RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-25_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.44 24.7958 0.900624 2 to 25 15.57 26.0240 0.925975 3 to 26 15.71 7.5354 0.024501 4 to 27 15.68 16.9492 0.542184 5 to 28 15.84 22.4758 0.832895 6 to 29 15.69 21.4403 0.792787 7 to 30 15.90 12.6536 0.240953 8 to 31 15.74 19.5257 0.700798 9 to 32 15.74 15.9732 0.474264 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.430592 Tough bday spacings test for dh-ranFile-2016-01-25_06:31: 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 8 38 73 99 109 76 47 32 9 5 4 (O-E)^2/E 0.1 0.1 0.0 0.0 1.3 0.1 0.5 0.2 2.3 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.974, p= 0.107 RESULTS OF GCD FOR dh-ranFile-2016-01-25_06:31 Euclid's algorithm: p-value, steps to gcd: 0.323946 p-value, dist. of gcd's: 0.072813 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-25_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.397 0.207 0.324 0.561 0.996 0.215 0.804 0.794 Bits 8 to 15---> 0.860 0.875 0.961 0.655 0.945 0.971 0.987 0.077 Bits 16 to 23---> 0.843 0.350 0.952 0.391 0.914 0.765 0.498 0.653 Bits 24 to 31---> 0.079 0.634 0.633 0.050 0.902 0.738 0.173 0.644 KS test for the above 32 p values: 0.983 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-25_06:31, p-values for 5 runs: 0.8464, 0.5593, 0.8693, 0.6168, 0.4684 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-25_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 4953 5134.0 6.382 7.657 r= 30 23189 23103.0 0.320 7.977 r= 31 11663 11551.5 1.076 9.052 chi-square = 9.052 with df = 3; p-value = 0.971 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-25_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5167 5134.0 0.212 0.646 r= 31 23130 23103.0 0.031 0.678 r= 32 11482 11551.5 0.418 1.096 chi-square = 1.096 with df = 3; p-value = 0.222 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-25_06:31 b-rank test for bits 1 to 8, p=0.84471 b-rank test for bits 2 to 9, p=0.19312 b-rank test for bits 3 to 10, p=0.35473 b-rank test for bits 4 to 11, p=0.00747 b-rank test for bits 5 to 12, p=0.76061 b-rank test for bits 6 to 13, p=0.93882 b-rank test for bits 7 to 14, p=0.76364 b-rank test for bits 8 to 15, p=0.88007 b-rank test for bits 9 to 16, p=0.17274 b-rank test for bits 10 to 17, p=0.45613 b-rank test for bits 11 to 18, p=0.28964 b-rank test for bits 12 to 19, p=0.35477 b-rank test for bits 13 to 20, p=0.66223 b-rank test for bits 14 to 21, p=0.68526 b-rank test for bits 15 to 22, p=0.62355 b-rank test for bits 16 to 23, p=0.55973 b-rank test for bits 17 to 24, p=0.53052 b-rank test for bits 18 to 25, p=0.55459 b-rank test for bits 19 to 26, p=0.00552 b-rank test for bits 20 to 27, p=0.45765 b-rank test for bits 21 to 28, p=0.04061 b-rank test for bits 22 to 29, p=0.63466 b-rank test for bits 23 to 30, p=0.79132 b-rank test for bits 24 to 31, p=0.31732 b-rank test for bits 25 to 32, p=0.51994 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 = 0.678005 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-25_06:31 (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 142021 0.26 0.602920 2 142068 0.37 0.644579 3 142002 0.22 0.585708 4 142348 1.02 0.847302 5 141530 -0.89 0.187732 6 141609 -0.70 0.241431 7 142576 1.56 0.940341 8 141988 0.18 0.572918 9 141901 -0.02 0.492236 10 142121 0.49 0.689543 11 141621 -0.67 0.250261 12 141974 0.15 0.560051 13 