Article View: comp.lang.fortran
Article #6528Re: Precision of floating point multiply
From: James Giles
Date: Mon, 29 Sep 2003 22:35
Date: Mon, 29 Sep 2003 22:35
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Glen Herrmannsfeldt wrote: > "James Giles" <jamesgiles@worldnet.att.net> wrote in message > news:r%0eb.163529$3o3.11771639@bgtnsc05-news.ops.worldnet.att.net... ... >> That's probably a correct assessment. In fact, on the system in question, >> where "rounding" results to single precision is done by truncation, it >> could be argued that leaving "garbage bits" simulates the missing data! >> Yes, I have heard appalling reasoning of that kind. > > Well, since truncating is systematic at puting in zeros, random bits would, > on the average, be closer. > > The process of digitizing analog data, such as converting analog audio into > digital form, works best with a process called dithering. Random noise of > approximately 1 LSB in amplitude is added before sampling. The left over > bits in registers might not be very random, though. Using true random > bits, one might even be able to sum into a single precision register and get > good results! Or not. The problem is that using "garbage bits" doesn't permit any useful or reliable analysis of the algorithms. Clearing the bits does. Further, clearing the bits allows algorithmic work-arounds (like Kahan's summation). Keeping "garbage bits" simply makes that inoperable. -- J. Giles
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: fd4af,7830916812112af0 X-Google-Attributes: gidfd4af,public X-Google-Thread: 102b75,7830916812112af0 X-Google-Attributes: gid102b75,public X-Google-Thread: fd705,7830916812112af0 X-Google-Attributes: gidfd705,public X-Google-Thread: 1094ba,7830916812112af0 X-Google-Attributes: gid1094ba,public X-Google-ArrivalTime: 2003-09-29 15:35:38 PST Path: arc1-ca.pugleaf.net!news1.google.com!newsfeed.stanford.edu!logbridge.uoregon.edu!feed2.news.rcn.net!rcn!wn14feed!worldnet.att.net!bgtnsc04-news.ops.worldnet.att.net.POSTED!not-for-mail From: "James Giles" <jamesgiles@worldnet.att.net> Newsgroups: comp.lang.fortran,comp.arch,bit.listserv.ibm-main,alt.folklore.computers References: <dG4db.598668$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> Subject: Re: Precision of floating point multiply Lines: 29 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1158 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 Message-ID: <Zs2eb.157980$0v4.11847973@bgtnsc04-news.ops.worldnet.att.net> Date: Mon, 29 Sep 2003 22:35:37 GMT NNTP-Posting-Host: 12.83.93.37 X-Complaints-To: abuse@worldnet.att.net X-Trace: bgtnsc04-news.ops.worldnet.att.net 1064874937 12.83.93.37 (Mon, 29 Sep 2003 22:35:37 GMT) NNTP-Posting-Date: Mon, 29 Sep 2003 22:35:37 GMT Organization: AT&T Worldnet