Skip to main content Accessibility help
Hostname: page-component-5959bf8d4d-c2ftz Total loading time: 0.313 Render date: 2022-12-10T00:11:42.518Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Evaluation of splittable pseudo-random generators*

Published online by Cambridge University Press:  17 June 2015

Aalesund University College, Pb. 1517, N-6025 Ålesund, Norway (e-mail:
Rights & Permissions[Opens in a new window]


HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Pseudo-random number generation is a fundamental problem in computer programming. In the case of sequential processing the problem is very well researched, but parallel processing raises new problems whereof far too little is currently understood. Splittable pseudo-random generators (S-PRNG) have been proposed to meet the challenges of parallelism. While applicable to any programming paradigm, they are designed to be particularly suitable for pure functional programming. In this paper, we review and evaluate known constructions of such generators, and we identify flaws in several large classes of generators, including Lehmer trees, the implementation in Haskell's standard library, leapfrog, and subsequencing (substreaming).

Copyright © Cambridge University Press 2015 



The research was partially funded by Regionalt Forskingsfond Midt-Norge through the project Dynamic Resource Allocation with Maritime Application (DRAMA), grant no. ES504913.


Brown, R. G. (2015 January) Dieharder: A Random Number Test Suite. Software. Available from Scholar
Burton, F. W. & Page, R. L. (1992) Distributed random number generation. J. Funct. Program. 2 (2), 203212.CrossRefGoogle Scholar
Bye, R. T. & Schaathun, H. G. (2014) An improved receding horizon genetic algorithm for the tug fleet optimisation problem. In Proceedings of the 28th European Conference on Modelling and Simulation (ECMS 2014). ECMS European Council for Modelling and Simulation, pp. 682–690.Google Scholar
Carta, D. G. (1990) Two fast implementations of the minimal standard random number generator. Commun. ACM 33 (1), 8788.CrossRefGoogle Scholar
Claessen, K. & Pałka, M. H. (2013a) Splittable pseudorandom number generators using cryptographic hashing. In Proceedings of the 2013 ACM SIGPLAN Symposium on Haskell. Haskell'13. New York, NY, USA: ACM, pp. 4758.CrossRefGoogle Scholar
Claessen, K. & Pałka, M. H. (2013b) The tf-Random Package. Accessed 2015-01-15. Online at: Scholar
Cuccaro, S. A., Mascagni, M., & Pryor, D. V. (1995) Techniques for testing the quality of parallel pseudorandom number generators. In Proceedings of the 7th SIAM Conference on Parallel Processing for Scientific Computing, Bailey, D. H., Bjørstad, P. E., Gilbert, J. R., Mascagni, M., Schreiber, R. S., Simon, H. D., Torczon, V. J., & Watson, L.T. (eds), SIAM, pp. 279284.Google Scholar
De Matteis, A. & Pagnutti, S. (1990) Long-range correlations in linear and non-linear random number generators. Parallel Comput. 14 (2), 207210.CrossRefGoogle Scholar
Eddy, W. F. (1990) Random number generators for parallel processors. J. Comput. Appl. Math., 31 (1), 6371.CrossRefGoogle Scholar
Frederickson, P., Hiromoto, R., Jordan, T. L., Smith, B. & Warnock, T. (1984) Pseudo-random trees in Monte Carlo. Parallel Comput. 1 (2), 175180.CrossRefGoogle Scholar
Hackage. (2011) The Random Package. Haskell Random Number Library. Documentation. Accessed 2015-01-16. Online at: Scholar
Halton, J. H. (1989) Pseudo-random trees: Multiple independent sequence generators for parallel and branching computations. J. Comput. Phys. 84 (1), 156.CrossRefGoogle Scholar
Klamkin, M. S. & Newman, D. J. (1967) Extensions of the birthday surprise. J. Comb. Theory 3 (3), 279282.CrossRefGoogle Scholar
Knuth, D. E. (1998) The Art of Computer Programming, vol. 2: Seminumerical Algorithms, 3rd ed., Addison-Wesley.Google Scholar
