Concepts inOn the xorshift random number generators
Xorshift
Xorshift random number generators form a class of pseudorandom number generators that was discovered by George Marsaglia. They generate the next number in their sequence by repeatedly taking the exclusive or of a number with a bit shifted version of itself. This makes them extremely fast on modern computer architectures. They are a subclass of Linear feedback shift registers, but their simple implementation typically makes them faster and use less space.
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George Marsaglia
George Marsaglia (March 12, 1924 – February 15, 2011) was an American mathematician and computer scientist. He established the lattice structure of congruential random number generators in the paper "Random numbers fall mainly in the planes". This phenomenon is sometimes called the Marsaglia effect. He also developed the so-called "diehard tests", a series of tests to determine whether or not a sequence of numbers have the statistical properties that could be expected from a random sequence.
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Mersenne twister
The Mersenne twister is a pseudorandom number generator developed in 1997 by Makoto Matsumoto and Takuji Nishimura that is based on a matrix linear recurrence over a finite binary field . It provides for fast generation of very high-quality pseudorandom numbers, having been designed specifically to rectify many of the flaws found in older algorithms. Its name derives from the fact that period length is chosen to be a Mersenne prime.
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Random number generation
A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. The many applications of randomness have led to the development of several different methods for generating random data. Many of these have existed since ancient times, including dice, coin flipping, the shuffling of playing cards, the use of yarrow stalks (by divination) in the I Ching, and many other techniques.
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Equidistributed sequence
In mathematics, a bounded sequence {s1, s2, s3, …} of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that interval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carlo integration.
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Statistical hypothesis testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study (not controlled). In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level.
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