RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-02_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 14.0608 0.337206 2 to 25 15.91 35.5664 0.994762 3 to 26 16.14 18.0830 0.616375 4 to 27 15.71 15.0089 0.405159 5 to 28 15.74 21.0325 0.775161 6 to 29 15.80 16.6432 0.521217 7 to 30 15.68 22.8591 0.846106 8 to 31 15.71 23.0484 0.852319 9 to 32 15.80 12.5809 0.236242 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.322959 Tough bday spacings test for dh-ranFile-2017-02-02_13:31: 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 11 35 70 103 97 80 56 23 17 5 3 (O-E)^2/E 0.4 0.1 0.1 0.3 0.0 0.0 0.3 1.5 0.3 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 3.733, p= 0.041 RESULTS OF GCD FOR dh-ranFile-2017-02-02_13:31 Euclid's algorithm: p-value, steps to gcd: 0.666364 p-value, dist. of gcd's: 0.955630 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-02_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.160 0.799 0.598 0.606 0.310 0.201 0.485 0.721 Bits 8 to 15---> 0.120 0.087 0.522 0.485 0.644 0.257 0.467 0.813 Bits 16 to 23---> 0.783 0.072 0.746 0.365 0.371 0.315 0.470 0.191 Bits 24 to 31---> 0.914 0.253 0.836 0.268 0.707 0.130 0.648 0.861 KS test for the above 32 p values: 0.349 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-02_13:31, p-values for 5 runs: 0.1088, 0.4632, 0.4473, 0.6353, 0.9941 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-02_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5203 5134.0 0.927 1.800 r= 30 23039 23103.0 0.178 1.977 r= 31 11533 11551.5 0.030 2.007 chi-square = 2.007 with df = 3; p-value = 0.429 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-02_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 237 211.4 3.095 3.095 r= 30 5042 5134.0 1.649 4.744 r= 31 23267 23103.0 1.163 5.908 r= 32 11454 11551.5 0.823 6.731 chi-square = 6.731 with df = 3; p-value = 0.919 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-02_13:31 b-rank test for bits 1 to 8, p=0.27068 b-rank test for bits 2 to 9, p=0.07356 b-rank test for bits 3 to 10, p=0.55235 b-rank test for bits 4 to 11, p=0.20995 b-rank test for bits 5 to 12, p=0.28851 b-rank test for bits 6 to 13, p=0.49946 b-rank test for bits 7 to 14, p=0.29985 b-rank test for bits 8 to 15, p=0.47800 b-rank test for bits 9 to 16, p=0.19597 b-rank test for bits 10 to 17, p=0.21019 b-rank test for bits 11 to 18, p=0.36508 b-rank test for bits 12 to 19, p=0.37235 b-rank test for bits 13 to 20, p=0.26519 b-rank test for bits 14 to 21, p=0.07963 b-rank test for bits 15 to 22, p=0.24510 b-rank test for bits 16 to 23, p=0.40769 b-rank test for bits 17 to 24, p=0.55784 b-rank test for bits 18 to 25, p=0.14727 b-rank test for bits 19 to 26, p=0.32078 b-rank test for bits 20 to 27, p=0.25065 b-rank test for bits 21 to 28, p=0.51492 b-rank test for bits 22 to 29, p=0.12354 b-rank test for bits 23 to 30, p=0.78756 b-rank test for bits 24 to 31, p=0.55257 b-rank test for bits 25 to 32, p=0.25774 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 = 0.002020 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-02_13:31 (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 142327 0.98 0.835434 2 141021 -2.08 0.018968 3 141747 -0.38 0.352242 4 141516 -0.92 0.179049 5 143589 3.92 0.999957 6 141783 -0.30 0.383935 7 141652 -0.60 0.273841 8 142135 0.53 0.700996 9 141452 -1.07 0.142641 10 141565 -0.80 0.210551 11 142400 1.15 0.874190 12 