RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-14_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 24.4836 0.893120 2 to 25 15.82 16.8519 0.535560 3 to 26 15.52 19.3116 0.689058 4 to 27 16.06 15.2394 0.421755 5 to 28 15.91 15.6894 0.454049 6 to 29 15.55 28.9855 0.965340 7 to 30 15.32 26.2653 0.930240 8 to 31 15.36 29.9880 0.973568 9 to 32 15.93 13.8733 0.323948 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.053496 Tough bday spacings test for dh-ranFile-2018-04-14_00:31: 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 40 80 89 99 80 50 28 15 8 2 (O-E)^2/E 0.0 0.3 0.6 0.8 0.0 0.0 0.1 0.1 0.0 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 3.296, p= 0.026 RESULTS OF GCD FOR dh-ranFile-2018-04-14_00:31 Euclid's algorithm: p-value, steps to gcd: 0.306234 p-value, dist. of gcd's: 0.978504 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-14_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.125 0.010 0.900 0.430 0.194 0.160 0.875 0.740 Bits 8 to 15---> 0.995 0.480 0.208 0.559 0.714 0.088 0.296 0.158 Bits 16 to 23---> 0.571 0.513 0.746 0.349 0.170 0.263 0.166 0.040 Bits 24 to 31---> 0.225 0.626 0.847 0.747 0.121 0.551 0.882 0.286 KS test for the above 32 p values: 0.662 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-14_00:31, p-values for 5 runs: 0.2402, 0.4137, 0.6928, 0.5746, 0.6688 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-14_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5252 5134.0 2.712 3.695 r= 30 22913 23103.0 1.563 5.258 r= 31 11638 11551.5 0.647 5.906 chi-square = 5.906 with df = 3; p-value = 0.884 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-14_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5240 5134.0 2.188 2.536 r= 31 22941 23103.0 1.137 3.673 r= 32 11599 11551.5 0.195 3.868 chi-square = 3.868 with df = 3; p-value = 0.724 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-14_00:31 b-rank test for bits 1 to 8, p=0.08434 b-rank test for bits 2 to 9, p=0.52119 b-rank test for bits 3 to 10, p=0.54902 b-rank test for bits 4 to 11, p=0.75915 b-rank test for bits 5 to 12, p=0.92527 b-rank test for bits 6 to 13, p=0.68977 b-rank test for bits 7 to 14, p=0.19868 b-rank test for bits 8 to 15, p=0.55293 b-rank test for bits 9 to 16, p=0.70797 b-rank test for bits 10 to 17, p=0.71157 b-rank test for bits 11 to 18, p=0.25510 b-rank test for bits 12 to 19, p=0.17788 b-rank test for bits 13 to 20, p=0.78391 b-rank test for bits 14 to 21, p=0.49496 b-rank test for bits 15 to 22, p=0.98767 b-rank test for bits 16 to 23, p=0.93817 b-rank test for bits 17 to 24, p=0.74188 b-rank test for bits 18 to 25, p=0.62973 b-rank test for bits 19 to 26, p=0.74261 b-rank test for bits 20 to 27, p=0.14406 b-rank test for bits 21 to 28, p=0.00079 b-rank test for bits 22 to 29, p=0.74978 b-rank test for bits 23 to 30, p=0.17962 b-rank test for bits 24 to 31, p=0.50981 b-rank test for bits 25 to 32, p=0.18415 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 = 0.579644 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-14_00:31 (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 142373 1.08 0.860672 2 142089 0.42 0.662681 3 141941 0.07 0.529493 4 141802 -0.25 0.400996 5 141426 -1.13 0.129391 6 141987 0.18 0.572001 7 141256 -1.53 0.063446 8 142071 0.38 0.647186 9 142234 0.76 0.775947 10 142355 1.04 0.851128 11 141856 -0.12 0.450419 12 141919 0.02 0.509013 13 