Article View: comp.lang.fortran
Article #6542Re: True probabilistic rounding [was Re: Precision ...]
From: Nick Maclaren
Date: Wed, 01 Oct 2003 10:26
Date: Wed, 01 Oct 2003 10:26
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2246 bytes
In article <3F7AA528.5422AAD9@mediasec.de>, Jan C. =?iso-8859-1?Q?Vorbr=FCggen?= <jvorbrueggen@mediasec.de> writes: |> > 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...? Yup :-) Regards, Nick Maclaren.
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: fd4af,7830916812112af0 X-Google-Attributes: gidfd4af,public X-Google-Thread: 1094ba,7830916812112af0 X-Google-Attributes: gid1094ba,public X-Google-Thread: 102b75,7830916812112af0 X-Google-Attributes: gid102b75,public X-Google-ArrivalTime: 2003-10-01 03:26:37 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news2.google.com!newsfeed.stanford.edu!bloom-beacon.mit.edu!nycmny1-snh1.gtei.net!nycmny1-snf1.gtei.net!news.gtei.net!colt.net!news.tele.dk!news.tele.dk!small.news.tele.dk!lnewsoutpeer01.lnd.ops.eu.uu.net!lnewsinpeer00.lnd.ops.eu.uu.net!emea.uu.net!server1.netnews.ja.net!pegasus.csx.cam.ac.uk!nmm1 From: nmm1@cus.cam.ac.uk (Nick Maclaren) Newsgroups: comp.lang.fortran,comp.arch,bit.listserv.ibm-main Subject: Re: True probabilistic rounding [was Re: Precision ...] Date: 1 Oct 2003 10:26:34 GMT Organization: University of Cambridge, England Lines: 16 Message-ID: <blea4q$42p$1@pegasus.csx.cam.ac.uk> References: <dG4db.598668$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: libra.cus.cam.ac.uk Originator: nmm1@libra.cus.cam.ac.uk