RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-01_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 15.9790 0.474678 2 to 25 15.78 12.9613 0.261226 3 to 26 15.70 26.5637 0.935215 4 to 27 15.68 15.2738 0.424230 5 to 28 15.71 10.0659 0.099176 6 to 29 15.52 24.8817 0.902611 7 to 30 15.56 18.0808 0.616238 8 to 31 15.70 13.0038 0.264068 9 to 32 15.38 26.5156 0.934435 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.696759 Tough bday spacings test for dh-ranFile-2015-08-01_08:31: 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 15 45 52 103 114 66 51 30 13 8 3 (O-E)^2/E 3.7 1.9 6.2 0.3 2.7 1.9 0.0 0.0 0.2 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 17.546, p= 0.937 RESULTS OF GCD FOR dh-ranFile-2015-08-01_08:31 Euclid's algorithm: p-value, steps to gcd: 0.258914 p-value, dist. of gcd's: 0.293615 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-01_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.920 0.861 0.535 0.782 0.763 0.735 0.814 0.016 Bits 8 to 15---> 0.943 0.930 0.430 0.939 0.361 0.741 0.479 0.845 Bits 16 to 23---> 0.466 0.017 0.654 0.925 0.089 0.078 0.521 0.598 Bits 24 to 31---> 0.416 0.710 0.374 0.675 0.400 0.394 0.538 0.667 KS test for the above 32 p values: 0.879 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-01_08:31, p-values for 5 runs: 0.4505, 0.6692, 0.2892, 0.8306, 0.1964 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-01_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5150 5134.0 0.050 0.579 r= 30 23190 23103.0 0.327 0.907 r= 31 11438 11551.5 1.116 2.022 chi-square = 2.022 with df = 3; p-value = 0.432 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-01_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5158 5134.0 0.112 0.747 r= 31 23083 23103.0 0.017 0.764 r= 32 11536 11551.5 0.021 0.785 chi-square = 0.785 with df = 3; p-value = 0.147 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-01_08:31 b-rank test for bits 1 to 8, p=0.37482 b-rank test for bits 2 to 9, p=0.01409 b-rank test for bits 3 to 10, p=0.64219 b-rank test for bits 4 to 11, p=0.21639 b-rank test for bits 5 to 12, p=0.81733 b-rank test for bits 6 to 13, p=0.50406 b-rank test for bits 7 to 14, p=0.10966 b-rank test for bits 8 to 15, p=0.29639 b-rank test for bits 9 to 16, p=0.36308 b-rank test for bits 10 to 17, p=0.15045 b-rank test for bits 11 to 18, p=0.08414 b-rank test for bits 12 to 19, p=0.91230 b-rank test for bits 13 to 20, p=0.96428 b-rank test for bits 14 to 21, p=0.23797 b-rank test for bits 15 to 22, p=0.60438 b-rank test for bits 16 to 23, p=0.68001 b-rank test for bits 17 to 24, p=0.20781 b-rank test for bits 18 to 25, p=0.92151 b-rank test for bits 19 to 26, p=0.39776 b-rank test for bits 20 to 27, p=0.18805 b-rank test for bits 21 to 28, p=0.70999 b-rank test for bits 22 to 29, p=0.54003 b-rank test for bits 23 to 30, p=0.86822 b-rank test for bits 24 to 31, p=0.49971 b-rank test for bits 25 to 32, p=0.87442 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 = 0.994733 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-01_08:31 (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 141687 -0.52 0.301719 2 141809 -0.23 0.407331 3 141448 -1.08 0.140545 4 142080 0.40 0.654966 5 141451 -1.07 0.142115 6 141464 -1.04 0.149056 7 142172 0.61 0.730298 8 142126 0.51 0.693655 9 141594 -0.74 0.230637 10 141587 -0.75 0.225693 11 142338 1.00 0.841723 12 141836 -0.17 