FFT-Based Dense Polynomial Arithmetic on Multi-cores

• Published in: High Performance Computing Systems and Applications pp. 378 - 399
• Main Authors: Moreno Maza, Marc, Xie, Yuzhen
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2010
• Series: Lecture Notes in Computer Science
• Subjects: Cilk; multi-core; parallel multi-dimensional FFT/TFT; parallel normal form; Parallel polynomial arithmetic; parallel polynomial multiplication
• ISBN: 3642126588; 9783642126581
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-12659-8_28

We report efficient implementation techniques for FFT-based dense multivariate polynomial arithmetic over finite fields, targeting multi-cores. We have extended a preliminary study dedicated to polynomial multiplication and obtained a complete set of efficient parallel routines in Cilk++ for polynomial arithmetic such as normal form computation. Since bivariate multiplication applied to balanced data is a good kernel for these routines, we provide an in-depth study on the performance and the cut-off criteria of our different implementations for this operation. We also show that, not only optimized parallel multiplication can improve the performance of higher-level algorithms such as normal form computation but also this composition is necessary for parallel normal form computation to reach peak performance on a variety of problems that we have tested.