This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
New Redundant Representations of Complex Numbers and Vectors
July 1993 (vol. 42 no. 7)
pp. 817-824

The authors present a redundant representation for complex numbers called polygonal representation. This representation enables fast carry-free addition, in a way quite similar to the carry-free addition in signed-digit number systems and is convenient for multiplication. The technique is generalized in order to handle n-dimensional vectors.

[1] D. Matula, "Basic digit sets for radix representation,"J. Ass. Comput. Mach., vol. 29, pp. 1131-1143, 1982.
[2] M. Petkovsek, "Contiguous digit sets and local rounding," in9th Symp. Computer Arithmetic, Santa Monica, CA, Sept. 1989.
[3] T. Carter and J. Robertson, "The set theory of arithmetic decomposition,"IEEE Trans. Comput., vol. 39, Aug. 1990.
[4] A. Avizienis, "Signed-digit number representations for fast parallel arithmetic,"IRE Trans. Electron. Comput., vol. 10, pp. 389-400, 1961.
[5] D. E. Knuth,The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Reading, MA: Addison-Wesley, 1981.
[6] Y. Herreros, "Contribution&agrave l'arithmétique des ordinateurs," Ph.D. dissertation, INPG Grenoble, 1991.

Index Terms:
redundant representation; complex numbers; polygonal representation; carry-free addition; signed-digit number systems; multiplication; n-dimensional vectors; digital arithmetic.
Citation:
J. Duprat, Y. Herreros, S. Kla, "New Redundant Representations of Complex Numbers and Vectors," IEEE Transactions on Computers, vol. 42, no. 7, pp. 817-824, July 1993, doi:10.1109/12.237722
Usage of this product signifies your acceptance of the Terms of Use.