The Unum Number Format: Mathematical Foundations, Implementation and Comparison to IEEE 754 Floating-Point Numbers
For numerical computing researchers, this work provides a theoretical comparison of Unums to IEEE 754, but it is an incremental analysis without empirical results.
This thesis examines the Unum number format, an interval arithmetic-based alternative to IEEE 754 floating-point, and evaluates its potential where floating-point is inadequate. It builds theoretical foundations for both formats and interval arithmetic.
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.