RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-30_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 11.1704 0.152432 2 to 25 15.68 13.6703 0.309715 3 to 26 15.85 24.4097 0.891277 4 to 27 16.03 21.3873 0.790554 5 to 28 15.65 25.3974 0.913838 6 to 29 15.61 14.1112 0.340782 7 to 30 15.83 16.5916 0.517647 8 to 31 15.72 27.6381 0.950651 9 to 32 15.74 26.4925 0.934058 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.128109 Tough bday spacings test for dh-ranFile-2016-09-30_16:31: 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 11 34 71 86 101 76 54 41 17 4 5 (O-E)^2/E 0.4 0.2 0.1 1.4 0.1 0.1 0.1 4.2 0.3 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.053, p= 0.376 RESULTS OF GCD FOR dh-ranFile-2016-09-30_16:31 Euclid's algorithm: p-value, steps to gcd: 0.975592 p-value, dist. of gcd's: 0.666970 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-30_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.349 0.377 0.073 0.521 0.474 0.642 0.182 0.406 Bits 8 to 15---> 0.830 0.402 0.165 0.428 0.442 0.240 0.371 0.009 Bits 16 to 23---> 0.234 0.704 0.285 0.331 0.595 0.278 0.068 0.426 Bits 24 to 31---> 0.324 0.418 0.826 0.111 0.828 0.857 0.857 0.841 KS test for the above 32 p values: 0.829 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-30_16:31, p-values for 5 runs: 0.7404, 0.8777, 0.8727, 0.9238, 0.5909 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-30_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5186 5134.0 0.526 1.161 r= 30 23175 23103.0 0.224 1.385 r= 31 11416 11551.5 1.590 2.975 chi-square = 2.975 with df = 3; p-value = 0.605 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-30_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 238 211.4 3.342 3.342 r= 30 5134 5134.0 0.000 3.342 r= 31 23039 23103.0 0.178 3.520 r= 32 11589 11551.5 0.122 3.641 chi-square = 3.641 with df = 3; p-value = 0.697 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-30_16:31 b-rank test for bits 1 to 8, p=0.36638 b-rank test for bits 2 to 9, p=0.29537 b-rank test for bits 3 to 10, p=0.13804 b-rank test for bits 4 to 11, p=0.19186 b-rank test for bits 5 to 12, p=0.46295 b-rank test for bits 6 to 13, p=0.42556 b-rank test for bits 7 to 14, p=0.49944 b-rank test for bits 8 to 15, p=0.27293 b-rank test for bits 9 to 16, p=0.04905 b-rank test for bits 10 to 17, p=0.09914 b-rank test for bits 11 to 18, p=0.63808 b-rank test for bits 12 to 19, p=0.95945 b-rank test for bits 13 to 20, p=0.84939 b-rank test for bits 14 to 21, p=0.81646 b-rank test for bits 15 to 22, p=0.81923 b-rank test for bits 16 to 23, p=0.54655 b-rank test for bits 17 to 24, p=0.78901 b-rank test for bits 18 to 25, p=0.21117 b-rank test for bits 19 to 26, p=0.70380 b-rank test for bits 20 to 27, p=0.12407 b-rank test for bits 21 to 28, p=0.27304 b-rank test for bits 22 to 29, p=0.05923 b-rank test for bits 23 to 30, p=0.85856 b-rank test for bits 24 to 31, p=0.18029 b-rank test for bits 25 to 32, p=0.03695 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 = 0.323923 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-30_16:31 (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 142194 0.67 0.747012 2 141110 -1.87 0.030909 3 142080 0.40 0.654966 4 141071 -1.96 0.025073 5 142058 0.35 0.635840 6 142333 0.99 0.838884 7 141823 -0.20 0.420073 8 141824 -0.20 0.420987 9 141858 -0.12 0.452269 10 141964 0.13 0.550820 11 141834 -0.18 0.430145 