pith. machine review for the scientific record. sign in

arxiv: 2605.05099 · v1 · submitted 2026-05-06 · 📊 stat.AP · cs.MS

Recognition: unknown

Randompack: Cross-Platform Reproducible Random Number Generation and Distribution Sampling

Kristj\'an J\'onasson

Pith reviewed 2026-05-08 15:37 UTC · model grok-4.3

classification 📊 stat.AP cs.MS
keywords random number generationreproducibilitycross-platformC librarydistribution samplingparallel simulationstatistical computingpermutation sampling
0
0 comments X

The pith

Randompack separates random engines from distribution samplers to deliver faster performance and identical results from the same seeds across languages, hardware, and compilers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents Randompack as a C library that implements multiple modern random number engines and 14 continuous distributions while keeping the engine layer fully independent of the distribution layer. Benchmarks indicate overall speed advantages ranging from 1x to 15x over competing libraries depending on the specific engine, distribution, interface, and platform. The design ensures that identical seeds produce bit-for-bit compatible output streams regardless of programming language, operating system, CPU architecture, or compiler. This reproducibility directly supports reliable parallel simulations and verification of statistical results. The library ships with a test suite, benchmark programs, and language interfaces under a permissive MIT license.

Core claim

Randompack is a C library that implements engines including xoshiro256, PCG64, Philox, ranlux++, and sfc64 together with uniform, normal, exponential, gamma, beta, multivariate normal, and other distributions; any engine can be paired with any distribution because the layers are separated, and the same seeds produce identical results on every supported platform and language.

What carries the argument

The separation of the random engine layer from the distribution sampling layer, which allows independent selection while preserving cross-platform bit compatibility.

If this is right

  • Parallel simulations can use the same seed on different machines and obtain identical results without additional synchronization.
  • Any of the supported engines can be swapped into any distribution sampler without rewriting code or losing reproducibility.
  • Raw bit streams, bounded integers, permutations, and sampling without replacement are all available through the same interface.
  • Interfaces for Fortran, Python, Julia, and R deliver the same performance and reproducibility guarantees as the core C implementation.
  • The MIT license permits free integration into both open-source and proprietary statistical software.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The modular design could reduce the frequency of platform-specific bugs that currently appear when the same statistical model is reimplemented in different languages.
  • Adoption might allow research groups to share exact random sequences for peer review without needing to archive large binary files.
  • The emphasis on raw bit streams and permutations suggests the library could serve as a foundation for Monte Carlo methods beyond the distributions explicitly listed.
  • Because the library is packaged through conda-forge, it lowers the barrier for reproducible environments in data-science pipelines that mix C and Python code.

Load-bearing premise

The benchmarks used fair, fully optimized configurations of the competing libraries and Randompack contains no hidden bugs that would affect either speed or the claimed cross-platform reproducibility.

What would settle it

Execute the library's own benchmark programs and test suite on at least two different CPU architectures or compilers with identical seeds and observe either slower performance than the best competing library or any difference in generated values.

Figures

Figures reproduced from arXiv: 2605.05099 by Kristj\'an J\'onasson.

Figure 1
Figure 1. Figure 1: Illustration of the ziggurat method for the exponential distribution and 3 strips: Strip 1 is view at source ↗
read the original abstract

A C library for random number generation, Randompack, is presented. The library implements several modern random number generators (engines), including xoshiro256, PCG64, Philox, ranlux++, and sfc64; 14 continuous distributions including uniform, normal, exponential, gamma, beta, and multivariate normal; raw bit streams, bounded integers, permutations, and sampling without replacement. The engine and the distribution layers are separated so any engine can be used with any distribution. Benchmarks show that Randompack is faster overall than competing libraries, with speedup factors ranging from about 1 to 15 depending on engine, distribution, interface, and platform. A distinguishing feature is reproducibility: with the same seeds Randompack gives compatible results across programming languages, computers, CPU architectures, and compilers. The library includes comprehensive support for parallel simulation. It is accompanied by a comprehensive test suite, benchmarking programs, and example programs. Interfaces to Fortran, Python, Julia, and R have been implemented; their benchmark results are included, although their design and implementation are otherwise outside the scope of the article. Unlike other available C libraries with comparable scope, Randompack is permissively licensed under the MIT license, and it is open source and publicly available through GitHub and conda-forge.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript presents Randompack, a permissively licensed C library for random number generation and distribution sampling. It separates RNG engines (xoshiro256, PCG64, Philox, ranlux++, sfc64) from distribution samplers for 14 continuous distributions (uniform, normal, exponential, gamma, beta, multivariate normal, etc.), plus raw bits, bounded integers, permutations, and sampling without replacement. The library supports parallel simulation, includes a test suite and benchmarking programs, and provides interfaces to Fortran, Python, Julia, and R. Benchmarks indicate overall faster performance than competing libraries with speedups ranging from 1x to 15x depending on engine, distribution, interface, and platform. A core feature is cross-platform reproducibility: identical seeds produce compatible results across programming languages, computers, CPU architectures, and compilers. The library is open source via GitHub and conda-forge.

