RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-08_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 13.9502 0.329379 2 to 25 15.71 23.1212 0.854655 3 to 26 15.82 5.7687 0.005390 4 to 27 15.67 15.1136 0.412700 5 to 28 15.93 18.1403 0.619958 6 to 29 15.90 15.8005 0.461982 7 to 30 15.65 11.9191 0.194991 8 to 31 15.78 16.4504 0.507838 9 to 32 15.35 40.5436 0.998916 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.562994 Tough bday spacings test for dh-ranFile-2015-12-08_21:31: 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 9 34 78 79 100 81 54 34 12 12 7 (O-E)^2/E 0.0 0.2 0.3 3.6 0.1 0.1 0.1 0.6 0.6 4.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 11.960, p= 0.712 RESULTS OF GCD FOR dh-ranFile-2015-12-08_21:31 Euclid's algorithm: p-value, steps to gcd: 0.555214 p-value, dist. of gcd's: 0.268964 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-08_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.101 0.366 0.390 0.007 0.055 0.638 0.571 0.601 Bits 8 to 15---> 0.964 0.115 0.693 0.720 0.974 0.157 0.599 0.930 Bits 16 to 23---> 0.025 0.682 0.588 0.942 0.414 0.985 0.511 0.962 Bits 24 to 31---> 0.583 0.482 0.297 0.717 0.315 0.476 0.520 0.711 KS test for the above 32 p values: 0.562 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-08_21:31, p-values for 5 runs: 0.9229, 0.6987, 0.2130, 0.5227, 0.8456 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-08_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 187 211.4 2.820 2.820 r= 29 5113 5134.0 0.086 2.906 r= 30 23202 23103.0 0.424 3.330 r= 31 11498 11551.5 0.248 3.578 chi-square = 3.578 with df = 3; p-value = 0.689 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-08_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5082 5134.0 0.527 0.626 r= 31 23194 23103.0 0.358 0.984 r= 32 11508 11551.5 0.164 1.148 chi-square = 1.148 with df = 3; p-value = 0.235 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-08_21:31 b-rank test for bits 1 to 8, p=0.73181 b-rank test for bits 2 to 9, p=0.30006 b-rank test for bits 3 to 10, p=0.39126 b-rank test for bits 4 to 11, p=0.57337 b-rank test for bits 5 to 12, p=0.28119 b-rank test for bits 6 to 13, p=0.19287 b-rank test for bits 7 to 14, p=0.03600 b-rank test for bits 8 to 15, p=0.48639 b-rank test for bits 9 to 16, p=0.38656 b-rank test for bits 10 to 17, p=0.93409 b-rank test for bits 11 to 18, p=0.60959 b-rank test for bits 12 to 19, p=0.05667 b-rank test for bits 13 to 20, p=0.77708 b-rank test for bits 14 to 21, p=0.66648 b-rank test for bits 15 to 22, p=0.67413 b-rank test for bits 16 to 23, p=0.58763 b-rank test for bits 17 to 24, p=0.46588 b-rank test for bits 18 to 25, p=0.07626 b-rank test for bits 19 to 26, p=0.13041 b-rank test for bits 20 to 27, p=0.73497 b-rank test for bits 21 to 28, p=0.50249 b-rank test for bits 22 to 29, p=0.93240 b-rank test for bits 23 to 30, p=0.89796 b-rank test for bits 24 to 31, p=0.48836 b-rank test for bits 25 to 32, p=0.24458 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 = 0.956952 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-08_21:31 (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 141450 -1.07 0.141591 2 141900 -0.02 0.491304 3 141814 -0.22 0.411871 4 141615 -0.69 0.245825 5 142068 0.37 0.644579 6 141505 -0.94 0.172407 7 141401 -1.19 0.117478 8 143165 2.93 0.998326 9 142027 0.27 0.608315 10 141899 -0.02 0.490372 11 141088 -1.92 0.027492 