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Am 11.01.2015 14:51, schrieb John Pryce:
On 11 Jan 2015, at 09:25, Oliver Heimlich <oliver@xxxxxxxxxxxxxxxxxxx> wrote:Am 11.01.2015 um 08:17 schrieb John Pryce: [...]The precedence rule for sumAbs, implied by this Level 1 meaning, would then be If an sNaN is encountered, sNaN shall be returned. Otherwise, if an Infinity is encountered, +oo shall be returned. Otherwise, if a qNaN is encountered, qNaN shall be returned. I guess this affects dot and sum also, and maybe the "All other behavior" on p63 line 27. Michel, and others expert in low-level aspects, can say if this fits well with the 754-defined behaviour of sNaN and qNaN, and if it can implemented efficiently enough that the extra clarity outweighs the cost.I have already stated in the comments of the ballot [1] that I believe the current definition of the reduction operations does not quite fit to the rest of the standard, especially a set-based interval arithmetic. You explain how NaNs should be interpreted and that they could possibly stand for unknown numbers. Nowhere else in the standard NaNs are used (except for a possible choice of encoding [Empty])...I find this a strong, but not clinching argument. As I recall -- though I haven't re-studied the lengthy debates on the relevant motions -- several knowledgeable people in P1788 had the view that reduction operations (ROs) for interval vectors were not very useful, and this is why we left them out. (I sent a separate email to Siegfried Rump about this, as he is one of the "knowledgeable people".) Namely, (I think the argument was) one uses ROs most effectively not as interval ROs, but as point ROs with directed rounding, within an interval algorithm. If so, that makes them part of the Level 3 toolkit for writing Level 2 operations. Maybe they should be moved to Clause 14? Knowledgeable people, please comment. John Pryce
I prepared a few comments on mails that were exchanged in the group this week. Please see the attachment.
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
Attachment:
COMMENTS.pdf
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