RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-10_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 14.1069 0.340477 2 to 25 15.78 16.7400 0.527886 3 to 26 15.52 24.7657 0.899921 4 to 27 15.47 32.6229 0.987422 5 to 28 15.79 15.1018 0.411847 6 to 29 15.73 26.5194 0.934497 7 to 30 15.82 32.2391 0.985949 8 to 31 15.69 28.5434 0.961024 9 to 32 15.76 16.9083 0.539404 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.005712 Tough bday spacings test for dh-ranFile-2016-04-10_16:31: 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 26 80 103 97 70 49 37 16 7 5 (O-E)^2/E 0.1 3.1 0.6 0.3 0.0 0.8 0.2 1.8 0.1 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.186, p= 0.292 RESULTS OF GCD FOR dh-ranFile-2016-04-10_16:31 Euclid's algorithm: p-value, steps to gcd: 0.792598 p-value, dist. of gcd's: 0.838163 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-10_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.417 0.719 0.817 0.180 0.757 0.549 0.248 0.168 Bits 8 to 15---> 0.662 0.862 0.615 0.977 0.363 0.458 0.760 0.923 Bits 16 to 23---> 0.583 0.013 0.447 0.770 0.178 0.363 0.391 0.524 Bits 24 to 31---> 0.534 0.060 0.821 0.302 0.932 0.919 0.075 0.201 KS test for the above 32 p values: 0.004 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-10_16:31, p-values for 5 runs: 0.1907, 0.1215, 0.1928, 0.1241, 0.2629 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-10_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 4998 5134.0 3.603 4.023 r= 30 23284 23103.0 1.417 5.440 r= 31 11516 11551.5 0.109 5.549 chi-square = 5.549 with df = 3; p-value = 0.864 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-10_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 194 211.4 1.435 1.435 r= 30 5099 5134.0 0.239 1.674 r= 31 23221 23103.0 0.602 2.276 r= 32 11486 11551.5 0.372 2.648 chi-square = 2.648 with df = 3; p-value = 0.551 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-10_16:31 b-rank test for bits 1 to 8, p=0.37621 b-rank test for bits 2 to 9, p=0.38433 b-rank test for bits 3 to 10, p=0.30043 b-rank test for bits 4 to 11, p=0.45465 b-rank test for bits 5 to 12, p=0.63360 b-rank test for bits 6 to 13, p=0.91212 b-rank test for bits 7 to 14, p=0.45204 b-rank test for bits 8 to 15, p=0.46311 b-rank test for bits 9 to 16, p=0.32921 b-rank test for bits 10 to 17, p=0.38712 b-rank test for bits 11 to 18, p=0.07345 b-rank test for bits 12 to 19, p=0.83302 b-rank test for bits 13 to 20, p=0.47029 b-rank test for bits 14 to 21, p=0.38353 b-rank test for bits 15 to 22, p=0.51893 b-rank test for bits 16 to 23, p=0.55706 b-rank test for bits 17 to 24, p=0.24742 b-rank test for bits 18 to 25, p=0.48530 b-rank test for bits 19 to 26, p=0.95130 b-rank test for bits 20 to 27, p=0.95419 b-rank test for bits 21 to 28, p=0.01311 b-rank test for bits 22 to 29, p=0.57412 b-rank test for bits 23 to 30, p=0.94216 b-rank test for bits 24 to 31, p=0.55951 b-rank test for bits 25 to 32, p=0.45381 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 = 0.263018 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-10_16:31 (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 141573 -0.79 0.215987 2 141615 -0.69 0.245825 3 141770 -0.33 0.372387 4 142284 0.88 0.809321 5 141151 -1.77 0.038214 6 141840 -0.16 0.435658 7 141943 0.08 0.531352 8 142883 2.27 0.988545 9 142245 0.78 0.783561 10 142189 0.65 0.743262 11 142205 0.69 0.755160 12 