List of random number generators (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "List of random number generators" in English language version.

refsWebsite

Global rank English rank

22doi.org

2^nd place

9semanticscholar.org

11^th place

8^th place

7arxiv.org

69^th place

59^th place

5harvard.edu

18^th place

17^th place

2ams.org

451^st place

277^th place

2jstor.org

26^th place

20^th place

2psu.edu

207^th place

136^th place

2web.archive.org

1^st place

2github.com

383^rd place

320^th place

1microsoft.com

153^rd place

151^st place

1python.org

2,232^nd place

1,903^rd place

1siam.org

low place

6,473^rd place

1worldcat.org

5^th place

1firstpr.com.au

low place

1cppreference.com

low place

9,420^th place

1projecteuclid.org

3,707^th place

2,409^th place

1researchgate.net

120^th place

125^th place

1groups.google.com

1,518^th place

1,072^nd place

1umontreal.ca

6,223^rd place

6,135^th place

1burtleburtle.net

low place

1sourceforge.net

1,669^th place

1,290^th place

1numpy.org

low place

1oswego.edu

low place

1pcg-random.org

low place

1books.google.com

3^rd place

1tubitak.gov.tr

7,316^th place

low place

ams.org

Tausworthe, R. C. (1965). "Random Numbers Generated by Linear Recurrence Modulo Two" (PDF). Mathematics of Computation. 19 (90): 201–209. doi:10.1090/S0025-5718-1965-0184406-1.
Couture, Raymond; L'Ecuyer, Pierre (1997). "Distribution properties of multiply-with-carry random number generators" (PDF). Mathematics of Computation. 66 Number. 218 (218): 591–607. Bibcode:1997MaCom..66..591C. doi:10.1090/S0025-5718-97-00827-2.

arxiv.org

Martin, Lüscher (1994). "A portable high-quality random number generator for lattice field theory simulations". Computer Physics Communications. 79 (1): 100–110. arXiv:hep-lat/9309020. Bibcode:1994CoPhC..79..100L. doi:10.1016/0010-4655(94)90232-1. S2CID 17608961.
Balkova, Lubomira; Bucci, Michelangelo; De Luca, Alessandro; Hladky, Jiri; Puzynina, Svetlana (September 2016). "Aperiodic pseudorandom number generators based on infinite words". Theoretical Computer Science. 647: 85–100. arXiv:1311.6002. doi:10.1016/j.tcs.2016.07.042. S2CID 2175443.
Widynski, Bernard (2017). "Middle-Square Weyl Sequence RNG". arXiv:1704.00358 [cs.CR].
Blackman, David; Vigna, Sebastiano (2018). "Scrambled Linear Pseudorandom Generators". arXiv:1805.01407 [cs.DS].
Harase, S.; Kimoto, T. (2018). "Implementing 64-bit Maximally Equidistributed F₂-Linear Generators with Mersenne Prime Period". ACM Transactions on Mathematical Software. 44 (3): 30:1–30:11. arXiv:1505.06582. doi:10.1145/3159444. S2CID 14923086.
Widynski, Bernard (2020). "Squares: A Fast Counter-Based RNG". arXiv:2004.06278 [cs.DS].
Działa, Tomasz R. (2023). "Collatz-Weyl Generators: High Quality and High Throughput Parameterized Pseudorandom Number Generators". arXiv:2312.17043 [cs.CE].

books.google.com

Kneusel, Ron (2018). Random Numbers and Computers (1 ed.). Springer. pp. 13–14. ISBN 9783319776972.

burtleburtle.net

Jenkins, Bob (2009). "A small noncryptographic PRNG".

cppreference.com

en.cppreference.com

"Pseudo-random number generation". cppreference.com. Retrieved 14 November 2021.