0.431981 13 142039 0.30 0.619043 14 142343 1.01 0.844529 15 141713 -0.46 0.323219 16 142692 1.83 0.966275 17 142068 0.37 0.644579 18 142476 1.32 0.907248 19 142790 2.06 0.980188 20 142003 0.22 0.586619 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-01_08:31 Bits used No. missing words z-score p-value 23 to 32 141498 -1.4184 0.078040 22 to 31 141707 -0.6977 0.242686 21 to 30 141676 -0.8046 0.210529 20 to 29 142021 0.3851 0.649907 19 to 28 141700 -0.7218 0.235200 18 to 27 141744 -0.5701 0.284304 17 to 26 141900 -0.0322 0.487167 16 to 25 141818 -0.3149 0.376407 15 to 24 142244 1.1540 0.875757 14 to 23 141301 -2.0977 0.017966 13 to 22 142026 0.4023 0.656272 12 to 21 141823 -0.2977 0.382970 11 to 20 141730 -0.6184 0.268163 10 to 19 141664 -0.8460 0.198786 9 to 18 141377 -1.8356 0.033207 8 to 17 141797 -0.3873 0.349251 7 to 16 141905 -0.0149 0.494044 6 to 15 141977 0.2333 0.592253 5 to 14 141686 -0.7701 0.220619 4 to 13 141611 -1.0287 0.151805 3 to 12 141534 -1.2942 0.097791 2 to 11 141428 -1.6598 0.048482 1 to 10 141841 -0.2356 0.406864 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-01_08:31 Bits used No. missing words z-score p-value 28 to 32 141997 0.2972 0.616838 27 to 31 141918 0.0294 0.511723 26 to 30 142094 0.6260 0.734343 25 to 29 141640 -0.9130 0.180626 24 to 28 141710 -0.6757 0.249617 23 to 27 142241 1.1243 0.869558 22 to 26 141973 0.2158 0.585440 21 to 25 142602 2.3480 0.990564 20 to 24 141495 -1.4045 0.080084 19 to 23 142280 1.2565 0.895534 18 to 22 142385 1.6124 0.946567 17 to 21 141390 -1.7604 0.039167 16 to 20 141836 -0.2486 0.401844 15 to 19 142174 0.8972 0.815190 14 to 18 142481 1.9379 0.973680 13 to 17 142211 1.0226 0.846754 12 to 16 142142 0.7887 0.784860 11 to 15 142322 1.3989 0.919076 10 to 14 142059 0.5074 0.694048 9 to 13 141495 -1.4045 0.080084 8 to 12 141673 -0.8011 0.211532 7 to 11 142806 3.0396 0.998815 6 to 10 142081 0.5819 0.719694 5 to 9 141414 -1.6791 0.046568 4 to 8 141775 -0.4554 0.324427 3 to 7 142544 2.1514 0.984279 2 to 6 141590 -1.0825 0.139521 1 to 5 141176 -2.4859 0.006462 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-01_08:31 Bits used No. missing words z-score p-value 31 to 32 141527 -1.1278 0.129699 30 to 31 141661 -0.7325 0.231921 29 to 30 142543 1.8692 0.969205 28 to 29 142504 1.7542 0.960301 27 to 28 141627 -0.8328 0.202470 26 to 27 141558 -1.0364 0.150014 25 to 26 142366 1.3471 0.911027 24 to 25 141683 -0.6676 0.252182 23 to 24 142204 0.8692 0.807640 22 to 23 142438 1.5595 0.940561 21 to 22 141329 -1.7119 0.043459 20 to 21 141286 -1.8387 0.032977 19 to 20 142124 0.6332 0.736713 18 to 19 141471 -1.2930 0.098004 17 to 18 142129 0.6480 0.741506 16 to 17 141867 -0.1249 0.450314 15 to 16 142241 0.9784 0.836056 14 to 15 141840 -0.2045 0.418976 13 to 14 142340 1.2704 0.898031 12 to 13 142026 0.3442 0.634637 11 to 12 141899 -0.0305 0.487845 10 to 11 142045 0.4002 0.655498 9 to 10 142705 2.3471 0.990540 8 to 9 141746 -0.4818 0.314974 7 to 8 141337 -1.6883 0.045678 6 to 7 141809 -0.2960 0.383631 5 to 6 141985 0.2232 0.588316 4 to 5 141433 -1.4051 0.079995 3 to 4 141532 -1.1131 0.132840 2 to 3 141550 -1.0600 0.144579 1 to 2 141477 -1.2753 0.101100 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-01_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2549.26 0.697 0.757005 Test results for specific bytes for dh-ranFile-2015-08-01_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2559.42 