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)


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.


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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

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