doi.org

Thomson, W. E. (1958). "A Modified Congruence Method of Generating Pseudo-random Numbers". The Computer Journal. 1 (2): 83. doi:10.1093/comjnl/1.2.83.
Rotenberg, A. (1960). "A New Pseudo-Random Number Generator". Journal of the ACM. 7 (1): 75–77. doi:10.1145/321008.321019. S2CID 16770825.
Tausworthe, R. C. (1965). "Random Numbers Generated by Linear Recurrence Modulo Two" (PDF). Mathematics of Computation. 19 (90): 201–209. doi:10.1090/S0025-5718-1965-0184406-1.
Wichmann, Brian A.; Hill, David I. (1982). "Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator". Journal of the Royal Statistical Society. Series C (Applied Statistics). 31 (2): 188–190. doi:10.2307/2347988. JSTOR 2347988.
Wolfram, S. (1983). "Statistical mechanics of cellular automata". Rev. Mod. Phys. 55 (3): 601–644. Bibcode:1983RvMP...55..601W. doi:10.1103/RevModPhys.55.601.
Eichenauer, Jürgen; Lehn, Jürgen (1986). "A nonlinear congruential pseudorandom number generator". Statistische Hefte. 27: 315–326. doi:10.1007/BF02932576. S2CID 122052399.
Blum, L.; Blum, M.; Shub, M. (1 May 1986). "A Simple Unpredictable Pseudo-Random Number Generator". SIAM Journal on Computing. 15 (2): 364–383. doi:10.1137/0215025. ISSN 0097-5397.
Park, Stephen K.; Miller, Keith W. (1988). "Random Number Generators: Good Ones Are Hard To Find" (PDF). Communications of the ACM. 31 (10): 1192–1201. doi:10.1145/63039.63042. S2CID 207575300.
Wikramaratna, R. S. (1989). "ACORN — A new method for generating sequences of uniformly distributed Pseudo-random Numbers". Journal of Computational Physics. 83 (1): 16–31. Bibcode:1989JCoPh..83...16W. doi:10.1016/0021-9991(89)90221-0.
Wikramaratna, R.S. Theoretical and empirical convergence results for additive congruential random number generators, Journal of Computational and Applied Mathematics (2009), doi:10.1016/j.cam.2009.10.015
Savvidy, G.K; Ter-Arutyunyan-Savvidy, N.G (1991). "On the Monte Carlo simulation of physical systems". Journal of Computational Physics. 97 (2): 566. Bibcode:1991JCoPh..97..566S. doi:10.1016/0021-9991(91)90015-D.
George, Marsaglia; Zaman, Arif (1991). "A new class of random number generators". Annals of Applied Probability. 1 (3): 462–480. doi:10.1214/aoap/1177005878.
Martin, Lüscher (1994). "A portable high-quality random number generator for lattice field theory simulations". Computer Physics Communications. 79 (1): 100–110. arXiv:hep-lat/9309020. Bibcode:1994CoPhC..79..100L. doi:10.1016/0010-4655(94)90232-1. S2CID 17608961.
Koç, Cemal (1995). "Recurring-with-Carry Sequences". Journal of Applied Probability. 32 (4): 966–971. doi:10.2307/3215210. JSTOR 3215210. S2CID 123798320.
Couture, Raymond; L'Ecuyer, Pierre (1997). "Distribution properties of multiply-with-carry random number generators" (PDF). Mathematics of Computation. 66 Number. 218 (218): 591–607. Bibcode:1997MaCom..66..591C. doi:10.1090/S0025-5718-97-00827-2.
Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling and Computer Simulation. 8 (1): 3–30. CiteSeerX 10.1.1.215.1141. doi:10.1145/272991.272995. S2CID 3332028.
Marsaglia, George (July 2003). "Xorshift RNGs". Journal of Statistical Software. 8 (14). doi:10.18637/jss.v008.i14.
Panneton, François O.; l'Ecuyer, Pierre; Matsumoto, Pierre (March 2006). "Improved long-period generators based on linear recurrences modulo 2" (PDF). ACM Transactions on Mathematical Software. 32 (1): 1–16. CiteSeerX 10.1.1.73.5499. doi:10.1145/1132973.1132974. S2CID 7368302.
Salmon, John; Moraes, Mark; Dror, Ron; Shaw, David (2011). "Parallel random numbers: as easy as 1, 2, 3". Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, Article No. 16. doi:10.1145/2063384.2063405.
Balkova, Lubomira; Bucci, Michelangelo; De Luca, Alessandro; Hladky, Jiri; Puzynina, Svetlana (September 2016). "Aperiodic pseudorandom number generators based on infinite words". Theoretical Computer Science. 647: 85–100. arXiv:1311.6002. doi:10.1016/j.tcs.2016.07.042. S2CID 2175443.
Çabuk, Umut Can; Aydin, Ömer; Dalkiliç, Gökhan (2017). "A random number generator for lightweight authentication protocols: xorshiftR+". Turkish Journal of Electrical Engineering & Computer Sciences. 25: 4818–4828. doi:10.3906/elk-1703-361.
Harase, S.; Kimoto, T. (2018). "Implementing 64-bit Maximally Equidistributed F₂-Linear Generators with Mersenne Prime Period". ACM Transactions on Mathematical Software. 44 (3): 30:1–30:11. arXiv:1505.06582. doi:10.1145/3159444. S2CID 14923086.

