FPGA Gaussian Random Number Generators with Guaranteed Statistical Accuracy

Many types of stochastic algorithms, such as Monte-Carlo simulations and Bit-Error-Rate testing, require very high run-times and are often trivially parallelisable, so are natural candidates for execution using FPGAs. However, the applications are reliant on Gaussian Random Number Generators (GRNGs) with good statistical properties, as very small biases over trillions of random samples can lead to incorrect results. Previous hardware GRNGs have focussed on area-efficient algorithms to produce Gaussian distributions under idealised assumptions, but do not make statements about the actual distribution coming out of real fixed-point hardware. In this paper, we present a new type of GRNG called a Piecewise-CLT, which uses a weighted blend of many small smooth distributions to approximate the Gaussian. By adjusting the weights, it is possible to directly target the distribution of the Gaussian, resulting in a circuit with an exactly quantified output distribution. Three members of the PwCLT family are presented, ranging from medium-area with good quality, up to a generator providing guaranteed statistical accuracy out to 12-sigma. We also show that PwCLT provides a better area-accuracy tradeoff than all existing high-speed scalar FPGA GRNGs, and can provide extremely high levels of statistical quality not possible in any previous methods.