Precision Arithmetic: A New Floating-Point Arithmetic
<|reference_start|>Precision Arithmetic: A New Floating-Point Arithmetic: 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.<|reference_end|>
@article{wang2006precision,
    title={Precision Arithmetic: A New Floating-Point Arithmetic},
    author={Chengpu Wang},
    journal={arXiv preprint arXiv:cs/0606103},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0606103},
    primaryClass={cs.DM cs.DS cs.NA}
}