Cache complexity and multicore implementation for univariate real root isolation

Abstract

Isolating the real roots of a univariate polynomial is a driving subject in computer algebra. This problem has been studied under various angles from algebraic algorithms [1, 2, 7] to implementation techniques [3, 5]. Today, multicores are the most popular parallel hardware architectures. Beside, understanding the implications of hierarchical memory on performance software engineering has become essential. These observations motivate our study. We analyze the cache complexity of the core routine of many real root isolation algorithms namely, the Taylor shift. Then, we present efficient multithreaded implementation on multicores.