Pseudorandom number generator

A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, pseudorandom number generators are important in practice for their speed in number generation and their reproducibility.The list of widely used generators that should be discarded is ... Check the default of your favorite software and be ready to replace it if needed. This last recommendation has been made over and over again over the past 40 years. Perhaps amazingly, it remains as relevant today as it was 40 years ago. A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, pseudorandom number generators are important in practice for their speed in number generation and their reproducibility. PRNGs are central in applications such as simulations (e.g. for the Monte Carlo method), electronic games (e.g. for procedural generation), and cryptography. Cryptographic applications require the output not to be predictable from earlier outputs, and more elaborate algorithms, which do not inherit the linearity of simpler PRNGs, are needed. Good statistical properties are a central requirement for the output of a PRNG. In general, careful mathematical analysis is required to have any confidence that a PRNG generates numbers that are sufficiently close to random to suit the intended use. John von Neumann cautioned about the misinterpretation of a PRNG as a truly random generator, and joked that 'Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.' In practice, the output from many common PRNGs exhibit artifacts that cause them to fail statistical pattern-detection tests. These include: Defects exhibited by flawed PRNGs range from unnoticeable (and unknown) to very obvious. An example was the RANDU random number algorithm used for decades on mainframe computers. It was seriously flawed, but its inadequacy went undetected for a very long time. In many fields, much research work prior to the 21st century that relied on random selection or on Monte Carlo simulations, or in other ways relied on PRNGs, is much less reliable than it might have been as a result of using poor-quality PRNGs. Even today, caution is sometimes required, as illustrated by the following warning, which is given in the International Encyclopedia of Statistical Science (2010). As an illustration, consider the widely used programming language Java. As of 2017, Java still relies on a linear congruential generator (LCG) for its PRNG; yet LCGs are of low quality—see further below. The first PRNG to avoid major problems and still run fairly quickly was the Mersenne Twister (discussed below), which was published in 1998. Other high-quality PRNGs have since been developed. In the second half of the 20th century, the standard class of algorithms used for PRNGs comprised linear congruential generators. The quality of LCGs was known to be inadequate, but better methods were unavailable. Press et al. (2007) described the result thus: 'If all scientific papers whose results are in doubt because of were to disappear from library shelves, there would be a gap on each shelf about as big as your fist'.