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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.
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.
ACORN generator proposed recently […] is in fact equivalent to a MLCG with matrix A such that a~ = 1 for i 2 j, aq = 0 otherwise" [10] but the analysis is not taken further. ACORN is not the same as ACG (Additive Congruential Generator) and should not be confused with it - ACG appears to have been used for a variant of the LCG ( Linear ...
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 ]
It means that each generator is associated to a fixed IMP polynomial. Such a condition is sufficient for maximum period of each inversive congruential generator [8] and finally for maximum period of the compound generator. The construction of IMP polynomials is the most efficient approach to find parameters for inversive congruential generator ...