Fast Parallel Multi-point Evaluation of Sparse Polynomials

We present a parallel algorithm to evaluate a sparse polynomial in Zp[x0, ..., xn] into many bivariate images, based on the fast multi-point evaluation technique described by van der Hoeven and Lecerf [11]. We have implemented the fast parallel algorithm in Cilk C. We present benchmarks demonstrating good parallel speedup for multi-core computers. Our algorithm was developed with a specific application in mind, namely, the sparse polynomial GCD algorithm of Hu and Monagan [6] which requires evaluations of this form. We present benchmarks showing a large speedup for the polynomial GCD problem.