RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-07_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.02 8.8711 0.055782 2 to 25 15.39 29.4030 0.969014 3 to 26 15.71 22.5420 0.835237 4 to 27 15.59 21.0572 0.776258 5 to 28 15.67 15.2971 0.425911 6 to 29 16.05 14.3735 0.359493 7 to 30 15.81 22.0103 0.815676 8 to 31 15.80 20.5574 0.753286 9 to 32 15.76 11.9428 0.196410 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.622400 Tough bday spacings test for dh-ranFile-2016-02-07_03:31: 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 27 86 96 92 90 42 31 14 8 5 (O-E)^2/E 0.0 2.5 2.2 0.0 0.3 1.8 2.0 0.1 0.1 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.472, p= 0.512 RESULTS OF GCD FOR dh-ranFile-2016-02-07_03:31 Euclid's algorithm: p-value, steps to gcd: 0.080370 p-value, dist. of gcd's: 0.043779 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-07_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.148 0.040 0.153 0.406 0.500 0.296 0.133 0.739 Bits 8 to 15---> 0.749 0.617 0.889 0.311 0.029 0.026 0.065 0.213 Bits 16 to 23---> 0.681 0.060 0.674 0.221 0.479 0.342 0.511 0.434 Bits 24 to 31---> 0.684 0.726 0.135 0.464 0.930 0.385 0.570 0.643 KS test for the above 32 p values: 0.862 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-07_03:31, p-values for 5 runs: 0.4584, 0.4400, 0.7557, 0.3079, 0.5363 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-07_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5058 5134.0 1.125 2.274 r= 30 23212 23103.0 0.514 2.788 r= 31 11503 11551.5 0.204 2.991 chi-square = 2.991 with df = 3; p-value = 0.607 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-07_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 192 211.4 1.783 1.783 r= 30 5087 5134.0 0.430 2.214 r= 31 23196 23103.0 0.374 2.588 r= 32 11525 11551.5 0.061 2.649 chi-square = 2.649 with df = 3; p-value = 0.551 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-07_03:31 b-rank test for bits 1 to 8, p=0.45830 b-rank test for bits 2 to 9, p=0.29324 b-rank test for bits 3 to 10, p=0.14814 b-rank test for bits 4 to 11, p=0.04247 b-rank test for bits 5 to 12, p=0.74345 b-rank test for bits 6 to 13, p=0.34517 b-rank test for bits 7 to 14, p=0.95978 b-rank test for bits 8 to 15, p=0.68130 b-rank test for bits 9 to 16, p=0.77857 b-rank test for bits 10 to 17, p=0.71870 b-rank test for bits 11 to 18, p=0.43766 b-rank test for bits 12 to 19, p=0.63890 b-rank test for bits 13 to 20, p=0.93162 b-rank test for bits 14 to 21, p=0.49152 b-rank test for bits 15 to 22, p=0.04183 b-rank test for bits 16 to 23, p=0.76951 b-rank test for bits 17 to 24, p=0.81430 b-rank test for bits 18 to 25, p=0.92213 b-rank test for bits 19 to 26, p=0.06105 b-rank test for bits 20 to 27, p=0.80920 b-rank test for bits 21 to 28, p=0.09061 b-rank test for bits 22 to 29, p=0.07776 b-rank test for bits 23 to 30, p=0.51774 b-rank test for bits 24 to 31, p=0.05333 b-rank test for bits 25 to 32, p=0.37493 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 = 0.628379 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-07_03:31 (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 142134 0.52 0.700184 2 141534 -0.88 0.190260 3 142245 0.78 0.783561 4 142162 0.59 0.722522 5 142111 0.47 0.681248 6 141751 -0.37 0.355717 7 141598 -0.73 0.233489 8 142192 0.66 0.745516 9 141872 -0.09 0.465249 10 141474 -1.02 0.154547 11 141352 -1.30 0.096429 12 