RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-27_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 15.89 15.3152 0.427213 2 to 25 15.81 13.3903 0.290308 3 to 26 15.72 20.6922 0.759637 4 to 27 15.69 19.7307 0.711764 5 to 28 15.64 19.1057 0.677499 6 to 29 15.91 10.2128 0.105548 7 to 30 15.80 18.1475 0.620408 8 to 31 15.80 12.2874 0.217567 9 to 32 15.56 25.5731 0.917403 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.964577 Tough bday spacings test for dh-ranFile-2016-06-27_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 13 40 83 90 98 73 42 37 11 7 6 (O-E)^2/E 1.6 0.3 1.3 0.6 0.0 0.3 2.0 1.8 1.0 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.829, p= 0.544 RESULTS OF GCD FOR dh-ranFile-2016-06-27_06:31 Euclid's algorithm: p-value, steps to gcd: 0.899672 p-value, dist. of gcd's: 0.499230 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-27_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.776 0.589 0.969 0.253 0.559 0.226 0.232 0.320 Bits 8 to 15---> 0.852 0.837 0.736 0.686 0.010 0.595 0.612 0.649 Bits 16 to 23---> 0.045 0.389 0.860 0.850 0.660 0.301 0.936 0.294 Bits 24 to 31---> 0.074 0.262 0.588 0.339 0.657 0.035 0.288 0.398 KS test for the above 32 p values: 0.102 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-27_06:31, p-values for 5 runs: 0.1639, 0.0997, 0.3283, 0.8556, 0.7898 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-27_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5068 5134.0 0.849 0.941 r= 30 22986 23103.0 0.593 1.534 r= 31 11739 11551.5 3.043 4.577 chi-square = 4.577 with df = 3; p-value = 0.794 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-27_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5098 5134.0 0.253 0.262 r= 31 23202 23103.0 0.424 0.686 r= 32 11490 11551.5 0.328 1.014 chi-square = 1.014 with df = 3; p-value = 0.202 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-27_06:31 b-rank test for bits 1 to 8, p=0.16679 b-rank test for bits 2 to 9, p=0.23276 b-rank test for bits 3 to 10, p=0.08512 b-rank test for bits 4 to 11, p=0.69966 b-rank test for bits 5 to 12, p=0.54899 b-rank test for bits 6 to 13, p=0.10899 b-rank test for bits 7 to 14, p=0.09280 b-rank test for bits 8 to 15, p=0.20744 b-rank test for bits 9 to 16, p=0.63658 b-rank test for bits 10 to 17, p=0.49236 b-rank test for bits 11 to 18, p=0.43624 b-rank test for bits 12 to 19, p=0.69145 b-rank test for bits 13 to 20, p=0.89907 b-rank test for bits 14 to 21, p=0.05540 b-rank test for bits 15 to 22, p=0.68272 b-rank test for bits 16 to 23, p=0.46385 b-rank test for bits 17 to 24, p=0.22361 b-rank test for bits 18 to 25, p=0.49788 b-rank test for bits 19 to 26, p=0.99103 b-rank test for bits 20 to 27, p=0.55980 b-rank test for bits 21 to 28, p=0.24369 b-rank test for bits 22 to 29, p=0.34195 b-rank test for bits 23 to 30, p=0.72514 b-rank test for bits 24 to 31, p=0.09055 b-rank test for bits 25 to 32, p=0.18737 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 = 0.192372 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-27_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 141231 -1.58 0.056496 2 142490 1.36 0.912563 3 142015 0.25 0.597504 4 141966 0.13 0.552669 5 142137 0.53 0.702616 6 142336 1.00 0.840592 7 141753 -0.37 0.357460 8 141188 -1.69 0.045960 9 142495 1.37 0.914405 10 142340 1.01 0.842850 11 142332 0.99 0.838313 12 142106 0.46 0.677066 13 