马萨格里亚异或移位发生器的实验探索，
An experimental exploration of Marsaglia's xorshift generators, scrambled
摘要：
Marsaglia最近提出了异或移位生成器作为一类非常快速，高质量的伪随机数生成器。Panneton和L'Ecuyer随后的分析降低了Marsaglia论文提出的期望，显示了这种生成器的几个弱点，使用TestU01套件进行了实验验证。尽管如此，如果xorshift生成器的结果被非线性操作扰乱（如Marsaglia最初提出的），那么xorshift生成器的许多弱点就会消失。在本文中，我们探讨了空间的可能生成器通过乘以一个适当的常数的xorshift生成器的结果。我们在发电机的状态空间的100个等距点上对发电机进行采样，并获得详细的统计数据，这些统计数据使我们能够选择改进当前参数的参数。然后，我们第一次探索空间的高维xorshift发电机，以下另一个建议在Marsaglia的文件，找到选择的参数提供周期的长度$2^{1024} - 1$和$2^{4096} - 1$。由此产生的发电机具有极高的质量，比目前类似的替代品更快，并产生长周期序列，通过强大的统计测试，只使用八个逻辑运算，一个加法和一个常数乘法。
英文摘要：
Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several weaknesses of such generators, verified experimentally using the TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a non-linear operation (as originally suggested by Marsaglia). In this paper we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant. We sample generators at 100 equispaced points of their state space and obtain detailed statistics that lead us to choices of parameters that improve on the current ones. We then explore for the first time the space of high-dimensional xorshift generators, following another suggestion in Marsaglia's paper, finding choices of parameters providing periods of length $2^{1024} - 1$ and $2^{4096} - 1$. The resulting generators are of extremely high quality, faster than current similar alternatives, and generate long-period sequences passing strong statistical tests using only eight logical operations, one addition and one multiplication by a constant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