142318 0.95 0.830170 13 141796 -0.26 0.395586 14 141509 -0.94 0.174804 15 141927 0.04 0.516466 16 140886 -2.39 0.008402 17 141645 -0.62 0.268422 18 142014 0.24 0.596600 19 142848 2.19 0.985852 20 142408 1.17 0.878014 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-02_13:31 Bits used No. missing words z-score p-value 23 to 32 141736 -0.5977 0.275024 22 to 31 142136 0.7816 0.782781 21 to 30 142016 0.3678 0.643499 20 to 29 141446 -1.5977 0.055056 19 to 28 141837 -0.2494 0.401520 18 to 27 141890 -0.0667 0.473428 17 to 26 141760 -0.5149 0.303301 16 to 25 142189 0.9644 0.832572 15 to 24 141835 -0.2563 0.398856 14 to 23 141872 -0.1287 0.448788 13 to 22 141665 -0.8425 0.199749 12 to 21 141573 -1.1598 0.123074 11 to 20 142314 1.3954 0.918554 10 to 19 142335 1.4678 0.928924 9 to 18 142338 1.4782 0.930319 8 to 17 142083 0.5989 0.725368 7 to 16 142260 1.2092 0.886708 6 to 15 141546 -1.2529 0.105128 5 to 14 142111 0.6954 0.756602 4 to 13 141682 -0.7839 0.216550 3 to 12 142171 0.9023 0.816554 2 to 11 141695 -0.7391 0.229933 1 to 10 142228 1.0989 0.864086 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-02_13:31 Bits used No. missing words z-score p-value 28 to 32 142361 1.5311 0.937126 27 to 31 142232 1.0938 0.862978 26 to 30 141335 -1.9469 0.025774 25 to 29 141820 -0.3028 0.381016 24 to 28 142045 0.4599 0.677205 23 to 27 141851 -0.1977 0.421629 22 to 26 142118 0.7074 0.760327 21 to 25 141779 -0.4418 0.329318 20 to 24 141730 -0.6079 0.271628 19 to 23 141802 -0.3638 0.357992 18 to 22 142073 0.5548 0.710489 17 to 21 141704 -0.6960 0.243204 16 to 20 142269 1.2192 0.888620 15 to 19 141987 0.2633 0.603836 14 to 18 141619 -0.9842 0.162516 13 to 17 142037 0.4328 0.667413 12 to 16 142198 0.9785 0.836097 11 to 15 142050 0.4768 0.683265 10 to 14 141689 -0.7469 0.227568 9 to 13 141872 -0.1265 0.449651 8 to 12 141850 -0.2011 0.420303 7 to 11 141329 -1.9672 0.024579 6 to 10 141937 0.0938 0.537365 5 to 9 141585 -1.0994 0.135792 4 to 8 142169 0.8802 0.810635 3 to 7 141802 -0.3638 0.357992 2 to 6 142479 1.9311 0.973264 1 to 5 141921 0.0396 0.515778 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-02_13:31 Bits used No. missing words z-score p-value 31 to 32 141633 -0.8151 0.207498 30 to 31 142251 1.0079 0.843243 29 to 30 142460 1.6244 0.947854 28 to 29 141478 -1.2724 0.101623 27 to 28 141586 -0.9538 0.170099 26 to 27 142126 0.6391 0.738636 25 to 26 141945 0.1052 0.541900 24 to 25 141872 -0.1101 0.456158 23 to 24 141810 -0.2930 0.384758 22 to 23 142204 0.8692 0.807640 21 to 22 141628 -0.8299 0.203303 20 to 21 141459 -1.3284 0.092022 19 to 20 142271 1.0669 0.856985 18 to 19 141982 0.2144 0.584869 17 to 18 141682 -0.6706 0.251241 16 to 17 141670 -0.7060 0.240098 15 to 16 142000 0.2675 0.605444 14 to 15 141858 -0.1514 0.439824 13 to 14 142012 0.3029 0.619002 12 to 13 141982 0.2144 0.584869 11 to 12 141330 -1.7089 0.043731 10 to 11 141407 -1.4818 0.069197 9 to 10 141877 -0.0954 0.462011 8 to 9 142198 0.8515 0.802764 7 to 8 141959 0.1465 0.558244 6 to 7 142412 1.4828 0.930937 5 to 6 142159 0.7365 0.769284 4 to 5 141865 -0.1308 0.447980 3 to 4 141711 -0.5850 0.279259 2 to 3 141842 -0.1986 0.421283 1 to 2 142012 0.3029 0.619002 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-02_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2333.84 -2.350 0.009392 Test results for specific bytes for dh-ranFile-2017-02-02_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2582.31 