{"title":"除法和平方根的有效初始逼近和快速收敛方法","authors":"Masayuki Ito, N. Takagi, S. Yajima","doi":"10.1109/ARITH.1995.465383","DOIUrl":null,"url":null,"abstract":"Efficient initial approximations and fast converging algorithms are important to achieve the desired precision faster at lower hardware cost in multiplicative division and square root. In this paper, a new initial approximation method for division, an accelerated higher order converging division algorithm, and a new square root algorithm are proposed. They are all suitable for implementation on an arithmetic unit where one multiply-accumulate operation, can be executed in one cycle. In the case of division, the combination of our initial approximation method and our converging algorithm, enables a single iteration of the converging algorithm to produce double-precision quotients. Our new square root algorithm can form, double-precision square roots faster using smaller look-up tables than the Newton-Raphson method.<<ETX>>","PeriodicalId":332829,"journal":{"name":"Proceedings of the 12th Symposium on Computer Arithmetic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1995-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"37","resultStr":"{\"title\":\"Efficient initial approximation and fast converging methods for division and square root\",\"authors\":\"Masayuki Ito, N. Takagi, S. Yajima\",\"doi\":\"10.1109/ARITH.1995.465383\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Efficient initial approximations and fast converging algorithms are important to achieve the desired precision faster at lower hardware cost in multiplicative division and square root. In this paper, a new initial approximation method for division, an accelerated higher order converging division algorithm, and a new square root algorithm are proposed. They are all suitable for implementation on an arithmetic unit where one multiply-accumulate operation, can be executed in one cycle. In the case of division, the combination of our initial approximation method and our converging algorithm, enables a single iteration of the converging algorithm to produce double-precision quotients. Our new square root algorithm can form, double-precision square roots faster using smaller look-up tables than the Newton-Raphson method.<<ETX>>\",\"PeriodicalId\":332829,\"journal\":{\"name\":\"Proceedings of the 12th Symposium on Computer Arithmetic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"37\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 12th Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1995.465383\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 12th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1995.465383","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Efficient initial approximation and fast converging methods for division and square root
Efficient initial approximations and fast converging algorithms are important to achieve the desired precision faster at lower hardware cost in multiplicative division and square root. In this paper, a new initial approximation method for division, an accelerated higher order converging division algorithm, and a new square root algorithm are proposed. They are all suitable for implementation on an arithmetic unit where one multiply-accumulate operation, can be executed in one cycle. In the case of division, the combination of our initial approximation method and our converging algorithm, enables a single iteration of the converging algorithm to produce double-precision quotients. Our new square root algorithm can form, double-precision square roots faster using smaller look-up tables than the Newton-Raphson method.<>