RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-15_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 15.88 10.0231 0.097362 2 to 25 15.74 20.1410 0.732920 3 to 26 15.72 11.6315 0.178082 4 to 27 15.71 16.6215 0.519716 5 to 28 15.66 25.1503 0.908605 6 to 29 15.92 21.0295 0.775028 7 to 30 15.97 23.2224 0.857851 8 to 31 15.65 18.5012 0.642096 9 to 32 15.75 24.5253 0.894150 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.280130 Tough bday spacings test for dh-ranFile-2016-11-15_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 4 31 53 103 109 85 56 30 11 11 7 (O-E)^2/E 2.9 0.9 5.6 0.3 1.3 0.6 0.3 0.0 1.0 2.9 2.1 Birthday Spacings: Sum(O-E)^2/E= 17.907, p= 0.943 RESULTS OF GCD FOR dh-ranFile-2016-11-15_18:31 Euclid's algorithm: p-value, steps to gcd: 0.686203 p-value, dist. of gcd's: 0.753982 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-15_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.786 0.408 0.857 0.888 0.414 0.447 0.494 0.832 Bits 8 to 15---> 0.345 0.573 0.254 0.325 0.597 0.736 0.899 0.719 Bits 16 to 23---> 0.913 0.851 0.953 0.390 0.012 0.636 0.144 0.157 Bits 24 to 31---> 0.555 0.680 0.419 0.833 0.729 0.846 0.804 0.529 KS test for the above 32 p values: 0.922 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-15_18:31, p-values for 5 runs: 0.5996, 0.3601, 0.3961, 0.1661, 0.4711 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-15_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5154 5134.0 0.078 0.170 r= 30 23081 23103.0 0.021 0.191 r= 31 11558 11551.5 0.004 0.195 chi-square = 0.195 with df = 3; p-value = 0.022 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-15_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 235 211.4 2.630 2.630 r= 30 5177 5134.0 0.360 2.990 r= 31 23029 23103.0 0.237 3.228 r= 32 11559 11551.5 0.005 3.233 chi-square = 3.233 with df = 3; p-value = 0.643 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-15_18:31 b-rank test for bits 1 to 8, p=0.75502 b-rank test for bits 2 to 9, p=0.91743 b-rank test for bits 3 to 10, p=0.69087 b-rank test for bits 4 to 11, p=0.71531 b-rank test for bits 5 to 12, p=0.64872 b-rank test for bits 6 to 13, p=0.76382 b-rank test for bits 7 to 14, p=0.39913 b-rank test for bits 8 to 15, p=0.03891 b-rank test for bits 9 to 16, p=0.83605 b-rank test for bits 10 to 17, p=0.96411 b-rank test for bits 11 to 18, p=0.85627 b-rank test for bits 12 to 19, p=0.55006 b-rank test for bits 13 to 20, p=0.69430 b-rank test for bits 14 to 21, p=0.81490 b-rank test for bits 15 to 22, p=0.47583 b-rank test for bits 16 to 23, p=0.01387 b-rank test for bits 17 to 24, p=0.75659 b-rank test for bits 18 to 25, p=0.77689 b-rank test for bits 19 to 26, p=0.47519 b-rank test for bits 20 to 27, p=0.96518 b-rank test for bits 21 to 28, p=0.61776 b-rank test for bits 22 to 29, p=0.71793 b-rank test for bits 23 to 30, p=0.98233 b-rank test for bits 24 to 31, p=0.77012 b-rank test for bits 25 to 32, p=0.91261 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 = 0.001266 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-15_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 142314 0.95 0.827796 2 142159 0.58 0.720168 3 142330 0.98 0.837165 4 141856 -0.12 0.450419 5 142316 0.95 0.828985 6 141783 -0.30 0.383935 7 141368 -1.26 0.102973 8 141823 -0.20 0.420073 9 141763 -0.34 0.366216 10 142650 1.73 0.958233 11 141865 -0.10 0.458753 12 141636 -0.64 0.261535 13 141614 -0.69 0.245090 14 141670 -0.56 0.288019 15 142389 1.12 0.868797 16 141888 -0.05 0.480126 17 141983 0.17 0.568331 18 141411 -1.16 0.122147 19 141668 -0.56 0.286426 20 143286 3.22 0.999351 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-15_18:31 Bits used No. missing words z-score p-value 23 to 32 141645 -0.9115 0.181021 22 to 31 142153 0.8402 0.799614 21 to 30 141653 -0.8839 0.188376 20 to 29 141914 0.0161 0.506424 19 to 28 141989 0.2747 0.608236 18 to 27 141934 0.0851 0.533897 17 to 26 141721 -0.6494 0.258036 16 to 25 141591 -1.0977 0.136170 15 to 24 142026 0.4023 0.656272 14 to 23 142019 0.3782 0.647349 13 to 22 141755 -0.5322 0.297303 12 to 21 141393 -1.7804 0.037501 11 to 20 141589 -1.1046 0.134669 10 to 19 142062 0.5264 0.700712 9 to 18 141597 -1.0770 0.140740 8 to 17 141728 -0.6253 0.265895 7 to 16 142137 0.7851 0.783793 6 to 15 141721 -0.6494 0.258036 5 to 14 141789 -0.4149 0.339096 4 to 13 142071 0.5575 0.711401 3 to 12 141880 -0.1011 0.459721 2 to 11 142312 1.3885 0.917510 1 to 10 141896 -0.0460 0.481669 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-15_18:31 Bits used No. missing words z-score p-value 28 to 32 142155 0.8328 0.797516 27 to 31 141410 -1.6926 0.045262 26 to 30 142294 1.3040 0.903877 25 to 29 142298 1.3175 0.906169 24 to 28 141777 -0.4486 0.326869 23 to 27 142033 0.4192 0.662473 22 to 26 141707 -0.6859 0.246399 21 to 25 142461 1.8701 0.969263 20 to 24 141762 -0.4994 0.308741 19 to 23 141685 -0.7604 0.223496 18 to 22 141937 0.0938 0.537365 17 to 21 141523 -1.3096 0.095167 16 to 20 141429 -1.6282 0.051737 15 to 19 142000 0.3074 0.620714 14 to 18 141829 -0.2723 0.392694 13 to 17 141856 -0.1808 0.428270 12 to 16 142004 0.3209 0.625863 11 to 15 141942 0.1107 0.544091 10 to 14 141964 0.1853 0.573512 9 to 13 141772 -0.4655 0.320778 8 to 12 142152 0.8226 0.794635 7 to 11 142320 1.3921 0.918054 6 to 10 142218 1.0463 0.852298 5 to 9 142152 0.8226 0.794635 4 to 8 142204 0.9989 0.841074 3 to 7 141941 0.1074 0.542747 2 to 6 141830 -0.2689 0.393998 1 to 5 142027 0.3989 0.655010 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-15_18:31 Bits used No. missing words z-score p-value 31 to 32 141550 -1.0600 0.144579 30 to 31 142307 1.1731 0.879616 29 to 30 141883 -0.0777 0.469045 28 to 29 142456 1.6126 0.946584 27 to 28 141548 -1.0659 0.143241 26 to 27 141869 -0.1190 0.452651 25 to 26 141730 -0.5290 0.298404 24 to 25 142255 1.0197 0.846059 23 to 24 141627 -0.8328 0.202470 22 to 23 142146 0.6981 0.757456 21 to 22 141796 -0.3343 0.369074 20 to 21 141526 -1.1308 0.129077 19 to 20 141995 0.2527 0.599755 18 to 19 140997 -2.6912 0.003559 17 to 18 142331 1.2439 0.893225 16 to 17 141828 -0.2399 0.405199 15 to 16 141673 -0.6971 0.242858 14 to 15 142110 0.5919 0.723057 13 to 14 140932 -2.8830 0.001970 12 to 13 141671 -0.7030 0.241016 11 to 12 142174 0.7807 0.782522 10 to 11 141863 -0.1367 0.445647 9 to 10 141977 0.1996 0.579110 8 to 9 141728 -0.5349 0.296361 7 to 8 142283 1.1023 0.864828 6 to 7 142676 2.2616 0.988138 5 to 6 142006 0.2852 0.612240 4 to 5 141555 -1.0452 0.147960 3 to 4 142423 1.5153 0.935146 2 to 3 141950 0.1200 0.547747 1 to 2 142503 1.7512 0.960048 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-15_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2620.15 1.699 0.955359 Test results for specific bytes for dh-ranFile-2016-11-15_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2482.28 -0.251 0.401081 2 to 9 2571.90 1.017 0.845397 3 to 10 2645.17 2.053 0.979967 4 to 11 2524.97 0.353 0.638017 5 to 12 2486.50 -0.191 0.424287 6 to 13 2393.70 -1.503 0.066387 7 to 14 2519.19 0.271 0.606959 8 to 15 2446.87 -0.751 0.226197 9 to 16 2575.22 1.064 0.856283 10 to 17 2508.34 0.118 0.546929 11 to 18 2479.68 -0.287 0.386899 12 to 19 2546.43 0.657 0.744291 13 to 20 2346.62 -2.169 0.015038 14 to 21 2572.19 1.021 0.846340 15 to 22 2526.42 0.374 0.645672 16 to 23 2417.75 -1.163 0.122388 17 to 24 2597.35 1.377 0.915700 18 to 25 2419.28 -1.142 0.126807 19 to 26 2431.10 -0.974 0.164923 20 to 27 2323.05 -2.502 0.006168 21 to 28 2541.51 0.587 0.721393 22 to 29 2347.52 -2.156 0.015525 23 to 30 2421.38 -1.112 0.133091 24 to 31 2420.69 -1.122 0.131005 25 to 32 2490.67 -0.132 0.447492 CDPARK for dh-ranFile-2016-11-15_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 3507 -0.7306 0.232514 3515 -0.3653 0.357445 3541 0.8219 0.794438 3517 -0.2740 0.392053 3533 0.4566 0.676028 3517 -0.2740 0.392053 3539 0.7306 0.767486 3528 0.2283 0.590298 3552 1.3242 0.907282 3499 -1.0959 0.136563 Square side=100, avg. no. parked=3524.80 sample std.=15.75 p-value of the KSTEST for those 10 p-values: 0.912527 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-15_18:31 0.3764,0.9394,0.7587,0.7957,0.2232,0.3115,0.1298,0.0010,0.8909,0.9249, The KS test for those 10 p-values: 0.385078 The 3DSPHERES test for dh-ranFile-2016-11-15_18:31 sample no r^3 equiv. uni. 1 5.664 0.172041 2 2.268 0.072806 3 28.520 0.613511 4 21.502 0.511654 5 31.374 0.648589 6 2.115 0.068079 7 5.625 0.170969 8 0.999 0.032744 9 31.284 0.647537 10 6.041 0.182392 11 21.949 0.518874 12 2.296 0.073683 13 44.869 0.775890 14 29.105 0.620974 15 49.621 0.808724 16 18.271 0.456118 17 8.105 0.236736 18 32.555 0.662156 19 69.250 0.900572 20 120.581 0.982035 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.600852 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-15_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -2.0 1.5 -0.3 -0.6 -0.5 0.9 0.8 0.0 0.3 -1.0 -0.1 -0.8 1.6 -0.7 -1.1 -0.4 -0.0 0.6 -0.7 1.1 0.0 0.6 3.3 -1.4 -1.3 -0.0 -0.5 -1.6 0.1 -0.2 0.8 0.5 -0.1 0.8 -1.4 0.7 -1.0 0.1 -0.1 1.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:43.668895 z-score=0.182091, p-value=0.599602 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-15_18:31 Test no p-value 1 0.140835 2 0.063313 3 0.292772 4 0.067028 5 0.145593 6 0.457244 7 0.898811 8 0.807008 9 0.398314 10 0.483534 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.266799 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-15_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 66457 0.66 66683 0.00 3 25000.00 25115 0.53 24866 0.72 4 6666.67 6777 1.83 6772 1.66 5 1388.89 1390 0.00 1387 0.00 6 238.10 226 0.61 245 0.20 7 34.72 28 1.30 41 1.14 8 4.96 6 0.22 5 0.00 p=0.47507 p=0.28623 Number of rngs required: 691089, p-value: 0.999 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-15_18:31 No. of wins: Observed Expected 98201 98585.9 z-score=-1.721, pvalue=0.04260 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66499 66666.7 0.422 0.422 2 37599 37654.3 0.081 0.503 3 26873 26954.7 0.248 0.751 4 19515 19313.5 2.103 2.854 5 13835 13851.4 0.019 2.873 6 9997 9943.5 0.287 3.161 7 7210 7145.0 0.591 3.752 8 5229 5139.1 1.574 5.325 9 3679 3699.9 0.118 5.443 10 2695 2666.3 0.309 5.752 11 