{"title":"High Degree Toom'n'Half for Balanced and Unbalanced Multiplication","authors":"Marco Bodrato","doi":"10.1109/ARITH.2011.12","DOIUrl":null,"url":null,"abstract":"Some hints and tricks to automatically obtain high degree Toom-Cook implementations, i.e. functions for integer or polynomial multiplication with a reduced complexity. The described method generates quite an efficient sequence of operations and the memory footprint is kept low by using a new strategy: mixing evaluation, interpolation and recomposition phases. It is possible to automatise the whole procedure obtaining a general Toom-n function, and to extend the method to polynomials in any characteristic except two.","PeriodicalId":272151,"journal":{"name":"2011 IEEE 20th Symposium on Computer Arithmetic","volume":"67 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 IEEE 20th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.2011.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
Some hints and tricks to automatically obtain high degree Toom-Cook implementations, i.e. functions for integer or polynomial multiplication with a reduced complexity. The described method generates quite an efficient sequence of operations and the memory footprint is kept low by using a new strategy: mixing evaluation, interpolation and recomposition phases. It is possible to automatise the whole procedure obtaining a general Toom-n function, and to extend the method to polynomials in any characteristic except two.
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