The Unum Number Format: Mathematical Foundations, Implementation and Comparison to IEEE 754 Floating-Point Numbers

TL;DR

This paper explores the Unum number format based on interval arithmetic, compares it with IEEE 754 floating-point numbers, and establishes theoretical foundations for both formats and their applications.

Contribution

It introduces the Unum number format, develops its mathematical foundations, and compares its performance and suitability to IEEE 754 floating-point arithmetic.

Findings

Unums provide an alternative to floating-point with potential advantages in certain computations.

Theoretical foundations for Unums and IEEE 754 are established.

Comparison highlights scenarios where Unums outperform traditional floating-point numbers.

Abstract

This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are inadequate. In the course of this examination, this thesis builds theoretical foundations for IEEE 754 floating-point numbers, interval arithmetic based on the projectively extended real numbers and Unums.