采用多精度基础函数的混合精度优化方法  

Mixed-Precision Optimization Method Based on Multi-Precision Basic Functions

作　　者：郝江伟 周蓓[1] 许瑾晨[1] 庞建民[1] HAO Jiangwei;ZHOU Bei;XU Jinchen;PANG Jianmin(Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]信息工程大学,河南郑州450001

出　　处：《信息工程大学学报》2024年第6期703-709,共7页Journal of Information Engineering University

摘　　要：混合精度优化是一种浮点计算优化方法,通过混合使用不同精度的浮点变量和基础函数来提高程序性能。相比于浮点变量,基础函数的精度变化更多,但也大大扩充了混合精度优化空间,导致最优方案的搜索难度增加。针对上述问题,提出基于多精度基础函数的混合精度优化方法,实现函数级的快速混合精度优化。首先,通过区间归约和多项式逼近,自动生成指定区间的多精度基础函数;其次,基于帕累托最优策略,对包含基础函数的表达式实现最优混合精度方案的快速搜索。实验结果表明,在阈值为双精度版本的2倍平均误差的情况下,该方法可以为所有测试用例快速找到误差不高于误差阈值的最优混合精度,其相比于双精度版本的平均性能提升比为1.16。Mixed-precision optimization is a floating-point computation optimization method that im-proves program performance by using a combination of floating-point variables and basic functions with different precisions.Compared to floating-point variables,basic functions have more variations in precision,which greatly expands the mixed-precision optimization space,but also increases the diffi-culty of searching for optimal solutions.In response to the above problem,a mixed-precision optimiza-tion method based on multi-precision basic functions is proposed,which achieves fast mixed-precision optimization at the function level.Firstly,multi-precision basic functions for a specified interval are au-tomatically generated through interval reduction and polynomial approximation by this method.Sec-ondly,based on the Pareto optimal strategy,a fast search for the optimal mixed-precision solution is implemented for expressions containing basic functions.Experimental results show that,under the con-dition that the error threshold is twice the average error of the double-precision version,the optimal mixed-precision solutions for all cases with errors not exceeding the error threshold can be quickly found by this method.The average performance improvement of this method compared to the double precision version is 1.16.

关 键 词：浮点计算 混合精度 基础函数 帕累托优化 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论]