RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-01_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 26.1572 0.928355 2 to 25 15.55 25.9131 0.923942 3 to 26 15.80 25.0709 0.906865 4 to 27 15.61 12.0141 0.200719 5 to 28 15.89 19.8699 0.719061 6 to 29 15.66 24.9585 0.904359 7 to 30 16.01 17.8154 0.599428 8 to 31 15.67 21.6826 0.802766 9 to 32 15.88 12.8517 0.253945 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.042068 Tough bday spacings test for dh-ranFile-2016-02-01_11:31: 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 8 39 87 112 89 57 57 27 17 5 2 (O-E)^2/E 0.1 0.2 2.6 2.1 0.8 5.7 0.5 0.3 0.3 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.932, p= 0.824 RESULTS OF GCD FOR dh-ranFile-2016-02-01_11:31 Euclid's algorithm: p-value, steps to gcd: 0.176858 p-value, dist. of gcd's: 0.906524 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-01_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.919 0.767 0.394 0.169 0.957 0.322 0.616 0.487 Bits 8 to 15---> 0.550 0.296 0.508 0.059 0.763 0.116 0.801 0.686 Bits 16 to 23---> 0.549 0.836 0.633 0.549 0.792 0.826 0.283 0.705 Bits 24 to 31---> 0.180 0.910 0.387 0.914 0.072 0.384 0.658 0.131 KS test for the above 32 p values: 0.254 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-01_11:31, p-values for 5 runs: 0.2635, 0.3265, 0.5175, 0.1588, 0.0992 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-01_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5085 5134.0 0.468 0.673 r= 30 22936 23103.0 1.208 1.881 r= 31 11761 11551.5 3.799 5.679 chi-square = 5.679 with df = 3; p-value = 0.872 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-01_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 188 211.4 2.594 2.594 r= 30 5031 5134.0 2.067 4.661 r= 31 23346 23103.0 2.555 7.216 r= 32 11435 11551.5 1.175 8.391 chi-square = 8.391 with df = 3; p-value = 0.961 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-01_11:31 b-rank test for bits 1 to 8, p=0.82899 b-rank test for bits 2 to 9, p=0.06170 b-rank test for bits 3 to 10, p=0.97646 b-rank test for bits 4 to 11, p=0.28030 b-rank test for bits 5 to 12, p=0.77213 b-rank test for bits 6 to 13, p=0.44003 b-rank test for bits 7 to 14, p=0.95253 b-rank test for bits 8 to 15, p=0.74549 b-rank test for bits 9 to 16, p=0.72311 b-rank test for bits 10 to 17, p=0.33947 b-rank test for bits 11 to 18, p=0.29197 b-rank test for bits 12 to 19, p=0.55257 b-rank test for bits 13 to 20, p=0.44816 b-rank test for bits 14 to 21, p=0.92561 b-rank test for bits 15 to 22, p=0.13851 b-rank test for bits 16 to 23, p=0.14401 b-rank test for bits 17 to 24, p=0.16415 b-rank test for bits 18 to 25, p=0.52401 b-rank test for bits 19 to 26, p=0.41115 b-rank test for bits 20 to 27, p=0.27639 b-rank test for bits 21 to 28, p=0.83261 b-rank test for bits 22 to 29, p=0.24875 b-rank test for bits 23 to 30, p=0.07366 b-rank test for bits 24 to 31, p=0.31854 b-rank test for bits 25 to 32, p=0.65939 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 = 0.958866 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-01_11:31 (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 142322 0.96 0.832523 2 141812 -0.23 0.410054 3 141992 0.19 0.576581 4 142350 1.03 0.848402 5 141868 -0.10 0.461536 6 141772 -0.32 0.374157 7 141998 0.21 0.582063 8 142123 0.50 0.691191 9 142697 1.84 0.967142 10 141753 -0.37 0.357460 11 141616 -0.69 0.246561 