12 141873 -0.08 0.466177 13 142480 1.33 0.908790 14 141383 -1.23 0.109397 15 141862 -0.11 0.455973 16 141746 -0.38 0.351375 17 142816 2.12 0.982929 18 142409 1.17 0.878486 19 141805 -0.24 0.403708 20 142234 0.76 0.775947 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-30_16:31 Bits used No. missing words z-score p-value 23 to 32 141778 -0.4529 0.325324 22 to 31 141769 -0.4839 0.314230 21 to 30 141777 -0.4563 0.324083 20 to 29 141674 -0.8115 0.208544 19 to 28 142318 1.4092 0.920613 18 to 27 141505 -1.3942 0.081622 17 to 26 142345 1.5023 0.933492 16 to 25 142045 0.4678 0.680046 15 to 24 142250 1.1747 0.879947 14 to 23 142161 0.8678 0.807256 13 to 22 141947 0.1299 0.551676 12 to 21 141979 0.2402 0.594928 11 to 20 141964 0.1885 0.574764 10 to 19 141660 -0.8598 0.194961 9 to 18 141502 -1.4046 0.080072 8 to 17 142139 0.7920 0.785810 7 to 16 141918 0.0299 0.511925 6 to 15 141878 -0.1080 0.456984 5 to 14 142175 0.9161 0.820194 4 to 13 141434 -1.6391 0.050599 3 to 12 141850 -0.2046 0.418948 2 to 11 141719 -0.6563 0.255812 1 to 10 142213 1.0471 0.852482 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-30_16:31 Bits used No. missing words z-score p-value 28 to 32 142037 0.4328 0.667413 27 to 31 141646 -0.8926 0.186024 26 to 30 142066 0.5311 0.702320 25 to 29 142078 0.5718 0.716259 24 to 28 141686 -0.7571 0.224510 23 to 27 142575 2.2565 0.987981 22 to 26 142170 0.8836 0.811551 21 to 25 141916 0.0226 0.509019 20 to 24 142017 0.3650 0.642438 19 to 23 142004 0.3209 0.625863 18 to 22 142253 1.1650 0.877987 17 to 21 142090 0.6124 0.729877 16 to 20 142844 3.1684 0.999234 15 to 19 142365 1.5446 0.938784 14 to 18 142138 0.7752 0.780875 13 to 17 142037 0.4328 0.667413 12 to 16 141612 -1.0079 0.156752 11 to 15 142237 1.1107 0.866661 10 to 14 141232 -2.2960 0.010837 9 to 13 142147 0.8057 0.789781 8 to 12 141966 0.1921 0.576169 7 to 11 141895 -0.0486 0.480629 6 to 10 141827 -0.2791 0.390090 5 to 9 142138 0.7752 0.780875 4 to 8 141664 -0.8316 0.202810 3 to 7 141922 0.0429 0.517129 2 to 6 141438 -1.5977 0.055052 1 to 5 142042 0.4497 0.673547 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-30_16:31 Bits used No. missing words z-score p-value 31 to 32 141722 -0.5526 0.290270 30 to 31 141698 -0.6234 0.266513 29 to 30 142079 0.5005 0.691639 28 to 29 141566 -1.0128 0.155584 27 to 28 142173 0.7778 0.781653 26 to 27 141482 -1.2606 0.103734 25 to 26 141964 0.1613 0.564059 24 to 25 141546 -1.0718 0.141912 23 to 24 142118 0.6155 0.730903 22 to 23 142402 1.4533 0.926930 21 to 22 141747 -0.4788 0.316023 20 to 21 142163 0.7483 0.772857 19 to 20 142002 0.2734 0.607713 18 to 19 142141 0.6834 0.752821 17 to 18 141914 0.0138 0.505496 16 to 17 141840 -0.2045 0.418976 15 to 16 141594 -0.9302 0.176140 14 to 15 142053 0.4238 0.664146 13 to 14 141612 -0.8771 0.190222 12 to 13 141590 -0.9420 0.173102 11 to 12 141765 -0.4258 0.335144 10 to 11 141467 -1.3048 0.095979 9 to 10 141702 -0.6116 0.270404 8 to 9 141756 -0.4523 0.325526 7 to 8 142119 0.6185 0.731876 6 to 7 141836 -0.2163 0.414372 5 to 6 141668 -0.7119 0.238267 4 to 5 141975 0.1937 0.576801 3 to 4 141717 -0.5673 0.285240 2 to 3 142074 0.4858 0.686429 1 to 2 141634 -0.8122 0.208343 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-30_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2484.12 -0.225 0.411148 Test results for specific bytes for dh-ranFile-2016-09-30_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2476.84 -0.328 0.371614 2 to 9 2604.92 1.484 0.931064 3 to 10 2405.79 -1.332 0.091382 4 to 11 2575.72 1.071 0.857895 5 to 12 2575.41 1.066 0.856877 6 to 13 2578.01 1.103 0.865033 7 to 14 2383.66 -1.645 0.049961 8 to 15 2477.84 -0.313 0.376971 9 to 16 2504.20 0.059 0.523670 10 to 17 2509.03 0.128 0.550805 11 to 18 2392.95 -1.514 0.065016 12 to 19 2509.17 0.130 0.551580 13 to 20 2382.86 -1.657 0.048800 14 to 21 2505.09 0.072 0.528671 15 to 22 2457.27 -0.604 0.272820 16 to 23 2730.46 3.259 0.999441 17 to 24 2456.57 -0.614 0.269521 18 to 25 2407.55 -1.307 0.095525 19 to 26 2468.38 -0.447 0.327365 20 to 27 2594.22 1.332 0.908648 21 to 28 2513.99 0.198 0.578431 22 to 29 2561.93 0.876 0.809439 23 to 30 2450.57 -0.699 0.242282 24 to 31 2535.94 0.508 0.694382 25 to 32 2501.43 0.020 0.508059 CDPARK for dh-ranFile-2016-09-30_16:31: 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 3492 -1.4155 0.078457 3547 1.0959 0.863437 3540 0.7763 0.781201 3529 0.2740 0.607947 3547 1.0959 0.863437 3526 0.1370 0.554479 3515 -0.3653 0.357445 3554 1.4155 0.921543 3540 0.7763 0.781201 3505 -0.8219 0.205562 Square side=100, avg. no. parked=3529.50 sample std.=19.14 p-value of the KSTEST for those 10 p-values: 0.419392 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-30_16:31 0.4806,0.5028,0.7167,0.0167,0.5775,0.4436,0.5772,0.7254,0.1576,0.3737, The KS test for those 10 p-values: 0.457806 The 3DSPHERES test for dh-ranFile-2016-09-30_16:31 sample no r^3 equiv. uni. 1 2.966 0.094143 2 77.344 0.924085 3 2.311 0.074139 4 19.025 0.469623 5 46.741 0.789448 6 5.515 0.167922 7 8.901 0.256727 8 17.028 0.433122 9 14.952 0.392494 10 15.761 0.408663 11 0.977 0.032031 12 8.409 0.244440 13 157.504 0.994753 14 118.771 0.980919 15 17.020 0.432966 16 19.042 0.469921 17 8.785 0.253847 18 14.185 0.376762 19 20.582 0.496445 20 39.120 0.728556 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.420226 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-30_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 0.3 -0.1 -0.5 0.1 1.4 2.1 0.8 -1.5 -0.1 -0.3 0.5 0.0 -0.3 -1.7 0.2 1.0 -0.3 -1.4 0.4 0.1 1.5 -0.0 1.5 -0.7 -0.6 -1.3 0.5 0.7 -0.5 -0.1 -1.8 1.2 0.5 3.5 3.1 0.5 -0.4 -1.8 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:58.863157 z-score=1.839921, p-value=0.956333 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-30_16:31 Test no p-value 1 0.726854 2 0.014963 3 0.857799 4 0.081897 5 0.046988 6 0.053186 7 0.004232 8 0.609739 9 0.005935 10 0.472286 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000954 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-30_16:31: (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 66943 1.15 66619 0.03 3 25000.00 24811 1.43 25069 0.19 4 6666.67 6629 0.21 6639 0.11 5 1388.89 1343 1.52 1391 0.00 6 238.10 240 0.02 232 0.16 7 34.72 30 0.64 45 3.04 8 4.96 3 0.77 4 0.19 p=0.54645 p=0.28659 Number of rngs required: 689344, p-value: 0.863 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-30_16:31 No. of wins: Observed Expected 98119 98585.9 z-score=-2.088, pvalue=0.01840 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66442 66666.7 0.757 0.757 2 37344 37654.3 2.557 3.315 3 27050 26954.7 0.337 3.651 4 19370 19313.5 0.166 3.817 5 13895 13851.4 0.137 3.954 6 10090 9943.5 2.157 6.111 7 7205 7145.0 0.503 6.614 8 5147 5139.1 0.012 6.627 9 3742 3699.9 0.480 7.107 10 2736 2666.3 1.822 8.929 11 1900 