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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.
The ACORN generator has not seen the wide adoption of some other PRNGs, although it is included in the Fortran and C library routines of NAG Numerical Library. [5] Various reasons have been put forward for this. [6] Nevertheless, theoretical and empirical research is ongoing to further justify the continuing use of ACORN as a robust and ...
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] Linear-feedback shift register (LFSR) 1965 R. C. Tausworthe [6] A hugely influential design.
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.
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
In computational number theory, Marsaglia's theorem connects modular arithmetic and analytic geometry to describe the flaws with the pseudorandom numbers resulting from a linear congruential generator. As a direct consequence, it is now widely considered that linear congruential generators are weak for the purpose of generating random numbers.
A combined linear congruential generator (CLCG) is a pseudo-random number generator algorithm based on combining two or more linear congruential generators (LCG). A traditional LCG has a period which is inadequate for complex system simulation. [ 1 ]
An approach to nonlinear congruential methods of generating uniform pseudorandom numbers in the interval [0,1) is the Inversive congruential generator with prime modulus. A generalization for arbitrary composite moduli m = p 1 , … p r {\displaystyle m=p_{1},\dots p_{r}} with arbitrary distinct primes p 1 , … , p r ≥ 5 {\displaystyle p_{1 ...