12 141933 0.06 0.522052 13 142140 0.54 0.705039 14 141923 0.03 0.512740 15 142601 1.62 0.946958 16 142205 0.69 0.755160 17 142001 0.21 0.584798 18 141464 -1.04 0.149056 19 142276 0.86 0.804196 20 141240 -1.56 0.058926 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-01_11:31 Bits used No. missing words z-score p-value 23 to 32 141620 -0.9977 0.159215 22 to 31 141152 -2.6115 0.004508 21 to 30 141698 -0.7287 0.233085 20 to 29 141883 -0.0908 0.463829 19 to 28 142375 1.6058 0.945837 18 to 27 142046 0.4713 0.681278 17 to 26 142436 1.8161 0.965323 16 to 25 142366 1.5747 0.942340 15 to 24 141876 -0.1149 0.454250 14 to 23 141592 -1.0942 0.136925 13 to 22 141654 -0.8804 0.189308 12 to 21 142038 0.4437 0.671367 11 to 20 141756 -0.5287 0.298498 10 to 19 141903 -0.0218 0.491293 9 to 18 142097 0.6471 0.741229 8 to 17 141544 -1.2598 0.103878 7 to 16 141733 -0.6080 0.271582 6 to 15 142171 0.9023 0.816554 5 to 14 141806 -0.3563 0.360804 4 to 13 141924 0.0506 0.520172 3 to 12 141790 -0.4115 0.340359 2 to 11 141886 -0.0804 0.467940 1 to 10 141899 -0.0356 0.485792 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-01_11:31 Bits used No. missing words z-score p-value 28 to 32 141772 -0.4655 0.320778 27 to 31 141812 -0.3299 0.370726 26 to 30 141741 -0.5706 0.284132 25 to 29 141308 -2.0384 0.020755 24 to 28 141968 0.1989 0.578822 23 to 27 141868 -0.1401 0.444290 22 to 26 141539 -1.2554 0.104675 21 to 25 141521 -1.3164 0.094024 20 to 24 141581 -1.1130 0.132858 19 to 23 141238 -2.2757 0.011432 18 to 22 141687 -0.7537 0.225526 17 to 21 142157 0.8396 0.799422 16 to 20 141556 -1.1977 0.115511 15 to 19 141959 0.1684 0.566855 14 to 18 141683 -0.7672 0.221475 13 to 17 141788 -0.4113 0.340431 12 to 16 141382 -1.7876 0.036924 11 to 15 141756 -0.5198 0.301615 10 to 14 141791 -0.4011 0.344166 9 to 13 141687 -0.7537 0.225526 8 to 12 141610 -1.0147 0.155130 7 to 11 142164 0.8633 0.806011 6 to 10 142008 0.3345 0.630989 5 to 9 141737 -0.5842 0.279553 4 to 8 142116 0.7006 0.758216 3 to 7 142183 0.9277 0.823217 2 to 6 141993 0.2836 0.611652 1 to 5 141877 -0.1096 0.456366 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-01_11:31 Bits used No. missing words z-score p-value 31 to 32 141899 -0.0305 0.487845 30 to 31 141443 -1.3756 0.084472 29 to 30 141864 -0.1337 0.446813 28 to 29 142190 0.8279 0.796146 27 to 28 141628 -0.8299 0.203303 26 to 27 141755 -0.4553 0.324464 25 to 26 141822 -0.2576 0.398354 24 to 25 142018 0.3206 0.625728 23 to 24 141826 -0.2458 0.402914 22 to 23 141716 -0.5703 0.284239 21 to 22 141444 -1.3727 0.084930 20 to 21 141661 -0.7325 0.231921 19 to 20 141739 -0.5024 0.307676 18 to 19 142172 0.7748 0.780782 17 to 18 141630 -0.8240 0.204975 16 to 17 142024 0.3383 0.632416 15 to 16 141784 -0.3697 0.355801 14 to 15 141943 0.0993 0.539559 13 to 14 141713 -0.5791 0.281246 12 to 13 141249 -1.9479 0.025715 11 to 12 142101 0.5654 0.714099 10 to 11 141961 0.1524 0.560572 9 to 10 141674 -0.6942 0.243782 8 to 9 141494 -1.2252 0.110257 7 to 8 141825 -0.2488 0.401773 6 to 7 141743 -0.4906 0.311837 5 to 6 142133 0.6598 0.745307 4 to 5 141736 -0.5113 0.304571 3 to 4 141910 0.0020 0.500789 2 to 3 142295 1.1377 0.872371 1 to 2 141870 -0.1160 0.453819 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-01_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2505.44 0.077 0.530687 Test results for specific bytes for