RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-22_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 12.5578 0.234753 2 to 25 15.85 17.7959 0.598173 3 to 26 15.85 17.5658 0.583285 4 to 27 15.80 16.3700 0.502224 5 to 28 16.22 21.6584 0.801785 6 to 29 15.92 14.5139 0.369550 7 to 30 15.93 17.1225 0.553903 8 to 31 15.80 25.1223 0.907995 9 to 32 15.76 13.5001 0.297886 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.639705 Tough bday spacings test for dh-ranFile-2015-09-22_06:31: 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 38 64 89 96 85 58 26 17 12 4 (O-E)^2/E 0.4 0.1 1.2 0.8 0.0 0.6 0.7 0.5 0.3 4.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.825, p= 0.451 RESULTS OF GCD FOR dh-ranFile-2015-09-22_06:31 Euclid's algorithm: p-value, steps to gcd: 0.243158 p-value, dist. of gcd's: 0.801053 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-22_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.326 0.046 0.532 0.996 0.743 0.133 0.496 0.834 Bits 8 to 15---> 0.749 0.105 0.024 0.341 0.862 0.713 0.293 0.485 Bits 16 to 23---> 0.263 0.221 0.205 0.855 0.111 0.522 0.318 0.325 Bits 24 to 31---> 0.337 0.560 0.453 0.137 0.102 0.738 0.416 0.503 KS test for the above 32 p values: 0.752 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-22_06:31, p-values for 5 runs: 0.8472, 0.7010, 0.4130, 0.1536, 0.9294 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-22_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5116 5134.0 0.063 0.118 r= 30 23349 23103.0 2.618 2.737 r= 31 11327 11551.5 4.364 7.101 chi-square = 7.101 with df = 3; p-value = 0.931 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-22_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 235 211.4 2.630 2.630 r= 30 5127 5134.0 0.010 2.640 r= 31 22966 23103.0 0.813 3.453 r= 32 11672 11551.5 1.257 4.709 chi-square = 4.709 with df = 3; p-value = 0.806 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-22_06:31 b-rank test for bits 1 to 8, p=0.04162 b-rank test for bits 2 to 9, p=0.30575 b-rank test for bits 3 to 10, p=0.40069 b-rank test for bits 4 to 11, p=0.13587 b-rank test for bits 5 to 12, p=0.82845 b-rank test for bits 6 to 13, p=0.82713 b-rank test for bits 7 to 14, p=0.77184 b-rank test for bits 8 to 15, p=0.09399 b-rank test for bits 9 to 16, p=0.42444 b-rank test for bits 10 to 17, p=0.93985 b-rank test for bits 11 to 18, p=0.04427 b-rank test for bits 12 to 19, p=0.01651 b-rank test for bits 13 to 20, p=0.84862 b-rank test for bits 14 to 21, p=0.63618 b-rank test for bits 15 to 22, p=0.39603 b-rank test for bits 16 to 23, p=0.33462 b-rank test for bits 17 to 24, p=0.10523 b-rank test for bits 18 to 25, p=0.51994 b-rank test for bits 19 to 26, p=0.54608 b-rank test for bits 20 to 27, p=0.29855 b-rank test for bits 21 to 28, p=0.85866 b-rank test for bits 22 to 29, p=0.97026 b-rank test for bits 23 to 30, p=0.53157 b-rank test for bits 24 to 31, p=0.51424 b-rank test for bits 25 to 32, p=0.26975 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 = 0.807762 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-22_06:31 (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 142696 1.84 0.966970 2 142504 1.39 0.917647 3 142421 1.20 0.884052 4 141185 -1.69 0.045289 5 141999 0.21 0.582975 6 142979 2.50 0.993777 7 142172 0.61 0.730298 8 142209 0.70 0.758087 9 141795 -0.27 0.394686 10 143407 3.50 0.999767 11 142174 0.62 0.731840 