RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-28_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 13.5561 0.301764 2 to 25 16.04 15.2089 0.419559 3 to 26 15.96 23.8964 0.877723 4 to 27 16.14 18.7848 0.658974 5 to 28 16.00 19.2089 0.683325 6 to 29 15.75 18.2183 0.624806 7 to 30 15.80 19.5452 0.701848 8 to 31 16.10 14.3288 0.356295 9 to 32 15.92 12.3669 0.222573 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.602129 Tough bday spacings test for dh-ranFile-2018-03-28_19:31: 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 12 31 76 108 88 75 55 26 19 3 7 (O-E)^2/E 0.9 0.9 0.1 1.1 1.0 0.1 0.2 0.5 1.1 2.0 2.1 Birthday Spacings: Sum(O-E)^2/E= 9.896, p= 0.550 RESULTS OF GCD FOR dh-ranFile-2018-03-28_19:31 Euclid's algorithm: p-value, steps to gcd: 0.737975 p-value, dist. of gcd's: 0.760700 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-28_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.989 0.397 0.795 0.274 0.685 0.828 0.790 0.135 Bits 8 to 15---> 0.518 0.746 0.334 0.854 0.458 0.527 0.042 0.939 Bits 16 to 23---> 0.326 0.863 0.893 0.291 0.707 0.497 0.253 0.467 Bits 24 to 31---> 0.588 0.461 0.252 0.909 0.333 0.418 0.789 0.843 KS test for the above 32 p values: 0.768 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-28_19:31, p-values for 5 runs: 0.7728, 0.4908, 0.6324, 0.9044, 0.3601 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-28_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5171 5134.0 0.267 0.268 r= 30 23076 23103.0 0.032 0.300 r= 31 11541 11551.5 0.010 0.309 chi-square = 0.309 with df = 3; p-value = 0.042 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-28_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5168 5134.0 0.225 0.974 r= 31 23105 23103.0 0.000 0.974 r= 32 11503 11551.5 0.204 1.178 chi-square = 1.178 with df = 3; p-value = 0.242 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-28_19:31 b-rank test for bits 1 to 8, p=0.98403 b-rank test for bits 2 to 9, p=0.54340 b-rank test for bits 3 to 10, p=0.66127 b-rank test for bits 4 to 11, p=0.79868 b-rank test for bits 5 to 12, p=0.93518 b-rank test for bits 6 to 13, p=0.96309 b-rank test for bits 7 to 14, p=0.07761 b-rank test for bits 8 to 15, p=0.09980 b-rank test for bits 9 to 16, p=0.62246 b-rank test for bits 10 to 17, p=0.88347 b-rank test for bits 11 to 18, p=0.63890 b-rank test for bits 12 to 19, p=0.97151 b-rank test for bits 13 to 20, p=0.39363 b-rank test for bits 14 to 21, p=0.30058 b-rank test for bits 15 to 22, p=0.70605 b-rank test for bits 16 to 23, p=0.20262 b-rank test for bits 17 to 24, p=0.37544 b-rank test for bits 18 to 25, p=0.75827 b-rank test for bits 19 to 26, p=0.48427 b-rank test for bits 20 to 27, p=0.23234 b-rank test for bits 21 to 28, p=0.85687 b-rank test for bits 22 to 29, p=0.88044 b-rank test for bits 23 to 30, p=0.19773 b-rank test for bits 24 to 31, p=0.89119 b-rank test for bits 25 to 32, p=0.64869 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 = 0.104229 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-28_19:31 (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 141530 -0.89 0.187732 2 142046 0.32 0.625259 3 142086 0.41 0.660116 4 142077 0.39 0.652379 5 141883 -0.06 0.475473 6 141356 -1.29 0.098035 7 141634 -0.64 0.260017 8 141725 -0.43 0.333351 9 142993 2.53 0.994328 10 141202 -1.65 0.049202 11 142453 1.27 0.898003 12 142018 0.25 0.600214 13 142200 