Efficient and portable combined Tausworthe random number generators

Maximally equidistributed combined Tausworthe generators

“…Definition and implementation. Tausworthe generators [6,8,9,11] produce pseudorandom numbers by generating a sequence of bits from a linear recurrence modulo 2, and forming fractional numbers by taking blocks of successive bits. More precisely, let F 2 denote the finite field with two elements (say, 0 and 1).…”

“…, x (n−1)s+L−1 ). This is a slight generalization of the algorithm given in [11], where L = k was implicitly assumed. The vectorss n are maintained as unsigned (L-bit) integers, which are then multiplied by the normalization constant 2 −L to produce u n .…”

“…, 2 kJ −1) = (2 k1 −1)×· · ·×(2 kJ −1). Further, as shown in [11], the combined generator is equivalent to a Tausworthe generator with (reducible) characteristic polynomial P (z) = P 1 (z) · · · P J (z) and s such that…”

“…See [6, 11,13] for further details. The main interest of that kind of combination is that not only large periods can be achieved, but also P (z) typically has many nonzero coefficients even when the individual P j (z) are all trinomials.…”

“…In §4, we give the results of a computer search for near-ME, ME, and ME-CF combined Tausworthe generators, within certain classes of parameters that give rise to a fast implementation. A search for combined generators of that sort had already been performed within a small subclass of two-component combinations [11] with period length of approximately 2 60 . A value of L = 60 was used (implicitly).…”