RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-07_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 30.6698 0.978100 2 to 25 15.87 11.5554 0.173722 3 to 26 15.96 20.0050 0.726027 4 to 27 15.89 26.1741 0.928654 5 to 28 15.51 26.7669 0.938424 6 to 29 15.93 12.1150 0.206876 7 to 30 15.50 22.6758 0.839894 8 to 31 15.59 30.4657 0.976824 9 to 32 15.64 17.9563 0.608400 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.015728 Tough bday spacings test for dh-ranFile-2018-04-07_23:31: 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 7 35 92 92 108 77 39 31 10 7 2 (O-E)^2/E 0.5 0.1 4.8 0.3 1.1 0.0 3.3 0.1 1.6 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 12.830, p= 0.767 RESULTS OF GCD FOR dh-ranFile-2018-04-07_23:31 Euclid's algorithm: p-value, steps to gcd: 0.408784 p-value, dist. of gcd's: 0.339842 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-07_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.347 0.646 0.511 0.104 0.385 0.988 0.819 0.459 Bits 8 to 15---> 0.517 0.481 0.728 0.929 0.903 0.220 0.024 0.819 Bits 16 to 23---> 0.792 0.273 0.706 0.109 0.142 0.347 0.545 0.954 Bits 24 to 31---> 0.571 0.546 0.085 0.511 0.739 0.598 0.996 0.030 KS test for the above 32 p values: 0.157 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-07_23:31, p-values for 5 runs: 0.4626, 0.8744, 0.1059, 0.1197, 0.2338 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-07_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5180 5134.0 0.412 0.832 r= 30 23073 23103.0 0.039 0.871 r= 31 11545 11551.5 0.004 0.874 chi-square = 0.874 with df = 3; p-value = 0.168 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-07_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5117 5134.0 0.056 0.204 r= 31 23240 23103.0 0.812 1.016 r= 32 11426 11551.5 1.364 2.380 chi-square = 2.380 with df = 3; p-value = 0.503 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-07_23:31 b-rank test for bits 1 to 8, p=0.43904 b-rank test for bits 2 to 9, p=0.22978 b-rank test for bits 3 to 10, p=0.93395 b-rank test for bits 4 to 11, p=0.05514 b-rank test for bits 5 to 12, p=0.31140 b-rank test for bits 6 to 13, p=0.60616 b-rank test for bits 7 to 14, p=0.40664 b-rank test for bits 8 to 15, p=0.77881 b-rank test for bits 9 to 16, p=0.56625 b-rank test for bits 10 to 17, p=0.79200 b-rank test for bits 11 to 18, p=0.44811 b-rank test for bits 12 to 19, p=0.22625 b-rank test for bits 13 to 20, p=0.93278 b-rank test for bits 14 to 21, p=0.05000 b-rank test for bits 15 to 22, p=0.44696 b-rank test for bits 16 to 23, p=0.77527 b-rank test for bits 17 to 24, p=0.07646 b-rank test for bits 18 to 25, p=0.34872 b-rank test for bits 19 to 26, p=0.28056 b-rank test for bits 20 to 27, p=0.12203 b-rank test for bits 21 to 28, p=0.90535 b-rank test for bits 22 to 29, p=0.70972 b-rank test for bits 23 to 30, p=0.80446 b-rank test for bits 24 to 31, p=0.47111 b-rank test for bits 25 to 32, p=0.19336 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 = 0.946401 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-07_23:31 (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 142228 0.74 0.771730 2 140970 -2.19 0.014093 3 141955 0.11 0.542489 4 141655 -0.59 0.276180 5 141465 -1.04 0.149599 6 142952 2.44 0.992578 7 141710 -0.47 0.320706 8 141548 -0.84 0.199271 9 141980 0.17 0.565574 10 142359 1.05 0.853286 11 141330 -1.35 0.087936 12 141635 -0.64 0.260775 