Computer Science > Mathematical Software
[Submitted on 15 Oct 2023]
Title:A Number Representation Systems Library Supporting New Representations Based on Morris Tapered Floating-point with Hidden Exponent Bit
View PDFAbstract: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.
Current browse context:
cs.MS
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
Connected Papers (What is Connected Papers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.