RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 9.7414 0.085899 2 to 25 15.96 10.6579 0.126216 3 to 26 15.57 20.2789 0.739787 4 to 27 15.76 14.5384 0.371310 5 to 28 15.62 23.8003 0.875038 6 to 29 15.94 9.9876 0.095869 7 to 30 15.87 19.1275 0.678737 8 to 31 15.94 21.9603 0.813751 9 to 32 15.86 25.3311 0.912459 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.644362 Tough bday spacings test for dh-ranFile-2018-06-14_14:31: 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 32 67 105 85 83 62 31 11 14 2 (O-E)^2/E 0.1 0.6 0.5 0.5 1.6 0.3 1.9 0.1 1.0 8.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 16.003, p= 0.900 RESULTS OF GCD FOR dh-ranFile-2018-06-14_14:31 Euclid's algorithm: p-value, steps to gcd: 0.289494 p-value, dist. of gcd's: 0.400768 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.534 0.734 0.421 0.076 0.042 0.886 0.557 0.361 Bits 8 to 15---> 0.613 0.034 0.413 0.096 0.042 0.752 0.044 0.833 Bits 16 to 23---> 0.776 0.773 0.119 0.603 0.861 0.232 0.042 0.137 Bits 24 to 31---> 0.641 0.276 0.345 0.390 0.149 0.860 0.795 0.885 KS test for the above 32 p values: 0.771 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_14:31, p-values for 5 runs: 0.1214, 0.0865, 0.6499, 0.6260, 0.8355 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5075 5134.0 0.678 1.530 r= 30 23147 23103.0 0.084 1.613 r= 31 11580 11551.5 0.070 1.684 chi-square = 1.684 with df = 3; p-value = 0.359 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5074 5134.0 0.701 0.702 r= 31 23207 23103.0 0.468 1.170 r= 32 11508 11551.5 0.164 1.334 chi-square = 1.334 with df = 3; p-value = 0.279 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_14:31 b-rank test for bits 1 to 8, p=0.52241 b-rank test for bits 2 to 9, p=0.60761 b-rank test for bits 3 to 10, p=0.15979 b-rank test for bits 4 to 11, p=0.81090 b-rank test for bits 5 to 12, p=0.13916 b-rank test for bits 6 to 13, p=0.86933 b-rank test for bits 7 to 14, p=0.77510 b-rank test for bits 8 to 15, p=0.95715 b-rank test for bits 9 to 16, p=0.64004 b-rank test for bits 10 to 17, p=0.20362 b-rank test for bits 11 to 18, p=0.00245 b-rank test for bits 12 to 19, p=0.80879 b-rank test for bits 13 to 20, p=0.74912 b-rank test for bits 14 to 21, p=0.37708 b-rank test for bits 15 to 22, p=0.86294 b-rank test for bits 16 to 23, p=0.44087 b-rank test for bits 17 to 24, p=0.75429 b-rank test for bits 18 to 25, p=0.24215 b-rank test for bits 19 to 26, p=0.40026 b-rank test for bits 20 to 27, p=0.26243 b-rank test for bits 21 to 28, p=0.23010 b-rank test for bits 22 to 29, p=0.54067 b-rank test for bits 23 to 30, p=0.10756 b-rank test for bits 24 to 31, p=0.88417 b-rank test for bits 25 to 32, p=0.92565 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 = 0.812478 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_14:31 (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 141849 -0.14 0.443952 2 141952 0.10 0.539707 3 141774 -0.32 0.375929 4 141383 -1.23 0.109397 5 141930 0.05 0.519259 6 142082 0.40 0.656686 7 142015 0.25 0.597504 8 142318 0.95 0.830170 9 141721 -0.44 0.329960 10 142152 0.57 0.714638 11 142312 0.94 0.826601 12 141821 -0.21 0.418248 13 142575 1.56 0.940063 14 142126 0.51 0.693655 15 141717 -0.45 0.326583 16 142187 0.65 0.741754 17 142270 0.84 0.800298 18 142411 1.17 0.879427 19 