RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-05_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.04 10.8637 0.136437 2 to 25 15.71 20.0105 0.726310 3 to 26 15.63 21.0655 0.776626 4 to 27 15.63 13.3577 0.288067 5 to 28 15.69 17.6662 0.589816 6 to 29 16.02 11.3702 0.163315 7 to 30 16.00 21.0423 0.775597 8 to 31 15.70 17.4306 0.574422 9 to 32 15.71 19.1342 0.679119 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.666331 Tough bday spacings test for dh-ranFile-2016-02-05_07:31: 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 11 35 61 116 83 80 52 30 17 6 9 (O-E)^2/E 0.4 0.1 2.1 3.4 2.2 0.0 0.0 0.0 0.3 0.1 6.0 Birthday Spacings: Sum(O-E)^2/E= 14.528, p= 0.850 RESULTS OF GCD FOR dh-ranFile-2016-02-05_07:31 Euclid's algorithm: p-value, steps to gcd: 0.435169 p-value, dist. of gcd's: 0.628783 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-05_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.952 0.659 0.890 0.483 0.531 0.876 0.814 0.467 Bits 8 to 15---> 0.164 0.933 0.399 0.496 0.295 0.532 0.012 0.636 Bits 16 to 23---> 0.839 0.819 0.469 0.468 0.076 0.134 0.405 0.956 Bits 24 to 31---> 0.728 0.591 0.432 0.449 0.344 0.348 0.306 0.946 KS test for the above 32 p values: 0.584 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-05_07:31, p-values for 5 runs: 0.8808, 0.3242, 0.8439, 0.6916, 0.4007 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-05_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5195 5134.0 0.725 2.187 r= 30 23140 23103.0 0.059 2.246 r= 31 11436 11551.5 1.155 3.401 chi-square = 3.401 with df = 3; p-value = 0.666 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-05_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5192 5134.0 0.655 0.927 r= 31 23050 23103.0 0.122 1.049 r= 32 11539 11551.5 0.014 1.062 chi-square = 1.062 with df = 3; p-value = 0.214 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-05_07:31 b-rank test for bits 1 to 8, p=0.33835 b-rank test for bits 2 to 9, p=0.68370 b-rank test for bits 3 to 10, p=0.39548 b-rank test for bits 4 to 11, p=0.99624 b-rank test for bits 5 to 12, p=0.43020 b-rank test for bits 6 to 13, p=0.82756 b-rank test for bits 7 to 14, p=0.34302 b-rank test for bits 8 to 15, p=0.84233 b-rank test for bits 9 to 16, p=0.04123 b-rank test for bits 10 to 17, p=0.62384 b-rank test for bits 11 to 18, p=0.59401 b-rank test for bits 12 to 19, p=0.63672 b-rank test for bits 13 to 20, p=0.43650 b-rank test for bits 14 to 21, p=0.49510 b-rank test for bits 15 to 22, p=0.71568 b-rank test for bits 16 to 23, p=0.31290 b-rank test for bits 17 to 24, p=0.16833 b-rank test for bits 18 to 25, p=0.07512 b-rank test for bits 19 to 26, p=0.21652 b-rank test for bits 20 to 27, p=0.03293 b-rank test for bits 21 to 28, p=0.28416 b-rank test for bits 22 to 29, p=0.83542 b-rank test for bits 23 to 30, p=0.99052 b-rank test for bits 24 to 31, p=0.19617 b-rank test for bits 25 to 32, p=0.46706 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 = 0.846144 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-05_07:31 (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 141689 -0.51 0.303350 2 142157 0.58 0.718594 3 141505 -0.94 0.172407 4 142128 0.51 0.695293 5 141760 -0.35 0.363582 6 141840 -0.16 0.435658 7 142228 0.74 0.771730 8 142344 1.02 0.845086 9 141701 -0.49 0.313217 10 143192 3.00 0.998636 11 142181 0.63 0.737202 12 142774 2.02 0.978322 13 