RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-06_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.92 11.8727 0.192215 2 to 25 15.66 21.6634 0.801988 3 to 26 15.65 15.1708 0.416822 4 to 27 15.63 27.9290 0.954225 5 to 28 15.77 20.0419 0.727909 6 to 29 15.69 12.2584 0.215754 7 to 30 15.80 18.2745 0.628277 8 to 31 15.68 18.2298 0.625518 9 to 32 15.91 18.5254 0.643556 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.602672 Tough bday spacings test for dh-ranFile-2018-04-06_23:31: 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 6 34 80 103 88 86 40 39 14 8 2 (O-E)^2/E 1.1 0.2 0.6 0.3 1.0 0.8 2.8 2.9 0.1 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 10.999, p= 0.642 RESULTS OF GCD FOR dh-ranFile-2018-04-06_23:31 Euclid's algorithm: p-value, steps to gcd: 0.898128 p-value, dist. of gcd's: 0.185421 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-06_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.254 0.769 0.761 0.414 0.028 0.858 0.556 0.824 Bits 8 to 15---> 0.092 0.357 0.288 0.374 0.328 0.425 0.577 0.447 Bits 16 to 23---> 0.897 0.138 0.685 0.564 0.739 0.260 0.049 0.226 Bits 24 to 31---> 0.597 0.351 0.677 0.469 0.309 0.552 0.171 0.857 KS test for the above 32 p values: 0.471 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-06_23:31, p-values for 5 runs: 0.2760, 0.4146, 0.3177, 0.9555, 0.1813 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-06_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5199 5134.0 0.823 2.123 r= 30 22987 23103.0 0.583 2.706 r= 31 11586 11551.5 0.103 2.809 chi-square = 2.809 with df = 3; p-value = 0.578 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-06_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5124 5134.0 0.020 0.119 r= 31 23235 23103.0 0.754 0.872 r= 32 11425 11551.5 1.386 2.258 chi-square = 2.258 with df = 3; p-value = 0.479 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-06_23:31 b-rank test for bits 1 to 8, p=0.51753 b-rank test for bits 2 to 9, p=0.76596 b-rank test for bits 3 to 10, p=0.02866 b-rank test for bits 4 to 11, p=0.59764 b-rank test for bits 5 to 12, p=0.81939 b-rank test for bits 6 to 13, p=0.09075 b-rank test for bits 7 to 14, p=0.08233 b-rank test for bits 8 to 15, p=0.09509 b-rank test for bits 9 to 16, p=0.63544 b-rank test for bits 10 to 17, p=0.87315 b-rank test for bits 11 to 18, p=0.82034 b-rank test for bits 12 to 19, p=0.42394 b-rank test for bits 13 to 20, p=0.08047 b-rank test for bits 14 to 21, p=0.29686 b-rank test for bits 15 to 22, p=0.39275 b-rank test for bits 16 to 23, p=0.76460 b-rank test for bits 17 to 24, p=0.49030 b-rank test for bits 18 to 25, p=0.42654 b-rank test for bits 19 to 26, p=0.13377 b-rank test for bits 20 to 27, p=0.46900 b-rank test for bits 21 to 28, p=0.86855 b-rank test for bits 22 to 29, p=0.01565 b-rank test for bits 23 to 30, p=0.29375 b-rank test for bits 24 to 31, p=0.55243 b-rank test for bits 25 to 32, p=0.34487 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 = 0.355616 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-06_23:31 (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 141881 -0.07 0.473613 2 141329 -1.36 0.087564 3 142472 1.31 0.905686 4 142089 0.42 0.662681 5 141920 0.02 0.509945 6 141669 -0.56 0.287222 7 142299 0.91 0.818706 8 142013 0.24 0.595695 9 141559 -0.82 0.206528 10 142826 2.14 0.983893 11 140819 -2.55 0.005425 12 141616 -0.69 0.246561 