Precision Arithmetic: A New Floating-Point Arithmetic

TL;DR

Precision arithmetic is a new deterministic floating-point method that improves uncertainty tracking and bounding by using a novel rounding scheme and statistical uncertainty modeling, outperforming interval arithmetic.

Contribution

It introduces a new floating-point arithmetic that employs a unique rounding scheme and statistical uncertainty tracking, enhancing precision and bounding over existing methods.

Findings

Better uncertainty tracking than interval arithmetic

Tighter uncertainty bounding range

Stable rounding error distribution approximated by truncated normal

Abstract

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding range. Its stable rounding error distribution is approximated by a truncated normal distribution. Generic standards and systematic methods for validating uncertainty-bearing arithmetics are discussed. The precision arithmetic is found to be better than interval arithmetic in both uncertainty-tracking and uncertainty-bounding for normal usages. The precision arithmetic is available publicly at http://precisionarithm.sourceforge.net.