1923.3 0.283 9.212 12 1398 1388.7 0.062 9.273 13 1023 1003.7 0.371 9.644 14 778 726.1 3.704 13.348 15 526 525.8 0.000 13.348 16 398 381.2 0.745 14.093 17 274 276.5 0.023 14.116 18 187 200.8 0.952 15.068 19 134 146.0 0.984 16.052 20 95 106.2 1.184 17.236 21 266 287.1 1.553 18.789 Chisq= 18.79 for 20 degrees of freedom, p= 0.46442 SUMMARY of craptest p-value for no. of wins: 0.018396 p-value for throws/game: 0.464423 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-30_16:31 No. of wins: Observed Expected 98702 98585.9 z-score= 0.519, pvalue=0.69828 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66446 66666.7 0.730 0.730 2 37761 37654.3 0.302 1.033 3 27358 26954.7 6.033 7.066 4 19329 19313.5 0.013 7.078 5 13696 13851.4 1.744 8.822 6 9847 9943.5 0.937 9.760 7 7071 7145.0 0.767 10.527 8 5044 5139.1 1.759 12.285 9 3705 3699.9 0.007 12.293 10 2621 2666.3 0.770 13.062 11 1954 1923.3 0.489 13.551 12 1391 1388.7 0.004 13.555 13 1023 1003.7 0.371 13.925 14 771 726.1 2.771 16.697 15 579 525.8 5.375 22.072 16 375 381.2 0.099 22.171 17 275 276.5 0.009 22.180 18 193 200.8 0.305 22.485 19 159 146.0 1.160 23.645 20 114 106.2 0.571 24.216 21 288 287.1 0.003 24.219 Chisq= 24.22 for 20 degrees of freedom, p= 0.76703 SUMMARY of craptest p-value for no. of wins: 0.698277 p-value for throws/game: 0.767028 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0042,0.0059,0.0092,0.0108,0.0150,0.0167,0.0184,0.0251,0.0309, 0.0320,0.0369,0.0470,0.0488,0.0491,0.0500,0.0506,0.0532,0.0551,0.0592, 0.0650,0.0682,0.0727,0.0741,0.0785,0.0801,0.0816,0.0819,0.0914,0.0941, 0.0955,0.0960,0.0991,0.1037,0.1094,0.1110,0.1241,0.1281,0.1380,0.1419, 0.1524,0.1556,0.1568,0.1576,0.1649,0.1679,0.1731,0.1761,0.1803,0.1815, 0.1860,0.1902,0.1919,0.1950,0.2028,0.2056,0.2083,0.2085,0.2112,0.2245, 0.2344,0.2383,0.2395,0.2423,0.2444,0.2538,0.2558,0.2567,0.2665,0.2695, 0.2704,0.2728,0.2729,0.2730,0.2784,0.2851,0.2852,0.2866,0.2903,0.2954, 0.3097,0.3142,0.3160,0.3239,0.3241,0.3241,0.3253,0.3255,0.3274,0.3310, 0.3351,0.3408,0.3492,0.3514,0.3574,0.3664,0.3707,0.3716,0.3737,0.3763, 0.3768,0.3770,0.3770,0.3901,0.3925,0.4023,0.4037,0.4055,0.4087,0.4111, 0.4144,0.4176,0.4189,0.4190,0.4194,0.4201,0.4202,0.4210,0.4256,0.4263, 0.4277,0.4301,0.4330,0.4331,0.4420,0.4436,0.4523,0.4560,0.4570,0.4578, 0.4630,0.4644,0.4662,0.4696,0.4699,0.4723,0.4739,0.4806,0.4806,0.4964, 0.4994,0.5028,0.5055,0.5081,0.5090,0.5119,0.5171,0.5176,0.5213,0.5237, 0.5287,0.5464,0.5465,0.5508,0.5508,0.5516,0.5517,0.5545,0.5641,0.5748, 0.5762,0.5768,0.5772,0.5775,0.5784,0.5909,0.5949,0.5954,0.6045,0.6077, 0.6079,0.6097,0.6259,0.6358,0.6381,0.6416,0.6424,0.6550,0.6641,0.6670, 0.6674,0.6674,0.6735,0.6800,0.6864,0.6916,0.6944,0.6971,0.6983,0.7023, 0.7038,0.7044,0.7163,0.7167,0.7254,0.7269,0.7286,0.7299,0.7309,0.7319, 0.7404,0.7470,0.7528,0.7670,0.7729,0.7759,0.7809,0.7809,0.7812,0.7812, 0.7817,0.7858,0.7890,0.7894,0.7898,0.7906,0.8073,0.8094,0.8116,0.8165, 0.8192,0.8202,0.8265,0.8283,0.8290,0.8305,0.8389,0.8406,0.8494,0.8525, 0.8568,0.8569,0.8573,0.8578,0.8579,0.8586,0.8625,0.8634,0.8634,0.8650, 0.8667,0.8727,0.8777,0.8780,0.8785,0.8799,0.8913,0.9086,0.9088,0.9138, 0.9206,0.9215,0.9238,0.9241,0.9269,0.9311,0.9335,0.9341,0.9388,0.9507, 0.9563,0.9595,0.9756,0.9809,0.9829,0.9880,0.9948,0.9992,0.9994, Overall p-value after applying KStest on 269 p-values = 0.822219 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.