141016 -2.09 0.018434 13 142503 1.39 0.917291 14 142273 0.85 0.802253 15 141099 -1.89 0.029159 16 142303 0.92 0.821159 17 141358 -1.29 0.098846 18 142469 1.31 0.904502 19 141656 -0.59 0.276961 20 142213 0.71 0.760996 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-07_03:31 Bits used No. missing words z-score p-value 23 to 32 141697 -0.7322 0.232032 22 to 31 141601 -1.0632 0.143844 21 to 30 142187 0.9575 0.830838 20 to 29 142547 2.1989 0.986056 19 to 28 141872 -0.1287 0.448788 18 to 27 141924 0.0506 0.520172 17 to 26 141470 -1.5149 0.064895 16 to 25 141666 -0.8391 0.200715 15 to 24 141083 -2.8494 0.002190 14 to 23 141790 -0.4115 0.340359 13 to 22 141773 -0.4701 0.319141 12 to 21 141377 -1.8356 0.033207 11 to 20 141863 -0.1598 0.436536 10 to 19 141506 -1.3908 0.082144 9 to 18 141936 0.0920 0.536637 8 to 17 141729 -0.6218 0.267028 7 to 16 141886 -0.0804 0.467940 6 to 15 142146 0.8161 0.792780 5 to 14 142153 0.8402 0.799614 4 to 13 142063 0.5299 0.701908 3 to 12 141892 -0.0598 0.476174 2 to 11 141780 -0.4460 0.327811 1 to 10 142299 1.3437 0.910476 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-07_03:31 Bits used No. missing words z-score p-value 28 to 32 142156 0.8362 0.798470 27 to 31 141527 -1.2960 0.097482 26 to 30 141660 -0.8452 0.199003 25 to 29 142139 0.7785 0.781875 24 to 28 142321 1.3955 0.918566 23 to 27 141772 -0.4655 0.320778 22 to 26 141657 -0.8554 0.196177 21 to 25 142030 0.4091 0.658749 20 to 24 141852 -0.1943 0.422955 19 to 23 141613 -1.0045 0.157567 18 to 22 142049 0.4735 0.682057 17 to 21 141584 -1.1028 0.135054 16 to 20 141845 -0.2181 0.413688 15 to 19 142105 0.6633 0.746427 14 to 18 141994 0.2870 0.612950 13 to 17 141914 0.0158 0.506315 12 to 16 141775 -0.4554 0.324427 11 to 15 141983 0.2497 0.598602 10 to 14 141715 -0.6587 0.255030 9 to 13 141314 -2.0181 0.021792 8 to 12 141730 -0.6079 0.271628 7 to 11 141906 -0.0113 0.495497 6 to 10 141350 -1.8960 0.028978 5 to 9 142167 0.8735 0.808793 4 to 8 141185 -2.4554 0.007037 3 to 7 142063 0.5209 0.698787 2 to 6 141935 0.0870 0.534671 1 to 5 141600 -1.0486 0.147187 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-07_03:31 Bits used No. missing words z-score p-value 31 to 32 141699 -0.6204 0.267483 30 to 31 141936 0.0787 0.531354 29 to 30 142104 0.5742 0.717100 28 to 29 141846 -0.1868 0.425903 27 to 28 141414 -1.4612 0.071987 26 to 27 141762 -0.4346 0.331926 25 to 26 141695 -0.6322 0.263614 24 to 25 142091 0.5359 0.703986 23 to 24 141472 -1.2901 0.098515 22 to 23 142214 0.8987 0.815602 21 to 22 141920 0.0315 0.512555 20 to 21 142053 0.4238 0.664146 19 to 20 141497 -1.2163 0.111933 18 to 19 141906 -0.0098 0.496081 17 to 18 141792 -0.3461 0.364632 16 to 17 141815 -0.2783 0.390407 15 to 16 142512 1.7778 0.962281 14 to 15 141639 -0.7974 0.212600 13 to 14 142154 0.7217 0.764773 12 to 13 141469 -1.2989 0.096988 11 to 12 141886 -0.0688 0.472566 10 to 11 142414 1.4887 0.931717 9 to 10 141919 0.0285 0.511378 8 to 9 141902 -0.0216 0.491375 7 to 8 141815 -0.2783 0.390407 6 to 7 141790 -0.3520 0.362417 5 to 6 141789 -0.3550 0.361311 4 to 5 142059 0.4415 0.670576 3 to 4 142082 0.5094 0.694747 2 to 3 142240 0.9754 0.835326 1 to 2 141619 -0.8564 0.195880 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-07_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2527.71 0.392 0.652410 Test results for specific bytes for dh-ranFile-2016-02-07_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2562.78 