RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-30_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 15.2805 0.424714 2 to 25 15.81 12.7292 0.245885 3 to 26 15.44 19.9638 0.723914 4 to 27 15.69 16.2368 0.492884 5 to 28 15.99 28.2208 0.957577 6 to 29 15.84 17.6782 0.590594 7 to 30 15.75 21.6222 0.800310 8 to 31 15.71 9.8999 0.092245 9 to 32 15.59 26.9234 0.940800 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.696940 Tough bday spacings test for dh-ranFile-2018-03-30_18:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 10 42 73 86 93 92 49 34 11 7 3 (O-E)^2/E 0.1 0.8 0.0 1.4 0.2 2.5 0.2 0.6 1.0 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.044, p= 0.279 RESULTS OF GCD FOR dh-ranFile-2018-03-30_18:31 Euclid's algorithm: p-value, steps to gcd: 0.363767 p-value, dist. of gcd's: 0.381253 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-30_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.321 0.812 0.667 0.330 0.335 0.330 0.550 0.005 Bits 8 to 15---> 0.071 0.588 0.988 0.290 0.911 0.319 0.547 0.728 Bits 16 to 23---> 0.752 0.223 0.555 0.747 0.815 0.627 0.669 0.031 Bits 24 to 31---> 0.846 0.011 0.257 0.981 0.564 0.668 0.923 0.833 KS test for the above 32 p values: 0.502 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-30_18:31, p-values for 5 runs: 0.2022, 0.9536, 0.7984, 0.6074, 0.3691 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-30_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5160 5134.0 0.132 0.661 r= 30 23097 23103.0 0.002 0.663 r= 31 11521 11551.5 0.081 0.743 chi-square = 0.743 with df = 3; p-value = 0.137 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-30_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5190 5134.0 0.611 2.215 r= 31 23143 23103.0 0.069 2.284 r= 32 11474 11551.5 0.520 2.804 chi-square = 2.804 with df = 3; p-value = 0.577 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-30_18:31 b-rank test for bits 1 to 8, p=0.10874 b-rank test for bits 2 to 9, p=0.98637 b-rank test for bits 3 to 10, p=0.31199 b-rank test for bits 4 to 11, p=0.31028 b-rank test for bits 5 to 12, p=0.77526 b-rank test for bits 6 to 13, p=0.06347 b-rank test for bits 7 to 14, p=0.63070 b-rank test for bits 8 to 15, p=0.18786 b-rank test for bits 9 to 16, p=0.09119 b-rank test for bits 10 to 17, p=0.02685 b-rank test for bits 11 to 18, p=0.94791 b-rank test for bits 12 to 19, p=0.76970 b-rank test for bits 13 to 20, p=0.63251 b-rank test for bits 14 to 21, p=0.78728 b-rank test for bits 15 to 22, p=0.15421 b-rank test for bits 16 to 23, p=0.90864 b-rank test for bits 17 to 24, p=0.54908 b-rank test for bits 18 to 25, p=0.03880 b-rank test for bits 19 to 26, p=0.83133 b-rank test for bits 20 to 27, p=0.69687 b-rank test for bits 21 to 28, p=0.52465 b-rank test for bits 22 to 29, p=0.94161 b-rank test for bits 23 to 30, p=0.89737 b-rank test for bits 24 to 31, p=0.93795 b-rank test for bits 25 to 32, p=0.06270 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.227544 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-30_18:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141390 -1.21 0.112491 2 142681 1.80 0.964303 3 142093 0.43 0.666088 4 141916 0.02 0.506217 5 142344 1.02 0.845086 6 141900 -0.02 0.491304 7 141795 -0.27 0.394686 8 141931 0.05 0.520190 9 142034 0.29 0.614583 10 141679 -0.54 0.295235 11 141388 -1.22 0.111600 12 141739 -0.40 0.345327 13 