full period

[Euriece Jan]

I have read "Scrambled Linear Pseudorandom Number Generators", but I could not understand logically how to find the parameter of the full period. 

Can anyone help me understand it?

[Pierre L'Ecuyer]

When a generator is scrambled at the output only, its period is normally the same as the original linear recurrence (not scrambled).  The following papers (and the references given there) discuss the period length of these linear generators, modulo 2 and modulo m > 2:

1. f2lin.pdf P. L'Ecuyer and F. Panneton, ``F_2-Linear Random Number Generators'', published in "Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman," C. Alexopoulos, D. Goldsman, and J. R. Wilson Eds., Springer-Verlag, 2009, 169-193.
2. combmrg2.pdf P. L'Ecuyer, ``Good Parameter Sets for Combined Multiple Recursive Random Number Generators'', Shorter version in Operations Research, 47, 1 (1999), 159--164.

On 12/12/2021 4:49 AM, Euriece Jan wrote:

I have read "Scrambled Linear Pseudorandom Number Generators", but I could not understand logically how to find the parameter of the full period. 

Can anyone help me understand it?

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Pierre L'Ecuyer, Professeur Titulaire
CIRRELT, GERAD, and DIRO, Université de Montréal, Canada
http://www.iro.umontreal.ca/~lecuyer

[Euriece Jan]

Thank you very much. Do these two papers show how to find the period of xoroshiro?

2021年12月12日日曜日 23:11:24 UTC+9 lec...@iro.umontreal.ca:

[Pierre L'Ecuyer]

Xoroshiro uses an F_2-linear recurrence, so the theory and methods in the first paper apply.  For more specific discussions, see the xoroshiro paper by Blackman and Vigna, in ACM Trans. on Math Software,  http://arxiv.org/abs/1805.01407

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