RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-27_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 15.47 22.5313 0.834861 2 to 25 15.72 19.8175 0.716328 3 to 26 16.00 15.4294 0.435418 4 to 27 15.59 21.7460 0.805314 5 to 28 15.80 12.9211 0.258548 6 to 29 15.85 11.2833 0.158537 7 to 30 15.73 25.0938 0.907371 8 to 31 15.63 18.2635 0.627597 9 to 32 15.82 22.0141 0.815821 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.331299 Tough bday spacings test for dh-ranFile-2015-11-27_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 28 71 96 107 65 58 37 18 5 3 (O-E)^2/E 0.9 2.0 0.1 0.0 0.9 2.2 0.7 1.8 0.7 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.865, p= 0.548 RESULTS OF GCD FOR dh-ranFile-2015-11-27_05:31 Euclid's algorithm: p-value, steps to gcd: 0.935367 p-value, dist. of gcd's: 0.372413 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-27_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.083 0.344 0.370 0.753 0.453 0.618 0.336 0.493 Bits 8 to 15---> 0.130 0.261 0.068 0.453 0.725 0.171 0.813 0.440 Bits 16 to 23---> 0.442 0.167 0.013 0.488 0.076 0.697 0.195 0.480 Bits 24 to 31---> 0.408 0.497 0.021 0.986 0.165 0.490 0.282 0.201 KS test for the above 32 p values: 0.978 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-27_05:31, p-values for 5 runs: 0.6187, 0.6926, 0.2356, 0.5762, 0.0040 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-27_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 187 211.4 2.820 2.820 r= 29 5174 5134.0 0.311 3.132 r= 30 23100 23103.0 0.000 3.132 r= 31 11539 11551.5 0.014 3.146 chi-square = 3.146 with df = 3; p-value = 0.630 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-27_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5179 5134.0 0.394 0.814 r= 31 23072 23103.0 0.042 0.856 r= 32 11547 11551.5 0.002 0.857 chi-square = 0.857 with df = 3; p-value = 0.164 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-27_05:31 b-rank test for bits 1 to 8, p=0.98022 b-rank test for bits 2 to 9, p=0.84791 b-rank test for bits 3 to 10, p=0.57613 b-rank test for bits 4 to 11, p=0.81777 b-rank test for bits 5 to 12, p=0.02152 b-rank test for bits 6 to 13, p=0.81496 b-rank test for bits 7 to 14, p=0.82958 b-rank test for bits 8 to 15, p=0.44246 b-rank test for bits 9 to 16, p=0.84917 b-rank test for bits 10 to 17, p=0.61001 b-rank test for bits 11 to 18, p=0.61263 b-rank test for bits 12 to 19, p=0.65824 b-rank test for bits 13 to 20, p=0.30696 b-rank test for bits 14 to 21, p=0.02913 b-rank test for bits 15 to 22, p=0.06962 b-rank test for bits 16 to 23, p=0.13536 b-rank test for bits 17 to 24, p=0.09399 b-rank test for bits 18 to 25, p=0.10899 b-rank test for bits 19 to 26, p=0.58508 b-rank test for bits 20 to 27, p=0.47659 b-rank test for bits 21 to 28, p=0.81194 b-rank test for bits 22 to 29, p=0.33986 b-rank test for bits 23 to 30, p=0.71125 b-rank test for bits 24 to 31, p=0.12835 b-rank test for bits 25 to 32, p=0.05106 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 = 0.451705 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-27_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 142157 0.58 0.718594 2 142487 1.35 0.911443 3 142015 0.25 0.597504 4 141429 -1.12 0.130875 5 142664 1.76 0.961071 6 141949 0.09 0.536924 7 141850 -0.14 0.444875 8 142255 0.81 0.790351 9 141783 -0.30 0.383935 10 141680 -0.54 0.296042 11 141390 -1.21 0.112491 12 