Path: utzoo!utgpu!watserv1!watmath!att!pacbell!pacbell.com!ucsd!usc!snorkelwacker!paperboy!meissner From: meissner@osf.org (Michael Meissner) Newsgroups: comp.arch Subject: Re: Killer Micro II Message-ID: Date: 31 Aug 90 17:53:43 GMT References: <527@llnl.LLNL.GOV> <603@array.UUCP> <2482@l.cc.purdue.edu> <2868@inews.intel.com> <8442@fy.sei.cmu.edu> <3922@bingvaxu.cc.bi Sender: news@OSF.ORG Organization: Open Software Foundation Lines: 54 In-reply-to: vu0310@bingvaxu.cc.binghamton.edu's message of 31 Aug 90 15:18:39 GMT In article <3922@bingvaxu.cc.binghamton.edu> vu0310@bingvaxu.cc.binghamton.edu (R. Kym Horsell) writes: | Path: paperboy!snorkelwacker!usc!zaphod.mps.ohio-state.edu!rpi!leah!bingvaxu!vu0310 | From: vu0310@bingvaxu.cc.binghamton.edu (R. Kym Horsell) | Newsgroups: comp.arch | Date: 31 Aug 90 15:18:39 GMT | References: <527@llnl.LLNL.GOV> <603@array.UUCP> <2482@l.cc.purdue.edu> <2868@inews.intel.com> <8442@fy.sei.cmu.edu> | Reply-To: vu0310@bingvaxu.cc.binghamton.edu.cc.binghamton.edu (R. Kym Horsell) | Organization: SUNY Binghamton, NY | Lines: 20 | | In article meissner@osf.org (Michael Meissner) writes: | \\\ | >measurement only had 3-5 digits of accuracy. This means that any | >answer received cannot be more accurate than the input. Now in order | >to avoid round off error, you certainly need more digits internally, | >but IEEE double gives something 12-14 digits. One of the problems the | | Unfortunately, ``round off'' error is not the real problem. | *Loss of significance* results when, for example, two positive FP numbers with | similar magnitude are subtracted. The occurence of same is not | always predictable and the ``quick fix'' is to use more precision. | Despite this, the cliche of failing to invert a 100 x 100 matrix | still holds fairly well, no matter what the precision (unless we | leave the realm of FP altogether for modular arithmetic, etc). Using more precision still does not give you any more accuracy than the original input. GIGO. | Another point, although many quantities derrived from the real world are not | known to high accuracy, this is certainly not true of some common physical | constants, e.g. Plank's constant or the speed of light. That's true, but my assertion that the number of things that we know to that accuracy is small, compared to the number of things being calculated. We know pi to at least a million digits, but that doesn't help much when multiplying a radius by 2*pi if we only know the radius to 2 digits of accuracy. Somebody in private email mentioned to me about the problem of handling money to 10 signicant places (ie, financial transactions). I mentioned back that these type of calculations are (almost always) required to be in decimal (or scaled integer), and not floating point. Tying in with the other thread of discussion (ie, 64 bit ints), 64 bits is just barely enough bits to be able to handle COBOL's 18 digit accuracy requirements if you are doing the calculations in integer mode. -- Michael Meissner email: meissner@osf.org phone: 617-621-8861 Open Software Foundation, 11 Cambridge Center, Cambridge, MA, 02142 Do apple growers tell their kids money doesn't grow on bushes?