141413 -1.16 0.123096 14 141930 0.05 0.519259 15 141867 -0.10 0.460608 16 142153 0.57 0.715431 17 141343 -1.32 0.092884 18 142789 2.06 0.980075 19 141452 -1.07 0.142641 20 141747 -0.38 0.352242 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-05_07:31 Bits used No. missing words z-score p-value 23 to 32 141897 -0.0425 0.483043 22 to 31 141634 -0.9494 0.171205 21 to 30 141983 0.2540 0.600266 20 to 29 142153 0.8402 0.799614 19 to 28 141913 0.0127 0.505049 18 to 27 141927 0.0609 0.524293 17 to 26 141234 -2.3287 0.009937 16 to 25 141636 -0.9425 0.172964 15 to 24 141781 -0.4425 0.329058 14 to 23 141782 -0.4391 0.330306 13 to 22 141747 -0.5598 0.287822 12 to 21 141784 -0.4322 0.332808 11 to 20 142378 1.6161 0.946964 10 to 19 141470 -1.5149 0.064895 9 to 18 141626 -0.9770 0.164285 8 to 17 141808 -0.3494 0.363389 7 to 16 141895 -0.0494 0.480295 6 to 15 141669 -0.8287 0.203630 5 to 14 141766 -0.4942 0.310568 4 to 13 141793 -0.4011 0.344159 3 to 12 142052 0.4920 0.688628 2 to 11 142082 0.5954 0.724217 1 to 10 142089 0.6196 0.732224 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-05_07:31 Bits used No. missing words z-score p-value 28 to 32 141875 -0.1164 0.453679 27 to 31 142226 1.0735 0.858467 26 to 30 142095 0.6294 0.735453 25 to 29 141909 -0.0011 0.499554 24 to 28 141928 0.0633 0.525232 23 to 27 141784 -0.4248 0.335474 22 to 26 142173 0.8938 0.814285 21 to 25 142599 2.3379 0.990303 20 to 24 142049 0.4735 0.682057 19 to 23 142029 0.4057 0.657504 18 to 22 141777 -0.4486 0.326869 17 to 21 141816 -0.3164 0.375860 16 to 20 141958 0.1650 0.565521 15 to 19 142053 0.4870 0.686877 14 to 18 142013 0.3514 0.637365 13 to 17 142522 2.0768 0.981092 12 to 16 141942 0.1107 0.544091 11 to 15 141773 -0.4621 0.321992 10 to 14 142036 0.4294 0.666180 9 to 13 141632 -0.9401 0.173583 8 to 12 142173 0.8938 0.814285 7 to 11 141911 0.0057 0.502258 6 to 10 141454 -1.5435 0.061356 5 to 9 141862 -0.1604 0.436267 4 to 8 141600 -1.0486 0.147187 3 to 7 141667 -0.8215 0.205693 2 to 6 142104 0.6599 0.745341 1 to 5 142278 1.2497 0.894301 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-05_07:31 Bits used No. missing words z-score p-value 31 to 32 142628 2.1200 0.982996 30 to 31 141927 0.0521 0.520785 29 to 30 141616 -0.8653 0.193443 28 to 29 142372 1.3648 0.913843 27 to 28 141959 0.1465 0.558244 26 to 27 141987 0.2291 0.590610 25 to 26 141570 -1.0010 0.158420 24 to 25 141559 -1.0334 0.150703 23 to 24 141759 -0.4435 0.328720 22 to 23 142115 0.6067 0.727974 21 to 22 142208 0.8810 0.810850 20 to 21 141947 0.1111 0.544240 19 to 20 142139 0.6775 0.750953 18 to 19 142071 0.4769 0.683284 17 to 18 142073 0.4828 0.685382 16 to 17 142014 0.3088 0.621248 15 to 16 141368 -1.5968 0.055150 14 to 15 141988 0.2321 0.591756 13 to 14 141944 0.1023 0.540729 12 to 13 142154 0.7217 0.764773 11 to 12 141720 -0.5585 0.288253 10 to 11 142215 0.9017 0.816387 9 to 10 141572 -0.9951 0.159850 8 to 9 140907 -2.9567 0.001555 7 to 8 141997 0.2586 0.602033 6 to 7 142012 0.3029 0.619002 5 to 6 142191 0.8309 0.796981 4 to 5 141883 -0.0777 0.469045 3 to 4 141821 -0.2606 0.397216 2 to 3 141155 -2.2252 0.013035 1 to 2 141839 -0.2075 0.417824 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-05_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.57 -0.869 0.192493 Test results for specific bytes for dh-ranFile-2016-02-05_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2501.05 