RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-22_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 21.0128 0.774281 2 to 25 15.88 16.9605 0.542956 3 to 26 15.68 16.7926 0.531502 4 to 27 15.76 17.6600 0.589415 5 to 28 15.77 11.2372 0.156029 6 to 29 15.61 20.4720 0.749196 7 to 30 15.31 28.1325 0.956587 8 to 31 15.61 18.7331 0.655933 9 to 32 15.80 18.8692 0.663908 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.217134 Tough bday spacings test for dh-ranFile-2016-05-22_04:31: 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 8 44 72 104 91 77 55 29 15 4 1 (O-E)^2/E 0.1 1.5 0.0 0.4 0.5 0.0 0.2 0.0 0.0 1.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 6.062, p= 0.190 RESULTS OF GCD FOR dh-ranFile-2016-05-22_04:31 Euclid's algorithm: p-value, steps to gcd: 0.910032 p-value, dist. of gcd's: 0.638437 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-22_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.792 0.428 0.179 0.255 0.832 0.917 0.587 0.710 Bits 8 to 15---> 0.522 0.662 0.975 0.319 0.344 0.359 0.285 0.164 Bits 16 to 23---> 0.307 0.112 0.376 0.549 0.144 0.981 0.916 0.929 Bits 24 to 31---> 0.236 0.732 0.124 0.461 0.808 0.756 0.684 0.220 KS test for the above 32 p values: 0.215 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-22_04:31, p-values for 5 runs: 0.4611, 0.0611, 0.2126, 0.2248, 0.4630 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-22_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5119 5134.0 0.044 0.249 r= 30 22987 23103.0 0.583 0.832 r= 31 11676 11551.5 1.341 2.173 chi-square = 2.173 with df = 3; p-value = 0.463 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-22_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5030 5134.0 2.107 2.162 r= 31 23187 23103.0 0.305 2.467 r= 32 11575 11551.5 0.048 2.515 chi-square = 2.515 with df = 3; p-value = 0.527 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-22_04:31 b-rank test for bits 1 to 8, p=0.05863 b-rank test for bits 2 to 9, p=0.38859 b-rank test for bits 3 to 10, p=0.66155 b-rank test for bits 4 to 11, p=0.90221 b-rank test for bits 5 to 12, p=0.06461 b-rank test for bits 6 to 13, p=0.25800 b-rank test for bits 7 to 14, p=0.13373 b-rank test for bits 8 to 15, p=0.17049 b-rank test for bits 9 to 16, p=0.64331 b-rank test for bits 10 to 17, p=0.54054 b-rank test for bits 11 to 18, p=0.83815 b-rank test for bits 12 to 19, p=0.70128 b-rank test for bits 13 to 20, p=0.54257 b-rank test for bits 14 to 21, p=0.63356 b-rank test for bits 15 to 22, p=0.33535 b-rank test for bits 16 to 23, p=0.91540 b-rank test for bits 17 to 24, p=0.41428 b-rank test for bits 18 to 25, p=0.82766 b-rank test for bits 19 to 26, p=0.20017 b-rank test for bits 20 to 27, p=0.35758 b-rank test for bits 21 to 28, p=0.89601 b-rank test for bits 22 to 29, p=0.80710 b-rank test for bits 23 to 30, p=0.50468 b-rank test for bits 24 to 31, p=0.09481 b-rank test for bits 25 to 32, p=0.48127 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 = 0.987087 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-22_04:31 (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 142477 1.33 0.907635 2 142829 2.15 0.984173 3 141382 -1.23 0.108960 4 142013 0.24 0.595695 5 141884 -0.06 0.476404 6 141861 -0.11 0.455047 7 141638 -0.63 0.263057 8 141743 -0.39 0.348778 9 141229 -1.59 0.055967 10 141559 -0.82 0.206528 11 141404 -1.18 0.118865 12 141782 -0.30 