1.164 0.877797 2 to 9 2562.40 0.883 0.811247 3 to 10 2374.45 -1.776 0.037900 4 to 11 2565.70 0.929 0.823606 5 to 12 2467.46 -0.460 0.322710 6 to 13 2570.92 1.003 0.842064 7 to 14 2439.20 -0.860 0.194932 8 to 15 2535.65 0.504 0.692939 9 to 16 2570.12 0.992 0.839320 10 to 17 2531.57 0.447 0.672385 11 to 18 2394.48 -1.492 0.067820 12 to 19 2632.08 1.868 0.969114 13 to 20 2475.82 -0.342 0.366202 14 to 21 2567.69 0.957 0.830797 15 to 22 2409.77 -1.276 0.100972 16 to 23 2410.94 -1.259 0.103937 17 to 24 2343.34 -2.215 0.013364 18 to 25 2561.67 0.872 0.808420 19 to 26 2458.80 -0.583 0.280050 20 to 27 2605.62 1.494 0.932367 21 to 28 2475.50 -0.346 0.364502 22 to 29 2480.34 -0.278 0.390473 23 to 30 2514.11 0.200 0.579073 24 to 31 2451.95 -0.680 0.248403 25 to 32 2552.67 0.745 0.771820 CDPARK for dh-ranFile-2017-02-02_13:31: 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 3557 1.5525 0.939730 3529 0.2740 0.607947 3495 -1.2785 0.100530 3523 0.0000 0.500000 3492 -1.4155 0.078457 3503 -0.9132 0.180558 3534 0.5023 0.692266 3541 0.8219 0.794438 3467 -2.5571 0.005278 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3515.60 sample std.=25.37 p-value of the KSTEST for those 10 p-values: 0.551723 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-02_13:31 0.1375,0.4828,0.8513,0.2750,0.3779,0.4535,0.3642,0.0714,0.5342,0.2395, The KS test for those 10 p-values: 0.243026 The 3DSPHERES test for dh-ranFile-2017-02-02_13:31 sample no r^3 equiv. uni. 1 16.697 0.426832 2 45.384 0.779704 3 1.966 0.063428 4 16.461 0.422301 5 29.116 0.621121 6 18.664 0.463203 7 2.200 0.070698 8 21.758 0.515807 9 11.830 0.325870 10 9.956 0.282418 11 37.408 0.712620 12 8.366 0.243369 13 5.701 0.173060 14 65.038 0.885585 15 29.621 0.627440 16 15.066 0.394806 17 5.150 0.157737 18 67.563 0.894822 19 7.008 0.208332 20 21.770 0.515996 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.513283 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-02_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 -0.8 -0.1 -0.2 0.1 -0.6 0.3 -1.9 -2.1 -0.5 0.3 0.1 0.1 0.7 0.5 -0.8 0.4 -0.5 1.1 1.3 0.1 -0.4 -0.3 -0.0 1.5 -1.1 0.2 1.6 -1.2 -0.9 -1.4 -1.1 -0.8 -0.4 -0.3 -0.5 1.1 -0.4 -1.3 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:32.505659 z-score=-1.035918, p-value=0.146414 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-02_13:31 Test no p-value 1 0.282706 2 0.628507 3 0.136173 4 0.006469 5 0.385512 6 0.050862 7 0.007938 8 0.339317 9 0.015571 10 0.961949 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003835 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-02_13:31: (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 66367 1.35 66454 0.68 3 25000.00 25190 1.44 25047 0.09 4 6666.67 6767 1.51 6807 2.95 5 1388.89 1397 0.05 1377 0.10 6 238.10 241 0.04 271 4.55 7 34.72 30 0.64 39 0.53 8 4.96 7 0.84 4 0.19 p=0.56145 p=0.83105 Number of rngs required: 688273, p-value: 0.441 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-02_13:31 No. of wins: Observed Expected 98428 98585.9 z-score=-0.706, pvalue=0.24008 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66292 66666.7 2.106 2.106 2 37582 37654.3 0.139 2.245 3 26944 26954.7 0.004 2.249 4 19305 19313.5 0.004 2.253 5 13901 13851.4 0.177 2.430 6 10055 9943.5 1.249 3.679 7 7308 7145.0 3.717 7.397 8 5158 5139.1 0.070 7.466 9 3705 3699.9 0.007 7.473 10 2784 2666.3 5.196 12.669 11 1888 