142072 0.38 0.648053 13 141844 -0.15 0.439341 14 141170 -1.73 0.042047 15 141829 -0.19 0.425561 16 141687 -0.52 0.301719 17 142455 1.27 0.898833 18 141877 -0.08 0.469894 19 141985 0.18 0.570167 20 141933 0.06 0.522052 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-27_05:31 Bits used No. missing words z-score p-value 23 to 32 142120 0.7264 0.766218 22 to 31 142083 0.5989 0.725368 21 to 30 141949 0.1368 0.554403 20 to 29 141770 -0.4804 0.315454 19 to 28 142259 1.2058 0.886045 18 to 27 142189 0.9644 0.832572 17 to 26 142289 1.3092 0.904768 16 to 25 141893 -0.0563 0.477547 15 to 24 141752 -0.5425 0.293731 14 to 23 141825 -0.2908 0.385605 13 to 22 141412 -1.7149 0.043179 12 to 21 141689 -0.7598 0.223699 11 to 20 142244 1.1540 0.875757 10 to 19 141780 -0.4460 0.327811 9 to 18 141720 -0.6529 0.256923 8 to 17 141090 -2.8253 0.002362 7 to 16 141702 -0.7149 0.237326 6 to 15 142131 0.7644 0.777679 5 to 14 141925 0.0540 0.521546 4 to 13 142176 0.9196 0.821097 3 to 12 141647 -0.9046 0.182842 2 to 11 141903 -0.0218 0.491293 1 to 10 142334 1.4644 0.928455 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-27_05:31 Bits used No. missing words z-score p-value 28 to 32 141547 -1.2282 0.109679 27 to 31 141283 -2.1232 0.016871 26 to 30 142144 0.7955 0.786836 25 to 29 141937 0.0938 0.537365 24 to 28 142291 1.2938 0.902132 23 to 27 142389 1.6260 0.948025 22 to 26 141797 -0.3808 0.351683 21 to 25 142160 0.8497 0.802262 20 to 24 142778 2.9446 0.998383 19 to 23 141801 -0.3672 0.356727 18 to 22 142254 1.1684 0.878672 17 to 21 141797 -0.3808 0.351683 16 to 20 142483 1.9446 0.974091 15 to 19 142050 0.4768 0.683265 14 to 18 142108 0.6735 0.749672 13 to 17 141759 -0.5096 0.305168 12 to 16 141971 0.2091 0.582796 11 to 15 141796 -0.3842 0.350426 10 to 14 141889 -0.0689 0.472529 9 to 13 141722 -0.6350 0.262709 8 to 12 141718 -0.6486 0.258306 7 to 11 142115 0.6972 0.757157 6 to 10 141989 0.2701 0.606446 5 to 9 142157 0.8396 0.799422 4 to 8 142040 0.4429 0.671099 3 to 7 141612 -1.0079 0.156752 2 to 6 141635 -0.9299 0.176203 1 to 5 142064 0.5243 0.699967 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-27_05:31 Bits used No. missing words z-score p-value 31 to 32 142435 1.5506 0.939507 30 to 31 141822 -0.2576 0.398354 29 to 30 142037 0.3766 0.646767 28 to 29 141778 -0.3874 0.349229 27 to 28 142553 1.8987 0.971200 26 to 27 142046 0.4032 0.656583 25 to 26 142239 0.9725 0.834594 24 to 25 142193 0.8368 0.798643 23 to 24 141905 -0.0128 0.494905 22 to 23 141930 0.0610 0.524310 21 to 22 141903 -0.0187 0.492551 20 to 21 142171 0.7719 0.779910 19 to 20 141971 0.1819 0.572176 18 to 19 142560 1.9194 0.972532 17 to 18 142112 0.5978 0.725029 16 to 17 141619 -0.8564 0.195880 15 to 16 142258 1.0285 0.848149 14 to 15 142299 1.1495 0.874819 13 to 14 142197 0.8486 0.801944 12 to 13 141781 -0.3786 0.352509 11 to 12 141851 -0.1721 0.431693 10 to 11 141602 -0.9066 0.182315 9 to 10 142225 0.9312 0.824120 8 to 9 141706 -0.5998 0.274322 7 to 8 141709 -0.5909 0.277279 6 to 7 141585 -0.9567 0.169353 5 to 6 141554 -1.0482 0.147280 4 to 5 141777 -0.3904 0.348137 3 to 4 142427 1.5271 0.936626 2 to 3 141646 -0.7768 0.218643 1 to 2 142036 0.3737 0.645671 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-27_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2442.86 -0.808 0.209506 Test results for specific bytes for dh-ranFile-2015-11-27_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2479.86 -0.285 0.387889 2 to 9 2381.23 -1.680 0.046509 3 to 10 2589.46 1.265 0.897096 4 to 11 2620.01 1.697 0.955168 5 to 12 2489.35 -0.151 0.440140 6 to 13 2630.00 1.838 0.967004 7 to 14 2578.88 1.115 0.867678 8 to 15 2469.35 -0.433 0.332334 9 to 16 2414.49 -1.209 0.113275 10 to 17 2521.65 0.306 0.620245 11 to 18 2617.59 1.663 0.951837 12 to 19 2408.26 -1.297 0.097259 13 to 20 2522.43 0.317 0.624483 14 to 21 2575.01 1.061 0.855610 15 to 22 2429.04 -1.003 0.157813 16 to 23 2503.81 0.054 0.521476 17 to 24 2482.60 -0.246 0.402792 18 to 25 2573.69 1.042 0.851310 19 to 26 2508.67 0.123 0.548817 20 to 27 2571.35 1.009 0.843508 21 to 28 2517.59 0.249 0.598210 22 to 29 2524.08 0.341 0.633285 23 to 30 2495.62 -0.062 0.475322 24 to 31 2517.16 0.243 0.595890 25 to 32 2587.28 1.234 0.891457 CDPARK for dh-ranFile-2015-11-27_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 3487 -1.6438 0.050105 3548 1.1416 0.873180 3510 -0.5936 0.276387 3490 -1.5068 0.065925 3502 -0.9589 0.168804 3526 0.1370 0.554479 3524 0.0457 0.518210 3518 -0.2283 0.409702 3540 0.7763 0.781201 3535 0.5479 0.708135 Square side=100, avg. no. parked=3518.00 sample std.=19.59 p-value of the KSTEST for those 10 p-values: 0.863073 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-27_05:31 0.1229,0.4264,0.5228,0.4775,0.6813,0.1095,0.3967,0.5073,0.5071,0.5197, The KS test for those 10 p-values: 0.178747 The 3DSPHERES test for dh-ranFile-2015-11-27_05:31 sample no r^3 equiv. uni. 1 21.438 0.510606 2 0.157 0.005220 3 16.310 0.419385 4 72.972 0.912175 5 12.466 0.340011 6 3.154 0.099791 7 34.642 0.684859 8 14.109 0.375185 9 25.901 0.578263 10 9.561 0.272910 11 103.917 0.968692 12 41.608 0.750160 13 75.094 0.918173 14 4.278 0.132893 15 19.381 0.475888 16 4.789 0.147532 17 2.747 0.087510 18 15.645 0.406378 19 59.963 0.864499 20 9.310 0.266791 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.833987 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-27_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 -0.8 -0.5 0.1 -0.2 -0.2 -0.7 -0.1 1.4 1.0 1.5 0.3 0.3 0.5 0.5 -1.6 -0.6 -0.4 0.3 -0.4 0.3 -1.3 -0.9 -0.5 -0.8 1.1 1.9 1.1 -0.3 -1.0 -1.4 0.1 0.7 1.5 1.3 -0.7 -1.3 -0.8 -1.8 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:39.374222 z-score=-0.286496, p-value=0.413135 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-27_05:31 Test no p-value 1 0.152972 2 0.214968 3 0.464823 4 0.552575 5 0.026647 6 0.182521 7 0.141832 8 0.860664 9 0.414230 10 0.731955 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.294026 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-27_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 66791 0.23 66584 0.10 3 25000.00 24843 0.99 25136 0.74 4 6666.67 6671 0.00 6624 0.27 5 1388.89 1428 1.10 1371 0.23 6 238.10 220 1.38 236 0.02 7 34.72 40 0.80 40 0.80 8 4.96 6 0.22 8 1.86 p=0.41957 p=0.32745 Number of rngs required: 688839, p-value: 0.692 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-27_05:31 No. of wins: Observed Expected 98733 98585.9 z-score= 0.658, pvalue=0.74476 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66872 66666.7 0.632 0.632 2 37626 37654.3 0.021 0.654 3 26862 26954.7 0.319 0.973 4 19455 19313.5 1.037 2.010 5 13766 13851.4 0.527 2.537 6 9999 9943.5 0.309 2.846 7 7128 7145.0 0.041 2.887 8 5074 5139.1 0.824 3.711 9 3604 3699.9 2.484 6.195 10 2735 2666.3 1.770 7.965 11 1938 1923.3 