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Progresses in parallel random number generators

Kaşıkara Tenekecioğlu, Gülin
Monte Carlo simulations are embarrassingly parallel in nature, so having a parallel and efficient random number generator becomes crucial. To have a parallel generator with uncorrelated processors, parallelization methods are implemented together with a binary tree mapping. Although, this method has considerable advantages, because of the constraints arising from the binary tree structure, a situation defined as problem of falling off the tree occurs. In this thesis, a new spawning method that is based on binary tree traversal and new spawn processor appointment is proposed to use when falling off the tree problem is encountered. With this method, it is seen that, spawning operation becomes more costly but the independency of parallel processors is guaranteed. In Monte Carlo simulations, random number generation time should be unperceivable when compared with the execution time of the whole simulation. That is why; linear congruential generators with Mersenne prime moduli are used. In highly branching Monte Carlo simulations, cost of parameterization also gains importance and it becomes reasonable to consider other types of primes or other parallelization methods that provide different balance between parameterization cost and random number generation cost. With this idea in mind, in this thesis, for improving performance of linear congruential generators, two approaches are proposed. First one is using Sophie-Germain primes as moduli and second one is using a hybrid method combining both parameterization and splitting techniques. Performance consequences of Sophie-Germain primes over Mersenne primes are shown through graphics. It is observed that for some cases proposed approaches have better performance consequences.