RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-22_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.62 32.8164 0.988109 2 to 25 15.67 17.7341 0.594202 3 to 26 15.80 13.3431 0.287068 4 to 27 15.65 17.2484 0.562338 5 to 28 15.86 9.8162 0.088861 6 to 29 16.15 10.8898 0.137763 7 to 30 15.75 29.0465 0.965900 8 to 31 15.60 23.6177 0.869799 9 to 32 15.79 18.3703 0.634151 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.490720 Tough bday spacings test for dh-ranFile-2016-10-22_06:31: 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 5 38 83 103 96 84 47 23 13 5 3 (O-E)^2/E 1.9 0.1 1.3 0.3 0.0 0.4 0.5 1.5 0.2 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 6.941, p= 0.269 RESULTS OF GCD FOR dh-ranFile-2016-10-22_06:31 Euclid's algorithm: p-value, steps to gcd: 0.642092 p-value, dist. of gcd's: 0.697951 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-22_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.548 0.883 0.284 0.527 0.279 0.671 0.245 0.383 Bits 8 to 15---> 0.872 0.853 0.045 0.112 0.874 0.211 0.134 0.424 Bits 16 to 23---> 0.593 0.026 0.046 0.673 0.712 0.721 0.820 0.144 Bits 24 to 31---> 0.624 0.531 0.007 0.562 0.387 0.250 0.619 0.905 KS test for the above 32 p values: 0.291 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-22_06:31, p-values for 5 runs: 0.0890, 0.5395, 0.5404, 0.4070, 0.0970 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-22_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5021 5134.0 2.488 3.636 r= 30 23119 23103.0 0.011 3.647 r= 31 11633 11551.5 0.575 4.222 chi-square = 4.222 with df = 3; p-value = 0.762 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-22_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5124 5134.0 0.020 0.075 r= 31 23081 23103.0 0.021 0.096 r= 32 11587 11551.5 0.109 0.205 chi-square = 0.205 with df = 3; p-value = 0.023 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-22_06:31 b-rank test for bits 1 to 8, p=0.62090 b-rank test for bits 2 to 9, p=0.56708 b-rank test for bits 3 to 10, p=0.02281 b-rank test for bits 4 to 11, p=0.56219 b-rank test for bits 5 to 12, p=0.41847 b-rank test for bits 6 to 13, p=0.24402 b-rank test for bits 7 to 14, p=0.95754 b-rank test for bits 8 to 15, p=0.32519 b-rank test for bits 9 to 16, p=0.70443 b-rank test for bits 10 to 17, p=0.36325 b-rank test for bits 11 to 18, p=0.30514 b-rank test for bits 12 to 19, p=0.39532 b-rank test for bits 13 to 20, p=0.37977 b-rank test for bits 14 to 21, p=0.24002 b-rank test for bits 15 to 22, p=0.17916 b-rank test for bits 16 to 23, p=0.00244 b-rank test for bits 17 to 24, p=0.01674 b-rank test for bits 18 to 25, p=0.42190 b-rank test for bits 19 to 26, p=0.97514 b-rank test for bits 20 to 27, p=0.08715 b-rank test for bits 21 to 28, p=0.23172 b-rank test for bits 22 to 29, p=0.05597 b-rank test for bits 23 to 30, p=0.80416 b-rank test for bits 24 to 31, p=0.10265 b-rank test for bits 25 to 32, p=0.08603 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 = 0.020306 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-22_06:31 (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 142542 1.48 0.930323 2 141905 -0.01 0.495964 3 141798 -0.26 0.397387 4 142167 0.60 0.726424 5 141436 -1.11 0.134382 6 141459 -1.05 0.146360 7 140829 -2.52 0.005799 8 141990 0.19 0.574750 9 141843 -0.15 0.438420 10 141812 -0.23 0.410054 11 142175 0.62 0.732610 12 141935 0.06 0.523913 