Significance. If the performance and reproducibility claims hold under scrutiny, this provides a valuable, practical tool for reproducible Monte Carlo simulations and statistical computing workflows that span languages and hardware. The modular architecture (engine-distribution separation), comprehensive test suite, public benchmarks, and permissive MIT licensing are explicit strengths that facilitate adoption and verification. The cross-language interfaces and parallel support address real needs in multi-platform research, and the open availability mitigates concerns about hidden implementation details.

major comments (2)
  1. [Benchmarks] Benchmarks section: the overall 'faster' claim with speedups of 1-15x is central to the contribution, but the text does not specify the exact versions, compilation flags (e.g., -O3 vs. defaults), or hardware configurations used for all competing libraries (GSL, Boost, etc.); without this, the fairness of the comparisons cannot be fully assessed and the speedup range may not be reproducible.
  2. [Reproducibility] Reproducibility section: the claim that 'with the same seeds Randompack gives compatible results across programming languages, computers, CPU architectures, and compilers' is load-bearing for the distinguishing feature, yet the manuscript provides no concrete verification data, test outputs, or discussion of floating-point consistency in distribution sampling to support it beyond the architecture description.
minor comments (3)
  1. [Abstract] The abstract lists only a subset of the 14 distributions; a complete enumeration or reference to the full list in the library description section would improve clarity.
  2. Figure captions in the benchmark results should explicitly state the axes, units, and what each bar or line represents to allow readers to interpret the speedup factors without referring back to the text.
  3. [Examples] The parallel simulation support is described at a high level; adding a short code snippet or API usage example in the examples section would aid users implementing concurrent simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation for minor revision. We address each of the major comments below, providing clarifications and committing to revisions where appropriate to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Benchmarks] Benchmarks section: the overall 'faster' claim with speedups of 1-15x is central to the contribution, but the text does not specify the exact versions, compilation flags (e.g., -O3 vs. defaults), or hardware configurations used for all competing libraries (GSL, Boost, etc.); without this, the fairness of the comparisons cannot be fully assessed and the speedup range may not be reproducible.

    Authors: We agree that detailed specification of the benchmarking environment is necessary to substantiate the performance claims and allow for independent verification. In the revised manuscript, we will add comprehensive details on the hardware configurations (including CPU models, architectures, and operating systems), compiler versions, optimization flags (explicitly noting -O3 and any others used), and the exact versions of all competing libraries such as GSL and Boost. This information will be presented in a new table or expanded text within the Benchmarks section to ensure transparency and reproducibility of the reported speedups. revision: yes

  2. Referee: [Reproducibility] Reproducibility section: the claim that 'with the same seeds Randompack gives compatible results across programming languages, computers, CPU architectures, and compilers' is load-bearing for the distinguishing feature, yet the manuscript provides no concrete verification data, test outputs, or discussion of floating-point consistency in distribution sampling to support it beyond the architecture description.

