RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-17_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.21 17.3087 0.566353 2 to 25 16.07 16.4273 0.506226 3 to 26 15.83 9.7039 0.084435 4 to 27 16.01 14.4090 0.362028 5 to 28 15.73 15.2251 0.420729 6 to 29 15.79 15.7975 0.461768 7 to 30 15.68 27.0743 0.943014 8 to 31 15.87 18.6118 0.648738 9 to 32 16.01 12.8048 0.250848 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.751321 Tough bday spacings test for dh-ranFile-2018-03-17_12:31: 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 13 44 59 95 91 81 50 36 19 7 5 (O-E)^2/E 1.6 1.5 2.8 0.1 0.5 0.1 0.1 1.3 1.1 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.269, p= 0.493 RESULTS OF GCD FOR dh-ranFile-2018-03-17_12:31 Euclid's algorithm: p-value, steps to gcd: 0.699805 p-value, dist. of gcd's: 0.741301 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-17_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.564 0.086 0.700 0.008 0.435 0.386 0.999 0.804 Bits 8 to 15---> 0.291 0.047 0.879 0.778 0.149 0.660 0.735 0.835 Bits 16 to 23---> 0.410 0.759 0.157 0.686 0.637 0.119 0.193 0.129 Bits 24 to 31---> 0.236 0.492 0.386 0.920 0.719 0.375 0.910 0.196 KS test for the above 32 p values: 0.060 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-17_12:31, p-values for 5 runs: 0.1538, 0.1852, 0.6835, 0.6819, 0.3864 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-17_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5136 5134.0 0.001 0.061 r= 30 22992 23103.0 0.534 0.595 r= 31 11657 11551.5 0.963 1.558 chi-square = 1.558 with df = 3; p-value = 0.331 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-17_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5036 5134.0 1.871 2.018 r= 31 23100 23103.0 0.000 2.019 r= 32 11647 11551.5 0.789 2.808 chi-square = 2.808 with df = 3; p-value = 0.578 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-17_12:31 b-rank test for bits 1 to 8, p=0.20036 b-rank test for bits 2 to 9, p=0.47648 b-rank test for bits 3 to 10, p=0.36473 b-rank test for bits 4 to 11, p=0.40249 b-rank test for bits 5 to 12, p=0.97824 b-rank test for bits 6 to 13, p=0.95737 b-rank test for bits 7 to 14, p=0.66696 b-rank test for bits 8 to 15, p=0.85740 b-rank test for bits 9 to 16, p=0.65694 b-rank test for bits 10 to 17, p=0.62435 b-rank test for bits 11 to 18, p=0.38416 b-rank test for bits 12 to 19, p=0.07185 b-rank test for bits 13 to 20, p=0.93031 b-rank test for bits 14 to 21, p=0.60099 b-rank test for bits 15 to 22, p=0.80519 b-rank test for bits 16 to 23, p=0.43305 b-rank test for bits 17 to 24, p=0.81365 b-rank test for bits 18 to 25, p=0.12264 b-rank test for bits 19 to 26, p=0.49154 b-rank test for bits 20 to 27, p=0.57035 b-rank test for bits 21 to 28, p=0.21100 b-rank test for bits 22 to 29, p=0.57338 b-rank test for bits 23 to 30, p=0.47892 b-rank test for bits 24 to 31, p=0.14185 b-rank test for bits 25 to 32, p=0.90304 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 = 0.648889 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-17_12:31 (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 141464 -1.04 0.149056 2 141712 -0.46 0.322381 3 142366 1.07 0.857011 4 141614 -0.69 0.245090 5 141597 -0.73 0.232774 6 142304 0.92 0.821769 7 141687 -0.52 0.301719 8 142552 1.50 0.933395 9 142039 0.30 0.619043 10 141700 -0.49 0.312389 11 141372 -1.26 0.104659 12 142043 0.31 0.622599 