On a two-layer modular arithmetic

被引：0

作者：

Chen, Benjamin ^{[1
]}

Li, Yu ^{[1
]}

Zima, Eugene ^{[1
]}

机构：

[1] Univ Waterloo, Cheriton Sch Comp Sceince, Waterloo, ON N2L 3G1, Canada

来源：

ACM COMMUNICATIONS IN COMPUTER ALGEBRA | 2023年 / 57卷 / 03期

关键词：

D O I：

10.1145/3637529.3637534

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two-layer organization of modular arithmetic is considered. Lower layer uses many moduli at hardware precision and simultaneous conversion to/from RNS as described in [2]. Upper layer uses specially selected large moduli allowing for fast reduction and/or reconstruction. Implementation of two di.erent strategies for selecting moduli on the upper layer confirms practicality of proposed approach.

引用

页码：133 / 136

页数：4

共 8 条

[1]

[Anonymous], 2004, Scaled remainder trees

[2] Simultaneous Conversions with the Residue Number System Using Linear Algebra [J].

Doliskani, Javad ;

Giorgi, Pascal ;

Lebreton, Romain ;

Schost, Eric .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2018, 44 (03)

[3] Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages [J].

Dumas, Jean-Guillaume ;

Giorgi, Pascal ;

Pernet, Clement .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2008, 35 (03)

[4]

Geddes KeithO., 1992, Algorithms for Computer Algebra

[5]

Hoeven Joris, 2017, Mathematical Aspects of Computer and Information Sciences. 7th International Conference, MACIS 2017. Proceedings: LNCS 10693, P95, DOI 10.1007/978-3-319-72453-9_7

[6]

Knuth D. E., ART COMPUTER PROGRAM, V2

[7] MULTIPLIKATION GROSSER ZAHLEN [J].

SCHONHAGE, A .

COMPUTING, 1966, 1 (03) :182-+

[8] Cunningham numbers in modular arithmetic [J].

Zima, E. V. ;

Stewart, A. M. .

PROGRAMMING AND COMPUTER SOFTWARE, 2007, 33 (02) :80-86

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