RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-30_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 13.4002 0.290993 2 to 25 15.99 19.3136 0.689169 3 to 26 15.81 18.3831 0.634932 4 to 27 15.72 13.0018 0.263938 5 to 28 15.70 18.8746 0.664224 6 to 29 16.00 17.3402 0.568445 7 to 30 15.74 15.3043 0.426425 8 to 31 15.60 14.0047 0.333233 9 to 32 15.71 10.5336 0.120242 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.472725 Tough bday spacings test for dh-ranFile-2018-03-30_21:31: 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 9 34 74 101 101 73 54 29 13 6 6 (O-E)^2/E 0.0 0.2 0.0 0.1 0.1 0.3 0.1 0.0 0.2 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 2.068, p= 0.004 RESULTS OF GCD FOR dh-ranFile-2018-03-30_21:31 Euclid's algorithm: p-value, steps to gcd: 0.643591 p-value, dist. of gcd's: 0.640614 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-30_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.372 0.516 0.350 0.154 0.402 0.057 0.288 0.524 Bits 8 to 15---> 0.900 0.722 0.037 0.588 0.703 0.146 0.185 0.214 Bits 16 to 23---> 0.745 0.211 0.039 0.084 0.553 0.977 0.905 0.512 Bits 24 to 31---> 0.611 0.372 0.763 0.824 0.473 0.694 0.905 0.311 KS test for the above 32 p values: 0.043 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-30_21:31, p-values for 5 runs: 0.9941, 0.3093, 0.2563, 0.7961, 0.2896 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-30_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 171 211.4 7.727 7.727 r= 29 5069 5134.0 0.823 8.550 r= 30 23118 23103.0 0.010 8.560 r= 31 11642 11551.5 0.709 9.268 chi-square = 9.268 with df = 3; p-value = 0.974 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-30_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5254 5134.0 2.804 4.266 r= 31 23091 23103.0 0.006 4.273 r= 32 11426 11551.5 1.364 5.637 chi-square = 5.637 with df = 3; p-value = 0.869 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-30_21:31 b-rank test for bits 1 to 8, p=0.69847 b-rank test for bits 2 to 9, p=0.06536 b-rank test for bits 3 to 10, p=0.51202 b-rank test for bits 4 to 11, p=0.11104 b-rank test for bits 5 to 12, p=0.07203 b-rank test for bits 6 to 13, p=0.37657 b-rank test for bits 7 to 14, p=0.53906 b-rank test for bits 8 to 15, p=0.07262 b-rank test for bits 9 to 16, p=0.52553 b-rank test for bits 10 to 17, p=0.37607 b-rank test for bits 11 to 18, p=0.50600 b-rank test for bits 12 to 19, p=0.58044 b-rank test for bits 13 to 20, p=0.57028 b-rank test for bits 14 to 21, p=0.91126 b-rank test for bits 15 to 22, p=0.92765 b-rank test for bits 16 to 23, p=0.67194 b-rank test for bits 17 to 24, p=0.34838 b-rank test for bits 18 to 25, p=0.32324 b-rank test for bits 19 to 26, p=0.87446 b-rank test for bits 20 to 27, p=0.31936 b-rank test for bits 21 to 28, p=0.04917 b-rank test for bits 22 to 29, p=0.62006 b-rank test for bits 23 to 30, p=0.84402 b-rank test for bits 24 to 31, p=0.28683 b-rank test for bits 25 to 32, p=0.10388 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 = 0.531567 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-30_21:31 (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 141359 -1.29 0.099253 2 141235 -1.58 0.057566 3 141576 -0.78 0.218046 4 141101 -1.89 0.029471 5 141385 -1.23 0.110274 6 141862 -0.11 0.455973 7 141803 -0.25 0.401899 8 142055 0.34 0.633204 9 142185 0.64 0.740241 10 141633 -0.65 0.259259 11 142174 0.62 0.731840 