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*To*: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>*Subject*: Re: Alternate floating-point results under directed rounding*From*: "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>*Date*: Sun, 09 Nov 2008 06:04:30 -0600*Cc*: "Siegfried M. Rump" <rump@xxxxxxxxxxxxx>, John Pryce <j.d.pryce@xxxxxxxxxxxx>, stds-1788@xxxxxxxxxxxxxxxxx*Delivered-to*: mhonarc@xxxxxxxxxxxxxxxx*In-reply-to*: <4916C20D.4050301@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>*References*: <20081108131359.YOGB2093.aamtaout03-winn.ispmail.ntl.com@xxxxxxxxxxxxxxxxx> <op.ukbfckzhv059od@xxxxxxxxxxxx> <4916C20D.4050301@xxxxxxxxxxxx>*Sender*: stds-1788@xxxxxxxx*User-agent*: Thunderbird 2.0.0.6 (Windows/20070828)

Arnold et al, I'm getting a little confused here about the line between syntax and semantics. Yes, say, if we want to use some kind of epsilon inflation, we will start with a floating point variable that is the result of a long computation (such as a that done in an approximate solver for a system of linear or nonlinear equations). However, isn't that normally a single number in the constructor. Ultimately, the actual constructor acts upon a single entity to produce an interval, doesn't it? Furthermore, aren't we looking at standardizing these underlying operations, as opposed to the syntactic environment in which they occur? If the argument to the operation is the result of a long computation, that argument (in Siegfried's case maxreal+maxreal) could in principle be maxreal, inf, NaN, or anything else, and I question whether it is practical or even possible in general to figure out from the computation or the syntax of the program what was originally intended. However, at the risk of seeming somewhat biased, it does not make sense to me to convert any finite number, even maxreal, into the empty set. Baker Arnold Neumaier wrote:

Siegfried M. Rump schrieb:Although examples like intval(maxreal+maxreal) are a little constructed; usually we would assume the argument ofa constructor to be a constant.No. Frequently one needs an enclosure of a function value at a point.Then the argument of a constructor will be a float variable, computed inan arbitrary way.In any case, definitions in the standard must work for all allowed uses. Arnold Neumaier

-- --------------------------------------------------------------- R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA ---------------------------------------------------------------

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

**References**:**Re: Alternate floating-point results under directed rounding***From:*John Pryce

**Re: Alternate floating-point results under directed rounding***From:*Siegfried M. Rump

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

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