Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)

Searching for the hardest-to-round cases for the correct rounding of some function f on an interval I in a fixed precision can be done efficiently by first approximating the considered function by a polynomial, on which specific algorithms are then applied. One also needs to determine an enclosure of the range f(I), more precisely the exponent range. Our implementation currently uses Maple and the intpakX interval arithmetic package in order to compute both the exponent range and the polynomial approximation. But Maple/intpakX has various drawbacks. The GNU MPFR library has since been available and could be used for our computations in arbitrary precision. But we need an interval arithmetic on top of it. As reliability matters more than performance in this context, we seek to implement a minimal interval arithmetic by generating code on the fly using MPFR. The implementation should be as simple as possible so that it could easily be checked and/or proved formally.