RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 20.7007 0.760034 2 to 25 15.75 26.7802 0.938629 3 to 26 15.76 18.9593 0.669124 4 to 27 15.78 15.4035 0.433561 5 to 28 15.82 10.3415 0.111318 6 to 29 15.90 17.8251 0.600044 7 to 30 15.72 7.7792 0.028957 8 to 31 15.73 25.8058 0.921929 9 to 32 15.68 21.5317 0.796596 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.509281 Tough bday spacings test for dh-ranFile-2018-06-16_05:31: 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 39 65 103 93 83 41 26 21 11 6 (O-E)^2/E 0.9 0.2 0.9 0.3 0.2 0.3 2.4 0.5 2.5 2.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.961, p= 0.712 RESULTS OF GCD FOR dh-ranFile-2018-06-16_05:31 Euclid's algorithm: p-value, steps to gcd: 0.825192 p-value, dist. of gcd's: 0.300296 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.781 0.720 0.578 0.509 0.788 0.791 0.900 0.740 Bits 8 to 15---> 0.410 0.369 0.330 0.607 0.115 0.285 0.491 0.721 Bits 16 to 23---> 0.806 0.380 0.971 0.726 0.855 0.247 0.807 0.427 Bits 24 to 31---> 0.737 0.647 0.788 0.878 0.784 0.123 0.683 0.758 KS test for the above 32 p values: 0.986 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_05:31, p-values for 5 runs: 0.4377, 0.2854, 0.5040, 0.6330, 0.2826 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 187 211.4 2.820 2.820 r= 29 5076 5134.0 0.655 3.476 r= 30 23194 23103.0 0.358 3.834 r= 31 11543 11551.5 0.006 3.840 chi-square = 3.840 with df = 3; p-value = 0.721 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5103 5134.0 0.187 1.193 r= 31 23107 23103.0 0.001 1.194 r= 32 11564 11551.5 0.013 1.207 chi-square = 1.207 with df = 3; p-value = 0.249 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_05:31 b-rank test for bits 1 to 8, p=0.73515 b-rank test for bits 2 to 9, p=0.98760 b-rank test for bits 3 to 10, p=0.31738 b-rank test for bits 4 to 11, p=0.27899 b-rank test for bits 5 to 12, p=0.46413 b-rank test for bits 6 to 13, p=0.51071 b-rank test for bits 7 to 14, p=0.38687 b-rank test for bits 8 to 15, p=0.42798 b-rank test for bits 9 to 16, p=0.64224 b-rank test for bits 10 to 17, p=0.66863 b-rank test for bits 11 to 18, p=0.72636 b-rank test for bits 12 to 19, p=0.96587 b-rank test for bits 13 to 20, p=0.03742 b-rank test for bits 14 to 21, p=0.46385 b-rank test for bits 15 to 22, p=0.39616 b-rank test for bits 16 to 23, p=0.08606 b-rank test for bits 17 to 24, p=0.05435 b-rank test for bits 18 to 25, p=0.92282 b-rank test for bits 19 to 26, p=0.37602 b-rank test for bits 20 to 27, p=0.78436 b-rank test for bits 21 to 28, p=0.86867 b-rank test for bits 22 to 29, p=0.55536 b-rank test for bits 23 to 30, p=0.40106 b-rank test for bits 24 to 31, p=0.42013 b-rank test for bits 25 to 32, p=0.07784 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 = 0.832173 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_05:31 (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 141935 0.06 0.523913 2 141614 -0.69 0.245090 3 141325 -1.37 0.086086 4 142809 2.10 0.982225 5 141475 -1.01 0.155103 6 142557 1.51 0.934892 7 142027 0.27 0.608315 8 141766 -0.33 0.368857 9 141660 -0.58 0.280099 10 141869 -0.09 0.462464 11 141704 -0.48 0.315705 12 141981 0.17 0.566493 13 141763 -0.34 0.366216 14 142628 1.68 0.953437 15 142231 0.75 0.773844 16 141588 -0.75 0.226395 17 142306 0.93 0.822985 18 