RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-16_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 17.1657 0.556805 2 to 25 15.67 19.7796 0.714340 3 to 26 15.81 25.3522 0.912900 4 to 27 15.50 17.3896 0.571712 5 to 28 15.85 14.5984 0.375617 6 to 29 16.13 30.9301 0.979633 7 to 30 16.14 21.7800 0.806672 8 to 31 15.96 13.0827 0.269367 9 to 32 16.00 8.3616 0.041809 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.725398 Tough bday spacings test for dh-ranFile-2018-04-16_22:31: 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 12 32 71 101 98 83 41 32 17 5 8 (O-E)^2/E 0.9 0.6 0.1 0.1 0.0 0.3 2.4 0.2 0.3 0.4 3.8 Birthday Spacings: Sum(O-E)^2/E= 8.985, p= 0.466 RESULTS OF GCD FOR dh-ranFile-2018-04-16_22:31 Euclid's algorithm: p-value, steps to gcd: 0.432612 p-value, dist. of gcd's: 0.401786 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-16_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.725 0.268 0.282 0.055 0.694 0.055 0.059 0.530 Bits 8 to 15---> 0.296 0.043 0.170 0.688 0.169 0.226 0.191 0.861 Bits 16 to 23---> 0.270 0.180 0.867 0.028 0.937 0.492 0.673 0.772 Bits 24 to 31---> 0.843 0.338 0.684 0.031 0.061 0.124 0.819 0.641 KS test for the above 32 p values: 0.947 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-16_22:31, p-values for 5 runs: 0.3918, 0.4229, 0.6508, 0.6025, 0.7978 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-16_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5069 5134.0 0.823 0.878 r= 30 23059 23103.0 0.084 0.962 r= 31 11664 11551.5 1.095 2.058 chi-square = 2.058 with df = 3; p-value = 0.439 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-16_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5167 5134.0 0.212 0.224 r= 31 22988 23103.0 0.573 0.797 r= 32 11632 11551.5 0.561 1.357 chi-square = 1.357 with df = 3; p-value = 0.284 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-16_22:31 b-rank test for bits 1 to 8, p=0.60150 b-rank test for bits 2 to 9, p=0.42032 b-rank test for bits 3 to 10, p=0.02557 b-rank test for bits 4 to 11, p=0.82652 b-rank test for bits 5 to 12, p=0.62717 b-rank test for bits 6 to 13, p=0.98919 b-rank test for bits 7 to 14, p=0.89110 b-rank test for bits 8 to 15, p=0.81035 b-rank test for bits 9 to 16, p=0.97459 b-rank test for bits 10 to 17, p=0.57325 b-rank test for bits 11 to 18, p=0.88948 b-rank test for bits 12 to 19, p=0.74669 b-rank test for bits 13 to 20, p=0.07428 b-rank test for bits 14 to 21, p=0.29215 b-rank test for bits 15 to 22, p=0.06435 b-rank test for bits 16 to 23, p=0.86586 b-rank test for bits 17 to 24, p=0.85447 b-rank test for bits 18 to 25, p=0.18335 b-rank test for bits 19 to 26, p=0.76532 b-rank test for bits 20 to 27, p=0.90934 b-rank test for bits 21 to 28, p=0.48540 b-rank test for bits 22 to 29, p=0.66716 b-rank test for bits 23 to 30, p=0.63921 b-rank test for bits 24 to 31, p=0.79335 b-rank test for bits 25 to 32, p=0.74395 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 = 0.027871 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-16_22:31 (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 142197 0.67 0.749248 2 142189 0.65 0.743262 3 141308 -1.40 0.080014 4 142221 0.73 0.766755 5 141452 -1.07 0.142641 6 141526 -0.90 0.185225 7 141431 -1.12 0.131870 8 142933 2.39 0.991616 9 142215 0.71 0.762443 10 142034 0.29 0.614583 11 142047 0.32 0.626144 12 141097 -1.90 0.028850 13 