IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v79y2009i11p3328-3338.html
   My bibliography  Save this article

Polynomial pseudo-random number generator via cyclic phase

Author

Listed:
  • Marchi, A.
  • Liverani, A.
  • Del Giudice, A.

Abstract

Fast and reliable pseudo-random number generator (PRNG) is required for simulation and other applications in scientific computing. In this work, a polynomial PRNG algorithm, based on a linear feedback shift register (LFSR) is presented. LFSR generator of order k determines a 2k−1 cyclic sequence period when the associated polynomial is primitive. The main drawback of this generator is the cyclicality of the shifted binary sequence. A non-linear transformation is proposed, which eliminates the underlying cyclicality and maintains both the characteristics of the original generator and the feedback function. The modified generator assures a good trade off between fastness and reliability and passes both graphical and statistical tests.

Suggested Citation

  • Marchi, A. & Liverani, A. & Del Giudice, A., 2009. "Polynomial pseudo-random number generator via cyclic phase," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3328-3338.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:11:p:3328-3338
    DOI: 10.1016/j.matcom.2009.05.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475409001463
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2009.05.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hellekalek, P., 1998. "Good random number generators are (not so) easy to find," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 46(5), pages 485-505.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Massimo Gangi & Giulio E. Cantarella & Antonino Vitetta, 2019. "Solving stochastic frequency-based assignment to transit networks with pre-trip/en-route path choice," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 661-681, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.
    2. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    3. Ovidiu Bagdasar & Minsi Chen & Vasile Drăgan & Ivan Ganchev Ivanov & Ioan-Lucian Popa, 2023. "On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators," Mathematics, MDPI, vol. 11(5), pages 1-16, March.
    4. Kleiber Christian & Zeileis Achim, 2013. "Reproducible Econometric Simulations," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 89-99, July.
    5. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    6. Mascagni Michael & Hin Lin-Yee, 2013. "Parallel pseudo-random number generators: A derivative pricing perspective with the Heston stochastic volatility model," Monte Carlo Methods and Applications, De Gruyter, vol. 19(2), pages 77-105, July.
    7. Wegenkittl, Stefan, 2001. "Gambling tests for pseudorandom number generators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 281-288.
    8. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2019. "Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models," Papers 1904.04951, arXiv.org, revised Mar 2021.
    9. Mascagni Michael & Hin Lin-Yee, 2012. "Parallel random number generators in Monte Carlo derivative pricing: An application-based test," Monte Carlo Methods and Applications, De Gruyter, vol. 18(2), pages 161-179, January.
    10. Maximilian Beikirch & Torsten Trimborn, 2020. "Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model," Papers 2002.10222, arXiv.org.
    11. Ali Shakir Mahmood & Mohd Shafry Mohd Rahim & Nur Zuraifah Syazrah Othman, 2016. "Implementation of the Binary Random Number Generator Using the Knight Tour Problem," Modern Applied Science, Canadian Center of Science and Education, vol. 10(4), pages 1-35, April.
    12. Aljahdali Asia & Mascagni Michael, 2017. "Feistel-inspired scrambling improves the quality of linear congruential generators," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 89-99, June.
    13. Tan, Syn Kiat & Guan, Sheng-Uei, 2009. "Randomness quality of permuted pseudorandom binary sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1618-1626.
    14. Tang, Hui-Chin, 2002. "Modified decomposition method for multiple recursive random number generator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(5), pages 453-458.
    15. L’Ecuyer, Pierre & Munger, David & Oreshkin, Boris & Simard, Richard, 2017. "Random numbers for parallel computers: Requirements and methods, with emphasis on GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 3-17.
    16. Hawkins, Dollena S. & Allen, David M. & Stromberg, Arnold J., 2001. "Determining the number of components in mixtures of linear models," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 15-48, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:79:y:2009:i:11:p:3328-3338. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.