RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-08_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 12.6887 0.243235 2 to 25 15.52 20.7229 0.761070 3 to 26 15.96 21.5299 0.796520 4 to 27 15.81 17.8651 0.602604 5 to 28 15.51 26.7173 0.937653 6 to 29 15.68 14.1523 0.343704 7 to 30 15.89 17.8168 0.599512 8 to 31 15.82 12.2616 0.215957 9 to 32 16.08 24.3467 0.889683 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.531988 Tough bday spacings test for dh-ranFile-2015-08-08_07:31: 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 39 73 79 106 88 58 21 13 4 6 (O-E)^2/E 1.6 0.2 0.0 3.6 0.7 1.2 0.7 2.6 0.2 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 12.735, p= 0.761 RESULTS OF GCD FOR dh-ranFile-2015-08-08_07:31 Euclid's algorithm: p-value, steps to gcd: 0.476938 p-value, dist. of gcd's: 0.067388 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-08_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.478 0.300 0.450 0.683 0.529 0.544 0.507 0.667 Bits 8 to 15---> 0.899 0.302 0.366 0.322 0.965 0.273 0.764 0.670 Bits 16 to 23---> 0.682 0.525 0.558 0.035 0.279 0.022 0.002 0.268 Bits 24 to 31---> 0.101 0.868 0.918 0.544 0.989 0.671 0.553 0.447 KS test for the above 32 p values: 0.373 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-08_07:31, p-values for 5 runs: 0.1275, 0.4358, 0.0030, 0.5375, 0.5399 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-08_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5214 5134.0 1.246 2.098 r= 30 23063 23103.0 0.069 2.167 r= 31 11525 11551.5 0.061 2.228 chi-square = 2.228 with df = 3; p-value = 0.474 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-08_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5063 5134.0 0.982 1.187 r= 31 23167 23103.0 0.177 1.364 r= 32 11552 11551.5 0.000 1.364 chi-square = 1.364 with df = 3; p-value = 0.286 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-08_07:31 b-rank test for bits 1 to 8, p=0.60296 b-rank test for bits 2 to 9, p=0.59714 b-rank test for bits 3 to 10, p=0.71162 b-rank test for bits 4 to 11, p=0.55636 b-rank test for bits 5 to 12, p=0.29776 b-rank test for bits 6 to 13, p=0.13471 b-rank test for bits 7 to 14, p=0.61141 b-rank test for bits 8 to 15, p=0.21739 b-rank test for bits 9 to 16, p=0.41603 b-rank test for bits 10 to 17, p=0.70432 b-rank test for bits 11 to 18, p=0.07969 b-rank test for bits 12 to 19, p=0.80690 b-rank test for bits 13 to 20, p=0.32432 b-rank test for bits 14 to 21, p=0.44837 b-rank test for bits 15 to 22, p=0.26201 b-rank test for bits 16 to 23, p=0.96325 b-rank test for bits 17 to 24, p=0.99264 b-rank test for bits 18 to 25, p=0.99314 b-rank test for bits 19 to 26, p=0.44818 b-rank test for bits 20 to 27, p=0.73328 b-rank test for bits 21 to 28, p=0.27735 b-rank test for bits 22 to 29, p=0.28964 b-rank test for bits 23 to 30, p=0.79865 b-rank test for bits 24 to 31, p=0.08270 b-rank test for bits 25 to 32, p=0.31300 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 = 0.700497 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-08_07:31 (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 141973 0.15 0.559129 2 141767 -0.33 0.369738 3 141343 -1.32 0.092884 4 142128 0.51 0.695293 5 142264 0.83 0.796354 6 142043 0.31 0.622599 7 143100 2.78 0.997298 8 141294 -1.44 0.075261 9 141950 0.10 0.537852 10 143037 2.63 0.995790 11 142514 1.41 0.921140 12 142466 1.30 0.903308 