0.888 0.812677 2 to 9 2602.79 1.454 0.926978 3 to 10 2465.99 -0.481 0.315251 4 to 11 2351.14 -2.105 0.017634 5 to 12 2564.21 0.908 0.818084 6 to 13 2488.81 -0.158 0.437117 7 to 14 2497.55 -0.035 0.486153 8 to 15 2387.43 -1.592 0.055689 9 to 16 2484.91 -0.213 0.415504 10 to 17 2421.81 -1.106 0.134415 11 to 18 2433.89 -0.935 0.174918 12 to 19 2369.90 -1.840 0.032897 13 to 20 2494.28 -0.081 0.467742 14 to 21 2400.70 -1.404 0.080120 15 to 22 2430.92 -0.977 0.164303 16 to 23 2455.22 -0.633 0.263253 17 to 24 2451.01 -0.693 0.244226 18 to 25 2590.15 1.275 0.898825 19 to 26 2571.09 1.005 0.842640 20 to 27 2599.45 1.406 0.920200 21 to 28 2537.99 0.537 0.704440 22 to 29 2600.14 1.416 0.921641 23 to 30 2474.97 -0.354 0.361676 24 to 31 2401.17 -1.398 0.081100 25 to 32 2424.01 -1.075 0.141256 CDPARK for dh-ranFile-2016-02-07_03:31: 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 3522 -0.0457 0.481790 3479 -2.0091 0.022262 3474 -2.2374 0.012629 3509 -0.6393 0.261324 3540 0.7763 0.781201 3512 -0.5023 0.307734 3543 0.9132 0.819442 3490 -1.5068 0.065925 3520 -0.1370 0.445521 3493 -1.3699 0.085365 Square side=100, avg. no. parked=3508.20 sample std.=22.70 p-value of the KSTEST for those 10 p-values: 0.054394 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-07_03:31 0.3155,0.2682,0.6145,0.5624,0.4150,0.1981,0.0881,0.1823,0.9295,0.8214, The KS test for those 10 p-values: 0.815479 The 3DSPHERES test for dh-ranFile-2016-02-07_03:31 sample no r^3 equiv. uni. 1 28.024 0.607070 2 38.956 0.727070 3 26.209 0.582564 4 32.889 0.665890 5 62.167 0.874097 6 23.406 0.541689 7 43.341 0.764181 8 19.205 0.472801 9 28.551 0.613917 10 7.143 0.211888 11 16.151 0.416305 12 23.705 0.546230 13 24.004 0.550725 14 73.660 0.914165 15 15.252 0.398541 16 9.007 0.259344 17 34.420 0.682520 18 9.408 0.269184 19 19.801 0.483173 20 16.837 0.429496 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.132893 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-07_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -1.2 -2.5 0.6 0.4 1.4 0.1 0.6 -1.8 -0.9 -0.7 0.1 0.3 0.8 0.8 -0.3 -0.9 1.1 0.1 1.6 0.1 -0.4 0.4 -1.6 1.1 -2.3 -1.0 1.5 -0.6 -0.9 0.0 0.1 -0.0 -2.6 -0.9 -0.5 -1.9 0.8 -1.2 1.0 1.6 0.0 -1.1 Chi-square with 42 degrees of freedom:55.221048 z-score=1.442535, p-value=0.916994 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-07_03:31 Test no p-value 1 0.121168 2 0.465562 3 0.486672 4 0.556330 5 0.878450 6 0.576233 7 0.277708 8 0.824886 9 0.011068 10 0.484105 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.777462 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-07_03:31: (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 66755 0.12 66465 0.61 3 25000.00 25051 0.10 25158 1.00 4 6666.67 6508 3.78 6746 0.94 5 1388.89 1374 0.16 1368 0.31 6 238.10 271 4.55 220 1.38 7 34.72 30 0.64 35 0.00 8 4.96 10 5.12 7 0.84 p=0.97517 p=0.46683 Number of rngs required: 687413, p-value: 0.125 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-07_03:31 No. of wins: Observed Expected 98730 98585.9 z-score= 0.645, pvalue=0.74043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66921 66666.7 0.970 0.970 2 37416 37654.3 1.508 2.479 3 26833 26954.7 0.550 3.028 4 19448 19313.5 0.937 3.966 5 13895 13851.4 0.137 4.103 6 9916 9943.5 0.076 4.179 7 7160 7145.0 0.031 4.210 8 5202 5139.1 0.771 4.981 9 3719 3699.9 0.099 5.080 10 2612 2666.3 1.106 