141762 -0.34 0.365337 20 141469 -1.03 0.151785 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-14_14:31 Bits used No. missing words z-score p-value 23 to 32 141631 -0.9598 0.168588 22 to 31 142024 0.3954 0.653731 21 to 30 142047 0.4747 0.682508 20 to 29 142123 0.7368 0.769376 19 to 28 141490 -1.4460 0.074093 18 to 27 141554 -1.2253 0.110236 17 to 26 141784 -0.4322 0.332808 16 to 25 141837 -0.2494 0.401520 15 to 24 141856 -0.1839 0.427047 14 to 23 141984 0.2575 0.601597 13 to 22 141880 -0.1011 0.459721 12 to 21 142075 0.5713 0.716094 11 to 20 142099 0.6540 0.743455 10 to 19 141888 -0.0736 0.470684 9 to 18 142038 0.4437 0.671367 8 to 17 142146 0.8161 0.792780 7 to 16 141970 0.2092 0.582857 6 to 15 142044 0.4644 0.678812 5 to 14 142312 1.3885 0.917510 4 to 13 142136 0.7816 0.782781 3 to 12 141419 -1.6908 0.045438 2 to 11 141267 -2.2149 0.013382 1 to 10 141387 -1.8011 0.035841 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-14_14:31 Bits used No. missing words z-score p-value 28 to 32 142053 0.4870 0.686877 27 to 31 142179 0.9141 0.819677 26 to 30 141623 -0.9706 0.165871 25 to 29 141764 -0.4926 0.311132 24 to 28 141662 -0.8384 0.200901 23 to 27 141292 -2.0926 0.018190 22 to 26 142002 0.3141 0.623291 21 to 25 141902 -0.0248 0.490088 20 to 24 141151 -2.5706 0.005076 19 to 23 141566 -1.1638 0.122246 18 to 22 141813 -0.3265 0.372007 17 to 21 142462 1.8735 0.969497 16 to 20 142074 0.5582 0.711647 15 to 19 141850 -0.2011 0.420303 14 to 18 142026 0.3955 0.653760 13 to 17 141368 -1.8350 0.033252 12 to 16 141847 -0.2113 0.416331 11 to 15 142146 0.8023 0.788802 10 to 14 141785 -0.4215 0.336711 9 to 13 142146 0.8023 0.788802 8 to 12 142080 0.5785 0.718551 7 to 11 142064 0.5243 0.699967 6 to 10 141788 -0.4113 0.340431 5 to 9 142153 0.8260 0.795598 4 to 8 141654 -0.8655 0.193375 3 to 7 141668 -0.8181 0.206659 2 to 6 141780 -0.4384 0.330546 1 to 5 141872 -0.1265 0.449651 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-14_14:31 Bits used No. missing words z-score p-value 31 to 32 141868 -0.1219 0.451482 30 to 31 142584 1.9902 0.976714 29 to 30 142303 1.1613 0.877234 28 to 29 141684 -0.6647 0.253124 27 to 28 142219 0.9135 0.819505 26 to 27 142333 1.2498 0.894307 25 to 26 142340 1.2704 0.898031 24 to 25 141613 -0.8741 0.191024 23 to 24 142050 0.4150 0.660913 22 to 23 141395 -1.5172 0.064608 21 to 22 142499 1.7394 0.959021 20 to 21 142221 0.9194 0.821052 19 to 20 141677 -0.6853 0.246565 18 to 19 142696 2.3206 0.989845 17 to 18 141733 -0.5201 0.301480 16 to 17 141786 -0.3638 0.358002 15 to 16 142173 0.7778 0.781653 14 to 15 141781 -0.3786 0.352509 13 to 14 141914 0.0138 0.505496 12 to 13 142207 0.8781 0.810051 11 to 12 141834 -0.2222 0.412074 10 to 11 141291 -1.8240 0.034077 9 to 10 141902 -0.0216 0.491375 8 to 9 142266 1.0521 0.853629 7 to 8 142102 0.5683 0.715101 6 to 7 142114 0.6037 0.726994 5 to 6 142105 0.5772 0.718097 4 to 5 142100 0.5624 0.713095 3 to 4 141294 -1.8151 0.034752 2 to 3 142293 1.1318 0.871134 1 to 2 141919 0.0285 0.511378 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2291.86 -2.943 0.001623 Test results for specific bytes for dh-ranFile-2018-06-14_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2442.80 -0.809 0.209286 2 to 9 2515.16 0.214 0.584859 3 to 10 2585.00 1.202 0.885338 4 to 11 2478.56 -0.303 0.380891 