PCG is a family of simple fast space-efficient statistically good algorithms for random number generation. Unlike many general-purpose RNGs, they are also hard to predict. Unknown? * For the PCG family, arbitrary k -dimensional equidistribution (and the huge periods it implies) requires PCG's extended generation scheme.

2024年12月8日 · Permuted Congruential Generator（PCG） 是一种结合了线性同余生成器（LCG）和置换函数的伪随机数生成器。 PCG旨在提供高质量的随机数，具有较长的周期和优秀的统计特性，同时保持高效和易于实现的特点。 PCG有多个变种，如PCG32、PCG64等，适用于不同的应用需求。 高质量的随机性：通过结合LCG和置换函数，PCG生成的随机数序列在统计测试中表现优异。 长周期：PCG的周期长度远超传统的LCG，减少了周期重复的可能性。 高性 …

A permuted congruential generator (PCG) is a pseudorandom number generation algorithm developed in 2014 by Dr. M.E. O'Neill which applies an output permutation function to improve the statistical properties of a modulo-2 n linear congruential generator (LCG).

PCG turns an LCG into a good RNG: PCG is cunningly designed to use instruction-level parallelism to overlap the LCG state update and the output permutation. Different bitfields of the LCG state are used as the target of the permutation and to control the permutation.

If you just want a good RNG with the least amount of code possible, you may be fine with the minimal C implementation. In fact, if you want to “see the code”, the here's a complete PCG generator:

Almost all random-number generation on computers is done using algorithms to produce a stream of numbers that (hopefully) match the expectations statisticians would have about random numbers. In contrast, we often consider acts like “tossing a coin” (a real physical coin) or “seeing where a roulette ball lands” as examples of “true randomness”.

置换同余生成器（PCG, permuted congruential generator）是LCG的改进，2014产生。 它以更小的，快速的代码和小的状态量实现了出色的统计性能。 PCG与传统线性同余生成器在以下三个方面有所不同：

Permuted Congruential Generators (PCGs) are a family of RNGs which uses a linear congruential generator as the state-transition function, and uses permutation functions on tuples to produce output that is much more random than the RNG's internal state. 1

Once those are out of the picture, we examine some claims made by Melissa O'Neill on the remaining PCG generators, and provide simple counterexamples for each claim. In the end, we show simple generators based on congruential arithmetic that are faster and have better statistical properties of the only remaining 64-bit PCG generators.

2018年4月1日 · I have found that permuted congruential generator (PCG) is faster than Mersenne Twister (MT), and Mersenne Twister is faster than e.g. minstd_rand. Both Mersenne Twister and PCG satisfy the rand()%2 requirement.