RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-15_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 15.77 20.2519 0.738451 2 to 25 15.60 24.4369 0.891959 3 to 26 15.72 18.4669 0.640026 4 to 27 15.98 14.5079 0.369118 5 to 28 15.80 31.4835 0.982569 6 to 29 15.53 19.4216 0.695124 7 to 30 15.61 23.5200 0.866926 8 to 31 15.85 9.0098 0.060045 9 to 32 15.61 13.8548 0.322650 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.368871 Tough bday spacings test for dh-ranFile-2015-11-15_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 14 36 75 85 103 88 51 28 9 3 8 (O-E)^2/E 2.6 0.0 0.0 1.6 0.3 1.2 0.0 0.1 2.3 2.0 3.8 Birthday Spacings: Sum(O-E)^2/E= 14.028, p= 0.828 RESULTS OF GCD FOR dh-ranFile-2015-11-15_18:31 Euclid's algorithm: p-value, steps to gcd: 0.252534 p-value, dist. of gcd's: 0.023406 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-15_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.521 0.340 0.419 0.879 0.470 0.306 0.092 0.655 Bits 8 to 15---> 0.062 0.646 0.655 0.849 0.664 0.741 0.872 0.916 Bits 16 to 23---> 0.121 0.590 0.033 0.466 0.196 0.642 0.490 0.417 Bits 24 to 31---> 0.205 0.807 0.809 0.957 0.246 0.033 0.554 0.005 KS test for the above 32 p values: 0.082 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-15_18:31, p-values for 5 runs: 0.7728, 0.4552, 0.9359, 0.8004, 0.7597 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-15_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5233 5134.0 1.909 3.513 r= 30 23012 23103.0 0.359 3.872 r= 31 11562 11551.5 0.010 3.881 chi-square = 3.881 with df = 3; p-value = 0.725 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-15_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5146 5134.0 0.028 0.288 r= 31 23302 23103.0 1.713 2.002 r= 32 11348 11551.5 3.586 5.587 chi-square = 5.587 with df = 3; p-value = 0.866 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-15_18:31 b-rank test for bits 1 to 8, p=0.15853 b-rank test for bits 2 to 9, p=0.74052 b-rank test for bits 3 to 10, p=0.78672 b-rank test for bits 4 to 11, p=0.95002 b-rank test for bits 5 to 12, p=0.05204 b-rank test for bits 6 to 13, p=0.19728 b-rank test for bits 7 to 14, p=0.65180 b-rank test for bits 8 to 15, p=0.44003 b-rank test for bits 9 to 16, p=0.78477 b-rank test for bits 10 to 17, p=0.31581 b-rank test for bits 11 to 18, p=0.77814 b-rank test for bits 12 to 19, p=0.86451 b-rank test for bits 13 to 20, p=0.28940 b-rank test for bits 14 to 21, p=0.80067 b-rank test for bits 15 to 22, p=0.70927 b-rank test for bits 16 to 23, p=0.12345 b-rank test for bits 17 to 24, p=0.00961 b-rank test for bits 18 to 25, p=0.04845 b-rank test for bits 19 to 26, p=0.56488 b-rank test for bits 20 to 27, p=0.33701 b-rank test for bits 21 to 28, p=0.16204 b-rank test for bits 22 to 29, p=0.53878 b-rank test for bits 23 to 30, p=0.39606 b-rank test for bits 24 to 31, p=0.34379 b-rank test for bits 25 to 32, p=0.18844 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 = 0.623734 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-15_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 142107 0.46 0.677904 2 142208 0.70 0.757357 3 141607 -0.71 0.239976 4 141518 -0.91 0.180274 5 141730 -0.42 0.337610 6 141807 -0.24 0.405518 7 142055 0.34 0.633204 8 142033 0.29 0.613690 9 141787 -0.29 0.387509 10 141965 0.13 0.551745 11 141248 -1.55 0.061153 12 141952 0.10 0.539707 13 141602 -0.72 