Editing Lagged Fibonacci generator (section)

== Problems with LFGs ==
In a paper on four-tap shift registers, [[Robert M. Ziff]], referring to LFGs that use the XOR operator, states that "It is now widely known that such generators, in particular with the two-tap rules such as R(103, 250), have serious deficiencies.  [[George Marsaglia|Marsaglia]] observed very poor behavior with R(24, 55) and smaller generators, and advised against using generators of this type altogether.  ... The basic problem of two-tap generators R(a, b) is that they have a built-in three-point correlation between <math>x_{n}</math>, <math>x_{n-a}</math>, and <math>x_{n-b}</math>, simply given by the generator itself ... While these correlations are spread over the size <math>p = max(a, b, c, \ldots )</math> of the generator itself, they can evidently still lead to significant errors.".<ref>[https://arxiv.org/abs/cond-mat/9710104 "Four-tap shift-register-sequence random-number generators"], Robert M. Ziff, Computers in Physics, 12(4), Jul/Aug 1998, pp. 385–392</ref> This only refers to the standard LFG where each new number in the sequence depends on two previous numbers. A three-tap LFG has been shown to eliminate some statistical problems such as failing the [[Diehard tests|Birthday Spacings]] and Generalized Triple tests.<ref name="uniform" />