0.840 0.799634 2 to 9 2526.74 0.378 0.647326 3 to 10 2497.21 -0.039 0.484264 4 to 11 2567.92 0.961 0.831616 5 to 12 2589.16 1.261 0.896327 6 to 13 2482.13 -0.253 0.400268 7 to 14 2432.89 -0.949 0.171290 8 to 15 2525.29 0.358 0.639698 9 to 16 2508.99 0.127 0.550566 10 to 17 2516.07 0.227 0.589886 11 to 18 2413.22 -1.227 0.109865 12 to 19 2479.68 -0.287 0.386939 13 to 20 2408.32 -1.297 0.097386 14 to 21 2506.56 0.093 0.536937 15 to 22 2415.01 -1.202 0.114689 16 to 23 2496.83 -0.045 0.482093 17 to 24 2482.36 -0.250 0.401486 18 to 25 2432.55 -0.954 0.170084 19 to 26 2570.09 0.991 0.839201 20 to 27 2478.39 -0.306 0.379975 21 to 28 2516.77 0.237 0.593734 22 to 29 2588.50 1.252 0.894636 23 to 30 2462.49 -0.530 0.297901 24 to 31 2484.29 -0.222 0.412081 25 to 32 2458.95 -0.580 0.280797 CDPARK for dh-ranFile-2015-08-01_08:31: 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 3517 -0.2740 0.392053 3523 0.0000 0.500000 3473 -2.2831 0.011212 3517 -0.2740 0.392053 3537 0.6393 0.738676 3569 2.1005 0.982156 3540 0.7763 0.781201 3482 -1.8721 0.030593 3539 0.7306 0.767486 Square side=100, avg. no. parked=3523.40 sample std.=27.03 p-value of the KSTEST for those 10 p-values: 0.491333 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-01_08:31 0.2232,0.3727,0.7501,0.0944,0.8264,0.2183,0.6715,0.8485,0.2405,0.1985, The KS test for those 10 p-values: 0.596078 The 3DSPHERES test for dh-ranFile-2015-08-01_08:31 sample no r^3 equiv. uni. 1 113.491 0.977246 2 53.580 0.832373 3 3.027 0.095972 4 54.653 0.838258 5 60.347 0.866221 6 74.761 0.917259 7 42.172 0.754812 8 33.097 0.668199 9 4.611 0.142481 10 9.113 0.261961 11 26.101 0.581064 12 33.529 0.672942 13 131.458 0.987499 14 17.066 0.433842 15 32.446 0.660921 16 8.392 0.244020 17 3.917 0.122394 18 43.201 0.763081 19 6.684 0.199724 20 12.406 0.338680 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.421440 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-01_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.5 1.8 -0.7 0.9 1.9 0.5 -0.1 -0.6 -0.6 -1.3 1.2 -0.8 -0.4 -0.4 1.4 1.3 0.3 1.6 -0.4 0.6 -1.7 -0.1 -0.3 -0.2 -1.9 1.0 -2.4 -1.1 -1.7 1.7 1.7 -1.3 0.2 -1.3 0.6 0.0 1.8 0.1 -0.7 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:57.828794 z-score=1.727063, p-value=0.947258 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-01_08:31 Test no p-value 1 0.247413 2 0.501400 3 0.154283 4 0.165710 5 0.030728 6 0.304037 7 0.377144 8 0.099167 9 0.667328 10 0.022887 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011839 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-01_08:31: (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 66716 0.04 66562 0.16 3 25000.00 24974 0.03 25134 0.72 4 6666.67 6635 0.15 6629 0.21 5 1388.89 1393 0.01 1399 0.07 6 238.10 242 0.06 241 0.04 7 34.72 32 0.21 31 0.40 8 4.96 7 0.84 3 0.77 p=0.03073 p=0.11809 Number of rngs required: 690127, p-value: 0.979 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-01_08:31 No. of wins: Observed Expected 98297 98585.9 z-score=-1.292, pvalue=0.09819 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66181 66666.7 3.538 3.538 2 38084 37654.3 4.903 8.441 3 26945 26954.7 0.004 8.445 4 19389 19313.5 0.295 8.740 5 13919 13851.4 0.330 9.070 6 9838 9943.5 1.120 10.190 7 7229 7145.0 0.987 11.177 8 5158 5139.1 0.070 11.247 9 3735 3699.9 0.334 11.580 10 2645 2666.3 0.170 11.751 11 1896 1923.3 