RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-01_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 13.8921 0.325276 2 to 25 15.53 29.5808 0.970469 3 to 26 15.74 13.2467 0.280480 4 to 27 15.77 12.5294 0.232925 5 to 28 15.72 24.8795 0.902561 6 to 29 15.76 28.9502 0.965012 7 to 30 15.33 32.5365 0.987104 8 to 31 15.86 13.5419 0.300778 9 to 32 15.75 8.8957 0.056523 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.090784 Tough bday spacings test for dh-ranFile-2018-04-01_08:31: 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 17 43 74 95 99 75 46 28 16 2 5 (O-E)^2/E 6.7 1.1 0.0 0.1 0.0 0.1 0.7 0.1 0.1 3.2 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.386, p= 0.740 RESULTS OF GCD FOR dh-ranFile-2018-04-01_08:31 Euclid's algorithm: p-value, steps to gcd: 0.300190 p-value, dist. of gcd's: 0.400971 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-01_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.080 0.741 0.583 0.449 0.217 0.308 0.109 0.247 Bits 8 to 15---> 0.752 0.609 0.003 0.716 0.115 0.278 0.569 0.141 Bits 16 to 23---> 0.779 0.810 0.621 0.752 0.970 0.132 0.162 0.908 Bits 24 to 31---> 0.470 0.188 0.300 0.584 0.645 0.640 0.110 0.851 KS test for the above 32 p values: 0.408 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-01_08:31, p-values for 5 runs: 0.6195, 0.9462, 0.7689, 0.7759, 0.3242 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-01_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5090 5134.0 0.377 1.502 r= 30 22997 23103.0 0.487 1.988 r= 31 11717 11551.5 2.370 4.359 chi-square = 4.359 with df = 3; p-value = 0.775 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-01_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 191 211.4 1.972 1.972 r= 30 5197 5134.0 0.773 2.745 r= 31 23166 23103.0 0.172 2.916 r= 32 11446 11551.5 0.964 3.880 chi-square = 3.880 with df = 3; p-value = 0.725 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-01_08:31 b-rank test for bits 1 to 8, p=0.96093 b-rank test for bits 2 to 9, p=0.80329 b-rank test for bits 3 to 10, p=0.03669 b-rank test for bits 4 to 11, p=0.82427 b-rank test for bits 5 to 12, p=0.95094 b-rank test for bits 6 to 13, p=0.07651 b-rank test for bits 7 to 14, p=0.60134 b-rank test for bits 8 to 15, p=0.82098 b-rank test for bits 9 to 16, p=0.46130 b-rank test for bits 10 to 17, p=0.29306 b-rank test for bits 11 to 18, p=0.52197 b-rank test for bits 12 to 19, p=0.72051 b-rank test for bits 13 to 20, p=0.98792 b-rank test for bits 14 to 21, p=0.95032 b-rank test for bits 15 to 22, p=0.28980 b-rank test for bits 16 to 23, p=0.77084 b-rank test for bits 17 to 24, p=0.82505 b-rank test for bits 18 to 25, p=0.98650 b-rank test for bits 19 to 26, p=0.12949 b-rank test for bits 20 to 27, p=0.08411 b-rank test for bits 21 to 28, p=0.37391 b-rank test for bits 22 to 29, p=0.20221 b-rank test for bits 23 to 30, p=0.03823 b-rank test for bits 24 to 31, p=0.46677 b-rank test for bits 25 to 32, p=0.19165 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 = 0.289082 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-01_08:31 (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 141522 -0.90 0.182739 2 142606 1.63 0.948209 3 142095 0.43 0.667786 4 141310 -1.40 0.080711 5 141959 0.12 0.546194 6 141807 -0.24 0.405518 7 141344 -1.32 0.093273 8 141512 -0.93 0.176615 9 141658 -0.59 0.278528 10 141484 -0.99 0.160169 11 141702 -0.48 0.314045 