RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-16_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 18.7871 0.659109 2 to 25 15.85 30.8611 0.979237 3 to 26 15.59 26.6026 0.935841 4 to 27 15.78 22.6511 0.839043 5 to 28 15.83 11.1313 0.150340 6 to 29 16.08 14.2862 0.353249 7 to 30 16.03 17.4257 0.574095 8 to 31 15.75 18.6107 0.648673 9 to 32 15.58 27.8143 0.952845 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.084483 Tough bday spacings test for dh-ranFile-2016-09-16_02:31: 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 12 37 67 101 90 93 49 29 12 6 4 (O-E)^2/E 0.9 0.0 0.5 0.1 0.6 2.8 0.2 0.0 0.6 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.783, p= 0.167 RESULTS OF GCD FOR dh-ranFile-2016-09-16_02:31 Euclid's algorithm: p-value, steps to gcd: 0.272547 p-value, dist. of gcd's: 0.741831 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-16_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.465 0.467 0.642 0.523 0.086 0.228 0.862 0.716 Bits 8 to 15---> 0.439 0.407 0.972 0.098 0.454 0.847 0.977 0.004 Bits 16 to 23---> 0.229 0.702 0.418 0.205 0.172 0.646 0.413 0.990 Bits 24 to 31---> 0.470 0.565 0.628 0.054 0.497 0.199 0.885 0.538 KS test for the above 32 p values: 0.220 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-16_02:31, p-values for 5 runs: 0.4657, 0.5603, 0.1989, 0.5572, 0.0583 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-16_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5125 5134.0 0.016 1.316 r= 30 23073 23103.0 0.039 1.355 r= 31 11574 11551.5 0.044 1.399 chi-square = 1.399 with df = 3; p-value = 0.294 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-16_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5237 5134.0 2.066 3.528 r= 31 23292 23103.0 1.545 5.074 r= 32 11242 11551.5 8.294 13.367 chi-square = 13.367 with df = 3; p-value = 0.996 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-16_02:31 b-rank test for bits 1 to 8, p=0.03976 b-rank test for bits 2 to 9, p=0.62301 b-rank test for bits 3 to 10, p=0.70925 b-rank test for bits 4 to 11, p=0.24782 b-rank test for bits 5 to 12, p=0.69222 b-rank test for bits 6 to 13, p=0.83967 b-rank test for bits 7 to 14, p=0.16668 b-rank test for bits 8 to 15, p=0.03742 b-rank test for bits 9 to 16, p=0.76409 b-rank test for bits 10 to 17, p=0.11847 b-rank test for bits 11 to 18, p=0.12464 b-rank test for bits 12 to 19, p=0.60052 b-rank test for bits 13 to 20, p=0.85331 b-rank test for bits 14 to 21, p=0.70874 b-rank test for bits 15 to 22, p=0.15521 b-rank test for bits 16 to 23, p=0.52174 b-rank test for bits 17 to 24, p=0.93871 b-rank test for bits 18 to 25, p=0.79795 b-rank test for bits 19 to 26, p=0.73386 b-rank test for bits 20 to 27, p=0.69284 b-rank test for bits 21 to 28, p=0.09818 b-rank test for bits 22 to 29, p=0.37448 b-rank test for bits 23 to 30, p=0.63293 b-rank test for bits 24 to 31, p=0.53530 b-rank test for bits 25 to 32, p=0.26293 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 = 0.654307 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-16_02:31 (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 141083 -1.93 0.026761 2 141825 -0.20 0.421901 3 142941 2.41 0.992033 4 141845 -0.15 0.440263 5 142551 1.50 0.933093 6 142113 0.48 0.682915 7 141401 -1.19 0.117478 8 142229 0.75 0.772436 9 141807 -0.24 0.405518 10 141884 -0.06 0.476404 11 142441 1.24 0.892922 12 141655 -0.59 