Using FPGA resources for direct generation of multivariate Gaussian random numbers

The multivariate Gaussian distribution is used to model random processes with distinct pair-wise correlations, such as stock prices that tend to rise and fall together. Generation from a distribution with dimension n is usually achieved by starting with a vector of n independent Gaussian samples, then multiplying with a correlation inducing matrix, using O(n²) multiplications. This paper presents a method of generating vectors directly from the uniform distribution, removing the need for any multipliers or a scalar Gaussian generator. The method uses only small ROMs and adders, and so can be implemented using just basic FPGA resources (LUTs and FFs), saving DSP and block-RAM resources for the numerical simulation that the multivariate generator is driving. The method produces a new vector every cycle, unlike existing methods which produce vectors serially over n cycles, with only a modest increase in resource usage. This provides a ten times increase in performance over the fastest existing method, while also providing five times the performance per logic resource of the most efficient method.