1846 1923.3 3.109 8.861 12 1383 1388.7 0.024 8.885 13 1003 1003.7 0.001 8.885 14 717 726.1 0.115 9.000 15 512 525.8 0.364 9.364 16 368 381.2 0.454 9.818 17 273 276.5 0.045 9.863 18 209 200.8 0.332 10.196 19 155 146.0 0.557 10.752 20 114 106.2 0.571 11.323 21 289 287.1 0.012 11.335 Chisq= 11.34 for 20 degrees of freedom, p= 0.06294 SUMMARY of craptest p-value for no. of wins: 0.042597 p-value for throws/game: 0.062944 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-15_18:31 No. of wins: Observed Expected 98607 98585.9 z-score= 0.095, pvalue=0.53767 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66776 66666.7 0.179 0.179 2 37657 37654.3 0.000 0.179 3 26702 26954.7 2.370 2.549 4 19294 19313.5 0.020 2.569 5 13993 13851.4 1.447 4.016 6 9805 9943.5 1.930 5.946 7 7181 7145.0 0.181 6.127 8 5144 5139.1 0.005 6.132 9 3726 3699.9 0.185 6.317 10 2627 2666.3 0.579 6.896 11 1933 1923.3 0.049 6.945 12 1413 1388.7 0.424 7.368 13 1003 1003.7 0.001 7.369 14 741 726.1 0.304 7.673 15 587 525.8 7.114 14.787 16 404 381.2 1.370 16.157 17 297 276.5 1.514 17.671 18 175 200.8 3.322 20.993 19 148 146.0 0.028 21.021 20 108 106.2 0.030 21.051 21 286 287.1 0.004 21.055 Chisq= 21.06 for 20 degrees of freedom, p= 0.60611 SUMMARY of craptest p-value for no. of wins: 0.537667 p-value for throws/game: 0.606113 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0013,0.0020,0.0036,0.0062,0.0117,0.0139,0.0150,0.0155,0.0216, 0.0327,0.0375,0.0389,0.0426,0.0453,0.0517,0.0629,0.0633,0.0664,0.0670, 0.0681,0.0728,0.0737,0.0952,0.0974,0.1030,0.1221,0.1224,0.1268,0.1291, 0.1298,0.1310,0.1331,0.1347,0.1362,0.1366,0.1407,0.1408,0.1432,0.1439, 0.1446,0.1456,0.1480,0.1573,0.1649,0.1661,0.1710,0.1720,0.1781,0.1810, 0.1824,0.1884,0.2025,0.2232,0.2235,0.2262,0.2325,0.2367,0.2410,0.2429, 0.2451,0.2464,0.2537,0.2580,0.2580,0.2615,0.2659,0.2668,0.2801,0.2862, 0.2864,0.2880,0.2928,0.2964,0.2973,0.2984,0.3087,0.3115,0.3208,0.3251, 0.3269,0.3391,0.3450,0.3574,0.3601,0.3662,0.3691,0.3764,0.3839,0.3851, 0.3869,0.3901,0.3921,0.3921,0.3927,0.3940,0.3961,0.3983,0.3991,0.4011, 0.4052,0.4076,0.4145,0.4187,0.4201,0.4243,0.4283,0.4456,0.4474,0.4475, 0.4504,0.4527,0.4561,0.4572,0.4588,0.4597,0.4690,0.4711,0.4751,0.4752, 0.4758,0.4801,0.4817,0.4835,0.4941,0.5064,0.5117,0.5189,0.5197,0.5289, 0.5339,0.5374,0.5377,0.5427,0.5441,0.5469,0.5477,0.5501,0.5550,0.5683, 0.5732,0.5735,0.5791,0.5903,0.5972,0.5996,0.5996,0.5998,0.6009,0.6061, 0.6070,0.6082,0.6122,0.6135,0.6178,0.6207,0.6210,0.6259,0.6359,0.6380, 0.6421,0.6429,0.6457,0.6473,0.6475,0.6486,0.6487,0.6550,0.6563,0.6622, 0.6625,0.6760,0.6796,0.6862,0.6909,0.6943,0.7007,0.7114,0.7153,0.7179, 0.7187,0.7202,0.7214,0.7231,0.7289,0.7329,0.7363,0.7443,0.7540,0.7550, 0.7566,0.7575,0.7587,0.7638,0.7675,0.7701,0.7750,0.7759,0.7769,0.7825, 0.7838,0.7858,0.7944,0.7946,0.7946,0.7957,0.7975,0.7996,0.8041,0.8070, 0.8087,0.8149,0.8278,0.8290,0.8322,0.8329,0.8360,0.8372,0.8411,0.8454, 0.8461,0.8461,0.8463,0.8515,0.8523,0.8563,0.8563,0.8571,0.8579,0.8648, 0.8688,0.8796,0.8880,0.8909,0.8932,0.8941,0.8988,0.8989,0.9006,0.9039, 0.9062,0.9073,0.9086,0.9125,0.9126,0.9132,0.9157,0.9174,0.9175,0.9181, 0.9223,0.9249,0.9351,0.9394,0.9434,0.9466,0.9532,0.9554,0.9582,0.9600, 0.9641,0.9652,0.9693,0.9800,0.9820,0.9823,0.9881,0.9994,0.9994, Overall p-value after applying KStest on 269 p-values = 0.207231 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.