complete arithmetic

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Dear Van and P1788 members:

The first sentence in the section on Complete Arithmetic of DRAFT 7.1
of the Standard for Interval Arithmetic dated April 3, 2013 was:

An implementation that provides 754-conforming types shall provide
complete arithmetic, as specified in U. Kulisch and V. Snyder [4],
for the parent format F of at least one such type.

I was afraid that with this formulation we might get it only for simgle precision
and asked for an other formulation that would allow double precision.

Now in the latest DRAFT 9.2 dated May 7, 2014 the first sentence reads:

For each supported 754-conforming type, derived from a format F,
the implementation should provide complete arithmetic for F, as
specified in Kulisch and Snyder [8].

This formulation is suited to kill complete arithmetic definitely. The paper [8]
is very general. I repeatedly tried to get it exchanged by the much simpler paper:
The Exact Dot Product (see attachment). But with no success.

In this paper we say:

An implementation shall (or should) at least provide complete formats corresponding
to binary64 if it provides binary floating-point  and decimal 64 if it provides decimal
floating-point. Complete formats corresponeding to other floating-point formats may
be provided.

Please adapt DRAFT 9.2 appropriately.

With best regards
Ulrich

-- 
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch

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

Attachment: DotProdP1788.pdf
Description: Adobe PDF document