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題名 | 32位元二階質數乘餘法亂數產生器之探討=Second Order Multiplicative Congruential Random Number Generators with Prime Modulus for 32-bit Machine |
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作者姓名(中文) | 翁振益; | 書刊名 | 工業工程學刊 |
卷期 | 15:1 1998.01[民87.01] |
頁次 | 頁19-25 |
分類號 | 319.9 |
關鍵詞 | 亂數產生器; 理論測試; 經驗測試; 光譜檢定; Random number generator; Theoretical test; Empirical test; Spectral test; |
語文 | 中文(Chinese) |
中文摘要 | 研究中針對模數為32位元最大質數的二階質數乘餘法亂數產生器做部份搜尋,以 設計一理想的亂數產生器。分別採用理論與經驗測試檢定乘數 (a �窗Aa �� )。首先選擇在 32 位元一階質數乘餘法中光譜值最好與最差各 6 個乘數 a �砥A再分別對 a �善a舉搜尋, 共有 132 億組左右的乘數 (a �窗Aa �� ) 需要做測試。結果只有 11 組乘數通過全部的檢 定,同時乘數 a �砲�譜值的大小影響到乘數 (a �窗Aa �� ) 的統計性質。這些亂數產生器 的週期高達 2,符合隨機性且執行效率高,具有可攜帶性、重覆性及齊次性,滿足實際模擬 之需要。 |
英文摘要 | This paper presents the results of a partial analysis of the second order multiplicative congruential random number (RN) generators with the largest prime modulus in 32-bit machines in order to design good RN generators. Both theoretical and empirical tests are conducted extensively to test the multipliers (a ��, a �� ). By fixing a ��, the best and worst 6 mtltipliers are chosen from the previous study, and an exhaustive search for a �� were individually made. Approximately 13.2 billion sets of multipliers (a ��,a �� ) were tested. Eleven sets passed all the test. The 6 best multipliers and the 6 worse ones present very different statistical properties. The generators devised in this paper possess the following properties: a long period which approachies to 2, randomness, efficiency, portability, repeatability and homogeneity. These properties are required for simulation. |
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