Luo et al wrote in a recent paper [A Fast Algorithm for Computing gcd Based on Binary Multi Precision,this journal,2002,Vol.32,No.5,pp.542 545; MR 2003h:11161 ] that “the classical Euclid’s algorithm for computing t...Luo et al wrote in a recent paper [A Fast Algorithm for Computing gcd Based on Binary Multi Precision,this journal,2002,Vol.32,No.5,pp.542 545; MR 2003h:11161 ] that “the classical Euclid’s algorithm for computing the gcd of two integers takes time O(\%ln\% 3N)”, and “present” an improved algorithm (called “binary gcd” for short) based on binary multi precision with time complexity O(\%ln\% 2N). In this paper,we point out two well known facts: firstly,the binary gcd,without usefull implimentation improvements, is identical in mathematical theory to Stein’s Binary GCD algorithm published in 1967; secondly,both Euclid’s algorithm and Binary GCD have the same time complexity O(\%ln\% 2N).展开更多
文摘Luo et al wrote in a recent paper [A Fast Algorithm for Computing gcd Based on Binary Multi Precision,this journal,2002,Vol.32,No.5,pp.542 545; MR 2003h:11161 ] that “the classical Euclid’s algorithm for computing the gcd of two integers takes time O(\%ln\% 3N)”, and “present” an improved algorithm (called “binary gcd” for short) based on binary multi precision with time complexity O(\%ln\% 2N). In this paper,we point out two well known facts: firstly,the binary gcd,without usefull implimentation improvements, is identical in mathematical theory to Stein’s Binary GCD algorithm published in 1967; secondly,both Euclid’s algorithm and Binary GCD have the same time complexity O(\%ln\% 2N).
