RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-12_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.49 19.6592 0.707972 2 to 25 15.97 9.0080 0.059990 3 to 26 15.57 15.1742 0.417065 4 to 27 15.60 22.9946 0.850574 5 to 28 15.83 14.1868 0.346161 6 to 29 15.87 19.5810 0.703783 7 to 30 15.84 16.1174 0.484473 8 to 31 15.91 16.3347 0.499758 9 to 32 15.55 21.9626 0.813839 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.751556 Tough bday spacings test for dh-ranFile-2016-05-12_19:31: 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 6 32 71 106 89 65 61 40 19 7 4 (O-E)^2/E 1.1 0.6 0.1 0.7 0.8 2.2 1.5 3.5 1.1 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.633, p= 0.690 RESULTS OF GCD FOR dh-ranFile-2016-05-12_19:31 Euclid's algorithm: p-value, steps to gcd: 0.129388 p-value, dist. of gcd's: 0.227365 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-12_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.978 0.561 0.685 0.583 0.852 0.147 0.476 0.358 Bits 8 to 15---> 0.526 0.772 0.357 0.308 0.113 0.531 0.693 0.274 Bits 16 to 23---> 0.870 0.995 0.387 0.164 0.372 0.671 0.265 0.180 Bits 24 to 31---> 0.532 0.932 0.591 0.492 0.511 0.599 0.332 0.721 KS test for the above 32 p values: 0.611 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-12_19:31, p-values for 5 runs: 0.3140, 0.1280, 0.4712, 0.1765, 0.1978 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5105 5134.0 0.164 1.464 r= 30 23075 23103.0 0.034 1.499 r= 31 11592 11551.5 0.142 1.640 chi-square = 1.640 with df = 3; p-value = 0.350 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5054 5134.0 1.247 1.346 r= 31 23154 23103.0 0.112 1.459 r= 32 11576 11551.5 0.052 1.510 chi-square = 1.510 with df = 3; p-value = 0.320 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-12_19:31 b-rank test for bits 1 to 8, p=0.65346 b-rank test for bits 2 to 9, p=0.07471 b-rank test for bits 3 to 10, p=0.25320 b-rank test for bits 4 to 11, p=0.86126 b-rank test for bits 5 to 12, p=0.41545 b-rank test for bits 6 to 13, p=0.21155 b-rank test for bits 7 to 14, p=0.22341 b-rank test for bits 8 to 15, p=0.02852 b-rank test for bits 9 to 16, p=0.21601 b-rank test for bits 10 to 17, p=0.42210 b-rank test for bits 11 to 18, p=0.28913 b-rank test for bits 12 to 19, p=0.02755 b-rank test for bits 13 to 20, p=0.02260 b-rank test for bits 14 to 21, p=0.50484 b-rank test for bits 15 to 22, p=0.28977 b-rank test for bits 16 to 23, p=0.77589 b-rank test for bits 17 to 24, p=0.19483 b-rank test for bits 18 to 25, p=0.19759 b-rank test for bits 19 to 26, p=0.63544 b-rank test for bits 20 to 27, p=0.03214 b-rank test for bits 21 to 28, p=0.22378 b-rank test for bits 22 to 29, p=0.26450 b-rank test for bits 23 to 30, p=0.77805 b-rank test for bits 24 to 31, p=0.31931 b-rank test for bits 25 to 32, p=0.01908 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 = 0.001439 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-12_19:31 (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 142409 1.17 0.878486 2 142131 0.52 0.697743 3 141497 -0.96 0.167676 4 142592 1.60 0.944647 5 142279 0.86 0.806128 6 141477 -1.01 0.156220 7 140953 -2.23 0.012728 8 141711 -0.46 0.321543 9 140812 -2.56 0.005176 10 141453 -1.07 0.143169 11 141814 -0.22 0.411871 12 142324 0.97 0.833691 13 141465 -1.04 0.149599 14 141293 -1.44 0.074930 15 141211 -1.63 