12 142046 0.32 0.625259 13 142133 0.52 0.699371 14 142179 0.63 0.735676 15 142601 1.62 0.946958 16 140899 -2.36 0.009123 17 141227 -1.59 0.055442 18 141614 -0.69 0.245090 19 141921 0.03 0.510876 20 142249 0.79 0.786292 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-01_08:31 Bits used No. missing words z-score p-value 23 to 32 142285 1.2954 0.902411 22 to 31 141629 -0.9667 0.166858 21 to 30 141736 -0.5977 0.275024 20 to 29 141924 0.0506 0.520172 19 to 28 142732 2.8368 0.997722 18 to 27 142145 0.8127 0.791792 17 to 26 142098 0.6506 0.742343 16 to 25 142255 1.1920 0.883363 15 to 24 142220 1.0713 0.857977 14 to 23 141794 -0.3977 0.345430 13 to 22 141998 0.3058 0.620106 12 to 21 142040 0.4506 0.673856 11 to 20 141905 -0.0149 0.494044 10 to 19 142076 0.5747 0.717261 9 to 18 142274 1.2575 0.895711 8 to 17 141998 0.3058 0.620106 7 to 16 142497 2.0264 0.978641 6 to 15 141873 -0.1253 0.450153 5 to 14 141442 -1.6115 0.053537 4 to 13 141295 -2.1184 0.017071 3 to 12 141664 -0.8460 0.198786 2 to 11 141766 -0.4942 0.310568 1 to 10 141303 -2.0908 0.018273 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-01_08:31 Bits used No. missing words z-score p-value 28 to 32 142030 0.4091 0.658749 27 to 31 142029 0.4057 0.657504 26 to 30 142123 0.7243 0.765561 25 to 29 142043 0.4531 0.674768 24 to 28 141612 -1.0079 0.156752 23 to 27 141877 -0.1096 0.456366 22 to 26 141934 0.0836 0.533324 21 to 25 141825 -0.2859 0.387491 20 to 24 141586 -1.0960 0.136532 19 to 23 142205 1.0023 0.841894 18 to 22 141717 -0.6520 0.257212 17 to 21 141853 -0.1909 0.424283 16 to 20 142461 1.8701 0.969263 15 to 19 141916 0.0226 0.509019 14 to 18 141577 -1.1265 0.129968 13 to 17 141596 -1.0621 0.144087 12 to 16 141269 -2.1706 0.014980 11 to 15 142227 1.0768 0.859226 10 to 14 142225 1.0701 0.857706 9 to 13 141643 -0.9028 0.183312 8 to 12 142119 0.7107 0.761379 7 to 11 141961 0.1752 0.569520 6 to 10 141665 -0.8282 0.203768 5 to 9 141742 -0.5672 0.285282 4 to 8 141903 -0.0215 0.491440 3 to 7 142027 0.3989 0.655010 2 to 6 142110 0.6802 0.751823 1 to 5 141762 -0.4994 0.308741 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-01_08:31 Bits used No. missing words z-score p-value 31 to 32 142157 0.7306 0.767485 30 to 31 142189 0.8250 0.795310 29 to 30 142548 1.8840 0.970216 28 to 29 141895 -0.0423 0.483141 27 to 28 142049 0.4120 0.659832 26 to 27 141528 -1.1249 0.130323 25 to 26 141858 -0.1514 0.439824 24 to 25 142086 0.5212 0.698869 23 to 24 141755 -0.4553 0.324464 22 to 23 142411 1.4799 0.930544 21 to 22 141914 0.0138 0.505496 20 to 21 141852 -0.1691 0.432853 19 to 20 141526 -1.1308 0.129077 18 to 19 141208 -2.0688 0.019281 17 to 18 142147 0.7011 0.758377 16 to 17 141283 -1.8476 0.032331 15 to 16 141763 -0.4317 0.332997 14 to 15 141650 -0.7650 0.222140 13 to 14 142108 0.5860 0.721078 12 to 13 141843 -0.1957 0.422437 11 to 12 141652 -0.7591 0.223901 10 to 11 142079 0.5005 0.691639 9 to 10 141627 -0.8328 0.202470 8 to 9 141633 -0.8151 0.207498 7 to 8 142009 0.2940 0.615626 6 to 7 141933 0.0698 0.527833 5 to 6 142033 0.3648 0.642373 4 to 5 142234 0.9577 0.830900 3 to 4 141838 -0.2104 0.416673 2 to 3 142146 0.6981 0.757456 1 to 2 142085 0.5182 0.697841 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-01_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2454.59 -0.642 0.260351 Test results for specific bytes for dh-ranFile-2018-04-01_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2444.07 -0.791 0.214485 2 to 9 2455.93 -0.623 0.266572 3 to 10 2586.69 1.226 0.889894 4 to 11 2503.35 0.047 0.518868 5 to 12 2417.23 -1.171 0.120882 6 to 13 2485.45 -0.206 0.418472 7 to 14 2504.99 0.071 0.528113 8 to 15 2404.45 -1.351 0.088311 9 to 16 2485.67 -0.203 0.419698 10 to 17 2576.06 1.076 0.858967 11 to 18 2423.38 -1.084 0.139268 12 to 19 2528.44 0.402 0.656238 13 to 20 2594.39 1.335 0.909051 14 to 21 2439.86 -0.850 0.197537 15 to 22 2525.03 0.354 0.638346 16 to 23 2484.74 -0.216 0.414546 17 to 24 2451.96 -0.679 0.248462 18 to 25 2543.66 0.617 0.731534 19 to 26 2374.44 -1.776 0.037895 20 to 27 2571.56 1.012 0.844242 21 to 28 2511.94 0.169 0.567063 22 to 29 2505.23 0.074 0.529478 23 to 30 2502.33 0.033 0.513119 24 to 31 2437.26 -0.887 0.187449 25 to 32 2439.72 -0.853 0.196955 CDPARK for dh-ranFile-2018-04-01_08:31: 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 3494 -1.3242 0.092718 3508 -0.6849 0.246694 3521 -0.0913 0.463617 3523 0.0000 0.500000 3541 0.8219 0.794438 3495 -1.2785 0.100530 3512 -0.5023 0.307734 3496 -1.2329 0.108811 3479 -2.0091 0.022262 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3509.10 sample std.=17.42 p-value of the KSTEST for those 10 p-values: 0.059319 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-01_08:31 0.5473,0.7580,0.9492,0.2397,0.8615,0.0490,0.9055,0.2127,0.9423,0.7830, The KS test for those 10 p-values: 0.162760 The 3DSPHERES test for dh-ranFile-2018-04-01_08:31 sample no r^3 equiv. uni. 1 37.413 0.712659 2 26.639 0.588515 3 27.144 0.595374 4 3.908 0.122126 5 17.464 0.441286 6 14.382 0.380842 7 11.766 0.324437 8 2.164 0.069588 9 6.436 0.193090 10 22.402 0.526090 11 2.626 0.083802 12 21.759 0.515819 13 2.065 0.066530 14 22.713 0.530974 15 167.795 0.996277 16 34.972 0.688302 17 30.315 0.635968 18 10.159 0.287262 19 36.873 0.707449 20 17.538 0.442672 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.374973 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-01_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 -1.1 0.2 -0.3 -0.6 0.1 -0.6 1.0 0.4 -1.2 -0.1 -0.4 -1.8 -0.9 0.4 0.8 -0.7 1.8 -0.6 1.3 -1.6 0.4 0.9 0.6 -0.2 0.8 0.7 -0.7 1.1 -0.0 0.1 0.1 -1.1 1.0 -0.3 0.3 -1.7 -2.0 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:34.046424 z-score=-0.867806, p-value=0.196128 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-01_08:31 Test no p-value 1 0.202840 2 0.431992 3 0.013995 4 0.011992 5 0.104205 6 0.005350 7 0.014324 8 0.122991 9 0.002666 10 0.184798 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000000 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-01_08:31: (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 66752 0.11 66604 0.06 3 25000.00 24918 0.27 25082 0.27 4 6666.67 6682 0.04 6722 0.46 5 1388.89 1356 0.78 1321 3.32 6 238.10 239 0.00 238 0.00 7 34.72 47 4.34 29 0.94 8 4.96 5 0.00 3 0.77 p=0.52328 p=0.55664 Number of rngs required: 689021, p-value: 0.762 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-01_08:31 No. of wins: Observed Expected 98517 98585.9 z-score=-0.308, pvalue=0.37905 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66821 66666.7 0.357 0.357 2 37642 37654.3 0.004 0.361 3 26823 26954.7 0.644 1.005 4 19005 19313.5 4.927 5.932 5 13967 13851.4 0.964 6.896 6 9944 9943.5 0.000 6.896 7 7189 7145.0 0.271 7.167 8 5046 5139.1 1.686 8.852 9 3795 3699.9 2.446 11.299 10 2715 2666.3 0.890 12.188 11 1939 