Library of random number generators based on SSE command set

Pseudo random numbers, generated recursively by deterministic rules, represent one of important ingredients in algorithms for numerical simulations such as molecular dynamics and of Monte Carlo simulations, widely used in physics, chemistry, material science and cryptography [1]. It is a great challenge to design random number generators (RNGs) producing pseudo random numbers that behave as realizations of independent uniformly distributed random variables and approximate “true randomness” [2]. In the contribution we present a library of modern and most reliable RNGs known today. Namely, the realizations of the modern generators MT19937, MRG32k3a, LFSR113, GM19-SSE, GM31-SSE and GM61-SSE are presented. MT19937 is the 2002 version of the Mersenne Twister generator of Matsumoto and Nishimira [3], which is based on the recent generalizations to the GFSR method. MRG32k3a is the combined multiple recursive generator proposed in [4], and LFSR113 is the combined Tausworthe generator of L’Ecuyer [5]. The generators GM19-SSE, GM31-SSE and GM61-SSE are based on evolution of an ensemble of chaotic dynamical systems [6]. An important feature of our library is the ability to speed up the algorithms using Streaming SIMD (Single Instruction, Multiple Data) Extensions 2 (SSE2) technology, introduced in Intel Pentium 4 processors in 2001 [7], and also supported by AMD starting with their Opteron and Athlon 64 ranges of AMD64 64-bit CPUs in 2003. It allows to use 128-bit XMM-registers in a single operation to accelerate computations. In particular, for several operations, it allows simultaneous processing for four 32-bit numbers. Similar technique was previously used for implementing several RNGs [8, 6]. In the present work we demonstrate that this approach can essentially speed up most RNGs. We present library of the generators and of their SSE2 realizations.