12 141631 -0.65 0.257748 13 142047 0.32 0.626144 14 142606 1.63 0.948209 15 141910 0.00 0.500625 16 142053 0.34 0.631443 17 142236 0.76 0.777342 18 142207 0.70 0.756626 19 141880 -0.07 0.472683 20 142587 1.58 0.943328 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-30_21:31 Bits used No. missing words z-score p-value 23 to 32 141567 -1.1804 0.118911 22 to 31 141338 -1.9701 0.024413 21 to 30 142112 0.6989 0.757681 20 to 29 141610 -1.0322 0.150996 19 to 28 141908 -0.0046 0.498170 18 to 27 141784 -0.4322 0.332808 17 to 26 141712 -0.6804 0.248110 16 to 25 142551 2.2127 0.986539 15 to 24 142258 1.2023 0.885378 14 to 23 141943 0.1161 0.546215 13 to 22 141860 -0.1701 0.432464 12 to 21 141873 -0.1253 0.450153 11 to 20 141469 -1.5184 0.064459 10 to 19 141630 -0.9632 0.167722 9 to 18 141730 -0.6184 0.268163 8 to 17 142453 1.8747 0.969585 7 to 16 141935 0.0885 0.535267 6 to 15 142128 0.7540 0.774586 5 to 14 141656 -0.8736 0.191181 4 to 13 141885 -0.0839 0.466569 3 to 12 142280 1.2782 0.899406 2 to 11 141894 -0.0529 0.478921 1 to 10 141812 -0.3356 0.368579 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-30_21:31 Bits used No. missing words z-score p-value 28 to 32 143078 3.9616 0.999963 27 to 31 141850 -0.2011 0.420303 26 to 30 141835 -0.2520 0.400534 25 to 29 142030 0.4091 0.658749 24 to 28 142048 0.4701 0.680847 23 to 27 141742 -0.5672 0.285282 22 to 26 142382 1.6023 0.945452 21 to 25 141963 0.1819 0.572182 20 to 24 141945 0.1209 0.548121 19 to 23 141658 -0.8520 0.197116 18 to 22 142250 1.1548 0.875917 17 to 21 142104 0.6599 0.745341 16 to 20 141830 -0.2689 0.393998 15 to 19 141336 -1.9435 0.025978 14 to 18 141237 -2.2791 0.011331 13 to 17 141836 -0.2486 0.401844 12 to 16 141729 -0.6113 0.270504 11 to 15 142162 0.8565 0.804142 10 to 14 141825 -0.2859 0.387491 9 to 13 141815 -0.3198 0.374574 8 to 12 141680 -0.7774 0.218464 7 to 11 141961 0.1752 0.569520 6 to 10 141565 -1.1672 0.121561 5 to 9 142471 1.9040 0.971543 4 to 8 141716 -0.6554 0.256119 3 to 7 141422 -1.6520 0.049271 2 to 6 141375 -1.8113 0.035048 1 to 5 141669 -0.8147 0.207628 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-30_21:31 Bits used No. missing words z-score p-value 31 to 32 141822 -0.2576 0.398354 30 to 31 142171 0.7719 0.779910 29 to 30 141610 -0.8830 0.188624 28 to 29 142018 0.3206 0.625728 27 to 28 141968 0.1731 0.568701 26 to 27 141863 -0.1367 0.445647 25 to 26 142173 0.7778 0.781653 24 to 25 141401 -1.4995 0.066872 23 to 24 141988 0.2321 0.591756 22 to 23 141977 0.1996 0.579110 21 to 22 142367 1.3501 0.911501 20 to 21 141735 -0.5142 0.303539 19 to 20 142541 1.8633 0.968792 18 to 19 141580 -0.9715 0.165656 17 to 18 142333 1.2498 0.894307 16 to 17 141775 -0.3963 0.345959 15 to 16 141549 -1.0629 0.143909 14 to 15 141289 -1.8299 0.033634 13 to 14 141974 0.1908 0.575646 12 to 13 141775 -0.3963 0.345959 11 to 12 141679 -0.6794 0.248430 10 to 11 141813 -0.2842 0.388144 9 to 10 141943 0.0993 0.539559 8 to 9 141888 -0.0629 0.474915 7 to 8 142468 1.6480 0.950323 6 to 7 141760 -0.4405 0.329787 5 to 6 142600 2.0374 0.979194 4 to 5 141878 -0.0924 0.463183 3 to 4 141675 -0.6912 0.244708 2 to 3 142034 0.3678 0.643473 1 to 2 142157 0.7306 0.767485 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-30_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2371.04 -1.824 0.034097 Test results for specific bytes for dh-ranFile-2018-03-30_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2609.46 