RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-13_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 12.3273 0.220073 2 to 25 16.12 22.1472 0.820874 3 to 26 15.71 22.6097 0.837607 4 to 27 16.03 11.6244 0.177671 5 to 28 15.69 19.5951 0.704541 6 to 29 15.84 17.1446 0.555388 7 to 30 16.17 14.0877 0.339115 8 to 31 15.68 12.7840 0.249477 9 to 32 15.89 19.0652 0.675198 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.859637 Tough bday spacings test for dh-ranFile-2017-01-13_08:31: 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 28 74 98 99 86 44 32 17 8 4 (O-E)^2/E 0.1 2.0 0.0 0.0 0.0 0.8 1.3 0.2 0.3 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.944, p= 0.105 RESULTS OF GCD FOR dh-ranFile-2017-01-13_08:31 Euclid's algorithm: p-value, steps to gcd: 0.792556 p-value, dist. of gcd's: 0.618435 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-13_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.988 0.252 0.947 0.874 0.228 0.443 0.525 0.566 Bits 8 to 15---> 0.283 0.237 0.319 0.178 0.218 0.102 0.469 0.734 Bits 16 to 23---> 0.151 0.466 0.526 0.647 0.135 0.853 0.291 0.534 Bits 24 to 31---> 0.058 0.766 0.744 0.411 0.232 0.175 0.105 0.357 KS test for the above 32 p values: 0.788 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-13_08:31, p-values for 5 runs: 0.5344, 0.9990, 0.6342, 0.6580, 0.8324 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-13_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5139 5134.0 0.005 0.006 r= 30 22965 23103.0 0.825 0.831 r= 31 11685 11551.5 1.542 2.373 chi-square = 2.373 with df = 3; p-value = 0.501 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-13_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5007 5134.0 3.142 3.759 r= 31 23251 23103.0 0.947 4.706 r= 32 11542 11551.5 0.008 4.714 chi-square = 4.714 with df = 3; p-value = 0.806 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-13_08:31 b-rank test for bits 1 to 8, p=0.96454 b-rank test for bits 2 to 9, p=0.17513 b-rank test for bits 3 to 10, p=0.23546 b-rank test for bits 4 to 11, p=0.77424 b-rank test for bits 5 to 12, p=0.45113 b-rank test for bits 6 to 13, p=0.26755 b-rank test for bits 7 to 14, p=0.72285 b-rank test for bits 8 to 15, p=0.40612 b-rank test for bits 9 to 16, p=0.49196 b-rank test for bits 10 to 17, p=0.81310 b-rank test for bits 11 to 18, p=0.58193 b-rank test for bits 12 to 19, p=0.74304 b-rank test for bits 13 to 20, p=0.75948 b-rank test for bits 14 to 21, p=0.77667 b-rank test for bits 15 to 22, p=0.31099 b-rank test for bits 16 to 23, p=0.06325 b-rank test for bits 17 to 24, p=0.51014 b-rank test for bits 18 to 25, p=0.60986 b-rank test for bits 19 to 26, p=0.62614 b-rank test for bits 20 to 27, p=0.11384 b-rank test for bits 21 to 28, p=0.63223 b-rank test for bits 22 to 29, p=0.93485 b-rank test for bits 23 to 30, p=0.25051 b-rank test for bits 24 to 31, p=0.26431 b-rank test for bits 25 to 32, p=0.70729 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 = 0.725728 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-13_08:31 (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 141545 -0.85 0.197319 2 142202 0.68 0.752952 3 142430 1.22 0.888106 4 141895 -0.03 0.486645 5 142112 0.47 0.682082 6 141865 -0.10 0.458753 7 141619 -0.68 0.248778 8 142433 1.22 0.889435 9 141918 0.02 0.508081 10 141898 -0.03 0.489440 11 141622 -0.67 0.251005 12 141418 -1.15 0.125491 