Accelerated Polynomial Evaluation and Differentiation at Power Series in Multiple Double Precision
Abstract
The problem is to evaluate a polynomial in several variables and its gradient at a power series truncated to some finite degree with multiple double precision arithmetic. To compensate for the cost overhead of multiple double precision and power series arithmetic, data parallel algorithms for general purpose graphics processing units are presented. The reverse mode of algorithmic differentiation is organized into a massively parallel computation of many convolutions and additions of truncated power series. Experimental results demonstrate that teraflop performance is obtained in deca double precision with power series truncated at degree 152. The algorithms scale well for increasing precision and increasing degrees.
Cite
@article{arxiv.2101.10881,
title = {Accelerated Polynomial Evaluation and Differentiation at Power Series in Multiple Double Precision},
author = {Jan Verschelde},
journal= {arXiv preprint arXiv:2101.10881},
year = {2021}
}
Comments
Improved the introduction, adding two citations to related work; fixed error, added table on the fluctuations of wall clock times. To appear in the Proceedings of the 2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)