The Arithmetic of Even-Odd Trees

Even-Odd Trees are a canonical tree-based number representation derived from a bijection between trees defined by the data type equation T = 1 + T ∗ T ∗ + T ∗ T ∗ and positive natural numbers seen as iterated applications of o(x) = 2x and i(x) = 2x+ 1 Starting from 1. This paper introduces purely functional arithmetic algorithms for operations on Even-Odd Trees. While within constant factors from their traditional counterparts for their average case behavior, our algorithms make tractable important computations that are impossible with traditional number representations. Keywords—tree-based number representations, arithmetic with giant numbers, unconventional numbering systems, purely functional algorithms