firstpr.com.au

Park, Stephen K.; Miller, Keith W. (1988). "Random Number Generators: Good Ones Are Hard To Find" (PDF). Communications of the ACM. 31 (10): 1192–1201. doi:10.1145/63039.63042. S2CID 207575300.

github.com

Cookman, Richard (2016). "random cycle bit generator (rcb_generator)". Technical Report.
Harase, S.; Kimoto, T. (2018). "Implementing 64-bit Maximally Equidistributed F₂-Linear Generators with Mersenne Prime Period". ACM Transactions on Mathematical Software. 44 (3): 30:1–30:11. arXiv:1505.06582. doi:10.1145/3159444. S2CID 14923086.

groups.google.com

Post by George Marsaglia on the newsgroup sci.stat.math dated 1 August 2018 with title 'Yet another RNG'.

harvard.edu

ui.adsabs.harvard.edu

Wolfram, S. (1983). "Statistical mechanics of cellular automata". Rev. Mod. Phys. 55 (3): 601–644. Bibcode:1983RvMP...55..601W. doi:10.1103/RevModPhys.55.601.
Wikramaratna, R. S. (1989). "ACORN — A new method for generating sequences of uniformly distributed Pseudo-random Numbers". Journal of Computational Physics. 83 (1): 16–31. Bibcode:1989JCoPh..83...16W. doi:10.1016/0021-9991(89)90221-0.
Savvidy, G.K; Ter-Arutyunyan-Savvidy, N.G (1991). "On the Monte Carlo simulation of physical systems". Journal of Computational Physics. 97 (2): 566. Bibcode:1991JCoPh..97..566S. doi:10.1016/0021-9991(91)90015-D.
Martin, Lüscher (1994). "A portable high-quality random number generator for lattice field theory simulations". Computer Physics Communications. 79 (1): 100–110. arXiv:hep-lat/9309020. Bibcode:1994CoPhC..79..100L. doi:10.1016/0010-4655(94)90232-1. S2CID 17608961.
Couture, Raymond; L'Ecuyer, Pierre (1997). "Distribution properties of multiply-with-carry random number generators" (PDF). Mathematics of Computation. 66 Number. 218 (218): 591–607. Bibcode:1997MaCom..66..591C. doi:10.1090/S0025-5718-97-00827-2.

jstor.org

Wichmann, Brian A.; Hill, David I. (1982). "Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator". Journal of the Royal Statistical Society. Series C (Applied Statistics). 31 (2): 188–190. doi:10.2307/2347988. JSTOR 2347988.
Koç, Cemal (1995). "Recurring-with-Carry Sequences". Journal of Applied Probability. 32 (4): 966–971. doi:10.2307/3215210. JSTOR 3215210. S2CID 123798320.

microsoft.com

support.microsoft.com

"Microsoft Support - Description of the RAND function in Excel". 17 April 2018.

numpy.org

"SFC64 Small Fast Chaotic PRNG". NumPy v2.2 Manual. Archived from the original on 13 February 2025. Retrieved 13 February 2025.

oswego.edu

gee.cs.oswego.edu

Steele, Guy L. Jr.; Lea, Doug; Flood, Christine H. (2014). "Fast splittable pseudorandom number generators" (PDF). OOPSLA '14 Proceedings of the 2014 ACM International Conference on Object Oriented Programming Systems Languages & Applications.

pcg-random.org

O'Neill, Melissa E. (2014). "PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation" (PDF). Technical Report.

projecteuclid.org

George, Marsaglia; Zaman, Arif (1991). "A new class of random number generators". Annals of Applied Probability. 1 (3): 462–480. doi:10.1214/aoap/1177005878.

psu.edu

citeseerx.ist.psu.edu

Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling and Computer Simulation. 8 (1): 3–30. CiteSeerX 10.1.1.215.1141. doi:10.1145/272991.272995. S2CID 3332028.
Panneton, François O.; l'Ecuyer, Pierre; Matsumoto, Pierre (March 2006). "Improved long-period generators based on linear recurrences modulo 2" (PDF). ACM Transactions on Mathematical Software. 32 (1): 1–16. CiteSeerX 10.1.1.73.5499. doi:10.1145/1132973.1132974. S2CID 7368302.

python.org

docs.python.org

"Documentation » The Python Standard Library » 9. Numeric and Mathematical Modules » 9.6. random — Generate pseudo-random numbers".