142432 1.22 0.888993 14 141565 -0.80 0.210551 15 141586 -0.76 0.224991 16 142528 1.45 0.925840 17 141525 -0.90 0.184602 18 141723 -0.44 0.331654 19 141749 -0.37 0.353978 20 142362 1.06 0.854890 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-27_06:31 Bits used No. missing words z-score p-value 23 to 32 141963 0.1851 0.573413 22 to 31 142083 0.5989 0.725368 21 to 30 141907 -0.0080 0.496795 20 to 29 141551 -1.2356 0.108300 19 to 28 142242 1.1471 0.874338 18 to 27 141926 0.0575 0.522920 17 to 26 141769 -0.4839 0.314230 16 to 25 141207 -2.4218 0.007721 15 to 24 142092 0.6299 0.735619 14 to 23 141590 -1.1011 0.135418 13 to 22 142094 0.6368 0.737870 12 to 21 141445 -1.6011 0.054673 11 to 20 142054 0.4989 0.691062 10 to 19 141526 -1.3218 0.093113 9 to 18 141173 -2.5391 0.005557 8 to 17 142008 0.3402 0.633163 7 to 16 142251 1.1782 0.880636 6 to 15 141889 -0.0701 0.472056 5 to 14 141466 -1.5287 0.063166 4 to 13 141295 -2.1184 0.017071 3 to 12 141803 -0.3667 0.356938 2 to 11 141469 -1.5184 0.064459 1 to 10 142362 1.5609 0.940730 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-27_06:31 Bits used No. missing words z-score p-value 28 to 32 142170 0.8836 0.811551 27 to 31 141819 -0.3062 0.379725 26 to 30 142430 1.7650 0.961217 25 to 29 141642 -0.9062 0.182414 24 to 28 141757 -0.5164 0.302797 23 to 27 141942 0.1107 0.544091 22 to 26 141788 -0.4113 0.340431 21 to 25 142001 0.3107 0.622003 20 to 24 142294 1.3040 0.903877 19 to 23 141715 -0.6587 0.255030 18 to 22 141845 -0.2181 0.413688 17 to 21 141649 -0.8825 0.188760 16 to 20 142045 0.4599 0.677205 15 to 19 141622 -0.9740 0.165028 14 to 18 141795 -0.3876 0.349171 13 to 17 142046 0.4633 0.678421 12 to 16 141399 -1.7299 0.041821 11 to 15 141353 -1.8859 0.029657 10 to 14 141805 -0.3537 0.361797 9 to 13 141995 0.2904 0.614248 8 to 12 142160 0.8497 0.802262 7 to 11 141414 -1.6791 0.046568 6 to 10 142270 1.2226 0.889262 5 to 9 141669 -0.8147 0.207628 4 to 8 141455 -1.5401 0.061768 3 to 7 141923 0.0463 0.518480 2 to 6 141228 -2.3096 0.010455 1 to 5 142071 0.5480 0.708166 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-27_06:31 Bits used No. missing words z-score p-value 31 to 32 141703 -0.6086 0.271381 30 to 31 141947 0.1111 0.544240 29 to 30 142052 0.4209 0.663070 28 to 29 141920 0.0315 0.512555 27 to 28 142179 0.7955 0.786835 26 to 27 141892 -0.0511 0.479615 25 to 26 142319 1.2085 0.886566 24 to 25 141756 -0.4523 0.325526 23 to 24 142004 0.2793 0.609978 22 to 23 142289 1.1200 0.868637 21 to 22 141820 -0.2635 0.396079 20 to 21 141377 -1.5703 0.058173 19 to 20 142044 0.3973 0.654411 18 to 19 142192 0.8338 0.797813 17 to 18 141246 -1.9567 0.025190 16 to 17 141217 -2.0423 0.020562 15 to 16 141707 -0.5968 0.275306 14 to 15 142168 0.7630 0.777280 13 to 14 141297 -1.8063 0.035437 12 to 13 141500 -1.2075 0.113627 11 to 12 141813 -0.2842 0.388144 10 to 11 142165 0.7542 0.774632 9 to 10 142148 0.7040 0.759297 8 to 9 141347 -1.6588 0.048579 7 to 8 142029 0.3530 0.637959 6 to 7 142207 0.8781 0.810051 5 to 6 142423 1.5153 0.935146 4 to 5 141744 -0.4877 0.312882 3 to 4 141388 -1.5378 0.062043 2 to 3 142140 0.6804 0.751888 1 to 2 142088 0.5271 0.700921 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-27_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2509.26 0.131 0.552118 Test results for specific bytes for dh-ranFile-2016-06-27_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2461.58 -0.543 0.293427 2 to 9 2480.31 -0.278 0.390334 3 to 10 2379.93 -1.698 0.044755 4 to 11 2541.97 0.594 0.723577 5 to 12 2503.56 0.050 0.520093 6 to 13 2519.47 0.275 0.608463 7 to 14 2551.28 0.725 0.765860 8 to 15 2482.33 -0.250 0.401312 9 to 16 2610.61 1.564 0.941128 10 to 17 2492.02 -0.113 0.455064 11 to 18 2490.25 -0.138 0.445161 12 to 19 2461.78 -0.540 0.294435 13 to 20 2516.69 0.236 0.593277 14 to 21 2530.83 0.436 0.668572 15 to 22 2454.50 -0.643 0.259981 16 to 23 2632.30 1.871 0.969325 17 to 24 2526.37 0.373 0.645392 18 to 25 2518.58 0.263 0.603615 19 to 26 2467.88 -0.454 0.324845 20 to 27 2590.07 1.274 0.898622 21 to 28 2459.00 -0.580 0.280998 22 to 29 2512.43 0.176 0.569753 23 to 30 2452.54 -0.671 0.251042 24 to 31 2582.39 1.165 0.878012 25 to 32 2511.00 0.156 0.561822 CDPARK for dh-ranFile-2016-06-27_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 3504 -0.8676 0.192812 3506 -0.7763 0.218799 3512 -0.5023 0.307734 3551 1.2785 0.899470 3546 1.0502 0.853193 3553 1.3699 0.914635 3505 -0.8219 0.205562 3505 -0.8219 0.205562 3508 -0.6849 0.246694 3524 0.0457 0.518210 Square side=100, avg. no. parked=3521.40 sample std.=19.58 p-value of the KSTEST for those 10 p-values: 0.354531 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-27_06:31 0.2116,0.8072,0.7498,0.2960,0.1175,0.4571,0.3563,0.5540,0.7486,0.9990, The KS test for those 10 p-values: 0.727993 The 3DSPHERES test for dh-ranFile-2016-06-27_06:31 sample no r^3 equiv. uni. 1 0.174 0.005773 2 23.555 0.543957 3 39.425 0.731298 4 13.340 0.358952 5 125.661 0.984834 6 36.732 0.706068 7 68.124 0.896769 8 3.938 0.123015 9 26.101 0.581065 10 1.513 0.049178 11 3.417 0.107645 12 22.262 0.523871 13 31.597 0.651196 14 70.031 0.903128 15 73.395 0.913403 16 24.476 0.557751 17 17.634 0.444460 18 88.676 0.947967 19 51.782 0.822018 20 0.148 0.004916 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.281403 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-27_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.8 -1.1 0.4 -1.1 1.4 0.4 0.5 -0.5 0.2 -1.2 1.0 0.7 0.8 0.3 -1.3 0.6 -1.8 1.3 0.0 0.4 -1.9 1.5 -0.4 0.5 -0.3 -0.3 -1.2 -0.5 1.2 -0.1 -0.3 -0.5 -0.1 1.0 1.0 -1.0 0.1 -0.7 -0.6 2.0 -1.1 Chi-square with 42 degrees of freedom:36.374655 z-score=-0.613775, p-value=0.284381 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-27_06:31 Test no p-value 1 0.197141 2 0.603073 3 0.587777 4 0.051385 5 0.177033 6 0.340048 7 0.137429 8 0.324303 9 0.820021 10 0.674388 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.404589 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-27_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 66413 0.97 66565 0.16 3 25000.00 25172 1.18 24936 0.16 4 6666.67 6711 0.29 6770 1.60 5 1388.89 1437 1.67 1446 2.35 6 238.10 224 0.83 246 0.26 7 34.72 35 0.00 29 0.94 8 4.96 7 0.84 7 0.84 p=0.55237 p=0.61090 Number of rngs required: 688462, p-value: 0.527 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-27_06:31 No. of wins: Observed Expected 98497 98585.9 z-score=-0.397, pvalue=0.34553 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66610 66666.7 0.048 0.048 2 37977 37654.3 2.765 2.813 3 26705 26954.7 2.314 5.127 4 19426 19313.5 0.656 5.783 5 13854 13851.4 0.000 5.783 6 9801 9943.5 2.043 7.827 7 7208 7145.0 0.555 8.382 8 5221 5139.1 1.306 9.688 9 3689 3699.9 0.032 9.720 10 2637 2666.3 0.322 10.042 11 1853 1923.3 2.572 