6.186 11 1911 1923.3 0.079 6.265 12 1393 1388.7 0.013 6.278 13 1000 1003.7 0.014 6.291 14 708 726.1 0.453 6.745 15 518 525.8 0.117 6.861 16 396 381.2 0.579 7.440 17 245 276.5 3.597 11.037 18 197 200.8 0.073 11.110 19 124 146.0 3.311 14.421 20 123 106.2 2.652 17.073 21 263 287.1 2.025 19.099 Chisq= 19.10 for 20 degrees of freedom, p= 0.48457 SUMMARY of craptest p-value for no. of wins: 0.740434 p-value for throws/game: 0.484571 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-07_03:31 No. of wins: Observed Expected 98727 98585.9 z-score= 0.631, pvalue=0.73607 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66686 66666.7 0.006 0.006 2 37980 37654.3 2.817 2.822 3 26876 26954.7 0.230 3.052 4 19194 19313.5 0.739 3.791 5 13932 13851.4 0.469 4.260 6 9803 9943.5 1.986 6.247 7 7046 7145.0 1.372 7.619 8 5203 5139.1 0.795 8.414 9 3680 3699.9 0.107 8.521 10 2651 2666.3 0.088 8.609 11 1907 1923.3 0.139 8.747 12 1371 1388.7 0.227 8.974 13 1033 1003.7 0.854 9.828 14 766 726.1 2.188 12.016 15 518 525.8 0.117 12.133 16 403 381.2 1.253 13.386 17 262 276.5 0.764 14.150 18 184 200.8 1.410 15.560 19 127 146.0 2.469 18.029 20 107 106.2 0.006 18.035 21 271 287.1 0.904 18.939 Chisq= 18.94 for 20 degrees of freedom, p= 0.47423 SUMMARY of craptest p-value for no. of wins: 0.736067 p-value for throws/game: 0.474232 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0070,0.0111,0.0126,0.0176,0.0184,0.0218,0.0223,0.0263,0.0290, 0.0292,0.0294,0.0329,0.0332,0.0398,0.0418,0.0425,0.0438,0.0533,0.0544, 0.0557,0.0558,0.0605,0.0610,0.0647,0.0649,0.0659,0.0720,0.0778,0.0801, 0.0804,0.0811,0.0821,0.0854,0.0881,0.0906,0.0964,0.0970,0.0975,0.0985, 0.0988,0.1119,0.1212,0.1252,0.1329,0.1330,0.1344,0.1348,0.1351,0.1413, 0.1438,0.1472,0.1481,0.1485,0.1531,0.1545,0.1576,0.1643,0.1749,0.1823, 0.1903,0.1959,0.1962,0.1964,0.1981,0.1990,0.2007,0.2119,0.2126,0.2132, 0.2209,0.2320,0.2335,0.2442,0.2550,0.2593,0.2613,0.2633,0.2636,0.2670, 0.2675,0.2682,0.2692,0.2716,0.2770,0.2777,0.2932,0.2957,0.3077,0.3079, 0.3107,0.3153,0.3155,0.3191,0.3208,0.3244,0.3278,0.3319,0.3404,0.3421, 0.3452,0.3557,0.3595,0.3613,0.3617,0.3624,0.3646,0.3749,0.3849,0.3904, 0.3904,0.3985,0.4057,0.4137,0.4150,0.4155,0.4163,0.4230,0.4259,0.4259, 0.4295,0.4338,0.4365,0.4371,0.4377,0.4400,0.4455,0.4488,0.4583,0.4584, 0.4642,0.4652,0.4656,0.4668,0.4677,0.4679,0.4726,0.4728,0.4742,0.4762, 0.4792,0.4818,0.4832,0.4841,0.4846,0.4862,0.4867,0.4914,0.4915,0.4955, 0.4961,0.4995,0.5063,0.5106,0.5114,0.5120,0.5126,0.5177,0.5202,0.5314, 0.5347,0.5363,0.5366,0.5417,0.5462,0.5507,0.5510,0.5563,0.5624,0.5702, 0.5762,0.5826,0.5986,0.6071,0.6071,0.6130,0.6139,0.6145,0.6169,0.6224, 0.6284,0.6389,0.6434,0.6524,0.6587,0.6641,0.6659,0.6706,0.6745,0.6807, 0.6812,0.6813,0.6821,0.6825,0.6838,0.6947,0.6988,0.7002,0.7019,0.7040, 0.7044,0.7171,0.7187,0.7225,0.7257,0.7271,0.7361,0.7390,0.7404,0.7435, 0.7455,0.7464,0.7495,0.7533,0.7557,0.7610,0.7642,0.7648,0.7695,0.7763, 0.7775,0.7786,0.7812,0.7819,0.7836,0.7928,0.7985,0.7996,0.8023,0.8088, 0.8092,0.8127,0.8143,0.8155,0.8156,0.8157,0.8181,0.8194,0.8212,0.8214, 0.8249,0.8308,0.8352,0.8353,0.8426,0.8618,0.8741,0.8785,0.8886,0.8988, 0.9045,0.9105,0.9142,0.9170,0.9173,0.9186,0.9202,0.9216,0.9221,0.9270, 0.9295,0.9300,0.9316,0.9317,0.9598,0.9623,0.9690,0.9752,0.9861, Overall p-value after applying KStest on 269 p-values = 0.033013 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.