141589 -0.75 0.227099 14 141730 -0.42 0.337610 15 141418 -1.15 0.125491 16 141988 0.18 0.572918 17 142155 0.57 0.717015 18 142399 1.14 0.873707 19 141764 -0.34 0.367095 20 142111 0.47 0.681248 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-25_06:31 Bits used No. missing words z-score p-value 23 to 32 142242 1.1471 0.874338 22 to 31 141885 -0.0839 0.466569 21 to 30 141748 -0.5563 0.288999 20 to 29 142043 0.4609 0.677576 19 to 28 141708 -0.6942 0.243765 18 to 27 141844 -0.2253 0.410882 17 to 26 141298 -2.1080 0.017514 16 to 25 141593 -1.0908 0.137682 15 to 24 141429 -1.6563 0.048830 14 to 23 141544 -1.2598 0.103878 13 to 22 141765 -0.4977 0.309351 12 to 21 142165 0.8816 0.811009 11 to 20 141444 -1.6046 0.054292 10 to 19 142033 0.4264 0.665109 9 to 18 141750 -0.5494 0.291361 8 to 17 141521 -1.3391 0.090274 7 to 16 142426 1.7816 0.962594 6 to 15 141792 -0.4046 0.342891 5 to 14 142000 0.3127 0.622729 4 to 13 142041 0.4540 0.675098 3 to 12 142256 1.1954 0.884037 2 to 11 142213 1.0471 0.852482 1 to 10 141972 0.2161 0.585547 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-25_06:31 Bits used No. missing words z-score p-value 28 to 32 142346 1.4802 0.930595 27 to 31 141733 -0.5977 0.275010 26 to 30 142097 0.6362 0.737667 25 to 29 141581 -1.1130 0.132858 24 to 28 142020 0.3752 0.646227 23 to 27 142091 0.6158 0.730997 22 to 26 142292 1.2972 0.902717 21 to 25 142203 0.9955 0.840251 20 to 24 142082 0.5853 0.720834 19 to 23 141713 -0.6655 0.252857 18 to 22 141678 -0.7842 0.216470 17 to 21 141731 -0.6045 0.272753 16 to 20 141986 0.2599 0.602529 15 to 19 141574 -1.1367 0.127829 14 to 18 142070 0.5446 0.707001 13 to 17 141973 0.2158 0.585440 12 to 16 142395 1.6463 0.950153 11 to 15 141235 -2.2859 0.011131 10 to 14 141658 -0.8520 0.197116 9 to 13 142121 0.7175 0.763475 8 to 12 141356 -1.8757 0.030349 7 to 11 141758 -0.5130 0.303982 6 to 10 141598 -1.0554 0.145631 5 to 9 142344 1.4735 0.929686 4 to 8 142342 1.4667 0.928768 3 to 7 142203 0.9955 0.840251 2 to 6 141933 0.0802 0.531976 1 to 5 141954 0.1514 0.560179 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-25_06:31 Bits used No. missing words z-score p-value 31 to 32 141296 -1.8092 0.035207 30 to 31 142352 1.3058 0.904192 29 to 30 141767 -0.4199 0.337297 28 to 29 141788 -0.3579 0.360207 27 to 28 141720 -0.5585 0.288253 26 to 27 141782 -0.3756 0.353605 25 to 26 141973 0.1878 0.574490 24 to 25 142128 0.6450 0.740551 23 to 24 141566 -1.0128 0.155584 22 to 23 141469 -1.2989 0.096988 21 to 22 142211 0.8899 0.813235 20 to 21 142037 0.3766 0.646767 19 to 20 141798 -0.3284 0.371302 18 to 19 141602 -0.9066 0.182315 17 to 18 141624 -0.8417 0.199983 16 to 17 141881 -0.0836 0.466699 15 to 16 141423 -1.4346 0.075700 14 to 15 142091 0.5359 0.703986 13 to 14 142123 0.6303 0.735749 12 to 13 142199 0.8545 0.803582 11 to 12 141558 -1.0364 0.150014 10 to 11 142375 1.3737 0.915226 9 to 10 142345 1.2852 0.900632 8 to 9 141029 -2.5968 0.004704 7 to 8 141892 -0.0511 0.479615 6 to 7 142061 0.4474 0.672708 5 to 6 141785 -0.3668 0.356901 4 to 5 142270 1.0639 0.856318 3 to 4 141977 0.1996 0.579110 2 to 3 141535 -1.1042 0.134749 1 to 2 142017 0.3176 0.624610 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-25_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2403.45 -1.365 0.086052 Test results for specific bytes for dh-ranFile-2016-01-25_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2500.45 