141893 -0.04 0.484782 19 142367 1.07 0.857538 20 141236 -1.57 0.057836 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-16_05:31 Bits used No. missing words z-score p-value 23 to 32 142164 0.8782 0.810075 22 to 31 141838 -0.2460 0.402855 21 to 30 142140 0.7954 0.786814 20 to 29 142033 0.4264 0.665109 19 to 28 141838 -0.2460 0.402855 18 to 27 141894 -0.0529 0.478921 17 to 26 141785 -0.4287 0.334062 16 to 25 142052 0.4920 0.688628 15 to 24 142370 1.5885 0.943915 14 to 23 141964 0.1885 0.574764 13 to 22 141994 0.2920 0.614844 12 to 21 141729 -0.6218 0.267028 11 to 20 141936 0.0920 0.536637 10 to 19 141497 -1.4218 0.077538 9 to 18 142568 2.2713 0.988435 8 to 17 141735 -0.6011 0.273874 7 to 16 141989 0.2747 0.608236 6 to 15 142313 1.3920 0.918034 5 to 14 141785 -0.4287 0.334062 4 to 13 141778 -0.4529 0.325324 3 to 12 141939 0.1023 0.540745 2 to 11 142124 0.7402 0.770423 1 to 10 142393 1.6678 0.952325 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-16_05:31 Bits used No. missing words z-score p-value 28 to 32 141435 -1.6079 0.053929 27 to 31 141580 -1.1164 0.132131 26 to 30 142026 0.3955 0.653760 25 to 29 141761 -0.5028 0.307548 24 to 28 141674 -0.7977 0.212514 23 to 27 141273 -2.1571 0.015501 22 to 26 142231 1.0904 0.862233 21 to 25 141354 -1.8825 0.029886 20 to 24 142340 1.4599 0.927841 19 to 23 142264 1.2023 0.885371 18 to 22 141452 -1.5503 0.060538 17 to 21 142049 0.4735 0.682057 16 to 20 142096 0.6328 0.736561 15 to 19 141846 -0.2147 0.415009 14 to 18 142216 1.0396 0.850728 13 to 17 141625 -0.9638 0.167565 12 to 16 142271 1.2260 0.889901 11 to 15 142011 0.3446 0.634819 10 to 14 141677 -0.7876 0.215477 9 to 13 141260 -2.2011 0.013864 8 to 12 142252 1.1616 0.877300 7 to 11 141808 -0.3435 0.365614 6 to 10 142031 0.4124 0.659992 5 to 9 141789 -0.4079 0.341674 4 to 8 142016 0.3616 0.641172 3 to 7 141639 -0.9164 0.179736 2 to 6 141965 0.1887 0.574841 1 to 5 141854 -0.1876 0.425611 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-16_05:31 Bits used No. missing words z-score p-value 31 to 32 141957 0.1406 0.555915 30 to 31 142197 0.8486 0.801944 29 to 30 141556 -1.0423 0.148643 28 to 29 142198 0.8515 0.802764 27 to 28 142200 0.8574 0.804397 26 to 27 141465 -1.3107 0.094978 25 to 26 142835 2.7306 0.996839 24 to 25 142115 0.6067 0.727974 23 to 24 141627 -0.8328 0.202470 22 to 23 142022 0.3324 0.630191 21 to 22 141819 -0.2665 0.394942 20 to 21 141980 0.2085 0.582568 19 to 20 142056 0.4327 0.667367 18 to 19 141992 0.2439 0.596332 17 to 18 142231 0.9489 0.828659 16 to 17 141448 -1.3609 0.086780 15 to 16 141601 -0.9095 0.181536 14 to 15 141886 -0.0688 0.472566 13 to 14 141875 -0.1013 0.459669 12 to 13 142098 0.5565 0.711082 11 to 12 141037 -2.5732 0.005037 10 to 11 141882 -0.0806 0.467872 9 to 10 142043 0.3943 0.653323 8 to 9 141480 -1.2665 0.102674 7 to 8 142095 0.5477 0.708051 6 to 7 142344 1.2822 0.900116 5 to 6 141896 -0.0393 0.484317 4 to 5 142117 0.6126 0.729928 3 to 4 141796 -0.3343 0.369074 2 to 3 142211 0.8899 0.813235 1 to 2 142088 0.5271 0.700921 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2560.41 0.854 0.803551 Test results for specific bytes for dh-ranFile-2018-06-16_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2668.57 2.384 0.991437 2 to 9 2543.88 0.621 0.732554 3 to 10 2551.20 0.724 0.765487 4 to 11 2554.24 