13 141615 -0.69 0.245825 14 142731 1.92 0.972558 15 141833 -0.18 0.429228 16 142162 0.59 0.722522 17 142058 0.35 0.635840 18 141937 0.06 0.525774 19 141994 0.20 0.578410 20 141983 0.17 0.568331 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-13_08:31 Bits used No. missing words z-score p-value 23 to 32 141985 0.2609 0.602927 22 to 31 142355 1.5368 0.937828 21 to 30 142344 1.4989 0.933045 20 to 29 142095 0.6402 0.738992 19 to 28 142028 0.4092 0.658806 18 to 27 141915 0.0196 0.507800 17 to 26 141278 -2.1770 0.014740 16 to 25 141929 0.0678 0.527039 15 to 24 141805 -0.3598 0.359514 14 to 23 141763 -0.5046 0.306925 13 to 22 141905 -0.0149 0.494044 12 to 21 141411 -1.7184 0.042864 11 to 20 141970 0.2092 0.582857 10 to 19 142038 0.4437 0.671367 9 to 18 142104 0.6713 0.748978 8 to 17 141591 -1.0977 0.136170 7 to 16 142155 0.8471 0.801541 6 to 15 141796 -0.3908 0.347975 5 to 14 141866 -0.1494 0.440614 4 to 13 142174 0.9127 0.819288 3 to 12 141672 -0.8184 0.206570 2 to 11 141701 -0.7184 0.236262 1 to 10 142623 2.4609 0.993071 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-13_08:31 Bits used No. missing words z-score p-value 28 to 32 141531 -1.2825 0.099838 27 to 31 141965 0.1887 0.574841 26 to 30 141380 -1.7943 0.036380 25 to 29 141660 -0.8452 0.199003 24 to 28 141622 -0.9740 0.165028 23 to 27 141688 -0.7503 0.226546 22 to 26 141599 -1.0520 0.146408 21 to 25 142320 1.3921 0.918054 20 to 24 141932 0.0768 0.530628 19 to 23 142287 1.2802 0.899769 18 to 22 142124 0.7277 0.766600 17 to 21 141716 -0.6554 0.256119 16 to 20 141827 -0.2791 0.390090 15 to 19 141564 -1.1706 0.120878 14 to 18 142098 0.6396 0.738770 13 to 17 142031 0.4124 0.659992 12 to 16 141509 -1.3571 0.087383 11 to 15 142211 1.0226 0.846754 10 to 14 141539 -1.2554 0.104675 9 to 13 141477 -1.4655 0.071389 8 to 12 142079 0.5752 0.717406 7 to 11 142061 0.5141 0.696421 6 to 10 142137 0.7718 0.779873 5 to 9 142223 1.0633 0.856174 4 to 8 142087 0.6023 0.726503 3 to 7 141829 -0.2723 0.392694 2 to 6 141612 -1.0079 0.156752 1 to 5 141682 -0.7706 0.220469 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-13_08:31 Bits used No. missing words z-score p-value 31 to 32 142076 0.4917 0.688517 30 to 31 142097 0.5536 0.710073 29 to 30 141994 0.2498 0.598615 28 to 29 141827 -0.2429 0.404056 27 to 28 142094 0.5447 0.707037 26 to 27 141490 -1.2370 0.108051 25 to 26 142356 1.3176 0.906183 24 to 25 142014 0.3088 0.621248 23 to 24 142105 0.5772 0.718097 22 to 23 141162 -2.2045 0.013744 21 to 22 142032 0.3619 0.641271 20 to 21 141582 -0.9656 0.167128 19 to 20 142175 0.7837 0.783388 18 to 19 141873 -0.1072 0.457328 17 to 18 143061 3.3973 0.999660 16 to 17 142259 1.0315 0.848841 15 to 16 141853 -0.1662 0.434014 14 to 15 141508 -1.1839 0.118233 13 to 14 141947 0.1111 0.544240 12 to 13 141971 0.1819 0.572176 11 to 12 142022 0.3324 0.630191 10 to 11 141911 0.0049 0.501965 9 to 10 142079 0.5005 0.691639 8 to 9 141633 -0.8151 0.207498 7 to 8 141570 -1.0010 0.158420 6 to 7 141630 -0.8240 0.204975 5 to 6 142258 1.0285 0.848149 4 to 5 141856 -0.1573 0.437498 3 to 4 141928 0.0551 0.521960 2 to 3 141926 0.0492 0.519610 1 to 2 141210 -2.0629 0.019560 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-13_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2511.56 0.163 0.564937 Test results for specific bytes for dh-ranFile-2017-01-13_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.91 