RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-10_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 15.75 24.9857 0.904971 2 to 25 15.97 5.7320 0.005187 3 to 26 15.78 15.4761 0.438770 4 to 27 15.80 13.8732 0.323942 5 to 28 15.96 14.9278 0.399321 6 to 29 15.67 17.8898 0.604174 7 to 30 15.79 12.0629 0.203688 8 to 31 15.84 23.6597 0.871021 9 to 32 15.69 27.9051 0.953940 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.756522 Tough bday spacings test for dh-ranFile-2015-08-10_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 12 41 62 98 100 69 58 37 13 7 3 (O-E)^2/E 0.9 0.5 1.7 0.0 0.1 1.1 0.7 1.8 0.2 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.226, p= 0.296 RESULTS OF GCD FOR dh-ranFile-2015-08-10_23:31 Euclid's algorithm: p-value, steps to gcd: 0.542394 p-value, dist. of gcd's: 0.503830 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-10_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.401 0.228 0.340 0.523 0.528 0.407 0.964 0.692 Bits 8 to 15---> 0.119 0.382 0.113 0.839 0.461 0.042 0.637 0.498 Bits 16 to 23---> 0.129 0.636 0.543 0.170 0.005 0.813 0.287 0.809 Bits 24 to 31---> 0.723 0.586 0.358 0.769 0.289 0.649 0.879 0.671 KS test for the above 32 p values: 0.177 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-10_23:31, p-values for 5 runs: 0.0703, 0.6435, 0.0608, 0.3373, 0.7238 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-10_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5022 5134.0 2.444 2.957 r= 30 22996 23103.0 0.496 3.453 r= 31 11781 11551.5 4.559 8.012 chi-square = 8.012 with df = 3; p-value = 0.954 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-10_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5137 5134.0 0.002 1.150 r= 31 22944 23103.0 1.095 2.245 r= 32 11692 11551.5 1.708 3.953 chi-square = 3.953 with df = 3; p-value = 0.733 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-10_23:31 b-rank test for bits 1 to 8, p=0.03423 b-rank test for bits 2 to 9, p=0.77513 b-rank test for bits 3 to 10, p=0.42391 b-rank test for bits 4 to 11, p=0.79563 b-rank test for bits 5 to 12, p=0.02377 b-rank test for bits 6 to 13, p=0.11409 b-rank test for bits 7 to 14, p=0.59633 b-rank test for bits 8 to 15, p=0.47967 b-rank test for bits 9 to 16, p=0.51705 b-rank test for bits 10 to 17, p=0.01176 b-rank test for bits 11 to 18, p=0.05014 b-rank test for bits 12 to 19, p=0.00358 b-rank test for bits 13 to 20, p=0.72921 b-rank test for bits 14 to 21, p=0.27910 b-rank test for bits 15 to 22, p=0.02114 b-rank test for bits 16 to 23, p=0.59035 b-rank test for bits 17 to 24, p=0.78725 b-rank test for bits 18 to 25, p=0.98267 b-rank test for bits 19 to 26, p=0.64096 b-rank test for bits 20 to 27, p=0.65587 b-rank test for bits 21 to 28, p=0.20967 b-rank test for bits 22 to 29, p=0.34610 b-rank test for bits 23 to 30, p=0.48734 b-rank test for bits 24 to 31, p=0.47957 b-rank test for bits 25 to 32, p=0.27398 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 = 0.070085 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-10_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 140888 -2.39 0.008510 2 141162 -1.75 0.040397 3 141770 -0.33 0.372387 4 141604 -0.71 0.237803 5 141911 0.00 0.501557 6 141417 -1.15 0.125009 7 141912 0.01 0.502489 8 143005 2.56 0.994766 9 142359 1.05 0.853286 10 141795 -0.27 0.394686 11 141900 -0.02 0.491304 12 141800 -0.26 0.399190 13 