... collection¹

A previous version is published as technical report 97-1, ACPC - Austrian Center for Parallel Computation, University of Vienna, Austria, 1997.

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... $LCG(2^{35}-31,5^5 = 3125, 0, 1)$²

A similar generator Mgen() $=LCG(2^{26},5^5,0,1)$, used for shuffling purposes, is implemented in the simulation software C++SIM. Note that Mgen() shows satisfying spectral test results.

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... $LCG(10^8, 31415821, 1, 0)$³

This LCG corresponds to the function Uniform() implemented in the simulation software C++SIM.

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...MATLAB,Cle95a⁴

The manual [172] wrongly states $a = 7^7$ (no primitive root modulo $2^{31}-1$!) as multiplier.

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... SUPER-DUPER⁵

Sometimes this LCG itself is called Super-Duper [74,75].

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... CDC⁶

Further generators implemented on CDC computers are BCSLIB (see Section ) and $LCG(2^{47}, 84000335758957,0,1)$ [122,124,125].

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... SIMULA)⁷

See the Sections and .

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...Dem90a,PK89 ⁸

The latter authors initialize the parallel streams via the additive term of the LCG which is in a certain sense equivalent to a modular shifting of the sequences [53,132]. Related concepts applied to prime LCGs have recently been published by Mascagni [170].

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... below⁹

Similar results have also been obtained for different prime LCGs from Section .

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