Fast combined multiple recursive generators with multipliers of the form a=±2q±2r

We study a class of combined multiple recursive random number generators constructed in such a way that each component runs fast and is easy to implement, while the combination enjoys excellent structural properties as measured by the spectral test. Each component is a linear recurrence of order k>1, modulo a large prime number, and the coefficients are either 0 or are of the form a=±2^q or a=±2^q±2^r. This allows a simple and very fast implementation, because each modular multiplication by a power of 2 can be implemented via a shift, plus a few additional operations for the modular reduction. We select the parameters in terms of the performance of the combined generator in the spectral test. We provide a specific implementation