用移位和异或运算的长周期随机数发生器
Some long-period random number generators using shifts and xors
摘要：
Marsaglia最近推出了一类xorshift随机数生成器（RNG）的周期为2n-1，n = 32，64等，在这里，我们给一个概括的Marsaglia的xorshift生成器，以获得快速和高品质的RNG具有极长的周期。基于原始三项式的RNG可能不令人满意，因为三项式具有非常小的权重。相比之下，我们的生成元可以被选择，使得它们的最小多项式具有大的权重（非零项的数量）。使用Magma进行的计算机搜索发现了n的2次幂的良好发电机，最高可达4096。这些都是在免费的软件包xorgens中实现的。
英文摘要：
Marsaglia recently introduced a class of xorshift random number generators (RNGs) with periods 2n-1 for n = 32, 64, etc. Here we give a generalisation of Marsaglia's xorshift generators in order to obtain fast and high-quality RNGs with extremely long periods. RNGs based on primitive trinomials may be unsatisfactory because a trinomial has very small weight. In contrast, our generators can be chosen so that their minimal polynomials have large weight (number of nonzero terms). A computer search using Magma has found good generators for n a power of two up to 4096. These have been implemented in a free software package xorgens.
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