论文标题
使用多派参数减少计算基本函数
Computing elementary functions using multi-prime argument reduction
论文作者
论文摘要
我们描述了一种用于对基本函数（EXP，Log，log，sin，Atan等）任意过度计算的算法，该算法在廉价的预先登记后，该算法从几千位最高到数百万位的精确算法中给出了先前的先前最先进算法的要素两个。遵循sch {Ö} nhage的想法，我们使用素数的二芬太汀组合进行了降低参数。我们的贡献是使用大量的素数，而不是一对，在快速算法的帮助下解决相关的整数关系问题。我们还列出了新的，优化的类似机械的公式，以进行必要的对数和北极预算。
We describe an algorithm for arbitrary-precision computation of the elementary functions (exp, log, sin, atan, etc.) which, after a cheap precomputation, gives roughly a factor-two speedup over previous state-of-the-art algorithms at precision from a few thousand bits up to millions of bits. Following an idea of Sch{ö}nhage, we perform argument reduction using Diophantine combinations of logarithms of primes; our contribution is to use a large set of primes instead of a single pair, aided by a fast algorithm to solve the associated integer relation problem. We also list new, optimized Machin-like formulas for the necessary logarithm and arctangent precomputations.
