Lagged Fibonacci generator

A lagged Fibonacci generator is a kind of pseudorandom number generator meant as an improvement on the standard linear congruential generator. It generalizes the Fibonacci sequence: each new term is some combination of two earlier terms, taken j and k places back with j smaller than k, using addition, subtraction, multiplication or bitwise exclusive-or, and the result is reduced modulo a number m that is usually a power of two. The generator keeps the last k values as its state. The variant that uses addition is called an additive lagged Fibonacci generator, the multiplicative form uses multiplication, and the exclusive-or form is the two-tap generalized feedback shift register, of which the Mersenne Twister is a variation. The maximum period depends on the operation, and reaching it requires that the polynomial built from j and k be primitive over the integers modulo 2, with published lists of suitable lag pairs. These generators are sensitive to how they are initialized, and the two-tap exclusive-or forms have known statistical weaknesses that led Marsaglia to advise against small generators of this type.