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

5. Tests for Studying Random Databirthday birthdays sorted spacings spacings sorted305 71143 101 30 5285 122 21 6290 132 10 10331 143 11 1171 173 30 13122 186 13 15279 201 15 15101 228 27 15201 279 51 21173 285 6 26228 290 5 27132 305 15 30186 331 26 30346 346 15 51The collisions of “birthday spacings” are printed bold. We got three collisions.The mean of the Poisson distribution is µ¥3 15 34 365¥ 2¡3124n¥Constructor in birthday_spacing_test.hmbirthday_spacing_test(std::size_t runs,std::size_t birthdays,uint64_t days,std::size_t maxCollisions)runs number of birthday experiments to runbirthdays number of birthdays in a yeardays number of days in a yearmaxCollisions collision counts above this number are cumulated5.9. Collision test (Hash test)The χ 2 test statistic is meaningful only when each interval has more than, lets say, 5 samples.But this test is designed such that the number of intervals is much larger than the number ofsamples.Suppose we throw n balls randomly into m empty urns with m n. If a ball falls intoa nonempty urn we get a collision. This is the 1-dimensional collision test. To get the¡2-dimensional version, we have to sort the urns on a 2-dimensional array.Sometime this test is also called “Hash test”. The test can be interpreted as building anenormous hash table and generating an appropriate index. Some theory can be found in [16]or in [4]Select the number of “balls” n and the number of “urns” m. To do this make a listBALLS[n] and insert for ball i the urn in which it falls.32