RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-03_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 13.4391 0.293667 2 to 25 15.75 19.8037 0.715610 3 to 26 16.05 16.0431 0.479220 4 to 27 15.72 20.4639 0.748810 5 to 28 15.55 12.6962 0.243729 6 to 29 15.66 27.8958 0.953830 7 to 30 15.90 16.4654 0.508887 8 to 31 16.02 9.6348 0.081776 9 to 32 15.98 15.6444 0.450835 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.978707 Tough bday spacings test for dh-ranFile-2017-02-03_17:31: 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 14 40 74 91 97 82 52 33 10 6 1 (O-E)^2/E 2.6 0.3 0.0 0.5 0.0 0.2 0.0 0.4 1.6 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 7.853, p= 0.357 RESULTS OF GCD FOR dh-ranFile-2017-02-03_17:31 Euclid's algorithm: p-value, steps to gcd: 0.475733 p-value, dist. of gcd's: 0.292972 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-03_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.577 0.815 0.860 0.676 0.279 0.759 0.233 0.026 Bits 8 to 15---> 0.483 0.491 0.496 0.711 0.432 0.652 0.943 0.110 Bits 16 to 23---> 0.794 0.676 0.783 0.456 0.935 0.393 0.706 0.332 Bits 24 to 31---> 0.625 0.270 0.206 0.490 0.719 0.726 0.267 0.769 KS test for the above 32 p values: 0.761 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-03_17:31, p-values for 5 runs: 0.0579, 0.1045, 0.3791, 0.8431, 0.7400 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-03_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5072 5134.0 0.749 1.169 r= 30 23190 23103.0 0.327 1.496 r= 31 11536 11551.5 0.021 1.517 chi-square = 1.517 with df = 3; p-value = 0.322 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-03_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 242 211.4 4.424 4.424 r= 30 4906 5134.0 10.126 14.550 r= 31 23174 23103.0 0.218 14.768 r= 32 11678 11551.5 1.385 16.153 chi-square = 16.153 with df = 3; p-value = 0.999 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-03_17:31 b-rank test for bits 1 to 8, p=0.22316 b-rank test for bits 2 to 9, p=0.90298 b-rank test for bits 3 to 10, p=0.93319 b-rank test for bits 4 to 11, p=0.90322 b-rank test for bits 5 to 12, p=0.47590 b-rank test for bits 6 to 13, p=0.33932 b-rank test for bits 7 to 14, p=0.59394 b-rank test for bits 8 to 15, p=0.53414 b-rank test for bits 9 to 16, p=0.25650 b-rank test for bits 10 to 17, p=0.79802 b-rank test for bits 11 to 18, p=0.81427 b-rank test for bits 12 to 19, p=0.97267 b-rank test for bits 13 to 20, p=0.02520 b-rank test for bits 14 to 21, p=0.52914 b-rank test for bits 15 to 22, p=0.43316 b-rank test for bits 16 to 23, p=0.42564 b-rank test for bits 17 to 24, p=0.27439 b-rank test for bits 18 to 25, p=0.50680 b-rank test for bits 19 to 26, p=0.27936 b-rank test for bits 20 to 27, p=0.06996 b-rank test for bits 21 to 28, p=0.63503 b-rank test for bits 22 to 29, p=0.61062 b-rank test for bits 23 to 30, p=0.42860 b-rank test for bits 24 to 31, p=0.81139 b-rank test for bits 25 to 32, p=0.46706 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 = 0.714594 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-03_17:31 (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 142410 1.17 0.878957 2 141334 -1.34 0.089437 3 141312 -1.40 0.081413 4 142266 0.83 0.797674 5 141295 -1.44 0.075594 6 142455 1.27 0.898833 7 142009 0.23 0.592070 8 142054 0.34 0.632324 9 141524 -0.90 0.183979 10 142140 0.54 0.705039 11 141465 -1.04 0.149599 