1.548 0.939194 2 to 9 2456.77 -0.611 0.270467 3 to 10 2554.64 0.773 0.780167 4 to 11 2571.22 1.007 0.843077 5 to 12 2548.94 0.692 0.755580 6 to 13 2585.89 1.215 0.887743 7 to 14 2584.11 1.190 0.882883 8 to 15 2332.00 -2.376 0.008753 9 to 16 2426.20 -1.044 0.148300 10 to 17 2365.32 -1.905 0.028412 11 to 18 2454.71 -0.640 0.260935 12 to 19 2441.90 -0.822 0.205628 13 to 20 2607.67 1.523 0.936074 14 to 21 2442.91 -0.807 0.209745 15 to 22 2497.06 -0.042 0.483435 16 to 23 2550.68 0.717 0.763224 17 to 24 2479.12 -0.295 0.383873 18 to 25 2565.94 0.933 0.824462 19 to 26 2533.46 0.473 0.681968 20 to 27 2369.33 -1.848 0.032305 21 to 28 2461.10 -0.550 0.291096 22 to 29 2466.88 -0.468 0.319775 23 to 30 2495.69 -0.061 0.475702 24 to 31 2509.11 0.129 0.551279 25 to 32 2497.27 -0.039 0.484626 CDPARK for dh-ranFile-2018-03-30_21:31: 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 3526 0.1370 0.554479 3514 -0.4110 0.340551 3515 -0.3653 0.357445 3544 0.9589 0.831196 3517 -0.2740 0.392053 3530 0.3196 0.625377 3542 0.8676 0.807188 3555 1.4612 0.928018 3498 -1.1416 0.126820 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3526.10 sample std.=16.13 p-value of the KSTEST for those 10 p-values: 0.825612 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-30_21:31 0.2712,0.5248,0.3477,0.9343,0.5630,0.9295,0.3940,0.5316,0.6059,0.3621, The KS test for those 10 p-values: 0.413445 The 3DSPHERES test for dh-ranFile-2018-03-30_21:31 sample no r^3 equiv. uni. 1 55.400 0.842236 2 70.293 0.903972 3 11.441 0.317065 4 32.830 0.665235 5 18.971 0.468667 6 0.869 0.028550 7 21.166 0.506155 8 1.181 0.038603 9 14.842 0.390273 10 8.202 0.239203 11 19.366 0.475622 12 2.313 0.074199 13 5.158 0.157963 14 27.540 0.600686 15 19.656 0.480669 16 78.274 0.926402 17 68.855 0.899256 18 6.805 0.202940 19 40.680 0.742311 20 28.130 0.608458 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.967443 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-30_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 -0.1 0.3 -1.5 2.5 0.8 0.9 -0.0 0.1 -0.6 0.9 0.1 1.3 -1.2 0.1 -0.2 -1.5 0.5 -0.2 -0.4 -0.6 -0.4 -0.2 1.9 -0.5 1.0 0.5 -1.6 0.8 0.2 0.1 0.8 0.1 -1.9 0.8 2.1 -0.1 0.5 -0.1 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:38.219115 z-score=-0.412528, p-value=0.362336 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-30_21:31 Test no p-value 1 0.071373 2 0.495344 3 0.006106 4 0.604565 5 0.912307 6 0.872218 7 0.910586 8 0.931905 9 0.096221 10 0.000091 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.039009 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-30_21:31: (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 66634 0.02 66800 0.27 3 25000.00 24973 0.03 25003 0.00 4 6666.67 6687 0.06 6716 0.37 5 1388.89 1435 1.53 1237 16.61 6 238.10 237 0.01 204 4.88 7 34.72 29 0.94 34 0.01 8 4.96 4 0.19 5 0.00 p=0.16303 p=0.99886 Number of rngs required: 687810, p-value: 0.247 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-30_21:31 No. of wins: Observed Expected 98204 98585.9 z-score=-1.708, pvalue=0.04383 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66825 66666.7 0.376 0.376 2 37481 37654.3 0.798 1.174 3 26930 26954.7 0.023 1.197 4 19465 19313.5 1.189 2.386 5 13949 13851.4 0.687 3.073 6 9729 9943.5 4.629 7.702 7 7094 7145.0 0.364 8.066 8 5029 5139.1 2.358 10.424 9 3697 3699.9 0.002 10.426 10 2704 2666.3 0.533 10.959 