Koniges, A. E. & Leith, C. E. (1989) Parallel processing of random number generation for Monte Carlo turbulence simulation. J. Comput. Phys. 81 (1), 230235.CrossRefGoogle Scholar
Krawczyk, H. (1992) How to predict congruential generators. J. Algorithms 13 (4), 527545.CrossRefGoogle Scholar
L'Ecuyer, P. (1988) Efficient and portable combined random number generators. Commun. ACM 31 (6), 742749 and 774.CrossRefGoogle Scholar
L'Ecuyer, P. (2012) Random number generation. In Handbook of Computational Statistics: Concepts and Methods, Gentle, J. E., Härdle, W. K. & Mori, Y. (eds), 2nd ed., Springer, pp. 3571.CrossRefGoogle Scholar
L'Ecuyer, P. & Simard, R. (2007) TestU01: A C library for empirical testing of random number generators. ACM Trans. Math. Softw. 33 (4), Article no. 22.CrossRefGoogle Scholar
L'Ecuyer, P., Simard, R., Chen, E. J. & Kelton, W. D. (2002) An objected-oriented random-number package with many long streams and substreams. Oper. Res. 50 (6), 10731075.CrossRefGoogle Scholar
Leiserson, C. E., Schardl, T. B. & Sukha, J. (2012) Deterministic parallel random-number generation for dynamic-multithreading platforms. ACM SIGPLAN Not. 47 (8), 193204.CrossRefGoogle Scholar
Marlow, S. (2013) Parallel and Concurrent Programming in Haskell. O'Reilly.Google Scholar
Marsaglia, G. (1968) Random numbers fall mainly in the planes. Proc.Natl. Acad. Sci. United States Am. 61 (1), 2528.CrossRefGoogle ScholarPubMed
Mascagni, M. (1998) Parallel linear congruential generators with prime moduli. Parallel Comput. 24 (5–6), 923936.CrossRefGoogle Scholar
Matsumoto, M. & Nishimura, T. (1998) Dynamic creation of pseudorandom number generators. In Monte Carlo and quasi-Monte Carlo Methods, 1998: Proceedings of a Conference Held at the Claremont Graduate University, June 22–26, Niederreiter, H. & Spanier, J. (eds), Claremont, CA, USA: Springer, pp. 5669.Google Scholar
Matsumoto, M., Wada, I., Kuramoto, A. & Ashihara, H. (2007) Common defects in initialization of pseudorandom number generators. ACM Trans. Model. Comput. Simul. 17 (4), Article no. 15.CrossRefGoogle Scholar
Menezes, A. J., van Oorschot, P. C. & Vanstone, S. A. (1997) Handbook of Applied Cryptography. CRC Press.Google Scholar
O'Sullivan, B., Goerzen, J. & Stewart, D. (2008) Real World Haskell. O'Reilly.Google Scholar
Park, S. K. & Miller, K. W. (1988) Random number generators: Good ones are hard to find. Commun. ACM 31 (10), 11921201.CrossRefGoogle Scholar
Percus, Ora E. & Kalos, M. H. (1989) Random number generators for MIMD parallel processors. J. Parallel Distrib. Comput. 6 (3), 477497.CrossRefGoogle Scholar
Salmon, J. K., Moraes, M. A., Dror, R. O. & Shaw, D. E. (2011) Parallel random numbers: As easy as 1, 2, 3. In High performance computing, networking, storage and analysis (SC11), 2011 International conference for. ACM, pp. 1–12.Google Scholar
Schaathun, H. G. (2014) Parallell slump (Om å parallellisera genetiske algoritmar i Haskell) Norsk informatikkonferanse. Open access at: ISSN 1892-0721.Google Scholar
Steele, Guy L. Jr., Lea, D. & Flood, C. H. (2014) Fast splittable pseudorandom number generators. ACM SIGPLAN Not. 49 (10), 453472.CrossRefGoogle Scholar
Warnock, T. T. (1983) Synchronization of random number generators. Congressus Numerantium 37, 135144.Google Scholar
Wu, P.-C. & Huang, K.-C. (2006) Parallel use of multiplicative congruential random number generators. Comput. Phys. Commun. 175 (1), 2529.CrossRefGoogle Scholar
Submit a response


No Discussions have been published for this article.
You have Access
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Evaluation of splittable pseudo-random generators*
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Evaluation of splittable pseudo-random generators*
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Evaluation of splittable pseudo-random generators*
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *