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=-0.3 required=5.0 tests=BAYES_00, REPLYTO_WITHOUT_TO_CC autolearn=no autolearn_force=no version=3.4.4 X-Google-Thread: 103376,5412c98a3943e746 X-Google-NewGroupId: yes X-Google-Attributes: gida07f3367d7,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII-7-bit Received: by 10.68.235.4 with SMTP id ui4mr2348164pbc.3.1331723915710; Wed, 14 Mar 2012 04:18:35 -0700 (PDT) Path: h9ni24904pbe.0!nntp.google.com!news2.google.com!volia.net!news2.volia.net!feed-A.news.volia.net!news.musoftware.de!wum.musoftware.de!feeder.erje.net!news-1.dfn.de!news.dfn.de!news.uni-weimar.de!not-for-mail From: stefan-lucks@see-the.signature Newsgroups: comp.lang.ada Subject: REAL (was: Verified compilers?) Date: Wed, 14 Mar 2012 12:14:05 +0100 Organization: Bauhaus-Universitaet Weimar Message-ID: References: <9207716.776.1331054644462.JavaMail.geo-discussion-forums@ynaz38> <4edda5mav3cf$.149pbgyxl1wx5.dlg@40tude.net> <9rplcgF5a2U1@mid.individual.net> <1psd0g0womgxi.1sle7ol12x3d5.dlg@40tude.net> <9rsahhFmr3U1@mid.individual.net> <9rvdjvFfa8U1@mid.individual.net> <4pp58h1br5sp$.yylr20e5vzxb.dlg@40tude.net> <9s1s7tF6pcU1@mid.individual.net> <1oln2mjlozzh5$.1mxrd97lrgndo.dlg@40tude.net> <9s4mseFuoaU1@mid.individual.net> <9sb3l3Fs4oU1@mid.individual.net> <4f6063b7$0$6642$9b4e6d93@newsspool2.arcor-online.net> Reply-To: stefan-lucks@see-the.signature NNTP-Posting-Host: medsec1.medien.uni-weimar.de Mime-Version: 1.0 X-Trace: tigger.scc.uni-weimar.de 1331723915 20711 141.54.178.228 (14 Mar 2012 11:18:35 GMT) X-Complaints-To: news@tigger.scc.uni-weimar.de NNTP-Posting-Date: Wed, 14 Mar 2012 11:18:35 +0000 (UTC) X-X-Sender: lucks@medsec1.medien.uni-weimar.de In-Reply-To: <4f6063b7$0$6642$9b4e6d93@newsspool2.arcor-online.net> Content-Type: TEXT/PLAIN; charset=US-ASCII Date: 2012-03-14T12:14:05+01:00 List-Id: On Wed, 14 Mar 2012, Georg Bauhaus wrote: > Side note: WRT finiteness, language designers have made one > particular mistake again and again, following a convention, > by telling programmers about some type called REAL. The set > of supposed real numbers that programmers have heard about > before, in math lessons, is not finite [...] > > What the language designers usually mean, though, is some finite > Fraction_with_Split_Shifting thing, having infinitesimally > little to do with the reals. Consequence: an infinite supply > of surprises, cause by the name REAL. In general, floating point numbers are meant to approximate the real numbers (in the mathematical sense). Unfortunately, most programmers have been educated just to apply floating point arithmetic in their programs, expecting the result to be close enough to the "real result". Hardly anyone cares enough to analyze how the error grows from operation to operation. Hardly anyone even bothers to define how close the result should to be -- which depends on the application at hand, of course. And, to be honest, that approach works well most of the time. Which is precisely the reason why wrong results (= approximations not close enough to the real result) come as *surprises* ... -- ---- Stefan.Lucks (at) uni-weimar.de, University of Weimar, Germany ---- ------ I love the taste of Cryptanalysis in the morning! ------