RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-01_17:31 (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 19.0936 0.676816 2 to 25 15.76 18.5292 0.643786 3 to 26 15.84 13.0468 0.266952 4 to 27 15.81 26.9661 0.941433 5 to 28 15.82 17.1583 0.556309 6 to 29 15.89 12.7191 0.245221 7 to 30 15.64 21.0363 0.775327 8 to 31 15.82 11.8947 0.193528 9 to 32 16.02 25.0763 0.906986 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.679914 Tough bday spacings test for dh-ranFile-2015-11-01_17:31: 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 10 38 66 104 90 69 60 33 17 7 6 (O-E)^2/E 0.1 0.1 0.7 0.4 0.6 1.1 1.2 0.4 0.3 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.724, p= 0.162 RESULTS OF GCD FOR dh-ranFile-2015-11-01_17:31 Euclid's algorithm: p-value, steps to gcd: 0.465815 p-value, dist. of gcd's: 0.558922 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-01_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.436 0.156 0.719 0.358 0.824 0.853 0.142 0.314 Bits 8 to 15---> 0.184 0.207 0.443 0.620 0.927 0.089 0.618 0.346 Bits 16 to 23---> 0.787 0.299 0.908 0.622 0.701 0.192 0.598 0.037 Bits 24 to 31---> 0.657 0.767 0.151 0.709 0.433 0.211 0.554 0.466 KS test for the above 32 p values: 0.244 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-01_17:31, p-values for 5 runs: 0.8777, 0.7357, 0.5102, 0.9757, 0.5416 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-01_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5054 5134.0 1.247 2.371 r= 30 23252 23103.0 0.960 3.332 r= 31 11498 11551.5 0.248 3.580 chi-square = 3.580 with df = 3; p-value = 0.689 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-01_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5169 5134.0 0.238 0.499 r= 31 23163 23103.0 0.156 0.654 r= 32 11464 11551.5 0.663 1.317 chi-square = 1.317 with df = 3; p-value = 0.275 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-01_17:31 b-rank test for bits 1 to 8, p=0.43660 b-rank test for bits 2 to 9, p=0.04123 b-rank test for bits 3 to 10, p=0.71768 b-rank test for bits 4 to 11, p=0.70830 b-rank test for bits 5 to 12, p=0.69274 b-rank test for bits 6 to 13, p=0.31488 b-rank test for bits 7 to 14, p=0.24291 b-rank test for bits 8 to 15, p=0.44467 b-rank test for bits 9 to 16, p=0.94943 b-rank test for bits 10 to 17, p=0.54325 b-rank test for bits 11 to 18, p=0.11847 b-rank test for bits 12 to 19, p=0.92429 b-rank test for bits 13 to 20, p=0.78215 b-rank test for bits 14 to 21, p=0.91930 b-rank test for bits 15 to 22, p=0.69688 b-rank test for bits 16 to 23, p=0.47240 b-rank test for bits 17 to 24, p=0.81187 b-rank test for bits 18 to 25, p=0.09675 b-rank test for bits 19 to 26, p=0.65423 b-rank test for bits 20 to 27, p=0.36255 b-rank test for bits 21 to 28, p=0.81484 b-rank test for bits 22 to 29, p=0.15680 b-rank test for bits 23 to 30, p=0.53974 b-rank test for bits 24 to 31, p=0.75416 b-rank test for bits 25 to 32, p=0.59719 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 = 0.581789 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-01_17:31 (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 142056 0.34 0.634083 2 142039 0.30 0.619043 3 142050 0.33 0.628797 4 141642 -0.62 0.266116 5 140783 -2.63 0.004249 6 142207 0.70 0.756626 7 142204 0.69 0.754425 8 141608 -0.70 0.240703 9 141579 -0.77 0.220117 10 141887 -0.05 0.479196 11 141669 -0.56 0.287222 12 142739 1.94 