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The Lehmer random number generator [1] (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is
Lehmer generator: 1951 D. H. Lehmer [2] One of the very earliest and most influential designs. Linear congruential generator (LCG) 1958 W. E. Thomson; A. Rotenberg [3] [4] A generalisation of the Lehmer generator and historically the most influential and studied generator. Lagged Fibonacci generator (LFG) 1958 G. J. Mitchell and D. P. Moore [5]
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.
Couture and L'Ecuyer [3] have proved the surprising result that the lattice associated with a multiply-with-carry generator is very close to the lattice associated with the Lehmer generator it simulates. Thus, the mathematical techniques developed for Lehmer generators (such as the spectral test) can be applied to multiply-with-carry generators.
Lagged Fibonacci generator; Lehmer random number generator; Linear congruential generator; Linear-feedback shift register; M. Marsaglia polar method; Mersenne Twister;
In September 1949, he presented the pseudorandom number generator now known as the Lehmer random number generator. [4] D. H. Lehmer wrote the article "The Machine Tools of Combinatorics," which is the first chapter in Edwin Beckenbach's Applied Combinatorial Mathematics (1964). [5] It describes methods for producing permutations, combinations, etc.
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 ...
14.3 Pseudo-random numbers. 15 Arithmetic ... Lucas–Lehmer primality test; ... Cryptographically secure pseudo-random number generator; Middle-square method; Blum ...