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=-1.9 required=5.0 tests=BAYES_00 autolearn=ham autolearn_force=no version=3.4.4 X-Google-Thread: 103376,df84b868ad64e4f7 X-Google-Attributes: gid103376,public X-Google-Language: ENGLISH,ASCII-7-bit Path: g2news1.google.com!news4.google.com!news.glorb.com!border1.nntp.dca.giganews.com!local01.nntp.dca.giganews.com!nntp.comcast.com!news.comcast.com.POSTED!not-for-mail NNTP-Posting-Date: Sun, 31 Jul 2005 14:08:04 -0500 From: tmoran@acm.org Newsgroups: comp.lang.ada Subject: Re: OT: definition of "significant figures" References: <16rocpq66tyxr.x4l3edv2c9ce$.dlg@40tude.net> X-Newsreader: Tom's custom newsreader Message-ID: Date: Sun, 31 Jul 2005 14:08:04 -0500 NNTP-Posting-Host: 24.6.143.98 X-Trace: sv3-efweV/39xpPahrgQprba9bEroLoTpnGBGyFbjId0ZgD1dTw0pdODBIvEST7JvdwL4WvA9Jjdf9xqCnq!NuQgaVtA72g6T+CagbrfQouIu2Bq3/6IVMMmYDUkZ012skY+ciYYPEKU9o+3BaWDHcDqCTBJEko= X-Complaints-To: abuse@comcast.net X-DMCA-Complaints-To: dmca@comcast.net X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.32 Xref: g2news1.google.com comp.lang.ada:3866 Date: 2005-07-31T14:08:04-05:00 List-Id: > If you have, say, 100_000 approximately same FP numbers, > then a naive implementation > ... > would perform awfully. Near to the end of the loop you will heavily loose > accuracy. Because the ratio Sum to X (I) would be around 100_000. To > cascade it would be a better idea. For large N I keep log2(N) partial sums at the various scales. Is that what you mean by "cascade"? > So basically it is difficult to tell in advance how many "right" figures > you get. > > Also you can use interval arithmetic, then you'll exactly know the accuracy > of the result. I presume that for scientific publication one shows standard deviation or confidence intervals or some appropriate statistic. "significant figures" seems more a rough-and-ready approximate way to convey that information. My immediate application actually takes a single decimal latitude or longitude, whose accuracy I can only estimate from its number of digits, and produces degrees/minutes/seconds, with an appropriate number of significant fields/digits.