142088 0.42 0.661827 14 141662 -0.58 0.281675 15 142542 1.48 0.930323 16 140841 -2.50 0.006278 17 142194 0.67 0.747012 18 141945 0.08 0.533210 19 142088 0.42 0.661827 20 141990 0.19 0.574750 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-14_00:31 Bits used No. missing words z-score p-value 23 to 32 141333 -1.9873 0.023442 22 to 31 141914 0.0161 0.506424 21 to 30 141849 -0.2080 0.417601 20 to 29 142055 0.5023 0.692275 19 to 28 142352 1.5264 0.936551 18 to 27 141921 0.0402 0.516050 17 to 26 142176 0.9196 0.821097 16 to 25 142139 0.7920 0.785810 15 to 24 141604 -1.0529 0.146202 14 to 23 141888 -0.0736 0.470684 13 to 22 142607 2.4058 0.991931 12 to 21 142200 1.0023 0.841903 11 to 20 141781 -0.4425 0.329058 10 to 19 142312 1.3885 0.917510 9 to 18 141992 0.2851 0.612204 8 to 17 142016 0.3678 0.643499 7 to 16 142025 0.3989 0.655003 6 to 15 141880 -0.1011 0.459721 5 to 14 141494 -1.4322 0.076047 4 to 13 142407 1.7161 0.956928 3 to 12 141891 -0.0632 0.474801 2 to 11 141874 -0.1218 0.451518 1 to 10 141766 -0.4942 0.310568 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-14_00:31 Bits used No. missing words z-score p-value 28 to 32 141813 -0.3265 0.372007 27 to 31 141765 -0.4893 0.312331 26 to 30 142095 0.6294 0.735453 25 to 29 142214 1.0328 0.849147 24 to 28 142133 0.7582 0.775835 23 to 27 142064 0.5243 0.699967 22 to 26 141609 -1.0181 0.154323 21 to 25 142001 0.3107 0.622003 20 to 24 141742 -0.5672 0.285282 19 to 23 141891 -0.0621 0.475227 18 to 22 142056 0.4972 0.690471 17 to 21 141696 -0.7232 0.234793 16 to 20 142115 0.6972 0.757157 15 to 19 142635 2.4599 0.993051 14 to 18 141762 -0.4994 0.308741 13 to 17 142076 0.5650 0.713957 12 to 16 142003 0.3175 0.624578 11 to 15 141618 -0.9876 0.161684 10 to 14 141725 -0.6248 0.266036 9 to 13 142026 0.3955 0.653760 8 to 12 142436 1.7853 0.962895 7 to 11 141963 0.1819 0.572182 6 to 10 141533 -1.2757 0.101032 5 to 9 141569 -1.1537 0.124320 4 to 8 141943 0.1141 0.545435 3 to 7 142018 0.3684 0.643702 2 to 6 142322 1.3989 0.919076 1 to 5 142006 0.3277 0.628429 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-14_00:31 Bits used No. missing words z-score p-value 31 to 32 142231 0.9489 0.828659 30 to 31 141719 -0.5614 0.287247 29 to 30 142117 0.6126 0.729928 28 to 29 141612 -0.8771 0.190222 27 to 28 141978 0.2026 0.580263 26 to 27 141742 -0.4936 0.310795 25 to 26 141937 0.0816 0.532527 24 to 25 142078 0.4976 0.690600 23 to 24 141745 -0.4847 0.313927 22 to 23 141752 -0.4641 0.321288 21 to 22 141617 -0.8623 0.194253 20 to 21 142389 1.4150 0.921459 19 to 20 142065 0.4592 0.676956 18 to 19 141995 0.2527 0.599755 17 to 18 141705 -0.6027 0.273340 16 to 17 141744 -0.4877 0.312882 15 to 16 141882 -0.0806 0.467872 14 to 15 141989 0.2350 0.592901 13 to 14 141727 -0.5378 0.295342 12 to 13 141848 -0.1809 0.428217 11 to 12 142523 1.8102 0.964870 10 to 11 142557 1.9105 0.971968 9 to 10 141500 -1.2075 0.113627 8 to 9 141524 -1.1367 0.127839 7 to 8 142292 1.1288 0.870513 6 to 7 141784 -0.3697 0.355801 5 to 6 142129 0.6480 0.741506 4 to 5 142532 1.8368 0.966879 3 to 4 141972 0.1849 0.573333 2 to 3 141687 -0.6558 0.255963 1 to 2 142542 1.8663 0.968999 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-14_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2412.42 -1.239 0.107746 Test results for specific bytes for dh-ranFile-2018-04-14_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2482.66 -0.245 0.403164 2 to 9 2530.26 0.428 0.665655 3 to 10 2382.71 -1.659 0.048589 4 to 11 2535.53 0.502 0.692313 5 to 12 2538.68 0.547 0.707828 6 to 13 2420.18 -1.129 0.129475 7 to 14 2517.64 0.249 0.598477 8 to 15 2658.65 2.244 0.987571 9 to 16 2536.06 0.510 0.694966 10 to 17 2425.59 -1.052 0.146339 11 to 18 2590.76 1.284 0.900356 12 to 19 2479.19 -0.294 0.384269 13 to 20 2418.87 -1.147 0.125626 14 to 21 2426.27 -1.043 0.148556 15 to 22 2412.64 -1.235 0.108337 16 to 23 2620.95 1.710 0.956407 17 to 24 2401.17 -1.398 0.081112 18 to 25 2491.12 -0.126 0.450013 19 to 26 2516.52 0.234 0.592338 20 to 27 2487.43 -0.178 0.429432 21 to 28 2443.38 -0.801 0.211648 22 to 29 2591.35 1.292 0.901792 23 to 30 2536.47 0.516 0.696993 24 to 31 2479.74 -0.286 0.387265 25 to 32 2448.24 -0.732 0.232090 CDPARK for dh-ranFile-2018-04-14_00:31: 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 3496 -1.2329 0.108811 3553 1.3699 0.914635 3511 -0.5479 0.291865 3528 0.2283 0.590298 3526 0.1370 0.554479 3534 0.5023 0.692266 3522 -0.0457 0.481790 3533 0.4566 0.676028 3565 1.9178 0.972432 3525 0.0913 0.536383 Square side=100, avg. no. parked=3529.30 sample std.=18.44 p-value of the KSTEST for those 10 p-values: 0.536254 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-14_00:31 0.1840,0.6227,0.9793,0.5916,0.7204,0.0164,0.3402,0.1977,0.4445,0.4334, The KS test for those 10 p-values: 0.843729 The 3DSPHERES test for dh-ranFile-2018-04-14_00:31 sample no r^3 equiv. uni. 1 4.823 0.148506 2 50.268 0.812804 3 8.017 0.234512 4 55.873 0.844706 5 3.476 0.109406 6 42.747 0.759464 7 17.904 0.449425 8 23.556 0.543975 9 22.116 0.521552 10 64.948 0.885244 11 7.014 0.208488 12 32.263 0.658850 13 38.963 0.727132 14 15.911 0.411603 15 24.743 0.561669 16 27.742 0.603357 17 4.703 0.145086 18 14.281 0.378762 19 16.171 0.416688 20 11.575 0.320123 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.710997 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-14_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 0.1 -2.3 0.8 -0.1 -1.0 -0.1 0.8 1.1 0.1 0.6 0.8 -0.5 -0.3 -0.9 -0.3 1.1 3.1 -1.0 -0.5 -1.0 -0.8 -0.4 -0.9 -0.5 1.3 -0.6 0.8 -0.8 1.1 -0.4 -0.6 -0.0 -1.4 0.3 -1.2 0.3 -1.7 -0.8 -0.7 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:46.573824 z-score=0.499045, p-value=0.710274 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-14_00:31 Test no p-value 1 0.740716 2 0.240825 3 0.404887 4 0.022959 5 0.456667 6 0.407953 7 0.005739 8 0.005314 9 0.095953 10 0.584351 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011868 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-14_00:31: (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 66700 0.02 66928 1.02 3 25000.00 25001 0.00 24841 1.01 4 6666.67 6665 0.00 6556 1.84 5 1388.89 1382 0.03 1386 0.01 6 238.10 220 1.38 247 0.33 7 34.72 28 1.30 34 0.01 8 4.96 3 0.77 7 0.84 p=0.25626 p=0.46460 Number of rngs required: 687888, p-value: 0.276 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-14_00:31 No. of wins: Observed Expected 98851 98585.9 z-score= 1.186, pvalue=0.88216 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66751 66666.7 0.107 0.107 2 37864 37654.3 1.168 1.274 3 26769 26954.7 1.280 2.554 4 19290 19313.5 0.029 2.583 5 13776 13851.4 0.411 2.993 6 9777 9943.5 2.789 5.783 7 7121 7145.0 0.081 5.863 8 5133 5139.1 0.007 5.871 9 3734 3699.9 0.315 6.186 10 2667 2666.3 0.000 6.186 11 1979 