0.767 0.778469 5 to 12 2528.38 0.401 0.655932 6 to 13 2523.26 0.329 0.628886 7 to 14 2417.37 -1.169 0.121281 8 to 15 2604.71 1.481 0.930682 9 to 16 2457.39 -0.603 0.273408 10 to 17 2433.73 -0.937 0.174338 11 to 18 2509.36 0.132 0.552630 12 to 19 2477.47 -0.319 0.374994 13 to 20 2552.70 0.745 0.771961 14 to 21 2565.41 0.925 0.822526 15 to 22 2465.06 -0.494 0.310603 16 to 23 2385.80 -1.615 0.053158 17 to 24 2533.89 0.479 0.684147 18 to 25 2419.07 -1.145 0.126190 19 to 26 2491.54 -0.120 0.452376 20 to 27 2482.78 -0.244 0.403789 21 to 28 2548.95 0.692 0.755623 22 to 29 2415.17 -1.200 0.115142 23 to 30 2472.42 -0.390 0.348231 24 to 31 2518.86 0.267 0.605145 25 to 32 2498.69 -0.018 0.492633 CDPARK for dh-ranFile-2018-06-16_05:31: 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 3543 0.9132 0.819442 3563 1.8265 0.966111 3486 -1.6895 0.045562 3518 -0.2283 0.409702 3538 0.6849 0.753306 3550 1.2329 0.891189 3557 1.5525 0.939730 3524 0.0457 0.518210 3534 0.5023 0.692266 3524 0.0457 0.518210 Square side=100, avg. no. parked=3533.70 sample std.=21.17 p-value of the KSTEST for those 10 p-values: 0.137758 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_05:31 0.1350,0.3215,0.5177,0.9545,0.5186,0.8973,0.0413,0.2026,0.8209,0.8469, The KS test for those 10 p-values: 0.877969 The 3DSPHERES test for dh-ranFile-2018-06-16_05:31 sample no r^3 equiv. uni. 1 0.145 0.004808 2 32.069 0.656636 3 41.069 0.745627 4 5.429 0.165544 5 21.098 0.505038 6 9.523 0.271996 7 19.203 0.472768 8 6.941 0.206550 9 20.397 0.493324 10 30.032 0.632516 11 41.470 0.749008 12 8.366 0.243368 13 4.331 0.134440 14 73.207 0.912860 15 68.493 0.898033 16 84.478 0.940151 17 40.778 0.743154 18 43.315 0.763975 19 12.720 0.345581 20 48.184 0.799337 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.830886 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 1.3 0.3 1.1 0.1 1.7 0.9 -1.2 1.4 -0.4 1.1 -1.0 0.1 -0.7 0.0 -1.9 1.0 -0.3 0.3 -0.2 -0.6 1.8 1.4 -0.5 -2.2 -1.2 0.2 0.3 1.9 0.7 0.4 -0.4 0.1 -0.1 0.2 0.7 -0.1 -1.2 1.0 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:44.201913 z-score=0.240248, p-value=0.621219 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-16_05:31 Test no p-value 1 0.992513 2 0.075299 3 0.087411 4 0.967356 5 0.132651 6 0.192291 7 0.195811 8 0.355750 9 0.131979 10 0.828857 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.069010 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_05:31: (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 66801 0.27 66596 0.07 3 25000.00 24968 0.04 25050 0.10 4 6666.67 6534 2.64 6743 0.87 5 1388.89 1445 2.27 1353 0.93 6 238.10 213 2.65 228 0.43 7 34.72 33 0.09 25 2.72 8 4.96 5 0.00 4 0.19 p=0.75815 p=0.49545 Number of rngs required: 687177, p-value: 0.076 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_05:31 No. of wins: Observed Expected 98206 98585.9 z-score=-1.699, pvalue=0.04466 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66136 66666.7 4.224 4.224 2 37851 37654.3 1.027 5.251 3 27059 26954.7 0.403 5.655 4 19316 19313.5 0.000 5.655 5 13856 13851.4 0.002 5.657 6 10074 9943.5 1.712 7.368 7 7212 7145.0 0.628 7.996 8 5111 5139.1 0.153 8.149 9 3778 3699.9 1.650 9.799 10 2642 2666.3 0.221 10.021 11 1860 1923.3 2.085 12.106 12 1407 1388.7 0.240 12.346 13 1038 1003.7 1.171 13.517 14 713 726.1 0.238 