Universal coding of the reals: alternatives to IEEE floating point

Abstract

We propose a modular framework for representing the real numbers that generalizes ieee, posits, and related floating-point number systems, and which has its roots in universal codes for the positive integers such as the Elias codes. This framework unifies several known but seemingly unrelated representations within a single schema while also introducing new representations. We particularly focus on variable-length encoding of the binary exponent and on the manner in which fraction bits are mapped to values. Our framework builds upon and shares many of the attractive properties of posits but allows for independent experimentation with exponent codes, fraction mappings, reciprocal closure, rounding modes, handling of under- and overflow, and underlying precision.