0.051381 16 141845 -0.15 0.440263 17 141737 -0.40 0.343607 18 141642 -0.62 0.266116 19 141427 -1.13 0.129884 20 141460 -1.05 0.146897 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-12_19:31 Bits used No. missing words z-score p-value 23 to 32 142106 0.6782 0.751169 22 to 31 142176 0.9196 0.821097 21 to 30 141357 -1.9046 0.028417 20 to 29 141984 0.2575 0.601597 19 to 28 141817 -0.3184 0.375099 18 to 27 141740 -0.5839 0.279645 17 to 26 141826 -0.2873 0.386924 16 to 25 141865 -0.1529 0.439254 15 to 24 142106 0.6782 0.751169 14 to 23 142121 0.7299 0.767273 13 to 22 141978 0.2368 0.593591 12 to 21 142167 0.8885 0.812869 11 to 20 142279 1.2747 0.898797 10 to 19 141867 -0.1460 0.441974 9 to 18 142451 1.8678 0.969107 8 to 17 142126 0.7471 0.772510 7 to 16 141793 -0.4011 0.344159 6 to 15 141696 -0.7356 0.230981 5 to 14 142036 0.4368 0.668869 4 to 13 141602 -1.0598 0.144627 3 to 12 141398 -1.7632 0.038933 2 to 11 142318 1.4092 0.920613 1 to 10 141745 -0.5667 0.285474 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-12_19:31 Bits used No. missing words z-score p-value 28 to 32 141824 -0.2893 0.386193 27 to 31 141980 0.2396 0.594664 26 to 30 142498 1.9955 0.977005 25 to 29 142169 0.8802 0.810635 24 to 28 142141 0.7853 0.783868 23 to 27 142035 0.4260 0.664946 22 to 26 141463 -1.5130 0.065142 21 to 25 141812 -0.3299 0.370726 20 to 24 142366 1.5480 0.939193 19 to 23 141414 -1.6791 0.046568 18 to 22 142442 1.8057 0.964514 17 to 21 142019 0.3718 0.644965 16 to 20 141987 0.2633 0.603836 15 to 19 141224 -2.3232 0.010085 14 to 18 141338 -1.9367 0.026390 13 to 17 142408 1.6904 0.954525 12 to 16 141715 -0.6587 0.255030 11 to 15 141578 -1.1232 0.130686 10 to 14 141668 -0.8181 0.206659 9 to 13 142130 0.7480 0.772780 8 to 12 141984 0.2531 0.599912 7 to 11 141782 -0.4316 0.333006 6 to 10 141223 -2.3265 0.009995 5 to 9 141853 -0.1909 0.424283 4 to 8 141642 -0.9062 0.182414 3 to 7 142281 1.2599 0.896147 2 to 6 142169 0.8802 0.810635 1 to 5 142172 0.8904 0.813376 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-12_19:31 Bits used No. missing words z-score p-value 31 to 32 142209 0.8840 0.811647 30 to 31 142618 2.0905 0.981712 29 to 30 142059 0.4415 0.670576 28 to 29 141644 -0.7827 0.216906 27 to 28 141729 -0.5319 0.297381 26 to 27 141871 -0.1131 0.454988 25 to 26 141586 -0.9538 0.170099 24 to 25 141745 -0.4847 0.313927 23 to 24 142277 1.0846 0.860944 22 to 23 141986 0.2262 0.589464 21 to 22 142282 1.0993 0.864186 20 to 21 141790 -0.3520 0.362417 19 to 20 141909 -0.0010 0.499612 18 to 19 141913 0.0108 0.504319 17 to 18 141683 -0.6676 0.252182 16 to 17 142043 0.3943 0.653323 15 to 16 141833 -0.2252 0.410927 14 to 15 142271 1.0669 0.856985 13 to 14 141936 0.0787 0.531354 12 to 13 142368 1.3530 0.911974 11 to 12 141886 -0.0688 0.472566 10 to 11 141823 -0.2547 0.399493 9 to 10 142153 0.7188 0.763865 8 to 9 141786 -0.3638 0.358002 7 to 8 141700 -0.6175 0.268455 6 to 7 141890 -0.0570 0.477264 5 to 6 141927 0.0521 0.520785 4 to 5 141548 -1.0659 0.143241 3 to 4 142764 2.5212 0.994151 2 to 3 142065 0.4592 0.676956 1 to 2 142210 0.8869 0.812442 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2647.90 2.092 0.981763 Test results for specific bytes for dh-ranFile-2016-05-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2589.20 1.261 0.896422 2 to 9 2487.73 -0.174 0.431109 3 to 10 2527.59 0.390 