13.755 15 537 525.8 0.237 13.992 16 370 381.2 0.326 14.318 17 295 276.5 1.232 15.551 18 191 200.8 0.481 16.032 19 147 146.0 0.007 16.039 20 115 106.2 0.727 16.765 21 292 287.1 0.083 16.849 Chisq= 16.85 for 20 degrees of freedom, p= 0.33721 SUMMARY of craptest p-value for no. of wins: 0.044664 p-value for throws/game: 0.337212 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_05:31 No. of wins: Observed Expected 98749 98585.9 z-score= 0.730, pvalue=0.76720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66979 66666.7 1.463 1.463 2 37470 37654.3 0.902 2.366 3 26848 26954.7 0.423 2.788 4 19165 19313.5 1.141 3.929 5 13813 13851.4 0.107 4.036 6 9811 9943.5 1.767 5.803 7 7301 7145.0 3.405 9.208 8 5208 5139.1 0.924 10.132 9 3718 3699.9 0.089 10.221 10 2700 2666.3 0.426 10.647 11 1918 1923.3 0.015 10.662 12 1331 1388.7 2.401 13.062 13 1048 1003.7 1.954 15.016 14 734 726.1 0.085 15.101 15 518 525.8 0.117 15.218 16 391 381.2 0.255 15.473 17 294 276.5 1.102 16.575 18 193 200.8 0.305 16.880 19 146 146.0 0.000 16.880 20 105 106.2 0.014 16.894 21 309 287.1 1.668 18.563 Chisq= 18.56 for 20 degrees of freedom, p= 0.44960 SUMMARY of craptest p-value for no. of wins: 0.767202 p-value for throws/game: 0.449604 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0048,0.0050,0.0139,0.0155,0.0290,0.0299,0.0374,0.0413,0.0447,0.0456, 0.0532,0.0539,0.0543,0.0578,0.0605,0.0690,0.0753,0.0763,0.0775,0.0778, 0.0861,0.0861,0.0868,0.0874,0.0950,0.1027,0.1113,0.1145,0.1151,0.1213, 0.1231,0.1262,0.1320,0.1321,0.1327,0.1344,0.1350,0.1378,0.1486,0.1551, 0.1655,0.1676,0.1743,0.1797,0.1815,0.1923,0.1958,0.2025,0.2026,0.2066, 0.2125,0.2155,0.2264,0.2434,0.2451,0.2469,0.2487,0.2670,0.2720,0.2734, 0.2739,0.2790,0.2801,0.2826,0.2854,0.2854,0.3003,0.3075,0.3106,0.3157, 0.3174,0.3215,0.3253,0.3295,0.3341,0.3341,0.3372,0.3417,0.3456,0.3482, 0.3557,0.3656,0.3662,0.3689,0.3691,0.3691,0.3750,0.3760,0.3803,0.3869, 0.3949,0.3962,0.4011,0.4029,0.4029,0.4038,0.4097,0.4099,0.4150,0.4201, 0.4256,0.4269,0.4280,0.4336,0.4377,0.4496,0.4524,0.4597,0.4625,0.4639, 0.4641,0.4679,0.4726,0.4728,0.4789,0.4843,0.4848,0.4906,0.4926,0.4933, 0.4954,0.5040,0.5050,0.5092,0.5093,0.5107,0.5177,0.5182,0.5182,0.5186, 0.5239,0.5366,0.5407,0.5526,0.5554,0.5559,0.5665,0.5748,0.5748,0.5784, 0.5826,0.5963,0.6000,0.6051,0.6068,0.6082,0.6083,0.6148,0.6212,0.6289, 0.6302,0.6325,0.6330,0.6348,0.6412,0.6422,0.6468,0.6533,0.6538,0.6559, 0.6566,0.6600,0.6651,0.6674,0.6686,0.6691,0.6821,0.6830,0.6841,0.6886, 0.6923,0.7009,0.7081,0.7111,0.7124,0.7202,0.7207,0.7214,0.7262,0.7264, 0.7280,0.7299,0.7326,0.7351,0.7366,0.7370,0.7405,0.7432,0.7456,0.7490, 0.7533,0.7556,0.7580,0.7582,0.7600,0.7640,0.7655,0.7672,0.7704,0.7720, 0.7738,0.7785,0.7810,0.7839,0.7844,0.7868,0.7877,0.7881,0.7913,0.7966, 0.7993,0.8019,0.8028,0.8036,0.8044,0.8060,0.8074,0.8101,0.8132,0.8194, 0.8209,0.8225,0.8230,0.8252,0.8287,0.8289,0.8309,0.8322,0.8469,0.8507, 0.8549,0.8575,0.8622,0.8687,0.8773,0.8778,0.8780,0.8854,0.8899,0.8912, 0.8973,0.8980,0.8999,0.9001,0.9129,0.9180,0.9219,0.9228,0.9278,0.9307, 0.9349,0.9386,0.9397,0.9402,0.9439,0.9523,0.9534,0.9545,0.9659,0.9661, 0.9674,0.9711,0.9822,0.9855,0.9876,0.9884,0.9914,0.9925,0.9968, Overall p-value after applying KStest on 269 p-values = 0.078620 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.