Advertisement

Journal of Signal Processing Systems

, Volume 85, Issue 1, pp 113–128 | Cite as

Fast Integer Word-length Optimization for Fixed-point Systems

Integer Word-length Optimization
  • Riham Nehmeh
  • Daniel Menard
  • Erwan Nogues
  • Andrei Banciu
  • Thierry Michel
  • Romuald Rocher
Article

Abstract

Time-to-market and implementation cost are high-priority considerations in the automation of digital hardware design. Nowadays, digital signal processing applications are implemented into fixed-point architectures due to its advantage of manipulating data with lower word-length. Thus, floating-point to fixed point conversion is mandatory. This conversion is translated into optimizing the integer word length and fractional word length. Optimizing the integer word-length can significantly reduce the cost when the application is tolerant to a low probability of overflow. In this paper, a new selective simulation technique to accelerate overflow effect analysis is introduced. A new integer word-length optimization algorithm that exploits this selective simulation technique is proposed to reduce both implementation cost and optimization time. The efficiency of our proposals is illustrated through experiments, where selective simulation technique allows accelerating the execution time of up to 1200 and 1000 when applied on Global Positioning System and on Fast Fourier Transform part (FFT) of Orthogonal Frequency Division Multiplexing chain respectively. Moreover, applying the optimization algorithm on the FFT part leads to a cost reduction between 17 to 22 % with respect to interval arithmetic and an acceleration factor of up to 617 with respect to classical max-1 algorithm.

Keywords

Fixed-point arithmetic Overflow effect analysis Fixed-point simulation acceleration Fixed-point optimization 