1923.3 0.649 13.318 12 1405 1388.7 0.190 13.509 13 1012 1003.7 0.068 13.577 14 707 726.1 0.505 14.082 15 531 525.8 0.051 14.132 16 385 381.2 0.039 14.171 17 257 276.5 1.381 15.552 18 224 200.8 2.673 18.225 19 165 146.0 2.477 20.702 20 115 106.2 0.727 21.429 21 277 287.1 0.356 21.785 Chisq= 21.78 for 20 degrees of freedom, p= 0.64770 SUMMARY of craptest p-value for no. of wins: 0.240083 p-value for throws/game: 0.647700 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-02_13:31 No. of wins: Observed Expected 98411 98585.9 z-score=-0.782, pvalue=0.21709 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66515 66666.7 0.345 0.345 2 38072 37654.3 4.633 4.978 3 26928 26954.7 0.027 5.005 4 19320 19313.5 0.002 5.007 5 13757 13851.4 0.644 5.650 6 10096 9943.5 2.338 7.988 7 7090 7145.0 0.424 8.412 8 5064 5139.1 1.097 9.508 9 3624 3699.9 1.556 11.064 10 2670 2666.3 0.005 11.069 11 1828 1923.3 4.725 15.794 12 1404 1388.7 0.168 15.962 13 992 1003.7 0.137 16.099 14 726 726.1 0.000 16.099 15 562 525.8 2.487 18.586 16 373 381.2 0.174 18.760 17 265 276.5 0.482 19.242 18 177 200.8 2.828 22.069 19 132 146.0 1.340 23.409 20 122 106.2 2.346 25.755 21 283 287.1 0.059 25.813 Chisq= 25.81 for 20 degrees of freedom, p= 0.82794 SUMMARY of craptest p-value for no. of wins: 0.217087 p-value for throws/game: 0.827939 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0020,0.0038,0.0053,0.0065,0.0079,0.0084,0.0094,0.0134,0.0156,0.0190, 0.0246,0.0258,0.0379,0.0414,0.0437,0.0509,0.0551,0.0634,0.0678,0.0692, 0.0707,0.0714,0.0716,0.0736,0.0785,0.0796,0.0874,0.0920,0.1005,0.1010, 0.1016,0.1039,0.1051,0.1088,0.1204,0.1231,0.1235,0.1298,0.1358,0.1362, 0.1375,0.1426,0.1464,0.1473,0.1577,0.1600,0.1625,0.1701,0.1731,0.1748, 0.1790,0.1806,0.1913,0.1949,0.1960,0.1997,0.2008,0.2033,0.2075,0.2083, 0.2099,0.2102,0.2106,0.2166,0.2171,0.2276,0.2299,0.2362,0.2395,0.2401, 0.2401,0.2430,0.2432,0.2434,0.2451,0.2484,0.2506,0.2512,0.2534,0.2570, 0.2577,0.2652,0.2682,0.2684,0.2707,0.2716,0.2738,0.2750,0.2750,0.2793, 0.2801,0.2824,0.2827,0.2885,0.2998,0.3033,0.3097,0.3149,0.3208,0.3227, 0.3230,0.3259,0.3293,0.3372,0.3393,0.3492,0.3522,0.3574,0.3580,0.3580, 0.3642,0.3645,0.3648,0.3651,0.3662,0.3712,0.3724,0.3779,0.3810,0.3839, 0.3848,0.3855,0.3905,0.3948,0.3956,0.3989,0.4015,0.4052,0.4077,0.4203, 0.4213,0.4216,0.4223,0.4268,0.4290,0.4398,0.4406,0.4473,0.4480,0.4488, 0.4497,0.4535,0.4562,0.4620,0.4632,0.4632,0.4668,0.4699,0.4734,0.4780, 0.4828,0.4849,0.4849,0.4995,0.5000,0.5133,0.5149,0.5158,0.5158,0.5160, 0.5165,0.5212,0.5216,0.5342,0.5374,0.5419,0.5517,0.5523,0.5526,0.5578, 0.5582,0.5615,0.5791,0.5849,0.5849,0.5966,0.5979,0.6038,0.6054,0.6062, 0.6079,0.6164,0.6190,0.6190,0.6211,0.6274,0.6285,0.6353,0.6435,0.6440, 0.6477,0.6481,0.6664,0.6674,0.6724,0.6772,0.6833,0.6923,0.6929,0.7010, 0.7069,0.7105,0.7126,0.7207,0.7254,0.7386,0.7460,0.7566,0.7603,0.7693, 0.7718,0.7752,0.7797,0.7828,0.7830,0.7876,0.7944,0.7994,0.8028,0.8076, 0.8084,0.8106,0.8112,0.8127,0.8166,0.8236,0.8279,0.8302,0.8308,0.8311, 0.8326,0.8354,0.8361,0.8365,0.8393,0.8421,0.8432,0.8461,0.8513,0.8523, 0.8570,0.8611,0.8630,0.8641,0.8742,0.8778,0.8780,0.8856,0.8867,0.8886, 0.8948,0.9144,0.9186,0.9190,0.9289,0.9303,0.9309,0.9324,0.9371,0.9397, 0.9479,0.9556,0.9619,0.9691,0.9733,0.9859,0.9941,0.9948,1.0000, Overall p-value after applying KStest on 269 p-values = 0.043484 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.