13 141900 -0.02 0.491304 14 142239 0.77 0.779426 15 141490 -0.98 0.163607 16 142154 0.57 0.716223 17 141891 -0.04 0.482920 18 142771 2.01 0.977956 19 142239 0.77 0.779426 20 140505 -3.28 0.000517 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-22_06:31 Bits used No. missing words z-score p-value 23 to 32 141996 0.2989 0.617477 22 to 31 142280 1.2782 0.899406 21 to 30 142243 1.1506 0.875049 20 to 29 141952 0.1471 0.558488 19 to 28 142265 1.2264 0.889985 18 to 27 142374 1.6023 0.945457 17 to 26 142237 1.1299 0.870740 16 to 25 141683 -0.7804 0.217564 15 to 24 141690 -0.7563 0.224732 14 to 23 142162 0.8713 0.808198 13 to 22 141742 -0.5770 0.281970 12 to 21 142274 1.2575 0.895711 11 to 20 142124 0.7402 0.770423 10 to 19 141663 -0.8494 0.197826 9 to 18 141840 -0.2391 0.405526 8 to 17 141237 -2.3184 0.010214 7 to 16 141804 -0.3632 0.358225 6 to 15 141657 -0.8701 0.192122 5 to 14 141932 0.0782 0.531155 4 to 13 141734 -0.6046 0.272727 3 to 12 141883 -0.0908 0.463829 2 to 11 141735 -0.6011 0.273874 1 to 10 141609 -1.0356 0.150190 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-22_06:31 Bits used No. missing words z-score p-value 28 to 32 141876 -0.1130 0.455022 27 to 31 141901 -0.0282 0.488737 26 to 30 141509 -1.3571 0.087383 25 to 29 142106 0.6667 0.747511 24 to 28 142185 0.9345 0.824970 23 to 27 142020 0.3752 0.646227 22 to 26 141841 -0.2316 0.408414 21 to 25 141849 -0.2045 0.418978 20 to 24 141668 -0.8181 0.206659 19 to 23 141525 -1.3028 0.096319 18 to 22 142138 0.7752 0.780875 17 to 21 142401 1.6667 0.952211 16 to 20 141636 -0.9265 0.177082 15 to 19 141794 -0.3909 0.347917 14 to 18 141837 -0.2452 0.403156 13 to 17 141635 -0.9299 0.176203 12 to 16 141601 -1.0452 0.147968 11 to 15 141533 -1.2757 0.101032 10 to 14 142315 1.3752 0.915458 9 to 13 141905 -0.0147 0.494145 8 to 12 141849 -0.2045 0.418978 7 to 11 141825 -0.2859 0.387491 6 to 10 142150 0.8158 0.792702 5 to 9 141898 -0.0384 0.484682 4 to 8 141785 -0.4215 0.336711 3 to 7 141680 -0.7774 0.218464 2 to 6 141871 -0.1299 0.448310 1 to 5 142245 1.1379 0.872411 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-22_06:31 Bits used No. missing words z-score p-value 31 to 32 141971 0.1819 0.572176 30 to 31 141978 0.2026 0.580263 29 to 30 142179 0.7955 0.786835 28 to 29 142169 0.7660 0.778158 27 to 28 142275 1.0787 0.859633 26 to 27 141712 -0.5821 0.280252 25 to 26 142235 0.9607 0.831643 24 to 25 141597 -0.9213 0.178440 23 to 24 141877 -0.0954 0.462011 22 to 23 142000 0.2675 0.605444 21 to 22 141987 0.2291 0.590610 20 to 21 141688 -0.6529 0.256913 19 to 20 141447 -1.3638 0.086314 18 to 19 141717 -0.5673 0.285240 17 to 18 141609 -0.8859 0.187828 16 to 17 141823 -0.2547 0.399493 15 to 16 141783 -0.3727 0.354703 14 to 15 141543 -1.0806 0.139933 13 to 14 142096 0.5506 0.709063 12 to 13 141491 -1.2340 0.108599 11 to 12 141853 -0.1662 0.434014 10 to 11 142139 0.6775 0.750953 9 to 10 142563 1.9282 0.973087 8 to 9 141715 -0.5732 0.283240 7 to 8 142066 0.4622 0.678014 6 to 7 141972 0.1849 0.573333 5 to 6 142014 0.3088 0.621248 4 to 5 141649 -0.7679 0.221263 3 to 4 141911 0.0049 0.501965 2 to 3 141717 -0.5673 0.285240 1 to 2 141755 -0.4553 0.324464 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-22_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2507.64 0.108 0.543041 Test results for specific bytes for dh-ranFile-2016-10-22_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2516.35 