Accelerated Polynomial Evaluation and Differentiation at Power Series in Multiple Double Precision

Jan Verschelde

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arXiv · 2101.10881

Accelerated Polynomial Evaluation and Differentiation at Power Series in Multiple Double Precision

Jan Verschelde

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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.

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Jan Verschelde. 2021-01-22. Accelerated Polynomial Evaluation and Differentiation at Power Series in Multiple Double Precision. https://arxiv.org/abs/2101.10881

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