0.236360 14 141444 -1.09 0.138470 15 141277 -1.48 0.069783 16 141496 -0.97 0.167091 17 141216 -1.62 0.052624 18 141399 -1.19 0.116560 19 141704 -0.48 0.315705 20 141098 -1.90 0.029004 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-15_18:31 Bits used No. missing words z-score p-value 23 to 32 142611 2.4196 0.992230 22 to 31 141779 -0.4494 0.326567 21 to 30 141486 -1.4598 0.072178 20 to 29 142139 0.7920 0.785810 19 to 28 142187 0.9575 0.830838 18 to 27 141712 -0.6804 0.248110 17 to 26 141656 -0.8736 0.191181 16 to 25 141765 -0.4977 0.309351 15 to 24 141423 -1.6770 0.046771 14 to 23 141709 -0.6908 0.244848 13 to 22 142255 1.1920 0.883363 12 to 21 142130 0.7609 0.776651 11 to 20 142188 0.9609 0.831707 10 to 19 141726 -0.6322 0.263637 9 to 18 141549 -1.2425 0.107023 8 to 17 141845 -0.2218 0.412224 7 to 16 142111 0.6954 0.756602 6 to 15 141597 -1.0770 0.140740 5 to 14 141311 -2.0632 0.019546 4 to 13 141228 -2.3494 0.009402 3 to 12 141922 0.0437 0.517424 2 to 11 142094 0.6368 0.737870 1 to 10 141890 -0.0667 0.473428 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-15_18:31 Bits used No. missing words z-score p-value 28 to 32 141882 -0.0926 0.463093 27 to 31 142203 0.9955 0.840251 26 to 30 141622 -0.9740 0.165028 25 to 29 142018 0.3684 0.643702 24 to 28 141618 -0.9876 0.161684 23 to 27 141243 -2.2587 0.011950 22 to 26 141556 -1.1977 0.115511 21 to 25 141487 -1.4316 0.076125 20 to 24 141505 -1.3706 0.085248 19 to 23 141766 -0.4859 0.313532 18 to 22 141755 -0.5232 0.300434 17 to 21 142012 0.3480 0.636093 16 to 20 141895 -0.0486 0.480629 15 to 19 141587 -1.0926 0.137275 14 to 18 141438 -1.5977 0.055052 13 to 17 141587 -1.0926 0.137275 12 to 16 142347 1.4836 0.931046 11 to 15 142271 1.2260 0.889901 10 to 14 142600 2.3413 0.990390 9 to 13 141957 0.1616 0.564187 8 to 12 141674 -0.7977 0.212514 7 to 11 141793 -0.3943 0.346665 6 to 10 142046 0.4633 0.678421 5 to 9 141711 -0.6723 0.250695 4 to 8 141611 -1.0113 0.155939 3 to 7 141851 -0.1977 0.421629 2 to 6 141541 -1.2486 0.105910 1 to 5 141817 -0.3130 0.377147 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-15_18:31 Bits used No. missing words z-score p-value 31 to 32 141464 -1.3137 0.094481 30 to 31 141347 -1.6588 0.048579 29 to 30 142032 0.3619 0.641271 28 to 29 141798 -0.3284 0.371302 27 to 28 142201 0.8604 0.805211 26 to 27 142639 2.1524 0.984318 25 to 26 141869 -0.1190 0.452651 24 to 25 141763 -0.4317 0.332997 23 to 24 141998 0.2616 0.603171 22 to 23 141779 -0.3845 0.350321 21 to 22 141373 -1.5821 0.056814 20 to 21 142556 1.9076 0.971777 19 to 20 141973 0.1878 0.574490 18 to 19 141833 -0.2252 0.410927 17 to 18 142627 2.1170 0.982871 16 to 17 141509 -1.1809 0.118818 15 to 16 141715 -0.5732 0.283240 14 to 15 141144 -2.2576 0.011985 13 to 14 142124 0.6332 0.736713 12 to 13 141695 -0.6322 0.263614 11 to 12 141460 -1.3255 0.092510 10 to 11 141828 -0.2399 0.405199 9 to 10 141406 -1.4847 0.068805 8 to 9 141633 -0.8151 0.207498 7 to 8 141330 -1.7089 0.043731 6 to 7 141861 -0.1426 0.443316 5 to 6 141208 -2.0688 0.019281 4 to 5 141608 -0.8889 0.187034 3 to 4 141753 -0.4612 0.322345 2 to 3 141541 -1.0865 0.138625 1 to 2 141836 -0.2163 0.414372 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-15_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2473.97 -0.368 0.356398 Test results for specific bytes for dh-ranFile-2015-11-15_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2430.46 -0.983 0.162697 2 to 9 2489.43 -0.150 0.440575 3 to 10 2507.53 0.106 0.542406 4 to 11 2412.90 -1.232 0.109024 5 to 12 2477.22 -0.322 0.373677 6 to 13 2531.90 0.451 0.674074 7 to 14 2479.59 -0.289 0.386413 8 to 15 2531.07 0.439 0.669811 9 to 16 2570.40 0.996 0.840274 10 to 17 2374.27 -1.778 0.037694 11 to 18 2387.00 -1.598 0.055019 12 to 19 2532.09 0.454 0.674998 13 to 20 2548.48 0.686 0.753524 14 to 21 2445.46 -0.771 0.220279 15 to 22 2291.38 -2.950 0.001587 16 to 23 2469.51 -0.431 0.333170 17 to 24 2381.16 -1.681 0.046420 18 to 25 2460.05 -0.565 0.286024 19 to 26 2533.72 0.477 0.683273 20 to 27 2344.52 -2.199 0.013947 21 to 28 2521.75 0.308 0.620808 22 to 29 2455.62 -0.628 0.265115 23 to 30 2542.78 0.605 0.727415 24 to 31 2528.10 0.397 0.654480 25 to 32 2410.44 -1.267 0.102649 CDPARK for dh-ranFile-2015-11-15_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 3504 -0.8676 0.192812 3516 -0.3196 0.374623 3513 -0.4566 0.323972 3505 -0.8219 0.205562 3536 0.5936 0.723613 3533 0.4566 0.676028 3525 0.0913 0.536383 3512 -0.5023 0.307734 3520 -0.1370 0.445521 3500 -1.0502 0.146807 Square side=100, avg. no. parked=3516.40 sample std.=11.53 p-value of the KSTEST for those 10 p-values: 0.242984 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-15_18:31 0.5335,0.1714,0.1824,0.3977,0.8730,0.8781,0.4577,0.6997,0.6953,0.6237, The KS test for those 10 p-values: 0.744063 The 3DSPHERES test for dh-ranFile-2015-11-15_18:31 sample no r^3 equiv. uni. 1 26.801 0.590724 2 34.222 0.680412 3 103.188 0.967923 4 11.016 0.307337 5 14.176 0.376581 6 16.310 0.419383 7 23.942 0.549801 8 1.516 0.049269 9 36.409 0.702886 10 7.509 0.221432 11 6.591 0.197251 12 10.112 0.286149 13 26.342 0.584421 14 44.590 0.773803 15 5.643 0.171470 16 54.023 0.834829 17 63.876 0.881067 18 1.702 0.055158 19 19.192 0.472560 20 1.476 0.048009 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.897577 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-15_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 2.2 -2.3 0.3 -0.9 2.7 0.1 0.6 0.2 0.5 -0.1 0.2 1.0 -0.4 -2.1 -0.8 1.0 -0.6 0.8 -0.2 -1.2 -1.1 0.9 0.8 -1.2 0.6 1.7 0.9 -0.8 2.7 -1.1 0.3 2.4 0.8 -0.8 -1.4 0.7 -0.1 0.5 -1.8 1.6 0.0 -1.1 Chi-square with 42 degrees of freedom:63.066689 z-score=2.298564, p-value=0.980697 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-15_18:31 Test no p-value 1 0.917871 2 0.026073 3 0.118570 4 0.591349 5 0.655054 6 0.159360 7 0.058859 8 0.607883 9 0.854351 10 0.893201 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.516828 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-15_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 66744 0.09 66670 0.00 3 25000.00 24932 0.18 24944 0.13 4 6666.67 6637 0.13 6760 1.31 5 1388.89 1404 0.16 1364 0.45 6 238.10 242 0.06 215 2.24 7 34.72 33 0.09 40 0.80 8 4.96 7 0.84 6 0.22 p=0.04455 p=0.47395 Number of rngs required: 688424, p-value: 0.510 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-15_18:31 No. of wins: Observed Expected 98834 98585.9 z-score= 1.110, pvalue=0.86646 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66595 66666.7 0.077 0.077 2 37657 37654.3 0.000 0.077 3 26851 26954.7 0.399 0.476 4 19313 19313.5 0.000 0.476 5 14026 13851.4 2.200 2.677 6 9838 9943.5 1.120 3.797 7 7180 7145.0 0.171 3.968 8 5182 5139.1 0.359 4.327 9 3621 3699.9 1.681 6.008 10 2691 2666.3 0.229 6.237 11 2062 1923.3 