13 141827 -0.19 0.423730 14 141898 -0.03 0.489440 15 141715 -0.45 0.324899 16 142309 0.93 0.824799 17 141846 -0.15 0.441184 18 142077 0.39 0.652379 19 142289 0.89 0.812482 20 142462 1.29 0.901698 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-17_12:31 Bits used No. missing words z-score p-value 23 to 32 141950 0.1402 0.555765 22 to 31 142120 0.7264 0.766218 21 to 30 141806 -0.3563 0.360804 20 to 29 141803 -0.3667 0.356938 19 to 28 141749 -0.5529 0.290179 18 to 27 142718 2.7885 0.997353 17 to 26 141886 -0.0804 0.467940 16 to 25 141876 -0.1149 0.454250 15 to 24 141831 -0.2701 0.393540 14 to 23 141597 -1.0770 0.140740 13 to 22 142227 1.0954 0.863332 12 to 21 142180 0.9333 0.824679 11 to 20 142135 0.7782 0.781766 10 to 19 141531 -1.3046 0.096017 9 to 18 142074 0.5678 0.714924 8 to 17 141650 -0.8942 0.185596 7 to 16 142045 0.4678 0.680046 6 to 15 141876 -0.1149 0.454250 5 to 14 141866 -0.1494 0.440614 4 to 13 141797 -0.3873 0.349251 3 to 12 141313 -2.0563 0.019876 2 to 11 141650 -0.8942 0.185596 1 to 10 141944 0.1196 0.547581 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-17_12:31 Bits used No. missing words z-score p-value 28 to 32 141783 -0.4282 0.334239 27 to 31 141633 -0.9367 0.174453 26 to 30 141900 -0.0316 0.487385 25 to 29 142147 0.8057 0.789781 24 to 28 142032 0.4158 0.661233 23 to 27 141970 0.2057 0.581472 22 to 26 142257 1.1785 0.880710 21 to 25 141281 -2.1299 0.016589 20 to 24 141640 -0.9130 0.180626 19 to 23 142035 0.4260 0.664946 18 to 22 142471 1.9040 0.971543 17 to 21 142293 1.3006 0.903298 16 to 20 141980 0.2396 0.594664 15 to 19 141954 0.1514 0.560179 14 to 18 141860 -0.1672 0.433598 13 to 17 141916 0.0226 0.509019 12 to 16 141816 -0.3164 0.375860 11 to 15 142051 0.4802 0.684471 10 to 14 142077 0.5684 0.715109 9 to 13 142007 0.3311 0.629710 8 to 12 141695 -0.7265 0.233753 7 to 11 141786 -0.4181 0.337949 6 to 10 141417 -1.6689 0.047567 5 to 9 141331 -1.9604 0.024972 4 to 8 141983 0.2497 0.598602 3 to 7 142197 0.9752 0.835258 2 to 6 141684 -0.7638 0.222484 1 to 5 141287 -2.1096 0.017447 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-17_12:31 Bits used No. missing words z-score p-value 31 to 32 141823 -0.2547 0.399493 30 to 31 141618 -0.8594 0.195065 29 to 30 142571 1.9518 0.974521 28 to 29 141322 -1.7325 0.041589 27 to 28 141599 -0.9154 0.179984 26 to 27 142101 0.5654 0.714099 25 to 26 141588 -0.9479 0.171596 24 to 25 142033 0.3648 0.642373 23 to 24 142221 0.9194 0.821052 22 to 23 141918 0.0256 0.510202 21 to 22 141191 -2.1190 0.017047 20 to 21 141581 -0.9685 0.166391 19 to 20 141814 -0.2812 0.389275 18 to 19 141811 -0.2901 0.385886 17 to 18 142244 0.9872 0.838234 16 to 17 141322 -1.7325 0.041589 15 to 16 141872 -0.1101 0.456158 14 to 15 142002 0.2734 0.607713 13 to 14 142042 0.3914 0.652233 12 to 13 141566 -1.0128 0.155584 11 to 12 142246 0.9931 0.839676 10 to 11 142212 0.8928 0.814026 9 to 10 142534 1.8427 0.967312 8 to 9 141963 0.1583 0.562897 7 to 8 141784 -0.3697 0.355801 6 to 7 141879 -0.0895 0.464355 5 to 6 141773 -0.4022 0.343786 4 to 5 141201 -2.0895 0.018333 3 to 4 142091 0.5359 0.703986 2 to 3 141924 0.0433 0.517259 1 to 2 141820 -0.2635 0.396079 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-17_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2532.32 0.457 0.676204 Test results for specific bytes for dh-ranFile-2018-03-17_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2470.36 -0.419 0.337553 2 to 9 2514.65 0.207 0.582039 3 to 10 2411.26 -1.255 0.104739 4 to 11 2417.91 -1.161 0.122846 5 to 12 2346.49 -2.171 0.014966 6 to 13 2586.72 1.226 0.889985 7 to 14 2379.64 -1.702 0.044367 8 to 15 2475.58 -0.345 0.364905 9 to 16 2559.29 0.838 0.799124 10 to 17 2627.11 1.798 0.963884 11 to 18 2492.14 -0.111 0.455744 12 to 19 2475.74 -0.343 0.365745 13 to 20 2419.48 -1.139 0.127399 14 to 21 2447.85 -0.738 0.230388 15 to 22 2465.76 -0.484 0.314095 16 to 23 2489.13 -0.154 0.438892 17 to 24 2462.28 -0.533 0.296861 18 to 25 2385.54 -1.619 0.052752 19 to 26 2536.92 0.522 0.699203 20 to 27 2613.01 1.598 0.944995 21 to 28 2514.64 0.207 0.582008 22 to 29 2384.19 -1.638 0.050738 23 to 30 2466.89 -0.468 0.319809 24 to 31 2555.59 0.786 0.784134 25 to 32 2488.99 -0.156 0.438133 CDPARK for dh-ranFile-2018-03-17_12:31: 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 3500 -1.0502 0.146807 3554 1.4155 0.921543 3503 -0.9132 0.180558 3485 -1.7352 0.041356 3521 -0.0913 0.463617 3550 1.2329 0.891189 3525 0.0913 0.536383 3566 1.9635 0.975204 3556 1.5068 0.934075 3505 -0.8219 0.205562 Square side=100, avg. no. parked=3526.50 sample std.=26.85 p-value of the KSTEST for those 10 p-values: 0.353951 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-17_12:31 0.0850,0.8739,0.9340,0.6533,0.2174,0.0659,0.1742,0.4748,0.5614,0.5194, The KS test for those 10 p-values: 0.900017 The 3DSPHERES test for dh-ranFile-2018-03-17_12:31 sample no r^3 equiv. uni. 1 24.217 0.553903 2 2.453 0.078520 3 10.210 0.288471 4 15.224 0.397985 5 48.091 0.798716 6 60.399 0.866454 7 32.449 0.660958 8 19.776 0.482742 9 7.273 0.215293 10 4.542 0.140502 11 53.212 0.830303 12 9.676 0.275691 13 48.951 0.804401 14 14.239 0.377897 15 34.136 0.679503 16 56.895 0.849909 17 1.281 0.041811 18 47.995 0.798070 19 126.566 0.985285 20 79.584 0.929546 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.677292 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-17_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.1 -1.1 -1.6 1.9 0.6 -0.6 0.2 -2.0 -0.2 1.7 -0.0 0.0 -0.9 -0.1 -1.0 -1.0 1.8 0.2 0.3 0.5 0.2 0.2 -0.5 0.3 -1.0 -0.9 1.4 0.0 0.9 1.6 0.6 0.0 0.2 -0.3 0.5 -1.7 0.5 -0.1 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:34.361720 z-score=-0.833405, p-value=0.207224 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-17_12:31 Test no p-value 1 0.659954 2 0.398239 3 0.348984 4 0.456468 5 0.304200 6 0.392610 7 0.718038 8 0.005304 9 0.599569 10 0.188493 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.291133 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-17_12:31: (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 66790 0.23 66943 1.15 3 25000.00 24914 0.30 24868 0.70 4 6666.67 6639 0.11 6577 1.21 5 1388.89 1378 0.09 1337 1.94 6 238.10 246 0.26 234 0.07 7 34.72 27 1.72 36 0.05 8 4.96 5 0.00 4 0.19 p=0.15497 p=0.49287 Number of rngs required: 688315, p-value: 0.460 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-17_12:31 No. of wins: Observed Expected 98426 98585.9 z-score=-0.715, pvalue=0.23731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66516 66666.7 0.341 0.341 2 37696 37654.3 0.046 0.387 3 26795 26954.7 0.947 1.333 4 19446 19313.5 0.910 2.243 5 13933 13851.4 0.480 2.723 6 10002 9943.5 0.344 3.067 7 7097 7145.0 0.323 3.390 8 5248 5139.1 2.309 5.699 9 3753 3699.9 0.763 6.462 10 2672 2666.3 0.012 6.474 11 1890 