RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-13_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 14.9797 0.403058 2 to 25 15.96 8.0137 0.033747 3 to 26 15.89 17.3716 0.570522 4 to 27 16.01 28.5734 0.961332 5 to 28 15.91 14.8405 0.393029 6 to 29 15.53 33.6996 0.990822 7 to 30 15.79 12.2998 0.218344 8 to 31 15.59 22.8357 0.845323 9 to 32 15.62 16.4021 0.504469 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.616027 Tough bday spacings test for dh-ranFile-2018-04-13_22:31: 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 35 77 89 97 75 59 37 9 4 6 (O-E)^2/E 0.9 0.1 0.2 0.8 0.0 0.1 0.9 1.8 2.3 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.000, p= 0.468 RESULTS OF GCD FOR dh-ranFile-2018-04-13_22:31 Euclid's algorithm: p-value, steps to gcd: 0.913629 p-value, dist. of gcd's: 0.836481 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-13_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.926 0.850 0.766 0.290 0.485 0.028 0.078 0.420 Bits 8 to 15---> 0.812 0.620 0.236 0.995 0.317 0.516 0.211 0.891 Bits 16 to 23---> 0.176 0.509 0.592 0.464 0.285 0.403 0.518 0.478 Bits 24 to 31---> 0.723 0.991 0.943 0.935 0.660 0.587 0.328 0.178 KS test for the above 32 p values: 0.391 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-13_22:31, p-values for 5 runs: 0.5171, 0.7354, 0.3412, 0.5166, 0.9588 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-13_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5052 5134.0 1.310 1.371 r= 30 23223 23103.0 0.623 1.994 r= 31 11510 11551.5 0.149 2.143 chi-square = 2.143 with df = 3; p-value = 0.457 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-13_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 183 211.4 3.820 3.820 r= 30 5091 5134.0 0.360 4.180 r= 31 23179 23103.0 0.250 4.430 r= 32 11547 11551.5 0.002 4.432 chi-square = 4.432 with df = 3; p-value = 0.782 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-13_22:31 b-rank test for bits 1 to 8, p=0.52140 b-rank test for bits 2 to 9, p=0.55165 b-rank test for bits 3 to 10, p=0.14309 b-rank test for bits 4 to 11, p=0.42299 b-rank test for bits 5 to 12, p=0.72989 b-rank test for bits 6 to 13, p=0.14204 b-rank test for bits 7 to 14, p=0.45447 b-rank test for bits 8 to 15, p=0.36733 b-rank test for bits 9 to 16, p=0.31985 b-rank test for bits 10 to 17, p=0.01163 b-rank test for bits 11 to 18, p=0.71069 b-rank test for bits 12 to 19, p=0.20036 b-rank test for bits 13 to 20, p=0.51888 b-rank test for bits 14 to 21, p=0.16813 b-rank test for bits 15 to 22, p=0.01273 b-rank test for bits 16 to 23, p=0.85281 b-rank test for bits 17 to 24, p=0.96618 b-rank test for bits 18 to 25, p=0.02402 b-rank test for bits 19 to 26, p=0.79434 b-rank test for bits 20 to 27, p=0.14483 b-rank test for bits 21 to 28, p=0.09887 b-rank test for bits 22 to 29, p=0.65061 b-rank test for bits 23 to 30, p=0.51744 b-rank test for bits 24 to 31, p=0.17524 b-rank test for bits 25 to 32, p=0.13650 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 = 0.059743 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-13_22:31 (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 141433 -1.11 0.132871 2 141674 -0.55 0.291216 3 142523 1.43 0.924187 4 141074 -1.95 0.025487 5 141555 -0.83 0.203871 6 141250 -1.54 0.061720 7 142041 0.31 0.620822 8 141944 0.08 0.532281 9 141195 -1.67 0.047559 10 141998 0.21 0.582063 11 142220 0.73 0.766039 12 