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From: meissner@osf.org (Michael Meissner)
Newsgroups: comp.arch
Subject: Re: Killer Micro II
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vu0310@bingvaxu.cc.binghamton.edu (R. Kym Horsell) writes:
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 In article meissner@osf.org (Michael Meissner) writes:
 \\\
 >measurement only had 35 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 1214 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: 6176218861
Open Software Foundation, 11 Cambridge Center, Cambridge, MA, 02142
Do apple growers tell their kids money doesn't grow on bushes?