0.651778 4 to 11 2592.57 1.309 0.904766 5 to 12 2334.59 -2.339 0.009660 6 to 13 2621.56 1.719 0.957206 7 to 14 2478.47 -0.305 0.380370 8 to 15 2512.31 0.174 0.569096 9 to 16 2375.76 -1.757 0.039452 10 to 17 2446.64 -0.755 0.225220 11 to 18 2454.57 -0.642 0.260295 12 to 19 2546.78 0.662 0.745864 13 to 20 2595.80 1.355 0.912260 14 to 21 2555.87 0.790 0.785269 15 to 22 2220.11 -3.958 0.000038 16 to 23 2432.15 -0.959 0.168655 17 to 24 2530.86 0.436 0.668716 18 to 25 2586.50 1.223 0.889380 19 to 26 2510.25 0.145 0.557644 20 to 27 2381.24 -1.680 0.046527 21 to 28 2525.50 0.361 0.640826 22 to 29 2627.52 1.803 0.964335 23 to 30 2515.91 0.225 0.589016 24 to 31 2528.86 0.408 0.658403 25 to 32 2442.37 -0.815 0.207517 CDPARK for dh-ranFile-2016-05-12_19:31: 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 3520 -0.1370 0.445521 3540 0.7763 0.781201 3523 0.0000 0.500000 3532 0.4110 0.659449 3502 -0.9589 0.168804 3554 1.4155 0.921543 3515 -0.3653 0.357445 3521 -0.0913 0.463617 3527 0.1826 0.572463 3535 0.5479 0.708135 Square side=100, avg. no. parked=3526.90 sample std.=13.63 p-value of the KSTEST for those 10 p-values: 0.554437 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-12_19:31 0.1531,0.2483,0.7832,0.7170,0.4169,0.8804,0.2308,0.0559,0.2145,0.7617, The KS test for those 10 p-values: 0.718193 The 3DSPHERES test for dh-ranFile-2016-05-12_19:31 sample no r^3 equiv. uni. 1 15.349 0.400485 2 3.941 0.123117 3 20.932 0.502287 4 9.145 0.262754 5 9.988 0.283178 6 14.474 0.382732 7 21.914 0.518323 8 12.517 0.341126 9 21.065 0.504492 10 39.414 0.731201 11 40.402 0.739912 12 29.524 0.626241 13 15.097 0.395430 14 8.000 0.234067 15 82.333 0.935716 16 23.445 0.542287 17 22.712 0.530957 18 36.915 0.707855 19 16.207 0.417379 20 35.585 0.694605 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.224263 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-12_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 1.1 0.0 -1.0 1.8 -0.4 0.4 -0.3 1.0 0.9 0.4 0.5 0.6 0.6 0.1 -0.9 1.5 -0.9 0.8 0.2 -2.8 0.4 -1.3 1.0 -1.1 -0.1 -1.7 -2.3 1.4 -0.5 0.2 -0.2 0.1 0.1 0.6 1.9 -0.1 0.5 0.4 1.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:46.829354 z-score=0.526926, p-value=0.719088 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-12_19:31 Test no p-value 1 0.083970 2 0.776858 3 0.543631 4 0.162445 5 0.678991 6 0.004242 7 0.368509 8 0.523541 9 0.002573 10 0.352111 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.059880 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-12_19:31: (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 66601 0.06 66320 1.80 3 25000.00 25160 1.02 25327 4.28 4 6666.67 6607 0.53 6598 0.71 5 1388.89 1373 0.18 1468 4.51 6 238.10 220 1.38 245 0.20 7 34.72 34 0.01 38 0.31 8 4.96 4 0.19 3 0.77 p=0.24021 p=0.94975 Number of rngs required: 688738, p-value: 0.650 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-12_19:31 No. of wins: Observed Expected 98805 98585.9 z-score= 0.980, pvalue=0.83649 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66785 66666.7 0.210 0.210 2 37488 37654.3 0.735 0.945 3 27223 26954.7 2.670 3.615 4 19217 19313.5 0.482 4.096 5 13794 13851.4 0.238 4.334 6 9958 9943.5 0.021 4.355 7 7110 7145.0 0.172 4.527 8 5126 5139.1 0.033 4.560 9 3751 3699.9 0.707 5.267 10 2655 2666.3 0.048 5.315 11 1935 1923.3 0.071 5.386 12 1436 1388.7 1.608 