0.68 0.751474 14 141878 -0.07 0.470823 15 141399 -1.19 0.116560 16 141738 -0.40 0.344466 17 141327 -1.36 0.086823 18 141412 -1.16 0.122621 19 140919 -2.31 0.010338 20 141288 -1.45 0.073292 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-28_19:31 Bits used No. missing words z-score p-value 23 to 32 141774 -0.4667 0.320373 22 to 31 142334 1.4644 0.928455 21 to 30 141263 -2.2287 0.012916 20 to 29 142159 0.8609 0.805362 19 to 28 141952 0.1471 0.558488 18 to 27 141470 -1.5149 0.064895 17 to 26 141945 0.1230 0.548947 16 to 25 141728 -0.6253 0.265895 15 to 24 142098 0.6506 0.742343 14 to 23 141582 -1.1287 0.129507 13 to 22 141807 -0.3529 0.362096 12 to 21 141508 -1.3839 0.083195 11 to 20 140991 -3.1667 0.000771 10 to 19 141839 -0.2425 0.404190 9 to 18 141527 -1.3184 0.093688 8 to 17 141941 0.1092 0.543481 7 to 16 142238 1.1333 0.871465 6 to 15 142261 1.2127 0.887369 5 to 14 142107 0.6816 0.752261 4 to 13 142001 0.3161 0.624038 3 to 12 142108 0.6851 0.753350 2 to 11 141606 -1.0460 0.147789 1 to 10 141904 -0.0184 0.492668 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-28_19:31 Bits used No. missing words z-score p-value 28 to 32 142479 1.9311 0.973264 27 to 31 141411 -1.6893 0.045585 26 to 30 142146 0.8023 0.788802 25 to 29 141729 -0.6113 0.270504 24 to 28 141923 0.0463 0.518480 23 to 27 142282 1.2633 0.896757 22 to 26 141714 -0.6621 0.253942 21 to 25 142074 0.5582 0.711647 20 to 24 142471 1.9040 0.971543 19 to 23 141833 -0.2587 0.397916 18 to 22 142314 1.3718 0.914931 17 to 21 141688 -0.7503 0.226546 16 to 20 141802 -0.3638 0.357992 15 to 19 141734 -0.5943 0.276143 14 to 18 141634 -0.9333 0.175327 13 to 17 142657 2.5345 0.994369 12 to 16 141793 -0.3943 0.346665 11 to 15 142489 1.9650 0.975292 10 to 14 142061 0.5141 0.696421 9 to 13 141878 -0.1062 0.457711 8 to 12 141704 -0.6960 0.243204 7 to 11 141718 -0.6486 0.258306 6 to 10 141858 -0.1740 0.430933 5 to 9 141900 -0.0316 0.487385 4 to 8 142047 0.4667 0.679635 3 to 7 141964 0.1853 0.573512 2 to 6 141936 0.0904 0.536018 1 to 5 142085 0.5955 0.724243 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-28_19:31 Bits used No. missing words z-score p-value 31 to 32 142269 1.0610 0.855649 30 to 31 141929 0.0580 0.523135 29 to 30 141714 -0.5762 0.282242 28 to 29 142263 1.0433 0.851589 27 to 28 141954 0.1318 0.552417 26 to 27 141394 -1.5201 0.064237 25 to 26 141767 -0.4199 0.337297 24 to 25 142681 2.2763 0.988586 23 to 24 141824 -0.2517 0.400632 22 to 23 141575 -0.9862 0.162012 21 to 22 142541 1.8633 0.968792 20 to 21 141828 -0.2399 0.405199 19 to 20 141610 -0.8830 0.188624 18 to 19 141922 0.0374 0.514907 17 to 18 142127 0.6421 0.739594 16 to 17 142009 0.2940 0.615626 15 to 16 141880 -0.0865 0.465527 14 to 15 141400 -1.5024 0.066491 13 to 14 142430 1.5359 0.937719 12 to 13 142128 0.6450 0.740551 11 to 12 142281 1.0964 0.863542 10 to 11 141858 -0.1514 0.439824 9 to 10 141715 -0.5732 0.283240 8 to 9 142010 0.2970 0.616752 7 to 8 141541 -1.0865 0.138625 6 to 7 142052 0.4209 0.663070 5 to 6 142405 1.4622 0.928150 4 to 5 141301 -1.7945 0.036368 3 to 4 142053 0.4238 0.664146 2 to 3 141804 -0.3107 0.378011 1 to 2 141493 -1.2281 0.109702 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-28_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2470.07 -0.423 0.336066 Test results for specific bytes for dh-ranFile-2018-03-28_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2564.04 