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Am 29.01.2016 um 16:47 schrieb John
Pryce:
John: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 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 |