RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-14_15:31 (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 13.1775 0.275772 2 to 25 15.86 16.1158 0.484356 3 to 26 15.97 13.8089 0.319420 4 to 27 15.73 8.2148 0.038265 5 to 28 15.89 7.9421 0.032230 6 to 29 15.85 22.5216 0.834518 7 to 30 15.68 12.1838 0.211117 8 to 31 15.62 17.0816 0.551148 9 to 32 15.68 13.6233 0.306438 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.142601 Tough bday spacings test for dh-ranFile-2018-03-14_15:31: 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 9 30 74 103 94 76 52 36 14 9 3 (O-E)^2/E 0.0 1.2 0.0 0.3 0.1 0.1 0.0 1.3 0.1 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.193, p= 0.062 RESULTS OF GCD FOR dh-ranFile-2018-03-14_15:31 Euclid's algorithm: p-value, steps to gcd: 0.560722 p-value, dist. of gcd's: 0.154694 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-14_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.275 0.135 0.993 0.603 0.855 0.547 0.124 0.817 Bits 8 to 15---> 0.105 0.439 0.335 0.747 0.935 0.711 0.004 0.515 Bits 16 to 23---> 0.116 0.260 0.816 0.812 0.708 0.112 0.709 0.617 Bits 24 to 31---> 0.163 0.994 0.868 0.209 0.744 0.527 0.482 0.836 KS test for the above 32 p values: 0.419 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-14_15:31, p-values for 5 runs: 0.1362, 0.2728, 0.8901, 0.6222, 0.7243 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-14_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5155 5134.0 0.086 0.720 r= 30 23156 23103.0 0.121 0.842 r= 31 11466 11551.5 0.633 1.475 chi-square = 1.475 with df = 3; p-value = 0.312 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-14_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5104 5134.0 0.175 0.176 r= 31 23199 23103.0 0.399 0.575 r= 32 11486 11551.5 0.372 0.946 chi-square = 0.946 with df = 3; p-value = 0.186 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-14_15:31 b-rank test for bits 1 to 8, p=0.24337 b-rank test for bits 2 to 9, p=0.32785 b-rank test for bits 3 to 10, p=0.44673 b-rank test for bits 4 to 11, p=0.79163 b-rank test for bits 5 to 12, p=0.81074 b-rank test for bits 6 to 13, p=0.92425 b-rank test for bits 7 to 14, p=0.48910 b-rank test for bits 8 to 15, p=0.38195 b-rank test for bits 9 to 16, p=0.64996 b-rank test for bits 10 to 17, p=0.44653 b-rank test for bits 11 to 18, p=0.99438 b-rank test for bits 12 to 19, p=0.55539 b-rank test for bits 13 to 20, p=0.43612 b-rank test for bits 14 to 21, p=0.18767 b-rank test for bits 15 to 22, p=0.05431 b-rank test for bits 16 to 23, p=0.81358 b-rank test for bits 17 to 24, p=0.89110 b-rank test for bits 18 to 25, p=0.88862 b-rank test for bits 19 to 26, p=0.63979 b-rank test for bits 20 to 27, p=0.25966 b-rank test for bits 21 to 28, p=0.51456 b-rank test for bits 22 to 29, p=0.10803 b-rank test for bits 23 to 30, p=0.01940 b-rank test for bits 24 to 31, p=0.15942 b-rank test for bits 25 to 32, p=0.14761 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 = 0.993844 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-14_15:31 (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 142440 1.24 0.892491 2 141427 -1.13 0.129884 3 141871 -0.09 0.464320 4 141413 -1.16 0.123096 5 141320 -1.38 0.084266 6 141317 -1.38 0.083187 7 141234 -1.58 0.057297 8 141114 -1.86 0.031567 9 141933 0.06 0.522052 10 141611 -0.70 0.242891 11 141509 -0.94 0.174804 12 141179 -1.71 0.043969 13 141857 -0.12 0.451344 14 141963 0.13 0.549895 15 141783 -0.30 0.383935 16 142113 0.48 0.682915 17 142128 0.51 0.695293 18 140871 -2.43 0.007633 19 142068 0.37 0.644579 20 142062 0.36 0.639344 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-14_15:31 Bits used No. missing words z-score p-value 23 to 32 141893 -0.0563 0.477547 22 to 31 142290 1.3127 0.905350 21 to 30 141379 -1.8287 0.033720 20 to 29 141921 0.0402 0.516050 19 to 28 141894 -0.0529 0.478921 18 to 27 141993 0.2885 0.613525 17 to 26 141975 0.2264 0.589574 16 to 25 142301 1.3506 0.911586 15 to 24 141901 -0.0287 0.488542 14 to 23 142256 1.1954 0.884037 13 to 22 142134 0.7747 0.780749 12 to 21 141895 -0.0494 0.480295 11 to 20 141358 -1.9011 0.028642 10 to 19 141843 -0.2287 0.409542 9 to 18 142058 0.5127 0.695904 8 to 17 141953 0.1506 0.559849 7 to 16 142005 0.3299 0.629261 6 to 15 142142 0.8023 0.788813 5 to 14 142253 1.1851 0.882005 4 to 13 141918 0.0299 0.511925 3 to 12 141518 -1.3494 0.088602 2 to 11 141793 -0.4011 0.344159 1 to 10 142226 1.0920 0.862576 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-14_15:31 Bits used No. missing words z-score p-value 28 to 32 142484 1.9480 0.974295 27 to 31 142148 0.8091 0.790757 26 to 30 141951 0.1413 0.556166 25 to 29 141422 -1.6520 0.049271 24 to 28 141744 -0.5604 0.287589 23 to 27 141741 -0.5706 0.284132 22 to 26 141609 -1.0181 0.154323 21 to 25 141936 0.0904 0.536018 20 to 24 141748 -0.5469 0.292230 19 to 23 142107 0.6701 0.748593 18 to 22 141502 -1.3808 0.083673 17 to 21 142153 0.8260 0.795598 16 to 20 142228 1.0802 0.859982 15 to 19 142351 1.4972 0.932828 14 to 18 141616 -0.9943 0.160029 13 to 17 141757 -0.5164 0.302797 12 to 16 141786 -0.4181 0.337949 11 to 15 142084 0.5921 0.723109 10 to 14 141998 0.3006 0.618131 9 to 13 141822 -0.2960 0.383602 8 to 12 142064 0.5243 0.699967 7 to 11 142032 0.4158 0.661233 6 to 10 142124 0.7277 0.766600 5 to 9 141995 0.2904 0.614248 4 to 8 141828 -0.2757 0.391391 3 to 7 141677 -0.7876 0.215477 2 to 6 142018 0.3684 0.643702 1 to 5 141715 -0.6587 0.255030 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-14_15:31 Bits used No. missing words z-score p-value 31 to 32 141255 -1.9302 0.026792 30 to 31 142303 1.1613 0.877234 29 to 30 142022 0.3324 0.630191 28 to 29 142490 1.7129 0.956634 27 to 28 141917 0.0226 0.509025 26 to 27 141681 -0.6735 0.250302 25 to 26 142244 0.9872 0.838234 24 to 25 142032 0.3619 0.641271 23 to 24 141879 -0.0895 0.464355 22 to 23 141209 -2.0659 0.019420 21 to 22 141917 0.0226 0.509025 20 to 21 142331 1.2439 0.893225 19 to 20 141796 -0.3343 0.369074 18 to 19 141888 -0.0629 0.474915 17 to 18 141846 -0.1868 0.425903 16 to 17 141273 -1.8771 0.030254 15 to 16 141562 -1.0246 0.152783 14 to 15 141863 -0.1367 0.445647 13 to 14 142212 0.8928 0.814026 12 to 13 141828 -0.2399 0.405199 11 to 12 142622 2.1023 0.982235 10 to 11 142199 0.8545 0.803582 9 to 10 142161 0.7424 0.771074 8 to 9 141558 -1.0364 0.150014 7 to 8 141686 -0.6588 0.255015 6 to 7 142145 0.6952 0.756532 5 to 6 141772 -0.4051 0.342701 4 to 5 141954 0.1318 0.552417 3 to 4 142252 1.0108 0.843950 2 to 3 141645 -0.7797 0.217774 1 to 2 141725 -0.5437 0.293308 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-14_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2589.17 1.261 0.896354 Test results for specific bytes for dh-ranFile-2018-03-14_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2491.61 -0.119 0.452765 2 to 9 2601.79 1.440 0.924998 3 to 10 2441.93 -0.821 0.205747 4 to 11 2487.84 -0.172 0.431729 5 to 12 2338.87 -2.279 0.011342 6 to 13 2534.74 0.491 0.688406 7 to 14 2560.45 0.855 0.803686 8 to 15 2447.02 -0.749 0.226850 9 to 16 2418.21 -1.157 0.123707 10 to 17 2513.74 0.194 0.577021 11 to 18 2466.08 -0.480 0.315706 12 to 19 2518.61 0.263 0.603799 13 to 20 2511.61 0.164 0.565216 14 to 21 2511.94 0.169 0.567041 15 to 22 2596.86 1.370 0.914637 16 to 23 2440.00 -0.849 0.198053 17 to 24 2532.01 0.453 0.674627 18 to 25 2597.25 1.375 0.915494 19 to 26 2578.01 1.103 0.865031 20 to 27 2412.37 -1.239 0.107615 21 to 28 2591.93 1.300 0.903206 22 to 29 2526.60 0.376 0.646606 23 to 30 2400.45 -1.408 0.079593 24 to 31 2503.62 0.051 0.520407 25 to 32 2560.31 0.853 0.803160 CDPARK for dh-ranFile-2018-03-14_15:31: 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 3474 -2.2374 0.012629 3501 -1.0046 0.157553 3505 -0.8219 0.205562 3552 1.3242 0.907282 3541 0.8219 0.794438 3527 0.1826 0.572463 3534 0.5023 0.692266 3535 0.5479 0.708135 3506 -0.7763 0.218799 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3518.50 sample std.=22.16 p-value of the KSTEST for those 10 p-values: 0.803580 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-14_15:31 0.6234,0.1336,0.5921,0.5342,0.3046,0.4028,0.8402,0.6883,0.1711,0.6299, The KS test for those 10 p-values: 0.702637 The 3DSPHERES test for dh-ranFile-2018-03-14_15:31 sample no r^3 equiv. uni. 1 81.314 0.933495 2 105.433 0.970235 3 21.311 0.508538 4 2.423 0.077604 5 23.002 0.535479 6 37.100 0.709647 7 6.597 0.197404 8 76.746 0.922557 9 14.815 0.389710 10 14.349 0.380162 11 25.057 0.566231 12 24.110 0.552319 13 58.378 0.857147 14 5.960 0.180186 15 92.219 0.953762 16 48.634 0.802328 17 2.562 0.081848 18 12.613 0.343239 19 19.309 0.474613 20 22.522 0.527979 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.645193 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-14_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 1.1 0.3 1.0 -0.1 0.4 -1.2 1.0 -0.5 -1.8 0.0 2.0 0.5 2.0 -0.4 -0.4 -0.6 -0.5 -2.0 2.1 -1.5 0.5 1.2 -1.2 0.0 -0.3 -1.1 1.3 1.5 -0.4 1.0 -2.3 0.1 -2.4 -1.9 0.3 -0.1 0.1 -1.3 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:55.581799 z-score=1.481896, p-value=0.921887 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-14_15:31 Test no p-value 1 0.576530 2 0.314843 3 0.305461 4 0.603480 5 0.519996 6 0.006404 7 0.426350 8 0.192415 9 0.002222 10 0.263038 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.035088 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-14_15:31: (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 66530 0.28 66373 1.29 3 25000.00 25060 0.14 25232 2.15 4 6666.67 6754 1.14 6746 0.94 5 1388.89 1360 0.60 1365 0.41 6 238.10 253 0.93 237 0.01 7 34.72 35 0.00 43 1.97 8 4.96 7 0.84 3 0.77 p=0.31567 p=0.72750 Number of rngs required: 688057, p-value: 0.345 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-14_15:31 No. of wins: Observed Expected 98688 98585.9 z-score= 0.457, pvalue=0.67611 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66719 66666.7 0.041 0.041 2 37688 37654.3 0.030 0.071 3 27071 26954.7 0.502 0.573 4 19374 19313.5 0.190 0.762 5 13738 13851.4 0.929 1.691 6 9887 9943.5 0.322 2.013 7 7197 7145.0 0.378 2.391 8 5143 5139.1 0.003 2.394 9 3623 3699.9 1.597 3.991 10 2631 2666.3 0.467 