6.994 13 960 1003.7 1.904 8.898 14 703 726.1 0.737 9.635 15 529 525.8 0.019 9.655 16 350 381.2 2.546 12.200 17 253 276.5 2.004 14.204 18 191 200.8 0.481 14.685 19 141 146.0 0.170 14.855 20 100 106.2 0.364 15.219 21 295 287.1 0.217 15.436 Chisq= 15.44 for 20 degrees of freedom, p= 0.24904 SUMMARY of craptest p-value for no. of wins: 0.836489 p-value for throws/game: 0.249043 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-12_19:31 No. of wins: Observed Expected 98346 98585.9 z-score=-1.073, pvalue=0.14168 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66825 66666.7 0.376 0.376 2 37766 37654.3 0.331 0.707 3 26658 26954.7 3.267 3.974 4 19319 19313.5 0.002 3.975 5 13997 13851.4 1.530 5.506 6 9935 9943.5 0.007 5.513 7 7113 7145.0 0.144 5.656 8 5051 5139.1 1.509 7.166 9 3725 3699.9 0.171 7.337 10 2617 2666.3 0.911 8.248 11 1959 1923.3 0.662 8.910 12 1427 1388.7 1.054 9.964 13 973 1003.7 0.940 10.904 14 755 726.1 1.147 12.050 15 538 525.8 0.281 12.332 16 380 381.2 0.003 12.335 17 256 276.5 1.526 13.861 18 187 200.8 0.952 14.813 19 140 146.0 0.245 15.059 20 98 106.2 0.635 15.694 21 281 287.1 0.130 15.824 Chisq= 15.82 for 20 degrees of freedom, p= 0.27253 SUMMARY of craptest p-value for no. of wins: 0.141683 p-value for throws/game: 0.272531 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0014,0.0026,0.0042,0.0052,0.0097,0.0100,0.0101,0.0127,0.0191, 0.0226,0.0264,0.0276,0.0284,0.0285,0.0321,0.0389,0.0395,0.0465,0.0466, 0.0514,0.0559,0.0599,0.0600,0.0651,0.0747,0.0749,0.0840,0.1127,0.1231, 0.1280,0.1294,0.1299,0.1307,0.1417,0.1432,0.1432,0.1446,0.1469,0.1473, 0.1496,0.1531,0.1562,0.1624,0.1640,0.1677,0.1687,0.1688,0.1701,0.1765, 0.1796,0.1824,0.1948,0.1976,0.1978,0.2067,0.2075,0.2116,0.2145,0.2160, 0.2169,0.2234,0.2238,0.2243,0.2252,0.2274,0.2308,0.2310,0.2341,0.2402, 0.2483,0.2490,0.2522,0.2532,0.2550,0.2603,0.2628,0.2645,0.2650,0.2661, 0.2685,0.2725,0.2744,0.2796,0.2832,0.2855,0.2891,0.2898,0.2974,0.3075, 0.3139,0.3140,0.3193,0.3201,0.3215,0.3320,0.3330,0.3411,0.3436,0.3442, 0.3462,0.3497,0.3521,0.3572,0.3574,0.3580,0.3583,0.3624,0.3685,0.3707, 0.3721,0.3751,0.3804,0.3827,0.3862,0.3869,0.3875,0.3954,0.3995,0.4005, 0.4109,0.4119,0.4154,0.4169,0.4171,0.4174,0.4221,0.4243,0.4311,0.4393, 0.4403,0.4420,0.4455,0.4550,0.4636,0.4712,0.4726,0.4757,0.4773,0.4845, 0.4918,0.4996,0.4998,0.5000,0.5023,0.5043,0.5045,0.5048,0.5105,0.5183, 0.5208,0.5235,0.5261,0.5310,0.5314,0.5314,0.5320,0.5423,0.5436,0.5544, 0.5576,0.5615,0.5691,0.5725,0.5825,0.5890,0.5895,0.5911,0.5936,0.5947, 0.5988,0.5999,0.6016,0.6038,0.6109,0.6262,0.6354,0.6408,0.6450,0.6502, 0.6518,0.6533,0.6535,0.6584,0.6594,0.6649,0.6687,0.6689,0.6706,0.6709, 0.6770,0.6790,0.6848,0.6897,0.6930,0.6946,0.6977,0.7038,0.7079,0.7080, 0.7081,0.7170,0.7182,0.7191,0.7211,0.7312,0.7399,0.7459,0.7512,0.7512, 0.7516,0.7617,0.7639,0.7673,0.7716,0.7725,0.7728,0.7759,0.7769,0.7780, 0.7812,0.7832,0.7839,0.7853,0.8061,0.8106,0.8106,0.8116,0.8124,0.8129, 0.8134,0.8138,0.8211,0.8337,0.8365,0.8506,0.8525,0.8570,0.8609,0.8613, 0.8642,0.8698,0.8785,0.8804,0.8894,0.8961,0.8964,0.8988,0.9048,0.9120, 0.9123,0.9206,0.9215,0.9320,0.9357,0.9392,0.9446,0.9497,0.9545,0.9572, 0.9643,0.9645,0.9691,0.9770,0.9784,0.9817,0.9818,0.9942,0.9952, Overall p-value after applying KStest on 269 p-values = 0.206372 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.