References

  1. 1.
    Balfour, J.D. (2010). Efficient embedded computing, Ph.D. thesis, Stanford University.Google Scholar
  2. 2.
    Shi, C., & Brodersen, R. (2003). An automated floating-point to fixed-point conversion methodology. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). Hong Kong, pp. 529–532.Google Scholar
  3. 3.
    Menard, D., Banciu, A., Michel, T., Rocher, R., & Nehmeh, R. (2014). Integer word-length optimization for fixed-point systems. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP).Google Scholar
  4. 4.
    Bancu, A. (2012). A Stochastic Approach For The Range Evaluation, Ph.D. thesis, University of Rennes.Google Scholar
  5. 5.
    Kearfott, R. (1996). Interval Computations: Introduction, Uses, and Resources: Euromath Bulletin.Google Scholar
  6. 6.
    de Figueiredo, L.H., & Stolfi, J. (2004). Affine arithmetic: Concepts and applications, Numerical Algorithms.Google Scholar
  7. 7.
    Özer, E., Nisbet, A.P., & Gregg, D. (2008). A stochastic bitwidth estimation technique for compact and low-power custom processors: ACM TECS.Google Scholar
  8. 8.
    Ozer, E., Nisbet, A.P., & Gregg, D. (2003). Stochastic Bitwidth Approximation Using Extreme Value Theory for Customizable Processors, Tech. Rep. Dublin: Trinity College.Google Scholar
  9. 9.
    Chapoutot, A., Didier, L.S., & Villers, F. (2012). Range estimation of floating-point variables in simulink models. In: Conference on Design and Architectures for Signal and Image Processing (DASIP). (pp. 1–8).Google Scholar
  10. 10.
    Wu, B., Zhu, J., & Najm, F. (2004). An analytical approach for dynamic range estimation. In: Proceedings of the ACM/IEEE Design Automation Conference (DAC). (pp. 472–477). San Diego.Google Scholar
  11. 11.
    Banciu, A., Casseau, E., Menard, D., & Michel, T. (2011). Stochastic modeling for floating-point to fixed-point conversion. In: Proceedings of the IEEE International Workshop on Signal Processing Systems, (SIPS). Beirut.Google Scholar
  12. 12.
    Wu, B., Zhu, J., & Najm, F.N. (2004). Dynamic range estimation for nonlinear systems. In: IEEE/ACM International Conference on Computer Aided Design (ICCAD). (pp. 660–667).Google Scholar
  13. 13.
    Mathworks (2001). System-Level Design Products for DSP and communications.Google Scholar
  14. 14.
    Mentor Graphics (2008). Algorithmic C Data Types, Mentor Graphics, version 1.3 edition.Google Scholar
  15. 15.
    Open SystemC Initiative (2001). SystemC User’s Guide (ver 2.0), Tech. Rep., www.systemc.org.
  16. 16.
    Banciu, A., Casseau, E., Ménard, D., & Michel, T. (2010). A Case Study Of The Stochastic Modeling Approach For Range Estimation. In: Proceedings of the Workshop on Design and Architectures for Signal and Image Processing (DASIP). (pp. 301–308). Edinburgh.Google Scholar
  17. 17.
    Cmar, R., Rijnders, L., Schaumont, P., & Bolsens, I. (1999). A Methodology and Design Environment for DSP ASIC Fixed Point Refinement. In: Proceedings of the IEEE/ACM conference on Design, Automation and Test in Europe (DATE). (pp. 271–276). Munich.Google Scholar
  18. 18.
    Kim, S., & Sung, W. (1998). Fixed-Point Error Analysis and Word Length Optimization of 8x8 IDCT Architectures. IEEE Transactions on Circuits and Systems for Video Technology, 8(8), 935–940.CrossRefGoogle Scholar
  19. 19.
    Zhang, L., Zhang, Y., & Zhou, W. (2009). Floating-point to fixed-point transformation using extreme value theory. In: Eighth IEEE/ACIS International Conference on Computer and Information Science (ICIS). (pp. 271–276).Google Scholar
  20. 20.
    Caffarena, G., Lpez, J.A., Fernandez, ., & Carreras, C. (2010). SQNR Estimation of Fixed-Point DSP Algorithms. EURASIP Journal on Advance Signal Processing, 2010.Google Scholar
  21. 21.
    Lpez, J.A., Caffarena, G., Carreras, C., & Nieto-Taladriz, O. (2008). Fast and accurate computation of the roundoff noise of linear time-invariant systems. IET Circuits, Devices and Systems, 2(4), 393–408.CrossRefGoogle Scholar
  22. 22.
    Parashar, K., Menard, D., Rocher, R., Sentieys, O., Novo, D., & Catthoor, F. (2010). Fast Performance Evaluation of Fixed-Point Systems with Un-Smooth Operators. In: Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (ICCAD). San Jose, 11.Google Scholar
  23. 23.
    Rocher, R., Ménard, D., Scalart, O., & Sentieysand P. (2012). Analytical Approach for Numerical Accuracy Estimation of Fixed-Point Systems Based on Smooth Operations. IEEE Transactions on Circuits and Systems. Part I, Regular Papers, 59(10), 2326–2339.MathSciNetCrossRefGoogle Scholar
  24. 24.
    Kim, S., Kum, K.-I., & Sung, W. (1998). Fixed-point optimization utility for C and C ++ based digital signal processing programs. IEEE Transactions on Circuits and Systems II - Analog and Digital Signal Processing, 45(11), 1455–1464.Google Scholar
  25. 25.
    Morvan, A., Derrien, S., & Quinton, P. (2013). Polyhedral bubble insertion: A method to improve nested loop pipelining for high-level synthesis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 32(3), 339–352.CrossRefGoogle Scholar
  26. 26.
    Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers & operations research, 13(5).Google Scholar
  27. 27.
    Nguyen, H.-N., Menard, D., & Sentieys, O. (2011). Novel Algorithms for Word-length Optimization. In: Proceedings of the European Signal Processing Conference (EUSIPCO). Barcelona.Google Scholar
  28. 28.
    Zhao, Y. (2002). Standardization of mobile phone positioning for 3g systems. IEEE Communications Magazine, 40(7).Google Scholar
  29. 29.
    Bucher, R., & Misra, D. (2002). A synthesizable vhdl model of the exact solution for three-dimensional hyperbolic positioning system. Vlsi Design, 15(2), 507–520.CrossRefGoogle Scholar
  30. 30.
    Armstrong, J. (2009). Ofdm for optical communications. Lightwave Technology, 27(3), 189–204.CrossRefGoogle Scholar
  31. 31.
    Herve, N., Menard, D., & Sentieys, O. (2005). Data Wordlength Optimization for FPGA Synthesis. In: Proceedings of the IEEE SIPS.Google Scholar
  32. 32.
    Chissom, B.S. (1970). Interpretation of the kurtosis statistic, The American Statistician.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Riham Nehmeh
    • 1
    • 2
  • Daniel Menard
    • 2
  • Erwan Nogues
    • 2
  • Andrei Banciu
    • 1
  • Thierry Michel
    • 1
  • Romuald Rocher
    • 3
  1. 1.STMicroelectronicsCrollesFrance
  2. 2.UEBINSA Rennes, IETR, UMR 6164RennesFrance
  3. 3.UEBUniversity of Rennes, IRISA/INRIALannionFrance

Personalised recommendations