141746 -0.38 0.351375 14 142267 0.84 0.798332 15 142498 1.38 0.915496 16 142645 1.72 0.957180 17 142396 1.14 0.872247 18 141814 -0.22 0.411871 19 141421 -1.14 0.126944 20 142637 1.70 0.955450 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-30_18:31 Bits used No. missing words z-score p-value 23 to 32 141914 0.0161 0.506424 22 to 31 142361 1.5575 0.940322 21 to 30 142109 0.6885 0.754436 20 to 29 142389 1.6540 0.950940 19 to 28 142198 0.9954 0.840233 18 to 27 141622 -0.9908 0.160893 17 to 26 141630 -0.9632 0.167722 16 to 25 142220 1.0713 0.857977 15 to 24 142307 1.3713 0.914856 14 to 23 142172 0.9058 0.817468 13 to 22 141835 -0.2563 0.398856 12 to 21 142042 0.4575 0.676338 11 to 20 141628 -0.9701 0.165998 10 to 19 141445 -1.6011 0.054673 9 to 18 142387 1.6471 0.950235 8 to 17 141811 -0.3391 0.367279 7 to 16 142055 0.5023 0.692275 6 to 15 142029 0.4127 0.660070 5 to 14 142332 1.4575 0.927508 4 to 13 141720 -0.6529 0.256923 3 to 12 141645 -0.9115 0.181021 2 to 11 142053 0.4954 0.689846 1 to 10 141790 -0.4115 0.340359 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-30_18:31 Bits used No. missing words z-score p-value 28 to 32 141762 -0.4994 0.308741 27 to 31 141534 -1.2723 0.101632 26 to 30 142225 1.0701 0.857706 25 to 29 142339 1.4565 0.927374 24 to 28 142292 1.2972 0.902717 23 to 27 141884 -0.0859 0.465787 22 to 26 142139 0.7785 0.781875 21 to 25 142533 2.1141 0.982748 20 to 24 142062 0.5175 0.697605 19 to 23 142022 0.3819 0.648744 18 to 22 142012 0.3480 0.636093 17 to 21 142043 0.4531 0.674768 16 to 20 142213 1.0294 0.848352 15 to 19 141919 0.0328 0.513075 14 to 18 141556 -1.1977 0.115511 13 to 17 142164 0.8633 0.806011 12 to 16 142280 1.2565 0.895534 11 to 15 141953 0.1480 0.558842 10 to 14 142383 1.6057 0.945826 9 to 13 141245 -2.2520 0.012162 8 to 12 141930 0.0701 0.527930 7 to 11 142686 2.6328 0.995766 6 to 10 141492 -1.4147 0.078581 5 to 9 141551 -1.2147 0.112244 4 to 8 141037 -2.9571 0.001553 3 to 7 141692 -0.7367 0.230649 2 to 6 141692 -0.7367 0.230649 1 to 5 141951 0.1413 0.556166 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-30_18:31 Bits used No. missing words z-score p-value 31 to 32 141302 -1.7915 0.036604 30 to 31 142343 1.2793 0.899598 29 to 30 141101 -2.3845 0.008552 28 to 29 142285 1.1082 0.866106 27 to 28 141566 -1.0128 0.155584 26 to 27 142214 0.8987 0.815602 25 to 26 141746 -0.4818 0.314974 24 to 25 142084 0.5153 0.696811 23 to 24 141372 -1.5850 0.056478 22 to 23 142048 0.4091 0.658751 21 to 22 141865 -0.1308 0.447980 20 to 21 141898 -0.0334 0.486669 19 to 20 141872 -0.1101 0.456158 18 to 19 142018 0.3206 0.625728 17 to 18 142139 0.6775 0.750953 16 to 17 142152 0.7158 0.762955 15 to 16 142527 1.8220 0.965775 14 to 15 142141 0.6834 0.752821 13 to 14 141807 -0.3019 0.381380 12 to 13 141882 -0.0806 0.467872 11 to 12 142134 0.6627 0.746253 10 to 11 141625 -0.8387 0.200810 9 to 10 141751 -0.4671 0.320232 8 to 9 141415 -1.4582 0.072393 7 to 8 142063 0.4533 0.674835 6 to 7 142680 2.2734 0.988498 5 to 6 142298 1.1465 0.874210 4 to 5 142813 2.6657 0.996159 3 to 4 141919 0.0285 0.511378 2 to 3 142186 0.8161 0.792789 1 to 2 141548 -1.0659 0.143241 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-30_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2432.01 -0.961 0.168162 Test results for specific bytes for dh-ranFile-2018-03-30_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2381.83 -1.671 0.047345 2 to 9 2444.59 -0.784 0.216652 3 to 10 2634.14 1.897 0.971084 4 to 11 2438.13 -0.875 0.190782 5 to 12 2518.82 0.266 0.604952 6 to 13 2544.38 0.628 0.734884 7 to 14 2498.16 -0.026 0.489644 8 to 15 2464.37 -0.504 0.307193 9 to 16 2610.08 1.557 0.940240 10 to 17 2476.59 -0.331 0.370321 11 to 18 2414.27 -1.212 0.112668 12 to 19 2452.58 -0.671 0.251252 13 to 20 2496.11 -0.055 0.478089 14 to 21 2330.04 -2.404 0.008117 15 to 22 2612.22 1.587 0.943739 16 to 23 2435.75 -0.909 0.181780 17 to 24 2543.59 0.616 0.731212 18 to 25 2519.91 0.282 0.610865 19 to 26 2619.54 1.691 0.954538 20 to 27 2541.38 0.585 0.720809 21 to 28 2535.22 0.498 0.690792 22 to 29 2488.16 -0.167 0.433494 23 to 30 2385.69 -1.617 0.052987 24 to 31 2513.63 0.193 0.576418 25 to 32 2414.64 -1.207 0.113677 CDPARK for dh-ranFile-2018-03-30_18:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3533 0.4566 0.676028 3559 1.6438 0.949895 3513 -0.4566 0.323972 3516 -0.3196 0.374623 3529 0.2740 0.607947 3546 1.0502 0.853193 3516 -0.3196 0.374623 3525 0.0913 0.536383 3553 1.3699 0.914635 3526 0.1370 0.554479 Square side=100, avg. no. parked=3531.60 sample std.=15.27 p-value of the KSTEST for those 10 p-values: 0.278292 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-30_18:31 0.4112,0.7846,0.6987,0.7567,0.4527,0.8864,0.0216,0.9348,0.4985,0.6789, The KS test for those 10 p-values: 0.312582 The 3DSPHERES test for dh-ranFile-2018-03-30_18:31 sample no r^3 equiv. uni. 1 55.691 0.843761 2 40.990 0.744964 3 6.888 0.205145 4 9.981 0.283017 5 5.900 0.178541 6 17.235 0.437011 7 31.330 0.648078 8 4.648 0.143517 9 2.451 0.078443 10 47.726 0.796249 11 112.259 0.976292 12 83.944 0.939076 13 76.822 0.922751 14 1.162 0.037977 15 116.646 0.979518 16 12.192 0.333963 17 18.316 0.456934 18 22.915 0.534124 19 50.915 0.816796 20 1.282 0.041837 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.600224 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-30_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 -0.1 0.9 0.3 0.1 1.4 2.5 -0.0 -0.6 -2.0 2.1 -0.7 0.2 -0.0 -0.5 -0.4 0.6 -0.2 0.3 -1.3 0.1 0.7 -0.7 0.0 -0.4 0.9 -0.7 0.7 0.5 -0.7 0.9 0.2 -0.8 0.8 0.6 1.0 0.5 0.9 1.0 -1.3 1.0 -0.1 Chi-square with 42 degrees of freedom:36.439209 z-score=-0.606732, p-value=0.287012 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-30_18:31 Test no p-value 1 0.015609 2 0.048119 3 0.315067 4 0.493660 5 0.831016 6 0.208446 7 0.030632 8 0.143870 9 0.078476 10 0.426514 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007532 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-30_18:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66820 0.35 66657 0.00 3 25000.00 24673 4.28 25058 0.13 4 6666.67 6794 2.43 6696 0.13 5 1388.89 1435 1.53 1334 2.17 6 238.10 244 0.15 209 3.56 7 34.72 23 3.96 36 0.05 8 4.96 10 5.12 9 3.29 p=0.99329 p=0.84402 Number of rngs required: 688026, p-value: 0.332 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-30_18:31 No. of wins: Observed Expected 98988 98585.9 z-score= 1.799, pvalue=0.96396 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66683 66666.7 0.004 0.004 2 37785 37654.3 0.454 0.458 3 26827 26954.7 0.605 1.063 4 19470 19313.5 1.269 2.332 5 13796 13851.4 0.222 2.553 6 9874 9943.5 0.486 3.040 7 7047 7145.0 1.345 4.385 8 5099 5139.1 0.312 4.697 9 3651 3699.9 0.645 5.342 10 2738 2666.3 1.928 7.271 11 1950 1923.3 