Simulated division with approximate factoring for the multiple recursive generator with both unrestricted multiplier and non-mersenne prime modulus

This paper focuses on devising a general and efficient way of generating random numbers for the multiple recursive generator with both unrestricted multiplier and non-Mersenne prime modulus. We propose a new algorithm that embeds the technique of approximate factoring into the simulated division method. The proposed new algorithm improves the decomposition method in terms of both the suitability for various word-sizes of the computers and the efficiency characteristics, such as the number of arithmetic operations required and the computational time. Empirical simulations are conducted to compare and evaluate the computational time of this algorithm with the decomposition method for various computers.