0.383042 13 142456 1.28 0.899246 14 142536 1.46 0.928428 15 141468 -1.03 0.151236 16 142210 0.70 0.758816 17 142470 1.31 0.904898 18 142204 0.69 0.754425 19 142385 1.11 0.866797 20 142374 1.09 0.861189 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-22_04:31 Bits used No. missing words z-score p-value 23 to 32 141963 0.1851 0.573413 22 to 31 141765 -0.4977 0.309351 21 to 30 141637 -0.9391 0.173848 20 to 29 141527 -1.3184 0.093688 19 to 28 142281 1.2816 0.900012 18 to 27 142566 2.2644 0.988225 17 to 26 142266 1.2299 0.890632 16 to 25 141918 0.0299 0.511925 15 to 24 142164 0.8782 0.810075 14 to 23 142289 1.3092 0.904768 13 to 22 141898 -0.0391 0.484418 12 to 21 141472 -1.5080 0.065773 11 to 20 141495 -1.4287 0.076542 10 to 19 142015 0.3644 0.642213 9 to 18 142208 1.0299 0.848471 8 to 17 141909 -0.0011 0.499546 7 to 16 141552 -1.2322 0.108942 6 to 15 142347 1.5092 0.934377 5 to 14 141808 -0.3494 0.363389 4 to 13 142131 0.7644 0.777679 3 to 12 142014 0.3609 0.640925 2 to 11 142346 1.5058 0.933935 1 to 10 142038 0.4437 0.671367 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-22_04:31 Bits used No. missing words z-score p-value 28 to 32 141753 -0.5299 0.298080 27 to 31 142702 2.6870 0.996395 26 to 30 141323 -1.9876 0.023430 25 to 29 142389 1.6260 0.948025 24 to 28 142064 0.5243 0.699967 23 to 27 142540 2.1379 0.983736 22 to 26 141763 -0.4960 0.309935 21 to 25 141913 0.0124 0.504963 20 to 24 141924 0.0497 0.519831 19 to 23 142197 0.9752 0.835258 18 to 22 142088 0.6057 0.727630 17 to 21 142005 0.3243 0.627147 16 to 20 142169 0.8802 0.810635 15 to 19 141773 -0.4621 0.321992 14 to 18 142014 0.3548 0.638635 13 to 17 141888 -0.0723 0.471180 12 to 16 142229 1.0836 0.860735 11 to 15 141634 -0.9333 0.175327 10 to 14 141587 -1.0926 0.137275 9 to 13 141677 -0.7876 0.215477 8 to 12 142505 2.0192 0.978268 7 to 11 141907 -0.0079 0.496849 6 to 10 142145 0.7989 0.787820 5 to 9 142536 2.1243 0.983178 4 to 8 141847 -0.2113 0.416331 3 to 7 142212 1.0260 0.847554 2 to 6 142101 0.6497 0.742066 1 to 5 142252 1.1616 0.877300 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-22_04:31 Bits used No. missing words z-score p-value 31 to 32 142125 0.6362 0.737675 30 to 31 142301 1.1554 0.876030 29 to 30 141763 -0.4317 0.332997 28 to 29 142258 1.0285 0.848149 27 to 28 141769 -0.4140 0.339454 26 to 27 141634 -0.8122 0.208343 25 to 26 142411 1.4799 0.930544 24 to 25 142066 0.4622 0.678014 23 to 24 142085 0.5182 0.697841 22 to 23 142091 0.5359 0.703986 21 to 22 141810 -0.2930 0.384758 20 to 21 142864 2.8161 0.997570 19 to 20 142136 0.6686 0.748138 18 to 19 142142 0.6863 0.753751 17 to 18 142023 0.3353 0.631304 16 to 17 141872 -0.1101 0.456158 15 to 16 141951 0.1229 0.548915 14 to 15 142017 0.3176 0.624610 13 to 14 141882 -0.0806 0.467872 12 to 13 141979 0.2055 0.581416 11 to 12 142008 0.2911 0.614498 10 to 11 142246 0.9931 0.839676 9 to 10 142216 0.9046 0.817170 8 to 9 141867 -0.1249 0.450314 7 to 8 141024 -2.6116 0.004506 6 to 7 141899 -0.0305 0.487845 5 to 6 141469 -1.2989 0.096988 4 to 5 141822 -0.2576 0.398354 3 to 4 141950 0.1200 0.547747 2 to 3 141706 -0.5998 0.274322 1 to 2 142132 0.6568 0.744359 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-22_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2586.00 1.216 0.888055 Test results for specific bytes for dh-ranFile-2016-05-22_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2505.77 