RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-02_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.52 45.3186 0.999782 2 to 25 15.78 18.4354 0.638117 3 to 26 15.61 23.3805 0.862732 4 to 27 16.00 24.7624 0.899845 5 to 28 15.80 26.3783 0.932161 6 to 29 15.60 17.4332 0.574593 7 to 30 15.70 10.6767 0.127133 8 to 31 15.70 21.5561 0.797601 9 to 32 15.83 29.5903 0.970545 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.003778 Tough bday spacings test for dh-ranFile-2016-07-02_02:31: 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 11 37 75 98 111 68 49 31 15 5 0 (O-E)^2/E 0.4 0.0 0.0 0.0 1.8 1.3 0.2 0.1 0.0 0.4 4.1 Birthday Spacings: Sum(O-E)^2/E= 8.246, p= 0.395 RESULTS OF GCD FOR dh-ranFile-2016-07-02_02:31 Euclid's algorithm: p-value, steps to gcd: 0.154414 p-value, dist. of gcd's: 0.885865 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-02_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.266 0.499 0.180 0.187 0.540 0.559 0.995 0.754 Bits 8 to 15---> 0.052 0.826 0.300 0.951 0.704 0.892 0.589 0.769 Bits 16 to 23---> 0.225 0.284 0.050 0.352 0.611 0.434 0.207 0.342 Bits 24 to 31---> 0.037 0.359 0.873 0.637 0.935 0.109 0.194 0.584 KS test for the above 32 p values: 0.045 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-02_02:31, p-values for 5 runs: 0.7445, 0.1302, 0.4911, 0.6505, 0.9713 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-02_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5119 5134.0 0.044 0.105 r= 30 23029 23103.0 0.237 0.342 r= 31 11637 11551.5 0.632 0.974 chi-square = 0.974 with df = 3; p-value = 0.193 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-02_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5187 5134.0 0.547 0.639 r= 31 23129 23103.0 0.029 0.668 r= 32 11477 11551.5 0.481 1.149 chi-square = 1.149 with df = 3; p-value = 0.235 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-02_02:31 b-rank test for bits 1 to 8, p=0.59185 b-rank test for bits 2 to 9, p=0.06329 b-rank test for bits 3 to 10, p=0.09618 b-rank test for bits 4 to 11, p=0.70552 b-rank test for bits 5 to 12, p=0.01153 b-rank test for bits 6 to 13, p=0.81630 b-rank test for bits 7 to 14, p=0.90983 b-rank test for bits 8 to 15, p=0.84621 b-rank test for bits 9 to 16, p=0.58534 b-rank test for bits 10 to 17, p=0.06432 b-rank test for bits 11 to 18, p=0.17856 b-rank test for bits 12 to 19, p=0.42205 b-rank test for bits 13 to 20, p=0.11985 b-rank test for bits 14 to 21, p=0.71133 b-rank test for bits 15 to 22, p=0.17335 b-rank test for bits 16 to 23, p=0.47678 b-rank test for bits 17 to 24, p=0.40668 b-rank test for bits 18 to 25, p=0.33833 b-rank test for bits 19 to 26, p=0.23691 b-rank test for bits 20 to 27, p=0.71426 b-rank test for bits 21 to 28, p=0.32671 b-rank test for bits 22 to 29, p=0.73940 b-rank test for bits 23 to 30, p=0.67766 b-rank test for bits 24 to 31, p=0.27681 b-rank test for bits 25 to 32, p=0.58749 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 = 0.537676 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-02_02:31 (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 141440 -1.10 0.136416 2 142178 0.63 0.734911 3 142215 0.71 0.762443 4 142086 0.41 0.660116 5 141466 -1.04 0.150144 6 141564 -0.81 0.209878 7 142002 0.22 0.585708 8 142507 1.40 0.918707 9 141794 -0.27 0.393787 10 142142 0.54 0.706649 11 142396 1.14 0.872247 12 142431 1.22 0.888550 13 141361 -1.28 0.100071 14 142044 0.31 0.623486 15 142030 0.28 0.611005 16 141460 -1.05 0.146897 17 141924 0.03 0.513671 18 142045 0.32 0.624373 19 142254 0.81 0.789678 20 141727 -0.43 0.335052 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-02_02:31 Bits used No. missing words z-score p-value 23 to 32 141772 -0.4736 0.317910 22 to 31 142291 1.3161 0.905930 21 to 30 142022 0.3885 0.651183 20 to 29 142116 0.7127 0.761970 19 to 28 142246 1.1609 0.877165 18 to 27 142141 0.7989 0.787815 17 to 26 142600 2.3816 0.991382 16 to 25 141733 -0.6080 0.271582 15 to 24 141950 0.1402 0.555765 14 to 23 141944 0.1196 0.547581 13 to 22 142153 0.8402 0.799614 12 to 21 142407 1.7161 0.956928 11 to 20 141909 -0.0011 0.499546 10 to 19 142429 1.7920 0.963431 9 to 18 141637 -0.9391 0.173848 8 to 17 141832 -0.2667 0.394867 7 to 16 141867 -0.1460 0.441974 6 to 15 141798 -0.3839 0.350528 5 to 14 142162 0.8713 0.808198 4 to 13 141965 0.1920 0.576115 3 to 12 141981 0.2471 0.597599 2 to 11 141818 -0.3149 0.376407 1 to 10 142025 0.3989 0.655003 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-02_02:31 Bits used No. missing words z-score p-value 28 to 32 141786 -0.4181 0.337949 27 to 31 141712 -0.6689 0.251775 26 to 30 141749 -0.5435 0.293396 25 to 29 141942 0.1107 0.544091 24 to 28 141739 -0.5774 0.281838 23 to 27 141749 -0.5435 0.293396 22 to 26 141477 -1.4655 0.071389 21 to 25 141866 -0.1469 0.441613 20 to 24 141820 -0.3028 0.381016 19 to 23 141320 -1.9977 0.022873 18 to 22 142042 0.4497 0.673547 17 to 21 141948 0.1311 0.552146 16 to 20 142006 0.3277 0.628429 15 to 19 142063 0.5209 0.698787 14 to 18 141881 -0.0960 0.461747 13 to 17 142360 1.5277 0.936706 12 to 16 141632 -0.9401 0.173583 11 to 15 141850 -0.2011 0.420303 10 to 14 141569 -1.1537 0.124320 9 to 13 141673 -0.8011 0.211532 8 to 12 142059 0.5074 0.694048 7 to 11 142328 1.4192 0.922083 6 to 10 141800 -0.3706 0.355464 5 to 9 142311 1.3616 0.913337 4 to 8 141924 0.0497 0.519831 3 to 7 141827 -0.2791 0.390090 2 to 6 141855 -0.1842 0.426940 1 to 5 142376 1.5819 0.943167 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-02_02:31 Bits used No. missing words z-score p-value 31 to 32 141750 -0.4700 0.319178 30 to 31 142032 0.3619 0.641271 29 to 30 141578 -0.9774 0.164192 28 to 29 141992 0.2439 0.596332 27 to 28 141951 0.1229 0.548915 26 to 27 142071 0.4769 0.683284 25 to 26 142414 1.4887 0.931717 24 to 25 142067 0.4651 0.679071 23 to 24 142178 0.7925 0.785976 22 to 23 142294 1.1347 0.871754 21 to 22 142216 0.9046 0.817170 20 to 21 141995 0.2527 0.599755 19 to 20 141269 -1.8889 0.029454 18 to 19 141494 -1.2252 0.110257 17 to 18 142035 0.3707 0.644573 16 to 17 141766 -0.4228 0.336220 15 to 16 141914 0.0138 0.505496 14 to 15 141956 0.1377 0.554749 13 to 14 141951 0.1229 0.548915 12 to 13 142043 0.3943 0.653323 11 to 12 141783 -0.3727 0.354703 10 to 11 142334 1.2527 0.894845 9 to 10 141718 -0.5644 0.286243 8 to 9 141722 -0.5526 0.290270 7 to 8 141705 -0.6027 0.273340 6 to 7 142075 0.4887 0.687474 5 to 6 142285 1.1082 0.866106 4 to 5 142218 0.9105 0.818729 3 to 4 142337 1.2616 0.896447 2 to 3 141911 0.0049 0.501965 1 to 2 141701 -0.6145 0.269428 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-02_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2364.17 -1.921 0.027371 Test results for specific bytes for dh-ranFile-2016-07-02_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2453.17 -0.662 0.253878 2 to 9 2506.15 0.087 0.534637 3 to 10 2543.82 0.620 0.732283 4 to 11 2539.17 0.554 0.710213 5 to 12 2416.34 -1.183 0.118368 6 to 13 2631.37 1.858 0.968403 7 to 14 2560.27 0.852 0.802980 8 to 15 2508.25 0.117 0.546441 9 to 16 2431.20 -0.973 0.165275 10 to 17 2492.58 -0.105 0.458231 11 to 18 2517.31 0.245 0.596697 12 to 19 2539.10 0.553 0.709843 13 to 20 2463.24 -0.520 0.301566 14 to 21 2498.77 -0.017 0.493087 15 to 22 2540.86 0.578 0.718320 16 to 23 2464.65 -0.500 0.308549 17 to 24 2447.53 -0.742 0.229028 18 to 25 2430.25 -0.986 0.161982 19 to 26 2533.26 0.470 0.680975 20 to 27 2503.19 0.045 0.517973 21 to 28 2493.03 -0.099 0.460739 22 to 29 2371.51 -1.817 0.034595 23 to 30 2530.10 0.426 0.664805 24 to 31 2517.38 0.246 0.597077 25 to 32 2515.85 0.224 0.588703 CDPARK for dh-ranFile-2016-07-02_02:31: 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 3488 -1.5982 0.055002 3551 1.2785 0.899470 3496 -1.2329 0.108811 3556 1.5068 0.934075 3568 2.0548 0.980051 3525 0.0913 0.536383 3486 -1.6895 0.045562 3522 -0.0457 0.481790 3532 0.4110 0.659449 3473 -2.2831 0.011212 Square side=100, avg. no. parked=3519.70 sample std.=31.14 p-value of the KSTEST for those 10 p-values: 0.192535 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-02_02:31 0.3258,0.2744,0.5613,0.8818,0.9547,0.7937,0.8137,0.2285,0.6515,0.2087, The KS test for those 10 p-values: 0.683084 The 3DSPHERES test for dh-ranFile-2016-07-02_02:31 sample no r^3 equiv. uni. 1 80.942 0.932664 2 26.731 0.589773 3 7.968 0.233256 4 16.646 0.425853 5 20.775 0.499670 6 48.090 0.798706 7 1.991 0.064224 8 29.235 0.622621 9 25.836 0.577340 10 32.418 0.660611 11 228.552 0.999509 12 39.742 0.734125 13 16.955 0.431737 14 1.070 0.035037 15 29.879 0.630636 16 36.954 0.708233 17 39.144 0.728773 18 8.109 0.236838 19 8.481 0.246256 20 40.616 0.741757 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.476671 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-02_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 1.3 0.2 0.3 -1.1 0.5 0.3 1.4 -0.3 -0.8 -0.3 -0.2 -1.0 1.4 -0.7 -0.4 1.6 -1.3 1.0 -0.5 0.8 -0.5 -0.4 1.7 -1.5 0.9 -0.8 1.2 0.8 0.2 -2.9 -0.1 -1.3 -0.1 -0.1 -0.2 -0.4 -0.8 -1.3 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:40.383389 z-score=-0.176387, p-value=0.457931 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-02_02:31 Test no p-value 1 0.931655 2 0.908272 3 0.619768 4 0.400578 5 0.373336 6 0.015146 7 0.014282 8 0.014251 9 0.363582 10 0.003397 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009570 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-02_02:31: (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 66623 0.03 66459 0.65 3 25000.00 24978 0.02 25108 0.47 4 6666.67 6704 0.21 6737 0.74 5 1388.89 1414 0.45 1416 0.53 6 238.10 246 0.26 239 0.00 7 34.72 26 2.19 38 0.31 8 4.96 8 1.86 2 1.77 p=0.45960 p=0.38590 Number of rngs required: 688787, p-value: 0.671 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-02_02:31 No. of wins: Observed Expected 98600 98585.9 z-score= 0.063, pvalue=0.52522 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66930 66666.7 1.040 1.040 2 37459 37654.3 1.013 2.053 3 26819 26954.7 0.683 2.737 4 19095 19313.5 2.471 5.208 5 13943 13851.4 0.605 5.813 6 9822 9943.5 1.486 7.299 7 7233 7145.0 1.083 8.382 8 5226 5139.1 1.470 9.853 9 3806 3699.9 3.045 12.897 10 2734 2666.3 1.719 14.616 11 1920 1923.3 0.006 