{"title":"长整数的短除法","authors":"David Harvey, P. Zimmermann","doi":"10.1109/ARITH.2011.11","DOIUrl":null,"url":null,"abstract":"We consider the problem of short division -- i.e., approximate quotient -- of multiple-precision integers. We present ready-to-implement algorithms that yield an approximation of the quotient, with tight and rigorous error bounds. We exhibit speedups of up to 30% with respect to GMP division with remainder, and up to 10% with respect to GMP short division, with room for further improvements. This work enables one to implement fast correctly rounded division routines in multiple-precision software tools.","PeriodicalId":272151,"journal":{"name":"2011 IEEE 20th Symposium on Computer Arithmetic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Short Division of Long Integers\",\"authors\":\"David Harvey, P. Zimmermann\",\"doi\":\"10.1109/ARITH.2011.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of short division -- i.e., approximate quotient -- of multiple-precision integers. We present ready-to-implement algorithms that yield an approximation of the quotient, with tight and rigorous error bounds. We exhibit speedups of up to 30% with respect to GMP division with remainder, and up to 10% with respect to GMP short division, with room for further improvements. This work enables one to implement fast correctly rounded division routines in multiple-precision software tools.\",\"PeriodicalId\":272151,\"journal\":{\"name\":\"2011 IEEE 20th Symposium on Computer Arithmetic\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 IEEE 20th Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.2011.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 IEEE 20th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.2011.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the problem of short division -- i.e., approximate quotient -- of multiple-precision integers. We present ready-to-implement algorithms that yield an approximation of the quotient, with tight and rigorous error bounds. We exhibit speedups of up to 30% with respect to GMP division with remainder, and up to 10% with respect to GMP short division, with room for further improvements. This work enables one to implement fast correctly rounded division routines in multiple-precision software tools.
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