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頁籤選單縮合
題名 | Bit-Parallel Random Number Generation for Discrete Uniform Distributions=離散平均分佈的位元平行亂數產生器 |
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作者 | 吳培基; 黃國展; 歐陽士庭; | 書刊名 | 高速計算世界 |
卷期 | 7:2 民88.夏 |
頁次 | 頁25-35 |
分類號 | 319.16 |
關鍵詞 | 亂數產生器; 蒙地卡羅模擬; 隨機漫步; 離散平均分佈; 統計品質; Random number generators; Monte Carlo simulation; Random walks; Discrete uniform distribution; |
語文 | 英文(English) |
中文摘要 | 擲骰子遊戲的結果是六面中的一面朝上,此結果是離散且平均分佈在區間 R= {1,2,3,4,5,6}。產生此機率分佈的亂數並不難:得到一亂數 W �e W,取( w mod ︱ R ︳ ) +1,其中 W 為亂數的領域( domain )。然而,許多離散平均分佈的範圍都不大,如擲 骰子遊戲中,︱ R ︱= 6; 又如二維不可逆( nonreversal )隨機漫步中,︱ R ︱= 3 。數值 W 通常是一機器字組( machine word ),亦即在一 32 位元電腦中 log �砥]︱ W ︱)= 32,因此產生 log �砥]︱ R ︱)位元的亂數已耗去約 32 個亂數位元。當︱ W ︱ >> ︱ R ︱時,既浪費亂數位元又沒效率。 本計劃提出一快速的演算法以產生範圍︱ R ︱ 的離散平均分佈的亂數,此演算法在機器字組上採用平行的位元運算。計劃中我們將分析使 用此一演算法產生的亂數的統計品質,我們並將評估此一演算法在多個電腦平臺上的效能。 本計劃所提出的演算法預期可加速基於隨機漫步的蒙地卡羅模擬的應用。 |
英文摘要 | When a die is cast, the outcome is one of the six sides, i.e., the outcome is discrete and uniformly distributed over the range R={1,2,3,4,5,6}. Generating random numbers with such a distribution is very easy: obtain a random number w �e W, the domain of the random numbers, and take (w mod ︱ R ︱ ) + 1. However, many uniform discrete distributions have a rather short range, e.g., ︱ R ︱ =6 in a dice game, and ︱ R ︱ =3 for the walking directions of a 2-dimensional nonreversal random walk. The number w is typically a machine word, i.e., log �� (︱ W ︱ ) 32=in a 32-bit computer, so generating a log �� (︱ R ︱ )-bit random number has consumed about 32 random bits. When ︱ W ︱ >> ︱ R ︱, it is wasteful and hence inefficient. This paper presents an efficient algorithm for generating random numbers for the distributions with ︱ R ︱ discrete uniform outcomes. The algorithm uses parallel bit-wise operations on machine words. The performance results of the algorithm are presented. The statistical quality of the random numbers generated from this algorithm is also discussed. |
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