1923.3 0.578 7.051 12 1393 1388.7 0.013 7.064 13 983 1003.7 0.428 7.492 14 722 726.1 0.024 7.516 15 507 525.8 0.675 8.190 16 358 381.2 1.406 9.596 17 292 276.5 0.864 10.461 18 193 200.8 0.305 10.766 19 141 146.0 0.170 10.936 20 93 106.2 1.644 12.580 21 270 287.1 1.020 13.601 Chisq= 13.60 for 20 degrees of freedom, p= 0.14984 SUMMARY of craptest p-value for no. of wins: 0.237310 p-value for throws/game: 0.149843 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-17_12:31 No. of wins: Observed Expected 98626 98585.9 z-score= 0.180, pvalue=0.57124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66752 66666.7 0.109 0.109 2 37358 37654.3 2.332 2.441 3 27089 26954.7 0.669 3.110 4 19328 19313.5 0.011 3.121 5 13910 13851.4 0.248 3.369 6 9893 9943.5 0.257 3.626 7 7080 7145.0 0.592 4.217 8 5171 5139.1 0.198 4.416 9 3737 3699.9 0.373 4.788 10 2676 2666.3 0.035 4.824 11 1940 1923.3 0.144 4.968 12 1473 1388.7 5.112 10.081 13 1017 1003.7 0.176 10.256 14 720 726.1 0.052 10.308 15 508 525.8 0.605 10.913 16 384 381.2 0.021 10.935 17 258 276.5 1.243 12.177 18 184 200.8 1.410 13.588 19 119 146.0 4.988 18.576 20 112 106.2 0.315 18.891 21 291 287.1 0.053 18.943 Chisq= 18.94 for 20 degrees of freedom, p= 0.47449 SUMMARY of craptest p-value for no. of wins: 0.571242 p-value for throws/game: 0.474494 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0053,0.0080,0.0150,0.0166,0.0170,0.0174,0.0183,0.0199,0.0250,0.0414, 0.0416,0.0416,0.0418,0.0444,0.0469,0.0476,0.0507,0.0528,0.0602,0.0659, 0.0719,0.0785,0.0844,0.0850,0.0857,0.0960,0.1047,0.1047,0.1187,0.1226, 0.1228,0.1274,0.1293,0.1405,0.1407,0.1418,0.1468,0.1488,0.1491,0.1498, 0.1538,0.1550,0.1556,0.1570,0.1664,0.1716,0.1742,0.1745,0.1800,0.1806, 0.1806,0.1852,0.1856,0.1856,0.1885,0.1927,0.1951,0.1955,0.2004,0.2056, 0.2072,0.2110,0.2153,0.2174,0.2225,0.2304,0.2328,0.2338,0.2361,0.2373, 0.2451,0.2508,0.2757,0.2885,0.2902,0.2907,0.2911,0.2969,0.3017,0.3042, 0.3124,0.3141,0.3198,0.3224,0.3249,0.3311,0.3342,0.3376,0.3379,0.3438, 0.3490,0.3493,0.3540,0.3558,0.3569,0.3608,0.3620,0.3647,0.3649,0.3657, 0.3752,0.3759,0.3779,0.3842,0.3858,0.3859,0.3864,0.3864,0.3893,0.3926, 0.3935,0.3961,0.3980,0.3982,0.3995,0.4025,0.4104,0.4207,0.4237,0.4331, 0.4336,0.4346,0.4381,0.4389,0.4406,0.4412,0.4542,0.4542,0.4557,0.4562, 0.4565,0.4597,0.4618,0.4636,0.4644,0.4679,0.4745,0.4748,0.4765,0.4789, 0.4827,0.4874,0.4894,0.4915,0.4922,0.4929,0.4932,0.5062,0.5090,0.5102, 0.5173,0.5194,0.5364,0.5476,0.5539,0.5558,0.5602,0.5614,0.5629,0.5642, 0.5664,0.5703,0.5712,0.5734,0.5778,0.5815,0.5820,0.5820,0.5947,0.5986, 0.5996,0.6010,0.6077,0.6190,0.6226,0.6244,0.6297,0.6372,0.6424,0.6487, 0.6489,0.6522,0.6524,0.6533,0.6569,0.6600,0.6603,0.6610,0.6612,0.6649, 0.6670,0.6762,0.6773,0.6795,0.6800,0.6819,0.6835,0.6845,0.6862,0.6992, 0.6998,0.6999,0.7040,0.7141,0.7149,0.7151,0.7180,0.7189,0.7349,0.7413, 0.7513,0.7589,0.7662,0.7778,0.7818,0.7841,0.7898,0.7981,0.7987,0.7991, 0.8040,0.8044,0.8052,0.8125,0.8137,0.8140,0.8211,0.8218,0.8247,0.8248, 0.8303,0.8345,0.8353,0.8382,0.8397,0.8499,0.8570,0.8574,0.8633,0.8665, 0.8739,0.8794,0.8807,0.8900,0.8912,0.9000,0.9017,0.9030,0.9033,0.9102, 0.9195,0.9215,0.9295,0.9303,0.9334,0.9340,0.9341,0.9430,0.9450,0.9574, 0.9639,0.9673,0.9715,0.9745,0.9752,0.9782,0.9853,0.9974,0.9995, Overall p-value after applying KStest on 269 p-values = 0.476476 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.