Multiple precision numbers & computations for R via GNU MPFR www.mpfr.org and the GNU Multiple Precision arithmetic library GMP, both external C libraries which are free/libre (which is "open source" but even more).
Rmpfr provides S4 classes and methods for arithmetic including transcendental ("special") functions for arbitrary precision floating point numbers. To this end, it interfaces to the LGPL ed MPFR (Multiple Precision Floating-Point Reliable) Library which itself is based on the GMP (GNU Multiple Precision) Library.
In 2012, Rmpfr is also interfacing to the R package gmp. gmp implements exact arithmetic for large integers and rationals, the former also "modulo m",
The Rmpfr project summary page is here.