同符号数相加“大数吃小数”的界限：理论分析  

On bound of a large number annihilating a small number in addition operation of two numbers with same sign:theoretical analysis

作　　者：曹靖[1,2,3] 李建平[1,2,4] 

机构地区：[1]中国科学院大气物理研究所,北京100029 [2]中国科学院研究生院,北京100029 [3]天津理工大学理学院,天津300384 [4]北京师范大学全球变化与地球系统科学研究院,北京100875

出　　处：《天津师范大学学报（自然科学版）》2014年第4期25-27,共3页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(41375110);中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室(LASG)2012年度开放课题

摘　　要：研究计算机内部二进制浮点数IEEE754存储规则及相加过程,给出数值计算中两同号规范化数相加发生"大数吃小数"现象的严格理论界限,为实际数值计算中避免此类现象提供理论依据,并利用所得理论对数值试验中的现象及结论进行解释.By analyzing about storage pattern and addition operation of format binary floating-points based on IEEE754 standard, this paper found strict theoretical bounds for avoiding the phenomenon that a large number annihilating a small number in numerical computations when both of these two numbers are positive or negative. The bounds can be applied in practical numerical computations for any machine precision and any programming language. Moreover, the conclusions in this article give theoretical explanations for the phenomenons in numerical experiments.

关 键 词：“大数吃小数” 数值计算 IEEE754标准 规范化二进制浮点数 

分 类 号：O246[理学—计算数学]