Am 29.01.2016 um 16:47 schrieb John Pryce:
Dear Ulrich
On 29 Jan 2016, at 12:38, Ulrich Kulisch<ulrich.kulisch@xxxxxxx>
wrote:
I attach a copy of a page from the present version of the standard.
In the first 9 lines it 3 times refers to IEEE 754 by 754
conforming, 754 format, 754-conforming type. 12.13.4 even is
restricted to 754-conforming types. Then the example below again is
restricted to IEEE 754 binary 64. It is this restriction that leads
to the unreasonable huge register space of 4288 bits. Computing a
dot product exactly frequently was judged as being unrealistic
because of this huge register space.
In the IBM products ACRITH (1983) and ACRIITH-XSC (1990) the EDP is
done in a register space of about 1000 bits and I am not aware of
any applications where this caused any problem.
This text is from p66 in the published standard. It has two kinds of
references to IEEE 754.
- "754-conforming type". Some interval types are this, others aren't
(I believe that in practice, for some years, most will be). The text
says in various places that *if* a type is of this kind, it must
obey stricter rules than for a general type. In no way is this
"building on" 754.
- Stuff about operations that either input or output (at Level 1) a
number. This brings one to the boundary between the interval world
and the non-interval world, which *cannot be avoided* but which you
try to ignore. At Level 2 this number has to be a floating point
number. There have to be some rules about these. Did your interval
systems in ACRITH etc. completely do without FP numbers? If so, how?
As for EDP requiring 4288 bits, The text is simply quoting the
figures given in Kulisch and Snyder, reference [B7]. If about 1000
bits suffices, why did you not put us right long ago?
Regards
John P
John:
I said this repeatedly. See, for instance, page 16 of my book /Advanced
Arithmetic for the Digital Computer/, Springer 2002, or on page 264 of
the book /Computer Arithmetic and Validity/, de Gruyter, second edition
2013.
I also said this in mails repeatedly. See for instance my mail of June
10, 2013. I felt that you are listening to the wrong heros here and I
had no chance to turn this. Sorry to say this!
Best regards and best wishes
Ulrich
--
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