[R] (arbitrary) precision

[Gabor Grothendieck]

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).