13 141942 0.08 0.530422 14 142549 1.49 0.932485 15 141109 -1.87 0.030747 16 142312 0.94 0.826601 17 142725 1.91 0.971660 18 141416 -1.15 0.124529 19 141549 -0.84 0.199924 20 141734 -0.41 0.341032 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-08_07:31 Bits used No. missing words z-score p-value 23 to 32 141561 -1.2011 0.114849 22 to 31 141509 -1.3804 0.083724 21 to 30 141968 0.2023 0.580163 20 to 29 142270 1.2437 0.893193 19 to 28 142304 1.3609 0.913232 18 to 27 141609 -1.0356 0.150190 17 to 26 141160 -2.5839 0.004885 16 to 25 142172 0.9058 0.817468 15 to 24 142386 1.6437 0.949880 14 to 23 142094 0.6368 0.737870 13 to 22 142234 1.1196 0.868548 12 to 21 142411 1.7299 0.958176 11 to 20 142433 1.8058 0.964522 10 to 19 142075 0.5713 0.716094 9 to 18 142271 1.2471 0.893827 8 to 17 141372 -1.8529 0.031951 7 to 16 141753 -0.5391 0.294920 6 to 15 142005 0.3299 0.629261 5 to 14 141885 -0.0839 0.466569 4 to 13 141804 -0.3632 0.358225 3 to 12 142358 1.5471 0.939085 2 to 11 142421 1.7644 0.961166 1 to 10 142233 1.1161 0.867811 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-08_07:31 Bits used No. missing words z-score p-value 28 to 32 141593 -1.0723 0.141792 27 to 31 142055 0.4938 0.689275 26 to 30 142276 1.2429 0.893057 25 to 29 141791 -0.4011 0.344166 24 to 28 142286 1.2768 0.899172 23 to 27 141910 0.0023 0.500906 22 to 26 141667 -0.8215 0.205693 21 to 25 142211 1.0226 0.846754 20 to 24 142240 1.1209 0.868838 19 to 23 141747 -0.5503 0.291067 18 to 22 141948 0.1311 0.552146 17 to 21 142016 0.3616 0.641172 16 to 20 141702 -0.7028 0.241086 15 to 19 141308 -2.0384 0.020755 14 to 18 141770 -0.4723 0.318355 13 to 17 142116 0.7006 0.758216 12 to 16 141604 -1.0350 0.150331 11 to 15 141852 -0.1943 0.422955 10 to 14 142091 0.6158 0.730997 9 to 13 141708 -0.6825 0.247470 8 to 12 141992 0.2802 0.610352 7 to 11 141460 -1.5232 0.063860 6 to 10 142581 2.2768 0.988602 5 to 9 141690 -0.7435 0.228592 4 to 8 142163 0.8599 0.805077 3 to 7 140928 -3.3265 0.000440 2 to 6 141521 -1.3164 0.094024 1 to 5 141906 -0.0113 0.495497 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-08_07:31 Bits used No. missing words z-score p-value 31 to 32 141751 -0.4671 0.320232 30 to 31 141908 -0.0039 0.498435 29 to 30 141805 -0.3078 0.379133 28 to 29 142389 1.4150 0.921459 27 to 28 142060 0.4445 0.671643 26 to 27 142107 0.5831 0.720086 25 to 26 142171 0.7719 0.779910 24 to 25 141479 -1.2694 0.102147 23 to 24 141897 -0.0364 0.485493 22 to 23 142592 2.0138 0.977983 21 to 22 141517 -1.1573 0.123572 20 to 21 141574 -0.9892 0.161289 19 to 20 141907 -0.0069 0.497258 18 to 19 141586 -0.9538 0.170099 17 to 18 142422 1.5123 0.934771 16 to 17 141850 -0.1750 0.430534 15 to 16 141357 -1.6293 0.051626 14 to 15 141960 0.1495 0.559408 13 to 14 141971 0.1819 0.572176 12 to 13 141424 -1.4317 0.076122 11 to 12 142597 2.0285 0.978747 10 to 11 141634 -0.8122 0.208343 9 to 10 142859 2.8014 0.997456 8 to 9 141601 -0.9095 0.181536 7 to 8 142505 1.7571 0.960553 6 to 7 141887 -0.0659 0.473741 5 to 6 141696 -0.6293 0.264579 4 to 5 142137 0.6716 0.749079 3 to 4 141514 -1.1662 0.121774 2 to 3 141796 -0.3343 0.369074 1 to 2 141832 -0.2281 0.409780 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-08_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2479.82 -0.285 0.387676 Test results for specific bytes for dh-ranFile-2015-08-08_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2475.02 -0.353 0.361964 2 to 9 2403.91 -1.359 0.087077 3 to 10 2536.51 0.516 0.697168 4 to 11 2347.84 -2.152 0.015705 5 to 12 2526.37 0.373 0.645396 6 to 13 2586.14 1.218 0.888422 7 to 14 2582.67 1.169 0.878816 8 to 15 2484.63 -0.217 0.413986 9 to 16 2537.05 0.524 0.699832 10 to 17 2348.28 -2.146 0.015948 11 to 18 2519.48 0.275 0.608509 12 to 19 2517.57 0.248 0.598105 13 to 20 2605.49 1.492 0.932129 14 to 21 2517.21 0.243 0.596150 15 to 22 2475.36 -0.349 0.363732 16 to 23 2512.45 0.176 0.569873 17 to 24 2489.69 -0.146 0.442032 18 to 25 2521.50 0.304 0.619439 19 to 26 2645.58 2.059 0.980246 20 to 27 2480.35 -0.278 0.390538 21 to 28 2443.00 -0.806 0.210105 22 to 29 2557.34 0.811 0.791294 23 to 30 2478.29 -0.307 0.379406 24 to 31 2516.25 0.230 0.590892 25 to 32 2430.49 -0.983 0.162800 CDPARK for dh-ranFile-2015-08-08_07:31: 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 3507 -0.7306 0.232514 3544 0.9589 0.831196 3498 -1.1416 0.126820 3523 0.0000 0.500000 3534 0.5023 0.692266 3487 -1.6438 0.050105 3579 2.5571 0.994722 3545 1.0046 0.842447 3509 -0.6393 0.261324 3545 1.0046 0.842447 Square side=100, avg. no. parked=3527.10 sample std.=26.21 p-value of the KSTEST for those 10 p-values: 0.642961 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-08_07:31 0.3768,0.6151,0.5683,0.9824,0.8532,0.1288,0.7008,0.3604,0.0154,0.9894, The KS test for those 10 p-values: 0.465119 The 3DSPHERES test for dh-ranFile-2015-08-08_07:31 sample no r^3 equiv. uni. 1 3.570 0.112206 2 20.436 0.493987 3 42.241 0.755374 4 38.437 0.722304 5 43.593 0.766156 6 1.522 0.049468 7 4.131 0.128628 8 40.077 0.737080 9 55.588 0.843225 10 5.381 0.164192 11 37.319 0.711765 12 48.177 0.799290 13 0.304 0.010082 14 56.444 0.847632 15 28.551 0.613919 16 10.945 0.305686 17 8.988 0.258882 18 16.455 0.422185 19 38.202 0.720123 20 7.946 0.232704 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.604167 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-08_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 1.5 1.1 -0.2 0.9 -1.3 -0.8 0.7 -0.4 1.0 0.2 -0.8 0.9 1.2 1.0 -1.1 -0.5 -0.3 -0.9 -0.7 -0.1 1.8 0.2 -2.5 0.0 1.5 0.4 -0.4 1.9 -1.7 0.6 -1.3 0.1 0.3 0.4 -0.7 -0.7 -1.6 -1.3 1.6 0.0 -0.1 Chi-square with 42 degrees of freedom:45.044042 z-score=0.332132, p-value=0.654252 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-08_07:31 Test no p-value 1 0.001761 2 0.657931 3 0.189603 4 0.000176 5 0.054801 6 0.492270 7 0.936661 8 0.366403 9 0.130360 10 0.060140 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003498 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-08_07:31: (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 66742 0.09 66709 0.03 3 25000.00 24935 0.17 25006 0.00 4 6666.67 6625 0.26 6589 0.90 5 1388.89 1417 0.57 1399 0.07 6 238.10 237 0.01 256 1.35 7 34.72 40 0.80 37 0.15 8 4.96 3 0.77 3 0.77 p=0.15055 p=0.22670 Number of rngs required: 688182, p-value: 0.400 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-08_07:31 No. of wins: Observed Expected 98841 98585.9 z-score= 1.141, pvalue=0.87309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66956 66666.7 1.256 1.256 2 37254 37654.3 4.256 5.512 3 27304 26954.7 4.526 10.037 4 19113 19313.5 2.081 12.118 5 13903 13851.4 0.192 12.310 6 9963 9943.5 0.038 12.348 7 7200 7145.0 0.423 12.771 8 5193 5139.1 0.566 13.337 9 3624 3699.9 1.556 14.893 10 2641 2666.3 0.240 15.133 11 1821 1923.3 