0.388 12.139 12 1318 1388.7 3.603 15.742 13 1003 1003.7 0.001 15.743 14 751 726.1 0.851 16.594 15 566 525.8 3.068 19.662 16 370 381.2 0.326 19.988 17 230 276.5 7.832 27.820 18 187 200.8 0.952 28.772 19 145 146.0 0.007 28.779 20 115 106.2 0.727 29.506 21 296 287.1 0.275 29.781 Chisq= 29.78 for 20 degrees of freedom, p= 0.92651 SUMMARY of craptest p-value for no. of wins: 0.098188 p-value for throws/game: 0.926514 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-01_08:31 No. of wins: Observed Expected 98652 98585.9 z-score= 0.296, pvalue=0.61632 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66673 66666.7 0.001 0.001 2 37773 37654.3 0.374 0.375 3 26958 26954.7 0.000 0.375 4 19231 19313.5 0.352 0.727 5 13930 13851.4 0.446 1.173 6 9886 9943.5 0.333 1.506 7 7198 7145.0 0.393 1.899 8 5032 5139.1 2.231 4.130 9 3705 3699.9 0.007 4.137 10 2680 2666.3 0.070 4.207 11 1862 1923.3 1.956 6.163 12 1351 1388.7 1.026 7.188 13 1044 1003.7 1.617 8.805 14 720 726.1 0.052 8.857 15 526 525.8 0.000 8.857 16 400 381.2 0.932 9.789 17 298 276.5 1.665 11.455 18 171 200.8 4.431 15.885 19 152 146.0 0.248 16.133 20 120 106.2 1.789 17.922 21 290 287.1 0.029 17.951 Chisq= 17.95 for 20 degrees of freedom, p= 0.40939 SUMMARY of craptest p-value for no. of wins: 0.616317 p-value for throws/game: 0.409389 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0065,0.0112,0.0118,0.0141,0.0155,0.0168,0.0180,0.0229,0.0306,0.0307, 0.0307,0.0330,0.0332,0.0392,0.0435,0.0457,0.0466,0.0485,0.0780,0.0783, 0.0800,0.0801,0.0801,0.0841,0.0887,0.0944,0.0960,0.0974,0.0978,0.0980, 0.0982,0.0992,0.0992,0.1011,0.1097,0.1099,0.1147,0.1181,0.1224,0.1297, 0.1328,0.1395,0.1405,0.1421,0.1425,0.1446,0.1469,0.1491,0.1500,0.1504, 0.1518,0.1543,0.1657,0.1701,0.1713,0.1806,0.1881,0.1964,0.1985,0.1988, 0.1997,0.2025,0.2078,0.2105,0.2115,0.2164,0.2183,0.2206,0.2232,0.2257, 0.2306,0.2319,0.2352,0.2380,0.2405,0.2427,0.2440,0.2474,0.2496,0.2522, 0.2589,0.2612,0.2620,0.2641,0.2682,0.2808,0.2843,0.2892,0.2936,0.2964, 0.2979,0.3017,0.3040,0.3150,0.3232,0.3244,0.3387,0.3493,0.3612,0.3631, 0.3727,0.3735,0.3748,0.3764,0.3771,0.3800,0.3830,0.3836,0.3869,0.3921, 0.3921,0.3938,0.3978,0.4000,0.4003,0.4015,0.4018,0.4069,0.4073,0.4094, 0.4121,0.4159,0.4190,0.4214,0.4242,0.4297,0.4320,0.4322,0.4338,0.4503, 0.4505,0.4657,0.4747,0.4793,0.4821,0.4843,0.4872,0.4878,0.4913,0.4940, 0.4997,0.5000,0.5014,0.5041,0.5117,0.5210,0.5355,0.5369,0.5377,0.5400, 0.5506,0.5811,0.5854,0.5866,0.5883,0.5899,0.5923,0.5937,0.5961,0.5983, 0.6044,0.6162,0.6163,0.6168,0.6190,0.6346,0.6397,0.6422,0.6446,0.6473, 0.6499,0.6543,0.6550,0.6555,0.6563,0.6609,0.6672,0.6673,0.6682,0.6692, 0.6715,0.6729,0.6748,0.6800,0.6937,0.6940,0.6968,0.7100,0.7102,0.7197, 0.7303,0.7343,0.7346,0.7367,0.7387,0.7387,0.7409,0.7415,0.7501,0.7548, 0.7570,0.7631,0.7631,0.7675,0.7812,0.7823,0.7849,0.7996,0.8076,0.8141, 0.8152,0.8173,0.8264,0.8306,0.8316,0.8324,0.8361,0.8383,0.8392,0.8417, 0.8445,0.8447,0.8468,0.8485,0.8614,0.8662,0.8682,0.8696,0.8744,0.8758, 0.8791,0.8946,0.8955,0.8963,0.8980,0.9026,0.9072,0.9110,0.9123,0.9173, 0.9191,0.9205,0.9215,0.9247,0.9265,0.9305,0.9344,0.9352,0.9369,0.9390, 0.9406,0.9425,0.9466,0.9473,0.9603,0.9643,0.9663,0.9692,0.9737,0.9772, 0.9791,0.9802,0.9822,0.9843,0.9875,0.9905,0.9906,0.9947,0.9988, Overall p-value after applying KStest on 269 p-values = 0.405308 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.