RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-29_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 12.6024 0.237630 2 to 25 15.78 17.9822 0.610038 3 to 26 16.04 22.0780 0.818261 4 to 27 15.91 18.0381 0.613559 5 to 28 15.95 13.9885 0.332086 6 to 29 16.08 22.3857 0.829661 7 to 30 15.76 18.9722 0.669870 8 to 31 15.80 14.2817 0.352931 9 to 32 15.80 14.0533 0.336676 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.583396 Tough bday spacings test for dh-ranFile-2016-06-29_03:31: 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 32 66 99 107 83 47 29 18 6 5 (O-E)^2/E 0.1 0.6 0.7 0.0 0.9 0.3 0.5 0.0 0.7 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 4.102, p= 0.057 RESULTS OF GCD FOR dh-ranFile-2016-06-29_03:31 Euclid's algorithm: p-value, steps to gcd: 0.733348 p-value, dist. of gcd's: 0.935195 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-29_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.507 0.626 0.421 0.956 0.596 0.641 0.207 0.718 Bits 8 to 15---> 0.428 0.315 0.930 0.095 0.186 0.765 0.184 0.052 Bits 16 to 23---> 0.682 0.565 0.717 0.217 0.746 0.678 0.792 0.403 Bits 24 to 31---> 0.435 0.939 0.980 0.312 0.933 0.483 0.303 0.046 KS test for the above 32 p values: 0.118 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-29_03:31, p-values for 5 runs: 0.2040, 0.3122, 0.5117, 0.1056, 0.2473 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5228 5134.0 1.721 1.813 r= 30 23193 23103.0 0.350 2.163 r= 31 11372 11551.5 2.790 4.953 chi-square = 4.953 with df = 3; p-value = 0.825 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 175 211.4 6.273 6.273 r= 30 5126 5134.0 0.012 6.286 r= 31 23134 23103.0 0.041 6.327 r= 32 11565 11551.5 0.016 6.343 chi-square = 6.343 with df = 3; p-value = 0.904 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-29_03:31 b-rank test for bits 1 to 8, p=0.12035 b-rank test for bits 2 to 9, p=0.52467 b-rank test for bits 3 to 10, p=0.61340 b-rank test for bits 4 to 11, p=0.80233 b-rank test for bits 5 to 12, p=0.19317 b-rank test for bits 6 to 13, p=0.41635 b-rank test for bits 7 to 14, p=0.21845 b-rank test for bits 8 to 15, p=0.98031 b-rank test for bits 9 to 16, p=0.76063 b-rank test for bits 10 to 17, p=0.21238 b-rank test for bits 11 to 18, p=0.50658 b-rank test for bits 12 to 19, p=0.83494 b-rank test for bits 13 to 20, p=0.03543 b-rank test for bits 14 to 21, p=0.41375 b-rank test for bits 15 to 22, p=0.70646 b-rank test for bits 16 to 23, p=0.88437 b-rank test for bits 17 to 24, p=0.87793 b-rank test for bits 18 to 25, p=0.03166 b-rank test for bits 19 to 26, p=0.26979 b-rank test for bits 20 to 27, p=0.15958 b-rank test for bits 21 to 28, p=0.21777 b-rank test for bits 22 to 29, p=0.97075 b-rank test for bits 23 to 30, p=0.56265 b-rank test for bits 24 to 31, p=0.69467 b-rank test for bits 25 to 32, p=0.56317 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 = 0.990918 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-29_03:31 (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 141561 -0.81 0.207864 2 142204 0.69 0.754425 3 141629 -0.65 0.256241 4 141991 0.19 0.575666 5 141592 -0.74 0.229218 6 141339 -1.33 0.091340 7 142302 0.92 0.820547 8 140815 -2.56 0.005281 9 141554 -0.83 0.203210 10 142809 2.10 0.982225 11 142630 1.68 0.953891 12 142282 0.87 0.808048 13 142247 0.79 0.784929 14 