Middle-square method: Difference between revisions

Revision as of 17:49, 26 April 2021

Revision as of 19:53, 26 April 2021

Line 13:

method was invented by a Franciscan friar known only as Brother Edvin sometime between 1240 and 1250.<ref name="Ekeland1996">{{cite book|author=Ivar Ekeland|title=The Broken Dice, and Other Mathematical Tales of Chance|date=15 June 1996|publisher=University of Chicago Press|isbn=978-0-226-19992-4}}</ref> Supposedly, the manuscript is now lost, but [[Jorge Luis Borges]] sent Ekeland a copy that he made at the Vatican Library.

Modifying the middle square algorithm with a [[Weyl sequence]] improves period and randomness. <ref>{{cite book | title = Random Numbers and Computers | last = Kneusel | first = Ron | publisher = Springer | year = 2018 | edition = 1 | pages = 13-14 }}</ref> Examples of this may be found in the [[arXiv]] papers "Middle Square Weyl Sequence RNG"<ref>{{cite arXiv | last=Widynski | first=Bernard | eprint=1704.00358v5 | title=Middle Square Weyl Sequence RNG| date=April 2017}}</ref> and "Squares: A Fast Counter-Based RNG"<ref>{{cite arXiv| last=Widynski | first=Bernard | arxiv=2004.06278v3 | title=Squares: A Fast Counter-Based RNG | date=April 2020}}</ref>.

== The method ==