12 141581 -0.77 0.221503 13 141595 -0.73 0.231348 14 141911 0.00 0.501557 15 142689 1.82 0.965747 16 142141 0.54 0.705844 17 142734 1.93 0.972998 18 141813 -0.23 0.410962 19 142729 1.92 0.972261 20 141275 -1.48 0.069160 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-08_21:31 Bits used No. missing words z-score p-value 23 to 32 141799 -0.3804 0.351806 22 to 31 141534 -1.2942 0.097791 21 to 30 141632 -0.9563 0.169458 20 to 29 142090 0.6230 0.733358 19 to 28 141435 -1.6356 0.050960 18 to 27 142301 1.3506 0.911586 17 to 26 141646 -0.9080 0.181930 16 to 25 142510 2.0713 0.980833 15 to 24 141866 -0.1494 0.440614 14 to 23 142309 1.3782 0.915925 13 to 22 142090 0.6230 0.733358 12 to 21 141777 -0.4563 0.324083 11 to 20 141949 0.1368 0.554403 10 to 19 142335 1.4678 0.928924 9 to 18 142287 1.3023 0.903595 8 to 17 141802 -0.3701 0.355653 7 to 16 141781 -0.4425 0.329058 6 to 15 141797 -0.3873 0.349251 5 to 14 142157 0.8540 0.803457 4 to 13 141928 0.0644 0.525666 3 to 12 141618 -1.0046 0.157548 2 to 11 141575 -1.1529 0.124484 1 to 10 141471 -1.5115 0.065333 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-08_21:31 Bits used No. missing words z-score p-value 28 to 32 141831 -0.2655 0.395302 27 to 31 141958 0.1650 0.565521 26 to 30 141710 -0.6757 0.249617 25 to 29 141599 -1.0520 0.146408 24 to 28 141600 -1.0486 0.147187 23 to 27 141847 -0.2113 0.416331 22 to 26 141808 -0.3435 0.365614 21 to 25 142087 0.6023 0.726503 20 to 24 142206 1.0057 0.842711 19 to 23 142089 0.6091 0.728755 18 to 22 141744 -0.5604 0.287589 17 to 21 142113 0.6904 0.755031 16 to 20 141585 -1.0994 0.135792 15 to 19 142003 0.3175 0.624578 14 to 18 141586 -1.0960 0.136532 13 to 17 142162 0.8565 0.804142 12 to 16 141712 -0.6689 0.251775 11 to 15 142235 1.1040 0.865196 10 to 14 141667 -0.8215 0.205693 9 to 13 141631 -0.9435 0.172715 8 to 12 142601 2.3446 0.990477 7 to 11 142072 0.5514 0.709328 6 to 10 141883 -0.0893 0.464440 5 to 9 142486 1.9548 0.974697 4 to 8 142252 1.1616 0.877300 3 to 7 142005 0.3243 0.627147 2 to 6 141784 -0.4248 0.335474 1 to 5 141668 -0.8181 0.206659 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-08_21:31 Bits used No. missing words z-score p-value 31 to 32 142144 0.6922 0.755607 30 to 31 141925 0.0462 0.518434 29 to 30 141328 -1.7148 0.043188 28 to 29 142142 0.6863 0.753751 27 to 28 142429 1.5329 0.937356 26 to 27 141914 0.0138 0.505496 25 to 26 141354 -1.6381 0.050696 24 to 25 141314 -1.7561 0.039533 23 to 24 142231 0.9489 0.828659 22 to 23 142061 0.4474 0.672708 21 to 22 141603 -0.9036 0.183096 20 to 21 141668 -0.7119 0.238267 19 to 20 141811 -0.2901 0.385886 18 to 19 141965 0.1642 0.565220 17 to 18 141780 -0.3815 0.351415 16 to 17 141896 -0.0393 0.484317 15 to 16 141478 -1.2724 0.101623 14 to 15 141875 -0.1013 0.459669 13 to 14 142044 0.3973 0.654411 12 to 13 142201 0.8604 0.805211 11 to 12 141978 0.2026 0.580263 10 to 11 141575 -0.9862 0.162012 9 to 10 142148 0.7040 0.759297 8 to 9 140921 -2.9154 0.001776 7 to 8 141762 -0.4346 0.331926 6 to 7 141986 0.2262 0.589464 5 to 6 142273 1.0728 0.858314 4 to 5 141480 -1.2665 0.102674 3 to 4 141564 -1.0187 0.154179 2 to 3 141913 0.0108 0.504319 1 to 2 141627 -0.8328 0.202470 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-08_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2451.65 -0.684 0.247075 Test results for specific bytes for dh-ranFile-2015-12-08_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2389.06 -1.569 0.058330 2 to 9 2553.17 0.752 0.773972 3 to 10 2531.06 0.439 0.669768 4 to 11 2517.95 0.254 0.600169 5 to 12 2505.99 0.085 0.533764 6 to 13 2475.51 -0.346 0.364565 7 to 14 2689.99 2.687 0.996393 8 to 15 2438.24 -0.873 0.191201 9 to 16 2479.40 -0.291 0.385401 10 to 17 2348.64 -2.141 0.016153 11 to 18 2454.67 -0.641 0.260728 12 to 19 2635.33 1.914 0.972177 13 to 20 2514.46 0.204 0.580992 14 to 21 2446.94 -0.750 0.226513 15 to 22 2462.76 -0.527 0.299205 16 to 23 2592.65 1.310 0.904949 17 to 24 2545.01 0.637 0.737780 18 to 25 2412.97 -1.231 0.109213 19 to 26 2565.70 0.929 0.823602 20 to 27 2552.16 0.738 0.769636 21 to 28 2569.18 0.978 0.836051 22 to 29 2487.44 -0.178 0.429510 23 to 30 2419.96 -1.132 0.128818 24 to 31 2440.63 -0.840 0.200575 25 to 32 2647.64 2.088 0.981597 CDPARK for dh-ranFile-2015-12-08_21:31: 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 3523 0.0000 0.500000 3520 -0.1370 0.445521 3534 0.5023 0.692266 3546 1.0502 0.853193 3538 0.6849 0.753306 3521 -0.0913 0.463617 3537 0.6393 0.738676 3495 -1.2785 0.100530 3528 0.2283 0.590298 3544 0.9589 0.831196 Square side=100, avg. no. parked=3528.60 sample std.=14.21 p-value of the KSTEST for those 10 p-values: 0.307934 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-08_21:31 0.7406,0.1912,0.4472,0.3710,0.4010,0.2669,0.5984,0.2226,0.8032,0.2155, The KS test for those 10 p-values: 0.384879 The 3DSPHERES test for dh-ranFile-2015-12-08_21:31 sample no r^3 equiv. uni. 1 27.545 0.600746 2 30.973 0.643860 3 0.473 0.015634 4 8.473 0.246051 5 46.220 0.785762 6 12.132 0.332630 7 14.240 0.377905 8 3.878 0.121272 9 26.534 0.587066 10 7.177 0.212761 11 48.605 0.802133 12 3.360 0.105942 13 83.969 0.939127 14 26.659 0.588780 15 11.634 0.321446 16 13.090 0.353595 17 7.010 0.208384 18 25.450 0.571876 19 16.058 0.414495 20 4.021 0.125431 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.326048 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-08_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 -0.1 1.2 1.4 -0.8 0.2 -0.7 0.7 -0.8 -0.2 1.4 -0.7 0.3 1.2 0.1 0.3 -0.5 -0.7 -0.7 0.4 -1.1 0.7 -0.8 -1.2 1.3 -0.8 -0.2 1.8 1.5 0.5 0.1 -0.1 -0.9 -0.2 0.6 1.0 -1.3 0.5 3.2 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:42.323746 z-score=0.035324, p-value=0.543005 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-08_21:31 Test no p-value 1 0.170431 2 0.000851 3 0.633689 4 0.031024 5 0.252160 6 0.002992 7 0.003200 8 0.226906 9 0.353676 10 0.006269 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000003 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-08_21:31: (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 66664 0.00 66632 0.02 3 25000.00 25056 0.13 24913 0.30 4 6666.67 6692 0.10 6771 1.63 5 1388.89 1325 2.94 1409 0.29 6 238.10 224 0.83 227 0.52 7 34.72 36 0.05 41 1.14 8 4.96 2 1.77 6 0.22 p=0.55506 p=0.33897 Number of rngs required: 687741, p-value: 0.222 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-08_21:31 No. of wins: Observed Expected 98164 98585.9 z-score=-1.887, pvalue=0.02959 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66488 66666.7 0.479 0.479 2 37437 37654.3 1.254 1.733 3 26941 26954.7 0.007 1.740 4 19679 19313.5 6.918 8.658 5 13986 13851.4 1.308 9.966 6 9858 9943.5 0.736 10.702 7 7049 7145.0 1.291 11.992 8 5188 5139.1 0.466 12.458 9 3684 3699.9 0.068 12.526 10 2725 2666.3 1.292 13.819 11 