Precision Arithmetic: A New Floating-Point Arithmetic
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2006
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| _version_ | 1866908599839621120 |
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| author | Wang, Chengpu |
| author_facet | Wang, Chengpu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cs_0606103 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | Precision Arithmetic: A New Floating-Point Arithmetic Wang, Chengpu Discrete Mathematics Data Structures and Algorithms Numerical Analysis 65Y04, 65T50 G.1.0 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. |
| title | Precision Arithmetic: A New Floating-Point Arithmetic |
| topic | Discrete Mathematics Data Structures and Algorithms Numerical Analysis 65Y04, 65T50 G.1.0 |
| url | https://arxiv.org/abs/cs/0606103 |