用于缩放随机数生成器的比特回收
Bit recycling for scaling random number generators
AI总结：
本文讨论将随机数生成器输出的均匀样本从固定比特范围缩放到可变范围M的方法，分析其数学效率和计算速度。
摘要：
目前有许多随机数生成器（RNG）；它们分为两类：硬件RNG，提供“真正”的随机数，以及算法RNG，生成伪随机数（PRNG）。两种类型通常生成在范围$0,\cdots,2^{b-1}$内的独立均匀样本$(X_n)$，其中$b = 8, 16, 32$或$b = 64$。在应用中，有时需要将随机数抽取为范围$1, \cdots, M$内的独立均匀样本$(Y_n)$，并且M可能在每次抽取之间变化。将序列$(X_n)$变换为$(Y_n)$有时称为缩放。我们从数学效率和计算速度两方面讨论缩放RNG的不同方法。
英文摘要：
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers $(X_n)$ as independent uniform samples in a range $0,\cdots,2^{b-1}$, with $b = 8, 16, 32$ or $b = 64$. In applications, it is instead sometimes desirable to draw random numbers as independent uniform samples $(Y_n)$ in a range $1, \cdots, M$, where moreover M may change between drawings. Transforming the sequence $(X_n)$ to $(Y_n)$ is sometimes known as scaling. We discuss different methods for scaling the RNG, both in term of mathematical efficiency and of computational speed.
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。