9.998 16.235 12 1342 1388.7 1.573 17.808 13 1044 1003.7 1.617 19.425 14 724 726.1 0.006 19.431 15 518 525.8 0.117 19.548 16 375 381.2 0.099 19.647 17 273 276.5 0.045 19.692 18 171 200.8 4.431 24.123 19 142 146.0 0.109 24.232 20 110 106.2 0.135 24.367 21 285 287.1 0.016 24.382 Chisq= 24.38 for 20 degrees of freedom, p= 0.77391 SUMMARY of craptest p-value for no. of wins: 0.866465 p-value for throws/game: 0.773912 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-15_18:31 No. of wins: Observed Expected 98089 98585.9 z-score=-2.222, pvalue=0.01313 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66492 66666.7 0.458 0.458 2 37887 37654.3 1.438 1.895 3 26918 26954.7 0.050 1.945 4 19271 19313.5 0.093 2.039 5 13842 13851.4 0.006 2.045 6 9926 9943.5 0.031 2.076 7 7203 7145.0 0.470 2.547 8 5118 5139.1 0.086 2.633 9 3788 3699.9 2.099 4.732 10 2639 2666.3 0.279 5.012 11 1880 1923.3 0.976 5.988 12 1329 1388.7 2.570 8.558 13 1008 1003.7 0.018 8.576 14 716 726.1 0.142 8.718 15 528 525.8 0.009 8.727 16 432 381.2 6.784 15.511 17 267 276.5 0.329 15.840 18 178 200.8 2.595 18.435 19 154 146.0 0.440 18.875 20 113 106.2 0.433 19.308 21 311 287.1 1.987 21.296 Chisq= 21.30 for 20 degrees of freedom, p= 0.62008 SUMMARY of craptest p-value for no. of wins: 0.013133 p-value for throws/game: 0.620079 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0051,0.0094,0.0096,0.0119,0.0120,0.0131,0.0139,0.0193,0.0195, 0.0234,0.0261,0.0290,0.0330,0.0331,0.0377,0.0437,0.0445,0.0464,0.0468, 0.0480,0.0485,0.0486,0.0493,0.0520,0.0526,0.0550,0.0551,0.0552,0.0568, 0.0589,0.0600,0.0612,0.0619,0.0688,0.0698,0.0722,0.0761,0.0821,0.0852, 0.0919,0.0925,0.0945,0.1026,0.1059,0.1070,0.1090,0.1155,0.1166,0.1186, 0.1188,0.1206,0.1235,0.1373,0.1373,0.1385,0.1386,0.1407,0.1468,0.1559, 0.1585,0.1594,0.1617,0.1620,0.1627,0.1650,0.1671,0.1714,0.1715,0.1803, 0.1824,0.1870,0.1884,0.1912,0.1928,0.1963,0.1973,0.1973,0.2050,0.2056, 0.2075,0.2125,0.2203,0.2214,0.2364,0.2400,0.2430,0.2448,0.2457,0.2481, 0.2507,0.2525,0.2636,0.2636,0.2651,0.2832,0.2860,0.2861,0.2894,0.3004, 0.3060,0.3073,0.3077,0.3094,0.3135,0.3157,0.3158,0.3223,0.3227,0.3240, 0.3266,0.3330,0.3332,0.3370,0.3376,0.3401,0.3438,0.3467,0.3503,0.3564, 0.3689,0.3691,0.3713,0.3737,0.3746,0.3766,0.3771,0.3864,0.3875,0.3961, 0.3977,0.4052,0.4055,0.4109,0.4122,0.4144,0.4175,0.4187,0.4194,0.4216, 0.4400,0.4406,0.4433,0.4455,0.4527,0.4552,0.4577,0.4631,0.4664,0.4704, 0.4726,0.4734,0.4739,0.4806,0.4903,0.5096,0.5168,0.5174,0.5214,0.5335, 0.5364,0.5388,0.5397,0.5424,0.5498,0.5517,0.5538,0.5642,0.5649,0.5745, 0.5844,0.5900,0.5907,0.5913,0.6032,0.6079,0.6137,0.6201,0.6208,0.6237, 0.6237,0.6332,0.6361,0.6400,0.6413,0.6421,0.6437,0.6465,0.6518,0.6545, 0.6548,0.6550,0.6551,0.6643,0.6698,0.6741,0.6750,0.6760,0.6779,0.6784, 0.6804,0.6833,0.6951,0.6953,0.6997,0.7029,0.7093,0.7236,0.7254,0.7274, 0.7367,0.7379,0.7385,0.7405,0.7407,0.7441,0.7535,0.7566,0.7574,0.7597, 0.7728,0.7738,0.7739,0.7767,0.7781,0.7848,0.7858,0.7867,0.8004,0.8007, 0.8052,0.8067,0.8095,0.8283,0.8308,0.8317,0.8348,0.8403,0.8403,0.8488, 0.8544,0.8645,0.8665,0.8665,0.8669,0.8718,0.8730,0.8781,0.8792,0.8811, 0.8834,0.8899,0.8920,0.8932,0.8976,0.9161,0.9179,0.9310,0.9359,0.9500, 0.9573,0.9679,0.9718,0.9807,0.9826,0.9829,0.9843,0.9904,0.9922, Overall p-value after applying KStest on 269 p-values = 0.000653 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.