Re: "Built upon 754"

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John,

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.
So my answer to your question is this: If you eliminate all unnecessary references to IEEE 754 in the present text of IEEE 1788 and put in the requirement for an EDP again, the standard would have my full support.

Immediately after this mail I shall forward a mail to the group that I sent on June 6, 2013. Please read this mail very carefully. Everything is already said there. Before I sent this mail out in 2013 I got its approval from Dan Zuras:

It all looks good to me, Ulrich.  Go ahead & ship it.  - Dan

Dan always supported the requirement of an EDP in arithmetic standards.

Shortly after my mail of June 6, 2013 I gave up supporting the 1788 development. Little hope returned after Ned Nedialkof's reduced version appeared on the scene. But here the EDP is still missing.

A well done standard would pull interval arithmetic more into the centre of scientific computing. The present version will delay this by ten more years. It even carries the potential of killing it.

With best regards
your friend
Ulrich

P.S.: By an early estimate of Siegfried Rump (1980), in a verfied solution of a linear system the verification step can be done with less than 6 times the costs of computing an approximation. This estimate is independent of the number of equations and the condition number of the system.

A hardware implementation of the EDP at Karlsruhe in 1993 computed it in 1/4 of the time the Intel processor needed for computing a possibly wrong result in conventional floating-point arithmetic. A more recent implemetation at Berkeley even could reduce the computing time to 1/6.

In a verified solution of a linear system the verification step more or less consists of dot products. So an EDP would reduce the costs for the verification step to the one needed for computing an approximation (Gauss elimination).

Although a major number of highly qualified and carefully selected Numerical Analysts repeatedly asked to include the requirement of an EDP into arithmetic standards, IEEE 1788 reduced this requirement to a recommendation. I feel free to say that this is a tragic mistake. In practice a recommendation guarantees different behaviour on different processors.

Best regards once more
Ulrich

Am 27.01.2016 um 18:19 schrieb John Pryce:

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.

-- 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