A Word-Length Optimized Hardware Gaussian Random Number Generator Based on the Box-Muller Method

  • Yuan Li
  • Jiang Jiang
  • Minxuan Zhang
  • Shaojun Wei
Part of the Communications in Computer and Information Science book series (CCIS, volume 337)


In this paper, we proposed a hardware Gaussian random number generator based on the Box-Muller method. To reduce the resource complexity, an efficient word-length optimization model is proposed to find out the optimal word-lengths for signals. Experimental results show that our word-length optimized Fixed-Point generator runs as fast as 403.7 MHz on a Xilinx Virtex-6 FPGA device and is capable of generating 2 samples every clock cycle, which is 12.6 times faster compared to its corresponding dedicated software version. It uses up 442 Slices, 1517 FFs and 1517 LUTs, which is only about 1% of the device and saves almost 85% and 71% of area in comparison to the corresponding IEEE double & single Floating-Point generators, respectively. The statistical quality of the Gaussian samples produced by our design is verified by the common empirical test: the chi-square (X 2) test.


Box-Muller Method Hardware Gaussian Random Number Generator FPGA Word-Length Optimization 


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  1. 1.
    Lee, D., Villasenor, J.D., Luk, W., Leong, P.H.W.: A Hardware Gaussian Noise Generator Using the Box-Muller Method and Its Error Analysis. IEEE Transaction on Computers 55(6), 659–671 (2006)CrossRefGoogle Scholar
  2. 2.
    Bell, J.R.: Algorithm 334: Normal random deviates. Comm. ACM 11(7), 498 (1968)CrossRefGoogle Scholar
  3. 3.
    Box, G.E.P., Muller, M.E.: A note on the generation of random normal deviates. Annals Math. Stat. 29, 610–611 (1958)zbMATHCrossRefGoogle Scholar
  4. 4.
    Tezuka, S., L’Ecuyer, P.: Efficient and portable combined Tausworthe random number generators. ACM Transactions on Modeling and Computer Simulation 1(2), 99–112 (1991)zbMATHCrossRefGoogle Scholar
  5. 5.
    Brent, R.P.: Algorithm 488: A Gaussian pseudo-random number generator. Comm. ACM 17(12), 704–706 (1974)zbMATHCrossRefGoogle Scholar
  6. 6.
    Gebhardt, F.: Generating normally distributed random numbers by inverting the normal distribution function. Math. Computation 18(86), 302–306 (1964)MathSciNetGoogle Scholar
  7. 7.
    Zhang, G., Leong, P., Lee, D., Villasenor, J., Luk, W.: Ziggurat-Based Hardware Gaussian Random Number Generator. In: Proc. 16th IEEE Int. Conf. Field-Programmable Logic and its Applications, pp. 275–280 (2006)Google Scholar
  8. 8.
    Lee, D., Luk, W., Villasenor, J.D., Zhang, G., Leong, P.H.W.: A hardware Gaussian noise generator using the Wallace method. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 53(12), 911–920 (2007)Google Scholar
  9. 9.
    Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Modeling and Computer Simulation 8(1), 3–30 (1998)zbMATHCrossRefGoogle Scholar
  10. 10.
    Panneton, F., L’Ecuyer, P., Matsumoto, M.: Improved long-period generators based on linear recurrences modulo 2. ACM Trans. Mathematical Software 32(1), 1–16 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Li, Y., Jiang, J., Chow, P., Zhang, M.: Software/Hardware Framework for Generating Parallel Long-Period Random Numbers Using the WELL Method. In: Proc. 21st Int. Conf. Field Programmable Logic and Applications, pp. 110–115 (2011)Google Scholar
  12. 12.
    Muller, J.: Elementary Functions: Algorithms and Implementation, 2nd edn. Birkhauser, Boston (2006)zbMATHGoogle Scholar
  13. 13.
    de Figueiredo, L., Stolfi, J.: Self-validated numerical methods and applications. In: Brazilian Mathematics Colloquium Monograph. IMPA, Brazil (1997)Google Scholar
  14. 14.
    Lee, D., Gaffar, A.A., Mencer, O., Luk, W.: MiniBit: Bit-Width Optimization via Affine Arithmetic. In: Proc. ACM/IEEE Design Automation Conf., pp. 837–840 (2005)Google Scholar
  15. 15.
    Sung, W., Kurn, K.: Simulation-based word-length optimization method for fixed-point digital signal processing systems. IEEE Trans. on Signal Processing 43(12), 3087–3090 (1995)CrossRefGoogle Scholar
  16. 16.
    Han, K., Eo, I., Kim, K., Cho, H.: Numerical word-length optimization for CDMA demodulator. In: IEEE Int. Symposium on Circuits and Systems, vol. 4, pp. 290–293 (2001)Google Scholar
  17. 17.
    Snedecor, G.W., Cochran, W.G.: Statistical Methods. Iowa State University Press (1989)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yuan Li
    • 1
  • Jiang Jiang
    • 2
  • Minxuan Zhang
    • 1
  • Shaojun Wei
    • 3
  1. 1.School of ComputerNational University of Defense TechnologyChangshaP.R. China
  2. 2.Institute of MicroelectronicsShanghai Jiao Tong UniversityShanghaiP.R. China
  3. 3.Institute of MicroelectronicsTsinghua UniversityBeijingP.R. China

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