Implementations of Square-Root and Exponential Functions for Large FPGAs

  • Mariusz Bajger
  • Amos R. Omondi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4186)

Abstract

This paper discusses low-error, high-speed evaluation of two elementary functions: square-root (which is required in IEEE-754 standard on computer arithmetic) and exponential (which is common in scientific calculations). The basis of the proposed implementations is piecewise-linear interpolation but with the constants chosen in a way that minimizes relative error. We show that by placing certain constraints on the errors at three points within each interpolation interval, relative errors are greatly reduced. The implementation-targets are large FPGAs that have in-built multipliers, adders, and distributed memory.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Muller, J.M.: Elementary Functions: Algorithms and Implementation. Birkhäuser, Boston (1997)MATHGoogle Scholar
  2. [2]
    Omondi, A.R.: Computer Arithmetic Systems: Algorithms, Architecture, and Implementations. Prentice-Hall, UK (1994)MATHGoogle Scholar
  3. [3]
    Mencer, O., Luk, W.: Parameterized high throughput function evaluation for FPGAs. Journal of VLSI Signal Processing 36, 17–25 (2004)CrossRefGoogle Scholar
  4. [4]
    Pizer, S.M., Wallace, V.L.: To compute numerically: concepts and strategies. Little. Brown, Boston (1983)Google Scholar
  5. [5]
    Xilinx, Virtex-4 User Guide (2004)Google Scholar
  6. [6]
    Xilinx, XtremeDSP Design Considerations: User Guide (2004)Google Scholar
  7. [7]
    Ito, M., Takagi, N., Yajima, S.: Efficient Initial Approximation for Multiplicative Division and Square Root by a Multiplication with Operand Modification. IEEE Trans. Computers 46(4), 495–498 (1997)CrossRefMathSciNetGoogle Scholar
  8. [8]
    Waterloo Maple Inc.: Maple 8 Programming Guide (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mariusz Bajger
    • 1
  • Amos R. Omondi
    • 2
  1. 1.School of Informatics and EngineeringFlinders UniversityBedford ParkAustralia
  2. 2.School of Electrical and Electronic EngineeringYonsei UniversitySeoulKorea

Personalised recommendations