Two Fast Parallel GCD Algorithms of Many Integers
نویسنده
چکیده
We present two new parallel algorithms which compute the GCD of n integers of O(n) bits in O(n/ logn) time with O(n) processors in the worst case, for any ε > 0 in CRCW PRAM model. More generally, we prove that computing the GCD of m integers of O(n) bits can be achieved in O(n / logn) parallel time with O(mn ) processors, for any 2 ≤ m ≤ n/ logn, i.e. the parallel time does not depend on the number m of integers considered in this range. We suggest an extended GCD version for many integers as well as an algorithm to solve linear Diophantine equations.
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