142011 0.24 0.593884 15 142338 1.00 0.841723 16 141924 0.03 0.513671 17 142336 1.00 0.840592 18 141742 -0.39 0.347914 19 141935 0.06 0.523913 20 141627 -0.66 0.254739 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-29_03:31 Bits used No. missing words z-score p-value 23 to 32 141632 -0.9563 0.169458 22 to 31 142100 0.6575 0.744565 21 to 30 141881 -0.0977 0.461089 20 to 29 142076 0.5747 0.717261 19 to 28 141866 -0.1494 0.440614 18 to 27 141808 -0.3494 0.363389 17 to 26 141858 -0.1770 0.429754 16 to 25 141852 -0.1977 0.421644 15 to 24 141431 -1.6494 0.049531 14 to 23 142310 1.3816 0.916456 13 to 22 142516 2.0920 0.981779 12 to 21 141915 0.0196 0.507800 11 to 20 141948 0.1333 0.553040 10 to 19 142196 0.9885 0.838550 9 to 18 141847 -0.2149 0.414911 8 to 17 142522 2.1127 0.982685 7 to 16 142062 0.5264 0.700712 6 to 15 142027 0.4058 0.657540 5 to 14 142372 1.5954 0.944690 4 to 13 142371 1.5920 0.944304 3 to 12 142409 1.7230 0.957556 2 to 11 141840 -0.2391 0.405526 1 to 10 142135 0.7782 0.781766 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-29_03:31 Bits used No. missing words z-score p-value 28 to 32 141775 -0.4554 0.324427 27 to 31 141939 0.1006 0.540057 26 to 30 141746 -0.5537 0.289905 25 to 29 141506 -1.3672 0.085778 24 to 28 142359 1.5243 0.936284 23 to 27 142296 1.3107 0.905028 22 to 26 141506 -1.3672 0.085778 21 to 25 142112 0.6870 0.753964 20 to 24 142331 1.4294 0.923554 19 to 23 141783 -0.4282 0.334239 18 to 22 142240 1.1209 0.868838 17 to 21 142567 2.2294 0.987106 16 to 20 141670 -0.8113 0.208600 15 to 19 141893 -0.0554 0.477928 14 to 18 141831 -0.2655 0.395302 13 to 17 141705 -0.6926 0.244267 12 to 16 141557 -1.1943 0.116173 11 to 15 141695 -0.7265 0.233753 10 to 14 141800 -0.3706 0.355464 9 to 13 141568 -1.1571 0.123626 8 to 12 142001 0.3107 0.622003 7 to 11 142124 0.7277 0.766600 6 to 10 141969 0.2023 0.580148 5 to 9 142219 1.0497 0.853079 4 to 8 141812 -0.3299 0.370726 3 to 7 142119 0.7107 0.761379 2 to 6 142039 0.4396 0.669872 1 to 5 141499 -1.3909 0.082120 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-29_03:31 Bits used No. missing words z-score p-value 31 to 32 141819 -0.2665 0.394942 30 to 31 141834 -0.2222 0.412074 29 to 30 141636 -0.8063 0.210040 28 to 29 141562 -1.0246 0.152783 27 to 28 142000 0.2675 0.605444 26 to 27 142101 0.5654 0.714099 25 to 26 141299 -1.8004 0.035900 24 to 25 141787 -0.3609 0.359104 23 to 24 142212 0.8928 0.814026 22 to 23 141873 -0.1072 0.457328 21 to 22 142552 1.8958 0.971006 20 to 21 142013 0.3058 0.620126 19 to 20 142394 1.4297 0.923599 18 to 19 141971 0.1819 0.572176 17 to 18 141458 -1.3314 0.091536 16 to 17 142233 0.9548 0.830155 15 to 16 141644 -0.7827 0.216906 14 to 15 141532 -1.1131 0.132840 13 to 14 142726 2.4091 0.992003 12 to 13 141552 -1.0541 0.145925 11 to 12 141864 -0.1337 0.446813 10 to 11 141811 -0.2901 0.385886 9 to 10 142264 1.0462 0.852271 8 to 9 141978 0.2026 0.580263 7 to 8 141708 -0.5939 0.276292 6 to 7 141642 -0.7886 0.215178 5 to 6 142189 0.8250 0.795310 4 to 5 142408 1.4710 0.929355 3 to 4 141536 -1.1013 0.135390 2 to 3 142122 0.6273 0.734784 1 to 2 141007 -2.6617 0.003887 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2521.76 0.308 0.620840 Test results for specific bytes for dh-ranFile-2016-06-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2508.16 0.115 0.545947 2 to 