12.613 12 1411 1388.7 0.357 12.970 13 1012 1003.7 0.068 13.039 14 734 726.1 0.085 13.124 15 531 525.8 0.051 13.174 16 377 381.2 0.045 13.220 17 257 276.5 1.381 14.600 18 200 200.8 0.003 14.604 19 142 146.0 0.109 14.712 20 94 106.2 1.405 16.117 21 261 287.1 2.375 18.492 Chisq= 18.49 for 20 degrees of freedom, p= 0.44499 SUMMARY of craptest p-value for no. of wins: 0.345526 p-value for throws/game: 0.444986 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-27_06:31 No. of wins: Observed Expected 98737 98585.9 z-score= 0.676, pvalue=0.75048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66554 66666.7 0.190 0.190 2 37490 37654.3 0.717 0.907 3 26986 26954.7 0.036 0.944 4 19313 19313.5 0.000 0.944 5 13802 13851.4 0.176 1.120 6 10082 9943.5 1.928 3.048 7 7218 7145.0 0.745 3.793 8 5257 5139.1 2.706 6.499 9 3617 3699.9 1.856 8.355 10 2633 2666.3 0.416 8.771 11 1951 1923.3 0.398 9.169 12 1374 1388.7 0.156 9.326 13 993 1003.7 0.114 9.440 14 744 726.1 0.439 9.879 15 532 525.8 0.072 9.952 16 400 381.2 0.932 10.884 17 303 276.5 2.532 13.416 18 218 200.8 1.468 14.884 19 136 146.0 0.683 15.567 20 101 106.2 0.256 15.823 21 296 287.1 0.275 16.098 Chisq= 16.10 for 20 degrees of freedom, p= 0.28945 SUMMARY of craptest p-value for no. of wins: 0.750477 p-value for throws/game: 0.289449 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0049,0.0056,0.0058,0.0077,0.0099,0.0105,0.0171,0.0206,0.0252,0.0297, 0.0350,0.0354,0.0418,0.0448,0.0448,0.0460,0.0466,0.0486,0.0492,0.0514, 0.0547,0.0554,0.0565,0.0582,0.0618,0.0620,0.0632,0.0645,0.0741,0.0851, 0.0905,0.0928,0.0931,0.0997,0.1022,0.1055,0.1076,0.1083,0.1090,0.1136, 0.1175,0.1230,0.1354,0.1374,0.1639,0.1650,0.1668,0.1770,0.1824,0.1846, 0.1874,0.1888,0.1924,0.1928,0.1971,0.2020,0.2056,0.2056,0.2074,0.2076, 0.2106,0.2116,0.2176,0.2188,0.2236,0.2250,0.2264,0.2315,0.2328,0.2437, 0.2467,0.2510,0.2531,0.2550,0.2600,0.2622,0.2714,0.2753,0.2810,0.2814, 0.2844,0.2878,0.2894,0.2903,0.2934,0.2943,0.2944,0.2960,0.3010,0.3028, 0.3077,0.3129,0.3142,0.3198,0.3243,0.3248,0.3255,0.3283,0.3317,0.3392, 0.3400,0.3404,0.3420,0.3455,0.3492,0.3540,0.3545,0.3563,0.3569,0.3575, 0.3590,0.3618,0.3797,0.3881,0.3886,0.3903,0.3961,0.3984,0.4013,0.4046, 0.4137,0.4272,0.4362,0.4445,0.4450,0.4452,0.4551,0.4571,0.4639,0.4721, 0.4796,0.4924,0.4968,0.4979,0.4992,0.5126,0.5182,0.5185,0.5201,0.5229, 0.5239,0.5271,0.5440,0.5441,0.5442,0.5444,0.5490,0.5521,0.5524,0.5527, 0.5540,0.5578,0.5589,0.5598,0.5618,0.5698,0.5734,0.5811,0.5878,0.5884, 0.5894,0.5933,0.5947,0.5975,0.6031,0.6036,0.6085,0.6100,0.6109,0.6124, 0.6142,0.6204,0.6220,0.6332,0.6366,0.6380,0.6454,0.6485,0.6512,0.6544, 0.6566,0.6600,0.6631,0.6686,0.6744,0.6771,0.6772,0.6775,0.6784,0.6827, 0.6860,0.6911,0.6915,0.6997,0.7009,0.7026,0.7061,0.7082,0.7118,0.7236, 0.7251,0.7254,0.7280,0.7313,0.7356,0.7361,0.7379,0.7486,0.7498,0.7505, 0.7519,0.7593,0.7596,0.7659,0.7746,0.7761,0.7773,0.7868,0.7898,0.7945, 0.7978,0.8023,0.8072,0.8101,0.8116,0.8200,0.8220,0.8367,0.8383,0.8406, 0.8428,0.8499,0.8521,0.8532,0.8549,0.8556,0.8600,0.8686,0.8743,0.8780, 0.8806,0.8866,0.8890,0.8893,0.8968,0.8986,0.8991,0.8995,0.8997,0.9031, 0.9039,0.9126,0.9134,0.9144,0.9146,0.9174,0.9258,0.9351,0.9363,0.9407, 0.9411,0.9480,0.9612,0.9646,0.9693,0.9694,0.9848,0.9910,0.9990, Overall p-value after applying KStest on 269 p-values = 0.383270 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.