12 142415 1.18 0.881292 13 142007 0.23 0.590255 14 141245 -1.55 0.060310 15 141597 -0.73 0.232774 16 141496 -0.97 0.167091 17 141279 -1.47 0.070411 18 141835 -0.17 0.431063 19 141766 -0.33 0.368857 20 141697 -0.50 0.309913 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-22_06:31 Bits used No. missing words z-score p-value 23 to 32 141819 -0.3115 0.377717 22 to 31 141641 -0.9253 0.177411 21 to 30 141832 -0.2667 0.394867 20 to 29 142035 0.4333 0.667618 19 to 28 142080 0.5885 0.721907 18 to 27 142152 0.8368 0.798646 17 to 26 142087 0.6127 0.729948 16 to 25 142559 2.2402 0.987462 15 to 24 141695 -0.7391 0.229933 14 to 23 142058 0.5127 0.695904 13 to 22 140722 -4.0942 0.000021 12 to 21 140994 -3.1563 0.000799 11 to 20 141819 -0.3115 0.377717 10 to 19 141702 -0.7149 0.237326 9 to 18 141538 -1.2804 0.100194 8 to 17 141895 -0.0494 0.480295 7 to 16 142266 1.2299 0.890632 6 to 15 141907 -0.0080 0.496795 5 to 14 141988 0.2713 0.606911 4 to 13 141820 -0.3080 0.379028 3 to 12 141779 -0.4494 0.326567 2 to 11 141717 -0.6632 0.253599 1 to 10 141770 -0.4804 0.315454 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-22_06:31 Bits used No. missing words z-score p-value 28 to 32 141216 -2.3503 0.009380 27 to 31 142222 1.0599 0.855405 26 to 30 142272 1.2294 0.890537 25 to 29 141735 -0.5909 0.277277 24 to 28 141331 -1.9604 0.024972 23 to 27 141914 0.0158 0.506315 22 to 26 142246 1.1413 0.873118 21 to 25 142528 2.0972 0.982011 20 to 24 141626 -0.9604 0.168417 19 to 23 142385 1.6124 0.946567 18 to 22 141783 -0.4282 0.334239 17 to 21 141739 -0.5774 0.281838 16 to 20 141898 -0.0384 0.484682 15 to 19 141392 -1.7537 0.039744 14 to 18 141779 -0.4418 0.329318 13 to 17 142213 1.0294 0.848352 12 to 16 141747 -0.5503 0.291067 11 to 15 141876 -0.1130 0.455022 10 to 14 142260 1.1887 0.882723 9 to 13 142110 0.6802 0.751823 8 to 12 141839 -0.2384 0.405783 7 to 11 141800 -0.3706 0.355464 6 to 10 142169 0.8802 0.810635 5 to 9 142370 1.5616 0.940808 4 to 8 142572 2.2463 0.987659 3 to 7 142434 1.7785 0.962343 2 to 6 142092 0.6192 0.732114 1 to 5 141736 -0.5876 0.278414 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-22_06:31 Bits used No. missing words z-score p-value 31 to 32 142413 1.4858 0.931328 30 to 31 141615 -0.8682 0.192634 29 to 30 141996 0.2557 0.600895 28 to 29 141654 -0.7532 0.225669 27 to 28 142264 1.0462 0.852271 26 to 27 141663 -0.7266 0.233724 25 to 26 142110 0.5919 0.723057 24 to 25 141814 -0.2812 0.389275 23 to 24 141957 0.1406 0.555915 22 to 23 142416 1.4946 0.932491 21 to 22 143237 3.9164 0.999955 20 to 21 142109 0.5890 0.722068 19 to 20 141844 -0.1927 0.423592 18 to 19 141838 -0.2104 0.416673 17 to 18 141921 0.0344 0.513731 16 to 17 141391 -1.5290 0.063133 15 to 16 141168 -2.1868 0.014378 14 to 15 142428 1.5300 0.936992 13 to 14 141942 0.0964 0.538387 12 to 13 142240 0.9754 0.835326 11 to 12 141259 -1.9184 0.027532 10 to 11 142181 0.8014 0.788546 9 to 10 141911 0.0049 0.501965 8 to 9 141609 -0.8859 0.187828 7 to 8 141421 -1.4405 0.074863 6 to 7 142068 0.4681 0.680127 5 to 6 141540 -1.0895 0.137974 4 to 5 142014 0.3088 0.621248 3 to 4 142621 2.0993 0.982106 2 to 3 141781 -0.3786 0.352509 1 to 2 141188 -2.1278 0.016676 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-22_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2567.32 0.952 0.829468 Test results for specific bytes for dh-ranFile-2015-09-22_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2545.57 