5 to 12 2572.79 1.029 0.848369 6 to 13 2422.94 -1.090 0.137893 7 to 14 2618.29 1.673 0.952818 8 to 15 2483.96 -0.227 0.410280 9 to 16 2544.80 0.634 0.736819 10 to 17 2561.69 0.872 0.808531 11 to 18 2443.83 -0.794 0.213502 12 to 19 2595.82 1.355 0.912316 13 to 20 2411.62 -1.250 0.105670 14 to 21 2444.68 -0.782 0.217006 15 to 22 2508.53 0.121 0.548030 16 to 23 2447.72 -0.739 0.229831 17 to 24 2605.87 1.497 0.932828 18 to 25 2393.51 -1.506 0.066026 19 to 26 2484.71 -0.216 0.414381 20 to 27 2609.08 1.543 0.938544 21 to 28 2497.57 -0.034 0.486283 22 to 29 2592.99 1.315 0.905751 23 to 30 2582.35 1.165 0.877900 24 to 31 2594.33 1.334 0.908899 25 to 32 2578.27 1.107 0.865831 CDPARK for dh-ranFile-2018-06-14_14:31: 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 3542 0.8676 0.807188 3545 1.0046 0.842447 3501 -1.0046 0.157553 3530 0.3196 0.625377 3511 -0.5479 0.291865 3514 -0.4110 0.340551 3493 -1.3699 0.085365 3546 1.0502 0.853193 3530 0.3196 0.625377 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3522.40 sample std.=17.88 p-value of the KSTEST for those 10 p-values: 0.933094 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_14:31 0.8309,0.9569,0.2223,0.3379,0.0713,0.0379,0.1462,0.0651,0.0242,0.3609, The KS test for those 10 p-values: 0.018030 The 3DSPHERES test for dh-ranFile-2018-06-14_14:31 sample no r^3 equiv. uni. 1 1.366 0.044514 2 23.759 0.547054 3 52.877 0.828395 4 4.596 0.142029 5 6.219 0.187216 6 92.199 0.953731 7 21.431 0.510491 8 10.196 0.288147 9 30.289 0.635648 10 4.669 0.144128 11 0.179 0.005959 12 12.185 0.333792 13 53.312 0.830866 14 45.300 0.779089 15 8.896 0.256609 16 31.185 0.646370 17 2.996 0.095030 18 37.504 0.713532 19 41.623 0.750288 20 15.593 0.405348 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.796893 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 1.3 1.5 -0.4 -0.5 -0.9 -0.1 1.0 1.5 -0.3 -0.3 1.5 -1.4 -0.1 1.0 -0.7 -1.0 -0.1 2.2 -0.3 1.3 -0.6 -0.2 -1.0 0.2 -0.4 0.5 -1.2 -0.5 -1.9 -1.0 -0.5 -0.2 -1.1 0.5 1.3 -0.5 -0.4 1.7 -0.1 2.4 -1.0 -1.1 Chi-square with 42 degrees of freedom:46.529081 z-score=0.494163, p-value=0.708714 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-14_14:31 Test no p-value 1 0.419783 2 0.337420 3 0.080562 4 0.027547 5 0.327864 6 0.750980 7 0.682421 8 0.096475 9 0.381761 10 0.014017 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.045080 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_14:31: (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 66352 1.49 66687 0.01 3 25000.00 25295 3.48 25009 0.00 4 6666.67 6699 0.16 6644 0.08 5 1388.89 1391 0.00 1368 0.31 6 238.10 228 0.43 255 1.20 7 34.72 30 0.64 31 0.40 8 4.96 4 0.19 5 0.00 p=0.61819 p=0.08029 Number of rngs required: 689100, p-value: 0.790 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_14:31 No. of wins: Observed Expected 98821 98585.9 z-score= 1.052, pvalue=0.85353 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67112 66666.7 2.975 2.975 2 37610 37654.3 0.052 3.027 3 27130 26954.7 1.140 4.167 4 19217 19313.5 0.482 4.648 5 13804 13851.4 0.162 4.811 6 9750 9943.5 3.767 8.578 7 7172 7145.0 0.102 8.680 8 4988 5139.1 4.441 13.121 9 3693 3699.9 0.013 13.134 10 2696 2666.3 0.331 13.464 11 1793 1923.3 8.831 22.296 12 1323 1388.7 3.112 25.408 13 1020 1003.7 0.264 25.672 14 733 726.1 0.065 