12 141622 -0.67 0.251005 13 141931 0.05 0.520190 14 142135 0.53 0.700996 15 141601 -0.72 0.235640 16 141641 -0.63 0.265350 17 141539 -0.87 0.193449 18 141805 -0.24 0.403708 19 142201 0.68 0.752214 20 141837 -0.17 0.432900 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-03_17:31 Bits used No. missing words z-score p-value 23 to 32 141857 -0.1804 0.428400 22 to 31 142152 0.8368 0.798646 21 to 30 142058 0.5127 0.695904 20 to 29 141742 -0.5770 0.281970 19 to 28 142064 0.5333 0.703103 18 to 27 141272 -2.1977 0.013986 17 to 26 141944 0.1196 0.547581 16 to 25 142129 0.7575 0.775620 15 to 24 141902 -0.0253 0.489918 14 to 23 142206 1.0230 0.846846 13 to 22 141913 0.0127 0.505049 12 to 21 141911 0.0058 0.502297 11 to 20 142027 0.4058 0.657540 10 to 19 141945 0.1230 0.548947 9 to 18 141984 0.2575 0.601597 8 to 17 141803 -0.3667 0.356938 7 to 16 141437 -1.6287 0.051686 6 to 15 141342 -1.9563 0.025214 5 to 14 141999 0.3092 0.621418 4 to 13 141699 -0.7253 0.234141 3 to 12 141996 0.2989 0.617477 2 to 11 141931 0.0747 0.529783 1 to 10 142321 1.4196 0.922131 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-03_17:31 Bits used No. missing words z-score p-value 28 to 32 141692 -0.7367 0.230649 27 to 31 141865 -0.1503 0.440275 26 to 30 141608 -1.0215 0.153519 25 to 29 141881 -0.0960 0.461747 24 to 28 141390 -1.7604 0.039167 23 to 27 141866 -0.1469 0.441613 22 to 26 142071 0.5480 0.708166 21 to 25 142036 0.4294 0.666180 20 to 24 142130 0.7480 0.772780 19 to 23 142034 0.4226 0.663710 18 to 22 141993 0.2836 0.611652 17 to 21 141677 -0.7876 0.215477 16 to 20 141204 -2.3909 0.008402 15 to 19 142033 0.4192 0.662473 14 to 18 142352 1.5006 0.933267 13 to 17 142257 1.1785 0.880710 12 to 16 141942 0.1107 0.544091 11 to 15 142116 0.7006 0.758216 10 to 14 141749 -0.5435 0.293396 9 to 13 141701 -0.7062 0.240031 8 to 12 141835 -0.2520 0.400534 7 to 11 141744 -0.5604 0.287589 6 to 10 141927 0.0599 0.523882 5 to 9 142180 0.9175 0.820566 4 to 8 142499 1.9989 0.977189 3 to 7 141512 -1.3469 0.089009 2 to 6 141886 -0.0791 0.468483 1 to 5 142221 1.0565 0.854632 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-03_17:31 Bits used No. missing words z-score p-value 31 to 32 141831 -0.2311 0.408633 30 to 31 141955 0.1347 0.553583 29 to 30 142274 1.0757 0.858974 28 to 29 141059 -2.5083 0.006065 27 to 28 142135 0.6657 0.747196 26 to 27 141883 -0.0777 0.469045 25 to 26 142052 0.4209 0.663070 24 to 25 142215 0.9017 0.816387 23 to 24 141944 0.1023 0.540729 22 to 23 141732 -0.5231 0.300453 21 to 22 142388 1.4120 0.921026 20 to 21 141830 -0.2340 0.407488 19 to 20 141741 -0.4965 0.309754 18 to 19 142030 0.3560 0.639064 17 to 18 142034 0.3678 0.643473 16 to 17 141513 -1.1691 0.121179 15 to 16 142117 0.6126 0.729928 14 to 15 141812 -0.2871 0.387014 13 to 14 142001 0.2704 0.606579 12 to 13 142254 1.0167 0.845358 11 to 12 142031 0.3589 0.640168 10 to 11 142057 0.4356 0.668438 9 to 10 142034 0.3678 0.643473 8 to 9 141954 0.1318 0.552417 7 to 8 141618 -0.8594 0.195065 6 to 7 141880 -0.0865 0.465527 5 to 6 141615 -0.8682 0.192634 4 to 5 141521 -1.1455 0.125998 3 to 4 142191 0.8309 0.796981 2 to 3 141381 -1.5585 0.059558 1 to 2 141791 -0.3491 0.363524 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-03_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2533.64 0.476 0.682857 Test results for specific bytes for dh-ranFile-2017-02-03_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2503.52 