RNMULT128
swMATH ID:  17881 
Software Authors:  Dyadkin, Iosif G.; Hamilton, Kenneth G. 
Description:  A study of 128bit multipliers for congruential pseudorandom number generators. For the multiplicative congruential pseudorandom number generator Xn+1=AXn mod 2128, the authors search for good multipliers of the form A=5K mod 2128 with a prime number K≤231−1. The paper is the continuation of the authors’ paper [ibid. 103, No. 23, 103130 (1997; reviewed above)]. For these generators with a period of 2126, the naturally underlying lattice structure of pairs, triplets etc. is so fine that one cannot observe it. By using of parallel computing technique and mixing several flows of random numbers, this effect will even be amplified. The arbitrary postulate K>100000 and five rather rigorously working numbertheoretical tests, mainly from the literature (bitmap, crosstalk, lattice, lacunary and others) lead to a reduction of 2155 “good” primes K. They remained unnamed and can be taken from a CPC library. The used software and its origin is mentioned in detail. It follow statistical tests as frequency, KolmogorovSmirnov, gap, birthday spacing and others. The test results are presented graphically and well correspond to what expected. Difficulties in computational converting are discussed in detail. 
Homepage:  http://www.cpc.cs.qub.ac.uk/summaries/ADLK_v1_0.html 
Keywords:  random numbers; pseudorandom number generators; congruential methods; multipliers; parallel computation; MonteCarlo method; numerical examples 
Related Software:  Algorithm 719; Algorithm 693; MONC 
Cited in:  2 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

A study of 128bit multipliers for congruential pseudorandom number generators. Zbl 0980.65008 Dyadkin, Iosif G.; Hamilton, Kenneth G. 
2000

Cited by 4 Authors
1  Dyadkin, Iosif G. 
1  Hamilton, Kenneth G. 
1  Marchenko, Mikhail Aleksandrovich 
1  Mikhaĭlov, Gennadiĭ Alekseevich 
Cited in 2 Serials
1  Computer Physics Communications 
1  Automation and Remote Control 
Cited in 3 Fields
1  Number theory (11XX) 
1  Numerical analysis (65XX) 
1  Computer science (68XX) 