Precision Arithmetic: A New FloatingPoint Arithmetic
Abstract
A new deterministic floatingpoint 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 floatingpoint 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 uncertaintybearing arithmetics are discussed. The precision arithmetic is found to be better than interval arithmetic in both uncertaintytracking and uncertaintybounding for normal usages. The precision arithmetic is available publicly at http://precisionarithm.sourceforge.net.
 Publication:

arXiv eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:cs/0606103
 Bibcode:
 2006cs........6103W
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Data Structures and Algorithms;
 Computer Science  Numerical Analysis;
 65Y04;
 65T50;
 G.1.0
 EPrint:
 54 Pages, 32 Figures