141832 -0.18 0.428310 13 142068 0.37 0.644579 14 142279 0.86 0.806128 15 142197 0.67 0.749248 16 141822 -0.20 0.419160 17 142003 0.22 0.586619 18 142144 0.55 0.708255 19 141832 -0.18 0.428310 20 141429 -1.12 0.130875 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-10_16:31 Bits used No. missing words z-score p-value 23 to 32 142016 0.3678 0.643499 22 to 31 141996 0.2989 0.617477 21 to 30 141488 -1.4529 0.073131 20 to 29 141923 0.0471 0.518798 19 to 28 141940 0.1058 0.542113 18 to 27 141372 -1.8529 0.031951 17 to 26 141964 0.1885 0.574764 16 to 25 141389 -1.7942 0.036387 15 to 24 141388 -1.7977 0.036113 14 to 23 141323 -2.0218 0.021597 13 to 22 141545 -1.2563 0.104502 12 to 21 142023 0.3920 0.652458 11 to 20 141887 -0.0770 0.469312 10 to 19 141437 -1.6287 0.051686 9 to 18 141827 -0.2839 0.388245 8 to 17 141577 -1.1460 0.125905 7 to 16 142056 0.5058 0.693487 6 to 15 142001 0.3161 0.624038 5 to 14 141998 0.3058 0.620106 4 to 13 141562 -1.1977 0.115519 3 to 12 142446 1.8506 0.967885 2 to 11 141972 0.2161 0.585547 1 to 10 142180 0.9333 0.824679 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-10_16:31 Bits used No. missing words z-score p-value 28 to 32 142105 0.6633 0.746427 27 to 31 142386 1.6158 0.946935 26 to 30 142223 1.0633 0.856174 25 to 29 141966 0.1921 0.576169 24 to 28 142107 0.6701 0.748593 23 to 27 142080 0.5785 0.718551 22 to 26 141746 -0.5537 0.289905 21 to 25 141931 0.0735 0.529279 20 to 24 141993 0.2836 0.611652 19 to 23 141898 -0.0384 0.484682 18 to 22 141786 -0.4181 0.337949 17 to 21 141508 -1.3604 0.086845 16 to 20 141752 -0.5333 0.296905 15 to 19 141993 0.2836 0.611652 14 to 18 141770 -0.4723 0.318355 13 to 17 141557 -1.1943 0.116173 12 to 16 141975 0.2226 0.588081 11 to 15 142369 1.5582 0.940407 10 to 14 141869 -0.1367 0.445629 9 to 13 141758 -0.5130 0.303982 8 to 12 141869 -0.1367 0.445629 7 to 11 141977 0.2294 0.590717 6 to 10 142238 1.1141 0.867390 5 to 9 141704 -0.6960 0.243204 4 to 8 141812 -0.3299 0.370726 3 to 7 141532 -1.2791 0.100434 2 to 6 141589 -1.0859 0.138770 1 to 5 141507 -1.3638 0.086310 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-10_16:31 Bits used No. missing words z-score p-value 31 to 32 141332 -1.7030 0.044280 30 to 31 141717 -0.5673 0.285240 29 to 30 142099 0.5595 0.712089 28 to 29 141995 0.2527 0.599755 27 to 28 142034 0.3678 0.643473 26 to 27 141586 -0.9538 0.170099 25 to 26 141784 -0.3697 0.355801 24 to 25 142395 1.4327 0.924022 23 to 24 142268 1.0580 0.854978 22 to 23 141934 0.0728 0.529007 21 to 22 141558 -1.0364 0.150014 20 to 21 142416 1.4946 0.932491 19 to 20 142302 1.1583 0.876633 18 to 19 141468 -1.3019 0.096482 17 to 18 141616 -0.8653 0.193443 16 to 17 141748 -0.4759 0.317073 15 to 16 142548 1.8840 0.970216 14 to 15 141547 -1.0688 0.142575 13 to 14 141789 -0.3550 0.361311 12 to 13 142118 0.6155 0.730903 11 to 12 141456 -1.3373 0.090569 10 to 11 142226 0.9341 0.824882 9 to 10 142571 1.9518 0.974521 8 to 9 141527 -1.1278 0.129699 7 to 8 142061 0.4474 0.672708 6 to 7 141984 0.2203 0.587168 5 to 6 142382 1.3943 0.918388 4 to 5 142227 0.9371 0.825641 3 to 4 141946 0.1082 0.543070 2 to 3 141701 -0.6145 0.269428 1 to 2 141863 -0.1367 0.445647 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-10_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2494.69 -0.075 0.470091 Test results for specific bytes for dh-ranFile-2016-04-10_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2458.38 -0.589 0.278069 2 to 9 2501.69 0.024 0.509550 3 to 10 2479.38 -0.292 0.385272 4 to 11 2457.02 -0.608 0.271671 5 to 12 2420.90 -1.119 0.131658 6 to 13 2514.13 0.200 0.579168 7 to 14 2425.73 -1.050 0.146767 8 to 15 2414.90 -1.204 0.114380 9 to 16 2413.14 -1.228 0.109658 10 to 17 2452.15 -0.677 0.249278 11 to 18 2606.41 1.505 0.933826 12 to 19 2555.68 0.787 0.784472 13 to 20 2496.46 -0.050 0.480020 14 to 21 2540.93 0.579 0.718640 15 to 22 2478.19 -0.308 0.378869 16 to 23 2573.74 1.043 0.851501 17 to 24 2477.14 -0.323 0.373249 18 to 25 2482.44 -0.248 0.401942 19 to 26 2357.09 -2.021 0.021640 20 to 27 2561.96 0.876 0.809537 21 to 28 2550.04 0.708 0.760436 22 to 29 2485.50 -0.205 0.418784 23 to 30 2505.65 0.080 0.531831 24 to 31 2438.95 -0.863 0.193982 25 to 32 2481.02 -0.268 0.394193 CDPARK for dh-ranFile-2016-04-10_16:31: 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 3511 -0.5479 0.291865 3522 -0.0457 0.481790 3515 -0.3653 0.357445 3530 0.3196 0.625377 3530 0.3196 0.625377 3492 -1.4155 0.078457 3509 -0.6393 0.261324 3543 0.9132 0.819442 3524 0.0457 0.518210 3551 1.2785 0.899470 Square side=100, avg. no. parked=3522.70 sample std.=16.27 p-value of the KSTEST for those 10 p-values: 0.943969 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-10_16:31 0.8588,0.4113,0.8241,0.1389,0.0278,0.6080,0.2348,0.4483,0.2368,0.5877, The KS test for those 10 p-values: 0.843691 The 3DSPHERES test for dh-ranFile-2016-04-10_16:31 sample no r^3 equiv. uni. 1 60.917 0.868737 2 17.283 0.437911 3 48.727 0.802935 4 15.729 0.408023 5 6.166 0.185781 6 8.117 0.237061 7 25.118 0.567107 8 59.517 0.862470 9 17.293 0.438093 10 18.303 0.456707 11 4.221 0.131252 12 27.889 0.605304 13 6.374 0.191415 14 52.304 0.825085 15 12.689 0.344899 16 6.034 0.182184 17 1.269 0.041426 18 31.593 0.651148 19 34.672 0.685177 20 20.601 0.496763 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.765800 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-10_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -1.1 -0.1 0.7 -1.4 0.3 0.2 -0.5 -0.9 -0.4 -0.7 0.3 1.8 -0.5 -0.9 -1.0 0.1 0.4 -0.1 0.6 0.1 0.0 0.6 1.3 0.7 -0.3 -1.7 0.6 -1.1 -0.2 0.4 1.6 1.2 -1.6 2.0 1.0 -0.1 -0.8 -0.1 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:33.840688 z-score=-0.890254, p-value=0.189049 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-10_16:31 Test no p-value 1 0.356865 2 0.175526 3 0.419249 4 0.712536 5 0.669234 6 0.071976 7 0.132822 8 0.278325 9 0.655446 10 0.753893 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.586311 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-10_16:31: (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 66585 0.10 66864 0.58 3 25000.00 25032 0.04 24914 0.30 4 6666.67 6648 0.05 6565 1.55 5 1388.89 1430 1.22 1393 0.01 6 238.10 259 1.84 227 0.52 7 34.72 38 0.31 33 0.09 8 4.96 7 0.84 3 0.77 p=0.37654 p=0.29889 Number of rngs required: 688000, p-value: 0.321 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-10_16:31 No. of wins: Observed Expected 99257 98585.9 z-score= 3.002, pvalue=0.99866 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66807 66666.7 0.295 0.295 2 37427 37654.3 1.372 1.668 3 26960 26954.7 0.001 1.669 4 19336 19313.5 0.026 1.695 5 13879 13851.4 0.055 1.750 6 9956 9943.5 0.016 1.766 7 7062 7145.0 0.965 2.730 8 5166 5139.1 0.141 2.871 9 3714 3699.9 0.054 2.925 10 2658 2666.3 0.026 2.951 11 