4.458 11 1942 1923.3 0.181 4.639 12 1343 1388.7 1.507 6.146 13 1013 1003.7 0.086 6.232 14 710 726.1 0.359 6.590 15 511 525.8 0.419 7.009 16 385 381.2 0.039 7.048 17 283 276.5 0.151 7.199 18 195 200.8 0.169 7.368 19 154 146.0 0.440 7.808 20 105 106.2 0.014 7.822 21 288 287.1 0.003 7.825 Chisq= 7.82 for 20 degrees of freedom, p= 0.00703 SUMMARY of craptest p-value for no. of wins: 0.676106 p-value for throws/game: 0.007035 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-14_15:31 No. of wins: Observed Expected 98937 98585.9 z-score= 1.571, pvalue=0.94185 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66694 66666.7 0.011 0.011 2 37629 37654.3 0.017 0.028 3 26807 26954.7 0.810 0.838 4 19377 19313.5 0.209 1.047 5 13822 13851.4 0.062 1.109 6 9987 9943.5 0.190 1.299 7 7160 7145.0 0.031 1.331 8 5135 5139.1 0.003 1.334 9 3686 3699.9 0.052 1.386 10 2645 2666.3 0.170 1.556 11 1965 1923.3 0.903 2.459 12 1373 1388.7 0.178 2.637 13 1029 1003.7 0.637 3.274 14 756 726.1 1.228 4.502 15 519 525.8 0.089 4.591 16 379 381.2 0.012 4.603 17 304 276.5 2.727 7.330 18 215 200.8 1.000 8.330 19 142 146.0 0.109 8.438 20 109 106.2 0.073 8.512 21 267 287.1 1.409 9.921 Chisq= 9.92 for 20 degrees of freedom, p= 0.03041 SUMMARY of craptest p-value for no. of wins: 0.941852 p-value for throws/game: 0.030411 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0039,0.0064,0.0070,0.0076,0.0113,0.0126,0.0194,0.0194,0.0268, 0.0286,0.0303,0.0304,0.0316,0.0322,0.0337,0.0351,0.0383,0.0440,0.0493, 0.0543,0.0573,0.0618,0.0776,0.0796,0.0818,0.0832,0.0837,0.0843,0.0886, 0.1055,0.1076,0.1080,0.1116,0.1164,0.1231,0.1237,0.1243,0.1299,0.1336, 0.1348,0.1362,0.1426,0.1476,0.1500,0.1528,0.1543,0.1547,0.1576,0.1594, 0.1600,0.1626,0.1711,0.1748,0.1802,0.1858,0.1877,0.1924,0.1974,0.1981, 0.2056,0.2057,0.2091,0.2111,0.2155,0.2178,0.2188,0.2268,0.2429,0.2434, 0.2503,0.2550,0.2550,0.2597,0.2599,0.2630,0.2728,0.2750,0.2758,0.2764, 0.2841,0.2876,0.2922,0.2933,0.3028,0.3046,0.3055,0.3064,0.3119,0.3148, 0.3157,0.3157,0.3194,0.3279,0.3352,0.3379,0.3427,0.3432,0.3442,0.3451, 0.3691,0.3802,0.3820,0.3836,0.3839,0.3897,0.3914,0.4028,0.4052,0.4095, 0.4186,0.4259,0.4264,0.4317,0.4361,0.4389,0.4456,0.4465,0.4467,0.4513, 0.4528,0.4643,0.4644,0.4746,0.4749,0.4775,0.4789,0.4803,0.4825,0.4844, 0.4885,0.4891,0.5085,0.5090,0.5090,0.5119,0.5146,0.5151,0.5160,0.5200, 0.5204,0.5221,0.5274,0.5280,0.5342,0.5355,0.5360,0.5469,0.5499,0.5511, 0.5523,0.5524,0.5554,0.5562,0.5598,0.5607,0.5652,0.5662,0.5670,0.5725, 0.5765,0.5770,0.5896,0.5921,0.6026,0.6035,0.6038,0.6135,0.6142,0.6165, 0.6181,0.6222,0.6234,0.6293,0.6299,0.6302,0.6393,0.6398,0.6413,0.6437, 0.6446,0.6452,0.6466,0.6500,0.6612,0.6746,0.6761,0.6829,0.6883,0.6884, 0.6923,0.6953,0.6959,0.7000,0.7026,0.7080,0.7081,0.7093,0.7096,0.7113, 0.7231,0.7243,0.7275,0.7437,0.7475,0.7486,0.7565,0.7666,0.7711,0.7807, 0.7888,0.7908,0.7916,0.7944,0.7956,0.8023,0.8032,0.8036,0.8036,0.8037, 0.8107,0.8118,0.8136,0.8140,0.8161,0.8165,0.8345,0.8360,0.8382,0.8402, 0.8440,0.8551,0.8571,0.8600,0.8626,0.8650,0.8681,0.8772,0.8820,0.8840, 0.8886,0.8901,0.8911,0.8925,0.8932,0.8964,0.9032,0.9054,0.9073,0.9116, 0.9146,0.9155,0.9219,0.9226,0.9242,0.9250,0.9328,0.9335,0.9351,0.9419, 0.9538,0.9566,0.9702,0.9743,0.9822,0.9926,0.9938,0.9939,0.9944, Overall p-value after applying KStest on 269 p-values = 0.647327 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.