{"title":"On squaring and multiplying large integers","authors":"D. Zuras","doi":"10.1109/ARITH.1993.378084","DOIUrl":null,"url":null,"abstract":"Methods of squaring large integers are discussed. The obvious O(n/sup 2/) method turns out to be best for small numbers. The existing /spl ap/ O(n/sup 1.585/) method becomes better as the numbers get bigger. New methods that are /spl ap/ O(n/sup 1.465/) and /spl ap/ O(n/sup 2.404/) are presented. All of these methods can be generalized to multiplication and turn out to be faster than a fast Fourier transform (FFT) multiplication for numbers that can be quite large (>3,000,000 b). Squaring seems to be fundamentally faster than multiplication, but it is shown that T/sub mult/ /spl les/ 2T/sub sq/ + O(n).<<ETX>>","PeriodicalId":414758,"journal":{"name":"Proceedings of IEEE 11th Symposium on Computer Arithmetic","volume":"87 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"33","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of IEEE 11th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1993.378084","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 33
Abstract
Methods of squaring large integers are discussed. The obvious O(n/sup 2/) method turns out to be best for small numbers. The existing /spl ap/ O(n/sup 1.585/) method becomes better as the numbers get bigger. New methods that are /spl ap/ O(n/sup 1.465/) and /spl ap/ O(n/sup 2.404/) are presented. All of these methods can be generalized to multiplication and turn out to be faster than a fast Fourier transform (FFT) multiplication for numbers that can be quite large (>3,000,000 b). Squaring seems to be fundamentally faster than multiplication, but it is shown that T/sub mult/ /spl les/ 2T/sub sq/ + O(n).<>
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