0.644 0.740365 2 to 9 2438.45 -0.870 0.192035 3 to 10 2694.77 2.754 0.997060 4 to 11 2474.27 -0.364 0.357979 5 to 12 2485.29 -0.208 0.417595 6 to 13 2462.33 -0.533 0.297110 7 to 14 2570.92 1.003 0.842057 8 to 15 2661.70 2.287 0.988897 9 to 16 2454.48 -0.644 0.259863 10 to 17 2488.21 -0.167 0.433814 11 to 18 2485.25 -0.209 0.417373 12 to 19 2490.85 -0.129 0.448538 13 to 20 2481.83 -0.257 0.398601 14 to 21 2455.88 -0.624 0.266350 15 to 22 2471.68 -0.401 0.344370 16 to 23 2526.96 0.381 0.648509 17 to 24 2477.46 -0.319 0.374964 18 to 25 2329.15 -2.416 0.007843 19 to 26 2515.56 0.220 0.587071 20 to 27 2430.57 -0.982 0.163087 21 to 28 2425.31 -1.056 0.145425 22 to 29 2546.88 0.663 0.746347 23 to 30 2544.53 0.630 0.735555 24 to 31 2526.16 0.370 0.644306 25 to 32 2519.12 0.270 0.606550 CDPARK for dh-ranFile-2015-09-22_06:31: 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 3537 0.6393 0.738676 3537 0.6393 0.738676 3525 0.0913 0.536383 3549 1.1872 0.882429 3539 0.7306 0.767486 3485 -1.7352 0.041356 3514 -0.4110 0.340551 3569 2.1005 0.982156 3497 -1.1872 0.117571 Square side=100, avg. no. parked=3527.40 sample std.=23.35 p-value of the KSTEST for those 10 p-values: 0.766362 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-22_06:31 0.3525,0.3291,0.8884,0.0285,0.9011,0.0102,0.8256,0.1651,0.6222,0.7324, The KS test for those 10 p-values: 0.598674 The 3DSPHERES test for dh-ranFile-2015-09-22_06:31 sample no r^3 equiv. uni. 1 92.891 0.954787 2 5.006 0.153690 3 41.066 0.745603 4 8.897 0.256644 5 3.350 0.105663 6 55.160 0.840969 7 23.552 0.543906 8 11.070 0.308586 9 5.671 0.172236 10 16.900 0.430697 11 5.640 0.171380 12 28.013 0.606924 13 20.815 0.500337 14 16.235 0.417939 15 9.543 0.272462 16 73.589 0.913961 17 7.300 0.215980 18 15.230 0.398100 19 1.937 0.062536 20 40.437 0.740214 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.577885 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-22_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 0.6 0.6 0.9 -0.2 0.1 0.8 0.3 -0.3 -0.3 -0.1 -1.1 2.3 1.9 0.0 -1.1 -0.1 -0.7 -0.7 -1.9 1.4 -0.8 0.5 1.7 -0.3 -0.9 0.2 -1.2 -0.6 0.6 -0.2 0.1 -0.2 0.3 -0.3 1.0 -0.4 0.5 2.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:34.249418 z-score=-0.845658, p-value=0.203238 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-22_06:31 Test no p-value 1 0.768832 2 0.261483 3 0.006901 4 0.249361 5 0.142011 6 0.007299 7 0.011134 8 0.956692 9 0.821067 10 0.919916 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.028521 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-22_06:31: (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 66662 0.00 66745 0.09 3 25000.00 24987 0.01 24906 0.35 4 6666.67 6692 0.10 6706 0.23 5 1388.89 1384 0.02 1359 0.64 6 238.10 241 0.04 250 0.60 7 34.72 28 1.30 30 0.64 8 4.96 5 0.00 3 0.77 p=0.03770 p=0.23385 Number of rngs required: 687901, p-value: 0.281 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-22_06:31 No. of wins: Observed Expected 98429 98585.9 z-score=-0.702, pvalue=0.24148 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66440 66666.7 0.771 0.771 2 37580 37654.3 0.147 0.917 3 26998 26954.7 0.069 0.987 4 19388 19313.5 0.288 1.274 5 13838 13851.4 0.013 1.287 6 9875 9943.5 0.472 1.760 7 7269 7145.0 2.151 3.911 8 5098 5139.1 0.328 4.239 9 3795 3699.9 2.446 6.686 10 2798 2666.3 6.505 13.191 11 1891 