可变精度超越函数算法设计

Algorithm Design of Variable Precision Transcendental Functions

超越函数是基础数学函数库的主体部分,其精度和性能决定着上层应用的精度和性能。针对超越函数的实现繁琐易错、应用精度需求各异等问题,文中提出并实现兼顾通用性和函数数学特性的可变精度超越函数算法。依据超越函数的相似性,构建“转换-归约-逼近-重建”算法模板,实现常见的超越函数算法;并通过调整算法模板参数来控制误差,生成不同精度版本的函数代码。实验验证,所提算法能够生成常见超越函数的不同精度版本的函数代码,且相对标准数学库超越函数具有性能优势。

Transcendental functions are the main part of fundamental mathematical software library.Their accuracy and perfor-mance greatly determine those of the upper-layer applications.Aiming at the problems of tedious and error-prone implementation of transcendental functions as well as accuracy requirements of different applications,a variable precision transcendental function algorithm is proposed,which considers both generality and mathematical characteristics of functions.Based on the similarity of transcendental functions,a transformation-reduction-approximation-reconstruction algorithm template is constructed to unify common transcendental function algorithm implementations,and the algorithm template parameters are adjusted to handle errors to generate different precision versions of function codes.Experiment results show that the algorithm is able to generate function codes of different precision versions of common transcendental functions and has performance advantages over the corresponding functions in the standard mathematical software library.