13 142244 0.78 0.782875 14 141999 0.21 0.582975 15 142062 0.36 0.639344 16 141733 -0.41 0.340175 17 141557 -0.82 0.205197 18 142025 0.27 0.606519 19 141749 -0.37 0.353978 20 141167 -1.73 0.041422 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-07_23:31 Bits used No. missing words z-score p-value 23 to 32 141921 0.0402 0.516050 22 to 31 142067 0.5437 0.706673 21 to 30 141841 -0.2356 0.406864 20 to 29 142449 1.8609 0.968623 19 to 28 142139 0.7920 0.785810 18 to 27 141925 0.0540 0.521546 17 to 26 141808 -0.3494 0.363389 16 to 25 141927 0.0609 0.524293 15 to 24 142115 0.7092 0.760902 14 to 23 141881 -0.0977 0.461089 13 to 22 142215 1.0540 0.854066 12 to 21 142267 1.2333 0.891276 11 to 20 141776 -0.4598 0.322845 10 to 19 141910 0.0023 0.500922 9 to 18 142177 0.9230 0.821996 8 to 17 141951 0.1437 0.557127 7 to 16 141743 -0.5736 0.283136 6 to 15 141618 -1.0046 0.157548 5 to 14 141916 0.0230 0.509175 4 to 13 142028 0.4092 0.658806 3 to 12 141779 -0.4494 0.326567 2 to 11 141349 -1.9322 0.026669 1 to 10 141886 -0.0804 0.467940 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-07_23:31 Bits used No. missing words z-score p-value 28 to 32 141343 -1.9198 0.027444 27 to 31 141680 -0.7774 0.218464 26 to 30 141910 0.0023 0.500906 25 to 29 141852 -0.1943 0.422955 24 to 28 142191 0.9548 0.830164 23 to 27 141833 -0.2587 0.397916 22 to 26 141772 -0.4655 0.320778 21 to 25 141866 -0.1469 0.441613 20 to 24 141540 -1.2520 0.105291 19 to 23 142235 1.1040 0.865196 18 to 22 141838 -0.2418 0.404469 17 to 21 142055 0.4938 0.689275 16 to 20 142444 1.8124 0.965041 15 to 19 142420 1.7311 0.958282 14 to 18 142276 1.2429 0.893057 13 to 17 142049 0.4735 0.682057 12 to 16 141567 -1.1604 0.122935 11 to 15 141840 -0.2350 0.407098 10 to 14 142081 0.5819 0.719694 9 to 13 141886 -0.0791 0.468483 8 to 12 141776 -0.4520 0.325647 7 to 11 142220 1.0531 0.853857 6 to 10 141653 -0.8689 0.192447 5 to 9 142075 0.5616 0.712803 4 to 8 141832 -0.2621 0.396609 3 to 7 141289 -2.1028 0.017741 2 to 6 141867 -0.1435 0.442951 1 to 5 142162 0.8565 0.804142 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-07_23:31 Bits used No. missing words z-score p-value 31 to 32 141717 -0.5673 0.285240 30 to 31 142490 1.7129 0.956634 29 to 30 141364 -1.6086 0.053847 28 to 29 141534 -1.1072 0.134111 27 to 28 141688 -0.6529 0.256913 26 to 27 141687 -0.6558 0.255963 25 to 26 142108 0.5860 0.721078 24 to 25 142072 0.4799 0.684334 23 to 24 141976 0.1967 0.577956 22 to 23 141928 0.0551 0.521960 21 to 22 141584 -0.9597 0.168609 20 to 21 142261 1.0374 0.850219 19 to 20 141925 0.0462 0.518434 18 to 19 141613 -0.8741 0.191024 17 to 18 141955 0.1347 0.553583 16 to 17 141392 -1.5260 0.063499 15 to 16 141758 -0.4464 0.327654 14 to 15 141383 -1.5526 0.060260 13 to 14 142184 0.8102 0.791098 12 to 13 141294 -1.8151 0.034752 11 to 12 141897 -0.0364 0.485493 10 to 11 141803 -0.3137 0.376891 9 to 10 141765 -0.4258 0.335144 8 to 9 141615 -0.8682 0.192634 7 to 8 141122 -2.3225 0.010103 6 to 7 141825 -0.2488 0.401773 5 to 6 142094 0.5447 0.707037 4 to 5 141875 -0.1013 0.459669 3 to 4 141800 -0.3225 0.373534 2 to 3 141767 -0.4199 0.337297 1 to 2 142054 0.4268 0.665221 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-07_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2430.94 -0.977 0.164369 Test results for specific bytes for dh-ranFile-2018-04-07_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2530.89 