在64 及128 位元電腦上搜尋並評估高階遞迴亂數產生器

Abstract

許多便捷的高階遞迴亂數產生器已經在許多文獻上被發現，但是 絕大部分只適用於32 位元電腦。隨著科技進步，64 位元以上的電腦 將會越來越受歡迎，因此搜尋64 位元以上的亂數產生器是非常必要 的。在本篇論文裡，我們將遵循類似搜尋32 位元的便捷高階遞迴亂 數產生器的方法去尋找64 位元的便捷高階遞迴亂數產生器。並利用 TestU01 這套軟體去測試它們是否能通過許多統計上的嚴格檢驗，結 果顯示我們找出的64 位元便捷高階遞迴亂數產生器絕大部分都痛過 了測試並證明它們具有許多良好性質。除此之外，為了方便讀者們使 用，我們也設計了一個網頁供讀者們上網使用本篇論文所發現的亂數 產生器的參數和它們的程式碼

Several portable and e±cient Multiple Recursive Generators (MRGs) have been found in the literature and they are mostly for 32-bit computers. As the 64-bit (and eventually 128-bit) computers becomes more and more popular, there is a need to search for random number generators suitable for these computing platforms. In this thesis, we follow a similar approach taken by the search algorithm for 32-bit generators and we ‾nd several 64-bit and 128-bit generators that are e±cient with extreme long period lengths. We test their empirical performance with TestU01 packages. The results showed that all of them passed the stringent tests. In addition, Through an extensive computer search, we have found several large order MRGs and we list them in this thesis. In addition to these nice property, all of these generators have a property of equi-distribution over a high dimensional space. Following a similar approach for 32-bit MRGs, we also construct a collection of MRGs from a single MRG found which are useful for parallel simulation of 64-bit or 128-bit applications. For the convenience of interested users, we design a website program to automatically o®er the parameters and the associated program codes for our generators.