Precision Arithmetic: A New Floating-Point Arithmetic

Details Precision Arithmetic: A New Floating-Point Arithmetic Precision Arithmetic: A New Floating-Point Arithmetic

2006-06-25

arxiv.org/abs/cs/0606103v18

Computer Science

Discrete Mathematics

131 Pages, 55 Figures

Scientific paper

A new 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 its bounding range is much tighter. Its stable rounding error distribution is 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 uncertainty-tracking for linear algorithms. The precision arithmetic is available publicly at http://precisionarithm.sourceforge.net.

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