    Authors: The reproducibility feature is indeed central, and while the manuscript describes the architectural choices that enable it (such as portable RNG implementations and separation of concerns), we acknowledge the value of empirical verification. We will revise the Reproducibility section to include concrete test outputs demonstrating identical results across platforms for selected distributions and engines. We will also add a discussion of floating-point consistency, explaining that the library relies on standard C math functions and IEEE 754-compliant arithmetic, with any minor variations attributable to floating-point semantics rather than the RNG or sampling methods themselves. revision: yes

Circularity Check

0 steps flagged

No significant circularity in software implementation and benchmarking paper

full rationale

The paper presents a C library (Randompack) for RNG engines and distribution sampling, with benchmarks, test suites, and cross-language interfaces. It contains no mathematical derivations, equations, predictions, or self-referential claims of the types listed in the circularity patterns. Performance and reproducibility claims are grounded in the described artifacts, public code, and empirical benchmarks rather than any reduction to fitted inputs or self-citations by construction. This matches the reader's assessment of zero circularity for a non-derivational software paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is an engineering and software paper presenting a library implementation. No free parameters, mathematical axioms, or new invented entities are described in the abstract.

pith-pipeline@v0.9.0 · 5523 in / 1201 out tokens · 103515 ms · 2026-05-08T15:37:39.083415+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

68 extracted references · 48 canonical work pages

  1. [1]

    L. Yu. Barash and L. N. Shchur. 2014. PRAND: GPU accelerated parallel random number generation library: Using most reliable algorithms and applying parallelism of modern GPUs and CPUs.Computer Physics Communications185, 4 (2014), 1343–1353. doi:10.1016/j.cpc.2014.01.012

    work page doi:10.1016/j.cpc.2014.01.012 2014

  2. [2]

    Bernstein

    Daniel J. Bernstein. 2008. ChaCha, a variant of Salsa20. Workshop Record of SASC 2008: The State of the Art of Stream Ciphers, Vol. 8, pp. 3–5. https://cr.yp.to/chacha/chacha-20080128.pdf

    2008

  3. [3]

    Kamalika Bhattacharjee and Sukanta Das. 2022. A search for good pseudo-random number generators: survey and empirical studies.Computer Science Review45 (2022), 100471. doi:10.1016/j.cosrev.2022.100471

    work page doi:10.1016/j.cosrev.2022.100471 2022

  4. [4]

    David Blackman and Sebastiano Vigna. 2021. Scrambled linear pseudorandom number generators.ACM Trans. Math. Software47, 4 (2021), 36:1–36:32. doi:10.1145/3460772

    work page doi:10.1145/3460772 2021

  5. [5]

    George E. P. Box and Mervin E. Muller. 1958. A note on the generation of random normal deviates.The Annals of Mathematical Statistics29, 2 (1958), 610–611. doi:10.1214/aoms/1177706645

    work page doi:10.1214/aoms/1177706645 1958

  6. [6]

    Robert G. Brown. 2006.DieHarder: A Gnu Public License Random Number Tester. Technical Report. Duke University Physics Department, Durham, NC. https://rurban.github.io/dieharder/manual/dieharder.pdf

    2006

  7. [7]

    Diebold, Todd A

    Francis X. Diebold, Todd A. Gunther, and Anthony S. Tay. 1998. Evaluating density forecasts with applications to financial risk management. International Economic Review39, 4 (Nov. 1998), 863–883. doi:10.2307/2527342

    work page doi:10.2307/2527342 1998

  8. [8]

    Jurgen A. Doornik. 2005.An Improved Ziggurat Method to Generate Normal Random Samples. Technical Report. Nuffield College, University of Oxford. https://www.doornik.com/research/ziggurat.pdf

    2005

  9. [9]

    Chris Doty-Humphrey. 2010. PractRand: A practical random number generator test suite (including the SFC family of generators). http: //pracrand.sourceforge.net. Accessed 2026-02-23

    2010

  10. [10]

    Richard Durstenfeld. 1964. Algorithm 235: random permutation.Commun. ACM7, 7 (1964), 420. doi:10.1145/364520.364540

    work page doi:10.1145/364520.364540 1964

  11. [11]

    Tomasz R. Dziala. 2023. Collatz-Weyl generators: high quality and high throughput parameterized pseudorandom number generators. arXiv:2312.17043. https://arxiv.org/abs/2312.17043

    work page arXiv 2023

  12. [12]

    Fisher and Frank Yates

    Ronald A. Fisher and Frank Yates. 1938.Statistical Tables for Biological, Agricultural and Medical Research(3 ed.). Oliver and Boyd, London

    1938

  13. [13]

