基于高精度乘累加的LU分解加速器的设计

本文首先分析LU分解中舍入误差的积累过程,建立精度损失与矩阵规模的关系模型来预测大规模LU分解的精度;然后,根据定点加法的简单、快速、无精度损失的特点,设计高精度乘累加器(HPMAcc),并基于此实现一个细粒度并行LU分解加速器。实验结果表明,和高精度软件库QD或MPFR相比,4PE结构的LU分解加速器能够取得100倍的加速比,同时取得90多位的计算精度。

Design of a LU Decomposition Accelerator Based on High-Precision Multiplying and Accumulating

In this paper we analyze the course of rounding error accumulation in the LU decomposition, and create a model, between the loss accuracy of the result and the scale of matrix, to predict the accuracy of large scale LU decomposi-tions. Then, we design a high-precision multiplying-accumulating (HPMAcc) unit in terms of the features of the simple, fast and error-free fixed-point add, and a fine-grain parallel LU decomposition accelerator based on this multiplying-accumu-lating unit Compared to the implementation of a high-precision software library such as QD or MPFR, the speed-up factors up to more than 100 are obtained. Meanwhile, more than 90 bits of accuracy can be achieved.