1923.3 1.611 7.797 12 1384 1388.7 0.016 7.813 13 1065 1003.7 3.742 11.555 14 716 726.1 0.142 11.697 15 533 525.8 0.098 11.794 16 396 381.2 0.579 12.373 17 295 276.5 1.232 13.605 18 198 200.8 0.040 13.645 19 127 146.0 2.469 16.114 20 103 106.2 0.097 16.211 21 322 287.1 4.239 20.450 Chisq= 20.45 for 20 degrees of freedom, p= 0.56990 SUMMARY of craptest p-value for no. of wins: 0.882163 p-value for throws/game: 0.569896 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-14_00:31 No. of wins: Observed Expected 98562 98585.9 z-score=-0.107, pvalue=0.45751 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66615 66666.7 0.040 0.040 2 37434 37654.3 1.289 1.329 3 26912 26954.7 0.068 1.397 4 19544 19313.5 2.752 4.149 5 13986 13851.4 1.308 5.456 6 9878 9943.5 0.432 5.888 7 7026 7145.0 1.983 7.871 8 5140 5139.1 0.000 7.871 9 3762 3699.9 1.043 8.915 10 2686 2666.3 0.146 9.060 11 1973 1923.3 1.283 10.343 12 1387 1388.7 0.002 10.345 13 1026 1003.7 0.495 10.840 14 776 726.1 3.424 14.264 15 538 525.8 0.281 14.545 16 346 381.2 3.242 17.787 17 257 276.5 1.381 19.167 18 201 200.8 0.000 19.167 19 152 146.0 0.248 19.415 20 92 106.2 1.902 21.318 21 269 287.1 1.143 22.461 Chisq= 22.46 for 20 degrees of freedom, p= 0.68395 SUMMARY of craptest p-value for no. of wins: 0.457510 p-value for throws/game: 0.683954 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0053,0.0057,0.0063,0.0097,0.0119,0.0164,0.0230,0.0234,0.0264, 0.0398,0.0486,0.0535,0.0634,0.0760,0.0811,0.0843,0.0884,0.0960,0.1010, 0.1077,0.1083,0.1088,0.1094,0.1136,0.1210,0.1243,0.1255,0.1256,0.1278, 0.1294,0.1295,0.1441,0.1451,0.1462,0.1463,0.1485,0.1486,0.1543,0.1581, 0.1600,0.1617,0.1657,0.1701,0.1779,0.1796,0.1840,0.1842,0.1902,0.1939, 0.1943,0.1977,0.1987,0.2076,0.2085,0.2116,0.2252,0.2321,0.2345,0.2348, 0.2402,0.2408,0.2551,0.2560,0.2563,0.2628,0.2660,0.2733,0.2763,0.2817, 0.2853,0.2860,0.2872,0.2919,0.2953,0.2959,0.3062,0.3087,0.3106,0.3108, 0.3123,0.3129,0.3139,0.3201,0.3213,0.3239,0.3291,0.3402,0.3492,0.3558, 0.3720,0.3788,0.3843,0.3873,0.4010,0.4032,0.4049,0.4080,0.4116,0.4137, 0.4167,0.4176,0.4218,0.4282,0.4294,0.4298,0.4334,0.4445,0.4494,0.4500, 0.4504,0.4515,0.4540,0.4567,0.4575,0.4597,0.4646,0.4679,0.4707,0.4748, 0.4752,0.4801,0.4818,0.4950,0.5064,0.5090,0.5098,0.5134,0.5160,0.5212, 0.5216,0.5295,0.5325,0.5332,0.5356,0.5363,0.5364,0.5440,0.5454,0.5490, 0.5511,0.5529,0.5545,0.5595,0.5617,0.5699,0.5709,0.5720,0.5722,0.5733, 0.5746,0.5748,0.5796,0.5803,0.5844,0.5903,0.5916,0.5923,0.5929,0.5985, 0.5998,0.6034,0.6122,0.6220,0.6227,0.6246,0.6258,0.6284,0.6297,0.6435, 0.6437,0.6472,0.6538,0.6550,0.6588,0.6618,0.6618,0.6622,0.6627,0.6657, 0.6688,0.6760,0.6770,0.6840,0.6891,0.6898,0.6905,0.6906,0.6923,0.6923, 0.6923,0.6928,0.6950,0.6970,0.7000,0.7078,0.7080,0.7103,0.7110,0.7116, 0.7135,0.7140,0.7204,0.7239,0.7271,0.7299,0.7355,0.7399,0.7407,0.7415, 0.7419,0.7426,0.7458,0.7470,0.7470,0.7498,0.7572,0.7591,0.7595,0.7758, 0.7759,0.7839,0.7858,0.8128,0.8211,0.8287,0.8419,0.8437,0.8447,0.8469, 0.8491,0.8511,0.8607,0.8705,0.8751,0.8821,0.8822,0.8837,0.8852,0.8931, 0.8995,0.9004,0.9018,0.9146,0.9175,0.9191,0.9215,0.9253,0.9302,0.9303, 0.9366,0.9382,0.9564,0.9569,0.9629,0.9649,0.9653,0.9669,0.9690,0.9720, 0.9724,0.9736,0.9785,0.9793,0.9876,0.9877,0.9919,0.9931,0.9947, Overall p-value after applying KStest on 269 p-values = 0.440668 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.