1958 1923.3 0.625 3.576 12 1383 1388.7 0.024 3.600 13 1035 1003.7 0.975 4.575 14 730 726.1 0.021 4.596 15 502 525.8 1.080 5.676 16 395 381.2 0.503 6.179 17 274 276.5 0.023 6.203 18 200 200.8 0.003 6.206 19 143 146.0 0.061 6.267 20 116 106.2 0.901 7.168 21 299 287.1 0.492 7.661 Chisq= 7.66 for 20 degrees of freedom, p= 0.00611 SUMMARY of craptest p-value for no. of wins: 0.998658 p-value for throws/game: 0.006114 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-10_16:31 No. of wins: Observed Expected 99007 98585.9 z-score= 1.884, pvalue=0.97019 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66510 66666.7 0.368 0.368 2 37856 37654.3 1.080 1.448 3 27107 26954.7 0.860 2.309 4 19319 19313.5 0.002 2.310 5 13898 13851.4 0.157 2.467 6 9856 9943.5 0.771 3.237 7 7185 7145.0 0.224 3.461 8 5117 5139.1 0.095 3.556 9 3677 3699.9 0.141 3.697 10 2684 2666.3 0.118 3.815 11 1780 1923.3 10.681 14.496 12 1376 1388.7 0.117 14.613 13 977 1003.7 0.711 15.324 14 708 726.1 0.453 15.777 15 547 525.8 0.852 16.629 16 374 381.2 0.134 16.763 17 274 276.5 0.023 16.786 18 211 200.8 0.515 17.301 19 151 146.0 0.172 17.474 20 104 106.2 0.046 17.520 21 289 287.1 0.012 17.532 Chisq= 17.53 for 20 degrees of freedom, p= 0.38181 SUMMARY of craptest p-value for no. of wins: 0.970190 p-value for throws/game: 0.381806 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0045,0.0057,0.0061,0.0131,0.0133,0.0216,0.0216,0.0278,0.0320,0.0361, 0.0364,0.0382,0.0414,0.0443,0.0517,0.0600,0.0720,0.0731,0.0735,0.0751, 0.0785,0.0863,0.0868,0.0906,0.0965,0.1004,0.1045,0.1097,0.1144,0.1155, 0.1162,0.1215,0.1241,0.1259,0.1297,0.1309,0.1313,0.1317,0.1328,0.1388, 0.1389,0.1426,0.1468,0.1500,0.1679,0.1701,0.1755,0.1782,0.1801,0.1822, 0.1858,0.1890,0.1907,0.1914,0.1928,0.1934,0.1940,0.2013,0.2160,0.2348, 0.2368,0.2371,0.2432,0.2458,0.2474,0.2475,0.2493,0.2613,0.2629,0.2630, 0.2694,0.2717,0.2781,0.2783,0.2852,0.2899,0.2919,0.2922,0.2969,0.2989, 0.3004,0.3018,0.3040,0.3171,0.3184,0.3212,0.3292,0.3379,0.3405,0.3449, 0.3558,0.3569,0.3574,0.3613,0.3632,0.3633,0.3707,0.3724,0.3732,0.3762, 0.3765,0.3789,0.3818,0.3835,0.3843,0.3853,0.3871,0.3882,0.3913,0.3942, 0.4019,0.4080,0.4113,0.4118,0.4169,0.4188,0.4192,0.4192,0.4283,0.4283, 0.4357,0.4379,0.4381,0.4456,0.4456,0.4456,0.4472,0.4483,0.4520,0.4538, 0.4546,0.4567,0.4582,0.4631,0.4693,0.4701,0.4703,0.4800,0.4818,0.4847, 0.4853,0.4968,0.5095,0.5182,0.5188,0.5189,0.5236,0.5279,0.5290,0.5293, 0.5314,0.5318,0.5337,0.5394,0.5421,0.5431,0.5490,0.5508,0.5571,0.5595, 0.5671,0.5741,0.5748,0.5762,0.5792,0.5835,0.5855,0.5863,0.5866,0.5872, 0.5877,0.5881,0.5907,0.5998,0.6053,0.6080,0.6117,0.6117,0.6151,0.6175, 0.6201,0.6240,0.6254,0.6254,0.6336,0.6435,0.6435,0.6446,0.6511,0.6525, 0.6554,0.6618,0.6692,0.6727,0.6852,0.6935,0.7083,0.7121,0.7125,0.7186, 0.7186,0.7189,0.7309,0.7433,0.7464,0.7486,0.7492,0.7539,0.7552,0.7568, 0.7600,0.7604,0.7658,0.7696,0.7836,0.7845,0.7926,0.8029,0.8061,0.8093, 0.8095,0.8173,0.8194,0.8208,0.8241,0.8247,0.8249,0.8251,0.8256,0.8330, 0.8382,0.8437,0.8515,0.8550,0.8562,0.8588,0.8625,0.8625,0.8643,0.8674, 0.8687,0.8766,0.8995,0.8999,0.9121,0.9184,0.9192,0.9225,0.9240,0.9318, 0.9325,0.9338,0.9345,0.9404,0.9422,0.9440,0.9469,0.9513,0.9542,0.9610, 0.9679,0.9702,0.9702,0.9745,0.9769,0.9859,0.9874,0.9885,0.9987, Overall p-value after applying KStest on 269 p-values = 0.632821 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.