    Cameron Foreman, Richie Yeung, and Florian J. Curchod. 2024. Statistical testing of random number generators and their improvement using randomness extraction.Entropy26, 12 (2024), 1053. doi:10.3390/e26121053

    work page doi:10.3390/e26121053 2024

  14. [14]

    Jill Leslie Gibson, Fred Burke Jones, Michael Aaron Lively, Robert Currier Little, and Joel A. Kulesza. 2025.MCNP ® Site Support Newsletter First Quarter 2025. Technical Report LA-UR-25-21113. Los Alamos National Laboratory, Los Alamos, NM, USA. https://mcnp.lanl.gov/pdf_files/ TechReport_2025_LANL_LA-UR-25-21113_GibsonJonesEtAl.pdf Newsletter

    2025

  15. [15]

    Pré-publication, Document de travail

    Brian Gladman, Vincenzo Innocente, John Mather, and Paul Zimmermann. 2025. Accuracy of Mathematical Functions in Single, Double, Double Extended, and Quadruple Precision. HAL preprint / working paper. Listed in HAL as “Pré-publication, Document de travail”

    2025

  16. [16]

    Jonas Hahnfeld and Lorenzo Moneta. 2021. A Portable Implementation of RANLUX++.EPJ Web of Conferences251 (2021), 03008. doi:10.1051/ epjconf/202125103008

    work page arXiv 2021

  17. [17]

    Hiroshi Haramoto, Makoto Matsumoto, Takuji Nishimura, François Panneton, and Pierre L’Ecuyer. 2008. Efficient Jump Ahead forF 2-Linear Random Number Generators.INFORMS Journal on Computing20, 3 (2008), 385–390

    2008

  18. [18]

    Wolfgang Hörmann and Josef Leydold. 2000. Random-number and random-variate generation: automatic random variate generation for simulation input. InProceedings of the 32nd Conference on Winter Simulation (WSC 2000), Paul A. Fishwick, Keebom Kang, Jeffrey A. Joines, and Russell R. Barton (Eds.). IEEE Press, Piscataway, NJ, 675–682. doi:10.5555/510378.510475...

    work page doi:10.5555/510378.510475 2000

  19. [19]

    F. James. 1990. A review of pseudorandom number generators.Computer Physics Communications60, 3 (1990), 329–344. doi:10.1016/0010- 4655(90)90032-V

    work page doi:10.1016/0010- 1990

  20. [20]

    jirka h. 2021. ranluxpp-portable: Portable version of Ranlux++ RNG. GitHub repository. https://github.com/jirka-h/ranluxpp-portable Accessed 2026-03-15

    2021

  21. [21]

    2023.Reassessing the MCNP Random Number Generator

    Colin James Josey. 2023.Reassessing the MCNP Random Number Generator. Technical Report LA-UR-23-25111, Rev. 1. Los Alamos National Laboratory, Los Alamos, NM, USA. doi:10.2172/1998091

    work page doi:10.2172/1998091 2023

  22. [22]

    A. J. Kinderman and J. F. Monahan. 1977. Computer generation of random variables using the ratio of uniform deviates.ACM Trans. Math. Software 3, 3 (1977), 257–260. doi:10.1145/355744.355750

    work page doi:10.1145/355744.355750 1977

  23. [23]

    Donald E. Knuth. 1969.The Art of Computer Programming, Volume 2: Seminumerical Algorithms(1 ed.). Addison-Wesley, Reading, MA

    1969

  24. [24]

    Pierre L’Ecuyer. 1999. Good parameters and implementations for combined multiple recursive random number generators.Operations Research47, 1 (1999), 159–164. doi:10.1287/opre.47.1.159

    work page doi:10.1287/opre.47.1.159 1999

  25. [25]

    Pierre L’Ecuyer. 2015. Random number generation with multiple streams for sequential and parallel computing. InProceedings of the 2015 Winter Simulation Conference. IEEE, Huntington Beach, CA, USA, 31–44. doi:10.1109/WSC.2015.7408151

    work page doi:10.1109/wsc.2015.7408151 2015

  26. [26]

    Pierre L’Ecuyer. 2017. History of Uniform Random Number Generation. InProceedings of the 2017 Winter Simulation Conference. IEEE, Las Vegas, NV, USA, 202–230. doi:10.1109/WSC.2017.8247790

    work page doi:10.1109/wsc.2017.8247790 2017

  27. [27]