9 2562.77 0.888 0.812651 3 to 10 2504.46 0.063 0.525121 4 to 11 2657.20 2.223 0.986899 5 to 12 2566.11 0.935 0.825086 6 to 13 2393.74 -1.503 0.066454 7 to 14 2529.56 0.418 0.662019 8 to 15 2498.60 -0.020 0.492075 9 to 16 2528.58 0.404 0.656985 10 to 17 2567.81 0.959 0.831198 11 to 18 2572.88 1.031 0.848647 12 to 19 2523.27 0.329 0.628942 13 to 20 2615.96 1.640 0.949483 14 to 21 2518.92 0.268 0.605497 15 to 22 2588.70 1.254 0.895162 16 to 23 2555.61 0.786 0.784207 17 to 24 2499.83 -0.002 0.499046 18 to 25 2524.16 0.342 0.633698 19 to 26 2499.30 -0.010 0.496046 20 to 27 2389.05 -1.569 0.058309 21 to 28 2560.84 0.860 0.805219 22 to 29 2485.40 -0.207 0.418188 23 to 30 2567.36 0.953 0.829591 24 to 31 2388.55 -1.576 0.057492 25 to 32 2534.66 0.490 0.687986 CDPARK for dh-ranFile-2016-06-29_03:31: 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 3499 -1.0959 0.136563 3484 -1.7808 0.037471 3526 0.1370 0.554479 3501 -1.0046 0.157553 3505 -0.8219 0.205562 3537 0.6393 0.738676 3542 0.8676 0.807188 3549 1.1872 0.882429 3551 1.2785 0.899470 3545 1.0046 0.842447 Square side=100, avg. no. parked=3523.90 sample std.=23.25 p-value of the KSTEST for those 10 p-values: 0.563417 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-29_03:31 0.9675,0.7086,0.6018,0.4441,0.2355,0.2709,0.4866,0.7762,0.0450,0.6032, The KS test for those 10 p-values: 0.976421 The 3DSPHERES test for dh-ranFile-2016-06-29_03:31 sample no r^3 equiv. uni. 1 1.292 0.042147 2 20.742 0.499132 3 0.183 0.006076 4 14.890 0.391247 5 3.492 0.109892 6 55.717 0.843894 7 45.573 0.781091 8 33.782 0.675695 9 22.566 0.528677 10 99.846 0.964143 11 45.117 0.777737 12 22.886 0.533668 13 32.115 0.657160 14 58.612 0.858257 15 0.505 0.016680 16 13.834 0.369440 17 38.594 0.723758 18 10.403 0.293027 19 31.444 0.649409 20 35.381 0.692531 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.545576 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-29_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.8 -1.1 -2.0 -0.1 1.2 3.0 -0.4 0.2 -0.5 0.5 -0.7 0.8 2.1 -0.0 -1.4 -0.1 0.5 -0.0 0.3 -2.1 0.6 -0.4 -1.3 0.2 0.8 -1.5 0.4 0.6 0.6 -1.2 0.0 0.4 -1.3 -0.1 0.3 0.2 0.9 -0.1 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:41.695888 z-score=-0.033181, p-value=0.515795 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-29_03:31 Test no p-value 1 0.375204 2 0.226126 3 0.027985 4 0.404013 5 0.406880 6 0.000262 7 0.009098 8 0.172166 9 0.090993 10 0.093271 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000192 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-29_03:31: (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 66586 0.10 66857 0.54 3 25000.00 25082 0.27 24923 0.24 4 6666.67 6649 0.05 6544 2.26 5 1388.89 1398 0.06 1401 0.11 6 238.10 246 0.26 237 0.01 7 34.72 30 0.64 31 0.40 8 4.96 8 1.86 6 0.22 p=0.22189 p=0.29156 Number of rngs required: 687774, p-value: 0.234 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-29_03:31 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 66491 66666.7 0.463 0.463 2 37516 37654.3 0.508 0.971 3 26615 26954.7 4.282 5.253 4 19585 19313.5 3.818 9.071 5 13972 13851.4 1.050 10.120 6 10138 9943.5 3.803 13.923 7 7242 7145.0 1.316 15.239 8 5236 5139.1 1.828 17.067 9 3626 3699.9 1.475 18.542 10 2704 2666.3 0.533 19.075 11 1888 1923.3 0.649 19.724 12 1339 1388.7 1.782 21.506 13 1002 