Research Directions - ACORN random numbers

This page identifies current work and unpublished research on ACORN random numbers.

Period length for arbitrary order and modulus

Theorem on period length for any modulus and order (generalisation of earlier 2008 conjecture published in JCAM) has been stated and proved.

Write-up completed but is unpublished, March 2019.


Empirical testing with current (2018) version 1.2.3 of TestU01 (updates and extends previous test results using earlier version 0.6.1 of TestU01, completed and published in 2008).

Presented as a poster at the Conference on numerical algorithms for high-performance computational science, Royal Society (London), April 2019 - see references (click) to download.

Results of further empirical testing with version 1.2.3 of TestU01 (carried out in 2019)

to be presented at an Internal Seminar at the Numerical Analysis Group, Mathematical Institute, University of Oxford, June 11th 2019 - see references (click) to download.


Improve efficiency of ACORN implementation(s) in Fortran: speed-up of an order of magnitude is possible, by combining the benefits of using 64-bit integers on 64-bit hardware with alternative approaches to the modular arithmetic required in ACORN.

Completed, but as yet not written up.

Pascal's triangle

Describe relationship and link between ACORN algorithm and Pascal’s triangle (another illustration of the concept)

Presented as poster at Royal Society (London), April 2019
Conference on numerical algorithms for high-performance computational science - see references (click) to download.

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created 2019-01-31 / updated 2019-03-31