{"title":"有限精度算术的基础","authors":"D. Matula","doi":"10.1109/ARITH.1972.6153887","DOIUrl":null,"url":null,"abstract":"Completeness and uniqueness properties for the representation of the base 㬲 digital numbers by finite length radix polynomials with various digit sets are studied. The digit sets guaranteeing completeness and uniqueness are characterized. A digital conversion algorithm is introduced for determining a base β radix polynomial with digits from a specified set D having a particular value whenever such a radix polynomial exists. The notion of precision of a radix polynomial is formalized, and the determination of the precision from the given base β, digit set D, and real value a of the radix polynomial is investigated.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"7 1","pages":"1-35"},"PeriodicalIF":0.0000,"publicationDate":"1972-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Foundations of finite precision arithmetic\",\"authors\":\"D. Matula\",\"doi\":\"10.1109/ARITH.1972.6153887\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Completeness and uniqueness properties for the representation of the base 㬲 digital numbers by finite length radix polynomials with various digit sets are studied. The digit sets guaranteeing completeness and uniqueness are characterized. A digital conversion algorithm is introduced for determining a base β radix polynomial with digits from a specified set D having a particular value whenever such a radix polynomial exists. The notion of precision of a radix polynomial is formalized, and the determination of the precision from the given base β, digit set D, and real value a of the radix polynomial is investigated.\",\"PeriodicalId\":6526,\"journal\":{\"name\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"volume\":\"7 1\",\"pages\":\"1-35\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1972-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1972.6153887\",\"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.1972.6153887","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Completeness and uniqueness properties for the representation of the base 㬲 digital numbers by finite length radix polynomials with various digit sets are studied. The digit sets guaranteeing completeness and uniqueness are characterized. A digital conversion algorithm is introduced for determining a base β radix polynomial with digits from a specified set D having a particular value whenever such a radix polynomial exists. The notion of precision of a radix polynomial is formalized, and the determination of the precision from the given base β, digit set D, and real value a of the radix polynomial is investigated.
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