A Random Number Generator Test Suite for the C++ ... - ETH Zürich

We get gcd§216 256¨ ¥ 1,815225. Tests for Studying Random Data5.14. gcd test (greatest common divisor)This test calculates the greatest common divisor of two random numbers using Euclid’salgorithm. Now the number of steps to complete Euclid’s algorithm and the resulting gcdwhere checked against their expected probability.The idea of this test is described in [20] and some theory may be found in [16] in section4.5.2, in the exercises and in the accordingly answers.The problem is that the expected distribution of the number of steps and the gcd is unknown,so the comparison must be done with simulated values.Example:We calculate the gcd of 216 u¥and 256 v¥The algorithms gives:25621640¥16¥¥ ¥4040¤16216¤8816¤and the number of steps 4 k¥5.15. Gorilla testThis is a strong version of the monkey test from the Diehard test suite [17] . The test countsthe number of missing 26-bit “words” and compares it with the expected value. UnfortunatelyMarsaglia’s version is hard-wired so a more flexible implementation has to developthe associated statistic. The theory of the test and its implementation can be found in [20]5.16. Ising-model testThe Ising model [15] is one of the simplest and most fundamental models of statistical mechanics.It describes the properties resulting from interacting spins on a lattice.The system considered is an array of N fixed points called lattice sites that form an n-dimensional periodic lattice. Associated with each lattice site is a spin variable s1 which is a either¤number or that is 1 1. If s 1, the ith site is said to havespin up, and if s it is said to have spin down. A given set of numbers s i specifies aconfiguration of the whole system. The energy of the system in the configuration specifiedby si§i¥i is defined by the Hamiltonian¤ i¥ N¨ ¢¡¢¡¢¡ i¥∑ ¢ i j£s i s jJwhere J is the coupling energy. The sum is over pairs of nearest-neighbour sites on thelattice. H¥36