5.444 20.577 12 1370 1388.7 0.253 20.830 13 1012 1003.7 0.068 20.898 14 718 726.1 0.091 20.990 15 564 525.8 2.770 23.759 16 387 381.2 0.090 23.849 17 257 276.5 1.381 25.230 18 190 200.8 0.584 25.814 19 152 146.0 0.248 26.062 20 115 106.2 0.727 26.788 21 263 287.1 2.025 28.814 Chisq= 28.81 for 20 degrees of freedom, p= 0.90850 SUMMARY of craptest p-value for no. of wins: 0.873094 p-value for throws/game: 0.908504 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-08_07:31 No. of wins: Observed Expected 98626 98585.9 z-score= 0.180, pvalue=0.57124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66724 66666.7 0.049 0.049 2 37599 37654.3 0.081 0.131 3 27098 26954.7 0.761 0.892 4 19234 19313.5 0.327 1.219 5 13826 13851.4 0.047 1.266 6 10100 9943.5 2.462 3.727 7 7084 7145.0 0.521 4.249 8 5104 5139.1 0.239 4.488 9 3727 3699.9 0.199 4.687 10 2706 2666.3 0.591 5.278 11 1877 1923.3 1.116 6.394 12 1299 1388.7 5.799 12.193 13 978 1003.7 0.659 12.852 14 745 726.1 0.490 13.342 15 530 525.8 0.033 13.375 16 359 381.2 1.287 14.662 17 280 276.5 0.043 14.705 18 203 200.8 0.023 14.729 19 120 146.0 4.625 19.354 20 108 106.2 0.030 19.384 21 299 287.1 0.492 19.876 Chisq= 19.88 for 20 degrees of freedom, p= 0.53429 SUMMARY of craptest p-value for no. of wins: 0.571242 p-value for throws/game: 0.534288 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0004,0.0018,0.0025,0.0030,0.0035,0.0049,0.0101,0.0154,0.0157, 0.0159,0.0208,0.0219,0.0307,0.0320,0.0354,0.0495,0.0501,0.0516,0.0548, 0.0601,0.0639,0.0674,0.0753,0.0761,0.0797,0.0827,0.0837,0.0871,0.0929, 0.0940,0.1009,0.1021,0.1122,0.1148,0.1218,0.1236,0.1245,0.1268,0.1275, 0.1286,0.1288,0.1304,0.1347,0.1418,0.1502,0.1503,0.1506,0.1613,0.1628, 0.1642,0.1701,0.1815,0.1896,0.1999,0.2057,0.2083,0.2101,0.2160,0.2174, 0.2267,0.2286,0.2325,0.2327,0.2411,0.2432,0.2475,0.2589,0.2613,0.2620, 0.2646,0.2677,0.2731,0.2773,0.2792,0.2860,0.2896,0.2911,0.2949,0.2978, 0.3000,0.3017,0.3057,0.3130,0.3184,0.3202,0.3221,0.3243,0.3410,0.3437, 0.3442,0.3582,0.3604,0.3620,0.3637,0.3661,0.3664,0.3691,0.3697,0.3733, 0.3768,0.3791,0.3794,0.3877,0.3905,0.3996,0.4098,0.4140,0.4160,0.4222, 0.4230,0.4305,0.4358,0.4420,0.4472,0.4482,0.4484,0.4501,0.4651,0.4666, 0.4736,0.4737,0.4769,0.4777,0.4855,0.4923,0.4940,0.4955,0.4973,0.4984, 0.5000,0.5009,0.5074,0.5249,0.5294,0.5304,0.5320,0.5343,0.5375,0.5379, 0.5399,0.5437,0.5442,0.5521,0.5528,0.5564,0.5582,0.5591,0.5594,0.5683, 0.5699,0.5712,0.5722,0.5802,0.5909,0.5961,0.5971,0.5981,0.5995,0.6026, 0.6030,0.6042,0.6085,0.6104,0.6114,0.6139,0.6151,0.6194,0.6226,0.6293, 0.6412,0.6430,0.6454,0.6543,0.6579,0.6673,0.6702,0.6711,0.6716,0.6815, 0.6829,0.6893,0.6923,0.6953,0.6972,0.6998,0.7005,0.7008,0.7043,0.7116, 0.7118,0.7161,0.7201,0.7201,0.7223,0.7310,0.7333,0.7371,0.7379,0.7491, 0.7554,0.7582,0.7611,0.7611,0.7643,0.7662,0.7799,0.7913,0.7964,0.7965, 0.7986,0.7993,0.8051,0.8069,0.8175,0.8266,0.8312,0.8424,0.8424,0.8432, 0.8468,0.8476,0.8532,0.8678,0.8679,0.8685,0.8688,0.8731,0.8788,0.8884, 0.8897,0.8931,0.8932,0.8938,0.8989,0.8992,0.9033,0.9085,0.9132,0.9181, 0.9211,0.9215,0.9321,0.9325,0.9348,0.9367,0.9377,0.9391,0.9499,0.9582, 0.9606,0.9612,0.9633,0.9645,0.9652,0.9717,0.9780,0.9787,0.9802,0.9824, 0.9886,0.9888,0.9894,0.9926,0.9931,0.9947,0.9958,0.9973,0.9975, Overall p-value after applying KStest on 269 p-values = 0.309077 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.