0.006 0.502556 2 to 9 2549.53 0.700 0.758160 3 to 10 2531.75 0.449 0.673288 4 to 11 2611.54 1.577 0.942648 5 to 12 2509.34 0.132 0.552521 6 to 13 2544.93 0.635 0.737403 7 to 14 2629.71 1.834 0.966696 8 to 15 2503.31 0.047 0.518664 9 to 16 2554.19 0.766 0.778269 10 to 17 2444.35 -0.787 0.215653 11 to 18 2527.12 0.384 0.649347 12 to 19 2585.78 1.213 0.887447 13 to 20 2506.63 0.094 0.537376 14 to 21 2520.11 0.284 0.611955 15 to 22 2620.28 1.701 0.955527 16 to 23 2469.38 -0.433 0.332502 17 to 24 2387.01 -1.598 0.055031 18 to 25 2436.73 -0.895 0.185468 19 to 26 2344.37 -2.201 0.013869 20 to 27 2454.82 -0.639 0.261426 21 to 28 2519.98 0.283 0.611247 22 to 29 2527.33 0.387 0.650452 23 to 30 2491.49 -0.120 0.452125 24 to 31 2473.39 -0.376 0.353343 25 to 32 2580.73 1.142 0.873197 CDPARK for dh-ranFile-2016-01-25_06:31: 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 3552 1.3242 0.907282 3504 -0.8676 0.192812 3552 1.3242 0.907282 3520 -0.1370 0.445521 3543 0.9132 0.819442 3549 1.1872 0.882429 3541 0.8219 0.794438 3523 0.0000 0.500000 3499 -1.0959 0.136563 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3529.80 sample std.=19.05 p-value of the KSTEST for those 10 p-values: 0.398269 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-25_06:31 0.3635,0.8636,0.0109,0.4806,0.1675,0.5801,0.8240,0.1219,0.2959,0.2469, The KS test for those 10 p-values: 0.458090 The 3DSPHERES test for dh-ranFile-2016-01-25_06:31 sample no r^3 equiv. uni. 1 14.270 0.378531 2 1.232 0.040242 3 21.251 0.507556 4 33.488 0.672495 5 91.623 0.952834 6 41.600 0.750089 7 4.141 0.128944 8 20.768 0.499552 9 15.899 0.411377 10 24.551 0.558841 11 10.874 0.304040 12 20.209 0.490150 13 14.086 0.374696 14 12.927 0.350076 15 17.952 0.450307 16 21.515 0.511870 17 31.863 0.654274 18 19.805 0.483243 19 7.217 0.213816 20 12.956 0.350702 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.170016 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-25_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 0.1 0.5 -0.1 -0.1 0.3 0.5 0.6 0.9 0.1 -1.5 1.1 -1.5 2.3 -0.5 -0.6 -1.4 0.3 0.4 0.9 0.7 -0.5 0.9 -0.5 -0.3 -1.0 0.2 -0.6 -1.3 -0.4 0.4 -0.0 -0.3 0.1 0.1 -1.2 -0.7 -0.4 0.4 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:26.170614 z-score=-1.727128, p-value=0.026553 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-25_06:31 Test no p-value 1 0.071342 2 0.937391 3 0.020970 4 0.474600 5 0.221229 6 0.282396 7 0.007466 8 0.310335 9 0.845928 10 0.951798 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.158355 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-25_06:31: (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 66957 1.26 66481 0.52 3 25000.00 24732 2.87 25080 0.26 4 6666.67 6608 0.52 6772 1.66 5 1388.89 1400 0.09 1370 0.26 6 238.10 260 2.02 257 1.50 7 34.72 37 0.15 32 0.21 8 4.96 5 0.00 7 0.84 p=0.67054 p=0.48750 Number of rngs required: 687473, p-value: 0.140 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-25_06:31 No. of wins: Observed Expected 98477 98585.9 z-score=-0.487, pvalue=0.31317 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66514 66666.7 0.350 0.350 2 37589 37654.3 0.113 0.463 3 27118 26954.7 0.989 1.452 4 19241 19313.5 0.272 1.724 5 13854 13851.4 0.000 1.724 6 9876 9943.5 0.459 2.183 7 7209 7145.0 0.573 2.756 8 5103 5139.1 0.253 3.009 9 3689 3699.9 0.032 3.041 10 2702 2666.3 0.478 3.519 11 2052 1923.3 8.608 