0.437 0.668886 2 to 9 2411.55 -1.251 0.105491 3 to 10 2344.27 -2.202 0.013819 4 to 11 2500.29 0.004 0.501658 5 to 12 2418.50 -1.153 0.124550 6 to 13 2455.48 -0.630 0.264478 7 to 14 2460.95 -0.552 0.290375 8 to 15 2633.19 1.884 0.970190 9 to 16 2526.65 0.377 0.646894 10 to 17 2415.54 -1.194 0.116153 11 to 18 2493.76 -0.088 0.464838 12 to 19 2498.02 -0.028 0.488812 13 to 20 2502.50 0.035 0.514129 14 to 21 2616.66 1.650 0.950505 15 to 22 2454.42 -0.645 0.259585 16 to 23 2358.64 -1.999 0.022799 17 to 24 2583.54 1.181 0.881281 18 to 25 2579.84 1.129 0.870565 19 to 26 2584.30 1.192 0.883402 20 to 27 2445.43 -0.772 0.220118 21 to 28 2561.43 0.869 0.807518 22 to 29 2454.75 -0.640 0.261105 23 to 30 2426.19 -1.044 0.148280 24 to 31 2401.32 -1.396 0.081422 25 to 32 2471.60 -0.402 0.343985 CDPARK for dh-ranFile-2018-04-07_23:31: 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 3527 0.1826 0.572463 3534 0.5023 0.692266 3514 -0.4110 0.340551 3537 0.6393 0.738676 3528 0.2283 0.590298 3551 1.2785 0.899470 3541 0.8219 0.794438 3577 2.4658 0.993164 3526 0.1370 0.554479 3524 0.0457 0.518210 Square side=100, avg. no. parked=3535.90 sample std.=16.76 p-value of the KSTEST for those 10 p-values: 0.079832 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-07_23:31 0.5772,0.1416,0.4238,0.3229,0.9715,0.7064,0.6545,0.2705,0.0473,0.8680, The KS test for those 10 p-values: 0.999874 The 3DSPHERES test for dh-ranFile-2018-04-07_23:31 sample no r^3 equiv. uni. 1 30.411 0.637127 2 46.602 0.788475 3 19.719 0.481743 4 1.789 0.057876 5 85.448 0.942055 6 5.070 0.155488 7 86.040 0.943188 8 8.164 0.238251 9 9.077 0.261074 10 111.483 0.975671 11 1.858 0.060052 12 14.680 0.386955 13 31.473 0.649748 14 6.566 0.196565 15 29.216 0.622386 16 30.717 0.640810 17 19.113 0.471182 18 49.910 0.810554 19 4.641 0.143316 20 4.019 0.125392 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.872237 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-07_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -1.1 0.8 0.7 0.5 -2.0 2.7 -1.3 1.2 1.6 0.5 0.4 0.4 0.1 0.5 2.3 -1.9 -1.6 -0.1 -0.3 -0.8 -0.1 -0.6 0.8 -1.6 1.4 0.5 -1.3 -0.7 -0.8 -1.3 -0.6 -0.3 -0.2 -0.8 0.3 -0.4 -0.4 1.0 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:48.304868 z-score=0.687917, p-value=0.766749 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-07_23:31 Test no p-value 1 0.929506 2 0.014945 3 0.014372 4 0.184617 5 0.005692 6 0.482164 7 0.074972 8 0.011599 9 0.000249 10 0.700890 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000024 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-07_23:31: (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 66826 0.38 66399 1.07 3 25000.00 24838 1.05 25193 1.49 4 6666.67 6659 0.01 6763 1.39 5 1388.89 1389 0.00 1375 0.14 6 238.10 250 0.60 230 0.28 7 34.72 30 0.64 32 0.21 8 4.96 7 0.84 7 0.84 p=0.25807 p=0.50917 Number of rngs required: 690123, p-value: 0.979 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-07_23:31 No. of wins: Observed Expected 98647 98585.9 z-score= 0.273, pvalue=0.60775 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66421 66666.7 0.905 0.905 2 37808 37654.3 0.627 1.532 3 27098 26954.7 0.761 2.294 4 19317 19313.5 0.001 2.295 5 13770 13851.4 0.479 2.773 6 9834 9943.5 1.207 3.980 7 7214 7145.0 0.666 4.646 8 5060 5139.1 1.217 5.862 9 3867 3699.9 7.550 13.413 10 2663 2666.3 0.004 13.417 11 1878 1923.3 