Date: Tue, 14 Aug 2012 12:37:16 -0500 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: freebsd-numerics@freebsd.org Subject: Status of expl logl Message-ID: <502A8CCC.5080606@missouri.edu>
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Are people working on expl, logl and log1pl?
I was trying to brainstorm ideas. If one had an expl, one could create
a logl as follows:
long double logl(long double x)
{
long double y;
y = log(x);
y -= 1 - x*expl(-y);
}
Of course you would need prechecks to make sure log(x) doesn't overflow,
etc.
But my thinking is this. Use log(x) as a starting value for Newton's
Method. Since Newton's Method roughly doubles the number digits of
precision, only one iteration is needed.
It doesn't work so well if 1/e < x < e.
Anyway, just throwing out an idea.
Also, I came across this algorithm:
http://en.wikipedia.org/wiki/Logarithm#Arithmetic-geometric_mean_approximation
It does need a few extra bits of precision than you want in the final
answer. But it is used by mpfr, and it is surprisingly fast.
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