Large integer multiplication on massively parallel processors

Author

Fagin, Barry S.

Author_Institution

Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH, USA

fYear

1990

fDate

8-10 Oct 1990

Firstpage

38

Lastpage

42

Abstract

Results obtained by multiplying large integers using the Fermat number transform are presented. The effectiveness of the approach was previously limited by word-length constraints, which are not a factor with many new computer architectures. A convolution algorithm on a massively parallel processor, based on the Fermat number transform, is presented. Examples of the tradeoffs between modulus, interprocessor communication steps, and input size are given. The application of this algorithm in the multiplication of large integers is then discussed, and performance results on a Connection Machine are reported. The results show multiplication times ranging from about 50 ms for 2-kb integers to 2600 ms for 8-Mb integers

Keywords

digital arithmetic; parallel algorithms; Connection Machine; Fermat number transform; convolution algorithm; input size; integer multiplication; interprocessor communication steps; massively parallel processors; modulus; word-length constraints; Arithmetic; Computer architecture; Convolution; Educational institutions; Multidimensional systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Frontiers of Massively Parallel Computation, 1990. Proceedings., 3rd Symposium on the

Conference_Location

College Park, MD

Print_ISBN

0-8186-2053-6

Type

conf

DOI

10.1109/FMPC.1990.89434

Filename

89434