{"title":"New Arithmetic Algorithms for Hereditarily Binary Natural Numbers","authors":"Paul Tarau","doi":"10.1109/SYNASC.2014.23","DOIUrl":null,"url":null,"abstract":"Hereditarily binary numbers are a tree-based number representation derived from a bijection between natural numbers and iterated applications of two simple functions corresponding to bijective base 2 numbers. This paper describes several new arithmetic algorithms on hereditarily binary numbers that, while within constant factors from their traditional counterparts for their average case behavior, make tractable important computations that are impossible with traditional number representations.","PeriodicalId":150575,"journal":{"name":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2014.23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
Hereditarily binary numbers are a tree-based number representation derived from a bijection between natural numbers and iterated applications of two simple functions corresponding to bijective base 2 numbers. This paper describes several new arithmetic algorithms on hereditarily binary numbers that, while within constant factors from their traditional counterparts for their average case behavior, make tractable important computations that are impossible with traditional number representations.
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