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

5.18. n-block test5.18. n-block testThis test checks the average of subsequences, so called blocks. This is done by calculatingthe average of many sequences of uniformly distributed random numbers (0 x i¡1) andincreasing a counter if the average of the sequence ¯x 1 2. This test is described in [28] anda implementation in Fortran can be found at http://www.physics.helsinki.fi/~vattulai/codes/nblocktest.fGenerate a sequence of n random numbers x 1 x 2 x ¢¡¢¡¢¡n where 0 x i¡1Calculate the average ¯x over the sequence, if ¯x 1 2 increase y 1Repeat the last two steps N timesCalculate the measured probability for ¯x 1 2 as y ¡with one degree of freedom on the y i2¥1 and perform a χ 2 testyVattulainens criterion for failing: Each test is repeated 3 times, and the generator failsfor fixed n if at least two out of three χ 2 failed, which should occur with a probabilityof about 3 400NExample:Lets generate 10 N¥sequences of n¥numbers8x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ¯x0.84 0.394 0.783 0.798 0.912 0.198 0.335 0.768 0.6290.278 0.554 0.477 0.629 0.365 0.513 0.952 0.916 0.5860.636 0.717 0.142 0.607 0.0163 0.243 0.137 0.804 0.4130.157 0.401 0.13 0.109 0.999 0.218 0.513 0.839 0.4210.613 0.296 0.638 0.524 0.494 0.973 0.293 0.771 0.5750.527 0.77 0.4 0.892 0.283 0.352 0.808 0.919 0.6190.0698 0.949 0.526 0.0861 0.192 0.663 0.89 0.349 0.4660.0642 0.02 0.458 0.0631 0.238 0.971 0.902 0.851 0.4460.267 0.54 0.375 0.76 0.513 0.668 0.532 0.0393 0.4620.438 0.932 0.931 0.721 0.284 0.739 0.64 0.354 0.63Now we check the averages ¯x and get y 5 1¥and y y N 2¥5 1¥Constructor in n_block_test.hn_block_test(std::size_t n, std::size_t block_size)n number of blocksblock_size size of each block39