0.276180 13 141756 -0.36 0.360079 14 141936 0.06 0.524843 15 142039 0.30 0.619043 16 142372 1.08 0.860153 17 141582 -0.76 0.222198 18 141694 -0.50 0.307444 19 141629 -0.65 0.256241 20 141800 -0.26 0.399190 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-16_02:31 Bits used No. missing words z-score p-value 23 to 32 142353 1.5299 0.936979 22 to 31 142460 1.8989 0.971209 21 to 30 141971 0.2127 0.584202 20 to 29 141705 -0.7046 0.240534 19 to 28 142523 2.1161 0.982832 18 to 27 142309 1.3782 0.915925 17 to 26 141792 -0.4046 0.342891 16 to 25 141970 0.2092 0.582857 15 to 24 141827 -0.2839 0.388245 14 to 23 142112 0.6989 0.757681 13 to 22 141762 -0.5080 0.305715 12 to 21 141399 -1.7598 0.039224 11 to 20 142270 1.2437 0.893193 10 to 19 141720 -0.6529 0.256923 9 to 18 141714 -0.6736 0.250298 8 to 17 142202 1.0092 0.843562 7 to 16 141795 -0.3942 0.346701 6 to 15 142187 0.9575 0.830838 5 to 14 141648 -0.9011 0.183758 4 to 13 142019 0.3782 0.647349 3 to 12 141676 -0.8046 0.210529 2 to 11 141621 -0.9942 0.160053 1 to 10 142072 0.5609 0.712578 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-16_02:31 Bits used No. missing words z-score p-value 28 to 32 141909 -0.0011 0.499554 27 to 31 142398 1.6565 0.951191 26 to 30 141675 -0.7943 0.213499 25 to 29 142013 0.3514 0.637365 24 to 28 141269 -2.1706 0.014980 23 to 27 142212 1.0260 0.847554 22 to 26 142304 1.3379 0.909530 21 to 25 141610 -1.0147 0.155130 20 to 24 142045 0.4599 0.677205 19 to 23 141379 -1.7977 0.036110 18 to 22 141602 -1.0418 0.148753 17 to 21 142027 0.3989 0.655010 16 to 20 142018 0.3684 0.643702 15 to 19 141670 -0.8113 0.208600 14 to 18 141975 0.2226 0.588081 13 to 17 142423 1.7413 0.959181 12 to 16 142256 1.1752 0.880033 11 to 15 142102 0.6531 0.743160 10 to 14 141735 -0.5909 0.277277 9 to 13 142180 0.9175 0.820566 8 to 12 142003 0.3175 0.624578 7 to 11 142290 1.2904 0.901545 6 to 10 142411 1.7006 0.955489 5 to 9 141429 -1.6282 0.051737 4 to 8 141897 -0.0418 0.483330 3 to 7 142266 1.2091 0.886678 2 to 6 142589 2.3040 0.989388 1 to 5 141726 -0.6215 0.267149 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-16_02:31 Bits used No. missing words z-score p-value 31 to 32 141790 -0.3520 0.362417 30 to 31 142295 1.1377 0.872371 29 to 30 142200 0.8574 0.804397 28 to 29 142027 0.3471 0.635745 27 to 28 142019 0.3235 0.626846 26 to 27 141648 -0.7709 0.220388 25 to 26 141831 -0.2311 0.408633 24 to 25 142110 0.5919 0.723057 23 to 24 141509 -1.1809 0.118818 22 to 23 141599 -0.9154 0.179984 21 to 22 141823 -0.2547 0.399493 20 to 21 141727 -0.5378 0.295342 19 to 20 142044 0.3973 0.654411 18 to 19 141398 -1.5083 0.065733 17 to 18 141720 -0.5585 0.288253 16 to 17 142581 1.9813 0.976223 15 to 16 141422 -1.4376 0.075281 14 to 15 141779 -0.3845 0.350321 13 to 14 141921 0.0344 0.513731 12 to 13 141623 -0.8446 0.199158 11 to 12 141968 0.1731 0.568701 10 to 11 142092 0.5388 0.705005 9 to 10 141775 -0.3963 0.345959 8 to 9 141790 -0.3520 0.362417 7 to 8 141848 -0.1809 0.428217 6 to 7 142337 1.2616 0.896447 5 to 6 141750 -0.4700 0.319178 4 to 5 142009 0.2940 0.615626 3 to 4 141682 -0.6706 0.251241 2 to 3 142382 1.3943 0.918388 1 to 2 142895 2.9076 0.998179 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-16_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2524.31 0.344 0.634526 Test results for specific bytes for dh-ranFile-2016-09-16_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2473.98 -0.368 0.356448 2 to 9 2503.98 0.056 0.522437 3 to 10 2567.28 0.952 0.829337 4 to 11 2523.37 0.331 0.629516 5 to 12 2647.70 2.089 0.981635 6 to 13 2482.67 -0.245 0.403218 7 to 14 2426.47 -1.040 0.149210 8 to 15 2485.45 -0.206 0.418472 9 to 16 2463.89 -0.511 0.304795 10 to 17 2475.57 -0.345 0.364870 11 to 18 2408.93 -1.288 0.098883 12 to 19 2456.98 -0.608 0.271476 13 to 20 2471.18 -0.408 0.341797 14 to 21 2533.87 0.479 0.684046 15 to 22 2528.13 0.398 0.654600 16 to 23 2551.12 0.723 0.765130 17 to 24 2598.13 1.388 0.917391 18 to 25 2419.03 -1.145 0.126083 19 to 26 2487.88 -0.171 0.431972 20 to 27 2473.91 -0.369 0.356090 21 to 28 2453.72 -0.654 0.256406 22 to 29 2596.33 1.362 0.913441 23 to 30 2543.48 0.615 0.730712 24 to 31 2474.37 -0.362 0.358498 25 to 32 2497.62 -0.034 0.486564 CDPARK for dh-ranFile-2016-09-16_02:31: 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 3504 -0.8676 0.192812 3519 -0.1826 0.427537 3559 1.6438 0.949895 3549 1.1872 0.882429 3515 -0.3653 0.357445 3547 1.0959 0.863437 3510 -0.5936 0.276387 3533 0.4566 0.676028 3546 1.0502 0.853193 3535 0.5479 0.708135 Square side=100, avg. no. parked=3531.70 sample std.=17.82 p-value of the KSTEST for those 10 p-values: 0.307697 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-16_02:31 0.9999,0.6851,0.4094,0.3194,0.5066,0.2580,0.0997,0.3273,0.5651,0.5024, The KS test for those 10 p-values: 0.283173 The 3DSPHERES test for dh-ranFile-2016-09-16_02:31 sample no r^3 equiv. uni. 1 9.902 0.281133 2 19.039 0.469879 3 14.036 0.373659 4 26.719 0.589604 5 19.134 0.471541 6 19.896 0.484800 7 21.127 0.505520 8 24.518 0.558365 9 40.758 0.742980 10 33.667 0.674446 11 0.468 0.015481 12 16.818 0.429130 13 16.156 0.416387 14 19.117 0.471250 15 18.448 0.459332 16 43.099 0.762274 17 18.047 0.452041 18 38.681 0.724555 19 118.566 0.980788 20 6.988 0.207795 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.172267 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-16_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 1.5 -1.3 -0.7 2.1 0.7 -1.5 0.2 0.7 -1.3 1.0 -1.1 -1.5 -0.1 0.3 0.4 1.3 -1.1 -0.6 0.3 0.4 -1.8 1.4 -0.0 0.0 1.4 2.3 0.2 -1.0 0.7 -0.5 -1.1 1.3 1.2 1.0 0.0 -1.3 -0.4 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:43.911342 z-score=0.208545, p-value=0.609499 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-16_02:31 Test no p-value 1 0.438605 2 0.424173 3 0.028380 4 0.033522 5 0.001331 6 0.112621 7 0.512807 8 0.961827 9 0.263740 10 0.134944 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.012280 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-16_02:31: (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 66452 0.69 66422 0.90 3 25000.00 25236 2.23 25186 1.38 4 6666.67 6652 0.03 6755 1.17 5 1388.89 1370 0.26 1345 1.39 6 238.10 253 0.93 252 0.81 7 34.72 30 0.64 35 0.00 8 4.96 6 0.22 4 0.19 p=0.45632 p=0.55856 Number of rngs required: 687885, p-value: 0.275 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-16_02:31 No. of wins: Observed Expected 98505 98585.9 z-score=-0.362, pvalue=0.35881 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66571 66666.7 0.137 0.137 2 37593 37654.3 0.100 0.237 3 26966 26954.7 0.005 0.242 4 19247 19313.5 0.229 0.471 5 13967 13851.4 0.964 1.435 6 9881 9943.5 0.393 1.828 7 7207 7145.0 0.538 2.366 8 5214 5139.1 1.092 3.458 9 3744 3699.9 0.526 3.985 10 2660 2666.3 0.015 4.000 11 1936 