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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.
A PCG differs from a classical linear congruential generator (LCG) in three ways: the LCG modulus and state is larger, usually twice the size of the desired output, it uses a power-of-2 modulus, which results in a particularly efficient implementation with a full period generator and unbiased output bits, and
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 ...
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 ...
The generator computes an odd 128-bit value and returns its upper 64 bits. This generator passes BigCrush from TestU01, but fails the TMFn test from PractRand. That test has been designed to catch exactly the defect of this type of generator: since the modulus is a power of 2, the period of the lowest bit in the output is only 2 62, rather than ...
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 ...
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.
It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence. The xorwow generator is the default generator in the CURAND library of the nVidia CUDA application programming interface for graphics processing units.