Balanced Dense Polynomial Multiplication on Multi-Cores

Abstract— In symbolic computation, polynomial multiplication is a fundamental operation akin to matrix multiplication in numerical computation. We present efficient implementation strategies for FFT-based dense polynomial multiplication targeting multi-cores. We show that balanced input data can maximize parallel speedup and minimize cache complexity for bivariate multiplication. However, unbalanced input data, which are common in symbolic computation, are challenging. We provide efficient techniques, what we call contraction and extension, to reduce multivariate (and univariate) multiplication to balanced bivariate multiplication. Our implementation in Cilk++ demonstrates good speedup on multi-cores. Keywords- parallel symbolic computation; parallel polynomial multiplication; parallel multi-dimensional FFT/TFT; Cilk++; multi-core;

• Type: Conference
• Year: 2009
• Where: PDCAT
• Authors: Marc Moreno Maza, Yuzhen Xie
• Keywords: Bivariate Multiplication, Distributed And Parallel Computing, PDCAT 2009, Polynomial Multiplication, Symbolic Computation