Article View: comp.lang.fortran
Article #6547Re: True probabilistic rounding [was Re: Precision ...]
From: Russell Wallace
Date: Wed, 01 Oct 2003 05:18
Date: Wed, 01 Oct 2003 05:18
37 lines
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3087 bytes
On 30 Sep 2003 10:42:58 GMT, nmm1@cus.cam.ac.uk (Nick Maclaren) wrote: [probabilistic floating point rounding] >The reason I say the last is that there is no need to calculate a >multiplication to full accuracy - all you need is to generate >enough bits for a decision. Of course, this means that operations >can take variable times, which is Not Approved Of. But it might >help, especially for extended precision multiplication. I'm no expert on numerical analysis, so tell me if I'm missing something obvious, but: Let's suppose you have N bits of precision (N ~= 53 for IEEE double precision IIRC). In the base case where rounding truncates; you have N bits of precision. If rounding is to nearest, .5 rounding away from zero (the simplest type of rounding, it requires the consideration of only one extra bit), you effectively have something like N+0.5 bits of precision in calculations. With more complicated rounding, such as to even (IIRC, IEEE supports modes like this, at considerable complexity penalty), or probabilistic, you effectively have something like N+0.5+epsilon bits. Now my question is: why is it worth so much trouble to get an extra epsilon of a bit, when by using e.g. Intel's 80 bit format for temporaries, you get something like an extra 16 bits? -- "Sore wa himitsu desu." To reply by email, remove the small snack from address. http://www.esatclear.ie/~rwallace
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X-Google-Language: ENGLISH,ASCII-7-bit 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: 2003-09-30 22:19:35 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!newsfeed.esat.net!feeder2.news.heanet.ie!news.indigo.ie!not-for-mail From: wallacethinmintr@eircom.net (Russell Wallace) Newsgroups: comp.lang.fortran,comp.arch,bit.listserv.ibm-main Subject: Re: True probabilistic rounding [was Re: Precision ...] Message-ID: <3f7a622d.113216013@news.eircom.net> 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.uk> X-Newsreader: Forte Free Agent 1.21/32.243 Lines: 37 Date: Wed, 01 Oct 2003 05:18:42 GMT NNTP-Posting-Host: 159.134.104.164 X-Complaints-To: abuse@eircom.net X-Trace: news.indigo.ie 1064985574 159.134.104.164 (Wed, 01 Oct 2003 06:19:34 BST) NNTP-Posting-Date: Wed, 01 Oct 2003 06:19:34 BST Organization: Eircom.Net http://www.eircom.net