RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-23_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.49 25.2981 0.911767 2 to 25 15.98 9.5581 0.078889 3 to 26 15.80 9.6192 0.081184 4 to 27 15.95 9.9928 0.096089 5 to 28 15.81 17.5081 0.579512 6 to 29 15.65 22.1036 0.819233 7 to 30 15.66 19.6144 0.705573 8 to 31 15.84 19.8705 0.719091 9 to 32 15.70 16.1206 0.484695 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.692365 Tough bday spacings test for dh-ranFile-2018-03-23_10:31: 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 11 46 68 95 100 80 45 30 17 6 2 (O-E)^2/E 0.4 2.4 0.4 0.1 0.1 0.0 1.0 0.0 0.3 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.694, p= 0.160 RESULTS OF GCD FOR dh-ranFile-2018-03-23_10:31 Euclid's algorithm: p-value, steps to gcd: 0.448660 p-value, dist. of gcd's: 0.700997 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-23_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.985 0.955 0.576 0.900 0.963 0.351 0.847 0.524 Bits 8 to 15---> 0.699 0.653 0.348 0.305 0.351 0.688 0.005 0.520 Bits 16 to 23---> 0.331 0.830 0.178 0.666 0.512 0.654 0.006 0.188 Bits 24 to 31---> 0.644 0.701 0.224 0.164 0.545 0.393 0.853 0.797 KS test for the above 32 p values: 0.450 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-23_10:31, p-values for 5 runs: 0.7381, 0.4415, 0.2853, 0.3497, 0.5122 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-23_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 190 211.4 2.170 2.170 r= 29 5124 5134.0 0.020 2.189 r= 30 23102 23103.0 0.000 2.189 r= 31 11584 11551.5 0.091 2.281 chi-square = 2.281 with df = 3; p-value = 0.484 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-23_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5202 5134.0 0.900 0.912 r= 31 23078 23103.0 0.027 0.939 r= 32 11507 11551.5 0.172 1.111 chi-square = 1.111 with df = 3; p-value = 0.226 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-23_10:31 b-rank test for bits 1 to 8, p=0.85831 b-rank test for bits 2 to 9, p=0.44250 b-rank test for bits 3 to 10, p=0.45141 b-rank test for bits 4 to 11, p=0.18679 b-rank test for bits 5 to 12, p=0.57482 b-rank test for bits 6 to 13, p=0.18419 b-rank test for bits 7 to 14, p=0.82775 b-rank test for bits 8 to 15, p=0.57476 b-rank test for bits 9 to 16, p=0.68182 b-rank test for bits 10 to 17, p=0.65010 b-rank test for bits 11 to 18, p=0.94362 b-rank test for bits 12 to 19, p=0.74768 b-rank test for bits 13 to 20, p=0.49196 b-rank test for bits 14 to 21, p=0.32093 b-rank test for bits 15 to 22, p=0.38534 b-rank test for bits 16 to 23, p=0.83413 b-rank test for bits 17 to 24, p=0.69476 b-rank test for bits 18 to 25, p=0.73415 b-rank test for bits 19 to 26, p=0.92409 b-rank test for bits 20 to 27, p=0.45846 b-rank test for bits 21 to 28, p=0.14209 b-rank test for bits 22 to 29, p=0.01923 b-rank test for bits 23 to 30, p=0.52192 b-rank test for bits 24 to 31, p=0.18841 b-rank test for bits 25 to 32, p=0.10676 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 = 0.937539 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-23_10:31 (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 141743 -0.39 0.348778 2 142499 1.38 0.915857 3 141473 -1.02 0.153992 4 141976 0.16 0.561893 5 142613 1.64 0.949921 6 141290 -1.45 0.073944 7 141948 0.09 0.535996 8 141837 -0.17 0.432900 9 141684 -0.53 0.299280 10 141944 0.08 0.532281 11 141475 -1.01 0.155103 12 