RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-25_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 15.80 18.4879 0.641298 2 to 25 15.88 14.9843 0.403387 3 to 26 16.03 8.9123 0.057028 4 to 27 15.55 19.7143 0.710898 5 to 28 15.65 18.5100 0.642626 6 to 29 15.87 9.6481 0.082287 7 to 30 15.75 14.9241 0.399054 8 to 31 15.89 26.0905 0.927173 9 to 32 15.62 19.1201 0.678319 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.843304 Tough bday spacings test for dh-ranFile-2015-09-25_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 3 39 81 95 102 69 48 33 18 9 3 (O-E)^2/E 4.1 0.2 0.8 0.1 0.2 1.1 0.3 0.4 0.7 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.909, p= 0.459 RESULTS OF GCD FOR dh-ranFile-2015-09-25_10:31 Euclid's algorithm: p-value, steps to gcd: 0.891763 p-value, dist. of gcd's: 0.891113 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-25_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.529 0.581 0.489 0.625 0.703 0.427 0.860 0.464 Bits 8 to 15---> 0.535 0.017 0.443 0.398 0.121 0.536 0.099 0.092 Bits 16 to 23---> 0.088 0.805 0.341 0.509 0.570 0.783 0.426 0.085 Bits 24 to 31---> 0.195 0.714 0.618 0.001 0.235 0.555 0.549 0.461 KS test for the above 32 p values: 0.913 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-25_10:31, p-values for 5 runs: 0.0002, 0.9471, 0.1892, 0.1191, 0.9320 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-25_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5011 5134.0 2.947 2.975 r= 30 23301 23103.0 1.696 4.671 r= 31 11479 11551.5 0.455 5.126 chi-square = 5.126 with df = 3; p-value = 0.837 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-25_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5071 5134.0 0.773 1.522 r= 31 23128 23103.0 0.027 1.549 r= 32 11577 11551.5 0.056 1.605 chi-square = 1.605 with df = 3; p-value = 0.342 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-25_10:31 b-rank test for bits 1 to 8, p=0.86753 b-rank test for bits 2 to 9, p=0.29697 b-rank test for bits 3 to 10, p=0.98675 b-rank test for bits 4 to 11, p=0.08261 b-rank test for bits 5 to 12, p=0.26548 b-rank test for bits 6 to 13, p=0.18799 b-rank test for bits 7 to 14, p=0.78159 b-rank test for bits 8 to 15, p=0.40255 b-rank test for bits 9 to 16, p=0.70474 b-rank test for bits 10 to 17, p=0.30193 b-rank test for bits 11 to 18, p=0.34491 b-rank test for bits 12 to 19, p=0.73358 b-rank test for bits 13 to 20, p=0.56145 b-rank test for bits 14 to 21, p=0.94084 b-rank test for bits 15 to 22, p=0.61289 b-rank test for bits 16 to 23, p=0.75483 b-rank test for bits 17 to 24, p=0.45941 b-rank test for bits 18 to 25, p=0.78611 b-rank test for bits 19 to 26, p=0.35890 b-rank test for bits 20 to 27, p=0.39981 b-rank test for bits 21 to 28, p=0.61265 b-rank test for bits 22 to 29, p=0.94403 b-rank test for bits 23 to 30, p=0.86140 b-rank test for bits 24 to 31, p=0.57163 b-rank test for bits 25 to 32, p=0.95122 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 = 0.187631 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-25_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 141360 -1.28 0.099662 2 141723 -0.44 0.331654 3 141561 -0.81 0.207864 4 142219 0.72 0.765322 5 141972 0.15 0.558207 6 141891 -0.04 0.482920 7 141954 0.10 0.541562 8 142495 1.37 0.914405 9 142284 0.88 0.809321 10 142007 0.23 0.590255 11 141952 0.10 0.539707 12 141561 -0.81 0.207864 13 141328 -1.36 0.087193 14 142377 1.09 0.862734 15 142157 0.58 0.718594 16 141765 -0.34 0.367976 17 142306 0.93 0.822985 18 141371 -1.26 0.104236 19 141617 -0.68 0.247299 20 141986 0.18 0.571084 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-25_10:31 Bits used No. missing words z-score p-value 23 to 32 142079 0.5851 0.720749 22 to 31 142122 0.7333 0.768326 21 to 30 141487 -1.4563 0.072653 20 to 29 141769 -0.4839 0.314230 19 to 28 141979 0.2402 0.594928 18 to 27 142130 0.7609 0.776651 17 to 26 142009 0.3437 0.634460 16 to 25 142147 0.8196 0.793764 15 to 24 141741 -0.5804 0.280806 14 to 23 141416 -1.7011 0.044459 13 to 22 142169 0.8954 0.814717 12 to 21 141408 -1.7287 0.041929 11 to 20 141902 -0.0253 0.489918 10 to 19 141726 -0.6322 0.263637 9 to 18 142701 2.7299 0.996832 8 to 17 142117 0.7161 0.763036 7 to 16 142040 0.4506 0.673856 6 to 15 142038 0.4437 0.671367 5 to 14 141863 -0.1598 0.436536 4 to 13 141338 -1.9701 0.024413 3 to 12 141458 -1.5563 0.059817 2 to 11 141932 0.0782 0.531155 1 to 10 141956 0.1609 0.563926 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-25_10:31 Bits used No. missing words z-score p-value 28 to 32 141292 -2.0926 0.018190 27 to 31 141631 -0.9435 0.172715 26 to 30 141896 -0.0452 0.481979 25 to 29 141853 -0.1909 0.424283 24 to 28 141663 -0.8350 0.201854 23 to 27 142199 0.9819 0.836933 22 to 26 141562 -1.1774 0.119520 21 to 25 142248 1.1480 0.874523 20 to 24 141525 -1.3028 0.096319 19 to 23 142209 1.0158 0.845145 18 to 22 141889 -0.0689 0.472529 17 to 21 141887 -0.0757 0.469831 16 to 20 141875 -0.1164 0.453679 15 to 19 141676 -0.7909 0.214487 14 to 18 141670 -0.8113 0.208600 13 to 17 142503 2.0124 0.977913 12 to 16 142361 1.5311 0.937126 11 to 15 141325 -1.9808 0.023808 10 to 14 142462 1.8735 0.969497 9 to 13 141727 -0.6181 0.268265 8 to 12 142081 0.5819 0.719694 7 to 11 141668 -0.8181 0.206659 6 to 10 141947 0.1277 0.550805 5 to 9 142267 1.2124 0.887328 4 to 8 142159 0.8463 0.801318 3 to 7 141755 -0.5232 0.300434 2 to 6 141424 -1.6452 0.049966 1 to 5 142209 1.0158 0.845145 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-25_10:31 Bits used No. missing words z-score p-value 31 to 32 142476 1.6716 0.952698 30 to 31 141733 -0.5201 0.301480 29 to 30 141495 -1.2222 0.110814 28 to 29 142757 2.5005 0.993799 27 to 28 142096 0.5506 0.709063 26 to 27 141793 -0.3432 0.365740 25 to 26 141493 -1.2281 0.109702 24 to 25 141998 0.2616 0.603171 23 to 24 141317 -1.7473 0.040294 22 to 23 141751 -0.4671 0.320232 21 to 22 142185 0.8132 0.791944 20 to 21 141519 -1.1514 0.124781 19 to 20 142023 0.3353 0.631304 18 to 19 141739 -0.5024 0.307676 17 to 18 141726 -0.5408 0.294324 16 to 17 141718 -0.5644 0.286243 15 to 16 141538 -1.0954 0.136678 14 to 15 141710 -0.5880 0.278268 13 to 14 141901 -0.0246 0.490198 12 to 13 141549 -1.0629 0.143909 11 to 12 141487 -1.2458 0.106417 10 to 11 141832 -0.2281 0.409780 9 to 10 142645 2.1701 0.985001 8 to 9 141727 -0.5378 0.295342 7 to 8 142091 0.5359 0.703986 6 to 7 141733 -0.5201 0.301480 5 to 6 142204 0.8692 0.807640 4 to 5 141470 -1.2960 0.097495 3 to 4 141745 -0.4847 0.313927 2 to 3 141626 -0.8358 0.201639 1 to 2 142053 0.4238 0.664146 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-25_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.93 0.409 0.658791 Test results for specific bytes for dh-ranFile-2015-09-25_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2456.43 -0.616 0.268874 2 to 9 2567.37 0.953 0.829634 3 to 10 2416.94 -1.175 0.120055 4 to 11 2539.32 0.556 0.710906 5 to 12 2473.47 -0.375 0.353744 6 to 13 2529.98 0.424 0.664215 7 to 14 2485.08 -0.211 0.416436 8 to 15 2562.62 0.886 0.812067 9 to 16 2542.70 0.604 0.727056 10 to 17 2393.10 -1.512 0.065294 11 to 18 2555.59 0.786 0.784111 12 to 19 2551.76 0.732 0.767913 13 to 20 2429.04 -1.003 0.157814 14 to 21 2474.92 -0.355 0.361420 15 to 22 2483.79 -0.229 0.409350 16 to 23 2442.42 -0.814 0.207726 17 to 24 2386.58 -1.604 0.054353 18 to 25 2405.03 -1.343 0.089612 19 to 26 2478.82 -0.299 0.382280 20 to 27 2554.68 0.773 0.780339 21 to 28 2372.11 -1.809 0.035251 22 to 29 2475.68 -0.344 0.365470 23 to 30 2499.52 -0.007 0.497305 24 to 31 2463.62 -0.514 0.303468 25 to 32 2498.37 -0.023 0.490816 CDPARK for dh-ranFile-2015-09-25_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 3562 1.7808 0.962529 3534 0.5023 0.692266 3523 0.0000 0.500000 3543 0.9132 0.819442 3505 -0.8219 0.205562 3548 1.1416 0.873180 3503 -0.9132 0.180558 3518 -0.2283 0.409702 3522 -0.0457 0.481790 3524 0.0457 0.518210 Square side=100, avg. no. parked=3528.20 sample std.=17.74 p-value of the KSTEST for those 10 p-values: 0.753697 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-25_10:31 0.6110,0.6361,0.6492,0.9711,0.8269,0.0573,0.2885,0.1856,0.4470,0.1020, The KS test for those 10 p-values: 0.982679 The 3DSPHERES test for dh-ranFile-2015-09-25_10:31 sample no r^3 equiv. uni. 1 38.800 0.725641 2 22.252 0.523705 3 11.074 0.308655 4 8.509 0.246963 5 194.529 0.998473 6 10.341 0.291569 7 2.538 0.081127 8 78.791 0.927660 9 80.064 0.930664 10 48.209 0.799505 11 34.992 0.688514 12 23.861 0.548589 13 23.680 0.545858 14 50.873 0.816542 15 31.047 0.644733 16 10.676 0.299432 17 13.059 0.352922 18 9.201 0.264141 19 44.668 0.774388 20 8.263 0.240750 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.545856 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-25_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.3 0.8 1.0 0.9 -0.6 -0.2 -0.3 -0.3 -0.5 -1.1 0.3 -0.0 0.6 -1.7 -0.4 -0.4 0.4 0.7 0.6 0.1 -0.0 1.4 0.3 -1.8 0.3 2.1 0.1 -0.9 0.4 1.2 -1.0 0.8 -0.2 -0.8 1.0 -0.4 0.1 -0.7 0.9 1.0 0.8 Chi-square with 42 degrees of freedom:28.686533 z-score=-1.452618, p-value=0.058462 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-25_10:31 Test no p-value 1 0.144846 2 0.153989 3 0.085682 4 0.012598 5 0.015367 6 0.252736 7 0.081970 8 0.897856 9 0.271688 10 0.368533 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001761 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-25_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 66550 0.20 66923 0.99 3 25000.00 25176 1.24 24696 3.70 4 6666.67 6639 0.11 6699 0.16 5 1388.89 1380 0.06 1417 0.57 6 238.10 216 2.05 222 1.09 7 34.72 33 0.09 38 0.31 8 4.96 5 0.00 4 0.19 p=0.28966 p=0.67838 Number of rngs required: 687129, p-value: 0.068 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-25_10:31 No. of wins: Observed Expected 98126 98585.9 z-score=-2.057, pvalue=0.01985 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66288 66666.7 2.151 2.151 2 37608 37654.3 0.057 2.208 3 26888 26954.7 0.165 2.373 4 19453 19313.5 1.008 3.381 5 14236 13851.4 10.678 14.059 6 9914 9943.5 0.088 14.147 7 7185 7145.0 0.224 14.370 8 5156 5139.1 0.056 14.426 9 3711 3699.9 0.034 14.460 10 2671 2666.3 0.008 14.468 11 1926 1923.3 0.004 