RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-12_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 15.4171 0.434532 2 to 25 15.79 20.6615 0.758202 3 to 26 15.78 12.6310 0.239484 4 to 27 15.94 12.6825 0.242830 5 to 28 16.02 8.8656 0.055616 6 to 29 15.54 22.6406 0.838678 7 to 30 15.80 10.6083 0.123814 8 to 31 15.94 16.7348 0.527533 9 to 32 15.78 13.6895 0.311055 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.489359 Tough bday spacings test for dh-ranFile-2018-04-12_13:31: 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 36 82 108 95 69 49 28 17 4 3 (O-E)^2/E 0.0 0.0 1.0 1.1 0.1 1.1 0.2 0.1 0.3 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.193, p= 0.122 RESULTS OF GCD FOR dh-ranFile-2018-04-12_13:31 Euclid's algorithm: p-value, steps to gcd: 0.153983 p-value, dist. of gcd's: 0.347715 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-12_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.607 0.606 0.306 0.439 0.725 0.916 0.886 0.756 Bits 8 to 15---> 0.212 0.379 0.048 0.092 0.369 0.792 0.564 0.477 Bits 16 to 23---> 0.192 0.772 0.778 0.004 0.506 0.269 0.506 0.900 Bits 24 to 31---> 0.886 0.598 0.342 0.822 0.726 0.813 0.196 0.505 KS test for the above 32 p values: 0.341 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-12_13:31, p-values for 5 runs: 0.9203, 0.4138, 0.5568, 0.8954, 0.0342 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-12_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5110 5134.0 0.112 0.547 r= 30 23107 23103.0 0.001 0.547 r= 31 11562 11551.5 0.010 0.557 chi-square = 0.557 with df = 3; p-value = 0.094 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-12_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5090 5134.0 0.377 0.438 r= 31 23129 23103.0 0.029 0.467 r= 32 11566 11551.5 0.018 0.485 chi-square = 0.485 with df = 3; p-value = 0.078 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-12_13:31 b-rank test for bits 1 to 8, p=0.87711 b-rank test for bits 2 to 9, p=0.11410 b-rank test for bits 3 to 10, p=0.32217 b-rank test for bits 4 to 11, p=0.36320 b-rank test for bits 5 to 12, p=0.31777 b-rank test for bits 6 to 13, p=0.22080 b-rank test for bits 7 to 14, p=0.70532 b-rank test for bits 8 to 15, p=0.53300 b-rank test for bits 9 to 16, p=0.60210 b-rank test for bits 10 to 17, p=0.56351 b-rank test for bits 11 to 18, p=0.98931 b-rank test for bits 12 to 19, p=0.60118 b-rank test for bits 13 to 20, p=0.39213 b-rank test for bits 14 to 21, p=0.42552 b-rank test for bits 15 to 22, p=0.37698 b-rank test for bits 16 to 23, p=0.61592 b-rank test for bits 17 to 24, p=0.92642 b-rank test for bits 18 to 25, p=0.75055 b-rank test for bits 19 to 26, p=0.82172 b-rank test for bits 20 to 27, p=0.40498 b-rank test for bits 21 to 28, p=0.49048 b-rank test for bits 22 to 29, p=0.47029 b-rank test for bits 23 to 30, p=0.21428 b-rank test for bits 24 to 31, p=0.41547 b-rank test for bits 25 to 32, p=0.68637 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 = 0.316419 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-12_13:31 (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 141284 -1.46 0.072001 2 142208 0.70 0.757357 3 141788 -0.28 0.388404 4 141983 0.17 0.568331 5 142517 1.42 0.922166 6 142197 0.67 0.749248 7 142067 0.37 0.643708 8 141637 -0.64 0.262295 9 141790 -0.28 0.390196 10 142409 1.17 0.878486 11 142679 1.80 0.963935 12 141875 -0.08 0.468035 13 