142389 1.12 0.868797 13 142215 0.71 0.762443 14 141485 -0.99 0.160739 15 142111 0.47 0.681248 16 142606 1.63 0.948209 17 141589 -0.75 0.227099 18 141928 0.04 0.517397 19 141617 -0.68 0.247299 20 141792 -0.27 0.391990 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-23_10:31 Bits used No. missing words z-score p-value 23 to 32 142200 1.0023 0.841903 22 to 31 142155 0.8471 0.801541 21 to 30 142051 0.4885 0.687408 20 to 29 142334 1.4644 0.928455 19 to 28 142120 0.7264 0.766218 18 to 27 141839 -0.2425 0.404190 17 to 26 142224 1.0851 0.861054 16 to 25 141686 -0.7701 0.220619 15 to 24 141644 -0.9149 0.180114 14 to 23 142007 0.3368 0.631864 13 to 22 142114 0.7058 0.759831 12 to 21 142109 0.6885 0.754436 11 to 20 142168 0.8920 0.813794 10 to 19 141775 -0.4632 0.321608 9 to 18 142194 0.9816 0.836857 8 to 17 141762 -0.5080 0.305715 7 to 16 141393 -1.7804 0.037501 6 to 15 141533 -1.2977 0.097197 5 to 14 141941 0.1092 0.543481 4 to 13 141927 0.0609 0.524293 3 to 12 142030 0.4161 0.661333 2 to 11 141578 -1.1425 0.126620 1 to 10 141814 -0.3287 0.371182 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-23_10:31 Bits used No. missing words z-score p-value 28 to 32 142509 2.0328 0.978963 27 to 31 142119 0.7107 0.761379 26 to 30 142030 0.4091 0.658749 25 to 29 141887 -0.0757 0.469831 24 to 28 142047 0.4667 0.679635 23 to 27 141901 -0.0282 0.488737 22 to 26 141964 0.1853 0.573512 21 to 25 142498 1.9955 0.977005 20 to 24 141728 -0.6147 0.269384 19 to 23 142467 1.8904 0.970648 18 to 22 141987 0.2633 0.603836 17 to 21 142146 0.8023 0.788802 16 to 20 141954 0.1514 0.560179 15 to 19 141833 -0.2587 0.397916 14 to 18 142305 1.3413 0.910081 13 to 17 141537 -1.2621 0.103450 12 to 16 141970 0.2057 0.581472 11 to 15 142005 0.3243 0.627147 10 to 14 142013 0.3514 0.637365 9 to 13 141716 -0.6554 0.256119 8 to 12 141794 -0.3909 0.347917 7 to 11 142081 0.5819 0.719694 6 to 10 142072 0.5514 0.709328 5 to 9 142189 0.9480 0.828444 4 to 8 142107 0.6701 0.748593 3 to 7 141989 0.2701 0.606446 2 to 6 141727 -0.6181 0.268265 1 to 5 142037 0.4328 0.667413 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-23_10:31 Bits used No. missing words z-score p-value 31 to 32 141819 -0.2665 0.394942 30 to 31 141692 -0.6411 0.260732 29 to 30 141891 -0.0541 0.478439 28 to 29 142160 0.7394 0.770180 27 to 28 141981 0.2114 0.583719 26 to 27 141855 -0.1603 0.436336 25 to 26 141640 -0.7945 0.213457 24 to 25 141996 0.2557 0.600895 23 to 24 142249 1.0020 0.841823 22 to 23 142023 0.3353 0.631304 21 to 22 141486 -1.2488 0.105876 20 to 21 142810 2.6568 0.996056 19 to 20 141582 -0.9656 0.167128 18 to 19 141544 -1.0777 0.140591 17 to 18 142325 1.2262 0.889932 16 to 17 142156 0.7276 0.766583 15 to 16 141930 0.0610 0.524310 14 to 15 141559 -1.0334 0.150703 13 to 14 141410 -1.4729 0.070382 12 to 13 142452 1.6008 0.945289 11 to 12 142102 0.5683 0.715101 10 to 11 142021 0.3294 0.629077 9 to 10 141935 0.0757 0.530180 8 to 9 141686 -0.6588 0.255015 7 to 8 141883 -0.0777 0.469045 6 to 7 141360 -1.6204 0.052569 5 to 6 141877 -0.0954 0.462011 4 to 5 142104 0.5742 0.717100 3 to 4 142282 1.0993 0.864186 2 to 3 141948 0.1141 0.545409 1 to 2 141854 -0.1632 0.435174 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-23_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2466.48 -0.474 0.317716 Test results for specific bytes for dh-ranFile-2018-03-23_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2652.23 