13 142015 0.25 0.597504 14 142158 0.58 0.719381 15 141494 -0.97 0.165924 16 141769 -0.33 0.371504 17 141774 -0.32 0.375929 18 141397 -1.20 0.115647 19 141544 -0.85 0.196670 20 142406 1.16 0.877066 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-06_23:31 Bits used No. missing words z-score p-value 23 to 32 142197 0.9920 0.839393 22 to 31 141967 0.1989 0.578815 21 to 30 142112 0.6989 0.757681 20 to 29 142075 0.5713 0.716094 19 to 28 142213 1.0471 0.852482 18 to 27 142028 0.4092 0.658806 17 to 26 141704 -0.7080 0.239462 16 to 25 141954 0.1540 0.561209 15 to 24 141184 -2.5011 0.006190 14 to 23 142179 0.9299 0.823788 13 to 22 141728 -0.6253 0.265895 12 to 21 141862 -0.1632 0.435178 11 to 20 142454 1.8782 0.969821 10 to 19 142099 0.6540 0.743455 9 to 18 142224 1.0851 0.861054 8 to 17 141665 -0.8425 0.199749 7 to 16 142081 0.5920 0.723063 6 to 15 142015 0.3644 0.642213 5 to 14 141771 -0.4770 0.316681 4 to 13 141945 0.1230 0.548947 3 to 12 142283 1.2885 0.901217 2 to 11 141651 -0.8908 0.186520 1 to 10 141708 -0.6942 0.243765 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-06_23:31 Bits used No. missing words z-score p-value 28 to 32 142372 1.5684 0.941603 27 to 31 141717 -0.6520 0.257212 26 to 30 141446 -1.5706 0.058137 25 to 29 141736 -0.5876 0.278414 24 to 28 142020 0.3752 0.646227 23 to 27 142349 1.4904 0.931941 22 to 26 141781 -0.4350 0.331775 21 to 25 142239 1.1175 0.868115 20 to 24 142104 0.6599 0.745341 19 to 23 141784 -0.4248 0.335474 18 to 22 142031 0.4124 0.659992 17 to 21 141464 -1.5096 0.065574 16 to 20 141667 -0.8215 0.205693 15 to 19 141777 -0.4486 0.326869 14 to 18 142214 1.0328 0.849147 13 to 17 142141 0.7853 0.783868 12 to 16 141893 -0.0554 0.477928 11 to 15 141405 -1.7096 0.043671 10 to 14 141774 -0.4587 0.323208 9 to 13 141613 -1.0045 0.157567 8 to 12 141467 -1.4994 0.066882 7 to 11 141938 0.0972 0.538711 6 to 10 141943 0.1141 0.545435 5 to 9 142211 1.0226 0.846754 4 to 8 141941 0.1074 0.542747 3 to 7 142182 0.9243 0.822336 2 to 6 141793 -0.3943 0.346665 1 to 5 141980 0.2396 0.594664 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-06_23:31 Bits used No. missing words z-score p-value 31 to 32 142313 1.1908 0.883127 30 to 31 142229 0.9430 0.827154 29 to 30 141673 -0.6971 0.242858 28 to 29 142060 0.4445 0.671643 27 to 28 141535 -1.1042 0.134749 26 to 27 142071 0.4769 0.683284 25 to 26 142400 1.4474 0.926108 24 to 25 141942 0.0964 0.538387 23 to 24 141391 -1.5290 0.063133 22 to 23 142079 0.5005 0.691639 21 to 22 142124 0.6332 0.736713 20 to 21 141805 -0.3078 0.379133 19 to 20 141561 -1.0275 0.152087 18 to 19 141728 -0.5349 0.296361 17 to 18 141190 -2.1219 0.016922 16 to 17 142060 0.4445 0.671643 15 to 16 142211 0.8899 0.813235 14 to 15 141798 -0.3284 0.371302 13 to 14 141091 -2.4140 0.007890 12 to 13 142096 0.5506 0.709063 11 to 12 142242 0.9813 0.836784 10 to 11 141897 -0.0364 0.485493 9 to 10 141716 -0.5703 0.284239 8 to 9 141790 -0.3520 0.362417 7 to 8 141568 -1.0069 0.156998 6 to 7 142554 1.9017 0.971394 5 to 6 141889 -0.0600 0.476090 4 to 5 141866 -0.1278 0.449147 3 to 4 141870 -0.1160 0.453819 2 to 3 142011 0.2999 0.617878 1 to 2 141558 -1.0364 0.150014 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-06_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2478.52 -0.304 0.380662 Test results for specific bytes for dh-ranFile-2018-04-06_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2495.69 -0.061 0.475705 2 to 9 2616.23 1.644 0.949889 3 to 10 2483.01 -0.240 0.405080 4 to 11 2462.30 -0.533 0.296974 5 to 12 2524.14 0.341 0.633617 6 to 13 2461.41 -0.546 0.292605 7 to 14 2465.12 -0.493 0.310914 8 to 15 2458.02 -0.594 0.276359 9 to 16 2634.91 1.908 0.971798 10 to 17 2558.40 0.826 0.795581 11 to 18 2622.61 1.734 0.958533 12 to 19 2437.62 -0.882 0.188828 13 to 20 2540.25 0.569 0.715415 14 to 21 2316.26 -2.598 0.004682 15 to 22 2507.92 0.112 0.544571 16 to 23 2463.55 -0.516 0.303095 17 to 24 2420.32 -1.127 0.129903 18 to 25 2502.54 0.036 0.514348 19 to 26 2505.48 0.077 0.530866 20 to 27 2428.22 -1.015 0.155022 21 to 28 2489.83 -0.144 0.442841 22 to 29 2448.22 -0.732 0.232006 23 to 30 2561.70 0.873 0.808559 24 to 31 2521.68 0.307 0.620409 25 to 32 2372.65 -1.801 0.035847 CDPARK for dh-ranFile-2018-04-06_23:31: 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 3519 -0.1826 0.427537 3530 0.3196 0.625377 3509 -0.6393 0.261324 3491 -1.4612 0.071982 3512 -0.5023 0.307734 3543 0.9132 0.819442 3530 0.3196 0.625377 3536 0.5936 0.723613 3512 -0.5023 0.307734 3530 0.3196 0.625377 Square side=100, avg. no. parked=3521.20 sample std.=14.70 p-value of the KSTEST for those 10 p-values: 0.723704 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-06_23:31 0.0440,0.4568,0.0206,0.3173,0.0617,0.8705,0.9134,0.2105,0.7798,0.9345, The KS test for those 10 p-values: 0.311413 The 3DSPHERES test for dh-ranFile-2018-04-06_23:31 sample no r^3 equiv. uni. 1 13.530 0.363011 2 14.365 0.380503 3 18.130 0.453567 4 24.021 0.550993 5 25.683 0.575182 6 20.770 0.499595 7 13.553 0.363497 8 36.205 0.700852 9 7.925 0.232166 10 4.061 0.126604 11 22.760 0.531708 12 41.681 0.750767 13 1.136 0.037172 14 44.700 0.774629 15 27.483 0.599923 16 25.299 0.569717 17 11.782 0.324786 18 20.961 0.502770 19 45.943 0.783774 20 20.412 0.493590 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.196914 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-06_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 0.1 0.3 -0.7 -0.2 -0.2 -0.2 -0.2 0.3 1.1 0.4 -1.6 -2.0 0.7 -0.2 0.2 0.0 -0.6 -0.7 0.5 1.3 -0.6 -0.1 -1.2 1.5 1.4 0.9 0.5 -0.3 0.4 -0.5 -0.1 1.1 0.3 2.7 -1.9 0.3 0.2 -0.8 1.0 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:43.695710 z-score=0.185017, p-value=0.600702 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-06_23:31 Test no p-value 1 0.059915 2 0.954481 3 0.502527 4 0.837246 5 0.403803 6 0.911600 7 0.339329 8 0.095633 9 0.449923 10 0.196045 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.893733 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-06_23:31: (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 66698 0.01 66739 0.08 3 25000.00 24936 0.16 24988 0.01 4 6666.67 6697 0.14 6613 0.43 5 1388.89 1392 0.01 1374 0.16 6 238.10 232 0.16 234 0.07 7 34.72 39 0.53 46 3.66 8 4.96 5 0.00 5 0.00 p=0.01467 p=0.37881 Number of rngs required: 689639, p-value: 0.925 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-06_23:31 No. of wins: Observed Expected 98868 98585.9 z-score= 1.262, pvalue=0.89651 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66778 66666.7 0.186 0.186 2 37549 37654.3 0.295 0.481 3 26944 26954.7 0.004 0.485 4 19323 19313.5 0.005 0.489 5 13885 13851.4 0.081 0.571 6 9844 9943.5 0.997 1.567 7 7157 7145.0 0.020 1.587 8 5248 5139.1 2.309 3.896 9 3719 3699.9 0.099 3.995 10 2541 2666.3 5.888 9.883 11 1893 1923.3 