0.231 0.591429 2 to 9 2356.52 -2.029 0.021226 3 to 10 2536.28 0.513 0.696056 4 to 11 2516.98 0.240 0.594867 5 to 12 2562.31 0.881 0.810899 6 to 13 2551.67 0.731 0.767532 7 to 14 2533.13 0.469 0.680300 8 to 15 2491.92 -0.114 0.454506 9 to 16 2425.74 -1.050 0.146819 10 to 17 2640.09 1.981 0.976216 11 to 18 2545.64 0.645 0.740659 12 to 19 2427.30 -1.028 0.151946 13 to 20 2600.83 1.426 0.923069 14 to 21 2441.06 -0.834 0.202266 15 to 22 2445.12 -0.776 0.218850 16 to 23 2453.65 -0.656 0.256066 17 to 24 2521.18 0.300 0.617729 18 to 25 2494.08 -0.084 0.466617 19 to 26 2494.51 -0.078 0.469073 20 to 27 2516.45 0.233 0.591978 21 to 28 2415.99 -1.188 0.117405 22 to 29 2518.41 0.260 0.602726 23 to 30 2589.92 1.272 0.898250 24 to 31 2443.26 -0.802 0.211174 25 to 32 2632.49 1.874 0.969514 CDPARK for dh-ranFile-2016-10-22_06:31: 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 3512 -0.5023 0.307734 3554 1.4155 0.921543 3501 -1.0046 0.157553 3518 -0.2283 0.409702 3525 0.0913 0.536383 3516 -0.3196 0.374623 3555 1.4612 0.928018 3529 0.2740 0.607947 3520 -0.1370 0.445521 3536 0.5936 0.723613 Square side=100, avg. no. parked=3526.60 sample std.=16.59 p-value of the KSTEST for those 10 p-values: 0.761296 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-22_06:31 0.3937,0.7460,0.5455,0.0046,0.0463,0.7425,0.5361,0.3515,0.7348,0.1125, The KS test for those 10 p-values: 0.381642 The 3DSPHERES test for dh-ranFile-2016-10-22_06:31 sample no r^3 equiv. uni. 1 11.144 0.310284 2 14.602 0.385359 3 6.422 0.192699 4 39.024 0.727686 5 67.179 0.893466 6 18.511 0.460452 7 4.646 0.143475 8 11.967 0.328932 9 7.185 0.212971 10 42.775 0.759695 11 60.838 0.868391 12 7.363 0.217643 13 16.385 0.420830 14 67.832 0.895761 15 42.040 0.753729 16 5.768 0.174925 17 18.136 0.453677 18 0.962 0.031556 19 37.356 0.712117 20 24.722 0.561360 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.859443 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-22_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -1.3 0.5 0.6 -0.6 1.5 -0.5 -1.6 0.1 -1.0 -0.8 0.9 -0.5 1.1 2.2 -1.3 1.6 -0.6 0.5 -0.6 -1.2 -0.7 0.4 -0.5 -0.5 -0.2 -0.5 -0.3 -1.5 1.8 1.2 2.2 1.0 0.9 1.5 1.7 -1.3 -0.4 1.0 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:46.771836 z-score=0.520650, p-value=0.717118 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-22_06:31 Test no p-value 1 0.524277 2 0.025122 3 0.036502 4 0.024243 5 0.435079 6 0.609416 7 0.653082 8 0.046857 9 0.380037 10 0.254277 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.017350 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-22_06:31: (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 66539 0.24 66602 0.06 3 25000.00 25071 0.20 25039 0.06 4 6666.67 6681 0.03 6615 0.40 5 1388.89 1422 0.79 1469 4.62 6 238.10 241 0.04 240 0.02 7 34.72 39 0.53 32 0.21 8 4.96 6 0.22 2 1.77 p=0.08471 p=0.69186 Number of rngs required: 688647, p-value: 0.611 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-22_06:31 No. of wins: Observed Expected 99032 98585.9 z-score= 1.995, pvalue=0.97700 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66825 66666.7 0.376 0.376 2 37595 37654.3 0.093 0.469 3 26853 26954.7 0.384 0.853 4 19273 19313.5 0.085 0.938 5 13819 13851.4 0.076 1.014 6 9945 9943.5 0.000 1.014 7 7141 7145.0 0.002 1.017 8 5271 5139.1 3.387 4.403 9 3648 3699.9 0.727 5.130 10 2633 2666.3 0.416 5.546 11 1982 