精确算术：一种新的浮点算术
Precision Arithmetic: A New Floating-Point Arithmetic
AI总结：
本文提出一种新的确定性浮点算术——精确算术，通过新颖舍入方案和基于统计的误差跟踪，在正常使用中比区间算术更紧地跟踪和界定不确定性。
摘要：
开发了一种新的确定性浮点算术，称为精确算术，用于跟踪算术计算的精度。它采用一种新颖的舍入方案，以避免传统浮点算术中过度的舍入误差传播。与区间算术不同，其不确定性跟踪基于统计学和中心极限定理，具有更紧的边界范围。其稳定的舍入误差分布由截断正态分布近似。讨论了验证具有不确定性的算术的通用标准和系统方法。在正常使用中，精确算术在不确定性跟踪和不确定性边界方面均优于区间算术。精确算术可在 http://precisionarithm.sourceforge.net 公开获取。
英文摘要：
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.
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