Gabor Grothendieck wrote:
Michael Grottke <Michael.Grottke <at> duke.edu> writes:
: I am currently using R for fitting a model to various data sets
: (minimizing the negative log-likelihood) and calculating a number of
: metrics based on the parameter estimates. Within these calculations, I
: have steps of the form
:
: log(log(1+x)),
:
: where x can be very small (e.g., around 1e-16). Unfortunately, the
: precision of doubles does not suffice for coping with the difference in
: the orders of magnitude of 1 and x: 1+x is rounded to 1.
:
: One way for solving this problem seems to be to use an arbitrary
: precision library implemented in C and call the respective routines for
: calculating the logarithm(s) from within R.
:
: My questions are as follows:
: 1. Is there any better/more direct way to solve the problem?
: 2. Is there any arbitrary precision library you can suggest in particular?
:
The approximation log(1+x) = x would be accuate to several decimal
places in your case so your expression would reduce to
log(log(1+x)) = log(x).
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Kjetil
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