Bounded floating point: Identifying and revealing floating-point error

Abstract

This paper presents a new floating-point technology: Bounded Floating Point (BFP) that constrains inexact floating-point values by adding a new field to the standard floating point data structure. This BFP extension to standard floating point identifies the number of significant bits of the representation of an infinitely accurate real value, which standard floating point cannot. The infinitely accurate real value of the calculated result is bounded between a lower bound and an upper bound. Presented herein are multiple demonstrations of the BFP software model, which identifies the number of significant bits remaining after a calculation and displays only the number of significant decimal digits. These show that BFP can be used to pinpoint failure points. This paper analyzes the thin triangle area algorithm presented by Kahan and compares it to an earlier algorithm by Heron. BFP is also used to demonstrate zero detection and to correctly identify an otherwise unstable matrix.