1.068 14.485 12 1394 1388.7 0.020 14.505 13 1026 1003.7 0.495 15.000 14 709 726.1 0.405 15.404 15 542 525.8 0.497 15.901 16 402 381.2 1.140 17.042 17 259 276.5 1.112 18.154 18 228 200.8 3.676 21.830 19 131 146.0 1.538 23.368 20 106 106.2 0.000 23.368 21 273 287.1 0.694 24.062 Chisq= 24.06 for 20 degrees of freedom, p= 0.76031 SUMMARY of craptest p-value for no. of wins: 0.607750 p-value for throws/game: 0.760313 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-07_23:31 No. of wins: Observed Expected 98595 98585.9 z-score= 0.041, pvalue=0.51631 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66409 66666.7 0.996 0.996 2 37494 37654.3 0.683 1.678 3 27084 26954.7 0.620 2.298 4 19358 19313.5 0.103 2.401 5 13731 13851.4 1.047 3.448 6 9948 9943.5 0.002 3.450 7 7319 7145.0 4.236 7.686 8 5139 5139.1 0.000 7.686 9 3741 3699.9 0.457 8.143 10 2807 2666.3 7.425 15.568 11 1940 1923.3 0.144 15.713 12 1379 1388.7 0.068 15.781 13 1048 1003.7 1.954 17.735 14 693 726.1 1.513 19.248 15 494 525.8 1.927 21.175 16 356 381.2 1.660 22.835 17 269 276.5 0.206 23.040 18 212 200.8 0.621 23.662 19 167 146.0 3.025 26.687 20 117 106.2 1.095 27.782 21 295 287.1 0.217 27.999 Chisq= 28.00 for 20 degrees of freedom, p= 0.89057 SUMMARY of craptest p-value for no. of wins: 0.516307 p-value for throws/game: 0.890567 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0002,0.0057,0.0101,0.0116,0.0138,0.0141,0.0144,0.0149,0.0157, 0.0177,0.0228,0.0242,0.0267,0.0274,0.0302,0.0348,0.0414,0.0473,0.0500, 0.0538,0.0551,0.0579,0.0601,0.0603,0.0635,0.0750,0.0765,0.0798,0.0814, 0.0855,0.0879,0.1039,0.1053,0.1055,0.1059,0.1094,0.1162,0.1197,0.1220, 0.1229,0.1245,0.1254,0.1341,0.1416,0.1419,0.1433,0.1483,0.1496,0.1555, 0.1572,0.1575,0.1644,0.1684,0.1686,0.1737,0.1846,0.1910,0.1924,0.1926, 0.1934,0.1966,0.1993,0.2052,0.2069,0.2185,0.2199,0.2201,0.2262,0.2298, 0.2338,0.2383,0.2560,0.2569,0.2581,0.2596,0.2608,0.2611,0.2611,0.2645, 0.2705,0.2731,0.2762,0.2806,0.2831,0.2852,0.2904,0.3114,0.3207,0.3208, 0.3228,0.3229,0.3256,0.3266,0.3277,0.3351,0.3373,0.3398,0.3402,0.3406, 0.3440,0.3465,0.3466,0.3487,0.3540,0.3634,0.3735,0.3769,0.3855,0.3870, 0.3966,0.3979,0.4018,0.4045,0.4066,0.4069,0.4071,0.4088,0.4230,0.4238, 0.4390,0.4416,0.4430,0.4470,0.4481,0.4585,0.4597,0.4611,0.4626,0.4648, 0.4679,0.4685,0.4711,0.4712,0.4814,0.4817,0.4822,0.4855,0.4888,0.5009, 0.5009,0.5017,0.5026,0.5092,0.5092,0.5111,0.5112,0.5141,0.5160,0.5163, 0.5174,0.5182,0.5184,0.5215,0.5220,0.5243,0.5425,0.5448,0.5462,0.5536, 0.5545,0.5571,0.5656,0.5662,0.5705,0.5725,0.5772,0.5780,0.5830,0.5903, 0.5982,0.6062,0.6065,0.6078,0.6084,0.6224,0.6371,0.6393,0.6408,0.6462, 0.6469,0.6497,0.6545,0.6588,0.6652,0.6689,0.6821,0.6843,0.6893,0.6923, 0.7009,0.7063,0.7064,0.7067,0.7070,0.7097,0.7128,0.7197,0.7211,0.7260, 0.7282,0.7387,0.7392,0.7603,0.7609,0.7666,0.7667,0.7717,0.7753,0.7788, 0.7829,0.7858,0.7885,0.7911,0.7919,0.7920,0.7944,0.8041,0.8045,0.8075, 0.8106,0.8194,0.8194,0.8220,0.8302,0.8399,0.8502,0.8533,0.8539,0.8541, 0.8652,0.8680,0.8706,0.8722,0.8744,0.8813,0.8834,0.8906,0.8913,0.8931, 0.8995,0.9029,0.9054,0.9287,0.9288,0.9295,0.9328,0.9340,0.9384,0.9421, 0.9432,0.9464,0.9505,0.9543,0.9566,0.9583,0.9650,0.9686,0.9702,0.9715, 0.9757,0.9768,0.9781,0.9789,0.9882,0.9926,0.9932,0.9956,0.9999, Overall p-value after applying KStest on 269 p-values = 0.307020 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.