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The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by Makoto Matsumoto (松本 眞) and Takuji Nishimura (西村 拓士). [1] [2] Its name derives from the choice of a Mersenne prime as its period length. The Mersenne Twister was designed specifically to rectify most of the flaws found in older PRNGs.
The xorwow generator is the default generator in the CURAND library of the nVidia CUDA application programming interface for graphics processing units. Well equidistributed long-period linear (WELL) 2006 F. Panneton, P. L'Ecuyer and M. Matsumoto [27] A LFSR closely related with Mersenne Twister, aiming at remedying some of its shortcomings.
It can be shown that if is a pseudo-random number generator for the uniform distribution on (,) and if is the CDF of some given probability distribution , then is a pseudo-random number generator for , where : (,) is the percentile of , i.e. ():= {: ()}. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard ...
The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.
Makoto Matsumoto (松本眞, born February 18, 1965) is a Japanese mathematician principally known as the inventor of the Mersenne Twister, [1] [2] a widely used pseudorandom number generator. He is also the author of the CryptMT stream cipher. [3]
The structure is similar to the Mersenne Twister, a large state made up of previous output words (32 bits each), from which a new output word is generated using linear recurrences modulo 2 over a finite binary field. However, a more complex recurrence produces a denser generator polynomial, producing better statistical properties.
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An xorshift+ generator can achieve an order of magnitude fewer failures than Mersenne Twister or WELL. A native C implementation of an xorshift+ generator that passes all tests from the BigCrush suite can typically generate a random number in fewer than 10 clock cycles on x86, thanks to instruction pipelining. [12]