142336 1.00 0.840592 14 141712 -0.46 0.322381 15 141727 -0.43 0.335052 16 142850 2.20 0.986019 17 141626 -0.66 0.253990 18 141641 -0.63 0.265350 19 141282 -1.47 0.071362 20 141476 -1.01 0.155661 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-12_13:31 Bits used No. missing words z-score p-value 23 to 32 142108 0.6851 0.753350 22 to 31 141983 0.2540 0.600266 21 to 30 141697 -0.7322 0.232032 20 to 29 141832 -0.2667 0.394867 19 to 28 142049 0.4816 0.684962 18 to 27 141627 -0.9736 0.165140 17 to 26 141933 0.0816 0.532526 16 to 25 141849 -0.2080 0.417601 15 to 24 142156 0.8506 0.802500 14 to 23 141771 -0.4770 0.316681 13 to 22 141626 -0.9770 0.164285 12 to 21 141893 -0.0563 0.477547 11 to 20 141610 -1.0322 0.150996 10 to 19 141791 -0.4080 0.341624 9 to 18 142002 0.3196 0.625346 8 to 17 141816 -0.3218 0.373792 7 to 16 141993 0.2885 0.613525 6 to 15 141896 -0.0460 0.481669 5 to 14 141940 0.1058 0.542113 4 to 13 141935 0.0885 0.535267 3 to 12 141645 -0.9115 0.181021 2 to 11 141809 -0.3460 0.364684 1 to 10 141951 0.1437 0.557127 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-12_13:31 Bits used No. missing words z-score p-value 28 to 32 142136 0.7684 0.778867 27 to 31 142293 1.3006 0.903298 26 to 30 141677 -0.7876 0.215477 25 to 29 142171 0.8870 0.812465 24 to 28 141713 -0.6655 0.252857 23 to 27 142116 0.7006 0.758216 22 to 26 142217 1.0429 0.851514 21 to 25 142014 0.3548 0.638635 20 to 24 141301 -2.0621 0.019597 19 to 23 141956 0.1582 0.562852 18 to 22 142396 1.6497 0.950501 17 to 21 142239 1.1175 0.868115 16 to 20 141658 -0.8520 0.197116 15 to 19 141590 -1.0825 0.139521 14 to 18 141680 -0.7774 0.218464 13 to 17 141706 -0.6893 0.245332 12 to 16 141752 -0.5333 0.296905 11 to 15 141590 -1.0825 0.139521 10 to 14 141943 0.1141 0.545435 9 to 13 141844 -0.2215 0.412368 8 to 12 141745 -0.5571 0.288746 7 to 11 142375 1.5785 0.942779 6 to 10 142175 0.9006 0.816093 5 to 9 141543 -1.2418 0.107156 4 to 8 142053 0.4870 0.686877 3 to 7 142166 0.8701 0.807868 2 to 6 141794 -0.3909 0.347917 1 to 5 141929 0.0667 0.526581 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-12_13:31 Bits used No. missing words z-score p-value 31 to 32 141287 -1.8358 0.033195 30 to 31 142179 0.7955 0.786835 29 to 30 141688 -0.6529 0.256913 28 to 29 142215 0.9017 0.816387 27 to 28 141806 -0.3048 0.380256 26 to 27 141583 -0.9626 0.167868 25 to 26 141517 -1.1573 0.123572 24 to 25 141845 -0.1898 0.424747 23 to 24 141948 0.1141 0.545409 22 to 23 142613 2.0757 0.981040 21 to 22 142338 1.2645 0.896977 20 to 21 142299 1.1495 0.874819 19 to 20 141472 -1.2901 0.098515 18 to 19 142451 1.5978 0.944961 17 to 18 141785 -0.3668 0.356901 16 to 17 142165 0.7542 0.774632 15 to 16 141968 0.1731 0.568701 14 to 15 142010 0.2970 0.616752 13 to 14 141857 -0.1544 0.438661 12 to 13 142295 1.1377 0.872371 11 to 12 142372 1.3648 0.913843 10 to 11 142141 0.6834 0.752821 9 to 10 141520 -1.1485 0.125388 8 to 9 141843 -0.1957 0.422437 7 to 8 141635 -0.8092 0.209191 6 to 7 142270 1.0639 0.856318 5 to 6 141975 0.1937 0.576801 4 to 5 141716 -0.5703 0.284239 3 to 4 141537 -1.0983 0.136033 2 to 3 141959 0.1465 0.558244 1 to 2 142563 1.9282 0.973087 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-12_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2601.12 1.430 0.923652 Test results for specific bytes for dh-ranFile-2018-04-12_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2445.54 -0.770 0.220600 2 to 9 2516.36 0.231 0.591460 3 to 10 2380.52 -1.690 0.045541 4 to 11 2526.24 0.371 0.644731 5 to 12 2484.65 -0.217 0.414077 6 to 13 2465.24 -0.492 0.311502 7 to 14 2441.79 -0.823 0.205209 8 to 15 2410.64 -1.264 0.103169 9 to 16 2487.01 -0.184 0.427114 10 to 17 2463.00 -0.523 0.300380 11 to 18 2499.64 -0.005 0.497990 12 to 19 2514.10 0.199 0.579054 13 to 20 2504.83 0.068 0.527233 14 to 21 2234.16 -3.760 0.000085 15 to 22 2456.66 -0.613 0.269971 16 to 23 2441.91 -0.822 0.205668 17 to 24 2387.78 -1.587 0.056246 18 to 25 2584.89 1.200 0.885022 19 to 26 2505.14 0.073 0.528964 20 to 27 2474.41 -0.362 0.358740 21 to 28 2490.74 -0.131 0.447911 22 to 29 2404.27 -1.354 0.087900 23 to 30 2484.08 -0.225 0.410907 24 to 31 2455.28 -0.632 0.263570 25 to 32 2584.36 1.193 0.883570 CDPARK for dh-ranFile-2018-04-12_13:31: 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 3509 -0.6393 0.261324 3543 0.9132 0.819442 3527 0.1826 0.572463 3515 -0.3653 0.357445 3523 0.0000 0.500000 3497 -1.1872 0.117571 3497 -1.1872 0.117571 3558 1.5982 0.944998 3560 1.6895 0.954438 3487 -1.6438 0.050105 Square side=100, avg. no. parked=3521.60 sample std.=24.29 p-value of the KSTEST for those 10 p-values: 0.767264 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-12_13:31 0.1394,0.2672,0.4294,0.8821,0.1829,0.2314,0.3628,0.7686,0.4479,0.4859, The KS test for those 10 p-values: 0.448442 The 3DSPHERES test for dh-ranFile-2018-04-12_13:31 sample no r^3 equiv. uni. 1 0.471 0.015584 2 1.432 0.046609 3 16.316 0.419496 4 24.656 0.560389 5 53.585 0.832399 6 114.922 0.978306 7 73.796 0.914553 8 5.585 0.169876 9 8.788 0.253923 10 2.823 0.089808 11 14.576 0.384843 12 5.399 0.164699 13 31.237 0.646976 14 34.949 0.688067 15 36.287 0.701674 16 33.189 0.669218 17 8.546 0.247884 18 92.527 0.954235 19 12.640 0.343837 20 0.713 0.023486 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.590139 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-12_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 -1.8 -0.4 -0.9 -2.1 -0.4 2.6 -0.7 -0.7 -0.7 1.0 2.2 0.9 -0.8 -0.6 -0.5 -0.4 -1.2 -0.2 1.5 0.7 0.4 0.0 0.3 -1.1 -0.5 -0.8 0.7 -1.1 0.6 0.3 -1.1 -3.1 -1.2 1.1 0.5 0.8 2.1 -1.3 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:57.347835 z-score=1.674586, p-value=0.942516 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-12_13:31 Test no p-value 1 0.280077 2 0.181327 3 0.137865 4 0.865026 5 0.005025 6 0.712604 7 0.371096 8 0.326305 9 0.000077 10 0.969337 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.062745 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-12_13:31: (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 66694 0.01 66765 0.15 3 25000.00 24965 0.05 24830 1.16 4 6666.67 6625 0.26 6749 1.02 5 1388.89 1440 1.88 1383 0.02 6 238.10 228 0.43 228 0.43 7 34.72 42 1.53 38 0.31 8 4.96 5 0.00 6 0.22 p=0.34446 p=0.22947 Number of rngs required: 687611, p-value: 0.180 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-12_13:31 No. of wins: Observed Expected 98943 98585.9 z-score= 1.597, pvalue=0.94491 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66722 66666.7 0.046 0.046 2 37858 37654.3 1.102 1.148 3 26820 26954.7 0.673 1.821 4 19320 19313.5 0.002 1.823 5 13820 13851.4 0.071 1.895 6 10048 9943.5 1.097 2.992 7 6990 7145.0 3.364 6.356 8 5172 5139.1 0.211 6.566 9 3711 3699.9 0.034 6.600 10 2614 2666.3 1.026 7.626 11 1945 