0.082 0.532498 2 to 9 2523.10 0.327 0.628051 3 to 10 2461.53 -0.544 0.293218 4 to 11 2499.54 -0.006 0.497418 5 to 12 2551.43 0.727 0.766468 6 to 13 2609.01 1.542 0.938420 7 to 14 2433.11 -0.946 0.172073 8 to 15 2622.93 1.739 0.958942 9 to 16 2546.97 0.664 0.746752 10 to 17 2419.33 -1.141 0.126968 11 to 18 2528.04 0.397 0.654157 12 to 19 2345.95 -2.179 0.014682 13 to 20 2569.73 0.986 0.837963 14 to 21 2571.96 1.018 0.845566 15 to 22 2458.29 -0.590 0.277622 16 to 23 2465.04 -0.494 0.310486 17 to 24 2440.26 -0.845 0.199103 18 to 25 2516.29 0.230 0.591089 19 to 26 2472.84 -0.384 0.350438 20 to 27 2419.12 -1.144 0.126359 21 to 28 2606.90 1.512 0.934714 22 to 29 2366.49 -1.888 0.029506 23 to 30 2555.92 0.791 0.785473 24 to 31 2556.11 0.794 0.786272 25 to 32 2438.07 -0.876 0.190552 CDPARK for dh-ranFile-2016-05-22_04:31: 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 3512 -0.5023 0.307734 3552 1.3242 0.907282 3531 0.3653 0.642555 3501 -1.0046 0.157553 3549 1.1872 0.882429 3516 -0.3196 0.374623 3527 0.1826 0.572463 3513 -0.4566 0.323972 3517 -0.2740 0.392053 3538 0.6849 0.753306 Square side=100, avg. no. parked=3525.60 sample std.=15.95 p-value of the KSTEST for those 10 p-values: 0.845170 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-22_04:31 0.5175,0.9371,0.5075,0.7730,0.5487,0.6245,0.2134,0.3367,0.7014,0.9980, The KS test for those 10 p-values: 0.244903 The 3DSPHERES test for dh-ranFile-2016-05-22_04:31 sample no r^3 equiv. uni. 1 34.047 0.678547 2 8.391 0.243987 3 52.826 0.828102 4 7.504 0.221308 5 4.142 0.128960 6 22.079 0.520959 7 80.888 0.932543 8 13.614 0.364794 9 7.032 0.208951 10 16.115 0.415600 11 77.945 0.925589 12 24.076 0.551802 13 31.940 0.655156 14 23.976 0.550307 15 45.112 0.777703 16 91.980 0.953393 17 47.671 0.795876 18 7.374 0.217917 19 19.547 0.478772 20 24.195 0.553578 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.614362 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-22_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.1 0.0 0.2 -1.5 0.0 -0.4 -0.7 0.5 -1.4 -1.1 0.9 0.1 1.8 -0.2 0.1 -0.4 -1.9 0.4 0.9 0.4 -0.3 1.5 1.7 -0.5 -0.7 -1.5 0.6 0.1 -2.5 -1.7 0.5 0.5 1.2 1.5 -1.2 -0.4 0.9 -0.7 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:42.437370 z-score=0.047721, p-value=0.547883 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-22_04:31 Test no p-value 1 0.013110 2 0.021456 3 0.156475 4 0.099712 5 0.786648 6 0.412347 7 0.294270 8 0.223912 9 0.050482 10 0.266037 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003129 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-22_04:31: (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 66773 0.17 66608 0.05 3 25000.00 24924 0.23 25107 0.46 4 6666.67 6674 0.01 6715 0.35 5 1388.89 1356 0.78 1298 5.95 6 238.10 234 0.07 222 1.09 7 34.72 33 0.09 41 1.14 8 4.96 5 0.00 8 1.86 p=0.03080 p=0.90832 Number of rngs required: 687313, p-value: 0.102 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-22_04:31 No. of wins: Observed Expected 98549 98585.9 z-score=-0.165, pvalue=0.43453 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66773 66666.7 0.170 0.170 2 37811 37654.3 0.652 0.822 3 26934 26954.7 0.016 0.837 4 19265 19313.5 0.122 0.959 5 13641 13851.4 3.197 4.156 6 9947 9943.5 0.001 4.157 7 7093 7145.0 0.379 4.536 8 5095 5139.1 0.378 4.914 9 3678 3699.9 0.129 5.043 10 2674 2666.3 0.022 5.065 11 2002 1923.3 3.218 