FPGA based RNG for random WOB method in unit cube capacitance calculation

Abstract

Monte Carlo (MC) method is widely used in resolving mathematical problems that are too complicated to solve analytically. The method involves with sampling process of the random numbers and probability to estimate the result. As MC method depending on a large number of good quality random numbers to produce a high accuracy result, developing a good random number generator (RNG) is vital. Most of random number generators are developed in software based, with the improvement of Field Programmable Gate Arrays (FPGA) density and speed in recent days, implementing random number generator (RNG) directly into hardware is feasible. Random Walk on the Boundary (WOB) is one of MC methods that applied to calculate the unit cube capacitance. The unique requirement of this method is the random numbers produced by RNG must fall within the Gaussian distribution and the maximum decimal values in the range of [0, 1]. Thus, in this paper we presented a novel hardware RNG for Random WOB method to calculate unit cube capacitance in FPGA. The RNG is implemented in floating-point base, using the combination of Cellular Automata Shift Register (CASR) and Linear Feedback Shift Register (LFSR) then channeled through Box-Muller transformation. There is linear approximation in computing logarithmic function applied in Box-Muller transformation. Based on statistical tests, the random numbers generated is nearly 97.5% resembling the standard normal distribution.