1923.3 0.543 13.734 12 1349 1388.7 1.137 14.872 13 1025 1003.7 0.451 15.323 14 709 726.1 0.405 15.728 15 518 525.8 0.117 15.844 16 375 381.2 0.099 15.944 17 285 276.5 0.259 16.203 18 227 200.8 3.410 19.613 19 133 146.0 1.155 20.768 20 127 106.2 4.067 24.835 21 282 287.1 0.091 24.926 Chisq= 24.93 for 20 degrees of freedom, p= 0.79572 SUMMARY of craptest p-value for no. of wins: 0.241476 p-value for throws/game: 0.795722 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-22_06:31 No. of wins: Observed Expected 98554 98585.9 z-score=-0.142, pvalue=0.44335 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66505 66666.7 0.392 0.392 2 37717 37654.3 0.104 0.496 3 26745 26954.7 1.632 2.128 4 19378 19313.5 0.216 2.344 5 13838 13851.4 0.013 2.357 6 10012 9943.5 0.471 2.828 7 7158 7145.0 0.024 2.852 8 5085 5139.1 0.569 3.421 9 3735 3699.9 0.334 3.754 10 2763 2666.3 3.507 7.262 11 1979 1923.3 1.611 8.873 12 1415 1388.7 0.497 9.370 13 990 1003.7 0.187 9.557 14 759 726.1 1.487 11.044 15 513 525.8 0.313 11.357 16 388 381.2 0.123 11.480 17 274 276.5 0.023 11.504 18 210 200.8 0.419 11.922 19 158 146.0 0.989 12.911 20 90 106.2 2.475 15.387 21 288 287.1 0.003 15.390 Chisq= 15.39 for 20 degrees of freedom, p= 0.24630 SUMMARY of craptest p-value for no. of wins: 0.443346 p-value for throws/game: 0.246303 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0008,0.0069,0.0073,0.0078,0.0094,0.0102,0.0111,0.0144,0.0165, 0.0167,0.0237,0.0250,0.0275,0.0285,0.0285,0.0377,0.0397,0.0414,0.0416, 0.0443,0.0453,0.0458,0.0603,0.0625,0.0631,0.0704,0.0749,0.0940,0.1002, 0.1025,0.1049,0.1052,0.1057,0.1111,0.1176,0.1329,0.1359,0.1374,0.1380, 0.1420,0.1454,0.1536,0.1537,0.1631,0.1651,0.1671,0.1684,0.1714,0.1722, 0.1774,0.1878,0.1920,0.1926,0.2032,0.2052,0.2160,0.2211,0.2257,0.2299, 0.2328,0.2337,0.2339,0.2348,0.2373,0.2415,0.2432,0.2463,0.2494,0.2536, 0.2566,0.2599,0.2615,0.2633,0.2663,0.2698,0.2725,0.2773,0.2784,0.2813, 0.2818,0.2911,0.2927,0.2971,0.2979,0.2986,0.3057,0.3086,0.3099,0.3155, 0.3176,0.3251,0.3257,0.3266,0.3291,0.3293,0.3342,0.3346,0.3366,0.3406, 0.3407,0.3444,0.3525,0.3525,0.3555,0.3580,0.3689,0.3695,0.3750,0.3777, 0.3777,0.3790,0.3893,0.3947,0.3949,0.3960,0.3981,0.3986,0.4007,0.4058, 0.4130,0.4156,0.4167,0.4174,0.4176,0.4179,0.4236,0.4244,0.4307,0.4311, 0.4338,0.4433,0.4485,0.4512,0.4532,0.4550,0.4803,0.4818,0.4846,0.4847, 0.4957,0.4968,0.5003,0.5020,0.5022,0.5027,0.5063,0.5137,0.5142,0.5199, 0.5222,0.5316,0.5321,0.5364,0.5384,0.5439,0.5461,0.5539,0.5559,0.5596, 0.5779,0.5830,0.5833,0.5871,0.5903,0.5982,0.5987,0.6009,0.6066,0.6069, 0.6069,0.6212,0.6222,0.6362,0.6397,0.6443,0.6485,0.6676,0.6801,0.6959, 0.7010,0.7134,0.7219,0.7221,0.7231,0.7299,0.7303,0.7318,0.7321,0.7324, 0.7356,0.7381,0.7387,0.7387,0.7402,0.7404,0.7430,0.7456,0.7463,0.7488, 0.7518,0.7519,0.7581,0.7664,0.7675,0.7688,0.7718,0.7885,0.7957,0.7986, 0.8011,0.8018,0.8056,0.8078,0.8106,0.8211,0.8256,0.8271,0.8284,0.8295, 0.8337,0.8353,0.8410,0.8421,0.8472,0.8484,0.8486,0.8523,0.8546,0.8554, 0.8587,0.8615,0.8731,0.8813,0.8824,0.8827,0.8841,0.8884,0.8905,0.8906, 0.9011,0.9080,0.9140,0.9176,0.9199,0.9294,0.9312,0.9313,0.9325,0.9370, 0.9399,0.9408,0.9466,0.9548,0.9567,0.9623,0.9670,0.9703,0.9820,0.9821, 0.9822,0.9875,0.9877,0.9889,0.9938,0.9964,0.9971,0.9998,1.0000, Overall p-value after applying KStest on 269 p-values = 0.288763 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.