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*To*: "Arnold Neumaier" <Arnold.Neumaier@xxxxxxxxxxxx>*Subject*: Re: Alternate floating-point results under directed rounding*From*: "Siegfried M. Rump" <rump@xxxxxxxxxxxxx>*Date*: Fri, 07 Nov 2008 15:07:13 -0100*Cc*: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>*Delivered-to*: mhonarc@xxxxxxxxxxxxxxxx*In-reply-to*: <491431F7.509@xxxxxxxxxxxx>*List-help*: <http://listserv.ieee.org/cgi-bin/wa?LIST=STDS-1788>, <mailto:LISTSERV@LISTSERV.IEEE.ORG?body=INFO%20STDS-1788>*List-owner*: <mailto:STDS-1788-request@LISTSERV.IEEE.ORG>*List-subscribe*: <mailto:STDS-1788-subscribe-request@LISTSERV.IEEE.ORG>*List-unsubscribe*: <mailto:STDS-1788-unsubscribe-request@LISTSERV.IEEE.ORG>*Organization*: Hamburg University of Technology*References*: <200810311555.m9VFtNru005903@xxxxxxxxxxxxxxxxxxx> <op.ujxpwjm5v059od@xxxxxxxxxxxx> <490EC8FA.3080302@xxxxxxxxxxxx> <op.uj5ac6agv059od@xxxxxxxxxxxx> <49119AE0.5070001@xxxxxxxxxxxx> <4471533ED9154CF892A590B5538A1563@proton> <491404B2.9020108@xxxxxxxxxxxx> <op.uj8yncn5v059od@xxxxxxxxxxxx> <491431F7.509@xxxxxxxxxxxx>*Sender*: stds-1788@xxxxxxxx*User-agent*: Opera Mail/9.62 (Win32)

I don't understand. To have 0*[1,inf] = [0,0], no interpretation of inf as floating-point is needed, since this automatically holds with the specification of [l,u] = set of reals between l and u. No conversion of inf to an interval is involved here.

Consider (in Matlab notation) X = intval(NaN); Y = 0*X The result is the empty set, in either way. We expect this. Consider X = intval(0.1); Y = 0*X The result is [0], in either way. We expect this. Consider X = intval(1e40); Y = 0*X The result is still [0], either way. We expect this. Consider X = intval(1e400); Y = 0*X Your result is the empty set. Strange? I think yes. As you say, we can define everything as we wish. I prefer a definition so that Y is still [0]. Cheers, Siegfried -- ===================================================== Prof. Dr. Siegfried M. Rump Institute for Reliable Computing Hamburg University of Technology Schwarzenbergstr. 95 21071 Hamburg Germany phone +49 40 42878 3027 fax +49 40 42878 2489 http://www.ti3.tu-harburg.de and Visiting Professor at Waseda University Faculty of Science and Engineering Shinjuku Lambdax Bldg. 902 2-4-12 Okubo, Shinjuku-ku Tokyo 169-0072 Japan phone/fax in Japan +81 3 5286 3414

**Follow-Ups**:**Re: Alternate floating-point results under directed rounding***From:*Arnold Neumaier

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