A Number Representation Systems Library Supporting New Representations Based on Morris Tapered Floating-point with Hidden Exponent Bit

Abstract: The introduction of posit reopened the debate about the utility of IEEE754 in specific domains. In this context, we propose a high-level language (Scala) library that aims to reduce the effort of designing and testing new number representation systems (NRSs). The library's efficiency is tested with three new NRSs derived from Morris Tapered Floating-Point by adding a hidden exponent bit. We call these NRSs MorrisHEB, MorrisBiasHEB, and MorrisUnaryHEB, respectively. We show that they offer a better dynamic range, better decimal accuracy for unary operations, more exact results for addition (37.61% in the case of MorrisUnaryHEB), and better average decimal accuracy for inexact results on binary operations than posit and IEEE754. Going through existing benchmarks in the literature, and favorable/unfavorable examples for IEEE754/posit, we show that these new NRSs produce similar (less than one decimal accuracy difference) or even better results than IEEE754 and posit. Given the entire spectrum of results, there are arguments for MorrisBiasHEB to be used as a replacement for IEEE754 in general computations. MorrisUnaryHEB has a more populated ``golden zone'' (+13.6%) and a better dynamic range (149X) than posit, making it a candidate for machine learning computations.