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FPGA Implementation of Variable-Precision Floating-Point Arithmetic

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Advanced Parallel Processing Technologies (APPT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6965))

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Abstract

This paper explores the capability of FPGA solutions to accelerate scientific applications with variable-precision floating-point (VP) arithmetic. First, we present a special-purpose Very Large Instruction Word (VLIW) architecture for VP arithmetic (VV-Processor) on FPGA, which uses unified hardware structure to implement various VP algebraic and transcendental functions. We take exponential and trigonometric functions (sine and cosine) as examples to illustrate the design of VP elementary algorithms in VV-Processor, where the optimal configuration is discussed in details in order to achieve minimum execution time. Finally, we create a prototype of VV-Processor unit and Boost Accelerator based-on VV-Processor into a Xilinx Virtex-6 XC6VLX760-2FF1760 FPGA chip. The experimental results show that our design, based on FPGA running at 253 MHz, outperforms the approach of a software-based library running on an Intel Core i3 530 CPU at 2.93GHz by a factor of 5-37X. Compared to the previous work, our design has higher performance and more flexibility to implement other VP elementary functions.

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References

  1. Bailey, D.H.: High-precision floating-point arithmetic in scientific computation. Computing in Science and Engineering 7(3), 54–61 (2005)

    Article  Google Scholar 

  2. Boost C++ libraries, http://live.boost.org/

  3. Brent, R.P., Zimmermann, P.: Modern Computer Arithmetic. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  4. Carter, T.M.: Cascade: Hardware for high/variable precision arithmetic. In: Proceedings of the 9th Symposium on Computer Arithmetic, pp. 184–191 (1989)

    Google Scholar 

  5. Chiarulli, D.M., Ruaa, W.G., Buell, D.A.: Draft: A dynamically reconfigurable processor for integer arithmetic. In: Proceedings of the 7th Symposium on Computer Arithmetic, pp. 309–318 (1985)

    Google Scholar 

  6. Cohen, M.S., Hull, T.E., Hamarcher, V.C.: Cadac: A controlled-precision decimal arithmetic unit. IEEE Transactions on Computers C-32, 370–377 (1983)

    Article  MATH  Google Scholar 

  7. Computational complexity of mathematical operations, http://en.wikipedia.org/wiki/Computational_complexity_of_mathematical_operations

  8. Dou, Y., Lei, Y., Wu, G.: FPGA accelerating double/quad-double high precision floating-point application for exascale computing. In: Proceedings of ICS 2010, pp. 325–336 (2010)

    Google Scholar 

  9. El-Araby, E., Gonzalez, I., El-Ghazawi, T.: Bringing high-performance reconfigurable computing to exact computations. In: Proceedings of FPL 2007, pp. 79–85 (August 2007)

    Google Scholar 

  10. Fisher, J.A.: Very Long Instruction Word architectures and the ELI-512. In: Proceedings of the 10th Annual International Symposium on Computer Architecture, pp. 140–150 (1983)

    Google Scholar 

  11. Fousse, L., Hanrot, G., Lefevre, V., Pelissier, P., Zimmermann, P.: MPFR: A multiple-precision binary floating-point library with correct rounding. Transactions on Mathematical Software 33(2), 1–15 (2007)

    Article  MathSciNet  Google Scholar 

  12. Fujimoto, J., Ishikawa, T., Perret-Gallix, D.: High precision numerical computations-a case for an happy design, ACPP IRG note, ACPP-N-1: KEK-CP-164 (May 2005)

    Google Scholar 

  13. GNU Multiple-Precision arithmetic library, http://www.swox.com/gmp

  14. Hormigo, J., Villalba, J., Schulte, M.: A hardware algorithm for variable-precision logarithm. In: Proceedings of ASAP 2000, pp. 215–224 (July 2000)

    Google Scholar 

  15. Hormigo, J., Villalba, J., Zapata, E.L.: Cordic processor for variable-precision interval arithmetic. Journal of VLSI Signal Processing 37, 21–39 (2004)

    Article  Google Scholar 

  16. Jones, A.K., Hoare, R., Kusic, D.: An FPGA-based VLIW Processor with Custom Hardware Execution. In: Proceedings of FPGA 2005, pp. 107–117 (2005)

    Google Scholar 

  17. Lei, Y., Dou, Y., Zhou, J., Wang, S.: VPFPAP: A special-purpose VLIW processor for variable-precision floating-point arithmetic. In: Proceedings of FPL 2011 (2011)

    Google Scholar 

  18. Parhi, K.K., Srinivas, H.R.: A fast radix-4 division algorithm and its architecture. IEEE Transactions on Computers 44(6), 826–831 (1995)

    Article  MATH  Google Scholar 

  19. Schulte, M.J., Swartzlander Jr., E.E.: A family of variable-precision, interval arithmetic processors. IEEE Transactions on Computers 49(5), 387–397 (2000)

    Article  Google Scholar 

  20. Schulte, M.J., Swartzlander Jr., E.E.: Hardware design and arithmetic algorithms for a variable-precision, interval arithmetic coprocessor. In: Proceedings of the 12th Symposium on Computer Arithmetic, pp. 222–228 (1995)

    Google Scholar 

  21. Tenca, A.F., Ercegovac, M.D.: A Variable Long-Precision Arithmetic Unit Design for Reconfigurable Coprocessor Architectures. In: Proceedings of FCCM 1998 (1998)

    Google Scholar 

  22. Underwood, K.: FPGAs vs. CPUs: trends in peak floating-point performance. In: Proceedings of FPGA 2004, pp. 171–180 (2004)

    Google Scholar 

  23. Zhou, J., Dou, Y., Lei, Y., Xu, J., Dong, Y.: Double precision hybrid-mode floating-point fpga cordic coprocessor. Proceedings of HPCC 2008, 182–189 (2008)

    Google Scholar 

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Lei, Y., Dou, Y., Guo, S., Zhou, J. (2011). FPGA Implementation of Variable-Precision Floating-Point Arithmetic. In: Temam, O., Yew, PC., Zang, B. (eds) Advanced Parallel Processing Technologies. APPT 2011. Lecture Notes in Computer Science, vol 6965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24151-2_10

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  • DOI: https://doi.org/10.1007/978-3-642-24151-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24150-5

  • Online ISBN: 978-3-642-24151-2

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