A PRNG Specialized in Double Precision Floating Point Numbers Using an Affine Transition

Abstract

We propose a pseudorandom number generator specialized to generate double precision floating point numbers. It generates 52-bit pseudorandom patterns supplemented by a constant most significant 12 bits (sign and exponent), so that the concatenated 64 bits represents a floating point number obeying the IEEE 754 format. To keep the constant part, we adopt an affine transition function instead of the usual \(\mathbb{F}_{2}\)-linear transition, and extend algorithms computing the period and the dimensions of equidistribution to the affine case. The resulted generator generates double precision floating point numbers faster than the Mersenne Twister, whoes output numbers only have 32-bit precision.