
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
B.S. Fagin, "Fast Addition of Large Integers," IEEE Transactions on Computers, vol. 41, no. 9, pp. 10691077, September, 1992.  
BibTex  x  
@article{ 10.1109/12.165389, author = {B.S. Fagin}, title = {Fast Addition of Large Integers}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {9}, issn = {00189340}, year = {1992}, pages = {10691077}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.165389}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Fast Addition of Large Integers IS  9 SN  00189340 SP1069 EP1077 EPD  10691077 A1  B.S. Fagin, PY  1992 KW  computation time asymmetry; large integers; computational model; massively parallel processor; massively parallel algorithms; carrylookahead; binary addition; average case behavior; large nbit additions; multiple bits; digital arithmetic; parallel algorithms. VL  41 JA  IEEE Transactions on Computers ER   
The basic computational model of a massively parallel processor is discussed, and three massively parallel algorithms using carrylookahead techniques for binary addition of large integers are presented. It is shown how performance can be improved by exploiting the average case behavior of large nbit additions and the asymmetry of the computation time of two particular operations. Even better performance is obtained by grouping multiple bits per processor. Performance measurements of all the algorithms are presented and discussed.
[1] J. Baer,Computer Systems Architecture, Potomac, MD: Computer Science Press, 1980.
[2] A. W. Burkset al., "Preliminary discussion of a logical computing instrument," Report to U. S. Army Ordinance Dep., 1946.
[3] B. Fagin, "Negacyclic convolution using polynomial transforms on hypercubes,"IEEE Trans. Signal Processing, vol. 40, no. 8, pp. 18451851, Aug. 1992.
[4] B. Fagin, "Multiplication of large integers on hypercubes,"J. Parallel Distributed Comput., Mar. 1990.
[5] B. Fagin, "Large integer multiplication on massively parallel processors,"Frontiers of Massively Parallel Computation, pp. 3842, 1990.
[6] B. Fagin, "Fast addition of large integers," Tech. Rep., Thayer School of Eng., Dartmouth College, Hanover, NH 03755.
[7] R. Floyd, "The exact time required to perform generalized addition," inProc. Sixteenth Annu. Symp. Foundations Comput. Sci., 1975, pp. 35.
[8] W. D. Hillis and G. L. Steele, Jr., "Data parallel algorithms,"Commun. ACM, vol. 29, no. 12, pp. 11701183, Dec. 1986.
[9] K. Hwang,Computer Arithmetic: Principles, Architecture, and Design. New York: Wiley, 1979.
[10] Hyman, A. 1984.Charles Babbage: Pioneer of the Computer. Oxford: Oxford University Press.
[11] D. E. Knuth,The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Reading, MA: AddisonWesley, 1981.
[12] R. E. Ladner and M. J. Fischer, "Parallel prefix computation,"J. ACM, vol. 27, no. 4, pp. 831838, Oct. 1980.
[13] U. Ofman, "On the algorithmic complexity of discrete functions,"Dokl. Akad. Nauk USSR, vol. 145, no. 1, pp. 4851, 1962 (in Russian).
[14] S. Peng and T. Hudson, "Parallel algorithms for multiplying very large integers," inProc. 18th Int. Conf. Parallel Processing, vol. 3, 1988, pp. 173177.
[15] T. Rhyne, "Limitations on carry lookahead networks,"IEEE Trans. Comput., vol. C33, no. 4, pp. 373374, Apr. 1984.
[16] P. Spira, "The time required for group multiplication,"J. ACM, vol. 16, no. 2 pp. 235243, Apr. 1969.
[17] Connection Machine Technical Summary, Thinking Machines Corp., Cambridge, MA, 1989.
[18] C/Paris 5.1 User's Manual, Thinking Machines Corporation, Cambridge, MA, 1989.
[19] J. Uspensky,Introduction to Mathematical Probability, New York: McGrawHill, 1937, pp. 7784.
[20] S. Winograd, "On the time required for binary addition,"J. ACM, vol. 12, pp. 277285, 1965.