From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.3 required=5.0 tests=BAYES_00,INVALID_MSGID autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,c7637cfdf68e766 X-Google-Attributes: gid103376,public X-Google-Thread: f8362,c7637cfdf68e766 X-Google-Attributes: gidf8362,public X-Google-Thread: f43e6,c7637cfdf68e766 X-Google-Attributes: gidf43e6,public X-Google-Thread: 107079,c7637cfdf68e766 X-Google-Attributes: gid107079,public X-Google-Thread: 109d8a,c7637cfdf68e766 X-Google-Attributes: gid109d8a,public From: jac@ibms48.scri.fsu.edu (Jim Carr) Subject: Re: floating point comparison Date: 1997/08/19 Message-ID: <5tc7kl$a19$1@news.fsu.edu>#1/1 X-Deja-AN: 267930451 References: <5t5976$rle$1@ccioffe.ioffe.rssi.ru> Distribution: inet Organization: Supercomputer Computations Research Institute Newsgroups: comp.lang.ada,sci.math.num-analysis,comp.software-eng,comp.theory,sci.math Date: 1997-08-19T00:00:00+00:00 List-Id: Andrew says << Strongly disagree. There ARE roundoff errors even in the IEEE 754 arithemtic model. Moreover, the standard clearly specifies rounding models.>> dewar@merv.cs.nyu.edu (Robert Dewar) writes: > >There are no *errors*, the discrepancies between IEEE arithmetic and >real arithmetic are not errors, they are simply differences that come from >two different arithmetic models. It could be useful to adopt the terminology of experimental science here, and use "uncertainty" to denote the variance between the results of real arithmetic and floating point arithmetic done 'correctly' in a particular model. The two have much in common, since one propagates those uncertainties in a similar way, and since the confusion associated with calling them "errors" is equally strong. And both are poorly known. ;-) >When we have integer arithmetic and we divide 10 by 3 to get 3, we do >not say this is an error. The result is different from the mathematical >value of 10.0/3.0, but there is no error here, just a different arithmetic >model. And you _should_ know that 10/3 = 3 could mean 3 +/- 0.5, or it could mean (10 +/- 0.5)/(3 +/- 0.5) depending on the circumstances. Or it could be an _error_ if you are using 10/3 as an exponent when you meant to use 10./3. = 3.33333.... >I know perfectly well that the phrase "rounding error" is well established, >but my point is that calling it an error leads people into the niave trap >of thinking of floating-point arithmetic as being real arithmetic. So is the phrase "experimental error" in physics and other fields, and it causes similar difficulties. It is not an error to read a ruler with the maximum possible accuracy. Similarly, it is not an error to store a floating point approximation with the maximum possible bits, correctly rounded per the floating point model. It _is_ an error to treat those numbers as if they were real numbers. -- James A. Carr | Commercial e-mail is _NOT_ http://www.scri.fsu.edu/~jac/ | desired to this or any address Supercomputer Computations Res. Inst. | that resolves to my account Florida State, Tallahassee FL 32306 | for any reason at any time.