1923.3 0.244 7.870 12 1399 1388.7 0.076 7.946 13 998 1003.7 0.033 7.978 14 732 726.1 0.047 8.026 15 498 525.8 1.474 9.499 16 370 381.2 0.326 9.825 17 282 276.5 0.108 9.933 18 184 200.8 1.410 11.344 19 122 146.0 3.940 15.284 20 116 106.2 0.901 16.185 21 279 287.1 0.229 16.415 Chisq= 16.41 for 20 degrees of freedom, p= 0.30941 SUMMARY of craptest p-value for no. of wins: 0.944906 p-value for throws/game: 0.309414 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-12_13:31 No. of wins: Observed Expected 98689 98585.9 z-score= 0.461, pvalue=0.67771 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66658 66666.7 0.001 0.001 2 37556 37654.3 0.257 0.258 3 26948 26954.7 0.002 0.260 4 19346 19313.5 0.055 0.314 5 13929 13851.4 0.435 0.749 6 9862 9943.5 0.669 1.418 7 7187 7145.0 0.247 1.664 8 5111 5139.1 0.153 1.818 9 3819 3699.9 3.836 5.654 10 2612 2666.3 1.106 6.759 11 2011 1923.3 3.996 10.756 12 1326 1388.7 2.834 13.590 13 1036 1003.7 1.038 14.629 14 743 726.1 0.391 15.020 15 548 525.8 0.934 15.954 16 366 381.2 0.602 16.556 17 253 276.5 2.004 18.560 18 185 200.8 1.248 19.808 19 143 146.0 0.061 19.869 20 100 106.2 0.364 20.233 21 261 287.1 2.375 22.608 Chisq= 22.61 for 20 degrees of freedom, p= 0.69154 SUMMARY of craptest p-value for no. of wins: 0.677711 p-value for throws/game: 0.691540 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0001,0.0042,0.0050,0.0156,0.0196,0.0235,0.0332,0.0342,0.0455, 0.0466,0.0477,0.0501,0.0556,0.0562,0.0627,0.0714,0.0720,0.0779,0.0879, 0.0898,0.0918,0.0937,0.0985,0.1032,0.1072,0.1141,0.1176,0.1176,0.1221, 0.1236,0.1238,0.1254,0.1360,0.1379,0.1394,0.1395,0.1395,0.1510,0.1540, 0.1557,0.1643,0.1647,0.1651,0.1679,0.1699,0.1797,0.1810,0.1813,0.1829, 0.1917,0.1962,0.1971,0.2052,0.2057,0.2092,0.2120,0.2143,0.2155,0.2185, 0.2206,0.2208,0.2295,0.2314,0.2320,0.2395,0.2428,0.2453,0.2479,0.2529, 0.2539,0.2540,0.2569,0.2613,0.2623,0.2636,0.2653,0.2672,0.2692,0.2700, 0.2801,0.2842,0.2887,0.2969,0.3004,0.3056,0.3094,0.3111,0.3115,0.3164, 0.3167,0.3178,0.3222,0.3224,0.3263,0.3351,0.3411,0.3416,0.3420,0.3438, 0.3445,0.3477,0.3479,0.3569,0.3574,0.3587,0.3628,0.3632,0.3647,0.3688, 0.3711,0.3738,0.3770,0.3787,0.3803,0.3848,0.3884,0.3902,0.3921,0.3949, 0.4050,0.4109,0.4124,0.4138,0.4141,0.4155,0.4176,0.4195,0.4224,0.4247, 0.4255,0.4271,0.4294,0.4345,0.4387,0.4387,0.4479,0.4479,0.4484,0.4680, 0.4703,0.4766,0.4775,0.4817,0.4859,0.4894,0.4905,0.4980,0.5000,0.5055, 0.5058,0.5061,0.5266,0.5272,0.5275,0.5290,0.5325,0.5330,0.5353,0.5421, 0.5454,0.5454,0.5568,0.5571,0.5582,0.5604,0.5629,0.5635,0.5636,0.5683, 0.5687,0.5725,0.5768,0.5791,0.5901,0.5915,0.5985,0.6003,0.6012,0.6021, 0.6062,0.6068,0.6135,0.6159,0.6168,0.6253,0.6386,0.6437,0.6447,0.6470, 0.6692,0.6777,0.6850,0.6864,0.6869,0.6881,0.6915,0.7017,0.7053,0.7126, 0.7253,0.7261,0.7492,0.7505,0.7528,0.7533,0.7561,0.7574,0.7582,0.7582, 0.7673,0.7686,0.7723,0.7746,0.7782,0.7789,0.7868,0.7917,0.8025,0.8079, 0.8125,0.8134,0.8161,0.8164,0.8194,0.8217,0.8219,0.8324,0.8387,0.8406, 0.8515,0.8563,0.8650,0.8681,0.8724,0.8748,0.8771,0.8785,0.8821,0.8836, 0.8850,0.8858,0.8862,0.8954,0.8970,0.8998,0.9033,0.9138,0.9146,0.9165, 0.9203,0.9222,0.9237,0.9264,0.9425,0.9428,0.9449,0.9450,0.9450,0.9505, 0.9542,0.9544,0.9639,0.9693,0.9731,0.9783,0.9810,0.9860,0.9893, Overall p-value after applying KStest on 269 p-values = 0.202898 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.