A Unified View of Long-period Random Number Generators

Two types of linear congruent.ial random number generator are considered: the conventional one using integer arithmetic and another using polynomial arithmetic over finite fields. We show t.hat most of the long-period random number generators currently used or recently proposed, which include multiple re.:ursive generators, shift register generators, add-with-carry and subtract-with-borrow generators, Twisted··GFSR generators, Wichmann-Hill generators, and combined Tausworthe generators, can be viewed as producing truncated linear congruential sequences with large moduli in terms of integer or polynomial arithmetic. On this basis, we compare the above generators with respect to generation efficiency, lattice structure, and portability.