Article View: comp.lang.fortran
Article #6548Re: True probabilistic rounding [was Re: Precision ...]
From: Terje Mathisen
Date: Wed, 01 Oct 2003 20:16
Date: Wed, 01 Oct 2003 20:16
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2609 bytes
Jan C. Vorbr�ggen wrote: >>In the case where the initial value of the sum is A and you are >>adding small numbers very near B, where the variation in B is less >>than A*eps/L, ANY true rounding will have error of order L*eps/4 >>(though with a much smaller factor than for truncation). True >>probabilistic rounding, however, maintains an order sqrt(L)*eps/2.8. > > > This sounds like the same argument for dithering in analog-to-digital > conversion...? It is _exactly_ analogous to that approach, it avoids biasing all the way down to below the actual precision of the sum. Terje -- - <Terje.Mathisen@hda.hydro.com> "almost all programming can be viewed as an exercise in caching"
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X-Google-Language: ENGLISH,ASCII X-Google-Thread: fd4af,7830916812112af0 X-Google-Attributes: gidfd4af,public X-Google-Thread: 102b75,7830916812112af0 X-Google-Attributes: gid102b75,public X-Google-Thread: 1094ba,7830916812112af0 X-Google-Attributes: gid1094ba,public X-Google-ArrivalTime: 2003-10-01 13:18:02 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news2.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!uio.no!newsfeed1.e.nsc.no!nsc.no!nextra.com!osl016lin.hda.hydro.com!not-for-mail From: Terje Mathisen <terje.mathisen@hda.hydro.com> Newsgroups: comp.lang.fortran,comp.arch,bit.listserv.ibm-main Subject: Re: True probabilistic rounding [was Re: Precision ...] Date: Wed, 01 Oct 2003 16:16:57 -0400 Organization: Hydro Lines: 20 Message-ID: <blfcnp$e2m$1@osl016lin.hda.hydro.com> References: <dG4db.598668$uu5.97984@sccrnsc04> <xrXdb.631209$Ho3.121609@sccrnsc03> <bl9ild$abv$1@pegasus.csx.cam.ac.uk> <Rh0eb.632709$Ho3.121617@sccrnsc03> <bla4k2$nas$1@pegasus.csx.cam.ac.uk> <FR0eb.637973$uu5.101567@sccrnsc04> <r%0eb.163529$3o3.11771639@bgtnsc05-news.ops.worldnet.att.net> <bY1eb.633341$Ho3.121512@sccrnsc03> <Zs2eb.157980$0v4.11847973@bgtnsc04-news.ops.worldnet.att.net> <blbcjf$lrn$1@pegasus.csx.cam.ac.uk> <QEbeb.377802$2x.116648@rwcrnsc52.ops.asp.att.net> <blbmni$g2$1@pegasus.csx.cam.ac. <ble09h$pn2$1@pegasus.csx.cam.ac.uk> <3F7AA528.5422AAD9@mediasec.de> NNTP-Posting-Host: 136.164.29.1 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Trace: osl016lin.hda.hydro.com 1065039419 14422 136.164.29.1 (1 Oct 2003 20:16:59 GMT) X-Complaints-To: news@hda.hydro.com NNTP-Posting-Date: Wed, 1 Oct 2003 20:16:59 +0000 (UTC) User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.5) Gecko/20030916 X-Accept-Language: en-us, en In-Reply-To: <3F7AA528.5422AAD9@mediasec.de>