Abstract

An optical outer-product architecture is presented that performs residue arithmetic operations with position-coded lookup tables. The architecture can implement arbitrary integer-valued functions of two independent variables in a single gate delay. The outer-product configuration possesses spatial complexity (a gate count) that grows linearly with the size of the modulus, and therefore with the system’s dynamic range, in contrast to traditional residue lookup tables, which have quadratic growth in spatial complexity. The use of linear arrays of sources and modulators leads to power requirements that also grow linearly with the size of the modulus.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).
  2. S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).
  3. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, Appl. Opt. 18, 149 (1979).
    [CrossRef] [PubMed]
  4. C. C. Guest, T. K. Gaylord, Appl. Opt. 19, 1201 (1980).
    [CrossRef] [PubMed]
  5. A. P. Goutzoulis, E. C. Malarkey, D. K. Davies, J. C. Bradley, P. R. Beaudet, Appl. Opt. 27, 1674 (1988).
    [CrossRef] [PubMed]
  6. C. D. Capps, R. A. Falk, T. L. Houk, Appl. Opt. 27, 1682 (1988).
    [CrossRef] [PubMed]
  7. R. A. Athale, W. C. Collins, Appl. Opt. 21, 2089 (1982).
    [CrossRef] [PubMed]
  8. A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.
  9. D. A. B. Miller, Opt. Eng. 26, 368 (1987).

1988 (2)

1987 (1)

D. A. B. Miller, Opt. Eng. 26, 368 (1987).

1982 (1)

1980 (1)

1979 (1)

1977 (1)

S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).

Athale, R. A.

Beaudet, P. R.

Bradley, J. C.

Capps, C. D.

Collins, S. A.

S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).

Collins, W. C.

Davies, D. K.

Eichmann, G.

A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.

Falk, R. A.

Gaylord, T. K.

Goodman, J. W.

Goutzoulis, A. P.

Guest, C. C.

Ha, B.

A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.

Houk, T. L.

Huang, A.

Ishihara, S.

Kim, D. H.

A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.

Kostrzewski, A.

A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.

Li, Y.

A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.

Malarkey, E. C.

Miller, D. A. B.

D. A. B. Miller, Opt. Eng. 26, 368 (1987).

Szabo, N. S.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Tanaka, R. I.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Tsunoda, Y.

Appl. Opt. (5)

Opt. Eng. (1)

D. A. B. Miller, Opt. Eng. 26, 368 (1987).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).

Other (2)

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

A. Kostrzewski, Y. Li, B. Ha, D. H. Kim, G. Eichmann, in Digest of Annual Meeting of the Optical Society of America (Optical Society of America, Washington, D.C., 1988), paper MAA4.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Modulo 7 position-coded RNS addition and multiplication LUT’s.

Fig. 2
Fig. 2

Direct implementation of a modulo 7 LUT using two-input AND gates as processing elements.

Fig. 3
Fig. 3

Modulo 7 SMOP LUT architecture.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I = ( r 1 , r 2 , r 3 ,…, r Ν ) .
r i = | I | m i ,
Μ ( i , j ) = a ( i ) * b ( j ) .
sc = i = 1 N ( m i ) LD + i = 1 N ( m i ) MD ,

Metrics