2.153 0.984334 2 to 9 2608.54 1.535 0.937600 3 to 10 2597.34 1.377 0.915691 4 to 11 2586.91 1.229 0.890468 5 to 12 2474.50 -0.361 0.359191 6 to 13 2385.98 -1.612 0.053430 7 to 14 2499.84 -0.002 0.499071 8 to 15 2429.17 -1.002 0.158235 9 to 16 2406.58 -1.321 0.093231 10 to 17 2410.51 -1.266 0.102841 11 to 18 2402.33 -1.381 0.083610 12 to 19 2475.57 -0.346 0.364838 13 to 20 2594.86 1.341 0.910114 14 to 21 2391.66 -1.532 0.062747 15 to 22 2504.19 0.059 0.523649 16 to 23 2432.39 -0.956 0.169516 17 to 24 2474.49 -0.361 0.359131 18 to 25 2451.39 -0.687 0.245909 19 to 26 2530.80 0.436 0.668434 20 to 27 2425.85 -1.049 0.147187 21 to 28 2628.80 1.822 0.965737 22 to 29 2550.88 0.719 0.764082 23 to 30 2436.98 -0.891 0.186402 24 to 31 2437.12 -0.889 0.186946 25 to 32 2441.70 -0.824 0.204836 CDPARK for dh-ranFile-2018-03-23_10:31: 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 3550 1.2329 0.891189 3502 -0.9589 0.168804 3525 0.0913 0.536383 3500 -1.0502 0.146807 3550 1.2329 0.891189 3481 -1.9178 0.027568 3545 1.0046 0.842447 3562 1.7808 0.962529 3491 -1.4612 0.071982 3554 1.4155 0.921543 Square side=100, avg. no. parked=3526.00 sample std.=28.45 p-value of the KSTEST for those 10 p-values: 0.163192 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-23_10:31 0.7313,0.8188,0.5461,0.7768,0.1728,0.4717,0.1877,0.9112,0.8221,0.2418, The KS test for those 10 p-values: 0.634909 The 3DSPHERES test for dh-ranFile-2018-03-23_10:31 sample no r^3 equiv. uni. 1 91.364 0.952426 2 32.272 0.658955 3 12.182 0.333732 4 2.350 0.075331 5 15.960 0.412564 6 32.429 0.660735 7 19.023 0.469595 8 5.219 0.159672 9 24.372 0.556206 10 2.999 0.095124 11 16.026 0.413852 12 93.101 0.955102 13 3.925 0.122648 14 94.225 0.956753 15 14.984 0.393145 16 81.827 0.934622 17 13.296 0.358011 18 66.830 0.892221 19 69.622 0.901797 20 42.215 0.755166 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.415617 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-23_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 0.1 -1.1 0.1 1.9 0.3 1.7 -0.5 0.0 0.6 -0.4 -0.1 1.6 -0.0 -0.8 1.3 -0.2 0.4 -0.2 0.9 -1.3 -0.5 -0.9 -1.4 -0.8 -1.4 0.3 0.1 1.9 -0.5 -1.1 -0.2 1.1 1.6 -0.8 1.9 -0.1 -1.2 -0.7 0.1 6.1 -1.1 Chi-square with 42 degrees of freedom:76.632386 z-score=3.778703, p-value=0.999128 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-23_10:31 Test no p-value 1 0.198706 2 0.572181 3 0.592841 4 0.633598 5 0.070424 6 0.939303 7 0.123062 8 0.091249 9 0.578265 10 0.552755 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.501855 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-23_10:31: (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 66501 0.41 66658 0.00 3 25000.00 24998 0.00 25045 0.08 4 6666.67 6789 2.24 6588 0.93 5 1388.89 1435 1.53 1446 2.35 6 238.10 242 0.06 215 2.24 7 34.72 30 0.64 37 0.15 8 4.96 4 0.19 10 5.12 p=0.46626 p=0.90752 Number of rngs required: 687841, p-value: 0.258 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-23_10:31 No. of wins: Observed Expected 98309 98585.9 z-score=-1.238, pvalue=0.10781 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66570 66666.7 0.140 0.140 2 37749 37654.3 0.238 0.378 3 27004 26954.7 0.090 0.468 4 19350 19313.5 0.069 0.537 5 13808 13851.4 0.136 0.674 6 9931 9943.5 0.016 0.689 7 7211 7145.0 0.609 1.299 8 5054 5139.1 1.408 2.707 9 3690 3699.9 0.026 2.733 10 2725 2666.3 1.292 4.026 11 1981 1923.3 