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Subject: Re: Towards a basis for Bruce Stark's Tables
From: Bruce Stark (Stark4677@XXX.XXX)
Date: Fri Jan 03 2003 - 15:06:24 EST
Fred,
I'm pretty sure the Gauss who invented addition and subtraction logs was not
the Gauss you're thinking of. In any event, Gaussian addition and subtraction
logs have nothing to do with Gauss' formulas.
In logarithmic calculation, a plus or minus sign between expressions is a
real pain in the neck. Everything comes to a halt while you reduce both
expressions from logarithmic to natural values, add or subtract and, in most
cases, convert back to a log. This is not only troublesome: accuracy can be
lost through rounding error buildup.
Gaussian logs provide a way past those plus and minus signs without loss of
accuracy. I'll explain addition logs only, since my system doesn't use
subtraction logs.
Suppose you have log x and log y, but what you want is log (x + y).
Log x - log y = log (x/y).
Enter the Gaussian table with log (x/y) and it gives you the log (x/y + 1).
Add log y to log (x/y + 1) and you have log (x + y). The very thing you were
looking for!
Since a Gaussian addition log is by nature positive, and every other log in
my system is negative, the Gaussian has to be subtracted from, rather than
added to, log y.
So much for now.
Bruce
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