0.015 0.505913 2 to 9 2380.79 -1.686 0.045907 3 to 10 2432.09 -0.960 0.168443 4 to 11 2413.89 -1.218 0.111644 5 to 12 2414.31 -1.212 0.112790 6 to 13 2509.21 0.130 0.551801 7 to 14 2470.84 -0.412 0.340024 8 to 15 2540.97 0.579 0.718829 9 to 16 2509.80 0.139 0.555100 10 to 17 2453.56 -0.657 0.255685 11 to 18 2408.68 -1.291 0.098274 12 to 19 2487.52 -0.176 0.429968 13 to 20 2446.72 -0.754 0.225570 14 to 21 2471.56 -0.402 0.343757 15 to 22 2471.35 -0.405 0.342690 16 to 23 2547.80 0.676 0.750482 17 to 24 2363.89 -1.925 0.027124 18 to 25 2569.95 0.989 0.838736 19 to 26 2524.26 0.343 0.634255 20 to 27 2616.66 1.650 0.950504 21 to 28 2438.68 -0.867 0.192924 22 to 29 2521.38 0.302 0.618825 23 to 30 2500.88 0.012 0.504948 24 to 31 2510.84 0.153 0.560907 25 to 32 2632.54 1.874 0.969561 CDPARK for dh-ranFile-2016-02-05_07:31: 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 3551 1.2785 0.899470 3531 0.3653 0.642555 3526 0.1370 0.554479 3519 -0.1826 0.427537 3538 0.6849 0.753306 3559 1.6438 0.949895 3546 1.0502 0.853193 3501 -1.0046 0.157553 3517 -0.2740 0.392053 3523 0.0000 0.500000 Square side=100, avg. no. parked=3531.10 sample std.=16.69 p-value of the KSTEST for those 10 p-values: 0.396272 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-05_07:31 0.1849,0.0367,0.2473,0.8266,0.3815,0.2916,0.1178,0.7871,0.1623,0.5672, The KS test for those 10 p-values: 0.207616 The 3DSPHERES test for dh-ranFile-2016-02-05_07:31 sample no r^3 equiv. uni. 1 22.566 0.528672 2 25.868 0.577793 3 1.105 0.036165 4 27.235 0.596604 5 10.530 0.296009 6 20.717 0.498701 7 21.564 0.512659 8 132.000 0.987723 9 35.862 0.697422 10 12.539 0.341614 11 5.164 0.158138 12 23.410 0.541746 13 47.312 0.793417 14 59.455 0.862181 15 4.770 0.146998 16 4.754 0.146558 17 22.611 0.529374 18 27.291 0.597349 19 5.885 0.178128 20 24.489 0.557930 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.574706 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-05_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 0.8 0.2 -0.6 0.4 0.3 0.3 -0.8 0.1 0.4 -0.1 -0.4 0.3 -0.4 -0.6 -0.7 1.4 -0.6 1.5 -0.7 1.5 0.8 -0.5 -0.8 -0.0 -0.7 -1.6 -0.2 0.2 0.2 -0.7 -1.1 -0.1 -0.9 1.5 -1.4 0.5 -1.6 0.4 -0.6 3.0 -0.1 Chi-square with 42 degrees of freedom:37.677616 z-score=-0.471611, p-value=0.338934 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-05_07:31 Test no p-value 1 0.695264 2 0.452370 3 0.010534 4 0.037423 5 0.725887 6 0.000614 7 0.801070 8 0.781087 9 0.002029 10 0.298841 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.008440 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-05_07:31: (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 66539 0.24 66456 0.67 3 25000.00 25092 0.34 25080 0.26 4 6666.67 6650 0.04 6767 1.51 5 1388.89 1435 1.53 1410 0.32 6 238.10 248 0.41 247 0.33 7 34.72 28 1.30 34 0.01 8 4.96 7 0.84 5 0.00 p=0.41813 p=0.20391 Number of rngs required: 688812, p-value: 0.681 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-05_07:31 No. of wins: Observed Expected 98798 98585.9 z-score= 0.949, pvalue=0.82864 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66734 66666.7 0.068 0.068 2 37691 37654.3 0.036 0.104 3 27165 26954.7 1.640 1.744 4 19202 19313.5 0.643 2.387 5 13918 13851.4 0.320 2.707 6 9796 9943.5 2.189 4.897 7 7100 7145.0 0.284 5.180 8 5075 5139.1 0.799 5.979 9 3746 3699.9 0.575 6.554 10 2696 2666.3 0.331 6.885 11 1818 1923.3 