14.622 12 1371 1388.7 0.227 14.849 13 999 1003.7 0.022 14.871 14 734 726.1 0.085 14.956 15 536 525.8 0.196 15.152 16 360 381.2 1.174 16.326 17 284 276.5 0.201 16.527 18 197 200.8 0.073 16.600 19 133 146.0 1.155 17.755 20 104 106.2 0.046 17.802 21 295 287.1 0.217 18.018 Chisq= 18.02 for 20 degrees of freedom, p= 0.41379 SUMMARY of craptest p-value for no. of wins: 0.525216 p-value for throws/game: 0.413786 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-02_02:31 No. of wins: Observed Expected 98519 98585.9 z-score=-0.299, pvalue=0.38246 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66477 66666.7 0.540 0.540 2 37452 37654.3 1.087 1.627 3 26985 26954.7 0.034 1.661 4 19435 19313.5 0.765 2.426 5 13696 13851.4 1.744 4.169 6 10132 9943.5 3.572 7.741 7 7109 7145.0 0.182 7.923 8 5096 5139.1 0.361 8.284 9 3827 3699.9 4.369 12.652 10 2671 2666.3 0.008 12.661 11 1945 1923.3 0.244 12.905 12 1445 1388.7 2.279 15.184 13 1019 1003.7 0.233 15.417 14 756 726.1 1.228 16.645 15 541 525.8 0.437 17.082 16 414 381.2 2.831 19.913 17 245 276.5 3.597 23.510 18 202 200.8 0.007 23.517 19 171 146.0 4.287 27.804 20 88 106.2 3.124 30.927 21 294 287.1 0.165 31.093 Chisq= 31.09 for 20 degrees of freedom, p= 0.94602 SUMMARY of craptest p-value for no. of wins: 0.382458 p-value for throws/game: 0.946020 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0034,0.0038,0.0096,0.0112,0.0115,0.0143,0.0143,0.0151,0.0229,0.0274, 0.0295,0.0346,0.0350,0.0373,0.0448,0.0456,0.0505,0.0524,0.0550,0.0633, 0.0642,0.0643,0.0714,0.0962,0.1001,0.1088,0.1090,0.1103,0.1184,0.1199, 0.1243,0.1271,0.1302,0.1364,0.1469,0.1501,0.1544,0.1620,0.1642,0.1653, 0.1733,0.1736,0.1738,0.1786,0.1796,0.1869,0.1925,0.1926,0.1942,0.2067, 0.2087,0.2099,0.2115,0.2254,0.2285,0.2290,0.2333,0.2348,0.2368,0.2369, 0.2463,0.2518,0.2539,0.2658,0.2694,0.2716,0.2733,0.2744,0.2768,0.2818, 0.2837,0.2862,0.2903,0.2934,0.2934,0.2999,0.3016,0.3085,0.3179,0.3192, 0.3258,0.3267,0.3351,0.3362,0.3379,0.3383,0.3425,0.3505,0.3517,0.3547, 0.3555,0.3593,0.3636,0.3733,0.3764,0.3810,0.3825,0.3859,0.3901,0.3938, 0.3949,0.3952,0.4006,0.4067,0.4138,0.4203,0.4221,0.4259,0.4269,0.4317, 0.4343,0.4416,0.4420,0.4579,0.4582,0.4596,0.4607,0.4617,0.4767,0.4768, 0.4818,0.4911,0.4931,0.4992,0.4995,0.4997,0.5020,0.5055,0.5137,0.5180, 0.5198,0.5252,0.5346,0.5364,0.5377,0.5399,0.5441,0.5464,0.5476,0.5489, 0.5489,0.5521,0.5547,0.5558,0.5589,0.5613,0.5746,0.5761,0.5773,0.5840, 0.5853,0.5857,0.5875,0.5887,0.5890,0.5898,0.5918,0.5963,0.5967,0.5971, 0.5976,0.5998,0.6108,0.6110,0.6198,0.6226,0.6235,0.6244,0.6284,0.6306, 0.6374,0.6381,0.6413,0.6446,0.6505,0.6512,0.6515,0.6533,0.6550,0.6594, 0.6601,0.6606,0.6648,0.6709,0.6735,0.6777,0.6791,0.6810,0.6831,0.6833, 0.6875,0.6940,0.6988,0.7036,0.7055,0.7066,0.7082,0.7098,0.7102,0.7113, 0.7143,0.7183,0.7288,0.7323,0.7341,0.7349,0.7394,0.7418,0.7445,0.7539, 0.7620,0.7624,0.7686,0.7860,0.7878,0.7897,0.7937,0.7976,0.7987,0.7996, 0.8030,0.8082,0.8137,0.8163,0.8172,0.8187,0.8261,0.8462,0.8627,0.8661, 0.8718,0.8722,0.8729,0.8772,0.8818,0.8859,0.8886,0.8918,0.8948,0.8964, 0.8995,0.8998,0.9059,0.9083,0.9098,0.9133,0.9187,0.9221,0.9317,0.9317, 0.9322,0.9327,0.9341,0.9353,0.9367,0.9432,0.9460,0.9513,0.9547,0.9569, 0.9634,0.9684,0.9705,0.9713,0.9801,0.9914,0.9951,0.9995,0.9998, Overall p-value after applying KStest on 269 p-values = 0.641395 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.