141570 -0.79 0.213939 14 141283 -1.46 0.071681 15 142130 0.52 0.696928 16 142138 0.53 0.703425 17 142841 2.18 0.985252 18 141836 -0.17 0.431981 19 141461 -1.05 0.147435 20 141971 0.14 0.557285 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-16_22:31 Bits used No. missing words z-score p-value 23 to 32 141999 0.3092 0.621418 22 to 31 142138 0.7885 0.784803 21 to 30 142371 1.5920 0.944304 20 to 29 142053 0.4954 0.689846 19 to 28 141717 -0.6632 0.253599 18 to 27 141698 -0.7287 0.233085 17 to 26 141857 -0.1804 0.428400 16 to 25 141508 -1.3839 0.083195 15 to 24 141610 -1.0322 0.150996 14 to 23 142083 0.5989 0.725368 13 to 22 141873 -0.1253 0.450153 12 to 21 141839 -0.2425 0.404190 11 to 20 142001 0.3161 0.624038 10 to 19 142129 0.7575 0.775620 9 to 18 142090 0.6230 0.733358 8 to 17 142057 0.5092 0.694696 7 to 16 141850 -0.2046 0.418948 6 to 15 142370 1.5885 0.943915 5 to 14 141616 -1.0115 0.155893 4 to 13 142056 0.5058 0.693487 3 to 12 142359 1.5506 0.939500 2 to 11 142124 0.7402 0.770423 1 to 10 142329 1.4471 0.926071 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-16_22:31 Bits used No. missing words z-score p-value 28 to 32 142019 0.3718 0.644965 27 to 31 142228 1.0802 0.859982 26 to 30 141863 -0.1571 0.437602 25 to 29 141891 -0.0621 0.475227 24 to 28 141671 -0.8079 0.209575 23 to 27 141866 -0.1469 0.441613 22 to 26 142166 0.8701 0.807868 21 to 25 141572 -1.1435 0.126417 20 to 24 141812 -0.3299 0.370726 19 to 23 141424 -1.6452 0.049966 18 to 22 141828 -0.2757 0.391391 17 to 21 141727 -0.6181 0.268265 16 to 20 142036 0.4294 0.666180 15 to 19 142014 0.3548 0.638635 14 to 18 141523 -1.3096 0.095167 13 to 17 142024 0.3887 0.651255 12 to 16 141892 -0.0587 0.476577 11 to 15 141848 -0.2079 0.417654 10 to 14 141644 -0.8994 0.184214 9 to 13 142041 0.4463 0.672324 8 to 12 141736 -0.5876 0.278414 7 to 11 141920 0.0362 0.514426 6 to 10 142181 0.9209 0.821453 5 to 9 141073 -2.8350 0.002291 4 to 8 142256 1.1752 0.880033 3 to 7 141780 -0.4384 0.330546 2 to 6 141853 -0.1909 0.424283 1 to 5 141875 -0.1164 0.453679 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-16_22:31 Bits used No. missing words z-score p-value 31 to 32 142155 0.7247 0.765679 30 to 31 141434 -1.4022 0.080435 29 to 30 142211 0.8899 0.813235 28 to 29 141814 -0.2812 0.389275 27 to 28 141990 0.2380 0.594046 26 to 27 141799 -0.3255 0.372418 25 to 26 142098 0.5565 0.711082 24 to 25 141520 -1.1485 0.125388 23 to 24 141926 0.0492 0.519610 22 to 23 141985 0.2232 0.588316 21 to 22 142105 0.5772 0.718097 20 to 21 141407 -1.4818 0.069197 19 to 20 141895 -0.0423 0.483141 18 to 19 141651 -0.7620 0.223019 17 to 18 142541 1.8633 0.968792 16 to 17 141655 -0.7502 0.226556 15 to 16 141831 -0.2311 0.408633 14 to 15 141887 -0.0659 0.473741 13 to 14 142284 1.1052 0.865468 12 to 13 142448 1.5890 0.943969 11 to 12 141452 -1.3491 0.088660 10 to 11 141904 -0.0157 0.493728 9 to 10 142239 0.9725 0.834594 8 to 9 142142 0.6863 0.753751 7 to 8 142007 0.2881 0.613370 6 to 7 142132 0.6568 0.744359 5 to 6 142166 0.7571 0.775517 4 to 5 142036 0.3737 0.645671 3 to 4 141873 -0.1072 0.457328 2 to 3 142049 0.4120 0.659832 1 to 2 141821 -0.2606 0.397216 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-16_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2453.33 -0.660 0.254639 Test results for specific bytes for dh-ranFile-2018-04-16_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2482.13 -0.253 0.400254 2 to 9 2488.22 -0.167 0.433866 3 to 10 2332.40 -2.370 0.008887 4 to 11 2454.65 -0.641 0.260631 5 to 12 2527.52 0.389 0.651408 6 to 13 2570.19 0.993 0.839568 7 to 14 2487.05 -0.183 0.427332 8 to 15 2508.31 0.118 0.546791 9 to 16 2497.94 -0.029 0.488389 10 to 17 2445.25 -0.774 0.219365 11 to 18 2443.79 -0.795 0.213343 12 to 19 2420.20 -1.128 0.129558 13 to 20 2647.97 2.093 0.981810 14 to 21 2485.12 -0.210 0.416684 15 to 22 2612.19 1.587 0.943697 16 to 23 2580.40 1.137 0.872243 17 to 24 2489.53 -0.148 0.441135 18 to 25 2549.65 0.702 0.758718 19 to 26 2574.38 1.052 0.853584 20 to 27 2440.30 -0.844 0.199237 21 to 28 2453.28 -0.661 0.254395 22 to 29 2590.56 1.281 0.899855 23 to 30 2499.76 -0.003 0.498646 24 to 31 2557.17 0.808 0.790584 25 to 32 2603.69 1.466 0.928732 CDPARK for dh-ranFile-2018-04-16_22:31: 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 3515 -0.3653 0.357445 3534 0.5023 0.692266 3547 1.0959 0.863437 3524 0.0457 0.518210 3537 0.6393 0.738676 3535 0.5479 0.708135 3547 1.0959 0.863437 3509 -0.6393 0.261324 3554 1.4155 0.921543 3554 1.4155 0.921543 Square side=100, avg. no. parked=3535.60 sample std.=14.86 p-value of the KSTEST for those 10 p-values: 0.063018 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-16_22:31 0.4679,0.7296,0.7180,0.6225,0.5705,0.7607,0.1569,0.2774,0.6200,0.2087, The KS test for those 10 p-values: 0.551985 The 3DSPHERES test for dh-ranFile-2018-04-16_22:31 sample no r^3 equiv. uni. 1 3.782 0.118442 2 85.629 0.942403 3 20.919 0.502075 4 74.823 0.917428 5 62.906 0.877159 6 75.243 0.918577 7 6.587 0.197135 8 8.035 0.234971 9 3.955 0.123520 10 3.949 0.123325 11 34.264 0.680861 12 9.179 0.263597 13 6.467 0.193914 14 79.964 0.930432 15 21.659 0.514196 16 21.636 0.513834 17 13.865 0.370084 18 22.613 0.529414 19 2.022 0.065185 20 17.399 0.440091 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.593629 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-16_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 1.3 -1.1 1.8 0.2 0.0 -0.3 -0.5 0.3 -1.0 -1.5 0.6 -0.8 0.5 0.0 -1.4 1.6 -0.3 2.1 -0.6 0.3 0.0 -1.0 0.4 0.4 0.1 -0.4 0.7 -0.7 -1.8 0.1 1.4 0.7 0.1 -0.8 1.4 -1.0 0.9 -0.1 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:37.081146 z-score=-0.536691, p-value=0.313608 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-16_22:31 Test no p-value 1 0.002975 2 0.291266 3 0.047665 4 0.385236 5 0.260752 6 0.946692 7 0.922258 8 0.543241 9 0.633017 10 0.200298 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.437984 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-16_22:31: (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 66814 0.33 66673 0.00 3 25000.00 24780 1.94 24994 0.00 4 6666.67 6759 1.28 6596 0.75 5 1388.89 1376 0.12 1443 2.11 6 238.10 237 0.01 254 1.06 7 34.72 30 0.64 36 0.05 8 4.96 3 0.77 3 0.77 p=0.46655 p=0.42288 Number of rngs required: 687698, p-value: 0.208 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-16_22:31 No. of wins: Observed Expected 98522 98585.9 z-score=-0.286, pvalue=0.38759 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66705 66666.7 0.022 0.022 2 37863 37654.3 1.156 1.179 3 26827 26954.7 0.605 1.784 4 19260 19313.5 0.148 1.932 5 13711 13851.4 1.424 3.355 6 9931 9943.5 0.016 3.371 7 7240 7145.0 1.262 4.634 8 5134 5139.1 0.005 4.639 9 3704 3699.9 0.005 4.643 10 2694 2666.3 0.288 4.931 11 1919 