1895 1923.3 0.417 14.236 12 1338 1388.7 1.854 16.090 13 997 1003.7 0.045 16.135 14 777 726.1 3.562 19.697 15 574 525.8 4.412 24.109 16 364 381.2 0.772 24.880 17 260 276.5 0.989 25.870 18 225 200.8 2.909 28.779 19 150 146.0 0.110 28.889 20 98 106.2 0.635 29.524 21 287 287.1 0.000 29.524 Chisq= 29.52 for 20 degrees of freedom, p= 0.92207 SUMMARY of craptest p-value for no. of wins: 0.029594 p-value for throws/game: 0.922065 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-08_21:31 No. of wins: Observed Expected 98607 98585.9 z-score= 0.095, pvalue=0.53767 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66535 66666.7 0.260 0.260 2 37461 37654.3 0.993 1.253 3 27305 26954.7 4.552 5.804 4 19321 19313.5 0.003 5.807 5 13704 13851.4 1.569 7.376 6 10089 9943.5 2.128 9.504 7 7091 7145.0 0.409 9.912 8 5156 5139.1 0.056 9.968 9 3748 3699.9 0.626 10.594 10 2608 2666.3 1.275 11.869 11 1966 1923.3 0.947 12.816 12 1374 1388.7 0.156 12.972 13 1023 1003.7 0.371 13.343 14 685 726.1 2.331 15.674 15 539 525.8 0.330 16.003 16 398 381.2 0.745 16.748 17 254 276.5 1.837 18.585 18 221 200.8 2.026 20.611 19 143 146.0 0.061 20.672 20 106 106.2 0.000 20.672 21 273 287.1 0.694 21.366 Chisq= 21.37 for 20 degrees of freedom, p= 0.62413 SUMMARY of craptest p-value for no. of wins: 0.537667 p-value for throws/game: 0.624129 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0009,0.0018,0.0030,0.0032,0.0054,0.0063,0.0067,0.0156,0.0162, 0.0245,0.0275,0.0296,0.0310,0.0360,0.0395,0.0432,0.0507,0.0510,0.0546, 0.0567,0.0583,0.0653,0.0692,0.0763,0.0978,0.1005,0.1008,0.1016,0.1027, 0.1059,0.1092,0.1151,0.1175,0.1213,0.1245,0.1254,0.1288,0.1304,0.1358, 0.1365,0.1416,0.1464,0.1472,0.1542,0.1574,0.1575,0.1620,0.1695,0.1704, 0.1724,0.1727,0.1819,0.1831,0.1912,0.1912,0.1929,0.1950,0.2006,0.2025, 0.2057,0.2067,0.2084,0.2128,0.2130,0.2155,0.2215,0.2222,0.2226,0.2265, 0.2269,0.2313,0.2346,0.2383,0.2446,0.2458,0.2461,0.2471,0.2496,0.2518, 0.2522,0.2607,0.2669,0.2690,0.2812,0.2876,0.2967,0.2992,0.3001,0.3079, 0.3146,0.3214,0.3241,0.3260,0.3291,0.3294,0.3319,0.3326,0.3355,0.3390, 0.3493,0.3514,0.3518,0.3536,0.3537,0.3557,0.3646,0.3656,0.3660,0.3710, 0.3779,0.3849,0.3854,0.3859,0.3866,0.3898,0.3913,0.3953,0.4010,0.4110, 0.4119,0.4127,0.4142,0.4145,0.4163,0.4295,0.4406,0.4455,0.4472,0.4597, 0.4620,0.4636,0.4644,0.4659,0.4761,0.4823,0.4843,0.4864,0.4884,0.4904, 0.4913,0.5000,0.5016,0.5025,0.5043,0.5055,0.5078,0.5108,0.5184,0.5199, 0.5227,0.5257,0.5338,0.5377,0.5430,0.5544,0.5551,0.5552,0.5622,0.5630, 0.5652,0.5655,0.5705,0.5719,0.5734,0.5803,0.5810,0.5830,0.5871,0.5876, 0.5877,0.5888,0.5895,0.5903,0.5984,0.5993,0.6002,0.6007,0.6013,0.6083, 0.6096,0.6200,0.6241,0.6246,0.6271,0.6337,0.6379,0.6439,0.6446,0.6544, 0.6665,0.6698,0.6727,0.6741,0.6818,0.6892,0.6923,0.6935,0.6987,0.7058, 0.7093,0.7110,0.7122,0.7169,0.7200,0.7265,0.7288,0.7318,0.7334,0.7334, 0.7350,0.7378,0.7387,0.7406,0.7533,0.7538,0.7550,0.7556,0.7593,0.7696, 0.7740,0.7771,0.7858,0.8021,0.8032,0.8035,0.8041,0.8052,0.8236,0.8287, 0.8312,0.8361,0.8427,0.8456,0.8532,0.8547,0.8583,0.8652,0.8773,0.8980, 0.9036,0.9049,0.9116,0.9159,0.9221,0.9229,0.9289,0.9297,0.9324,0.9341, 0.9374,0.9391,0.9419,0.9570,0.9621,0.9640,0.9657,0.9722,0.9723,0.9730, 0.9735,0.9747,0.9808,0.9816,0.9848,0.9905,0.9964,0.9983,0.9989, Overall p-value after applying KStest on 269 p-values = 0.149785 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.