5.768 12.654 12 1376 1388.7 0.117 12.770 13 1016 1003.7 0.150 12.921 14 727 726.1 0.001 12.922 15 534 525.8 0.127 13.049 16 381 381.2 0.000 13.049 17 293 276.5 0.980 14.028 18 211 200.8 0.515 14.543 19 145 146.0 0.007 14.550 20 94 106.2 1.405 15.955 21 282 287.1 0.091 16.046 Chisq= 16.05 for 20 degrees of freedom, p= 0.28623 SUMMARY of craptest p-value for no. of wins: 0.828644 p-value for throws/game: 0.286228 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-05_07:31 No. of wins: Observed Expected 98487 98585.9 z-score=-0.442, pvalue=0.32919 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66315 66666.7 1.855 1.855 2 37681 37654.3 0.019 1.874 3 27101 26954.7 0.794 2.668 4 19574 19313.5 3.515 6.182 5 13723 13851.4 1.191 7.373 6 9955 9943.5 0.013 7.386 7 7138 7145.0 0.007 7.393 8 5120 5139.1 0.071 7.464 9 3663 3699.9 0.367 7.831 10 2624 2666.3 0.671 8.502 11 1929 1923.3 0.017 8.519 12 1454 1388.7 3.067 11.586 13 1033 1003.7 0.854 12.440 14 685 726.1 2.331 14.771 15 553 525.8 1.403 16.174 16 394 381.2 0.433 16.607 17 313 276.5 4.807 21.414 18 182 200.8 1.765 23.180 19 138 146.0 0.437 23.617 20 137 106.2 8.922 32.539 21 288 287.1 0.003 32.542 Chisq= 32.54 for 20 degrees of freedom, p= 0.96214 SUMMARY of craptest p-value for no. of wins: 0.329189 p-value for throws/game: 0.962144 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0016,0.0020,0.0084,0.0099,0.0105,0.0125,0.0130,0.0271,0.0329, 0.0362,0.0367,0.0374,0.0412,0.0459,0.0552,0.0614,0.0649,0.0751,0.0756, 0.0929,0.0983,0.1116,0.1128,0.1178,0.1231,0.1344,0.1364,0.1426,0.1466, 0.1470,0.1472,0.1507,0.1576,0.1581,0.1584,0.1599,0.1623,0.1633,0.1636, 0.1643,0.1683,0.1684,0.1712,0.1724,0.1730,0.1736,0.1781,0.1849,0.1925, 0.1929,0.1934,0.1962,0.2036,0.2039,0.2057,0.2076,0.2138,0.2165,0.2256, 0.2473,0.2557,0.2842,0.2862,0.2878,0.2881,0.2883,0.2916,0.2953,0.2960, 0.2988,0.3034,0.3058,0.3106,0.3129,0.3132,0.3220,0.3242,0.3269,0.3287, 0.3291,0.3292,0.3303,0.3328,0.3355,0.3383,0.3389,0.3400,0.3416,0.3427, 0.3430,0.3438,0.3438,0.3442,0.3485,0.3522,0.3634,0.3636,0.3759,0.3815, 0.3921,0.3955,0.3963,0.3972,0.3987,0.4007,0.4053,0.4178,0.4181,0.4275, 0.4300,0.4302,0.4325,0.4352,0.4357,0.4363,0.4365,0.4487,0.4524,0.4537, 0.4606,0.4671,0.4675,0.4677,0.4690,0.4692,0.4803,0.4830,0.4831,0.4951, 0.4957,0.4987,0.4996,0.5000,0.5023,0.5049,0.5050,0.5059,0.5127,0.5193, 0.5208,0.5243,0.5252,0.5287,0.5294,0.5310,0.5316,0.5407,0.5417,0.5441, 0.5442,0.5518,0.5545,0.5551,0.5579,0.5582,0.5609,0.5655,0.5672,0.5744, 0.5747,0.5778,0.5843,0.5898,0.5906,0.5907,0.5918,0.5940,0.5966,0.5973, 0.6003,0.6020,0.6188,0.6190,0.6212,0.6238,0.6288,0.6343,0.6362,0.6367, 0.6374,0.6426,0.6575,0.6590,0.6662,0.6662,0.6663,0.6791,0.6813,0.6821, 0.6833,0.6837,0.6854,0.6869,0.6886,0.6916,0.6953,0.6953,0.6974,0.7154, 0.7157,0.7186,0.7188,0.7242,0.7259,0.7263,0.7280,0.7283,0.7322,0.7355, 0.7372,0.7453,0.7505,0.7510,0.7533,0.7648,0.7717,0.7756,0.7766,0.7811, 0.7871,0.7934,0.7970,0.7996,0.8011,0.8108,0.8138,0.8143,0.8143,0.8164, 0.8187,0.8266,0.8276,0.8286,0.8354,0.8387,0.8394,0.8423,0.8439,0.8451, 0.8461,0.8498,0.8532,0.8585,0.8622,0.8758,0.8808,0.8897,0.8943,0.8995, 0.9138,0.9333,0.9465,0.9470,0.9499,0.9505,0.9517,0.9562,0.9621,0.9696, 0.9783,0.9801,0.9811,0.9830,0.9877,0.9903,0.9905,0.9962,0.9986, Overall p-value after applying KStest on 269 p-values = 0.314188 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.