0.536 0.704071 2 to 9 2552.28 0.739 0.770148 3 to 10 2431.27 -0.972 0.165531 4 to 11 2444.77 -0.781 0.217383 5 to 12 2602.50 1.450 0.926412 6 to 13 2428.68 -1.009 0.156570 7 to 14 2559.17 0.837 0.798628 8 to 15 2482.33 -0.250 0.401337 9 to 16 2426.49 -1.040 0.149256 10 to 17 2488.65 -0.160 0.436266 11 to 18 2486.86 -0.186 0.426316 12 to 19 2481.84 -0.257 0.398643 13 to 20 2500.81 0.012 0.504590 14 to 21 2499.73 -0.004 0.498464 15 to 22 2375.11 -1.766 0.038680 16 to 23 2547.39 0.670 0.748638 17 to 24 2513.96 0.197 0.578226 18 to 25 2487.68 -0.174 0.430866 19 to 26 2556.29 0.796 0.786998 20 to 27 2538.45 0.544 0.706711 21 to 28 2460.62 -0.557 0.288784 22 to 29 2476.29 -0.335 0.368703 23 to 30 2609.60 1.550 0.939425 24 to 31 2467.44 -0.460 0.322584 25 to 32 2451.01 -0.693 0.244211 CDPARK for dh-ranFile-2017-01-13_08:31: 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 3528 0.2283 0.590298 3505 -0.8219 0.205562 3531 0.3653 0.642555 3498 -1.1416 0.126820 3554 1.4155 0.921543 3528 0.2283 0.590298 3550 1.2329 0.891189 3486 -1.6895 0.045562 3486 -1.6895 0.045562 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3517.20 sample std.=23.33 p-value of the KSTEST for those 10 p-values: 0.462019 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-13_08:31 0.1587,0.1371,0.0740,0.9720,0.4047,0.7785,0.2060,0.7012,0.6762,0.0829, The KS test for those 10 p-values: 0.420398 The 3DSPHERES test for dh-ranFile-2017-01-13_08:31 sample no r^3 equiv. uni. 1 47.932 0.797642 2 77.909 0.925501 3 16.214 0.417532 4 52.785 0.827872 5 20.763 0.499476 6 18.518 0.460585 7 23.924 0.549533 8 0.037 0.001216 9 44.845 0.775713 10 21.363 0.509390 11 32.843 0.665387 12 21.172 0.506251 13 5.243 0.160336 14 4.343 0.134786 15 50.344 0.813275 16 54.315 0.836428 17 81.283 0.933425 18 5.261 0.160844 19 1.959 0.063218 20 59.861 0.864036 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.498106 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-13_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 -0.4 0.0 -0.7 1.1 0.2 -1.9 -1.0 0.7 -0.8 -0.2 0.3 0.7 0.3 -0.8 0.6 0.7 -0.9 -0.9 0.7 -0.2 0.9 1.4 -0.6 -0.8 -1.1 -0.7 0.1 1.8 -0.1 -0.5 -0.9 2.1 0.2 -1.4 1.4 -1.0 2.5 -0.1 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:41.860928 z-score=-0.015174, p-value=0.522986 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-13_08:31 Test no p-value 1 0.034071 2 0.927609 3 0.041178 4 0.251484 5 0.577429 6 0.033373 7 0.018023 8 0.635229 9 0.774940 10 0.030823 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007135 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-13_08:31: (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 66781 0.20 66489 0.47 3 25000.00 24778 1.97 24974 0.03 4 6666.67 6818 3.44 6781 1.96 5 1388.89 1338 1.86 1444 2.19 6 238.10 236 0.02 265 3.04 7 34.72 46 3.66 38 0.31 8 4.96 2 1.77 8 1.86 p=0.95562 p=0.86938 Number of rngs required: 688299, p-value: 0.452 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-13_08:31 No. of wins: Observed Expected 98698 98585.9 z-score= 0.502, pvalue=0.69201 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66760 66666.7 0.131 0.131 2 37673 37654.3 0.009 0.140 3 26960 26954.7 0.001 0.141 4 19188 19313.5 0.815 0.956 5 13815 13851.4 0.096 1.052 6 9841 9943.5 1.057 2.109 7 7107 7145.0 0.202 2.312 8 5065 5139.1 1.068 3.379 9 3767 3699.9 1.218 4.597 10 2680 2666.3 0.070 4.668 11 2000 1923.3 