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Highly Efficient Structure of 64-Bit Exponential Function Implemented in FPGAs

  • Maciej Wielgosz
  • Ernest Jamro
  • Kazimierz Wiatr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4943)

Abstract

This paper presents implementation of the double precision exponential function. A novel table-based architecture, together with short Taylor expansion, provides low latency (30 clock cycles) which is comparable to 32-bit implementations. Low area consumption of a single exp() module (roughtly 4% of XC4LX200) allows implementation of several parallel modules on a single FPGAs. The exp() function was implemented on the SGI RASC platform, thus external memory interface limitation allowed only a twin module parallelism. Each module is capable of processing at speed of 200 MHz with max. error of 1 ulp, RMSE equals 0,62. This implementation aims primarily to meet quantum chemistry’s huge and strict requirements of precision and speed.

Keywords

HPRC (High Performance Reconfigurable Computing) FPGA elementary function exponent function 

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References

  1. 1.
    Doss, C.C., Riley Jr., R.L.: FPGA-Based Implementation of a Robust IEEE-754 Exponential Unit. In: 12th Annual IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM 2004), pp. 229–238 (2004)Google Scholar
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    Bui, H.T., Tahar, S.: Design and Synthesis of an IEEE-754 Exponential Function. In: 1999 IEEE Canadian Conference on Electrical and Computer Engineering Shaw Conference Center, Edmonton, Alberta, Canada, May 9-12, 1999 vol. 1, pp. 450–455 (1999)Google Scholar
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    Detrey, J., de Dinechin, F.: A parameterized foating-point exponential function for FPGAs. In: IEEE International Conference on Field-Programmable Technology (FPT 2005), Singapore, pp.27–34, December 2005 (2005)Google Scholar
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    Silicon Graphics, Inc. Reconfigurable Application-Specific Computing User’s Guide, Ver. 004, March 2006, SGIGoogle Scholar
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    The University of Texas in Austin, TACC Intel Math Kernel Library (November 22, 2007), http://www.tacc.utexas.edu/services/userguides/mkl/functions/exp.html

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maciej Wielgosz
    • 1
    • 2
  • Ernest Jamro
    • 1
    • 2
  • Kazimierz Wiatr
    • 1
    • 2
  1. 1.AGH University of Science and TechnologyKraków 
  2. 2.Academic Computer Centre Cyfronet AGHKraków 

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