P1788

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Dear colleagues,

on January 23 Dan Zuras (and/or myself) sent you my paper entitled:
Mathematics and Speed for Interval Arithmetic - A Complement to IEEE P1788.
I did not get any remark or comment on this paper from IEEE P1788. So I attach it once more (attachment 1) together with a few comments.

For some historic facts please read section 9 of the attached paper (atachment 1). Let me mention a few additional facts:

-- In 2007 and 2009 the IFIP Working Group 2.5 on Numerical Software sent two letters to IEEE 754 (attachment 2) and to IEEE P1788 (attachment 3) requiring that an exact multiply and accumulate operation (an exact dot product) should be included into future arithmetic standards. The exact dot product is essential for easily producing long real and long interval arithmetic by a given floating-point format. Long interval arithmetic is an appropriate tool for solving problems where simple interval arithmetic fails to produce close bounds.

-- In 2009 Van Snyder and myself submitted a motion (Motion9) to IEEE P1788 for including the exact dot product into a future standard for interval arithmetic. The motion was accepted. I sent a simplified version of motion 9 (attachment 4) together with the two IFIP WG 2.5 letters to colleagues at Intel. Their reaction was positive.

-- In August 2013, however, now under time presure the standards committee IEEE P1788 regrettably approved another motion which considerably weakens the original Motion 9. As reaction on this I prepared the  paper (attachment 1).

-- In December 2013 Intel published its new architecture:
Intel Architecture, Instruction Set Extensions Programming Reference.
See [36] in attachment 1. It provides register space of 16 K bits. Only about 4 K bits suffice for a complete register and computing the exact dot product.
So only four years validity of Motion 9 together with the IFIP WG 2.5 letters sufficed to get it into the Intel architecture. Early computers by IBM, Siemens, Hitachi, and others provided the exact dot product already in the 1980ies for computers of the /370 architecture.

A standard which only specifies naive interval arithmetic and does not address and emphasize features like speed and accuracy is counter-productive. It will just enhance old reservations against interval arithmetic.

With best regards
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

Attachment: axiomatic8.pdf
Description: Adobe PDF document

Attachment: IFIPWG-IEEE754R.pdf
Description: Adobe PDF document

Attachment: IFIPWG-IEEE-P1788.pdf
Description: Adobe PDF document

Attachment: DotProdP1788.pdf
Description: Adobe PDF document