基于高精度乘累加的LU分解加速器的设计  

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

作　　者：雷元武[1] 窦勇[1] 郭松[1] 李鑫[1] 雷国庆[1] 

机构地区：[1]国防科技大学计算机学院,湖南长沙410073

出　　处：《计算机工程与科学》2009年第11期33-36,共4页Computer Engineering & Science

基　　金：国家自然科学基金资助项目(60633050)

摘　　要：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。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 decompositions. 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-accumulating 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 he achieved.

关 键 词：舍入误差 LU分解 高精度乘累加 

分 类 号：TP303[自动化与计算机技术—计算机系统结构]