On Schoenhage's algorithm and subquadratic integer gcd computation
Abstract
We describe a new subquadratic lefttoright GCD algorithm, inspired by Schoenhage's algorithm for reduction of binary quadratic forms, and compare it to the first subquadratic GCD algorithm discovered by Knuth and Schoenhage, and to the binary recursive GCD algorithm of Stehle and Zimmermann. The new GCD algorithm runs slightly faster than earlier algorithms, and it is much simpler to implement. The key idea is to use a stop condition for HGCD that is based not on the size of the remainders, but on the size of the next difference. This subtle change is sufficient to eliminate the backup steps that are necessary in all previous subquadratic lefttoright GCD algorithms. The subquadratic GCD algorithms all have the same asymptotic running time, O(n (log n)^ 2 log log n) .
 Publication:

Mathematics of Computation
 Pub Date:
 March 2008
 DOI:
 10.1090/S0025571807020170
 Bibcode:
 2008MaCom..77..589M