{"title":"连分式在数字计算机上快速求函数的应用","authors":"Amnon Bracha","doi":"10.1109/ARITH.1972.6153908","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to develop a method for evaluation of certain elementary functions on a digital computer by the use of continued fractions. The time required for this evaluation is drastically reduced by using “short” operations like shift and add, instead of multiplications. Consistency is the most important factor that allows the expansion of a function into a continued fraction. Several cases are discussed and in particular the solution of the quadratic equation is discussed in more detail to demonstrate the convergence of the method.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"18 1","pages":"1-13"},"PeriodicalIF":0.0000,"publicationDate":"1972-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Application of continued fractions for fast evaluation of certain functions on a digital computer\",\"authors\":\"Amnon Bracha\",\"doi\":\"10.1109/ARITH.1972.6153908\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to develop a method for evaluation of certain elementary functions on a digital computer by the use of continued fractions. The time required for this evaluation is drastically reduced by using “short” operations like shift and add, instead of multiplications. Consistency is the most important factor that allows the expansion of a function into a continued fraction. Several cases are discussed and in particular the solution of the quadratic equation is discussed in more detail to demonstrate the convergence of the method.\",\"PeriodicalId\":6526,\"journal\":{\"name\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"volume\":\"18 1\",\"pages\":\"1-13\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1972-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1972.6153908\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE 22nd Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1972.6153908","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Application of continued fractions for fast evaluation of certain functions on a digital computer
The purpose of this paper is to develop a method for evaluation of certain elementary functions on a digital computer by the use of continued fractions. The time required for this evaluation is drastically reduced by using “short” operations like shift and add, instead of multiplications. Consistency is the most important factor that allows the expansion of a function into a continued fraction. Several cases are discussed and in particular the solution of the quadratic equation is discussed in more detail to demonstrate the convergence of the method.
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