A declarative specification of giant number arithmetic

Abstract

The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their bitsizes. While within constant factors from their traditional counterparts for their average and worst case behavior, our arithmetic operations open the doors for interesting numerical computations, intractable with a traditional number representation. We provide a complete specification of our algorithms in the form of a purely declarative Prolog program. © 2014 Springer International Publishing.