1923.3 0.128 12.316 12 1403 1388.7 0.146 12.462 13 1006 1003.7 0.005 12.467 14 755 726.1 1.147 13.614 15 542 525.8 0.497 14.111 16 371 381.2 0.270 14.382 17 290 276.5 0.655 15.037 18 185 200.8 1.248 16.285 19 149 146.0 0.062 16.347 20 98 106.2 0.635 16.982 21 315 287.1 2.708 19.691 Chisq= 19.69 for 20 degrees of freedom, p= 0.52258 SUMMARY of craptest p-value for no. of wins: 0.379050 p-value for throws/game: 0.522582 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-01_08:31 No. of wins: Observed Expected 99039 98585.9 z-score= 2.027, pvalue=0.97865 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66840 66666.7 0.451 0.451 2 37707 37654.3 0.074 0.524 3 27065 26954.7 0.451 0.975 4 19163 19313.5 1.172 2.148 5 13615 13851.4 4.035 6.183 6 9853 9943.5 0.824 7.007 7 7305 7145.0 3.582 10.589 8 5140 5139.1 0.000 10.589 9 3767 3699.9 1.218 11.807 10 2590 2666.3 2.183 13.991 11 1924 1923.3 0.000 13.991 12 1416 1388.7 0.535 14.526 13 1016 1003.7 0.150 14.676 14 709 726.1 0.405 15.081 15 518 525.8 0.117 15.198 16 378 381.2 0.026 15.224 17 277 276.5 0.001 15.225 18 194 200.8 0.232 15.457 19 129 146.0 1.976 17.433 20 119 106.2 1.539 18.972 21 275 287.1 0.511 19.483 Chisq= 19.48 for 20 degrees of freedom, p= 0.50934 SUMMARY of craptest p-value for no. of wins: 0.978654 p-value for throws/game: 0.509336 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0027,0.0029,0.0054,0.0091,0.0120,0.0140,0.0143,0.0150,0.0171, 0.0183,0.0193,0.0223,0.0323,0.0367,0.0379,0.0382,0.0490,0.0535,0.0554, 0.0565,0.0593,0.0665,0.0696,0.0765,0.0799,0.0807,0.0838,0.0841,0.0883, 0.0908,0.0927,0.0933,0.1005,0.1042,0.1088,0.1093,0.1100,0.1152,0.1209, 0.1221,0.1230,0.1291,0.1295,0.1300,0.1303,0.1317,0.1365,0.1393,0.1406, 0.1441,0.1568,0.1602,0.1623,0.1628,0.1669,0.1766,0.1827,0.1833,0.1848, 0.1874,0.1884,0.1916,0.1931,0.1961,0.1970,0.1975,0.1988,0.2022,0.2025, 0.2028,0.2038,0.2075,0.2127,0.2145,0.2169,0.2221,0.2239,0.2329,0.2397, 0.2451,0.2467,0.2475,0.2485,0.2572,0.2604,0.2666,0.2750,0.2784,0.2785, 0.2805,0.2853,0.2873,0.2891,0.2898,0.2931,0.2997,0.3002,0.3008,0.3077, 0.3085,0.3087,0.3106,0.3140,0.3242,0.3244,0.3245,0.3253,0.3330,0.3454, 0.3739,0.3750,0.3791,0.3808,0.3875,0.4010,0.4055,0.4079,0.4145,0.4167, 0.4185,0.4197,0.4224,0.4243,0.4320,0.4329,0.4398,0.4413,0.4427,0.4494, 0.4502,0.4564,0.4613,0.4636,0.4668,0.4696,0.4818,0.4831,0.4914,0.4940, 0.5000,0.5055,0.5090,0.5093,0.5109,0.5131,0.5158,0.5189,0.5202,0.5220, 0.5226,0.5233,0.5261,0.5278,0.5281,0.5295,0.5310,0.5333,0.5462,0.5473, 0.5566,0.5671,0.5689,0.5695,0.5829,0.5844,0.5885,0.5954,0.6013,0.6090, 0.6156,0.6195,0.6201,0.6201,0.6212,0.6253,0.6360,0.6383,0.6399,0.6424, 0.6453,0.6550,0.6562,0.6575,0.6587,0.6598,0.6678,0.6739,0.6748,0.6883, 0.6916,0.6978,0.6989,0.6994,0.7074,0.7127,0.7157,0.7173,0.7205,0.7211, 0.7253,0.7315,0.7357,0.7399,0.7413,0.7423,0.7516,0.7518,0.7520,0.7575, 0.7580,0.7584,0.7614,0.7622,0.7656,0.7675,0.7689,0.7708,0.7748,0.7759, 0.7789,0.7830,0.7863,0.7918,0.7944,0.7953,0.8033,0.8104,0.8210,0.8243, 0.8251,0.8309,0.8419,0.8442,0.8511,0.8577,0.8580,0.8590,0.8592,0.8615, 0.8834,0.8899,0.8957,0.9024,0.9026,0.9055,0.9083,0.9091,0.9305,0.9423, 0.9462,0.9470,0.9482,0.9492,0.9503,0.9509,0.9609,0.9650,0.9693,0.9700, 0.9702,0.9705,0.9786,0.9787,0.9865,0.9871,0.9879,0.9963,0.9977, Overall p-value after applying KStest on 269 p-values = 0.091571 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.