基于右移k-ary消减的递归最大公因子算法  

Recursive Greatest Common Divisor Algorithm Based on Right-Shift k-ary Reduction

作　　者：王广赛 曾光 韩文报 

机构地区：[1]数学工程与先进计算国家重点实验室,河南郑州450001

出　　处：《信息工程大学学报》2016年第2期190-193,共4页Journal of Information Engineering University

基　　金：国家自然科学基金资助项目(61003291);数学工程与先进计算国家重点实验室开放课题基金资助项目(2013A03;2013A10)

摘　　要：对于输入B和C,利用Sorenson的右移k-ary消减(right-shift k-ary reduction)思想提出一种算法用于寻找整数x和y,使得x和y满足Bx-Cy在二进制表示下低比特位部分为0,利用该算法能够大规模降低循环次数,再结合模算法,提出递归最大公因子算法。递归最大公因子算法复杂度虽然对Knuth-Schnhage算法的复杂度上没有提高,仍然是O(nlog2nloglogn),但是该算法相比于Knuth-Schnhage算法实现简单,正确性分析和复杂度分析都比较容易。For input B and C,an algorithm for finding the integers x and y,such that x and y satisfy the least significant bits of Bx- Cy were 0,is presented based on right-shift k-ary reduction proposed by Sorenson. It can reduce a large number of cycles by using the algorithm to find the integers x and y. A recursive GCD algorithm is proposed combined with mold algorithm. When the size of the input is n bits,the complexity of the recursive GCD algorithm is O（ nlog^2nloglogn）. Compared to KnuthSchnhage algorithm,our algorithm is easier to implement. Also it is easier to prove and analyze.

关 键 词：最大公因子算法 欧几里得算法 二进制GCD算法 右移k-ary消减 整数最大公因子算法 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]