Random number generator with large period for parallel programs.
A new quick-operating Assembler realization for DH generator of Dyadkin and Hamilton was developed. The convenient technique was also worked out for producing its independent subsequences of it and distribution them among the processors. Numerical simulation of a problem with known exact solution was carried out with the help of DH generator. If only one sample was executed on each processor, errors were always less then theoretical limit for statistical errors in Monte Carlo methods. Simultaneously true correlation coefficients among final temperatures produced on different processors were estimated to be not distinguished from zero and thus confirming independence of the subsequences. At the same time if on each processor the additional samples were carried out, which is the common practice for enlarging an overall statistical sample, then the errors appeared which exceeded theoretical Monte Carlo threshold. Their numerical values were represented in 13 different parallel computations for 16 processors with 14 additional samples on each. In this case estimations of true correlation coefficients happened to be already different from zero and established the occurrence of correlations between the final temperatures obtained with additional samples. In order to estimate the possible usefulness of additional samples it was suggested a special preliminary check with simulation of typical variant of a problem by means of two techniques.