researchgate.net

Matthews, Robert A. J. (1992). "Maximally periodic reciprocals". Bull. Inst. Math. Appl. 28: 147–148.

semanticscholar.org

api.semanticscholar.org

Rotenberg, A. (1960). "A New Pseudo-Random Number Generator". Journal of the ACM. 7 (1): 75–77. doi:10.1145/321008.321019. S2CID 16770825.
Eichenauer, Jürgen; Lehn, Jürgen (1986). "A nonlinear congruential pseudorandom number generator". Statistische Hefte. 27: 315–326. doi:10.1007/BF02932576. S2CID 122052399.
Park, Stephen K.; Miller, Keith W. (1988). "Random Number Generators: Good Ones Are Hard To Find" (PDF). Communications of the ACM. 31 (10): 1192–1201. doi:10.1145/63039.63042. S2CID 207575300.
Martin, Lüscher (1994). "A portable high-quality random number generator for lattice field theory simulations". Computer Physics Communications. 79 (1): 100–110. arXiv:hep-lat/9309020. Bibcode:1994CoPhC..79..100L. doi:10.1016/0010-4655(94)90232-1. S2CID 17608961.
Koç, Cemal (1995). "Recurring-with-Carry Sequences". Journal of Applied Probability. 32 (4): 966–971. doi:10.2307/3215210. JSTOR 3215210. S2CID 123798320.
Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling and Computer Simulation. 8 (1): 3–30. CiteSeerX 10.1.1.215.1141. doi:10.1145/272991.272995. S2CID 3332028.
Panneton, François O.; l'Ecuyer, Pierre; Matsumoto, Pierre (March 2006). "Improved long-period generators based on linear recurrences modulo 2" (PDF). ACM Transactions on Mathematical Software. 32 (1): 1–16. CiteSeerX 10.1.1.73.5499. doi:10.1145/1132973.1132974. S2CID 7368302.
Balkova, Lubomira; Bucci, Michelangelo; De Luca, Alessandro; Hladky, Jiri; Puzynina, Svetlana (September 2016). "Aperiodic pseudorandom number generators based on infinite words". Theoretical Computer Science. 647: 85–100. arXiv:1311.6002. doi:10.1016/j.tcs.2016.07.042. S2CID 2175443.
Harase, S.; Kimoto, T. (2018). "Implementing 64-bit Maximally Equidistributed F₂-Linear Generators with Mersenne Prime Period". ACM Transactions on Mathematical Software. 44 (3): 30:1–30:11. arXiv:1505.06582. doi:10.1145/3159444. S2CID 14923086.

siam.org

epubs.siam.org

Blum, L.; Blum, M.; Shub, M. (1 May 1986). "A Simple Unpredictable Pseudo-Random Number Generator". SIAM Journal on Computing. 15 (2): 364–383. doi:10.1137/0215025. ISSN 0097-5397.

sourceforge.net

pracrand.sourceforge.net

Doty-Humphrey, Chris. "RNG_engines.txt". Practically Random. Archived from the original on 17 December 2024. Retrieved 13 February 2025.

tubitak.gov.tr

journals.tubitak.gov.tr

Çabuk, Umut Can; Aydin, Ömer; Dalkiliç, Gökhan (2017). "A random number generator for lightweight authentication protocols: xorshiftR+". Turkish Journal of Electrical Engineering & Computer Sciences. 25: 4818–4828. doi:10.3906/elk-1703-361.

umontreal.ca

iro.umontreal.ca

Panneton, François O.; l'Ecuyer, Pierre; Matsumoto, Pierre (March 2006). "Improved long-period generators based on linear recurrences modulo 2" (PDF). ACM Transactions on Mathematical Software. 32 (1): 1–16. CiteSeerX 10.1.1.73.5499. doi:10.1145/1132973.1132974. S2CID 7368302.

web.archive.org

Doty-Humphrey, Chris. "RNG_engines.txt". Practically Random. Archived from the original on 17 December 2024. Retrieved 13 February 2025.
"SFC64 Small Fast Chaotic PRNG". NumPy v2.2 Manual. Archived from the original on 13 February 2025. Retrieved 13 February 2025.

worldcat.org

search.worldcat.org

Blum, L.; Blum, M.; Shub, M. (1 May 1986). "A Simple Unpredictable Pseudo-Random Number Generator". SIAM Journal on Computing. 15 (2): 364–383. doi:10.1137/0215025. ISSN 0097-5397.