dh-ranFile-2016-02-01_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2498.65 -0.019 0.492380 2 to 9 2542.75 0.605 0.727280 3 to 10 2460.97 -0.552 0.290487 4 to 11 2537.68 0.533 0.702959 5 to 12 2432.17 -0.959 0.168723 6 to 13 2568.78 0.973 0.834636 7 to 14 2515.67 0.222 0.587699 8 to 15 2512.47 0.176 0.570004 9 to 16 2561.90 0.875 0.809316 10 to 17 2479.44 -0.291 0.385627 11 to 18 2515.91 0.225 0.588998 12 to 19 2544.37 0.627 0.734823 13 to 20 2506.06 0.086 0.534151 14 to 21 2609.95 1.555 0.940021 15 to 22 2644.97 2.050 0.979825 16 to 23 2376.59 -1.745 0.040462 17 to 24 2530.70 0.434 0.667926 18 to 25 2535.76 0.506 0.693487 19 to 26 2527.00 0.382 0.648706 20 to 27 2608.98 1.541 0.938363 21 to 28 2518.25 0.258 0.601809 22 to 29 2510.75 0.152 0.560427 23 to 30 2450.61 -0.699 0.242431 24 to 31 2540.56 0.574 0.716862 25 to 32 2607.80 1.525 0.936316 CDPARK for dh-ranFile-2016-02-01_11:31: 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 3541 0.8219 0.794438 3543 0.9132 0.819442 3509 -0.6393 0.261324 3546 1.0502 0.853193 3509 -0.6393 0.261324 3526 0.1370 0.554479 3529 0.2740 0.607947 3554 1.4155 0.921543 3521 -0.0913 0.463617 3571 2.1918 0.985802 Square side=100, avg. no. parked=3534.90 sample std.=18.82 p-value of the KSTEST for those 10 p-values: 0.159560 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-01_11:31 0.6892,0.0103,0.6528,0.3278,0.5447,0.4009,0.6015,0.8051,0.4978,0.7856, The KS test for those 10 p-values: 0.495224 The 3DSPHERES test for dh-ranFile-2016-02-01_11:31 sample no r^3 equiv. uni. 1 48.522 0.801586 2 5.316 0.162395 3 22.719 0.531077 4 56.757 0.849216 5 5.931 0.179392 6 11.860 0.326544 7 12.064 0.331112 8 26.279 0.583547 9 64.963 0.885300 10 7.508 0.221417 11 4.884 0.150246 12 12.949 0.350550 13 26.813 0.590890 14 172.341 0.996800 15 1.292 0.042151 16 3.563 0.111982 17 8.564 0.248340 18 26.826 0.591062 19 63.920 0.881242 20 131.622 0.987567 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.656891 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-01_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -1.1 2.1 -0.5 -0.6 -0.3 1.0 -1.3 0.9 0.8 1.4 -0.4 -0.9 -0.7 -0.2 -0.4 -1.3 1.8 -0.6 -2.9 0.7 0.8 1.8 0.1 0.9 1.4 0.9 0.6 -1.9 0.4 -0.9 0.5 -1.6 0.1 -1.2 -0.2 0.5 0.9 0.4 1.6 1.0 -0.1 Chi-square with 42 degrees of freedom:50.094075 z-score=0.883136, p-value=0.816938 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-01_11:31 Test no p-value 1 0.237904 2 0.142932 3 0.217064 4 0.045655 5 0.672286 6 0.000461 7 0.022909 8 0.230881 9 0.017335 10 0.053645 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000039 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-01_11:31: (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 66939 1.11 66683 0.00 3 25000.00 24591 6.69 25100 0.40 4 6666.67 6828 3.90 6562 1.64 5 1388.89 1349 1.15 1359 0.64 6 238.10 252 0.81 257 1.50 7 34.72 35 0.00 35 0.00 8 4.96 5 0.00 3 0.77 p=0.96643 p=0.45213 Number of rngs required: 688166, p-value: 0.393 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-01_11:31 No. of wins: Observed Expected 98521 98585.9 z-score=-0.290, pvalue=0.38588 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66876 66666.7 0.657 0.657 2 37562 37654.3 0.226 0.884 3 26841 26954.7 0.480 1.364 4 19396 19313.5 0.353 1.716 5 13743 13851.4 0.849 2.565 6 9879 9943.5 0.419 2.984 7 7125 7145.0 0.056 3.040 8 5163 5139.1 0.111 3.151 9 3756 3699.9 0.852 4.003 10 2665 2666.3 0.001 4.004 