一种基数为4的高基数SRT立方根算法设计与实现  

Design and implementation of a high-radix SRT cube root algorithm with radix-4

作　　者：赵彩虹 刘梓璇 周建涛[1,3,4,5] ZHAO Caihong;LIU Zixuan;ZHOU Jiantao(College of Computer Science,Inner Mongolia University,Hohhot 010021;School of Software,Tsinghua University,Beijing 100084;Engineering Research Center of Ecological Big Data,Ministry of Education,Hohhot 010021;Inner Mongolia Engineering Laboratory for Cloud Computing and Service Software,Hohhot 010021;Inner Mongolia Engineering Laboratory for Big Data Analysis Technology,Hohhot 010021,China)

机构地区：[1]内蒙古大学计算机学院,内蒙古呼和浩特010021 [2]清华大学软件学院,北京100084 [3]生态大数据教育部工程研究中心,内蒙古呼和浩特010021 [4]内蒙古自治区云计算与服务软件工程实验室,内蒙古呼和浩特010021 [5]大数据分析技术内蒙古自治区工程实验室,内蒙古呼和浩特010021

出　　处：《计算机工程与科学》2025年第2期228-237,共10页Computer Engineering & Science

基　　金：国家自然科学基金(62162046);内蒙古科技攻关项目(2021GG0155);内蒙古自然科学基金重大项目(2019ZD15);内蒙古自治区关键技术攻关计划课题(2019GG372)。

摘　　要：SRT立方根算法在多媒体、计算机图形学等领域发挥着重要作用。虽然现有算法可通过增加基数以加快计算速度,但仍存在初始化处理缺乏、商位选择表设计复杂及实现困难的问题。研究设计并实现基数为4的SRT立方根算法。首先,提出一种高基数SRT立方根初始化算法,保证后续迭代计算的可执行性;设计基数为4的SRT立方根算法的商位选择表,为商位选择提供必要条件;优化即时转换算法,能够避免转换过程中出现多次进位的情况。其次,基于PyRTL工具改进并实现了上述基数为4的SRT立方根算法,有效缓解了高基数SRT立方根算法困难的问题。最后,与现有基数为2的SRT立方根算法进行对比,以证明该算法的有效性和优越性。The SRT cube root algorithm plays a significant role in fields such as multimedia and computer graphics.Although existing algorithms can accelerate computation by increasing the radix,they still face issues such as a lack of initialization processing,complex design of the quotient digit selection table,and implementation difficulties.This paper designs and implements an SRT cube root algorithm with radix-4.Firstly,proposing a high-radix SRT cube root initialization algorithm to ensure the feasibility of subsequent iterative calculations;designing a quotient digit selection table for the radix-4 SRT cube root algorithm to provide necessary conditions for quotient digit selection;optimizing the timely conversion algorithm to avoid multiple carries during the conversion process.Secondly,the above radix-4 SRT cube root algorithm is improved and implemented based on the PyRTL tool,effectively mitigat-ing the implementation challenges of high-radix SRT cube root algorithms.Finally,a comparison with the existing radix-2 SRT cube root algorithm demonstrates the effectiveness and superiority of the proposed algorithm.

关 键 词：SRT立方根算法 高基数 商位选择表 硬件算法 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]