Optimizing and parallelizing the modular GCD algorithm

Abstract

Our goal is to design and implement a high performance modular GCD algorithm for polynomial GCD computation in Zp[x1, x2, ..., xn] for multi-core computers which will be used to compute the GCD of polynomials over Z. For n = 2 we have designed and implemented in C a highly optimized serial code for primes p < 263. For n > 2 we parallelized in Cilk C Brown's dense modular GCD algorithm using our serial bivariate code at the base. For n = 3, we obtain good parallel speedup on multi-core computers with 16 and 20 cores. We also compare our code with the GCD codes in Maple and Magma.