25.737 15 544 525.8 0.627 26.364 16 390 381.2 0.205 26.570 17 268 276.5 0.264 26.833 18 203 200.8 0.023 26.857 19 145 146.0 0.007 26.864 20 113 106.2 0.433 27.297 21 296 287.1 0.275 27.572 Chisq= 27.57 for 20 degrees of freedom, p= 0.88007 SUMMARY of craptest p-value for no. of wins: 0.853529 p-value for throws/game: 0.880074 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_14:31 No. of wins: Observed Expected 99004 98585.9 z-score= 1.870, pvalue=0.96927 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66884 66666.7 0.709 0.709 2 37666 37654.3 0.004 0.712 3 26724 26954.7 1.975 2.687 4 19504 19313.5 1.880 4.567 5 14025 13851.4 2.175 6.742 6 9644 9943.5 9.024 15.766 7 7101 7145.0 0.271 16.037 8 5222 5139.1 1.338 17.375 9 3748 3699.9 0.626 18.001 10 2552 2666.3 4.900 22.901 11 1948 1923.3 0.316 23.218 12 1387 1388.7 0.002 23.220 13 980 1003.7 0.560 23.780 14 730 726.1 0.021 23.801 15 516 525.8 0.184 23.985 16 375 381.2 0.099 24.084 17 273 276.5 0.045 24.129 18 200 200.8 0.003 24.133 19 150 146.0 0.110 24.243 20 109 106.2 0.073 24.316 21 262 287.1 2.197 26.513 Chisq= 26.51 for 20 degrees of freedom, p= 0.85046 SUMMARY of craptest p-value for no. of wins: 0.969270 p-value for throws/game: 0.850462 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0024,0.0051,0.0060,0.0134,0.0140,0.0180,0.0182,0.0242,0.0275, 0.0333,0.0341,0.0342,0.0348,0.0358,0.0379,0.0422,0.0423,0.0425,0.0444, 0.0445,0.0451,0.0454,0.0646,0.0651,0.0660,0.0713,0.0741,0.0762,0.0803, 0.0806,0.0854,0.0859,0.0865,0.0950,0.0958,0.0959,0.0965,0.1057,0.1076, 0.1094,0.1102,0.1189,0.1214,0.1222,0.1262,0.1373,0.1379,0.1392,0.1420, 0.1441,0.1462,0.1493,0.1518,0.1576,0.1598,0.1659,0.1686,0.1872,0.1910, 0.1934,0.2009,0.2036,0.2067,0.2093,0.2135,0.2170,0.2223,0.2298,0.2301, 0.2320,0.2421,0.2466,0.2531,0.2566,0.2624,0.2760,0.2789,0.2881,0.2895, 0.2919,0.3015,0.3077,0.3111,0.3266,0.3279,0.3300,0.3305,0.3328,0.3338, 0.3367,0.3374,0.3379,0.3404,0.3406,0.3447,0.3525,0.3580,0.3594,0.3609, 0.3611,0.3653,0.3713,0.3720,0.3759,0.3771,0.3809,0.3818,0.3903,0.4003, 0.4008,0.4015,0.4053,0.4103,0.4121,0.4131,0.4144,0.4163,0.4182,0.4198, 0.4203,0.4208,0.4270,0.4409,0.4440,0.4497,0.4515,0.4597,0.4707,0.4863, 0.4901,0.4914,0.5055,0.5105,0.5114,0.5193,0.5224,0.5343,0.5397,0.5407, 0.5471,0.5480,0.5573,0.5829,0.5849,0.5975,0.6016,0.6027,0.6076,0.6131, 0.6182,0.6233,0.6254,0.6254,0.6260,0.6356,0.6400,0.6408,0.6444,0.6464, 0.6499,0.6537,0.6538,0.6567,0.6609,0.6714,0.6787,0.6788,0.6824,0.6825, 0.6869,0.6937,0.7000,0.7087,0.7116,0.7131,0.7135,0.7146,0.7151,0.7161, 0.7181,0.7186,0.7270,0.7344,0.7368,0.7398,0.7418,0.7435,0.7491,0.7503, 0.7510,0.7518,0.7543,0.7694,0.7709,0.7734,0.7751,0.7757,0.7791,0.7817, 0.7828,0.7888,0.7888,0.7898,0.7928,0.7950,0.7956,0.7969,0.8003,0.8072, 0.8085,0.8088,0.8101,0.8109,0.8125,0.8138,0.8195,0.8197,0.8211,0.8266, 0.8284,0.8302,0.8309,0.8309,0.8333,0.8355,0.8424,0.8484,0.8505,0.8532, 0.8535,0.8536,0.8600,0.8613,0.8629,0.8658,0.8693,0.8711,0.8750,0.8772, 0.8779,0.8794,0.8801,0.8842,0.8852,0.8853,0.8858,0.8943,0.8980,0.9004, 0.9058,0.9089,0.9123,0.9125,0.9175,0.9257,0.9328,0.9331,0.9385,0.9401, 0.9528,0.9537,0.9569,0.9571,0.9590,0.9693,0.9695,0.9767,0.9898, Overall p-value after applying KStest on 269 p-values = 0.106666 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.