A multiple recursive non-linear congruential pseudo random number generator |
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Authors: | Jürgen Eichenauer Holger Grothe Jürgen Lehn Alev Topuzoğlu |
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Affiliation: | (1) Technische Hochschule Fachbereich Mathematik, Schloßgartenstr. 7, D-6100 Darmstadt;(2) Department of Mathematics, Middle East Technical University, Ankara, Turkey |
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Abstract: | On-linear multiple recursive congruential pseudo random number generator with prime modulus p is introduced. Let x, n0, be the sequence generated by a usual linear (r+1)-step recursive congruential generator with prime modulus p and denote by N(n), n0, the sequence of non-negative integers with xN(n)0 (mod p). The non-linear generator is defined by znxN(n)+1·xN(n)–1 (mod p), n0, where xN(n)–1 denotes the inverse element of xN(n) in the Galois field GF(p). A condition is given which ensures that the generated sequence is purely periodic with period length pr and all (p–1)r r-tupels (y1,...,yr) with 1y1,...,yrp are generated once per period when r-tupels of consecutive numbers of the generated sequence are formed. For r=1 this generator coincides with the generator introduced by Eichenauer and Lehn [2]. |
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