I received the B.S. and M.S. degrees (both in Mathematics) from the University of Salzburg and completed the PhD on Mathematics at the same University.

For pLab I studied parallel streams of linear congruential random numbers ,and as a small hobby, I 'collected' classical random number generators ;-)

I further implemented the Mathematica Version of our package and set up the links page. In our series of empirical tests, I was responsible for run tests and the spectral test .

[Image of Karl Entacher]

Below, you will find

a biographical sketch
conference participations


Overview * Team * Generators * Tests * News * Literature * Links




School of Telecommunications Engineering,
Salzburg University of Applied Sciences & Technologies

Schillerstrasse 30
A-5020 Salzburg, Austria

fon: +43 (662) 4665 621
fax: +43 (662) 4665 559

email: karl.entacher@fh-sbg.ac.at
home: http://www.fh-sbg.ac.at/~kentache/


1986-92 M.S. Mathematics,
1993-95 Ph.D. Mathematics, University of Salzburg, Austria.

1993 - Senior Research Assistant at the Department of Mathematics, University of Salzburg within Prof. Peter Hellekalek's PLAB research project on pseudorandom number generation http://random.mat.sbg.ac.at (Austrian Science Fund (FWF) grants P11143-MAT and P9285-TEC and CEI-PACT Projekt WP5;)
1998 - 1999 Research Assistant at Prof. Gerhard Larcher's research project on low-discrepancy point sets (FWF grant P12441-MAT) at the same Department.
1999 - 2000 Research Assistant in Peter Hellekalek's Austrian National Bank project 7576 on parallel streams of random numbers, responsible for the Spectral Test Server.
  Assistant Prof. at the Dept. of Scientific Computing, University of Salzburg


Science and Research Prize 1997/98, Rotary Club Salzburg, Austria.


Random number generation, parallel streams of random numbers, Monte Carlo- and quasi-Monte Carlo methods, low-discrepancy point sets and sequences, uniform distribution modulo one.


  1. K. Entacher.
    Quasi-Monte Carlo methods for numerical integration of multivariate Haar series. BIT, 37(4):845-860, 1997 (paper.ps).

  2. K. Entacher.
    Quasi-Monte Carlo methods for numerical integration of multivariate Haar series II. BIT, 38(2):283-292, 1998.

  3. K. Entacher.
    Haar Function Based Estimates of the Star-Discrepancy of Plane Digital Nets. Monatshefte für Mathematik, 130 2000, pp. 99-108.

  4. K. Entacher.
    Bad subsequences of well-known linear congruential pseudorandom number generators. ACM TOMACS special issue on Random Number Generation, 8(1), 1998.

  5. K. Entacher.
    On the Cray-System Random Number Generator. Simulation, 72(3): 163-169, 1999.

  6. K. Entacher.
    Parallel Streams of Linear Random Numbers in the Spectral Test. ACM Transactions on Modeling and Computer Simulation, 9(1):31-44, 1999.

  7. K. Entacher, A. Uhl, and S. Wegenkittl.
    Linear Congruential Generators for Parallel Monte-Carlo: the Leap-Frog Case. Monte Carlo Methods and Appl., 4(1):1-16, 1998.

  8. K. Entacher, A. Uhl, and S. Wegenkittl.
    Linear and Inversive Pseudorandom Numbers for Parallel and Distributed Simulation. In Twelfth Workshop on Parallel and Distributed Simultation PADS'98, May 26th - 29th, Banff, Alberta, Canada, 1998. Simulation Digest 28(1), ACM SIGSIM Newsletter, pages 90-97, IEEE Computer Society, Los Alamitos, California.

  9. K. Entacher, P. Hellekalek, and P. L'Ecuyer.
    Quasi-Monte Carlo Node Sets from Linear Congruential Generators. In H. Niederreiter and J. Spanier, editors, Monte Carlo and Quasi-Monte Carlo Methods 1998, pages 188-198. Springer-Verlag, 2000.

  10. K. Entacher and T. Schell.
    From ``Pseudo'' to ``Quasi''. In Proceedings of the international conference MONTE CARLO SIMULATION MCS2000, Monaco, 2000, to appear.

