In the introduction, we rst discuss the motivation for autotuned high performance
polynomial multiplication library. Second, we provide a formal problem statement of
the thesis from both the algorithmic and the program generation perspectives. Third,
we review the state-of-the-art of related work as well as their limitations. Fourth, we
summarize the contribution of the thesis, including new algorithms and optimization
techniques, and extensions and enhancements for a library generation system. Finally,
we brie
y introduce the organization of this thesis.