On all existing processors interval operations are slower by magnitudes
than the corresponding floating-point operations. This is the great
hindrance to a wider acceptance. The main reasons why software
simulations of interval arithmetic are slow are the case selections for
interval multiplication (9 cases) and for division (14 cases) and the
simulation and frequent changes of the rounding mode.
in a Dagstuhl seminar in January 2006, Branimir Lambov showed how to use
*existing* hardware (namely SSE-2) to get fast interval arithmetic. See
kathrin.dagstuhl.de/files/Materials/06/06021/06021.LambovBranimir.Slides.pdf,
especially slide 18. Does any current implementation make use of his ideas?
Paul Zimmermann