Parallel Univariate Real Root Isolation on Multicore Processors

We present parallel algorithms with optimal cache complexity for the kernel routine of many real root isolation algorithms, namely, Taylor shift, targeting multicore processors. We then report an efficient multithreaded implementation for isolating the real roots of univariate polynomials based on the parallel Taylor shift algorithms. For processing some well‐known benchmark examples with sufficiently large size, our software tool reaches linear speedup on a 8‐core machine. In addition, we show that our software is able to fully utilize the many cores and the memory space of a 32‐core machine to tackle large problems that are out of reach for a desktop implementation.