141163 -1.74 0.040600 13 141453 -1.07 0.143169 14 141507 -0.94 0.173603 15 141733 -0.41 0.340175 16 142102 0.45 0.673704 17 141453 -1.07 0.143169 18 141785 -0.29 0.385720 19 141397 -1.20 0.115647 20 142575 1.56 0.940063 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-13_22:31 Bits used No. missing words z-score p-value 23 to 32 142246 1.1609 0.877165 22 to 31 141997 0.3023 0.618792 21 to 30 141729 -0.6218 0.267028 20 to 29 142048 0.4782 0.683736 19 to 28 142323 1.4264 0.923131 18 to 27 141923 0.0471 0.518798 17 to 26 142130 0.7609 0.776651 16 to 25 142156 0.8506 0.802500 15 to 24 141958 0.1678 0.566641 14 to 23 142031 0.4196 0.662594 13 to 22 142211 1.0402 0.850886 12 to 21 141519 -1.3460 0.089157 11 to 20 141679 -0.7942 0.213528 10 to 19 141474 -1.5011 0.066660 9 to 18 142511 2.0747 0.980994 8 to 17 141590 -1.1011 0.135418 7 to 16 141518 -1.3494 0.088602 6 to 15 141819 -0.3115 0.377717 5 to 14 142035 0.4333 0.667618 4 to 13 142094 0.6368 0.737870 3 to 12 141900 -0.0322 0.487167 2 to 11 141883 -0.0908 0.463829 1 to 10 142247 1.1644 0.877865 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-13_22:31 Bits used No. missing words z-score p-value 28 to 32 141565 -1.1672 0.121561 27 to 31 142175 0.9006 0.816093 26 to 30 141952 0.1446 0.557504 25 to 29 141386 -1.7740 0.038032 24 to 28 141704 -0.6960 0.243204 23 to 27 141674 -0.7977 0.212514 22 to 26 141718 -0.6486 0.258306 21 to 25 142012 0.3480 0.636093 20 to 24 141763 -0.4960 0.309935 19 to 23 142063 0.5209 0.698787 18 to 22 141901 -0.0282 0.488737 17 to 21 142091 0.6158 0.730997 16 to 20 141784 -0.4248 0.335474 15 to 19 142350 1.4938 0.932386 14 to 18 141794 -0.3909 0.347917 13 to 17 142007 0.3311 0.629710 12 to 16 142085 0.5955 0.724243 11 to 15 142341 1.4633 0.928306 10 to 14 141308 -2.0384 0.020755 9 to 13 141553 -1.2079 0.113543 8 to 12 142236 1.1074 0.865930 7 to 11 141913 0.0124 0.504963 6 to 10 141907 -0.0079 0.496849 5 to 9 142044 0.4565 0.675988 4 to 8 142302 1.3311 0.908419 3 to 7 141834 -0.2554 0.399224 2 to 6 141769 -0.4757 0.317146 1 to 5 142427 1.7548 0.960354 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-13_22:31 Bits used No. missing words z-score p-value 31 to 32 142256 1.0226 0.846758 30 to 31 141483 -1.2576 0.104266 29 to 30 141899 -0.0305 0.487845 28 to 29 142144 0.6922 0.755607 27 to 28 141361 -1.6175 0.052886 26 to 27 142184 0.8102 0.791098 25 to 26 142205 0.8722 0.808446 24 to 25 141702 -0.6116 0.270404 23 to 24 141928 0.0551 0.521960 22 to 23 142360 1.3294 0.908144 21 to 22 141954 0.1318 0.552417 20 to 21 142362 1.3353 0.909113 19 to 20 141824 -0.2517 0.400632 18 to 19 142397 1.4386 0.924862 17 to 18 141909 -0.0010 0.499612 16 to 17 141579 -0.9744 0.164923 15 to 16 142333 1.2498 0.894307 14 to 15 142227 0.9371 0.825641 13 to 14 141791 -0.3491 0.363524 12 to 13 141855 -0.1603 0.436336 11 to 12 142706 2.3501 0.990615 10 to 11 142167 0.7601 0.776399 9 to 10 142413 1.4858 0.931328 8 to 9 142172 0.7748 0.780782 7 to 8 141773 -0.4022 0.343786 6 to 7 141670 -0.7060 0.240098 5 to 6 141890 -0.0570 0.477264 4 to 5 141664 -0.7237 0.234629 3 to 4 142048 0.4091 0.658751 2 to 3 141772 -0.4051 0.342701 1 to 2 141374 -1.5791 0.057151 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-13_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2428.23 -1.015 0.155057 Test results for specific bytes for dh-ranFile-2018-04-13_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2393.93 -1.500 0.066801 2 to 9 2280.38 -3.106 0.000948 3 to 10 2435.72 -0.909 0.181658 4 to 11 2472.41 -0.390 0.348189 5 to 12 2474.13 -0.366 0.357251 6 to 13 2483.98 -0.226 0.410409 7 to 14 2500.49 0.007 0.502744 8 to 15 2521.55 0.305 0.619736 9 to 16 2574.83 1.058 0.855041 10 to 17 2590.98 1.287 0.900880 11 to 18 2474.25 -0.364 0.357882 12 to 19 2400.74 -1.404 0.080203 13 to 20 2472.09 -0.395 0.346544 14 to 21 2540.91 0.579 0.718545 15 to 22 2442.41 -0.814 0.207704 16 to 23 2515.11 0.214 0.584584 17 to 24 2573.00 1.032 0.849056 18 to 25 2533.72 0.477 0.683267 19 to 26 2440.58 -0.840 0.200379 20 to 27 2509.01 0.127 0.550681 21 to 28 2502.18 0.031 0.512274 22 to 29 2473.22 -0.379 0.352459 23 to 30 2599.94 1.413 0.921222 24 to 31 2467.32 -0.462 0.321957 25 to 32 2538.73 0.548 0.708083 CDPARK for dh-ranFile-2018-04-13_22:31: 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 3500 -1.0502 0.146807 3505 -0.8219 0.205562 3552 1.3242 0.907282 3531 0.3653 0.642555 3517 -0.2740 0.392053 3534 0.5023 0.692266 3527 0.1826 0.572463 3505 -0.8219 0.205562 3493 -1.3699 0.085365 3526 0.1370 0.554479 Square side=100, avg. no. parked=3519.00 sample std.=17.33 p-value of the KSTEST for those 10 p-values: 0.777877 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-13_22:31 0.2314,0.0287,0.1443,0.0528,0.5162,0.7674,0.4023,0.6156,0.2799,0.9525, The KS test for those 10 p-values: 0.492624 The 3DSPHERES test for dh-ranFile-2018-04-13_22:31 sample no r^3 equiv. uni. 1 61.017 0.869176 2 12.228 0.334757 3 33.377 0.671286 4 81.193 0.933225 5 11.897 0.327375 6 36.041 0.699219 7 26.997 0.593396 8 36.705 0.705798 9 0.057 0.001896 10 29.534 0.626363 11 69.840 0.902508 12 18.007 0.451314 13 83.174 0.937493 14 47.730 0.796277 15 3.535 0.111146 16 62.980 0.877464 17 29.877 0.630613 18 66.159 0.889784 19 68.120 0.896758 20 24.169 0.553201 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.030985 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-13_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 0.8 -0.3 0.3 0.6 -2.3 -0.1 0.9 -0.1 0.2 0.0 -0.3 0.7 -0.8 1.3 -0.8 -1.3 0.7 0.9 1.4 -0.7 -0.5 -0.6 0.7 -0.3 0.9 -0.1 -1.3 -1.3 -0.0 0.0 -0.5 0.5 -0.9 0.1 1.0 -1.3 0.1 2.1 -1.3 1.0 0.8 Chi-square with 42 degrees of freedom:35.001069 z-score=-0.763646, p-value=0.230606 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-13_22:31 Test no p-value 1 0.747812 2 0.575457 3 0.022697 4 0.123098 5 0.374762 6 0.049323 7 0.114143 8 0.066609 9 0.028928 10 0.063482 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000535 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-13_22:31: (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 66559 0.17 66461 0.63 3 25000.00 25031 0.04 25309 3.82 4 6666.67 6731 0.62 6618 0.36 5 1388.89 1390 0.00 1332 2.33 6 238.10 246 0.26 248 0.41 7 34.72 35 0.00 29 0.94 8 4.96 7 0.84 2 1.77 p=0.07466 p=0.88588 Number of rngs required: 688962, p-value: 0.741 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-13_22:31 No. of wins: Observed Expected 98596 98585.9 z-score= 0.045, pvalue=0.51809 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66969 66666.7 1.371 1.371 2 37544 37654.3 0.323 1.694 3 26973 26954.7 0.012 1.707 4 19251 19313.5 0.202 1.909 5 13851 13851.4 0.000 1.909 6 9756 9943.5 3.537 5.446 7 7163 7145.0 0.045 5.491 8 5112 5139.1 0.143 5.634 9 3718 3699.9 0.089 5.723 10 2765 2666.3 3.654 