141847 -0.15 0.442106 14 141867 -0.10 0.460608 15 142075 0.39 0.650651 16 141701 -0.49 0.313217 17 142299 0.91 0.818706 18 141725 -0.43 0.333351 19 141885 -0.06 0.477334 20 141677 -0.54 0.293624 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-10_23:31 Bits used No. missing words z-score p-value 23 to 32 141755 -0.5322 0.297303 22 to 31 142243 1.1506 0.875049 21 to 30 141966 0.1954 0.577466 20 to 29 141754 -0.5356 0.296110 19 to 28 141585 -1.1184 0.131703 18 to 27 141863 -0.1598 0.436536 17 to 26 141606 -1.0460 0.147789 16 to 25 141755 -0.5322 0.297303 15 to 24 142155 0.8471 0.801541 14 to 23 141625 -0.9804 0.163432 13 to 22 141838 -0.2460 0.402855 12 to 21 141537 -1.2839 0.099589 11 to 20 141591 -1.0977 0.136170 10 to 19 141642 -0.9218 0.178309 9 to 18 141637 -0.9391 0.173848 8 to 17 142098 0.6506 0.742343 7 to 16 141827 -0.2839 0.388245 6 to 15 141737 -0.5942 0.276175 5 to 14 142410 1.7264 0.957867 4 to 13 141728 -0.6253 0.265895 3 to 12 142251 1.1782 0.880636 2 to 11 141876 -0.1149 0.454250 1 to 10 141330 -1.9977 0.022875 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-10_23:31 Bits used No. missing words z-score p-value 28 to 32 142272 1.2294 0.890537 27 to 31 142008 0.3345 0.630989 26 to 30 141377 -1.8045 0.035576 25 to 29 142028 0.4023 0.656258 24 to 28 141934 0.0836 0.533324 23 to 27 142114 0.6938 0.756095 22 to 26 141835 -0.2520 0.400534 21 to 25 141766 -0.4859 0.313532 20 to 24 141433 -1.6147 0.053190 19 to 23 142015 0.3582 0.639905 18 to 22 141540 -1.2520 0.105291 17 to 21 141488 -1.4282 0.076612 16 to 20 142430 1.7650 0.961217 15 to 19 142287 1.2802 0.899769 14 to 18 142165 0.8667 0.806941 13 to 17 142044 0.4565 0.675988 12 to 16 142102 0.6531 0.743160 11 to 15 141875 -0.1164 0.453679 10 to 14 141410 -1.6926 0.045262 9 to 13 141849 -0.2045 0.418978 8 to 12 141996 0.2938 0.615543 7 to 11 142455 1.8497 0.967824 6 to 10 141946 0.1243 0.549463 5 to 9 142432 1.7718 0.961783 4 to 8 142399 1.6599 0.951533 3 to 7 142220 1.0531 0.853857 2 to 6 142273 1.2328 0.891171 1 to 5 141923 0.0463 0.518480 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-10_23:31 Bits used No. missing words z-score p-value 31 to 32 141660 -0.7355 0.231022 30 to 31 141580 -0.9715 0.165656 29 to 30 141691 -0.6440 0.259774 28 to 29 141620 -0.8535 0.196696 27 to 28 141654 -0.7532 0.225669 26 to 27 141499 -1.2104 0.113060 25 to 26 141619 -0.8564 0.195880 24 to 25 141487 -1.2458 0.106417 23 to 24 141901 -0.0246 0.490198 22 to 23 142284 1.1052 0.865468 21 to 22 141937 0.0816 0.532527 20 to 21 142021 0.3294 0.629077 19 to 20 141682 -0.6706 0.251241 18 to 19 142480 1.6834 0.953850 17 to 18 141929 0.0580 0.523135 16 to 17 141886 -0.0688 0.472566 15 to 16 142023 0.3353 0.631304 14 to 15 141462 -1.3196 0.093491 13 to 14 141836 -0.2163 0.414372 12 to 13 141721 -0.5555 0.289261 11 to 12 141461 -1.3225 0.093000 10 to 11 142664 2.2262 0.986998 9 to 10 142503 1.7512 0.960048 8 to 9 141811 -0.2901 0.385886 7 to 8 140917 -2.9272 0.001710 6 to 7 142159 0.7365 0.769284 5 to 6 141905 -0.0128 0.494905 4 to 5 141617 -0.8623 0.194253 3 to 4 141818 -0.2694 0.393807 2 to 3 141571 -0.9980 0.159134 1 to 2 141947 0.1111 0.544240 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-10_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2395.99 -1.471 0.070657 Test results for specific bytes for dh-ranFile-2015-08-10_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2570.58 