0.112 8.077 12 1374 1388.7 0.156 8.233 13 983 1003.7 0.428 8.661 14 698 726.1 1.091 9.751 15 488 525.8 2.722 12.474 16 377 381.2 0.045 12.519 17 316 276.5 5.631 18.150 18 199 200.8 0.017 18.166 19 142 146.0 0.109 18.275 20 112 106.2 0.315 18.590 21 252 287.1 4.294 22.885 Chisq= 22.88 for 20 degrees of freedom, p= 0.70550 SUMMARY of craptest p-value for no. of wins: 0.744764 p-value for throws/game: 0.705500 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-27_05:31 No. of wins: Observed Expected 98588 98585.9 z-score= 0.010, pvalue=0.50382 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67011 66666.7 1.778 1.778 2 37684 37654.3 0.023 1.802 3 27061 26954.7 0.419 2.221 4 19109 19313.5 2.165 4.385 5 13786 13851.4 0.309 4.694 6 9917 9943.5 0.071 4.765 7 6995 7145.0 3.150 7.915 8 5029 5139.1 2.358 10.273 9 3635 3699.9 1.137 11.410 10 2736 2666.3 1.822 13.232 11 1939 1923.3 0.128 13.360 12 1371 1388.7 0.227 13.587 13 1018 1003.7 0.203 13.790 14 760 726.1 1.579 15.369 15 538 525.8 0.281 15.650 16 421 381.2 4.166 19.816 17 301 276.5 2.164 21.980 18 180 200.8 2.160 24.140 19 133 146.0 1.155 25.295 20 107 106.2 0.006 25.301 21 269 287.1 1.143 26.444 Chisq= 26.44 for 20 degrees of freedom, p= 0.84835 SUMMARY of craptest p-value for no. of wins: 0.503821 p-value for throws/game: 0.848354 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0040,0.0052,0.0129,0.0169,0.0213,0.0215,0.0266,0.0291,0.0420, 0.0432,0.0465,0.0501,0.0511,0.0659,0.0679,0.0696,0.0757,0.0828,0.0875, 0.0940,0.0973,0.0998,0.1090,0.1095,0.1097,0.1125,0.1133,0.1229,0.1284, 0.1303,0.1309,0.1329,0.1354,0.1418,0.1473,0.1475,0.1530,0.1568,0.1578, 0.1585,0.1643,0.1646,0.1670,0.1688,0.1694,0.1714,0.1762,0.1787,0.1823, 0.1825,0.1828,0.1950,0.1959,0.2005,0.2095,0.2150,0.2186,0.2237,0.2356, 0.2373,0.2569,0.2583,0.2585,0.2615,0.2627,0.2668,0.2729,0.2743,0.2764, 0.2773,0.2823,0.2937,0.2940,0.2960,0.3017,0.3052,0.3070,0.3155,0.3275, 0.3278,0.3313,0.3323,0.3361,0.3399,0.3400,0.3435,0.3481,0.3492,0.3504, 0.3517,0.3517,0.3525,0.3567,0.3696,0.3724,0.3752,0.3839,0.3856,0.3879, 0.3967,0.3984,0.4028,0.4064,0.4080,0.4097,0.4131,0.4142,0.4194,0.4196, 0.4256,0.4264,0.4317,0.4354,0.4393,0.4401,0.4404,0.4424,0.4425,0.4449, 0.4517,0.4526,0.4529,0.4648,0.4699,0.4725,0.4753,0.4759,0.4766,0.4775, 0.4775,0.4801,0.4882,0.4903,0.4913,0.4926,0.4932,0.4949,0.4968,0.5038, 0.5071,0.5073,0.5106,0.5182,0.5197,0.5215,0.5215,0.5221,0.5228,0.5243, 0.5369,0.5374,0.5476,0.5488,0.5526,0.5544,0.5545,0.5702,0.5722,0.5761, 0.5762,0.5783,0.5828,0.5851,0.5959,0.5975,0.5982,0.6064,0.6100,0.6126, 0.6182,0.6187,0.6202,0.6245,0.6276,0.6303,0.6333,0.6457,0.6468,0.6481, 0.6566,0.6582,0.6711,0.6813,0.6833,0.6849,0.6923,0.6926,0.6966,0.7000, 0.7055,0.7081,0.7113,0.7163,0.7186,0.7250,0.7251,0.7254,0.7320,0.7448, 0.7497,0.7502,0.7525,0.7572,0.7662,0.7777,0.7799,0.7812,0.7868,0.7904, 0.7986,0.7994,0.8019,0.8023,0.8053,0.8119,0.8129,0.8150,0.8158,0.8178, 0.8211,0.8241,0.8296,0.8326,0.8340,0.8346,0.8349,0.8435,0.8479,0.8481, 0.8484,0.8492,0.8513,0.8556,0.8607,0.8631,0.8645,0.8677,0.8732,0.8748, 0.8758,0.8787,0.8860,0.8915,0.8971,0.8988,0.9021,0.9048,0.9074,0.9114, 0.9122,0.9182,0.9285,0.9354,0.9366,0.9395,0.9480,0.9518,0.9552,0.9611, 0.9670,0.9687,0.9712,0.9725,0.9741,0.9776,0.9802,0.9860,0.9984, Overall p-value after applying KStest on 269 p-values = 0.892693 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.