11 1931 1923.3 0.031 10.990 12 1412 1388.7 0.390 11.379 13 1021 1003.7 0.298 11.677 14 707 726.1 0.505 12.182 15 562 525.8 2.487 14.669 16 428 381.2 5.759 20.427 17 266 276.5 0.402 20.829 18 206 200.8 0.133 20.962 19 151 146.0 0.172 21.134 20 116 106.2 0.901 22.036 21 297 287.1 0.340 22.376 Chisq= 22.38 for 20 degrees of freedom, p= 0.67955 SUMMARY of craptest p-value for no. of wins: 0.043828 p-value for throws/game: 0.679552 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-30_21:31 No. of wins: Observed Expected 98528 98585.9 z-score=-0.259, pvalue=0.39790 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66475 66666.7 0.551 0.551 2 37878 37654.3 1.329 1.880 3 26952 26954.7 0.000 1.880 4 19215 19313.5 0.502 2.382 5 13884 13851.4 0.077 2.459 6 9916 9943.5 0.076 2.535 7 7011 7145.0 2.514 5.049 8 5175 5139.1 0.251 5.300 9 3778 3699.9 1.650 6.950 10 2683 2666.3 0.105 7.055 11 1917 1923.3 0.021 7.076 12 1422 1388.7 0.797 7.872 13 990 1003.7 0.187 8.060 14 735 726.1 0.108 8.168 15 562 525.8 2.487 10.655 16 368 381.2 0.454 11.109 17 259 276.5 1.112 12.221 18 203 200.8 0.023 12.245 19 143 146.0 0.061 12.306 20 124 106.2 2.978 15.283 21 310 287.1 1.824 17.108 Chisq= 17.11 for 20 degrees of freedom, p= 0.35403 SUMMARY of craptest p-value for no. of wins: 0.397904 p-value for throws/game: 0.354030 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0042,0.0061,0.0088,0.0113,0.0244,0.0260,0.0284,0.0286,0.0295, 0.0323,0.0336,0.0341,0.0350,0.0371,0.0386,0.0386,0.0390,0.0433,0.0438, 0.0492,0.0493,0.0571,0.0576,0.0645,0.0654,0.0669,0.0714,0.0720,0.0726, 0.0742,0.0835,0.0962,0.0993,0.1039,0.1103,0.1110,0.1189,0.1202,0.1216, 0.1268,0.1439,0.1457,0.1483,0.1510,0.1538,0.1580,0.1630,0.1657,0.1677, 0.1851,0.1886,0.1912,0.1971,0.2029,0.2056,0.2076,0.2097,0.2105,0.2136, 0.2180,0.2185,0.2392,0.2447,0.2468,0.2481,0.2484,0.2561,0.2563,0.2577, 0.2593,0.2609,0.2639,0.2682,0.2705,0.2705,0.2712,0.2853,0.2868,0.2876, 0.2896,0.2910,0.2911,0.3035,0.3093,0.3111,0.3171,0.3194,0.3198,0.3232, 0.3298,0.3328,0.3332,0.3406,0.3460,0.3460,0.3477,0.3484,0.3499,0.3540, 0.3574,0.3621,0.3623,0.3686,0.3719,0.3720,0.3746,0.3761,0.3766,0.3839, 0.3875,0.3881,0.3903,0.3921,0.3940,0.3940,0.3979,0.3984,0.4005,0.4018, 0.4019,0.4023,0.4134,0.4203,0.4264,0.4325,0.4455,0.4456,0.4502,0.4560, 0.4632,0.4666,0.4687,0.4727,0.4727,0.4733,0.4749,0.4756,0.4757,0.4789, 0.4807,0.4834,0.4846,0.4953,0.4982,0.5006,0.5060,0.5062,0.5116,0.5120, 0.5155,0.5235,0.5248,0.5255,0.5316,0.5316,0.5353,0.5391,0.5396,0.5462, 0.5481,0.5513,0.5531,0.5545,0.5630,0.5684,0.5687,0.5695,0.5703,0.5722, 0.5756,0.5791,0.5804,0.5880,0.5918,0.6007,0.6046,0.6059,0.6085,0.6108, 0.6201,0.6254,0.6257,0.6261,0.6314,0.6332,0.6349,0.6406,0.6435,0.6436, 0.6587,0.6642,0.6652,0.6719,0.6796,0.6808,0.6820,0.6892,0.6938,0.6985, 0.7033,0.7223,0.7318,0.7402,0.7423,0.7447,0.7453,0.7556,0.7566,0.7577, 0.7628,0.7632,0.7675,0.7746,0.7773,0.7799,0.7802,0.7817,0.7961,0.8041, 0.8072,0.8238,0.8245,0.8256,0.8312,0.8422,0.8431,0.8440,0.8693,0.8722, 0.8745,0.8759,0.8829,0.8854,0.8877,0.8943,0.8993,0.8994,0.9000,0.9040, 0.9048,0.9054,0.9106,0.9113,0.9115,0.9123,0.9264,0.9276,0.9280,0.9295, 0.9319,0.9343,0.9361,0.9392,0.9433,0.9455,0.9482,0.9503,0.9674,0.9688, 0.9696,0.9715,0.9741,0.9766,0.9792,0.9865,0.9941,0.9989,1.0000, Overall p-value after applying KStest on 269 p-values = 0.244804 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.