0.050 0.519872 2 to 9 2569.89 0.988 0.838510 3 to 10 2479.93 -0.284 0.388295 4 to 11 2466.37 -0.476 0.317160 5 to 12 2482.35 -0.250 0.401470 6 to 13 2501.33 0.019 0.507483 7 to 14 2495.74 -0.060 0.475961 8 to 15 2434.58 -0.925 0.177439 9 to 16 2585.47 1.209 0.886603 10 to 17 2447.95 -0.736 0.230816 11 to 18 2495.18 -0.068 0.472836 12 to 19 2492.35 -0.108 0.456909 13 to 20 2530.76 0.435 0.668220 14 to 21 2557.21 0.809 0.790782 15 to 22 2533.35 0.472 0.681426 16 to 23 2409.69 -1.277 0.100771 17 to 24 2581.31 1.150 0.874904 18 to 25 2443.18 -0.804 0.210831 19 to 26 2454.82 -0.639 0.261450 20 to 27 2559.50 0.841 0.799956 21 to 28 2504.15 0.059 0.523376 22 to 29 2549.51 0.700 0.758070 23 to 30 2391.12 -1.540 0.061806 24 to 31 2630.42 1.844 0.967435 25 to 32 2535.46 0.501 0.691962 CDPARK for dh-ranFile-2017-02-03_17:31: 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 3561 1.7352 0.958644 3537 0.6393 0.738676 3516 -0.3196 0.374623 3504 -0.8676 0.192812 3534 0.5023 0.692266 3558 1.5982 0.944998 3559 1.6438 0.949895 3515 -0.3653 0.357445 3495 -1.2785 0.100530 3505 -0.8219 0.205562 Square side=100, avg. no. parked=3528.40 sample std.=23.61 p-value of the KSTEST for those 10 p-values: 0.454318 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-03_17:31 0.4002,0.1986,0.4984,0.1756,0.8059,0.3679,0.6333,0.5355,0.2663,0.2006, The KS test for those 10 p-values: 0.307876 The 3DSPHERES test for dh-ranFile-2017-02-03_17:31 sample no r^3 equiv. uni. 1 40.916 0.744326 2 63.604 0.879982 3 10.113 0.286158 4 21.934 0.518636 5 14.093 0.374846 6 3.205 0.101334 7 0.716 0.023592 8 2.835 0.090181 9 75.700 0.919809 10 36.444 0.703235 11 1.315 0.042871 12 28.006 0.606844 13 4.886 0.150293 14 13.466 0.361651 15 4.755 0.146588 16 18.514 0.460518 17 74.142 0.915533 18 38.598 0.723787 19 14.199 0.377066 20 16.604 0.425044 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.647145 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-03_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 1.8 -1.6 0.3 0.0 0.3 -0.9 1.5 1.6 0.5 0.2 -0.9 0.3 0.2 0.5 -1.7 -0.7 -0.5 -0.6 1.4 0.6 -1.6 1.6 -0.9 1.1 -1.1 -1.2 1.3 1.0 0.9 0.5 1.4 -1.8 1.0 0.4 -0.5 0.2 -0.4 0.4 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:45.883686 z-score=0.423745, p-value=0.685674 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-03_17:31 Test no p-value 1 0.043495 2 0.026333 3 0.721753 4 0.409410 5 0.255948 6 0.958741 7 0.866470 8 0.090071 9 0.640667 10 0.000370 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.086454 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-03_17:31: (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 66657 0.00 66755 0.12 3 25000.00 25047 0.09 25034 0.05 4 6666.67 6646 0.06 6609 0.50 5 1388.89 1389 0.00 1308 4.71 6 238.10 224 0.83 247 0.33 7 34.72 32 0.21 41 1.14 8 4.96 4 0.19 5 0.00 p=0.03337 p=0.66434 Number of rngs required: 688221, p-value: 0.417 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-03_17:31 No. of wins: Observed Expected 98503 98585.9 z-score=-0.371, pvalue=0.35547 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66617 66666.7 0.037 0.037 2 37755 37654.3 0.269 0.306 3 26724 26954.7 1.975 2.281 4 19086 19313.5 2.679 4.960 5 13972 13851.4 1.050 6.010 6 9972 9943.5 0.081 6.091 7 7073 7145.0 0.726 6.817 8 5305 5139.1 5.357 12.175 9 3739 3699.9 0.414 12.589 10 2679 2666.3 0.061 12.649 11 1928 