基于LCG的组合发生器及其结构的改进

１．引 言 伪随机数发生器是随机模拟的基础性工具之一．好的发生器有利于模拟工作的进行，低劣的发生器则会毁掉模拟工作． 随着认识的深入，人们发现一些曾广泛使用的发生器生成的伪随机数序列或者在周期，或者在晶格结构（ｌａｔｔｉｃｅ ｓｔｒｕｃｔｕｒｅ），或者在其它方面却存在着严重的缺陷［１］．从而逐渐认识到在寻找一个好的发生器的过程中会面临的巨大困难与需要遵循的基本准则［２－３］． 尽管如此，出于随机模拟的实际需要，多种新的发生器与伪随机数的生成方法仍然不断地被提出，以改进或者替代旧的发生器［４］．特别，…

THE COMBINED GENERATOR BASED ON LCGS AND ITS STRUCTURE IMPROVEMENT

This paper deals with the problems concerning the equivalence and period of LCG and combined pseudorandom number generator based on LCGs. It indicates that the LCG with modulus M being prime and greater than 1/2M is unique in the sense of equivalence. It proves that the combined generator based on LCGs is still a LCG provided that the moduli M1, ooo, MJ of all these LCGs would be pairwise relatively prime integers. It also proves that the period of combined generator equals the least common multiple of periods T1, ..., TJ of all these combining generators provided that the highest power of every prime factor pi in canonical factorizations of T1, o., T~ would not appear more than one time and (Mi, &j) 1 for j = 1, .., J. In addition, by digital example it demonstrates that combination of LCGs and generators which are non-LCG might make the structure of combined generator be improved.