1923.3 1.790 7.336 12 1362 1388.7 0.515 7.851 13 1005 1003.7 0.002 7.853 14 696 726.1 1.251 9.104 15 565 525.8 2.917 12.021 16 387 381.2 0.090 12.110 17 271 276.5 0.111 12.221 18 202 200.8 0.007 12.228 19 153 146.0 0.337 12.565 20 104 106.2 0.046 12.611 21 270 287.1 1.020 13.632 Chisq= 13.63 for 20 degrees of freedom, p= 0.15133 SUMMARY of craptest p-value for no. of wins: 0.977001 p-value for throws/game: 0.151325 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-22_06:31 No. of wins: Observed Expected 98479 98585.9 z-score=-0.478, pvalue=0.31635 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66779 66666.7 0.189 0.189 2 37567 37654.3 0.202 0.392 3 27085 26954.7 0.630 1.021 4 19203 19313.5 0.632 1.653 5 14022 13851.4 2.101 3.754 6 9888 9943.5 0.310 4.064 7 7072 7145.0 0.746 4.810 8 5108 5139.1 0.188 4.998 9 3770 3699.9 1.329 6.328 10 2576 2666.3 3.058 9.386 11 1946 1923.3 0.267 9.653 12 1362 1388.7 0.515 10.168 13 944 1003.7 3.553 13.721 14 727 726.1 0.001 13.722 15 510 525.8 0.477 14.199 16 380 381.2 0.003 14.202 17 294 276.5 1.102 15.304 18 207 200.8 0.190 15.494 19 161 146.0 1.544 17.039 20 121 106.2 2.058 19.096 21 278 287.1 0.289 19.386 Chisq= 19.39 for 20 degrees of freedom, p= 0.50311 SUMMARY of craptest p-value for no. of wins: 0.316349 p-value for throws/game: 0.503109 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0024,0.0046,0.0058,0.0071,0.0102,0.0167,0.0174,0.0203,0.0212, 0.0228,0.0232,0.0242,0.0251,0.0265,0.0316,0.0365,0.0451,0.0461,0.0463, 0.0469,0.0560,0.0847,0.0860,0.0863,0.0871,0.0874,0.0889,0.0890,0.0963, 0.0970,0.1010,0.1027,0.1086,0.1122,0.1125,0.1174,0.1336,0.1344,0.1378, 0.1399,0.1435,0.1435,0.1464,0.1468,0.1480,0.1502,0.1513,0.1519,0.1576, 0.1636,0.1749,0.1762,0.1771,0.1784,0.1792,0.1878,0.1921,0.1927,0.1978, 0.2023,0.2067,0.2112,0.2114,0.2130,0.2176,0.2176,0.2185,0.2188,0.2213, 0.2247,0.2317,0.2400,0.2440,0.2453,0.2496,0.2543,0.2561,0.2569,0.2690, 0.2727,0.2739,0.2790,0.2803,0.2820,0.2832,0.2842,0.2852,0.2852,0.2871, 0.2908,0.3051,0.3077,0.3103,0.3163,0.3245,0.3252,0.3289,0.3367,0.3479, 0.3515,0.3547,0.3582,0.3633,0.3746,0.3798,0.3800,0.3816,0.3825,0.3854, 0.3869,0.3875,0.3937,0.3953,0.3974,0.3995,0.4032,0.4055,0.4070,0.4084, 0.4097,0.4101,0.4185,0.4190,0.4190,0.4208,0.4219,0.4242,0.4340,0.4351, 0.4384,0.4455,0.4483,0.4537,0.4545,0.4550,0.4605,0.4620,0.4638,0.4666, 0.4691,0.4829,0.4847,0.4887,0.4907,0.4913,0.4941,0.4960,0.5020,0.5031, 0.5239,0.5243,0.5274,0.5312,0.5313,0.5361,0.5364,0.5395,0.5404,0.5430, 0.5455,0.5485,0.5585,0.5614,0.5620,0.5622,0.5623,0.5671,0.5722,0.5733, 0.5748,0.5803,0.5906,0.5914,0.5920,0.5930,0.5942,0.5949,0.6027,0.6054, 0.6079,0.6094,0.6106,0.6175,0.6177,0.6194,0.6209,0.6212,0.6237,0.6342, 0.6421,0.6462,0.6531,0.6713,0.6726,0.6780,0.6803,0.6919,0.6961,0.6980, 0.7044,0.7091,0.7121,0.7124,0.7162,0.7171,0.7210,0.7236,0.7264,0.7277, 0.7326,0.7348,0.7407,0.7425,0.7460,0.7475,0.7510,0.7537,0.7597,0.7613, 0.7615,0.7675,0.7704,0.7782,0.7794,0.7794,0.7809,0.7868,0.7927,0.8042, 0.8082,0.8109,0.8202,0.8250,0.8316,0.8534,0.8594,0.8596,0.8684,0.8698, 0.8707,0.8724,0.8724,0.8736,0.8750,0.8825,0.8900,0.8935,0.8957,0.8958, 0.8983,0.8994,0.9048,0.9155,0.9215,0.9231,0.9280,0.9303,0.9455,0.9522, 0.9575,0.9659,0.9695,0.9731,0.9751,0.9762,0.9770,0.9780,0.9881, Overall p-value after applying KStest on 269 p-values = 0.060722 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.