    Pierre L’Ecuyer, David Munger, Boris Oreshkin, and Richard Simard. 2017. Random numbers for parallel computers: requirements and methods, with emphasis on GPUs.Mathematics and Computers in Simulation135 (2017), 3–17. doi:10.1016/j.matcom.2016.05.005

    work page doi:10.1016/j.matcom.2016.05.005 2017

  28. [28]

    Pierre L’Ecuyer and Richard Simard. 2007. TestU01: a C library for empirical testing of random number generators.ACM Trans. Math. Software33, 4 (2007), 22:1–22:40. doi:10.1145/1268776.1268777

    work page doi:10.1145/1268776.1268777 2007

  29. [29]

    Chen, and W

    Pierre L’Ecuyer, Richard Simard, Eric J. Chen, and W. David Kelton. 2002. An object-oriented random-number package with many long streams and substreams.Operations Research50, 6 (2002), 1073–1075. doi:10.1287/opre.50.6.1073.358

    work page doi:10.1287/opre.50.6.1073.358 2002

  30. [30]

    Derrick Henry Lehmer. 1951. Mathematical methods in large-scale computing units. InProceedings of the Second Symposium on Large-Scale Digital Calculating Machinery (Annals of the Computation Laboratory, Vol. 26). Harvard University Press, Cambridge, MA, 141–146

    1951

  31. [31]

    Daniel Lemire. 2019. Fast random integer generation in an interval.ACM Transactions on Modeling and Computer Simulation29, 1, Article 3 (2019), 12 pages. doi:10.1145/3230636

    work page doi:10.1145/3230636 2019

  32. [32]

    Daniel Lemire and Melissa E. O’Neill. 2019. xorshift1024*, xorshift1024+, xorshift128+ and xoroshiro128+ fail statistical tests for linearity. Computational and Applied Mathematics350 (2019), 139–142. doi:10.1016/j.cam.2018.10.019

    work page doi:10.1016/j.cam.2018.10.019 2019

  33. [33]

    Joseph L. Leva. 1992. A fast normal random number generator.ACM Trans. Math. Software18, 4 (1992), 449–453. doi:10.1145/138351.138364

    work page doi:10.1145/138351.138364 1992

  34. [34]

    Martin Lüscher. 1994. A portable high-quality random number generator for lattice field theory simulations.Computer Physics Communications79, 1 (1994), 100–110. doi:10.1016/0010-4655(94)90232-1

    work page doi:10.1016/0010-4655(94)90232-1 1994

  35. [35]

    George Marsaglia. 1964. Generating a variable from the tail of the normal distribution.Technometrics6, 1 (1964), 101–102. doi:10.1080/00401706. 1964.10490150

    work page doi:10.1080/00401706 1964

  36. [36]

    George Marsaglia. 1996. DIEHARD: A Battery of Tests of Randomness. http://stat.fsu.edu/pub/diehard/

    1996

  37. [37]

    George Marsaglia. 2003. xorshift RNGs.Journal of Statistical Software8, 14 (2003), 1–6. doi:10.18637/jss.v008.i14

    work page doi:10.18637/jss.v008.i14 2003

  38. [38]

    George Marsaglia and Wai Wan Tsang. 1984. A fast, easily implemented method for sampling from decreasing or symmetric unimodal density functions.SIAM J. Sci. Statist. Comput.5, 2 (1984), 349–359. doi:10.1137/0905027

    work page doi:10.1137/0905027 1984

  39. [39]

    George Marsaglia and Wai Wan Tsang. 2000. A simple method for generating gamma variables.ACM Trans. Math. Software26, 3 (2000), 363–372. doi:10.1145/358407.358414

    work page doi:10.1145/358407.358414 2000

  40. [40]

    George Marsaglia and Wai Wan Tsang. 2000. The ziggurat method for generating random variables.Journal of Statistical Software5, 8 (2000), 1–7. doi:10.18637/jss.v005.i08

    work page doi:10.18637/jss.v005.i08 2000

  41. [41]

