关键词: 现场可编程门阵列, 随机数生成, 高斯分布, Ziggurat 算法

Abstract:

In order to improve the approximation precision of the Gaussian probability density function ( PDF) ,anew generation algorithm of Gaussian random number is proposed based on the Ziggurat algorithm.In this algorithm,the Gaussian PDF is divided into three subareas including the top,the middle and the tail regions,and thesubareas are further partitioned into rectangles via nested segmentation.After that,one of the rectangles is randomlychosen with the probability being in direct proportion to the rectangle area，and the random points ( x,y),whosePDF is identical to the rectangle,are generated,with x being the output as a Gaussian random number.Moreover,the tail region is treated separately to take into consideration the extreme values occurring in the simulation.Thenew algorithm is implemented on Xilinx Virtex 4,and the simulated results indicate that the proposed algorithmwith simple structure is easy to implement on FPGA,and that the generated random numbers can successfully passthe statistical tests of Gaussian distribution and randomness.

Key words: field-programmable gate arrays, random number generation, Gaussian distribution, Ziggurat algorithm