12.127 12 1350 1388.7 1.081 13.208 13 1017 1003.7 0.176 13.384 14 745 726.1 0.490 13.873 15 535 525.8 0.160 14.033 16 392 381.2 0.309 14.342 17 260 276.5 0.989 15.331 18 213 200.8 0.737 16.069 19 162 146.0 1.757 17.826 20 113 106.2 0.433 18.259 21 266 287.1 1.553 19.812 Chisq= 19.81 for 20 degrees of freedom, p= 0.53024 SUMMARY of craptest p-value for no. of wins: 0.313172 p-value for throws/game: 0.530243 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-25_06:31 No. of wins: Observed Expected 98422 98585.9 z-score=-0.733, pvalue=0.23182 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66176 66666.7 3.611 3.611 2 37773 37654.3 0.374 3.985 3 27211 26954.7 2.436 6.422 4 19520 19313.5 2.209 8.630 5 13754 13851.4 0.685 9.316 6 9928 9943.5 0.024 9.340 7 7092 7145.0 0.394 9.733 8 5140 5139.1 0.000 9.734 9 3595 3699.9 2.972 12.706 10 2668 2666.3 0.001 12.707 11 1936 1923.3 0.083 12.790 12 1354 1388.7 0.869 13.659 13 1099 1003.7 9.046 22.705 14 752 726.1 0.921 23.626 15 544 525.8 0.627 24.253 16 417 381.2 3.372 27.625 17 270 276.5 0.155 27.780 18 227 200.8 3.410 31.190 19 153 146.0 0.337 31.527 20 112 106.2 0.315 31.842 21 279 287.1 0.229 32.072 Chisq= 32.07 for 20 degrees of freedom, p= 0.95746 SUMMARY of craptest p-value for no. of wins: 0.231819 p-value for throws/game: 0.957459 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0047,0.0055,0.0075,0.0075,0.0109,0.0111,0.0139,0.0175,0.0210,0.0245, 0.0266,0.0303,0.0352,0.0402,0.0406,0.0488,0.0495,0.0543,0.0550,0.0713, 0.0728,0.0757,0.0771,0.0795,0.0861,0.0903,0.0970,0.1039,0.1071,0.1219, 0.1255,0.1278,0.1289,0.1329,0.1347,0.1366,0.1377,0.1404,0.1456,0.1500, 0.1556,0.1584,0.1675,0.1700,0.1727,0.1728,0.1823,0.1855,0.1877,0.1928, 0.1931,0.1971,0.2000,0.2074,0.2138,0.2153,0.2157,0.2165,0.2212,0.2220, 0.2271,0.2318,0.2410,0.2414,0.2438,0.2469,0.2503,0.2529,0.2614,0.2728, 0.2750,0.2824,0.2883,0.2890,0.2896,0.2914,0.2959,0.3040,0.3040,0.3094, 0.3103,0.3132,0.3173,0.3236,0.3239,0.3325,0.3373,0.3376,0.3429,0.3501, 0.3502,0.3507,0.3533,0.3536,0.3547,0.3548,0.3569,0.3574,0.3602,0.3635, 0.3671,0.3713,0.3747,0.3785,0.3910,0.3968,0.3983,0.4109,0.4114,0.4306, 0.4455,0.4503,0.4521,0.4561,0.4576,0.4581,0.4666,0.4667,0.4684,0.4743, 0.4746,0.4796,0.4806,0.4832,0.4875,0.4902,0.4922,0.4984,0.4996,0.5000, 0.5026,0.5076,0.5119,0.5187,0.5199,0.5302,0.5305,0.5320,0.5374,0.5422, 0.5525,0.5546,0.5588,0.5593,0.5597,0.5601,0.5602,0.5605,0.5729,0.5729, 0.5745,0.5791,0.5801,0.5854,0.5855,0.5857,0.6025,0.6029,0.6112,0.6120, 0.6168,0.6227,0.6236,0.6246,0.6332,0.6337,0.6347,0.6438,0.6446,0.6462, 0.6468,0.6493,0.6505,0.6527,0.6543,0.6548,0.6622,0.6651,0.6705,0.6725, 0.6727,0.6733,0.6751,0.6776,0.6780,0.6812,0.6853,0.6895,0.7008,0.7040, 0.7070,0.7170,0.7208,0.7310,0.7357,0.7374,0.7377,0.7379,0.7406,0.7501, 0.7582,0.7606,0.7635,0.7636,0.7652,0.7783,0.7913,0.7928,0.7944,0.7945, 0.8036,0.8045,0.8110,0.8132,0.8194,0.8240,0.8329,0.8403,0.8403,0.8431, 0.8447,0.8459,0.8464,0.8473,0.8525,0.8563,0.8596,0.8636,0.8693,0.8732, 0.8737,0.8743,0.8753,0.8801,0.8824,0.8840,0.8874,0.9006,0.9006,0.9017, 0.9027,0.9042,0.9073,0.9073,0.9136,0.9152,0.9260,0.9288,0.9297,0.9306, 0.9374,0.9388,0.9403,0.9426,0.9452,0.9502,0.9518,0.9522,0.9528,0.9555, 0.9575,0.9605,0.9626,0.9667,0.9712,0.9714,0.9828,0.9870,0.9963, Overall p-value after applying KStest on 269 p-values = 0.841922 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.