9.376 11 1922 1923.3 0.001 9.377 12 1382 1388.7 0.033 9.410 13 1012 1003.7 0.068 9.478 14 716 726.1 0.142 9.620 15 515 525.8 0.223 9.843 16 392 381.2 0.309 10.152 17 259 276.5 1.112 11.265 18 199 200.8 0.017 11.281 19 139 146.0 0.334 11.615 20 96 106.2 0.982 12.598 21 266 287.1 1.553 14.151 Chisq= 14.15 for 20 degrees of freedom, p= 0.17722 SUMMARY of craptest p-value for no. of wins: 0.518089 p-value for throws/game: 0.177223 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-13_22:31 No. of wins: Observed Expected 98582 98585.9 z-score=-0.017, pvalue=0.49312 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66731 66666.7 0.062 0.062 2 37679 37654.3 0.016 0.078 3 26801 26954.7 0.877 0.955 4 19339 19313.5 0.034 0.989 5 13869 13851.4 0.022 1.011 6 9993 9943.5 0.246 1.257 7 7047 7145.0 1.345 2.602 8 5114 5139.1 0.122 2.724 9 3695 3699.9 0.006 2.731 10 2685 2666.3 0.131 2.862 11 1912 1923.3 0.067 2.929 12 1442 1388.7 2.043 4.971 13 1013 1003.7 0.086 5.057 14 750 726.1 0.784 5.841 15 552 525.8 1.302 7.143 16 375 381.2 0.099 7.242 17 289 276.5 0.561 7.804 18 205 200.8 0.087 7.890 19 130 146.0 1.750 9.640 20 114 106.2 0.571 10.211 21 265 287.1 1.703 11.914 Chisq= 11.91 for 20 degrees of freedom, p= 0.08100 SUMMARY of craptest p-value for no. of wins: 0.493115 p-value for throws/game: 0.081002 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0009,0.0019,0.0116,0.0127,0.0208,0.0227,0.0240,0.0255,0.0280, 0.0287,0.0289,0.0310,0.0337,0.0380,0.0406,0.0476,0.0493,0.0528,0.0529, 0.0572,0.0597,0.0617,0.0635,0.0666,0.0667,0.0668,0.0747,0.0778,0.0802, 0.0810,0.0854,0.0886,0.0892,0.0989,0.1043,0.1111,0.1135,0.1141,0.1156, 0.1216,0.1231,0.1329,0.1354,0.1365,0.1420,0.1431,0.1432,0.1432,0.1443, 0.1448,0.1468,0.1551,0.1649,0.1681,0.1736,0.1752,0.1758,0.1772,0.1776, 0.1817,0.2004,0.2004,0.2039,0.2056,0.2056,0.2077,0.2107,0.2125,0.2135, 0.2183,0.2306,0.2314,0.2346,0.2356,0.2401,0.2432,0.2583,0.2670,0.2704, 0.2799,0.2849,0.2897,0.2912,0.3099,0.3171,0.3171,0.3199,0.3220,0.3274, 0.3282,0.3348,0.3355,0.3402,0.3412,0.3427,0.3438,0.3465,0.3479,0.3482, 0.3525,0.3573,0.3579,0.3635,0.3673,0.3748,0.3777,0.3857,0.3914,0.3921, 0.3930,0.3992,0.4006,0.4023,0.4028,0.4031,0.4104,0.4205,0.4230,0.4363, 0.4513,0.4545,0.4567,0.4637,0.4638,0.4679,0.4773,0.4782,0.4850,0.4872, 0.4878,0.4887,0.4926,0.4931,0.4968,0.4996,0.5027,0.5045,0.5050,0.5088, 0.5123,0.5157,0.5162,0.5166,0.5171,0.5174,0.5180,0.5181,0.5188,0.5189, 0.5214,0.5220,0.5323,0.5507,0.5517,0.5524,0.5532,0.5545,0.5575,0.5666, 0.5705,0.5725,0.5755,0.5821,0.5846,0.5868,0.5920,0.5934,0.6156,0.6160, 0.6188,0.6197,0.6204,0.6208,0.6264,0.6297,0.6306,0.6361,0.6426,0.6506, 0.6588,0.6603,0.6626,0.6676,0.6713,0.6737,0.6760,0.6833,0.6837,0.6923, 0.6988,0.6992,0.7058,0.7081,0.7107,0.7185,0.7232,0.7242,0.7299,0.7310, 0.7354,0.7379,0.7405,0.7478,0.7556,0.7660,0.7663,0.7674,0.7764,0.7767, 0.7779,0.7808,0.7815,0.7911,0.7943,0.7963,0.8025,0.8084,0.8123,0.8161, 0.8256,0.8365,0.8453,0.8468,0.8491,0.8504,0.8509,0.8528,0.8550,0.8659, 0.8692,0.8772,0.8775,0.8779,0.8859,0.8898,0.8910,0.8943,0.8968,0.9009, 0.9025,0.9073,0.9081,0.9084,0.9091,0.9136,0.9212,0.9231,0.9242,0.9249, 0.9264,0.9283,0.9313,0.9324,0.9332,0.9349,0.9375,0.9401,0.9433,0.9525, 0.9588,0.9604,0.9613,0.9662,0.9810,0.9906,0.9908,0.9912,0.9951, Overall p-value after applying KStest on 269 p-values = 0.429076 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.