RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-06_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 19.2501 0.685632 2 to 25 15.91 18.2243 0.625174 3 to 26 15.94 16.2530 0.494028 4 to 27 16.13 8.7920 0.053437 5 to 28 15.93 9.7219 0.085133 6 to 29 15.84 15.9794 0.474704 7 to 30 15.88 14.4134 0.362345 8 to 31 15.85 26.3254 0.931268 9 to 32 15.79 22.8677 0.846392 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.981940 Tough bday spacings test for dh-ranFile-2016-02-06_09:31: 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 2 34 87 85 97 84 58 26 18 6 3 (O-E)^2/E 5.6 0.2 2.6 1.6 0.0 0.4 0.7 0.5 0.7 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.584, p= 0.752 RESULTS OF GCD FOR dh-ranFile-2016-02-06_09:31 Euclid's algorithm: p-value, steps to gcd: 0.980863 p-value, dist. of gcd's: 0.941293 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-06_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.727 0.700 0.117 0.030 0.271 0.298 0.505 0.140 Bits 8 to 15---> 0.974 0.694 0.681 0.702 0.211 0.178 0.611 0.037 Bits 16 to 23---> 0.120 0.658 0.188 0.782 0.405 0.957 0.480 0.394 Bits 24 to 31---> 0.313 0.444 0.385 0.616 0.805 0.860 0.274 0.489 KS test for the above 32 p values: 0.165 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-06_09:31, p-values for 5 runs: 0.6117, 0.4125, 0.1126, 0.5538, 0.7336 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-06_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5158 5134.0 0.112 1.261 r= 30 23111 23103.0 0.003 1.263 r= 31 11504 11551.5 0.196 1.459 chi-square = 1.459 with df = 3; p-value = 0.308 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-06_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5009 5134.0 3.044 3.896 r= 31 23287 23103.0 1.465 5.360 r= 32 11506 11551.5 0.179 5.540 chi-square = 5.540 with df = 3; p-value = 0.864 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-06_09:31 b-rank test for bits 1 to 8, p=0.77588 b-rank test for bits 2 to 9, p=0.87922 b-rank test for bits 3 to 10, p=0.85509 b-rank test for bits 4 to 11, p=0.84013 b-rank test for bits 5 to 12, p=0.58335 b-rank test for bits 6 to 13, p=0.32659 b-rank test for bits 7 to 14, p=0.86451 b-rank test for bits 8 to 15, p=0.64394 b-rank test for bits 9 to 16, p=0.10407 b-rank test for bits 10 to 17, p=0.18208 b-rank test for bits 11 to 18, p=0.33453 b-rank test for bits 12 to 19, p=0.09120 b-rank test for bits 13 to 20, p=0.87873 b-rank test for bits 14 to 21, p=0.43537 b-rank test for bits 15 to 22, p=0.50139 b-rank test for bits 16 to 23, p=0.50774 b-rank test for bits 17 to 24, p=0.62955 b-rank test for bits 18 to 25, p=0.18809 b-rank test for bits 19 to 26, p=0.86236 b-rank test for bits 20 to 27, p=0.18961 b-rank test for bits 21 to 28, p=0.24489 b-rank test for bits 22 to 29, p=0.98627 b-rank test for bits 23 to 30, p=0.03197 b-rank test for bits 24 to 31, p=0.34080 b-rank test for bits 25 to 32, p=0.27166 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 = 0.919165 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-06_09:31 (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 141787 -0.29 0.387509 2 141678 -0.54 0.294429 3 141597 -0.73 0.232774 4 142043 0.31 0.622599 5 142339 1.00 0.842287 6 141298 -1.43 0.076597 7 142383 1.11 0.865789 8 141833 -0.18 0.429228 9 142228 0.74 0.771730 10 142231 0.75 0.773844 11 142103 0.45 0.674546 12 142185 0.64 0.740241 13 