier and O. Shcherbina,
>   Safe bounds in linear and mixed-integer programming,
>   Math. Programming A 99 (2004), 283-296.
>   http://www.mat.univie.ac.at/~neum/papers.html#mip
> - Makino's range reduction technique; see Theorem 9.1 in
>   A. Neumaier,
>   Taylor forms - use and limits,
>   Reliable Computing 9 (2002), 43-79.
>   http://www.mat.univie.ac.at/~neum/papers.html#taylor
>
> I'd be interested in additional pointers for such mixed
> interval/directed rounding calculations.
>
>
> Arnold Neumaier
As the title of the paper says it just considers interval operations. 
Floating-point operations with directed roundings have been required 
already while IEEE 754 was developed around 1980 and again and again 
during the development of IEEE P754. I attach a collection of letters to 
the IEEE 754 revision group. See the letters dated   August 8, 2005 and 
January 2007   in particular.

Ulrich Kulisch

Attachment: LettersIEEE754R1.pdf
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