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Most commonly-used pseudo-random number generators (PNGs) in computer systems are based on linear recurrence. These deterministic PNGs have fast and compact implementations, andean ensure very long periods. However, the points generated by linear PNGs in fact have a regular lattice structure and are thus not suit able for applications that rely on the assumption of uniformly distributed pseudo-random numbers (PNs). In this paper we propose and evaluate several fast and compact linear, non-linear, and hybrid PNGs for a field- programmable gate array (FPGA). The PNGs have excellent equidistribution properties and very small autocorrelations, and have very long repetition periods. The distribution and long-range correlation properties of the new generators are efficiently, and much more rapidly, estimated at hardware speeds using designed modules within the FPGA. The results of these statistical tests confirm that the combination of several linear PNGs or the combination of even one small non-linear PNG with a linear PNG significantly improves the statistical properties of the generated PNs.