How can I increase precision in R when calculating with probabilities close to 0 and 1?

Question

I have the problem that a sum of variables representing probabilities in the [0,1] interval sum to 0 but should be >0. The problem

Answer 1

R itself can only deal with 64 bit floating point numbers, the Rmpfr package can deal with arbitrary precision floating point numbers:

library(Rmpfr)

> p1 = mpfr("0.8", 128)
> p2 = mpfr("0.9999999999999998", 128)

> p11 = p1 * p2
> p10 = p1 - p11
> p01 = p2 - p11
> p00 = 1 - p11 - p10 - p01

> p00
1 'mpfr' number of precision  128   bits 
[1] 4.00000000000000000000000461461738779728e-17

Edit: Use stings to define mpfr