0.906 0.817431 2 to 9 2452.60 -0.670 0.251326 3 to 10 2383.98 -1.641 0.050425 4 to 11 2543.99 0.622 0.733054 5 to 12 2531.21 0.441 0.670537 6 to 13 2599.76 1.411 0.920857 7 to 14 2704.31 2.889 0.998070 8 to 15 2449.85 -0.709 0.239091 9 to 16 2469.11 -0.437 0.331109 10 to 17 2574.71 1.057 0.854658 11 to 18 2440.65 -0.839 0.200644 12 to 19 2493.72 -0.089 0.464618 13 to 20 2522.95 0.325 0.627231 14 to 21 2688.85 2.671 0.996215 15 to 22 2721.39 3.131 0.999129 16 to 23 2555.12 0.779 0.782146 17 to 24 2548.02 0.679 0.751446 18 to 25 2554.97 0.777 0.781542 19 to 26 2633.67 1.890 0.970649 20 to 27 2415.44 -1.196 0.115863 21 to 28 2431.11 -0.974 0.164955 22 to 29 2459.87 -0.568 0.285159 23 to 30 2526.22 0.371 0.644625 24 to 31 2565.25 0.923 0.821944 25 to 32 2500.65 0.009 0.503674 CDPARK for dh-ranFile-2018-03-28_19:31: 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 3525 0.0913 0.536383 3523 0.0000 0.500000 3536 0.5936 0.723613 3502 -0.9589 0.168804 3545 1.0046 0.842447 3473 -2.2831 0.011212 3569 2.1005 0.982156 3540 0.7763 0.781201 3541 0.8219 0.794438 3538 0.6849 0.753306 Square side=100, avg. no. parked=3529.20 sample std.=24.83 p-value of the KSTEST for those 10 p-values: 0.259712 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-28_19:31 0.7779,0.0483,0.5805,0.4330,0.8895,0.8704,0.7239,0.9469,0.3615,0.1601, The KS test for those 10 p-values: 0.672926 The 3DSPHERES test for dh-ranFile-2018-03-28_19:31 sample no r^3 equiv. uni. 1 16.914 0.430965 2 68.924 0.899488 3 11.277 0.313328 4 29.475 0.625630 5 30.899 0.642980 6 44.534 0.773374 7 74.725 0.917159 8 17.747 0.446544 9 0.090 0.002980 10 12.572 0.342349 11 45.870 0.783248 12 19.742 0.482153 13 21.954 0.518958 14 37.732 0.715700 15 24.899 0.563930 16 32.239 0.658575 17 71.914 0.909022 18 2.551 0.081516 19 2.932 0.093096 20 72.075 0.909509 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.498039 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-28_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.6 -1.1 -1.4 -1.6 -0.2 -0.7 -0.7 0.4 0.1 -2.0 -0.4 -1.1 1.3 0.9 1.2 1.0 -1.4 -1.6 0.1 0.3 0.4 -0.5 -0.3 -0.5 1.6 1.1 0.5 0.5 1.6 0.1 1.4 0.5 -1.9 0.1 1.0 1.2 -0.7 -0.4 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:44.659189 z-score=0.290141, p-value=0.639335 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-28_19:31 Test no p-value 1 0.064204 2 0.468734 3 0.038576 4 0.020225 5 0.027183 6 0.737747 7 0.070803 8 0.144762 9 0.145580 10 0.074195 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000072 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-28_19:31: (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 66625 0.03 66650 0.00 3 25000.00 25002 0.00 24996 0.00 4 6666.67 6651 0.04 6683 0.04 5 1388.89 1441 1.96 1383 0.02 6 238.10 236 0.02 247 0.33 7 34.72 40 0.80 32 0.21 8 4.96 4 0.19 8 1.86 p=0.19434 p=0.12921 Number of rngs required: 688865, p-value: 0.703 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-28_19:31 No. of wins: Observed Expected 98705 98585.9 z-score= 0.533, pvalue=0.70294 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66796 66666.7 0.251 0.251 2 37735 37654.3 0.173 0.424 3 26962 26954.7 0.002 0.426 4 19019 19313.5 4.490 4.915 5 14097 13851.4 4.354 9.269 6 9991 9943.5 0.226 9.496 7 6938 7145.0 5.999 15.494 8 5084 5139.1 0.590 16.084 9 3795 3699.9 2.446 18.531 10 2652 2666.3 0.077 18.607 11 1874 1923.3 