基本初等函数的高精度快速计算的加速算法  

An Accelerated Algorithm for High Precision and Fast Calculation of Basic Elementary Functions

作　　者：蒋亚萍[1] 贺超[1] 秦惠增[1] 

机构地区：[1]山东理工大学理学院,山东淄博255049

出　　处：《数学的实践与认识》2017年第13期238-246,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61379009)

摘　　要：在现有的基本初等函数的高精度快速算法基础上,进一步研究基本初等函数的加速算法.现有的基本初等函数的高精度快速算法是通过对函数进行幂级数展开的方式来实现函数的任意精度快速计算.而其加速算法则是在幂级数展开之前,先利用函数的多种性质来缩减函数的参数,减少函数在进行幂级数展开时的计算难度,提高函数的计算速度.给出了加速算法,并从计算误差和算法复杂性两方面对该算法进行了分析,给出了误差最小,算法复杂性最低的最优加速算法.然后,对于三角函数、双曲函数、指数函数以及它们的反函数,在实数域上给出了的具体的加速过程和计算结果.In this paper, based on the existing high precision and fast algorithm of the basic elementary functions, we give the accelerated algorithm of the basic elementary functions. The existing high precision and fast algorithm of the basic elementary functions is achieved by studying the power series expansion of functions. And the accelerating algorithm is realized by reducing the size of the argument which is prior to the power series expansion of functions. In this way, we can decrease computational complexity and increase computing speed. Further more, we analyze the calculation error and the computational complexity of the algorithm, give the optimal acceleration algorithm which have the minimum error and the minimum algorithmic complexity. After that, for trigonometric function, hyperbolic function, exponential function and their inverse function, we give tile specific acceleration algorithm and errors in real number field.

关 键 词：基本初等函数 高精度快速计算加速算法 幂级数展开 参数缩减 

分 类 号：O174[理学—数学]