8.283 12 1437 1388.7 1.677 9.960 13 1008 1003.7 0.018 9.978 14 740 726.1 0.265 10.243 15 532 525.8 0.072 10.315 16 371 381.2 0.270 10.585 17 275 276.5 0.009 10.594 18 202 200.8 0.007 10.601 19 143 146.0 0.061 10.662 20 120 106.2 1.789 12.451 21 259 287.1 2.753 15.204 Chisq= 15.20 for 20 degrees of freedom, p= 0.23537 SUMMARY of craptest p-value for no. of wins: 0.434530 p-value for throws/game: 0.235368 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-22_04:31 No. of wins: Observed Expected 98532 98585.9 z-score=-0.241, pvalue=0.40482 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66435 66666.7 0.805 0.805 2 37802 37654.3 0.579 1.384 3 27011 26954.7 0.117 1.502 4 19422 19313.5 0.610 2.112 5 13668 13851.4 2.429 4.540 6 10013 9943.5 0.485 5.026 7 7289 7145.0 2.901 7.927 8 5213 5139.1 1.063 8.990 9 3561 3699.9 5.212 14.202 10 2695 2666.3 0.309 14.511 11 1895 1923.3 0.417 14.928 12 1368 1388.7 0.310 15.238 13 1011 1003.7 0.053 15.291 14 756 726.1 1.228 16.519 15 510 525.8 0.477 16.996 16 388 381.2 0.123 17.119 17 268 276.5 0.264 17.383 18 172 200.8 4.139 21.521 19 136 146.0 0.683 22.204 20 98 106.2 0.635 22.840 21 289 287.1 0.012 22.852 Chisq= 22.85 for 20 degrees of freedom, p= 0.70388 SUMMARY of craptest p-value for no. of wins: 0.404821 p-value for throws/game: 0.703876 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0031,0.0045,0.0131,0.0147,0.0215,0.0234,0.0295,0.0308,0.0505,0.0560, 0.0586,0.0611,0.0646,0.0658,0.0765,0.0937,0.0948,0.0970,0.0997,0.1024, 0.1089,0.1090,0.1119,0.1189,0.1241,0.1264,0.1270,0.1290,0.1337,0.1373, 0.1438,0.1512,0.1560,0.1565,0.1576,0.1645,0.1705,0.1721,0.1738,0.1753, 0.1795,0.1899,0.1906,0.1991,0.2002,0.2065,0.2083,0.2090,0.2126,0.2134, 0.2152,0.2155,0.2171,0.2179,0.2195,0.2213,0.2239,0.2248,0.2354,0.2359, 0.2440,0.2449,0.2555,0.2580,0.2631,0.2660,0.2743,0.2776,0.2851,0.2932, 0.2943,0.2981,0.3069,0.3077,0.3094,0.3099,0.3105,0.3188,0.3220,0.3240, 0.3330,0.3353,0.3367,0.3395,0.3439,0.3488,0.3504,0.3576,0.3594,0.3634, 0.3648,0.3746,0.3761,0.3830,0.3848,0.3886,0.3921,0.3984,0.4048,0.4123, 0.4143,0.4156,0.4163,0.4280,0.4345,0.4503,0.4550,0.4562,0.4607,0.4611, 0.4627,0.4630,0.4679,0.4712,0.4764,0.4788,0.4813,0.4844,0.4878,0.4968, 0.4974,0.4995,0.5047,0.5050,0.5075,0.5119,0.5175,0.5198,0.5210,0.5220, 0.5274,0.5315,0.5325,0.5405,0.5426,0.5430,0.5477,0.5479,0.5487,0.5489, 0.5492,0.5503,0.5518,0.5536,0.5725,0.5734,0.5814,0.5867,0.5894,0.5911, 0.5957,0.6144,0.6145,0.6245,0.6246,0.6271,0.6281,0.6313,0.6336,0.6384, 0.6386,0.6409,0.6422,0.6426,0.6433,0.6542,0.6552,0.6559,0.6615,0.6621, 0.6639,0.6714,0.6780,0.6785,0.6845,0.6978,0.7000,0.7013,0.7014,0.7039, 0.7040,0.7100,0.7276,0.7315,0.7377,0.7421,0.7444,0.7468,0.7481,0.7492, 0.7533,0.7538,0.7544,0.7563,0.7588,0.7665,0.7730,0.7743,0.7777,0.7777, 0.7855,0.7863,0.7866,0.7878,0.7916,0.7959,0.8071,0.8076,0.8101,0.8106, 0.8172,0.8277,0.8281,0.8324,0.8353,0.8380,0.8382,0.8397,0.8452,0.8456, 0.8476,0.8481,0.8485,0.8607,0.8612,0.8668,0.8760,0.8773,0.8824,0.8881, 0.8906,0.8960,0.8992,0.9000,0.9022,0.9048,0.9049,0.9073,0.9076,0.9083, 0.9100,0.9154,0.9162,0.9169,0.9256,0.9284,0.9294,0.9305,0.9325,0.9339, 0.9344,0.9347,0.9371,0.9384,0.9480,0.9534,0.9566,0.9589,0.9749,0.9783, 0.9811,0.9832,0.9837,0.9842,0.9871,0.9882,0.9964,0.9976,0.9980, Overall p-value after applying KStest on 269 p-values = 0.125616 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.