A Tapered Floating Point Extension for the Redundant Signed Radix 2 System Using the Canonical Recoding

TL;DR

This paper introduces a tapered floating point encoding using a redundant signed radix 2 system with canonical recoding, offering superior dynamic range and comparable or better precision than IEEE-754-1985 and Posit systems, with versatile extension capabilities.

Contribution

It presents a novel tapered floating point encoding leveraging ternary technology, surpassing existing systems in dynamic range and supporting multiple extensions.

Findings

Higher dynamic range than Posit and IEEE-754-1985

Comparable or improved precision at similar input sizes

Supports diverse extensions including complex numbers and system artifacts

Abstract

A tapered floating point encoding is proposed which uses the redundant signed radix 2 system and is based on the canonical recoding. By making use of ternary technology, the encoding has a dynamic range exceeding that of the recently-proposed Posit number system and the IEEE 754-1985 Standard for Floating Point Arithmetic (IEEE-754-1985), and precision equal to or better than that of the IEEE-754-1985 system and the recently proposed Posit system when equal input sizes are compared. In addition, the encoding is capable of supporting several proposed extensions, including extensions to integers, boolean values, complex numbers, higher number systems, low-dimensional vectors, and system artifacts such as machine instructions. A detailed analytic comparison is provided between the proposed encoding, the IEEE-754-1985 system, and the recently proposed Posit number system.