Dear John,
interval arithmetic and floating-point arithmetic are distinct
calculi. They should be kept stricly separate.
Interval
arithmetic developed over the sets R and F of real and
floating-point numbers leads to a closed calculus that is
totally free of exceptions, i.e., the result of any of the
operations plus, minus, multiply, divide and the dot product for
intervals of real numbers including elementary functions always
delivers a real interval again.
This
really is a wonderful and unique result in comparison
with conventional floating-point arithmetic with all its
exceptions. But I feel that many members of
the scientific computing community and even of IEEE 1788 have
not yet internalized this.
So
I think that idealy the two standards IEEE 754 and IEEE 1788 also
should be kept strictly separate. I would even say that any
mentioning of IEEE 754 and its exceptions in IEEE 1788 is a
possible source of confusion. If such mentionings like +0, -0,
NaN, IEEE 754 type, IEEE conformant type, and other hints to IEEE
754 would be eliminated in the text of IEEE 1788 I would fully
agree with it.
Best regards
Ulrich
Am 27.01.2016 um 12:53 schrieb John Pryce:
Dear Ulrich
On 27 Jan 2016, at 11:17, Ulrich Kulisch <ulrich.kulisch@xxxxxxx> wrote:
My mail is concerned with the major part of the standard and there is no
doubt that this is built upon IEEE 754.
I challenge you to quote, by clause and sentence, a single part of 1788 (concept, requirement, operation etc.) that is built upon IEEE 754.
Regards
John Pryce
--
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
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