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

n £ 1¨5. Tests for Studying Random Data5.7. Maximum of t testThe sequence of numbers is divided into n groups of t elements each, denoted as the vector§X it X it¡ ¢ t£ 1 it¡ for 0 i n. Then determine the maximum of each group. Thedistribution of the maxima should follow x t . This test is described in [16].¡ 1£¨ ¢¡¢¡¢¡£Divide the input sequence into n groups of t elements each, denoted by Vfor 0 i n.¡ i¥§X it X it¡ 1 X it¡ ¢ t£ 1£¨ ¢¡¢¡¢¡£XGenerate a new sequence max§V max§V 0¨max§V ¢¡¢¡¢¡ 1¨We apply the Kolmogorov-Smirnov test to the sequence of maxima with the distributionfunction t ,§0 x 1¨.F§x¨xWe make k equidistant bins between ¢ 0;1£ . To get the expected number of values ineach bin we have to subtract the probability for the lower bin from the probability forthe actual bin.¥We see that the percentage in bin 1¡¡k k¡i£ i 1is ¡tk . To get the expected valueswe multiply the value per bin with the number of groups n.t i¥Example:We have 50 random floating point numbers in 0;1¨. This numbers are alreadygrouped in sequences of elements, the maxima per group are printed bold.t¥ ¢ n¥5seq.random numbers1 0.911647 0.79844 0.783099 0.394383 0.8401882 0.55397 0.277775 0.76823 0.335223 0.1975513 0.95223 0.513401 0.364784 0.628871 0.4773974 0.606969 0.141603 0.717297 0.635712 0.9161955 0.156679 0.804177 0.137232 0.242887 0.01630066 0.218257 0.998925 0.108809 0.12979 0.4009447 0.637552 0.296032 0.61264 0.839112 0.5129328 0.771358 0.292517 0.972775 0.493583 0.5242879 0.283315 0.891529 0.400229 0.769914 0.52674510 0.949327 0.0697553 0.919026 0.807725 0.352458If we make a binning of the interval ¢ 0;1¨ into 10 subintervals we should know, howmany values we expect for each bin.30