牛顿迭代公式在定点数开立方中的运用  

Application of Newton iteration in fixed-point cubic-root calculation

作　　者：王科人[1] 张兴明[1] 杨镇西[1] 

机构地区：[1]国家数字交换系统工程技术研究中心,河南郑州450002

出　　处：《电子技术应用》2010年第4期51-53,57,共4页Application of Electronic Technique

基　　金：国家863计划重点项目(No.2008AA011002)

摘　　要：分析了牛顿迭代算法直接用于开立方的缺点,针对常见的32 bit定点数,提出一种变形的牛顿迭代法与查表法相结合的开立方算法,并进行了相应的软硬件仿真。结果表明,该算法误差精确到整数位,满足定点数开立方要求,占用资源合理,时延性能优于常见的逐位循环算法,是一种可行的快速开立方算法。The defect of standard Newton iteration used for cubic-root calculation is analyzed.For common 32 bit fixed-point integer,an algorithm based on the combination of modified newton iteration and look-up table is proposed, software and hardware simulation of which is implemented. The simulation results show that errors of this algorithm never exceed 1 ,which satisfies the requirement of fixed-point cubic-root, and the resources occupied is resonable. Besides,time delay of this algorithm outperforms digit-recurrence algorithm used commonly for square-root calculation. Therefore, it＇s an effective algorithm for rapid cubic-root calculation.

关 键 词：立方根 牛顿迭代 查表法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]