Effective and efficient restriction on producing the multipliers for the multiple recursive random number generator

The most efficient and easiest way for implementing a multiple recursive random number generator is the approximate factoring (AF) method. In the literature, the AF method can be applied in the three types of restriction on multiplier. This paper considers the effectiveness and efficiency of these restrictions from the theoretical and empirical points of view. The most effective and efficient restriction is presented. The number of arithmetic operations required by the AF method is also discussed.