0.370 7.640 12 1439 1388.7 1.819 9.459 13 1018 1003.7 0.203 9.663 14 729 726.1 0.011 9.674 15 525 525.8 0.001 9.675 16 352 381.2 2.229 11.905 17 300 276.5 1.990 13.895 18 209 200.8 0.332 14.227 19 137 146.0 0.553 14.780 20 103 106.2 0.097 14.878 21 268 287.1 1.272 16.150 Chisq= 16.15 for 20 degrees of freedom, p= 0.29273 SUMMARY of craptest p-value for no. of wins: 0.963960 p-value for throws/game: 0.292734 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-30_18:31 No. of wins: Observed Expected 98797 98585.9 z-score= 0.944, pvalue=0.82750 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66665 66666.7 0.000 0.000 2 37732 37654.3 0.160 0.160 3 26962 26954.7 0.002 0.162 4 19316 19313.5 0.000 0.163 5 13759 13851.4 0.617 0.779 6 9773 9943.5 2.925 3.704 7 7188 7145.0 0.258 3.963 8 5159 5139.1 0.077 4.040 9 3697 3699.9 0.002 4.042 10 2648 2666.3 0.126 4.168 11 1946 1923.3 0.267 4.435 12 1387 1388.7 0.002 4.437 13 1026 1003.7 0.495 4.932 14 752 726.1 0.921 5.853 15 516 525.8 0.184 6.037 16 425 381.2 5.045 11.081 17 283 276.5 0.151 11.232 18 210 200.8 0.419 11.651 19 134 146.0 0.984 12.635 20 100 106.2 0.364 12.999 21 322 287.1 4.239 17.238 Chisq= 17.24 for 20 degrees of freedom, p= 0.36250 SUMMARY of craptest p-value for no. of wins: 0.827504 p-value for throws/game: 0.362499 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0047,0.0075,0.0081,0.0086,0.0111,0.0122,0.0156,0.0216,0.0268, 0.0306,0.0308,0.0366,0.0380,0.0388,0.0418,0.0473,0.0481,0.0530,0.0547, 0.0565,0.0627,0.0635,0.0710,0.0724,0.0784,0.0785,0.0786,0.0912,0.0922, 0.1016,0.1087,0.1116,0.1122,0.1125,0.1127,0.1137,0.1155,0.1269,0.1371, 0.1432,0.1435,0.1439,0.1542,0.1556,0.1609,0.1660,0.1677,0.1682,0.1785, 0.1810,0.1818,0.1879,0.1908,0.2008,0.2022,0.2051,0.2084,0.2167,0.2234, 0.2275,0.2306,0.2306,0.2459,0.2513,0.2569,0.2574,0.2783,0.2787,0.2830, 0.2870,0.2897,0.2927,0.2952,0.3072,0.3087,0.3103,0.3120,0.3126,0.3150, 0.3151,0.3193,0.3202,0.3209,0.3240,0.3299,0.3300,0.3320,0.3340,0.3347, 0.3404,0.3453,0.3514,0.3625,0.3638,0.3673,0.3691,0.3703,0.3746,0.3746, 0.3813,0.3814,0.3947,0.3989,0.4112,0.4119,0.4247,0.4265,0.4335,0.4370, 0.4480,0.4527,0.4562,0.4569,0.4658,0.4679,0.4781,0.4867,0.4896,0.4913, 0.4929,0.4937,0.4985,0.5023,0.5062,0.5064,0.5114,0.5131,0.5202,0.5246, 0.5279,0.5341,0.5364,0.5470,0.5491,0.5499,0.5545,0.5551,0.5562,0.5588, 0.5641,0.5764,0.5772,0.5878,0.5906,0.6002,0.6050,0.6074,0.6079,0.6109, 0.6146,0.6257,0.6273,0.6307,0.6325,0.6361,0.6481,0.6487,0.6588,0.6601, 0.6661,0.6673,0.6680,0.6686,0.6748,0.6748,0.6760,0.6763,0.6789,0.6898, 0.6908,0.6923,0.6968,0.6969,0.6969,0.6976,0.6987,0.7208,0.7239,0.7276, 0.7312,0.7349,0.7450,0.7463,0.7470,0.7510,0.7518,0.7528,0.7544,0.7567, 0.7630,0.7697,0.7753,0.7819,0.7846,0.7873,0.7928,0.7962,0.7983,0.7984, 0.8003,0.8060,0.8115,0.8152,0.8156,0.8168,0.8175,0.8275,0.8310,0.8313, 0.8333,0.8402,0.8438,0.8440,0.8451,0.8463,0.8484,0.8532,0.8577,0.8580, 0.8661,0.8722,0.8742,0.8864,0.8955,0.8974,0.8996,0.9027,0.9086,0.9107, 0.9146,0.9149,0.9155,0.9228,0.9230,0.9274,0.9275,0.9348,0.9379,0.9391, 0.9402,0.9403,0.9408,0.9416,0.9437,0.9458,0.9479,0.9499,0.9502,0.9509, 0.9536,0.9545,0.9554,0.9572,0.9576,0.9640,0.9643,0.9658,0.9711,0.9763, 0.9795,0.9807,0.9827,0.9864,0.9880,0.9885,0.9933,0.9958,0.9962, Overall p-value after applying KStest on 269 p-values = 0.040698 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.