1923.3 0.083 4.083 12 1402 1388.7 0.127 4.210 13 1014 1003.7 0.105 4.315 14 687 726.1 2.110 6.425 15 557 525.8 1.847 8.272 16 382 381.2 0.002 8.274 17 259 276.5 1.112 9.386 18 202 200.8 0.007 9.393 19 136 146.0 0.683 10.076 20 99 106.2 0.490 10.566 21 276 287.1 0.430 10.996 Chisq= 11.00 for 20 degrees of freedom, p= 0.05368 SUMMARY of craptest p-value for no. of wins: 0.358808 p-value for throws/game: 0.053682 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-16_02:31 No. of wins: Observed Expected 98531 98585.9 z-score=-0.245, pvalue=0.40309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66011 66666.7 6.448 6.448 2 37799 37654.3 0.556 7.004 3 27160 26954.7 1.563 8.568 4 19470 19313.5 1.269 9.836 5 13955 13851.4 0.775 10.611 6 9911 9943.5 0.107 10.717 7 7183 7145.0 0.202 10.919 8 5146 5139.1 0.009 10.929 9 3724 3699.9 0.157 11.086 10 2748 2666.3 2.504 13.590 11 1937 1923.3 0.097 13.687 12 1294 1388.7 6.463 20.150 13 1033 1003.7 0.854 21.004 14 742 726.1 0.346 21.351 15 515 525.8 0.223 21.574 16 369 381.2 0.387 21.961 17 295 276.5 1.232 23.194 18 195 200.8 0.169 23.363 19 143 146.0 0.061 23.424 20 107 106.2 0.006 23.430 21 263 287.1 2.025 25.455 Chisq= 25.46 for 20 degrees of freedom, p= 0.81543 SUMMARY of craptest p-value for no. of wins: 0.403089 p-value for throws/game: 0.815428 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0037,0.0123,0.0150,0.0155,0.0268,0.0284,0.0335,0.0361,0.0374, 0.0392,0.0398,0.0517,0.0537,0.0543,0.0583,0.0657,0.0753,0.0845,0.0862, 0.0982,0.0985,0.0989,0.0997,0.1126,0.1175,0.1185,0.1188,0.1246,0.1261, 0.1349,0.1488,0.1492,0.1503,0.1551,0.1552,0.1601,0.1667,0.1668,0.1721, 0.1723,0.1800,0.1838,0.1928,0.1989,0.1990,0.1992,0.2050,0.2078,0.2086, 0.2105,0.2135,0.2202,0.2204,0.2222,0.2278,0.2293,0.2405,0.2478,0.2503, 0.2512,0.2562,0.2564,0.2569,0.2580,0.2629,0.2637,0.2671,0.2715,0.2725, 0.2751,0.2762,0.2764,0.2773,0.2811,0.2832,0.2883,0.2943,0.2953,0.3048, 0.3057,0.3074,0.3077,0.3192,0.3194,0.3273,0.3418,0.3429,0.3460,0.3467, 0.3503,0.3532,0.3561,0.3564,0.3574,0.3585,0.3588,0.3601,0.3624,0.3624, 0.3649,0.3737,0.3745,0.3882,0.3992,0.3995,0.4031,0.4032,0.4055,0.4073, 0.4086,0.4094,0.4132,0.4164,0.4185,0.4185,0.4219,0.4242,0.4275,0.4282, 0.4291,0.4320,0.4386,0.4390,0.4403,0.4520,0.4542,0.4563,0.4593,0.4646, 0.4657,0.4674,0.4698,0.4699,0.4712,0.4715,0.4764,0.4833,0.4848,0.4866, 0.4972,0.4996,0.5024,0.5055,0.5066,0.5128,0.5137,0.5217,0.5224,0.5233, 0.5248,0.5353,0.5381,0.5572,0.5584,0.5586,0.5603,0.5647,0.5651,0.5687, 0.5741,0.5829,0.5842,0.5881,0.5896,0.6005,0.6095,0.6156,0.6190,0.6230, 0.6246,0.6268,0.6284,0.6295,0.6329,0.6345,0.6357,0.6374,0.6417,0.6437, 0.6464,0.6473,0.6487,0.6543,0.6544,0.6546,0.6550,0.6591,0.6744,0.6760, 0.6772,0.6829,0.6840,0.6851,0.6922,0.6928,0.7016,0.7050,0.7081,0.7087, 0.7092,0.7126,0.7164,0.7231,0.7246,0.7307,0.7339,0.7418,0.7430,0.7432, 0.7577,0.7623,0.7641,0.7651,0.7724,0.7980,0.8044,0.8154,0.8206,0.8293, 0.8308,0.8390,0.8397,0.8436,0.8472,0.8476,0.8532,0.8533,0.8602,0.8616, 0.8634,0.8724,0.8800,0.8824,0.8853,0.8867,0.8929,0.8932,0.8964,0.9015, 0.9095,0.9134,0.9159,0.9174,0.9184,0.9331,0.9358,0.9370,0.9387,0.9499, 0.9512,0.9528,0.9555,0.9592,0.9618,0.9712,0.9721,0.9762,0.9773,0.9792, 0.9808,0.9816,0.9828,0.9894,0.9902,0.9920,0.9961,0.9982,0.9999, Overall p-value after applying KStest on 269 p-values = 0.533614 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.