0.478 10.362 12 1417 1388.7 0.575 10.937 13 930 1003.7 5.414 16.351 14 751 726.1 0.851 17.202 15 549 525.8 1.020 18.222 16 387 381.2 0.090 18.312 17 275 276.5 0.009 18.320 18 204 200.8 0.050 18.370 19 168 146.0 3.320 21.691 20 120 106.2 1.789 23.480 21 318 287.1 3.323 26.802 Chisq= 26.80 for 20 degrees of freedom, p= 0.85907 SUMMARY of craptest p-value for no. of wins: 0.896508 p-value for throws/game: 0.859074 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-06_23:31 No. of wins: Observed Expected 98241 98585.9 z-score=-1.542, pvalue=0.06149 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66489 66666.7 0.473 0.473 2 38003 37654.3 3.229 3.702 3 26935 26954.7 0.014 3.717 4 19307 19313.5 0.002 3.719 5 13802 13851.4 0.176 3.895 6 9908 9943.5 0.127 4.022 7 7123 7145.0 0.068 4.090 8 5195 5139.1 0.609 4.699 9 3555 3699.9 5.672 10.371 10 2719 2666.3 1.042 11.413 11 1984 1923.3 1.914 13.326 12 1346 1388.7 1.315 14.642 13 1012 1003.7 0.068 14.710 14 740 726.1 0.265 14.975 15 524 525.8 0.006 14.981 16 355 381.2 1.794 16.775 17 291 276.5 0.756 17.531 18 190 200.8 0.584 18.115 19 139 146.0 0.334 18.450 20 102 106.2 0.167 18.617 21 281 287.1 0.130 18.747 Chisq= 18.75 for 20 degrees of freedom, p= 0.46169 SUMMARY of craptest p-value for no. of wins: 0.061487 p-value for throws/game: 0.461686 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0047,0.0054,0.0062,0.0079,0.0147,0.0156,0.0169,0.0206,0.0278,0.0287, 0.0358,0.0372,0.0437,0.0440,0.0488,0.0581,0.0599,0.0615,0.0617,0.0631, 0.0656,0.0669,0.0720,0.0805,0.0823,0.0876,0.0907,0.0923,0.0951,0.0956, 0.1156,0.1266,0.1299,0.1338,0.1347,0.1382,0.1500,0.1521,0.1550,0.1570, 0.1576,0.1659,0.1714,0.1813,0.1854,0.1865,0.1888,0.1922,0.1960,0.1967, 0.1969,0.1997,0.2057,0.2065,0.2105,0.2158,0.2261,0.2320,0.2322,0.2395, 0.2429,0.2438,0.2466,0.2543,0.2572,0.2595,0.2613,0.2659,0.2760,0.2764, 0.2784,0.2842,0.2872,0.2876,0.2926,0.2938,0.2964,0.2969,0.2970,0.3031, 0.3077,0.3077,0.3090,0.3109,0.3114,0.3167,0.3173,0.3177,0.3232,0.3248, 0.3269,0.3275,0.3318,0.3355,0.3393,0.3449,0.3467,0.3505,0.3556,0.3573, 0.3624,0.3630,0.3635,0.3713,0.3715,0.3743,0.3759,0.3788,0.3791,0.3805, 0.3807,0.3928,0.4038,0.4051,0.4140,0.4146,0.4168,0.4239,0.4251,0.4265, 0.4275,0.4352,0.4428,0.4467,0.4491,0.4499,0.4536,0.4538,0.4568,0.4617, 0.4688,0.4690,0.4708,0.4736,0.4757,0.4761,0.4779,0.4794,0.4855,0.4903, 0.4936,0.4996,0.5025,0.5028,0.5099,0.5143,0.5175,0.5309,0.5317,0.5384, 0.5387,0.5427,0.5446,0.5454,0.5489,0.5510,0.5515,0.5524,0.5555,0.5612, 0.5643,0.5697,0.5752,0.5772,0.5780,0.5788,0.5947,0.5957,0.5970,0.5975, 0.5976,0.5999,0.6007,0.6027,0.6179,0.6204,0.6254,0.6254,0.6254,0.6255, 0.6283,0.6336,0.6354,0.6422,0.6424,0.6436,0.6462,0.6588,0.6600,0.6627, 0.6716,0.6716,0.6773,0.6833,0.6850,0.6916,0.7009,0.7091,0.7154,0.7161, 0.7194,0.7231,0.7236,0.7237,0.7279,0.7367,0.7390,0.7435,0.7453,0.7508, 0.7577,0.7609,0.7646,0.7660,0.7689,0.7746,0.7798,0.7838,0.7839,0.7956, 0.8020,0.8086,0.8132,0.8187,0.8194,0.8194,0.8203,0.8223,0.8238,0.8238, 0.8272,0.8368,0.8372,0.8394,0.8468,0.8491,0.8525,0.8571,0.8578,0.8591, 0.8611,0.8681,0.8685,0.8705,0.8731,0.8771,0.8831,0.8937,0.8965,0.8973, 0.8981,0.9012,0.9057,0.9116,0.9134,0.9254,0.9261,0.9319,0.9345,0.9416, 0.9499,0.9542,0.9545,0.9555,0.9585,0.9698,0.9714,0.9718,0.9839, Overall p-value after applying KStest on 269 p-values = 0.353300 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.