  11. K. Entacher.
    A collection of selected pseudorandom number generators with linear structures - advanced version. Technical report, Dept. of Mathematics, University Salzburg, Austria.
    The previous version is published as technical report 97-1, ACPC-Austrian Center for Parallel Computation, University of Vienna, Austria, 1997.


  1. International Workshop on Mathematical Methods and Tools in Computer Simulation. Mai 24-28, 1994, St. Petersburg, Russia
  2. International Workshop Parallel Numerics 94. September 19-21, 1994, Smolenice Castle, Slovakia. Lecture: ``Empirical tests of selected pseudorandom number generators.''
  3. 1. Salzburger Minisymposium über Pseudozufallszahlen und Quasi-Monte-Carlo Methoden. 18. November 1994, Salzburg, Austria. Lecture: ``Anwendungen von Haar-Systemen in der Theorie der Gleichverteilung modulo Eins.''
  4. Austrian Center for Parallel Computation - Workshop. November 25-26, 1994, Keutschach, Kärnten
  5. Seventh SIAM Conference on Parallel Processing for Scientific Computing. February 14-17, 1995, San Francisco, USA.
  6. International Workshop Parallel Numerics 95. September 27-29, 1995, Sorrento, Italy. Lecture: ``Parallel Stochastic Simulation: Inversive Pseudorandom Number Generators''.
  7. Wavelet Applications III, Teil des SPIE 10th International AeroSense Symposiums. April 8-12, 1996, Orlando, Florida, USA. Lecture: ``Generalized Haar function systems, digital nets, and quasi-Monte Carlo integration''.
  8. Second international conference on Monte Carlo and quasi-Monte Carlo methods in scientific computing. July 9-12, 1996, Universität Salzburg, Austria. Lecture: ``Rapidly converging Haar series and their numerical integration''.
  9. International Workshop Parallel Numerics 96. September 11-13, 1996, Gozd Martuljek, Slovenia. Lecture: ``On the Relevance of Splitting Properties and the Compound Method in Parallel Applications of Pseudorandom Number Generators''.
  10. International Workshop Parallel Numerics 97. September 5-7, 1997, Zakopane, Poland. Lecture: ``Analyzing Streams of Pseudorandom Numbers for Parallel Monte Carlo Integrations''.
  11. 12th Workshop on Parallel and Distributed Simulation PADS'98 May 26-29, 1998, Banff, Alberta, Canada. Lecture: ``Linear and Inversive Pseudorandom Numbers for Paralle and Distributed Simulation''.
  12. 4th International Conference of the ACPC, Universität Salzburg , 16 - 18, Feb. 1999. Lecture: ``Parallel random number generation: Long range correlations among multiple processors ''
  13. Second IMACS Seminar on Monte Carlo Methods MCM'99, 7-11 Juni 1999, Varna, Bulgarien. Lecture: ``Discrepancy Estimates Based on Haar Functions''.
  14. International Conference on Monte Carlo Simulation MCS_2000, Monte Carlo/Monaco, 18.-21. Juni 2000. Lecture: ``From Pseudo to Quasi''.
  15. International Workshop PARALLEL NUMERICS ParNum 2000, Bratislava, Slovakia, 18.-20. Sept. 2000. Lecture: ``Further remarks on long-range correlations among linear congruential random numbers''.
  16. Fourth International Conference On Monte Carlo and Quasi-Monte Carlo Methods In Scientific Computing, Hong Kong, November 27 - December 1, 2000. Lecture: ``On the Spectral Test Approximation using the LLL-Algorithm''.


  1. Technische Universität Graz, Institut für Statistik, November 21, 1997. Lecture: ``Gefahren bei der Verwendung von Teilströmen linearer Pseudozufallszahlen: Einfache Theoretische und Empirische Analysen.''
  2. Workshop: ``High Performance Monte Carlo Tools.'' April 23-24, 1998, Stennis Space Center, Stennis, USA ( http://www.ncsa.uiuc.edu/Apps/SPRNG/hpmct/).
  3. Workshop ``Pseudozufallszahlen'' Technische Universität Darmstadt, Okt. 14 1998, Lecture: ``Parallele Ströme linearer Zufallszahlen'';