11 1985 1923.3 1.977 5.981 12 1412 1388.7 0.390 6.371 13 963 1003.7 1.652 8.022 14 735 726.1 0.108 8.130 15 524 525.8 0.006 8.137 16 396 381.2 0.579 8.715 17 264 276.5 0.569 9.284 18 198 200.8 0.040 9.324 19 147 146.0 0.007 9.331 20 112 106.2 0.315 9.646 21 258 287.1 2.952 12.598 Chisq= 12.60 for 20 degrees of freedom, p= 0.10605 SUMMARY of craptest p-value for no. of wins: 0.385875 p-value for throws/game: 0.106048 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-01_11:31 No. of wins: Observed Expected 98563 98585.9 z-score=-0.102, pvalue=0.45928 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67004 66666.7 1.707 1.707 2 37588 37654.3 0.117 1.824 3 27107 26954.7 0.860 2.684 4 19097 19313.5 2.426 5.110 5 13728 13851.4 1.100 6.210 6 9817 9943.5 1.610 7.820 7 7239 7145.0 1.236 9.056 8 5034 5139.1 2.148 11.204 9 3775 3699.9 1.526 12.730 10 2652 2666.3 0.077 12.807 11 1955 1923.3 0.522 13.328 12 1363 1388.7 0.477 13.805 13 989 1003.7 0.216 14.021 14 794 726.1 6.342 20.363 15 501 525.8 1.173 21.536 16 398 381.2 0.745 22.281 17 259 276.5 1.112 23.393 18 190 200.8 0.584 23.977 19 147 146.0 0.007 23.984 20 93 106.2 1.644 25.628 21 270 287.1 1.020 26.648 Chisq= 26.65 for 20 degrees of freedom, p= 0.85455 SUMMARY of craptest p-value for no. of wins: 0.459284 p-value for throws/game: 0.854554 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0005,0.0045,0.0103,0.0114,0.0173,0.0208,0.0229,0.0257,0.0369, 0.0405,0.0421,0.0422,0.0457,0.0536,0.0589,0.0592,0.0617,0.0720,0.0737, 0.0845,0.0849,0.0940,0.0992,0.1039,0.1047,0.1060,0.1103,0.1120,0.1155, 0.1162,0.1313,0.1329,0.1369,0.1385,0.1429,0.1440,0.1491,0.1502,0.1551, 0.1588,0.1592,0.1596,0.1624,0.1641,0.1687,0.1688,0.1769,0.1794,0.1801, 0.1893,0.2007,0.2033,0.2050,0.2171,0.2214,0.2215,0.2255,0.2255,0.2309, 0.2319,0.2331,0.2379,0.2424,0.2438,0.2466,0.2483,0.2487,0.2537,0.2539, 0.2613,0.2613,0.2635,0.2716,0.2764,0.2796,0.2803,0.2812,0.2828,0.2841, 0.2842,0.2905,0.2920,0.2956,0.2985,0.3016,0.3046,0.3077,0.3118,0.3185, 0.3208,0.3224,0.3245,0.3265,0.3265,0.3278,0.3311,0.3395,0.3404,0.3404, 0.3442,0.3505,0.3558,0.3575,0.3608,0.3707,0.3742,0.3836,0.3856,0.3859, 0.3873,0.3925,0.3938,0.3984,0.4009,0.4018,0.4029,0.4101,0.4112,0.4400, 0.4443,0.4468,0.4482,0.4521,0.4538,0.4542,0.4564,0.4593,0.4615,0.4636, 0.4638,0.4679,0.4858,0.4875,0.4878,0.4913,0.4924,0.4952,0.4978,0.5008, 0.5079,0.5127,0.5175,0.5202,0.5221,0.5240,0.5307,0.5311,0.5342,0.5396, 0.5447,0.5487,0.5493,0.5496,0.5526,0.5545,0.5604,0.5606,0.5669,0.5700, 0.5766,0.5788,0.5821,0.5835,0.5848,0.5877,0.5890,0.5909,0.5911,0.5994, 0.6015,0.6018,0.6079,0.6117,0.6162,0.6257,0.6310,0.6324,0.6327,0.6487, 0.6528,0.6569,0.6580,0.6594,0.6679,0.6714,0.6723,0.6813,0.6860,0.6892, 0.6912,0.6935,0.7030,0.7050,0.7050,0.7141,0.7169,0.7191,0.7231,0.7273, 0.7348,0.7412,0.7453,0.7455,0.7552,0.7582,0.7627,0.7671,0.7721,0.7808, 0.7856,0.7920,0.7944,0.7961,0.7994,0.8012,0.8016,0.8028,0.8042,0.8051, 0.8060,0.8093,0.8166,0.8169,0.8194,0.8232,0.8239,0.8256,0.8290,0.8325, 0.8326,0.8346,0.8358,0.8484,0.8492,0.8532,0.8546,0.8717,0.8724,0.8812, 0.8853,0.9044,0.9065,0.9069,0.9103,0.9139,0.9190,0.9215,0.9239,0.9256, 0.9284,0.9363,0.9384,0.9400,0.9423,0.9458,0.9470,0.9525,0.9566,0.9589, 0.9614,0.9653,0.9664,0.9671,0.9765,0.9798,0.9858,0.9876,0.9968, Overall p-value after applying KStest on 269 p-values = 0.862540 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.