14.472 12 1410 1388.7 0.325 14.797 13 963 1003.7 1.652 16.449 14 708 726.1 0.453 16.902 15 510 525.8 0.477 17.379 16 353 381.2 2.079 19.458 17 273 276.5 0.045 19.503 18 219 200.8 1.644 21.147 19 149 146.0 0.062 21.209 20 110 106.2 0.135 21.344 21 269 287.1 1.143 22.487 Chisq= 22.49 for 20 degrees of freedom, p= 0.68532 SUMMARY of craptest p-value for no. of wins: 0.019855 p-value for throws/game: 0.685324 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-25_10:31 No. of wins: Observed Expected 98490 98585.9 z-score=-0.429, pvalue=0.33406 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66481 66666.7 0.517 0.517 2 37135 37654.3 7.162 7.679 3 26893 26954.7 0.141 7.821 4 19607 19313.5 4.461 12.282 5 13915 13851.4 0.292 12.574 6 9899 9943.5 0.200 12.774 7 7308 7145.0 3.717 16.491 8 5073 5139.1 0.849 17.340 9 3724 3699.9 0.157 17.498 10 2667 2666.3 0.000 17.498 11 2027 1923.3 5.588 23.086 12 1424 1388.7 0.895 23.981 13 1084 1003.7 6.422 30.403 14 764 726.1 1.974 32.377 15 525 525.8 0.001 32.378 16 377 381.2 0.045 32.424 17 288 276.5 0.475 32.899 18 212 200.8 0.621 33.520 19 141 146.0 0.170 33.690 20 127 106.2 4.067 37.757 21 329 287.1 6.111 43.868 Chisq= 43.87 for 20 degrees of freedom, p= 0.99843 SUMMARY of craptest p-value for no. of wins: 0.334058 p-value for throws/game: 0.998433 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0009,0.0018,0.0126,0.0154,0.0165,0.0182,0.0199,0.0238,0.0244, 0.0353,0.0403,0.0419,0.0445,0.0500,0.0544,0.0570,0.0573,0.0585,0.0598, 0.0653,0.0684,0.0727,0.0811,0.0820,0.0823,0.0826,0.0848,0.0857,0.0872, 0.0879,0.0896,0.0924,0.0963,0.0975,0.0993,0.0997,0.1020,0.1042,0.1064, 0.1097,0.1108,0.1191,0.1195,0.1201,0.1206,0.1248,0.1367,0.1439,0.1448, 0.1540,0.1578,0.1727,0.1806,0.1856,0.1876,0.1880,0.1892,0.1948,0.2016, 0.2019,0.2056,0.2067,0.2077,0.2079,0.2079,0.2086,0.2145,0.2347,0.2408, 0.2470,0.2473,0.2527,0.2636,0.2641,0.2655,0.2683,0.2689,0.2717,0.2783, 0.2808,0.2862,0.2885,0.2897,0.2916,0.2943,0.2953,0.2970,0.2994,0.3004, 0.3015,0.3015,0.3019,0.3035,0.3077,0.3087,0.3139,0.3142,0.3202,0.3317, 0.3341,0.3409,0.3418,0.3449,0.3529,0.3537,0.3589,0.3614,0.3655,0.3657, 0.3680,0.3685,0.3823,0.3975,0.3991,0.3998,0.4025,0.4034,0.4093,0.4097, 0.4098,0.4164,0.4243,0.4258,0.4266,0.4365,0.4434,0.4470,0.4537,0.4593, 0.4594,0.4615,0.4641,0.4698,0.4725,0.4818,0.4820,0.4829,0.4895,0.4899, 0.4902,0.4908,0.4973,0.5000,0.5090,0.5182,0.5237,0.5292,0.5312,0.5349, 0.5357,0.5397,0.5416,0.5459,0.5459,0.5486,0.5491,0.5508,0.5554,0.5582, 0.5615,0.5639,0.5700,0.5711,0.5716,0.5808,0.5903,0.5949,0.6032,0.6110, 0.6127,0.6129,0.6178,0.6246,0.6313,0.6345,0.6361,0.6413,0.6426,0.6447, 0.6492,0.6588,0.6641,0.6642,0.6714,0.6739,0.6783,0.6784,0.6853,0.6885, 0.6923,0.7031,0.7040,0.7047,0.7091,0.7109,0.7109,0.7144,0.7186,0.7197, 0.7207,0.7256,0.7271,0.7336,0.7537,0.7548,0.7630,0.7653,0.7679,0.7683, 0.7744,0.7767,0.7803,0.7816,0.7833,0.7841,0.7861,0.7919,0.7938,0.7995, 0.8013,0.8049,0.8076,0.8093,0.8121,0.8147,0.8165,0.8194,0.8230,0.8269, 0.8296,0.8369,0.8372,0.8433,0.8451,0.8451,0.8598,0.8614,0.8627,0.8675, 0.8732,0.8745,0.8873,0.8911,0.8918,0.8979,0.9128,0.9144,0.9272,0.9277, 0.9307,0.9320,0.9371,0.9408,0.9440,0.9471,0.9512,0.9527,0.9625,0.9695, 0.9711,0.9779,0.9827,0.9850,0.9867,0.9938,0.9968,0.9984,0.9985, Overall p-value after applying KStest on 269 p-values = 0.329646 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.