Path: news.mathworks.com!newsfeed-00.mathworks.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews.google.com!news2.google.com!npeer02.iad.highwinds-media.com!news.highwinds-media.com!feed-me.highwinds-media.com!post01.iad.highwinds-media.com!newsfe21.iad.POSTED!00000000!not-for-mail From: Walter Roberson <roberson@hushmail.com> User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X 10.5; en-US; rv:1.9.2.12) Gecko/20101027 Thunderbird/3.1.6 MIME-Version: 1.0 Newsgroups: comp.soft-sys.matlab Subject: Re: Bug when doing simple subraction/multiplication References: <icho0p$bjb$1@fred.mathworks.com> <4cec6b32$0$1592$742ec2ed@news.sonic.net> <ici2vb$pbe$1@fred.mathworks.com> In-Reply-To: <ici2vb$pbe$1@fred.mathworks.com> Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Lines: 36 Message-ID: <772Ho.35021$sK1.22037@newsfe21.iad> NNTP-Posting-Host: 24.79.143.47 X-Complaints-To: internet.abuse@sjrb.ca X-Trace: newsfe21.iad 1290579523 24.79.143.47 (Wed, 24 Nov 2010 06:18:43 UTC) NNTP-Posting-Date: Wed, 24 Nov 2010 06:18:43 UTC Date: Wed, 24 Nov 2010 00:18:43 -0600 Xref: news.mathworks.com comp.soft-sys.matlab:689560 On 23/11/10 10:06 PM, Roger Stafford wrote: > The basic reason there are errors in the decimal arithmetic you show, > Lisett, is that the digital computers we all use have a base of two for > their storage and computations. That is, they use binary numbers. If > they had used base ten numbers as with many hand calculators, the > computations you show would have been done without error but there would > be errors when fractions such as 1/3 or 1/7 occurred. Roger, it might amuse you to know that IBM has maintained decimal arithmetic capabilities since the 1960's, primarily for financial applications. Their current offerings that support decimal arithmetic are under their Zeos operating system, but I do not recall at the moment if the current model with the decimal CPU is the Z90 or Z900 (when I last looked at the documentation, it implied the Z90 is still supported but has been superceded by the Z900, but I could find very little information about the Z900.) IEEE is either in the process, or already has, approved a decimal arithmetic extension to IEEE 754; apparently there is some interest from some other manufacturers as well. >> If you want infinite precision you need to use an analog computer. Stan, how do you propose to implement that infinite precision in an analog computer? What kind of physical or electrical measurement is robust down past the scale of brownian motion and yet is not quantized? If you measure at the quantum level, how will your infinite precision proceed once you get into Planck Scale measurements, down around 1E-74, where it is suspected that space itself is quantized? I do not recall at the moment whether it was last month's Scientific American, or last month's American Scientist, but one of the two had an article that had as an implication that measurements below 1E-70 are effectively impossible: at those scales, the mass-equivalent of energy twists space enough (gravitational "frame dragging") that you cannot measure more accurately.