Skip to main content

Advertisement

Log in

Novel Pipelined Architecture for Efficient Evaluation of the Square Root Using a Modified Non-Restoring Algorithm

  • Published:
Journal of Signal Processing Systems Aims and scope Submit manuscript

Abstract

The square root is a basic arithmetic operation in image and signal processing. We present a novel pipelined architecture to implement N-bit fixed-point square root operation on an FPGA using a non-restoring pipelined algorithm that does not require floating-point hardware. Pipelining hazards in its hardware realization are avoided by modifying the classic non-restoring algorithm, thus resulting in a 13% improved latency. Furthermore, the proposed architecture is flexible allowing modification as per individual application needs. It is demonstrated that the proposed architecture is approximately four times faster than its popular counterparts and at the same time it consumes 50% less energy for envelope detection at 268 MHz sampling rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  1. Sklar, B. (2001). Digital communications fundamentals and applications, 2nd ed. Person Education.

  2. Rappaport, T. S. (2002). Wireless communications principles and practice, 2nd ed. Prentice Hall Communication.

  3. Frerking, M. (2003). Digital signal processing in communications systems, 9th ed. Kluwer publisher.

  4. Li, Y., & Chu, W. (1997). Implementation of single precision floating point square root on FPGAs, Proceeding of the 5th IEEE symposium on FPGA-based custom computing Machines, 226–232.

  5. Liao, J. R. (2000). Real-time image reconstruction for spiral mri using fixed-point calculation. IEEE Transactions on Medical Imaging, 19(7), 690–698.

    Article  Google Scholar 

  6. Oberstar, E. L. (2007). Fixed-point representation & fractional math, http://www.superkits.net/whitepapers.htm.

  7. Sajid, I., Ahmed, M. M., Taj, I., & Humayun, M. (2008). Design of high performance fpga based face recognition system, Proceeding of Progress In Electromagnetic Research Symposium (PIERS) in Cambridge USA, 504–510.

  8. Kwon, T., & Draper, J. (2009). Floating point division and square root using a Taylor-series expansion algorithm. Microelectronics Journal, 40(11), 1601–1605.

    Article  Google Scholar 

  9. Wilkinson, J. H. (1962). Error analysis of eigenvalue techniques based on orthogonal transformations. Journal of the Society for Industrial and Applied Mathematics, 10(1), 162–195.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ortega, J. M. (1963). An error analysis of Householder’s method for the symmetric Eigenvalue problem. Numerische Mathematik, 5(1), 1–225.

    Article  MathSciNet  Google Scholar 

  11. Burden, R. L., & Faires, J. D. (2005). Numerical analysis, 7th ed. Thomson.

  12. Piromsopa, K., Arporntewan, C., & Chongstitvatana, P. (2001). An FPGA implementation of a fixed-point square root operation, Proceedings of the International Symposium on Communications and Information Technology, ChiangMai, Thailand, 587–589.

  13. Soderquist, P., & Leeser, M. (1996). Area and performance tradeoffs in floating-point divide and square-root implementations. ACM Computing Surveys, 28(3), 518–564.

    Article  Google Scholar 

  14. Ronald, S., & Viktor, P. K. (2004). Computing Lennard-Jones potentials and forces with recogfigurable hardware, International Conference on Engineering of Reconfigurable Systems and Algorithms, 284–290.

  15. Soderquist, P., & Leeser, M. (1997). Division and square root choosing the right implementation, IEEE Micro, 52–66.

  16. Louca L., Cook, T. A., & Johnson, W. H. (1996). Implementation of IEEE single precision floating point addition and multiplication on FPGAs, Proceeding of IEEE Symposium on FPGAs for Custom Computing Machines, IEEE Computer Society Press, 107–116.

  17. Shirazi, N., Walters, A., & Athanas, P. (1995). Quantitative analysis of floating point arithmetic on FPGA based custom computing machines, Proceeding of IEEE Symposium on FPGAs for Custom Computing Machines, IEEE Computer Society Press, 155–162.

  18. Thakkar, A. J., & Ejnioui, A. (2006). Design and implementation of double precision floating point division and square root on FPGAs, IEEE proceeding Aerospace Conference.

  19. Thakkar, A. J., & Ejnioui, A. (2006). Pipelining of double precision floating point division and square root operations, Proceedings of the 44th annual Southeast regional conference, 488–493.

  20. Deschamps, J., Jean, G., & Sutter, G. (2006). Synthesis of arithmetic circuits FPGA, ASIC, and embedded systems. Wiley.

  21. Power PC processor reference guide (2003). Embedded development kit.

  22. Oberman, S. F., & Flynn, M. J. (1997). Design issues in division and other floating-point operations. IEEE Transactions on Computers, 46(2), 154–161.

    Article  MathSciNet  Google Scholar 

  23. Bravo, I., Jimenez, P., Mazo, M., Lazaro, J. L., & Gardel, A. (2006). Implementation in FPGAS of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem, Proceeding of International Conference on Field Programmable Logic and Applications, 1–4.

  24. Ray, A. (1998). A survey of CORDIC algorithms for FPGA based computers, Proceeding of the ACM/SIGDA 6th International Symposium on Field-Programmable Gate Arrays, 191–200.

  25. Karp, A. H., & Markstein, P. (1997). High-precision division and square root. ACM Transactions on Mathematical Software, 23(4), 561–589.

    Article  MathSciNet  MATH  Google Scholar 

  26. Mailloux, G. J., Simard, S., & Beguenance, R. (2007). Implementaion of division and square root using XSG for FPGA-based vector control drives. International Journal of Electrical and Power Engineering, 5(1), 524–529.

    Google Scholar 

  27. Shang, L., Kaviani, A. S., & Bathala, K. (2002). Dynamic power consumption in Virtex-II FPGA family, Proceedings of the 2002 ACM/SIGDA tenth international symposium on Field-programmable gate arrays, USA, 157–164.

  28. Wang, X., & Nelson, B. E. (2003). Tradeoffs of designing floating point division and square root on Virtex FPGAs, IEEE Proceeding of Symposium on Field Programmable Custom Computing Machines, 195–203.

  29. Altera Application note 74 (2001). Evaluating Power for Altera Devices.

  30. Li, Y., & Chu, W. (1997). Parallel-array implementations of a non-restoring square root algorithm, International Conference on Computer Design, Texas, USA, 690–695.

  31. Li, Y., & Chu, W. (1996). A new non-restoring square root algorithm and its VLSI implementations, International Conference on Computer Design, USA, 538–544.

  32. Chu, W., & Li, Y. (1999). Cost/performance tradeoff of n-select square root implementations. In: Fifth Australasian Computer Architecture Conference, 9–16.

  33. Samavi, S., Sadrabadi, A., & Fanian, A. (2008). Modular array structure for non-restoring square root circuit. Journal of System Architecture, 54, 957–966.

    Article  Google Scholar 

  34. DS003-1, Virtex 2.5 field programmable gate arrays, 2001.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sotirios G. Ziavras.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sajid, I., Ahmed, M.M. & Ziavras, S.G. Novel Pipelined Architecture for Efficient Evaluation of the Square Root Using a Modified Non-Restoring Algorithm. J Sign Process Syst 67, 157–166 (2012). https://doi.org/10.1007/s11265-010-0530-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11265-010-0530-5

Keywords

Navigation