0.973718 13 142145 0.55 0.709057 14 141128 -1.83 0.033960 15 141966 0.13 0.552669 16 141959 0.12 0.546194 17 141917 0.02 0.507149 18 141353 -1.30 0.096829 19 142153 0.57 0.715431 20 141690 -0.51 0.304167 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-01_17:31 Bits used No. missing words z-score p-value 23 to 32 142601 2.3851 0.991462 22 to 31 142396 1.6782 0.953343 21 to 30 141845 -0.2218 0.412224 20 to 29 142328 1.4437 0.925587 19 to 28 142079 0.5851 0.720749 18 to 27 141838 -0.2460 0.402855 17 to 26 141653 -0.8839 0.188376 16 to 25 141824 -0.2942 0.384287 15 to 24 142109 0.6885 0.754436 14 to 23 141751 -0.5460 0.292545 13 to 22 142107 0.6816 0.752261 12 to 21 142070 0.5540 0.710222 11 to 20 142069 0.5506 0.709041 10 to 19 141862 -0.1632 0.435178 9 to 18 141991 0.2816 0.610883 8 to 17 141614 -1.0184 0.154249 7 to 16 141689 -0.7598 0.223699 6 to 15 141931 0.0747 0.529783 5 to 14 141749 -0.5529 0.290179 4 to 13 142274 1.2575 0.895711 3 to 12 142082 0.5954 0.724217 2 to 11 142586 2.3333 0.990185 1 to 10 141817 -0.3184 0.375099 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-01_17:31 Bits used No. missing words z-score p-value 28 to 32 142180 0.9175 0.820566 27 to 31 142001 0.3107 0.622003 26 to 30 141821 -0.2994 0.382308 25 to 29 141594 -1.0689 0.142554 24 to 28 142097 0.6362 0.737667 23 to 27 142174 0.8972 0.815190 22 to 26 142216 1.0396 0.850728 21 to 25 142091 0.6158 0.730997 20 to 24 141838 -0.2418 0.404469 19 to 23 141772 -0.4655 0.320778 18 to 22 142078 0.5718 0.716259 17 to 21 142001 0.3107 0.622003 16 to 20 142023 0.3853 0.650001 15 to 19 142002 0.3141 0.623291 14 to 18 142677 2.6023 0.995370 13 to 17 141712 -0.6689 0.251775 12 to 16 141815 -0.3198 0.374574 11 to 15 141886 -0.0791 0.468483 10 to 14 141428 -1.6316 0.051379 9 to 13 141697 -0.7198 0.235836 8 to 12 141684 -0.7638 0.222484 7 to 11 142509 2.0328 0.978963 6 to 10 141501 -1.3842 0.083153 5 to 9 141827 -0.2791 0.390090 4 to 8 142054 0.4904 0.688077 3 to 7 142197 0.9752 0.835258 2 to 6 142093 0.6226 0.733230 1 to 5 141584 -1.1028 0.135054 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-01_17:31 Bits used No. missing words z-score p-value 31 to 32 141602 -0.9066 0.182315 30 to 31 141554 -1.0482 0.147280 29 to 30 141376 -1.5732 0.057831 28 to 29 141411 -1.4700 0.070781 27 to 28 142085 0.5182 0.697841 26 to 27 141927 0.0521 0.520785 25 to 26 141952 0.1259 0.550083 24 to 25 142423 1.5153 0.935146 23 to 24 141848 -0.1809 0.428217 22 to 23 142329 1.2380 0.892135 21 to 22 141559 -1.0334 0.150703 20 to 21 141403 -1.4936 0.067640 19 to 20 141575 -0.9862 0.162012 18 to 19 142255 1.0197 0.846059 17 to 18 142318 1.2055 0.885998 16 to 17 142221 0.9194 0.821052 15 to 16 141727 -0.5378 0.295342 14 to 15 142043 0.3943 0.653323 13 to 14 141910 0.0020 0.500789 12 to 13 142216 0.9046 0.817170 11 to 12 141710 -0.5880 0.278268 10 to 11 141938 0.0846 0.533699 9 to 10 142334 1.2527 0.894845 8 to 9 141978 0.2026 0.580263 7 to 8 141730 -0.5290 0.298404 6 to 7 142359 1.3265 0.907656 5 to 6 141883 -0.0777 0.469045 4 to 5 141956 0.1377 0.554749 3 to 4 141711 -0.5850 0.279259 2 to 3 141526 -1.1308 0.129077 1 to 2 141909 -0.0010 0.499612 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-01_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2553.12 0.751 0.773756 Test results for specific bytes for dh-ranFile-2015-11-01_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2375.45 -1.761 0.039085 2 to 9 2468.65 -0.443 0.328771 3 to 10 2523.29 0.329 0.629046 4 to 11 2472.95 -0.382 0.351049 5 to 12 2527.88 0.394 0.653311 6 to 13 2529.23 0.413 0.660350 7 to 14 2558.18 0.823 0.794692 8 to 15 2619.40 1.689 0.954352 9 to 16 2507.42 0.105 0.541805 10 to 17 2585.93 1.215 0.887872 11 to 18 2440.13 -0.847 0.198580 12 to 19 2577.04 1.090 0.862035 13 to 20 2560.34 0.853 0.803248 14 to 21 2462.67 -0.528 0.298767 15 to 22 2486.00 -0.198 0.421536 16 to 23 2566.57 0.941 0.826746 17 to 24 2532.49 0.460 0.677067 18 to 25 2469.04 -0.438 0.330754 19 to 26 2440.51 -0.841 0.200103 20 to 27 2488.36 -0.165 0.434608 21 to 28 2489.80 -0.144 0.442658 22 to 29 2525.37 0.359 0.640146 23 to 30 2643.19 2.025 0.978568 24 to 31 2622.73 1.736 0.958685 25 to 32 2475.34 -0.349 0.363622 CDPARK for dh-ranFile-2015-11-01_17:31: 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 3537 0.6393 0.738676 3534 0.5023 0.692266 3519 -0.1826 0.427537 3513 -0.4566 0.323972 3516 -0.3196 0.374623 3517 -0.2740 0.392053 3521 -0.0913 0.463617 3502 -0.9589 0.168804 3519 -0.1826 0.427537 3542 0.8676 0.807188 Square side=100, avg. no. parked=3522.00 sample std.=11.53 p-value of the KSTEST for those 10 p-values: 0.407573 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-01_17:31 0.2997,0.6536,0.4743,0.0909,0.5953,0.6025,0.7570,0.8780,0.3675,0.9275, The KS test for those 10 p-values: 0.787084 The 3DSPHERES test for dh-ranFile-2015-11-01_17:31 sample no r^3 equiv. uni. 1 20.884 0.501484 2 5.517 0.167982 3 112.344 0.976360 4 48.901 0.804080 5 17.743 0.446466 6 1.722 0.055792 7 1.728 0.055977 8 7.909 0.231732 9 6.693 0.199976 10 43.767 0.767505 11 12.492 0.340579 12 9.658 0.275243 13 12.237 0.334957 14 11.745 0.323952 15 43.229 0.763305 16 6.995 0.207982 17 3.611 0.113397 18 62.707 0.876343 19 33.932 0.677314 20 1.261 0.041156 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.227159 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-01_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 1.3 0.5 -2.3 -1.4 1.5 0.7 2.9 -0.4 0.4 -0.9 -1.4 1.0 0.8 1.3 0.1 -0.1 -0.1 0.4 -2.0 0.6 -1.9 -0.2 -1.8 1.3 -0.6 0.6 -0.3 -0.4 1.2 1.6 0.1 -1.0 -0.5 2.4 -0.5 0.5 0.9 1.0 -0.6 2.0 0.8 Chi-square with 42 degrees of freedom:61.562754 z-score=2.134471, p-value=0.973922 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-01_17:31 Test no p-value 1 0.318242 2 0.180398 3 0.003910 4 0.003080 5 0.255434 6 0.269086 7 0.005713 8 0.726823 9 0.967875 10 0.028803 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000901 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-01_17:31: (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 66870 0.62 66692 0.01 3 25000.00 24849 0.91 24907 0.35 4 6666.67 6648 0.05 6740 0.81 5 1388.89 1393 0.01 1373 0.18 6 238.10 203 5.17 246 0.26 7 34.72 34 0.01 34 0.01 8 4.96 2 1.77 7 0.84 p=0.79955 p=0.12712 Number of rngs required: 687723, p-value: 0.216 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-01_17:31 No. of wins: Observed Expected 98355 98585.9 z-score=-1.033, pvalue=0.15091 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66566 66666.7 0.152 0.152 2 37583 37654.3 0.135 0.287 3 27147 26954.7 1.371 1.659 4 19398 19313.5 0.370 2.029 5 13748 13851.4 0.772 2.801 6 9863 9943.5 0.652 3.453 7 7130 7145.0 0.032 3.485 8 5224 5139.1 1.404 4.888 9 3755 3699.9 0.822 5.710 10 2577 2666.3 2.991 8.701 11 1916 