    Makoto Matsumoto and Takuji Nishimura. 1998. Mersenne Twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Transactions on Modeling and Computer Simulation8, 1 (1998), 3–30. doi:10.1145/272991.272995

    work page doi:10.1145/272991.272995 1998

  42. [42]

    Makoto Matsumoto, Isaku Wada, Ai Kuramoto, and Hyo Ashihara. 2007. Common defects in initialization of pseudorandom number generators. ACM Transactions on Modeling and Computer Simulation17, 4 (2007), 15:1–15:14. doi:10.1145/1276927.1276928

    work page doi:10.1145/1276927.1276928 2007

  43. [43]

    McFarland

    Christopher D. McFarland. 2016. A modified ziggurat algorithm for generating exponentially and normally distributed pseudorandom numbers. Journal of Statistical Computation and Simulation86, 7 (2016), 1281–1294. doi:10.1080/00949655.2015.1060234

    work page doi:10.1080/00949655.2015.1060234 2016

  44. [44]

    2025.Upgrading PCG64 with PCG64DXSM

    NumPy Developers. 2025.Upgrading PCG64 with PCG64DXSM. https://numpy.org/doc/stable/reference/random/upgrading-pcg64.html Accessed 2026-03-14

    2025

  45. [45]

    Melissa E. O’Neill. 2014.PCG: A family of simple fast space-efficient statistically good algorithms for random number generation. Technical Report HMC-CS-2014-0905. Harvey Mudd College. Available at https://www.pcg-random.org/pdf/hmc-cs-2014-0905.pdf

    2014

  46. [46]

    Melissa E. O’Neill. 2015. Developing a seed_seq Alternative. PCG, A Better Random Number Generator (blog). https://www.pcg-random.org/posts/ developing-a-seed_seq-alternative.html Accessed 2026-03-08

    2015

  47. [47]

    Melissa E. O’Neill. 2019. Post on NumPy issue #13635: Decide on new PRNG BitGenerator default. https://github.com/numpy/numpy/issues/ 13635#issuecomment-506088698 GitHub issue comment

    2019

  48. [48]

    François Panneton and Pierre L’Ecuyer. 2005. On the xorshift random number generators.ACM Transactions on Modeling and Computer Simulation 15, 4 (Oct. 2005), 346–361. doi:10.1145/1113316.1113319 Manuscript submitted to ACM Randompack: Cross-Platform Reproducible Random Number Generation and Distribution Sampling 19

    work page doi:10.1145/1113316.1113319 2005

  49. [49]

    François Panneton, Pierre L’Ecuyer, and Makoto Matsumoto. 2006. Improved long-period generators based on linear recurrences modulo 2.ACM Trans. Math. Software32, 1 (2006), 1–16. doi:10.1145/1132973.1132974

    work page doi:10.1145/1132973.1132974 2006

  50. [50]

    Park and Keith W

    Stephen K. Park and Keith W. Miller. 1988. Random number generators: good ones are hard to find.Commun. ACM31, 10 (1988), 1192–1201. doi:10.1145/63039.63042

    work page doi:10.1145/63039.63042 1988

  51. [51]

    2020.Security and Privacy Controls for Information Systems and Organizations

    Andrew Rukhin, Juan Soto, James Nechvatal, Miles Smid, Elaine Barker, Stefan Leigh, Mark Levenson, Mark Vangel, David Banks, Alan Heckert, James Dray, San Vo, and Lawrence E. Bassham III. 2010.A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. NIST Special Publication 800-22 Rev. 1a. National Institute o...

    work page doi:10.6028/nist.sp.800- 2010

  52. [52]

    Saarinen

    Markku-Juhani O. Saarinen. 2022. SP 800–22 and GM/T 0005–2012 tests: clearly obsolete, possibly harmful. In2022 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW). IEEE, Genoa, Italy, 31–37. doi:10.1109/EuroSPW55150.2022.00011

    work page doi:10.1109/eurospw55150.2022.00011 2022

  53. [53]

    Salmon, Mark A

    John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw. 2011. Parallel Random Numbers: As Easy as 1, 2, 3. InProceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC ’11). ACM, New York, NY, USA, 16:1–16:12. doi:10.1145/2063384.2063405

    work page doi:10.1145/2063384.2063405 2011

  54. [54]

