Polynomial Roots - how to interpret realprecision?

[Gordon Royle <gordon@csse.uwa.edu.au>]

I want to use "polroots" to calculate the roots of a large number of 
*integer* polynomials.

The documentation indicates that the precision is kept in the variable 
realprecision.... and then it says

".. it is guaranteed to converge and to give the roots to the required 
precision"


Now, does this mean that the roots that are output are guaranteed 
correct to that number of places? From my (admittedly limited) 
understanding of the sensitivity of roots of polynomials, I was under 
the impression that this would require some intermediate calculations 
to be performed to a greater precision ...  is this so?

Thanks

Gordon