华南理工大学学报（自然科学版）
華南理工大學學報（自然科學版）
화남리공대학학보（자연과학판）
JOURNAL OF SOUTH CHINA UNIVERSITY OF TECHNOLOGY(NATURAL SCIENCE EDITION)
2013年
11期
1-7
,共7页
现场可编程门阵列%随机数生成%高斯分布%Ziggurat算法
現場可編程門陣列%隨機數生成%高斯分佈%Ziggurat算法
현장가편정문진렬%수궤수생성%고사분포%Ziggurat산법
field-programmable gate arrays%random number generation%Gaussian distribution%Ziggurat algorithm
为提高对高斯分布概率密度函数的近似精度，提出一种基于Ziggurat算法的新的高斯分布随机数生成算法。新算法将高斯分布概率密度函数分成顶部、中部、尾部3个子区域分别进行矩形嵌套分层分割，分割后以正比于矩形面积的概率随机选择一个矩形区域，生成概率密度函数为对应矩形的随机数点（x，y），其横坐标x为输出的高斯分布随机数。针对仿真中出现的极值情况，进一步对尾部区域进行了优化处理。此外，基于Xilinx Virtex 4完成了改进后算法的硬件设计。仿真结果表明，新算法结构简单，易于FPGA硬件实现，生成的随机数能通过高斯分布特性和随机性统计检验。
為提高對高斯分佈概率密度函數的近似精度，提齣一種基于Ziggurat算法的新的高斯分佈隨機數生成算法。新算法將高斯分佈概率密度函數分成頂部、中部、尾部3箇子區域分彆進行矩形嵌套分層分割，分割後以正比于矩形麵積的概率隨機選擇一箇矩形區域，生成概率密度函數為對應矩形的隨機數點（x，y），其橫坐標x為輸齣的高斯分佈隨機數。針對倣真中齣現的極值情況，進一步對尾部區域進行瞭優化處理。此外，基于Xilinx Virtex 4完成瞭改進後算法的硬件設計。倣真結果錶明，新算法結構簡單，易于FPGA硬件實現，生成的隨機數能通過高斯分佈特性和隨機性統計檢驗。
위제고대고사분포개솔밀도함수적근사정도，제출일충기우Ziggurat산법적신적고사분포수궤수생성산법。신산법장고사분포개솔밀도함수분성정부、중부、미부3개자구역분별진행구형감투분층분할，분할후이정비우구형면적적개솔수궤선택일개구형구역，생성개솔밀도함수위대응구형적수궤수점（x，y），기횡좌표x위수출적고사분포수궤수。침대방진중출현적겁치정황，진일보대미부구역진행료우화처리。차외，기우Xilinx Virtex 4완성료개진후산법적경건설계。방진결과표명，신산법결구간단，역우FPGA경건실현，생성적수궤수능통과고사분포특성화수궤성통계검험。
In order to improve the approximation precision of the Gaussian probability density function (PDF),a new generation algorithm of Gaussian random number is proposed based on the Ziggurat algorithm.In this algo-rithm,the Gaussian PDF is divided into three subareas including the top,the middle and the tail regions,and the subareas are further partitioned into rectangles via nested segmentation.After that,one of the rectangles is random-ly chosen with the probability being in direct proportion to the rectangle area,and the random points (x,y),whose PDF 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.The new algorithm is implemented on Xilinx Virtex 4,and the simulated results indicate that the proposed algorithm with simple structure is easy to implement on FPGA,and that the generated random numbers can successfully pass the statistical tests of Gaussian distribution and randomness.