1923.3 0.010 4.941 12 1408 1388.7 0.267 5.208 13 1005 1003.7 0.002 5.210 14 748 726.1 0.658 5.868 15 502 525.8 1.080 6.948 16 374 381.2 0.134 7.082 17 261 276.5 0.873 7.955 18 189 200.8 0.697 8.652 19 135 146.0 0.827 9.479 20 108 106.2 0.030 9.509 21 282 287.1 0.091 9.600 Chisq= 9.60 for 20 degrees of freedom, p= 0.02514 SUMMARY of craptest p-value for no. of wins: 0.387587 p-value for throws/game: 0.025139 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-16_22:31 No. of wins: Observed Expected 98978 98585.9 z-score= 1.754, pvalue=0.96027 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67076 66666.7 2.513 2.513 2 37434 37654.3 1.289 3.802 3 26817 26954.7 0.704 4.506 4 19177 19313.5 0.964 5.470 5 14028 13851.4 2.251 7.721 6 9940 9943.5 0.001 7.723 7 7201 7145.0 0.439 8.161 8 5102 5139.1 0.267 8.429 9 3729 3699.9 0.229 8.658 10 2599 2666.3 1.699 10.357 11 1864 1923.3 1.830 12.187 12 1410 1388.7 0.325 12.512 13 947 1003.7 3.205 15.717 14 718 726.1 0.091 15.808 15 557 525.8 1.847 17.655 16 391 381.2 0.255 17.910 17 295 276.5 1.232 19.142 18 190 200.8 0.584 19.726 19 148 146.0 0.028 19.754 20 94 106.2 1.405 21.159 21 283 287.1 0.059 21.218 Chisq= 21.22 for 20 degrees of freedom, p= 0.61558 SUMMARY of craptest p-value for no. of wins: 0.960275 p-value for throws/game: 0.615578 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0030,0.0089,0.0251,0.0256,0.0279,0.0281,0.0289,0.0307,0.0418, 0.0431,0.0477,0.0500,0.0551,0.0555,0.0591,0.0610,0.0630,0.0644,0.0652, 0.0692,0.0717,0.0743,0.0800,0.0804,0.0832,0.0887,0.0952,0.1184,0.1233, 0.1235,0.1236,0.1254,0.1264,0.1296,0.1319,0.1426,0.1474,0.1510,0.1559, 0.1569,0.1694,0.1704,0.1799,0.1833,0.1842,0.1852,0.1908,0.1939,0.1971, 0.1992,0.2003,0.2076,0.2087,0.2096,0.2133,0.2139,0.2194,0.2230,0.2257, 0.2266,0.2331,0.2350,0.2536,0.2544,0.2546,0.2606,0.2608,0.2613,0.2636, 0.2681,0.2683,0.2694,0.2698,0.2774,0.2784,0.2821,0.2844,0.2913,0.2922, 0.2955,0.3136,0.3305,0.3375,0.3574,0.3701,0.3707,0.3724,0.3756,0.3852, 0.3876,0.3893,0.3914,0.3918,0.3972,0.4003,0.4018,0.4042,0.4086,0.4167, 0.4177,0.4189,0.4203,0.4229,0.4229,0.4243,0.4273,0.4284,0.4320,0.4326, 0.4339,0.4376,0.4380,0.4395,0.4401,0.4411,0.4416,0.4502,0.4537,0.4573, 0.4664,0.4666,0.4679,0.4737,0.4752,0.4766,0.4831,0.4854,0.4884,0.4922, 0.4937,0.4986,0.5021,0.5138,0.5142,0.5144,0.5182,0.5196,0.5294,0.5300, 0.5432,0.5468,0.5520,0.5568,0.5573,0.5705,0.5717,0.5732,0.5883,0.5936, 0.5940,0.6015,0.6025,0.6134,0.6146,0.6156,0.6200,0.6214,0.6225,0.6240, 0.6261,0.6272,0.6330,0.6386,0.6392,0.6410,0.6450,0.6457,0.6508,0.6513, 0.6514,0.6598,0.6662,0.6672,0.6723,0.6728,0.6809,0.6842,0.6881,0.6898, 0.6923,0.6935,0.6945,0.6947,0.6969,0.7034,0.7081,0.7111,0.7143,0.7180, 0.7181,0.7250,0.7254,0.7254,0.7296,0.7334,0.7387,0.7433,0.7439,0.7444, 0.7467,0.7492,0.7538,0.7587,0.7607,0.7624,0.7653,0.7657,0.7668,0.7704, 0.7721,0.7755,0.7756,0.7848,0.7906,0.7934,0.7978,0.8067,0.8079,0.8103, 0.8132,0.8195,0.8215,0.8265,0.8346,0.8396,0.8429,0.8536,0.8545,0.8600, 0.8611,0.8634,0.8634,0.8655,0.8659,0.8669,0.8722,0.8772,0.8800,0.8895, 0.8911,0.8999,0.9093,0.9129,0.9174,0.9186,0.9215,0.9215,0.9223,0.9261, 0.9287,0.9304,0.9373,0.9395,0.9424,0.9437,0.9439,0.9440,0.9443,0.9467, 0.9468,0.9603,0.9688,0.9746,0.9796,0.9818,0.9853,0.9892,0.9916, Overall p-value after applying KStest on 269 p-values = 0.730634 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.