141219 -1.61 0.053381 14 141266 -1.50 0.066406 15 141990 0.19 0.574750 16 142102 0.45 0.673704 17 142151 0.56 0.713844 18 141848 -0.14 0.443029 19 142190 0.66 0.744014 20 141669 -0.56 0.287222 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-06_09:31 Bits used No. missing words z-score p-value 23 to 32 141653 -0.8839 0.188376 22 to 31 141387 -1.8011 0.035841 21 to 30 141538 -1.2804 0.100194 20 to 29 141203 -2.4356 0.007433 19 to 28 142057 0.5092 0.694696 18 to 27 141651 -0.8908 0.186520 17 to 26 141769 -0.4839 0.314230 16 to 25 141939 0.1023 0.540745 15 to 24 141601 -1.0632 0.143844 14 to 23 141729 -0.6218 0.267028 13 to 22 141521 -1.3391 0.090274 12 to 21 142212 1.0437 0.851686 11 to 20 141516 -1.3563 0.087500 10 to 19 141375 -1.8425 0.032700 9 to 18 141730 -0.6184 0.268163 8 to 17 141668 -0.8322 0.202656 7 to 16 141837 -0.2494 0.401520 6 to 15 141920 0.0368 0.514675 5 to 14 142273 1.2540 0.895085 4 to 13 142084 0.6023 0.726516 3 to 12 142211 1.0402 0.850886 2 to 11 141717 -0.6632 0.253599 1 to 10 142398 1.6851 0.954012 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-06_09:31 Bits used No. missing words z-score p-value 28 to 32 141994 0.2870 0.612950 27 to 31 141800 -0.3706 0.355464 26 to 30 141858 -0.1740 0.430933 25 to 29 141660 -0.8452 0.199003 24 to 28 141681 -0.7740 0.219465 23 to 27 141525 -1.3028 0.096319 22 to 26 141651 -0.8757 0.190598 21 to 25 142731 2.7853 0.997326 20 to 24 142012 0.3480 0.636093 19 to 23 142020 0.3752 0.646227 18 to 22 141354 -1.8825 0.029886 17 to 21 141291 -2.0960 0.018040 16 to 20 142279 1.2531 0.894919 15 to 19 141706 -0.6893 0.245332 14 to 18 141779 -0.4418 0.329318 13 to 17 142224 1.0667 0.856941 12 to 16 141968 0.1989 0.578822 11 to 15 141325 -1.9808 0.023808 10 to 14 141787 -0.4147 0.339189 9 to 13 141865 -0.1503 0.440275 8 to 12 142046 0.4633 0.678421 7 to 11 142109 0.6768 0.750749 6 to 10 142059 0.5074 0.694048 5 to 9 142381 1.5989 0.945077 4 to 8 141758 -0.5130 0.303982 3 to 7 141356 -1.8757 0.030349 2 to 6 142021 0.3785 0.647486 1 to 5 141864 -0.1537 0.438939 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-06_09:31 Bits used No. missing words z-score p-value 31 to 32 141819 -0.2665 0.394942 30 to 31 142171 0.7719 0.779910 29 to 30 141691 -0.6440 0.259774 28 to 29 142309 1.1790 0.880794 27 to 28 141706 -0.5998 0.274322 26 to 27 142078 0.4976 0.690600 25 to 26 141772 -0.4051 0.342701 24 to 25 142610 2.0669 0.980627 23 to 24 142343 1.2793 0.899598 22 to 23 141754 -0.4582 0.323404 21 to 22 142022 0.3324 0.630191 20 to 21 141404 -1.4906 0.068027 19 to 20 142129 0.6480 0.741506 18 to 19 141704 -0.6057 0.272359 17 to 18 141709 -0.5909 0.277279 16 to 17 142070 0.4740 0.682233 15 to 16 142249 1.0020 0.841823 14 to 15 141797 -0.3314 0.370187 13 to 14 141881 -0.0836 0.466699 12 to 13 142160 0.7394 0.770180 11 to 12 141919 0.0285 0.511378 10 to 11 141858 -0.1514 0.439824 9 to 10 141792 -0.3461 0.364632 8 to 9 141880 -0.0865 0.465527 7 to 8 142273 1.0728 0.858314 6 to 7 142044 0.3973 0.654411 5 to 6 141835 -0.2193 0.413223 4 to 5 141734 -0.5172 0.302509 3 to 4 142060 0.4445 0.671643 2 to 3 142500 1.7424 0.959280 1 to 2 142472 1.6598 0.951522 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-06_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.49 -0.007 0.497144 Test results for specific bytes for dh-ranFile-2016-02-06_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2452.07 -0.678 0.248936 2 to 9 2454.37 -0.645 0.259361 3 to 10 2450.91 -0.694 0.243765 4 to 11 2534.27 0.485 0.686062 5 to 12 2308.86 -2.703 0.003434 6 to 13 2631.91 1.865 0.968943 7 to 14 2580.97 1.145 0.873922 8 to 15 2566.04 0.934 0.824834 9 to 16 2353.83 -2.067 0.019360 10 to 17 2457.83 -0.596 0.275462 11 to 18 2465.38 -0.490 0.312216 12 to 19 2565.00 0.919 0.821020 13 to 20 2536.61 0.518 0.697666 14 to 21 2459.14 -0.578 0.281693 15 to 22 2417.85 -1.162 0.122658 16 to 23 2525.87 0.366 0.642760 17 to 24 2526.86 0.380 0.647977 18 to 25 2517.51 0.248 0.597804 19 to 26 2388.38 -1.578 0.057226 20 to 27 2594.35 1.334 0.908940 21 to 28 2524.55 0.347 0.635768 22 to 29 2336.23 -2.316 0.010278 23 to 30 2502.82 0.040 0.515933 24 to 31 2503.85 0.054 0.521688 25 to 32 2456.99 -0.608 0.271521 CDPARK for dh-ranFile-2016-02-06_09:31: 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 3545 1.0046 0.842447 3551 1.2785 0.899470 3521 -0.0913 0.463617 3534 0.5023 0.692266 3523 0.0000 0.500000 3554 1.4155 0.921543 3501 -1.0046 0.157553 3526 0.1370 0.554479 3500 -1.0502 0.146807 3547 1.0959 0.863437 Square side=100, avg. no. parked=3530.20 sample std.=18.53 p-value of the KSTEST for those 10 p-values: 0.389683 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-06_09:31 0.6760,0.6675,0.5421,0.8638,0.2778,0.7494,0.9645,0.8311,0.8314,0.5846, The KS test for those 10 p-values: 0.043118 The 3DSPHERES test for dh-ranFile-2016-02-06_09:31 sample no r^3 equiv. uni. 1 25.167 0.567821 2 17.999 0.451175 3 18.988 0.468967 4 0.466 0.015409 5 17.235 0.437012 6 44.631 0.774110 7 9.031 0.259938 8 21.394 0.509898 9 16.585 0.424683 10 108.125 0.972790 11 13.960 0.372079 12 4.584 0.141708 13 31.277 0.647448 14 3.517 0.110608 15 8.300 0.241680 16 20.252 0.490879 17 34.203 0.680217 18 24.410 0.556767 19 26.652 0.588681 20 6.851 0.204173 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.339338 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-06_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 0.8 -0.4 -2.1 0.1 0.3 1.4 -1.0 -0.4 0.5 0.3 0.5 -0.5 -0.3 -0.2 0.1 -0.1 0.6 -0.4 1.0 -0.6 -0.5 0.7 2.0 -0.5 -1.5 0.1 -1.7 -0.7 0.1 0.5 -0.5 -0.6 -1.7 3.1 0.3 -0.4 -0.8 3.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:55.451470 z-score=1.467676, p-value=0.920148 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-06_09:31 Test no p-value 1 0.406017 2 0.286878 3 0.307994 4 0.307485 5 0.221760 6 0.788422 7 0.739010 8 0.212283 9 0.760607 10 0.307710 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.276789 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-06_09:31: (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 66498 0.43 66572 0.13 3 25000.00 25156 0.97 25100 0.40 4 6666.67 6666 0.00 6707 0.24 5 1388.89 1370 0.26 1352 0.98 6 238.10 267 3.51 219 1.53 7 34.72 37 0.15 40 0.80 8 4.96 5 0.00 9 3.29 p=0.49606 p=0.71315 Number of rngs required: 687888, p-value: 0.276 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-06_09:31 No. of wins: Observed Expected 98361 98585.9 z-score=-1.006, pvalue=0.15728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66427 66666.7 0.862 0.862 2 37853 37654.3 1.048 1.910 3 27192 26954.7 2.089 3.998 4 19129 19313.5 1.762 5.760 5 14082 13851.4 3.838 9.599 6 9974 9943.5 0.093 9.692 7 7042 7145.0 1.486 11.177 8 5044 5139.1 1.759 12.936 9 3725 3699.9 0.171 13.107 10 2652 2666.3 0.077 13.184 11 1909 1923.3 0.107 