3.056 7.724 12 1485 1388.7 6.672 14.396 13 977 1003.7 0.711 15.107 14 738 726.1 0.194 15.301 15 516 525.8 0.184 15.485 16 393 381.2 0.368 15.853 17 287 276.5 0.396 16.249 18 216 200.8 1.146 17.395 19 150 146.0 0.110 17.506 20 89 106.2 2.790 20.296 21 293 287.1 0.121 20.416 Chisq= 20.42 for 20 degrees of freedom, p= 0.56783 SUMMARY of craptest p-value for no. of wins: 0.692012 p-value for throws/game: 0.567834 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-13_08:31 No. of wins: Observed Expected 98636 98585.9 z-score= 0.224, pvalue=0.58872 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66523 66666.7 0.310 0.310 2 37867 37654.3 1.201 1.511 3 26982 26954.7 0.028 1.538 4 19132 19313.5 1.705 3.243 5 13831 13851.4 0.030 3.273 6 10074 9943.5 1.712 4.985 7 7184 7145.0 0.213 5.198 8 5146 5139.1 0.009 5.207 9 3690 3699.9 0.026 5.233 10 2597 2666.3 1.801 7.034 11 1879 1923.3 1.022 8.056 12 1447 1388.7 2.444 10.500 13 1025 1003.7 0.451 10.951 14 705 726.1 0.615 11.567 15 565 525.8 2.917 14.484 16 379 381.2 0.012 14.496 17 282 276.5 0.108 14.604 18 214 200.8 0.864 15.468 19 144 146.0 0.027 15.495 20 82 106.2 5.521 21.015 21 252 287.1 4.294 25.310 Chisq= 25.31 for 20 degrees of freedom, p= 0.81016 SUMMARY of craptest p-value for no. of wins: 0.588723 p-value for throws/game: 0.810158 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0071,0.0137,0.0147,0.0180,0.0196,0.0308,0.0334,0.0341,0.0364, 0.0387,0.0412,0.0429,0.0456,0.0456,0.0583,0.0632,0.0632,0.0714,0.0740, 0.0829,0.0874,0.0998,0.1020,0.1047,0.1049,0.1051,0.1081,0.1138,0.1182, 0.1209,0.1255,0.1268,0.1348,0.1349,0.1362,0.1371,0.1464,0.1493,0.1513, 0.1566,0.1568,0.1584,0.1587,0.1603,0.1608,0.1650,0.1655,0.1671,0.1751, 0.1753,0.1777,0.1785,0.1973,0.1990,0.2050,0.2056,0.2060,0.2066,0.2075, 0.2174,0.2182,0.2188,0.2201,0.2205,0.2265,0.2278,0.2320,0.2355,0.2363, 0.2367,0.2442,0.2458,0.2488,0.2495,0.2505,0.2510,0.2515,0.2520,0.2561, 0.2643,0.2676,0.2832,0.2888,0.2914,0.3069,0.3110,0.3188,0.3226,0.3391, 0.3480,0.3571,0.3595,0.3687,0.3901,0.3927,0.3986,0.4013,0.4041,0.4047, 0.4061,0.4112,0.4175,0.4204,0.4263,0.4292,0.4309,0.4340,0.4363,0.4375, 0.4406,0.4428,0.4511,0.4524,0.4573,0.4588,0.4606,0.4620,0.4663,0.4693, 0.4866,0.4894,0.4920,0.4940,0.4981,0.4985,0.4995,0.5013,0.5020,0.5046, 0.5063,0.5078,0.5081,0.5094,0.5101,0.5196,0.5220,0.5230,0.5248,0.5258, 0.5261,0.5270,0.5306,0.5340,0.5344,0.5442,0.5495,0.5554,0.5649,0.5656, 0.5678,0.5683,0.5722,0.5748,0.5774,0.5782,0.5784,0.5819,0.5829,0.5887, 0.5903,0.5903,0.5986,0.6029,0.6099,0.6184,0.6212,0.6261,0.6302,0.6322, 0.6342,0.6352,0.6358,0.6413,0.6426,0.6471,0.6580,0.6588,0.6600,0.6654, 0.6714,0.6752,0.6762,0.6821,0.6885,0.6916,0.6920,0.6964,0.7012,0.7041, 0.7045,0.7067,0.7070,0.7073,0.7101,0.7174,0.7181,0.7225,0.7229,0.7257, 0.7265,0.7336,0.7388,0.7390,0.7430,0.7442,0.7486,0.7490,0.7530,0.7595, 0.7665,0.7666,0.7701,0.7742,0.7749,0.7757,0.7767,0.7785,0.7799,0.7834, 0.7870,0.7883,0.7926,0.7976,0.7986,0.8015,0.8060,0.8102,0.8131,0.8133, 0.8193,0.8209,0.8279,0.8324,0.8364,0.8376,0.8468,0.8481,0.8488,0.8527, 0.8562,0.8596,0.8640,0.8694,0.8737,0.8881,0.8894,0.8912,0.8998,0.9062, 0.9181,0.9215,0.9255,0.9264,0.9276,0.9330,0.9334,0.9349,0.9378,0.9394, 0.9470,0.9556,0.9645,0.9720,0.9726,0.9884,0.9931,0.9990,0.9997, Overall p-value after applying KStest on 269 p-values = 0.507802 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.