0.998 0.840906 2 to 9 2483.45 -0.234 0.407479 3 to 10 2448.47 -0.729 0.233078 4 to 11 2540.56 0.574 0.716885 5 to 12 2461.84 -0.540 0.294692 6 to 13 2450.20 -0.704 0.240628 7 to 14 2390.41 -1.550 0.060593 8 to 15 2514.18 0.201 0.579491 9 to 16 2364.72 -1.913 0.027868 10 to 17 2510.25 0.145 0.557642 11 to 18 2474.80 -0.356 0.360754 12 to 19 2495.07 -0.070 0.472207 13 to 20 2490.70 -0.131 0.447700 14 to 21 2448.06 -0.734 0.231326 15 to 22 2498.81 -0.017 0.493260 16 to 23 2471.23 -0.407 0.342037 17 to 24 2430.21 -0.987 0.161842 18 to 25 2552.52 0.743 0.771167 19 to 26 2480.98 -0.269 0.393962 20 to 27 2504.92 0.070 0.527710 21 to 28 2384.83 -1.629 0.051677 22 to 29 2536.81 0.521 0.698661 23 to 30 2461.64 -0.542 0.293755 24 to 31 2468.69 -0.443 0.328953 25 to 32 2444.15 -0.790 0.214801 CDPARK for dh-ranFile-2015-08-10_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 3553 1.3699 0.914635 3537 0.6393 0.738676 3534 0.5023 0.692266 3520 -0.1370 0.445521 3527 0.1826 0.572463 3522 -0.0457 0.481790 3557 1.5525 0.939730 3541 0.8219 0.794438 3512 -0.5023 0.307734 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3531.30 sample std.=15.24 p-value of the KSTEST for those 10 p-values: 0.338404 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-10_23:31 0.7047,0.3312,0.9649,0.0152,0.0636,0.0731,0.1861,0.7261,0.5053,0.5904, The KS test for those 10 p-values: 0.443775 The 3DSPHERES test for dh-ranFile-2015-08-10_23:31 sample no r^3 equiv. uni. 1 2.472 0.079105 2 21.238 0.507332 3 38.810 0.725740 4 40.878 0.744008 5 42.238 0.755348 6 19.501 0.477974 7 20.366 0.492803 8 6.723 0.200764 9 98.845 0.962925 10 38.945 0.726972 11 39.853 0.735110 12 9.711 0.276531 13 65.346 0.886756 14 11.475 0.317847 15 4.061 0.126598 16 74.735 0.917186 17 9.189 0.263846 18 107.963 0.972642 19 2.754 0.087704 20 58.814 0.859209 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.567740 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-10_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 -0.8 0.8 3.9 0.4 0.8 0.1 0.7 -0.1 1.4 -0.3 -0.2 -0.1 0.3 -1.6 -0.5 1.1 0.8 -0.8 -1.2 -0.1 -0.5 2.0 -1.0 -0.2 -0.3 2.3 1.0 -0.8 -2.7 -0.1 -1.4 0.7 0.9 0.4 -0.7 0.8 -0.8 -0.7 1.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:57.427350 z-score=1.683262, p-value=0.943324 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-10_23:31 Test no p-value 1 0.046111 2 0.408444 3 0.234014 4 0.009040 5 0.924770 6 0.301170 7 0.081096 8 0.916875 9 0.548729 10 0.776697 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.392644 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-10_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 66800 0.27 66615 0.04 3 25000.00 24779 1.95 25055 0.12 4 6666.67 6697 0.14 6692 0.10 5 1388.89 1476 5.46 1378 0.09 6 238.10 208 3.80 225 0.72 7 34.72 35 0.00 30 0.64 8 4.96 4 0.19 4 0.19 p=0.93375 p=0.07050 Number of rngs required: 688985, p-value: 0.749 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-10_23:31 No. of wins: Observed Expected 98454 98585.9 z-score=-0.590, pvalue=0.27768 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66560 66666.7 0.171 0.171 2 37417 37654.3 1.496 1.666 3 26916 26954.7 0.056 1.722 4 19382 19313.5 0.243 1.965 5 14076 13851.4 3.641 5.607 6 10011 9943.5 0.458 6.064 7 7106 7145.0 0.213 6.277 8 5072 5139.1 0.875 7.153 9 3702 3699.9 0.001 7.154 10 2702 2666.3 0.478 7.632 11 1967 1923.3 