1.729 5.755 12 1311 1388.7 4.352 10.107 13 984 1003.7 0.387 10.494 14 684 726.1 2.446 12.939 15 534 525.8 0.127 13.066 16 371 381.2 0.270 13.337 17 279 276.5 0.022 13.358 18 217 200.8 1.302 14.660 19 157 146.0 0.831 15.492 20 104 106.2 0.046 15.538 21 286 287.1 0.004 15.542 Chisq= 15.54 for 20 degrees of freedom, p= 0.25541 SUMMARY of craptest p-value for no. of wins: 0.107807 p-value for throws/game: 0.255406 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-23_10:31 No. of wins: Observed Expected 98869 98585.9 z-score= 1.266, pvalue=0.89731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66341 66666.7 1.591 1.591 2 37380 37654.3 1.998 3.589 3 27073 26954.7 0.519 4.108 4 19460 19313.5 1.112 5.220 5 13924 13851.4 0.380 5.600 6 10127 9943.5 3.385 8.985 7 7137 7145.0 0.009 8.994 8 5263 5139.1 2.988 11.983 9 3652 3699.9 0.619 12.602 10 2750 2666.3 2.628 15.230 11 1910 1923.3 0.092 15.322 12 1355 1388.7 0.820 16.142 13 992 1003.7 0.137 16.278 14 691 726.1 1.701 17.979 15 509 525.8 0.539 18.518 16 397 381.2 0.659 19.177 17 286 276.5 0.324 19.501 18 227 200.8 3.410 22.911 19 140 146.0 0.245 23.156 20 88 106.2 3.124 26.280 21 298 287.1 0.413 26.693 Chisq= 26.69 for 20 degrees of freedom, p= 0.85587 SUMMARY of craptest p-value for no. of wins: 0.897310 p-value for throws/game: 0.855872 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0050,0.0060,0.0192,0.0276,0.0375,0.0526,0.0534,0.0627,0.0704,0.0704, 0.0720,0.0739,0.0753,0.0789,0.0812,0.0836,0.0912,0.0932,0.0951,0.0961, 0.0972,0.1028,0.1035,0.1059,0.1068,0.1078,0.1226,0.1231,0.1266,0.1406, 0.1421,0.1468,0.1472,0.1507,0.1540,0.1551,0.1582,0.1597,0.1597,0.1607, 0.1632,0.1641,0.1671,0.1688,0.1695,0.1728,0.1779,0.1801,0.1842,0.1864, 0.1868,0.1869,0.1877,0.1884,0.1884,0.1987,0.2048,0.2135,0.2206,0.2242, 0.2256,0.2271,0.2418,0.2459,0.2473,0.2550,0.2554,0.2561,0.2583,0.2607, 0.2683,0.2694,0.2853,0.2993,0.3054,0.3057,0.3177,0.3209,0.3216,0.3314, 0.3337,0.3475,0.3479,0.3488,0.3497,0.3505,0.3512,0.3580,0.3591,0.3592, 0.3648,0.3712,0.3853,0.3920,0.3930,0.3931,0.3949,0.3979,0.4042,0.4126, 0.4139,0.4156,0.4329,0.4352,0.4363,0.4415,0.4425,0.4487,0.4498,0.4514, 0.4585,0.4620,0.4663,0.4690,0.4696,0.4698,0.4717,0.4784,0.4838,0.4847, 0.4887,0.4920,0.4991,0.5019,0.5116,0.5122,0.5174,0.5205,0.5219,0.5236, 0.5236,0.5243,0.5243,0.5302,0.5323,0.5360,0.5364,0.5435,0.5448,0.5454, 0.5461,0.5528,0.5562,0.5602,0.5619,0.5722,0.5735,0.5748,0.5748,0.5764, 0.5783,0.5795,0.5815,0.5837,0.5928,0.6009,0.6038,0.6064,0.6271,0.6291, 0.6313,0.6319,0.6336,0.6349,0.6374,0.6435,0.6501,0.6529,0.6536,0.6587, 0.6590,0.6607,0.6613,0.6663,0.6674,0.6684,0.6796,0.6812,0.6818,0.6874, 0.6877,0.6924,0.6948,0.6991,0.7006,0.7010,0.7056,0.7093,0.7151,0.7171, 0.7191,0.7197,0.7313,0.7341,0.7381,0.7477,0.7486,0.7544,0.7552,0.7598, 0.7614,0.7624,0.7641,0.7662,0.7666,0.7702,0.7768,0.7888,0.7973,0.8015, 0.8138,0.8188,0.8192,0.8221,0.8278,0.8284,0.8297,0.8341,0.8369,0.8418, 0.8419,0.8424,0.8469,0.8534,0.8559,0.8583,0.8611,0.8642,0.8688,0.8899, 0.8905,0.8912,0.8912,0.8922,0.8973,0.8998,0.9018,0.9075,0.9101,0.9101, 0.9112,0.9118,0.9157,0.9159,0.9215,0.9241,0.9285,0.9346,0.9375,0.9376, 0.9393,0.9436,0.9453,0.9482,0.9499,0.9524,0.9545,0.9551,0.9568,0.9625, 0.9635,0.9657,0.9706,0.9770,0.9790,0.9843,0.9854,0.9961,0.9991, Overall p-value after applying KStest on 269 p-values = 0.280021 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.