1923.3 0.028 8.728 12 1411 1388.7 0.357 9.085 13 971 1003.7 1.066 10.152 14 773 726.1 3.024 13.176 15 565 525.8 2.917 16.092 16 358 381.2 1.406 17.499 17 309 276.5 3.810 21.309 18 193 200.8 0.305 21.614 19 125 146.0 3.016 24.630 20 98 106.2 0.635 25.266 21 290 287.1 0.029 25.295 Chisq= 25.29 for 20 degrees of freedom, p= 0.80962 SUMMARY of craptest p-value for no. of wins: 0.150911 p-value for throws/game: 0.809619 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-01_17:31 No. of wins: Observed Expected 98370 98585.9 z-score=-0.965, pvalue=0.16716 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66492 66666.7 0.458 0.458 2 37721 37654.3 0.118 0.576 3 26912 26954.7 0.068 0.643 4 19452 19313.5 0.994 1.637 5 13966 13851.4 0.948 2.585 6 9955 9943.5 0.013 2.598 7 7189 7145.0 0.271 2.869 8 5200 5139.1 0.722 3.591 9 3717 3699.9 0.079 3.671 10 2534 2666.3 6.564 10.235 11 1934 1923.3 0.059 10.294 12 1318 1388.7 3.603 13.898 13 964 1003.7 1.571 15.469 14 734 726.1 0.085 15.554 15 551 525.8 1.204 16.758 16 355 381.2 1.794 18.552 17 296 276.5 1.369 19.922 18 191 200.8 0.481 20.403 19 144 146.0 0.027 20.430 20 98 106.2 0.635 21.065 21 277 287.1 0.356 21.422 Chisq= 21.42 for 20 degrees of freedom, p= 0.62731 SUMMARY of craptest p-value for no. of wins: 0.167161 p-value for throws/game: 0.627307 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0031,0.0039,0.0042,0.0057,0.0288,0.0340,0.0373,0.0391,0.0412, 0.0412,0.0514,0.0558,0.0560,0.0578,0.0676,0.0708,0.0832,0.0890,0.0909, 0.0967,0.0968,0.1134,0.1185,0.1271,0.1291,0.1351,0.1421,0.1426,0.1473, 0.1507,0.1509,0.1514,0.1542,0.1561,0.1568,0.1620,0.1621,0.1672,0.1680, 0.1688,0.1804,0.1823,0.1841,0.1884,0.1921,0.1935,0.1986,0.2000,0.2001, 0.2072,0.2080,0.2112,0.2160,0.2201,0.2225,0.2237,0.2272,0.2317,0.2358, 0.2407,0.2429,0.2442,0.2452,0.2518,0.2554,0.2661,0.2670,0.2691,0.2750, 0.2752,0.2783,0.2793,0.2872,0.2902,0.2925,0.2953,0.2984,0.2988,0.2989, 0.2997,0.3042,0.3137,0.3149,0.3182,0.3208,0.3240,0.3240,0.3288,0.3308, 0.3350,0.3406,0.3461,0.3510,0.3581,0.3626,0.3636,0.3675,0.3746,0.3746, 0.3751,0.3823,0.3843,0.3901,0.3921,0.4029,0.4045,0.4076,0.4122,0.4215, 0.4275,0.4275,0.4282,0.4330,0.4346,0.4352,0.4360,0.4366,0.4427,0.4434, 0.4447,0.4465,0.4636,0.4656,0.4658,0.4685,0.4690,0.4724,0.4743,0.4792, 0.4996,0.5008,0.5015,0.5071,0.5102,0.5208,0.5298,0.5337,0.5397,0.5416, 0.5418,0.5433,0.5462,0.5501,0.5527,0.5535,0.5547,0.5563,0.5589,0.5803, 0.5818,0.5953,0.5972,0.5977,0.6025,0.6109,0.6176,0.6190,0.6205,0.6220, 0.6220,0.6220,0.6233,0.6273,0.6288,0.6290,0.6341,0.6401,0.6438,0.6500, 0.6533,0.6533,0.6536,0.6542,0.6569,0.6604,0.6768,0.6771,0.6773,0.6799, 0.6881,0.6894,0.6923,0.6927,0.6969,0.6978,0.7008,0.7083,0.7090,0.7090, 0.7091,0.7102,0.7154,0.7163,0.7177,0.7193,0.7207,0.7242,0.7268,0.7310, 0.7332,0.7357,0.7377,0.7387,0.7523,0.7542,0.7544,0.7544,0.7566,0.7570, 0.7633,0.7667,0.7675,0.7738,0.7753,0.7822,0.7870,0.7871,0.7947,0.7996, 0.8032,0.8041,0.8072,0.8096,0.8119,0.8148,0.8152,0.8172,0.8206,0.8211, 0.8238,0.8267,0.8353,0.8461,0.8507,0.8527,0.8620,0.8763,0.8777,0.8780, 0.8860,0.8879,0.8921,0.8948,0.8957,0.9070,0.9077,0.9084,0.9193,0.9243, 0.9256,0.9268,0.9275,0.9351,0.9414,0.9494,0.9533,0.9544,0.9587,0.9679, 0.9737,0.9739,0.9757,0.9764,0.9786,0.9790,0.9902,0.9915,0.9954, Overall p-value after applying KStest on 269 p-values = 0.700374 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.