1003.7 0.003 21.509 14 732 726.1 0.047 21.556 15 544 525.8 0.627 22.183 16 412 381.2 2.497 24.680 17 256 276.5 1.526 26.206 18 187 200.8 0.952 27.158 19 155 146.0 0.557 27.715 20 90 106.2 2.475 30.190 21 270 287.1 1.020 31.211 Chisq= 31.21 for 20 degrees of freedom, p= 0.94753 SUMMARY of craptest p-value for no. of wins: 0.231819 p-value for throws/game: 0.947528 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-29_03:31 No. of wins: Observed Expected 98871 98585.9 z-score= 1.275, pvalue=0.89890 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66963 66666.7 1.317 1.317 2 37666 37654.3 0.004 1.321 3 27011 26954.7 0.117 1.438 4 19092 19313.5 2.539 3.978 5 13894 13851.4 0.131 4.109 6 9968 9943.5 0.060 4.169 7 7170 7145.0 0.087 4.256 8 5105 5139.1 0.226 4.482 9 3648 3699.9 0.727 5.209 10 2649 2666.3 0.112 5.321 11 1940 1923.3 0.144 5.466 12 1380 1388.7 0.055 5.521 13 981 1003.7 0.514 6.035 14 690 726.1 1.799 7.834 15 490 525.8 2.442 10.276 16 362 381.2 0.962 11.238 17 262 276.5 0.764 12.002 18 206 200.8 0.133 12.136 19 151 146.0 0.172 12.308 20 117 106.2 1.095 13.403 21 255 287.1 3.592 16.995 Chisq= 16.99 for 20 degrees of freedom, p= 0.34669 SUMMARY of craptest p-value for no. of wins: 0.898902 p-value for throws/game: 0.346694 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0003,0.0039,0.0053,0.0061,0.0091,0.0167,0.0280,0.0317,0.0354, 0.0359,0.0375,0.0421,0.0450,0.0459,0.0495,0.0517,0.0574,0.0575,0.0583, 0.0665,0.0821,0.0858,0.0858,0.0910,0.0913,0.0915,0.0933,0.0952,0.1056, 0.1099,0.1162,0.1178,0.1203,0.1236,0.1328,0.1354,0.1366,0.1459,0.1528, 0.1576,0.1596,0.1695,0.1722,0.1842,0.1863,0.1932,0.2032,0.2040,0.2056, 0.2072,0.2079,0.2086,0.2100,0.2124,0.2152,0.2169,0.2170,0.2178,0.2185, 0.2219,0.2261,0.2292,0.2318,0.2338,0.2338,0.2355,0.2376,0.2443,0.2473, 0.2547,0.2562,0.2698,0.2709,0.2763,0.2899,0.2916,0.2930,0.3026,0.3116, 0.3122,0.3151,0.3244,0.3321,0.3342,0.3367,0.3467,0.3479,0.3529,0.3555, 0.3591,0.3634,0.3694,0.3707,0.3752,0.3859,0.3912,0.3949,0.3953,0.4033, 0.4040,0.4055,0.4069,0.4121,0.4138,0.4149,0.4163,0.4182,0.4210,0.4216, 0.4282,0.4298,0.4354,0.4406,0.4441,0.4468,0.4573,0.4611,0.4779,0.4828, 0.4866,0.4921,0.4960,0.4990,0.4991,0.5066,0.5066,0.5078,0.5117,0.5137, 0.5158,0.5239,0.5247,0.5251,0.5287,0.5337,0.5401,0.5456,0.5459,0.5530, 0.5545,0.5627,0.5632,0.5634,0.5646,0.5722,0.5757,0.5801,0.5803,0.5834, 0.5939,0.5962,0.6018,0.6032,0.6054,0.6055,0.6100,0.6134,0.6136,0.6201, 0.6208,0.6220,0.6259,0.6289,0.6337,0.6406,0.6494,0.6570,0.6572,0.6575, 0.6620,0.6699,0.6699,0.6757,0.6779,0.6822,0.6880,0.6925,0.6947,0.7007, 0.7065,0.7086,0.7141,0.7173,0.7173,0.7178,0.7238,0.7333,0.7348,0.7387, 0.7446,0.7459,0.7540,0.7544,0.7606,0.7614,0.7652,0.7666,0.7762,0.7777, 0.7811,0.7818,0.7842,0.7849,0.7917,0.7953,0.8023,0.8052,0.8072,0.8080, 0.8127,0.8140,0.8183,0.8205,0.8247,0.8251,0.8296,0.8297,0.8302,0.8312, 0.8349,0.8386,0.8406,0.8417,0.8424,0.8439,0.8486,0.8523,0.8531,0.8583, 0.8688,0.8779,0.8824,0.8844,0.8952,0.8989,0.8995,0.9039,0.9050,0.9165, 0.9236,0.9236,0.9294,0.9299,0.9332,0.9352,0.9363,0.9388,0.9443,0.9447, 0.9475,0.9495,0.9539,0.9564,0.9576,0.9641,0.9675,0.9707,0.9710,0.9764, 0.9800,0.9803,0.9818,0.9822,0.9827,0.9869,0.9871,0.9909,0.9920, Overall p-value after applying KStest on 269 p-values = 0.418921 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.