Generation of the scrambled Halton sequence using accelerators

The Halton sequence is one of the most popular low-discrepancy sequences. In order to satisfy some practical requirements, the original sequence is usually modified in some way. The scrambling algorithm, proposed by Owen, has several theoretical advantages, but on the other hand is difficult to implement in practice due to the trade-off between high memory and high computational requirements. In our work we concentrate on the case when the number of coordinates is relatively high. The use of computational accelerators and especially GPUs is increasingly relevant for such practical applications, since more and more of the resources, available through the Grid and Cloud infrastructures, provide access to such accelerators, provided that the software can make use of them. In this paper we discuss our algorithm for generation of the Halton sequence with Owen-type scrambling implemented using NVIDIA CUDA. We also show numerical results, achieved on our GPU-enabled nodes, which are equipped with NVIDIA M2090 cards.