Re: Up-to date Interval Arithmetic

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Am 27.03.2015 um 15:31 schrieb Vincent Lefevre:

In addition to the problem of the meaning of "rigor", I don't
understand why:

1. The open interval J is valid.
For instance, take a = [1,1] and b = [2,2].
Then I = [RNDD(1+2),RNDU(1+2)] = [3,3]
 and J = (RNDD(1+2),RNDU(1+2)) = (3,3) = Empty

Dear Vincent:

Please let me know the rules with which you get the result for J?

Unum arithmetic delivers the closed interval for J also.

Concerning rigor let me say the following:
The book Computer Arithmetic and Validity considers floating-point and interval arithmetic as distinct calculi. It requires strictly to separate the two. Naturally in interval arithmetic the IEEE 754 exceptions do not occur. They may be reasonable in a floaqating-point computation. In IEEE P1788, however, they appear like a cuckoo's egg.  It unnecessarily complicates the implementation of interval arithmetic and the understanding of it for every user. It carries the potential of preventing interval arithmetic from wide spread usage.

Best wishes
Ulrich

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Prof. Ulrich Kulisch

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