1923.3 0.011 12.661 12 1438 1388.7 1.747 14.408 13 1038 1003.7 1.171 15.579 14 749 726.1 0.720 16.299 15 554 525.8 1.508 17.807 16 347 381.2 3.060 20.867 17 266 276.5 0.402 21.269 18 198 200.8 0.040 21.308 19 141 146.0 0.170 21.479 20 101 106.2 0.256 21.735 21 318 287.1 3.323 25.057 Chisq= 25.06 for 20 degrees of freedom, p= 0.80075 SUMMARY of craptest p-value for no. of wins: 0.355471 p-value for throws/game: 0.800750 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-03_17:31 No. of wins: Observed Expected 98325 98585.9 z-score=-1.167, pvalue=0.12166 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66453 66666.7 0.685 0.685 2 37811 37654.3 0.652 1.337 3 26588 26954.7 4.990 6.326 4 19479 19313.5 1.419 7.745 5 14078 13851.4 3.706 11.452 6 9901 9943.5 0.182 11.634 7 7255 7145.0 1.693 13.326 8 5183 5139.1 0.375 13.702 9 3690 3699.9 0.026 13.728 10 2705 2666.3 0.562 14.290 11 1927 1923.3 0.007 14.297 12 1332 1388.7 2.318 16.615 13 986 1003.7 0.313 16.928 14 724 726.1 0.006 16.934 15 510 525.8 0.477 17.411 16 385 381.2 0.039 17.450 17 283 276.5 0.151 17.601 18 180 200.8 2.160 19.761 19 127 146.0 2.469 22.230 20 111 106.2 0.216 22.446 21 292 287.1 0.083 22.529 Chisq= 22.53 for 20 degrees of freedom, p= 0.68748 SUMMARY of craptest p-value for no. of wins: 0.121663 p-value for throws/game: 0.687478 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0061,0.0084,0.0140,0.0236,0.0252,0.0252,0.0263,0.0265,0.0334, 0.0392,0.0429,0.0435,0.0517,0.0579,0.0596,0.0618,0.0700,0.0756,0.0814, 0.0818,0.0865,0.0890,0.0894,0.0901,0.0902,0.1005,0.1008,0.1013,0.1045, 0.1105,0.1212,0.1217,0.1260,0.1466,0.1496,0.1503,0.1535,0.1756,0.1774, 0.1840,0.1926,0.1928,0.1934,0.1951,0.1986,0.2006,0.2056,0.2056,0.2108, 0.2155,0.2232,0.2306,0.2308,0.2326,0.2341,0.2356,0.2400,0.2437,0.2510, 0.2559,0.2565,0.2615,0.2653,0.2663,0.2673,0.2698,0.2744,0.2793,0.2794, 0.2820,0.2862,0.2876,0.2930,0.2934,0.2937,0.3005,0.3079,0.3098,0.3172, 0.3216,0.3320,0.3393,0.3555,0.3568,0.3569,0.3574,0.3617,0.3635,0.3679, 0.3746,0.3748,0.3771,0.3791,0.3870,0.3883,0.3926,0.4002,0.4005,0.4015, 0.4037,0.4075,0.4086,0.4094,0.4171,0.4250,0.4256,0.4284,0.4286,0.4325, 0.4329,0.4332,0.4403,0.4416,0.4508,0.4543,0.4558,0.4569,0.4605,0.4617, 0.4655,0.4671,0.4685,0.4690,0.4728,0.4757,0.4759,0.4760,0.4792,0.4830, 0.4899,0.4899,0.4912,0.4956,0.4984,0.5023,0.5050,0.5068,0.5075,0.5089, 0.5186,0.5199,0.5202,0.5234,0.5239,0.5291,0.5298,0.5341,0.5355,0.5407, 0.5441,0.5476,0.5489,0.5524,0.5536,0.5771,0.5921,0.5939,0.6016,0.6066, 0.6068,0.6106,0.6117,0.6175,0.6214,0.6250,0.6323,0.6333,0.6350,0.6391, 0.6402,0.6407,0.6435,0.6435,0.6471,0.6521,0.6575,0.6625,0.6631,0.6637, 0.6643,0.6662,0.6682,0.6684,0.6760,0.6764,0.6814,0.6829,0.6857,0.6875, 0.6920,0.6923,0.6959,0.7010,0.7031,0.7032,0.7050,0.7063,0.7082,0.7111, 0.7146,0.7156,0.7186,0.7218,0.7238,0.7262,0.7299,0.7387,0.7400,0.7443, 0.7472,0.7488,0.7522,0.7581,0.7582,0.7591,0.7613,0.7685,0.7728,0.7756, 0.7833,0.7908,0.7943,0.7970,0.7977,0.7980,0.7986,0.8000,0.8008,0.8059, 0.8114,0.8143,0.8150,0.8164,0.8206,0.8385,0.8431,0.8454,0.8468,0.8546, 0.8590,0.8600,0.8665,0.8749,0.8790,0.8800,0.8807,0.8866,0.8988,0.9030, 0.9032,0.9155,0.9198,0.9210,0.9221,0.9332,0.9333,0.9347,0.9433,0.9450, 0.9499,0.9538,0.9586,0.9587,0.9674,0.9727,0.9772,0.9787,0.9989, Overall p-value after applying KStest on 269 p-values = 0.313964 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.