0.992 8.624 12 1403 1388.7 0.146 8.770 13 1053 1003.7 2.420 11.190 14 748 726.1 0.658 11.848 15 537 525.8 0.237 12.085 16 369 381.2 0.387 12.472 17 258 276.5 1.243 13.715 18 216 200.8 1.146 14.861 19 131 146.0 1.538 16.399 20 106 106.2 0.000 16.400 21 268 287.1 1.272 17.672 Chisq= 17.67 for 20 degrees of freedom, p= 0.39101 SUMMARY of craptest p-value for no. of wins: 0.277680 p-value for throws/game: 0.391008 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-10_23:31 No. of wins: Observed Expected 98369 98585.9 z-score=-0.970, pvalue=0.16604 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66632 66666.7 0.018 0.018 2 37360 37654.3 2.301 2.319 3 27115 26954.7 0.953 3.271 4 19432 19313.5 0.728 3.999 5 13946 13851.4 0.646 4.645 6 10064 9943.5 1.459 6.104 7 7097 7145.0 0.323 6.427 8 5176 5139.1 0.265 6.692 9 3665 3699.9 0.329 7.021 10 2600 2666.3 1.648 8.669 11 1981 1923.3 1.729 10.398 12 1336 1388.7 2.003 12.401 13 982 1003.7 0.470 12.871 14 699 726.1 1.014 13.886 15 505 525.8 0.826 14.711 16 385 381.2 0.039 14.750 17 304 276.5 2.727 17.477 18 215 200.8 1.000 18.477 19 147 146.0 0.007 18.484 20 111 106.2 0.216 18.699 21 248 287.1 5.329 24.028 Chisq= 24.03 for 20 degrees of freedom, p= 0.75883 SUMMARY of craptest p-value for no. of wins: 0.166044 p-value for throws/game: 0.758826 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0036,0.0050,0.0052,0.0085,0.0090,0.0118,0.0152,0.0211,0.0229, 0.0238,0.0279,0.0342,0.0356,0.0404,0.0419,0.0453,0.0461,0.0501,0.0517, 0.0532,0.0606,0.0608,0.0636,0.0701,0.0703,0.0705,0.0707,0.0731,0.0766, 0.0791,0.0811,0.0877,0.0930,0.0935,0.0996,0.1053,0.1064,0.1128,0.1131, 0.1141,0.1193,0.1250,0.1266,0.1290,0.1317,0.1362,0.1478,0.1591,0.1618, 0.1634,0.1657,0.1660,0.1700,0.1738,0.1771,0.1783,0.1861,0.1943,0.1959, 0.1967,0.2008,0.2037,0.2097,0.2148,0.2257,0.2284,0.2310,0.2313,0.2331, 0.2340,0.2378,0.2406,0.2512,0.2598,0.2638,0.2659,0.2740,0.2762,0.2764, 0.2765,0.2777,0.2791,0.2870,0.2888,0.2893,0.2936,0.2938,0.2947,0.2961, 0.2961,0.2973,0.2973,0.3012,0.3077,0.3132,0.3135,0.3178,0.3239,0.3290, 0.3312,0.3334,0.3373,0.3384,0.3403,0.3420,0.3461,0.3582,0.3608,0.3724, 0.3818,0.3859,0.3882,0.3910,0.3926,0.3938,0.3940,0.3947,0.3992,0.3993, 0.4005,0.4005,0.4029,0.4065,0.4075,0.4084,0.4144,0.4190,0.4239,0.4365, 0.4388,0.4421,0.4438,0.4455,0.4477,0.4537,0.4542,0.4606,0.4615,0.4722, 0.4726,0.4773,0.4780,0.4796,0.4797,0.4818,0.4873,0.4902,0.4913,0.4928, 0.4933,0.4949,0.4979,0.5016,0.5025,0.5038,0.5053,0.5073,0.5171,0.5185, 0.5228,0.5231,0.5277,0.5281,0.5325,0.5333,0.5424,0.5435,0.5442,0.5487, 0.5495,0.5576,0.5677,0.5725,0.5775,0.5795,0.5859,0.5904,0.5904,0.5963, 0.6042,0.6155,0.6291,0.6310,0.6313,0.6363,0.6372,0.6399,0.6410,0.6435, 0.6492,0.6507,0.6559,0.6563,0.6713,0.6760,0.6922,0.6923,0.6987,0.7047, 0.7169,0.7230,0.7238,0.7257,0.7261,0.7270,0.7292,0.7335,0.7351,0.7387, 0.7423,0.7432,0.7440,0.7491,0.7553,0.7561,0.7565,0.7588,0.7693,0.7693, 0.7712,0.7751,0.7767,0.7872,0.7944,0.7956,0.8015,0.8069,0.8087,0.8126, 0.8187,0.8394,0.8409,0.8533,0.8539,0.8592,0.8655,0.8710,0.8750,0.8785, 0.8806,0.8868,0.8905,0.8912,0.8998,0.9050,0.9146,0.9169,0.9172,0.9248, 0.9337,0.9397,0.9433,0.9515,0.9539,0.9539,0.9542,0.9579,0.9600,0.9612, 0.9618,0.9629,0.9644,0.9649,0.9678,0.9726,0.9827,0.9870,0.9948, Overall p-value after applying KStest on 269 p-values = 0.050296 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.