13.290 12 1389 1388.7 0.000 13.291 13 1021 1003.7 0.298 13.588 14 689 726.1 1.900 15.488 15 495 525.8 1.808 17.296 16 356 381.2 1.660 18.956 17 271 276.5 0.111 19.067 18 194 200.8 0.232 19.299 19 163 146.0 1.983 21.282 20 103 106.2 0.097 21.380 21 290 287.1 0.029 21.409 Chisq= 21.41 for 20 degrees of freedom, p= 0.62655 SUMMARY of craptest p-value for no. of wins: 0.157280 p-value for throws/game: 0.626555 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-06_09:31 No. of wins: Observed Expected 98651 98585.9 z-score= 0.291, pvalue=0.61461 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67139 66666.7 3.346 3.346 2 37607 37654.3 0.059 3.406 3 26764 26954.7 1.350 4.756 4 19089 19313.5 2.609 7.364 5 13921 13851.4 0.350 7.714 6 9899 9943.5 0.200 7.913 7 7073 7145.0 0.726 8.639 8 5052 5139.1 1.475 10.115 9 3716 3699.9 0.070 10.185 10 2690 2666.3 0.211 10.396 11 1939 1923.3 0.128 10.523 12 1410 1388.7 0.325 10.849 13 1026 1003.7 0.495 11.344 14 762 726.1 1.771 13.115 15 553 525.8 1.403 14.518 16 344 381.2 3.621 18.139 17 285 276.5 0.259 18.398 18 193 200.8 0.305 18.703 19 150 146.0 0.110 18.813 20 111 106.2 0.216 19.029 21 277 287.1 0.356 19.385 Chisq= 19.39 for 20 degrees of freedom, p= 0.50307 SUMMARY of craptest p-value for no. of wins: 0.614608 p-value for throws/game: 0.503075 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0034,0.0074,0.0103,0.0154,0.0180,0.0194,0.0238,0.0299,0.0302,0.0303, 0.0320,0.0327,0.0358,0.0373,0.0431,0.0534,0.0534,0.0572,0.0664,0.0680, 0.0766,0.0851,0.0875,0.0903,0.0912,0.0963,0.1002,0.1041,0.1106,0.1126, 0.1169,0.1203,0.1227,0.1403,0.1417,0.1438,0.1468,0.1573,0.1576,0.1652, 0.1783,0.1821,0.1865,0.1881,0.1884,0.1884,0.1896,0.1906,0.1990,0.2027, 0.2042,0.2105,0.2123,0.2195,0.2218,0.2328,0.2417,0.2438,0.2449,0.2453, 0.2489,0.2536,0.2594,0.2598,0.2599,0.2670,0.2682,0.2710,0.2715,0.2717, 0.2724,0.2743,0.2743,0.2755,0.2763,0.2768,0.2773,0.2778,0.2817,0.2869, 0.2872,0.2944,0.2980,0.3025,0.3040,0.3075,0.3077,0.3080,0.3082,0.3122, 0.3126,0.3142,0.3234,0.3266,0.3293,0.3345,0.3392,0.3393,0.3408,0.3427, 0.3555,0.3623,0.3646,0.3702,0.3721,0.3854,0.3875,0.3897,0.3939,0.3949, 0.4015,0.4046,0.4060,0.4125,0.4132,0.4247,0.4292,0.4309,0.4354,0.4370, 0.4389,0.4398,0.4403,0.4430,0.4445,0.4512,0.4636,0.4655,0.4667,0.4690, 0.4747,0.4804,0.4889,0.4909,0.4940,0.4961,0.4971,0.5000,0.5014,0.5031, 0.5051,0.5077,0.5099,0.5114,0.5147,0.5159,0.5217,0.5407,0.5421,0.5538, 0.5545,0.5568,0.5678,0.5748,0.5788,0.5833,0.5846,0.5887,0.5978,0.6110, 0.6117,0.6130,0.6146,0.6160,0.6226,0.6252,0.6266,0.6295,0.6302,0.6358, 0.6361,0.6428,0.6439,0.6462,0.6474,0.6475,0.6480,0.6544,0.6580,0.6675, 0.6716,0.6737,0.6745,0.6760,0.6784,0.6802,0.6812,0.6822,0.6856,0.6861, 0.6906,0.6923,0.6936,0.6940,0.6947,0.6977,0.6999,0.7023,0.7131,0.7138, 0.7265,0.7267,0.7336,0.7390,0.7402,0.7415,0.7440,0.7494,0.7507,0.7522, 0.7606,0.7702,0.7717,0.7738,0.7741,0.7759,0.7799,0.7820,0.7884,0.8047, 0.8210,0.8248,0.8311,0.8314,0.8401,0.8418,0.8423,0.8424,0.8464,0.8509, 0.8517,0.8551,0.8569,0.8583,0.8597,0.8624,0.8634,0.8637,0.8638,0.8645, 0.8658,0.8739,0.8787,0.8792,0.8808,0.8949,0.8951,0.8995,0.8996,0.9089, 0.9192,0.9201,0.9215,0.9313,0.9413,0.9451,0.9515,0.9540,0.9569,0.9593, 0.9645,0.9689,0.9728,0.9744,0.9806,0.9809,0.9819,0.9863,0.9973, Overall p-value after applying KStest on 269 p-values = 0.838824 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.