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.

中文翻译：

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多重双精度幂级数上的加速多项式评估和微分

问题是要用多个双精度算术来评估多项式中的多项式及其在幂级数被截断到一定程度的幂级数下的梯度。为了补偿多个双精度和幂级数算法的开销，提出了用于通用图形处理单元的数据并行算法。算法微分的反向模式被组织为大量卷积和截断幂级数加法的大规模并行计算。实验结果表明，以幂级数在152度处被截断，可以达到十进制双精度的万亿次性能。该算法可很好地扩展以提高精度和程度。