Exact rounding of mathematical functions

floating-point number x is the nearest floating-point number from the
exact value f(x), with respect to the given precision and rounding mode.
The exact rounding is a difficult problem; this is the main reason why
mathematical functions (exp, log, sin, ...) are not included in the IEEE
754 standard. We will present two kinds of methods for exact rounding:
one that works in fixed and not-too-large precision, and another that
works in arbitrary precision. We will also present a prototype
implementation of the latter method in the MPFR library, and a comparison
with other free packages (Pari, CLN) that do not guarantee exact rounding.