Word-Length Optimization and Error Analysis of a Multivariate Gaussian Random Number Generator

Monte Carlo simulation is one of the most widely used techniques for computationally intensive simulations in mathematical analysis and modeling. A multivariate Gaussian random number generator is one of the main building blocks of such a system. Field Programmable Gate Arrays (FPGAs) are gaining increased popularity as an alternative means to the traditional general purpose processors targeting the acceleration of the computationally expensive random number generator block. This paper presents a novel approach for mapping a multivariate Gaussian random number generator onto an FPGA by automatically optimizing the computational path with respect to the resource usage. The proposed approach is based on the Eigenvalue decomposition algorithm which decomposes the design into computational paths with different precision requirements. Moreover, an error analysis on the impact of the error due to truncation is performed in order to provide upper bounds of the error inserted into the system. The proposed methodology optimises the usage of the available FPGA resources leading to area efficient designs without any significant penalty on the overall performance. Experimental results reveal that the hardware resource usage on an FPGA is reduced by a factor of two in comparison to current methods.