Formal Verification and Code-Generation of Mersenne-Twister Algorithm

We formalize the pseudocode and linear-algebraic presentations of Mersenne-Twister, and formally establish their equivalence. Based on this formalization, we investigate the long-period property of Mersenne-Twister, formally proving that the property is reduced to the primitivity of the characteristic polynomial of the matrix representation. The formalization is done in COQ proof assistant. This enables us to generate a C program code from the verified pseudocode written in COQ.