Affiliation:
1. Kent State Univ., Kent, OH
Abstract
Since the greatest common divisor (GCD) of two integers is a basic arithmetic operation used in many mathematical software systems, new algorithms for its computation are of widespread interest. The accelerated integer GCD algorithm discussed here is based on a reduction step proposed by Sorenson (
k
-ary reduction), coupled with the dmod operation similar to Norton's smod. Some practical limitations of Sorenson's reduction have been eliminated. Worst-case complexity is still
O
(n
2
) for
n
-bit input, but actual implementations given input about 4096 bits long perform over 5.5 times as fast as the binary GCD on one computer architecture having a multiply instruction. Independent research by Jebelean points to the same conclusions.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
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