    Werner Schindler and Wolfgang Killmann. 2003. Evaluation Criteria for True (Physical) Random Number Generators Used in Cryptographic Applications. InCryptographic Hardware and Embedded Systems – CHES 2002 (Lecture Notes in Computer Science, Vol. 2523). Springer, Heidelberg, 431–449. doi:10.1007/3-540-36400-5_31

    work page doi:10.1007/3-540-36400-5_31 2003

  55. [55]

    Naoki Shibata. 2025. SLEEF: SIMD Library for Evaluating Elementary Functions. https://github.com/shibatch/sleef. GitHub repository

    2025

  56. [56]

    Naoki Shibata and Francesco Petrogalli. 2020. SLEEF: a portable vectorized library of C standard mathematical functions.IEEE Transactions on Parallel and Distributed Systems31, 6 (2020), 1316–1327. doi:10.1109/TPDS.2019.2960333

    work page doi:10.1109/tpds.2019.2960333 2020

  57. [57]

    Alexei Sibidanov. 2017. A revision of the subtract-with-borrow random number generators.Computer Physics Communications221 (Dec. 2017), 299–303. doi:10.1016/j.cpc.2017.09.005

    work page doi:10.1016/j.cpc.2017.09.005 2017

  58. [58]

    Steele, Guy L

    Jr. Steele, Guy L. and Sebastiano Vigna. 2021. LXM: better splittable pseudorandom number generators (and almost as fast).Proceedings of the ACM on Programming Languages5, OOPSLA (Oct. 2021), 148:1–148:31. doi:10.1145/3485525

    work page doi:10.1145/3485525 2021

  59. [59]

    Steele Jr., Doug Lea, and Christine H

    Guy L. Steele Jr., Doug Lea, and Christine H. Flood. 2014. Fast splittable pseudorandom number generators. InProceedings of the 2014 ACM International Conference on Object Oriented Programming Systems Languages & Applications (OOPSLA ’14). ACM, New York, NY, USA, 453–472. doi:10.1145/2714064.2660195

    work page doi:10.1145/2714064.2660195 2014

  60. [60]

    doi:10.1090/S0025- 5718-1970-0274029-X

    Robert C. Tausworthe. 1965. Random numbers generated by linear recurrence modulo two.Math. Comp.19, 90 (1965), 201–209. doi:10.1090/S0025- 5718-1965-0184406-1

    work page doi:10.1090/s0025- 1965

  61. [61]

    The Julia Project and the OpenLibm Authors. 2025. OpenLibm. Project website. https://openlibm.org/

    2025

  62. [62]

    Sebastiano Vigna. 2016. An experimental exploration of Marsaglia’s xorshift generators, scrambled.ACM Trans. Math. Software42, 4 (2016), 30:1–30:23. doi:10.1145/2845077

    work page doi:10.1145/2845077 2016

  63. [63]

    Sebastiano Vigna. 2017. Further scramblings of Marsaglia’s xorshift generators.J. Comput. Appl. Math.315 (2017), 175–181. doi:10.1016/j.cam.2016. 11.006

    work page doi:10.1016/j.cam.2016 2017

  64. [64]

    2026.A PRNG Shootout

    Sebastiano Vigna. 2026.A PRNG Shootout. https://prng.di.unimi.it/ Accessed 2026-03-14

    2026

  65. [65]

    Jeffrey S. Vitter. 1985. Random sampling with a reservoir.ACM Trans. Math. Software11, 1 (1985), 37–57. doi:10.1145/3147.3165

    work page doi:10.1145/3147.3165 1985

  66. [66]

    John von Neumann. 1951. Various techniques used in connection with random digits.Applied Mathematics Series12 (1951), 36–38

    1951

  67. [67]

    B. A. Wichmann and I. D. Hill. 1982. Algorithm AS 183: an efficient and portable pseudo-random number generator.Applied Statistics31, 2 (1982), 188–190. doi:10.2307/2347988

    work page doi:10.2307/2347988 1982

  68. [68]

    Bernard Widynski. 2020. Squares: a fast counter-based RNG. arXiv:2004.06278. arXiv:2004.06278 https://arxiv.org/abs/2004.06278 Manuscript submitted to ACM

    work page arXiv 2020