An experimental exploration of Marsaglia's xorshift generators, scrambled

Understand

Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators.

• Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several weaknesses of such generators, verified experimentally using the TestU01 suite.
• Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a non-linear operation (as originally suggested by Marsaglia).
• In this paper we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant.