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Neither IEEE 1788 nor IEEE 754 consider infinities as numbers.
In IEEE 754 the values inf and -inf denote the result of an overflow. In IEEE 1788 these special values are used to denote boundaries of an unbound interval -- not numbers.
For example, consider the following operation:
isMember (inf,[entire]) returns false according to IEEE 1788, where inf is a floating-point value according to IEEE 754.
So, I don't understand what you disagree with.
I forward a recent e-mail exchange:
-------- Weitergeleitete Nachricht --------
Thank you for inviting me repeatedly to join the IEEE P1788.1 committee. In the early days of the standard development I prepared several motions which all have been accepted. Among these motions was one that required an exact dot product (EDP). Hardware implementations of the EDP at Karlsruhe in 1993 and at Berkeley in 2013 show that it can be computed in about 1/6th of the time needed for computing a possibly wrong result in conventional floating-point arithmetic. However in 2013, the requirement of an EDP was withdrawn from the standard, perhaps in order to make Sun's Forte Fortran conform with the standard. A majority of IEEE1788 members was made to believe that everything can be done as well by a correctly rounded dot product which is built upon a conventional computation of the dot product in floating-point arithemtic followed by an accuracy refinement. So it is slower than the EDP by more than one magnitude. Another topic where I disagree with the majority of the IEEE1788 members is the treatment of the infinities. Interval airthmetic developed for closed real and floating-point intervals leads to an exception-free calculus (for proof see my books). IEEE1788, however, develops interval arithmetic over the IEEE754 numbers where ±infinity are considered as numbers. This pulls several IEEE754 concepts like NaN, +0, -0, NaI, and others into interval arithmetic where they are not needed and are a frequent source of confusion. I attach a short unpublished paper which shows my view of the matter in more detail. Best regards Ulrich Kulisch Am 11.07.2017 um 06:01 schrieb IEEE-SA: > You have new myProject notifications - please log onto https://development.standards.ieee.org/my-site to read them. > > ----Message Boundary---- > > > To: undisclosed-recipients:; > Cc: "C/MSC Project Staff Liaison" <c.bahn@xxxxxxxx> > Subject: Invitation for IEEE P1788.1 did NOT close! Your participation is important! > > > This notification is to advise you that the invitation for P1788.1 Standard for Interval Arithmetic (Simplified) has been extended by the chair. Please consider joining this ballot group and submitting your vote and comments on the document. Log on to myProject https://development.standards.ieee.org/my-site/open-ballot-invitations "Show/Join Open Ballot Invitations" to find the ballot group. Follow the on-screen instructions. Your participation is vital to the success of this project. > > Thank you. > IEEE-SA Balloting Center > > -- Karlsruher Institut für Technologie (KIT) Institut für Angewandte und Numerische Mathematik D-76128 Karlsruhe, Germany Prof. Ulrich Kulisch 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