Efficient CPU-specific algorithm for generating the generalized Faure sequences

The Faure sequences are a popular class of low-discrepancy sequences. Their generalized variants, with better equi-distribution properties, are extensively used in quasi-Monte Carlo methods, especially for very high dimensional problems. The task of generating these sequences can take substantial part of the overall CPU time of a quasi-Monte Carlo computation. We present an efficient algorithm for generating these sequences, and demonstrate how it may be tuned to use the extended instruction sets, available on many modern CPUs, to reduce drastically the CPU-time, spent for generating these sequences.