1.265 19.873 12 1336 1388.7 2.003 21.875 13 1030 1003.7 0.688 22.564 14 739 726.1 0.228 22.792 15 522 525.8 0.028 22.820 16 396 381.2 0.579 23.398 17 274 276.5 0.023 23.421 18 193 200.8 0.305 23.727 19 155 146.0 0.557 24.283 20 104 106.2 0.046 24.330 21 308 287.1 1.519 25.849 Chisq= 25.85 for 20 degrees of freedom, p= 0.82914 SUMMARY of craptest p-value for no. of wins: 0.702938 p-value for throws/game: 0.829141 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-28_19:31 No. of wins: Observed Expected 98874 98585.9 z-score= 1.289, pvalue=0.90126 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67027 66666.7 1.948 1.948 2 37543 37654.3 0.329 2.277 3 26683 26954.7 2.739 5.016 4 19371 19313.5 0.171 5.187 5 13763 13851.4 0.564 5.752 6 9945 9943.5 0.000 5.752 7 7067 7145.0 0.852 6.604 8 5197 5139.1 0.653 7.257 9 3803 3699.9 2.875 10.132 10 2648 2666.3 0.126 10.258 11 1984 1923.3 1.914 12.171 12 1399 1388.7 0.076 12.247 13 964 1003.7 1.571 13.819 14 720 726.1 0.052 13.871 15 524 525.8 0.006 13.877 16 366 381.2 0.602 14.479 17 269 276.5 0.206 14.685 18 195 200.8 0.169 14.854 19 153 146.0 0.337 15.191 20 89 106.2 2.790 17.981 21 290 287.1 0.029 18.010 Chisq= 18.01 for 20 degrees of freedom, p= 0.41328 SUMMARY of craptest p-value for no. of wins: 0.901255 p-value for throws/game: 0.413282 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0008,0.0030,0.0103,0.0112,0.0129,0.0202,0.0272,0.0364,0.0386, 0.0417,0.0421,0.0456,0.0483,0.0492,0.0504,0.0642,0.0642,0.0649,0.0665, 0.0708,0.0733,0.0742,0.0776,0.0815,0.0832,0.0868,0.0931,0.0937,0.0980, 0.0998,0.1042,0.1097,0.1159,0.1166,0.1226,0.1292,0.1295,0.1347,0.1386, 0.1448,0.1456,0.1478,0.1601,0.1620,0.1650,0.1688,0.1753,0.1877,0.1886, 0.1943,0.1977,0.2006,0.2026,0.2226,0.2265,0.2323,0.2391,0.2417,0.2432, 0.2513,0.2523,0.2530,0.2539,0.2583,0.2597,0.2600,0.2659,0.2705,0.2739, 0.2761,0.2822,0.2832,0.2852,0.2912,0.3006,0.3018,0.3133,0.3204,0.3264, 0.3311,0.3328,0.3334,0.3342,0.3361,0.3373,0.3423,0.3445,0.3467,0.3563, 0.3580,0.3601,0.3615,0.3621,0.3754,0.3780,0.3936,0.3972,0.3979,0.4006, 0.4042,0.4052,0.4133,0.4182,0.4196,0.4309,0.4310,0.4330,0.4398,0.4465, 0.4577,0.4582,0.4607,0.4646,0.4655,0.4667,0.4687,0.4708,0.4755,0.4822, 0.4843,0.4874,0.4908,0.4927,0.4969,0.4980,0.5000,0.5037,0.5149,0.5181, 0.5185,0.5190,0.5231,0.5273,0.5360,0.5364,0.5434,0.5435,0.5489,0.5503, 0.5524,0.5585,0.5639,0.5735,0.5805,0.5877,0.6002,0.6021,0.6156,0.6168, 0.6225,0.6240,0.6248,0.6253,0.6256,0.6272,0.6324,0.6389,0.6393,0.6430, 0.6446,0.6487,0.6524,0.6586,0.6590,0.6601,0.6613,0.6631,0.6641,0.6705, 0.6729,0.6796,0.6833,0.6853,0.6964,0.7018,0.7028,0.7029,0.7060,0.7066, 0.7116,0.7157,0.7236,0.7239,0.7242,0.7331,0.7377,0.7380,0.7396,0.7406, 0.7423,0.7457,0.7514,0.7515,0.7523,0.7533,0.7533,0.7583,0.7607,0.7681, 0.7728,0.7734,0.7779,0.7812,0.7815,0.7821,0.7832,0.7888,0.7895,0.7899, 0.7944,0.7952,0.7987,0.8054,0.8174,0.8219,0.8284,0.8291,0.8424,0.8426, 0.8516,0.8541,0.8547,0.8556,0.8569,0.8627,0.8635,0.8704,0.8715,0.8777, 0.8804,0.8835,0.8874,0.8895,0.8912,0.8927,0.8968,0.8980,0.8995,0.9013, 0.9044,0.9088,0.9090,0.9095,0.9149,0.9172,0.9209,0.9282,0.9285,0.9352, 0.9377,0.9388,0.9469,0.9631,0.9688,0.9706,0.9715,0.9715,0.9733,0.9753, 0.9822,0.9840,0.9886,0.9887,0.9943,0.9944,0.9962,0.9981,0.9991, Overall p-value after applying KStest on 269 p-values = 0.276095 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.