RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-09_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 20.0856 0.730127 2 to 25 15.32 31.8702 0.984384 3 to 26 15.79 14.7127 0.383830 4 to 27 15.96 16.2763 0.495659 5 to 28 15.59 14.8376 0.392824 6 to 29 15.76 28.2651 0.958065 7 to 30 15.78 18.6181 0.649111 8 to 31 15.84 13.4575 0.294937 9 to 32 15.71 21.1898 0.782083 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.249539 Tough bday spacings test for dh-ranFile-2016-12-09_15:31: 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 11 37 57 100 110 80 52 29 11 5 8 (O-E)^2/E 0.4 0.0 3.6 0.1 1.6 0.0 0.0 0.0 1.0 0.4 3.8 Birthday Spacings: Sum(O-E)^2/E= 10.871, p= 0.632 RESULTS OF GCD FOR dh-ranFile-2016-12-09_15:31 Euclid's algorithm: p-value, steps to gcd: 0.065937 p-value, dist. of gcd's: 0.811546 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-09_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.817 0.504 0.132 0.467 0.887 0.095 0.534 0.649 Bits 8 to 15---> 0.507 0.519 0.472 0.579 0.406 0.745 0.105 0.511 Bits 16 to 23---> 0.312 0.098 0.299 0.559 0.542 0.956 0.954 0.253 Bits 24 to 31---> 0.312 0.612 0.134 0.487 0.309 0.926 0.344 0.913 KS test for the above 32 p values: 0.484 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-09_15:31, p-values for 5 runs: 0.4565, 0.4382, 0.3243, 0.8443, 0.9920 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-09_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 4994 5134.0 3.818 3.966 r= 30 22998 23103.0 0.478 4.443 r= 31 11791 11551.5 4.965 9.408 chi-square = 9.408 with df = 3; p-value = 0.976 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-09_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5114 5134.0 0.078 0.088 r= 31 23116 23103.0 0.007 0.095 r= 32 11560 11551.5 0.006 0.101 chi-square = 0.101 with df = 3; p-value = 0.008 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-09_15:31 b-rank test for bits 1 to 8, p=0.25454 b-rank test for bits 2 to 9, p=0.44354 b-rank test for bits 3 to 10, p=0.47321 b-rank test for bits 4 to 11, p=0.81767 b-rank test for bits 5 to 12, p=0.95790 b-rank test for bits 6 to 13, p=0.09180 b-rank test for bits 7 to 14, p=0.75495 b-rank test for bits 8 to 15, p=0.04998 b-rank test for bits 9 to 16, p=0.98835 b-rank test for bits 10 to 17, p=0.25159 b-rank test for bits 11 to 18, p=0.66584 b-rank test for bits 12 to 19, p=0.81112 b-rank test for bits 13 to 20, p=0.28455 b-rank test for bits 14 to 21, p=0.76485 b-rank test for bits 15 to 22, p=0.35942 b-rank test for bits 16 to 23, p=0.02895 b-rank test for bits 17 to 24, p=0.56366 b-rank test for bits 18 to 25, p=0.92986 b-rank test for bits 19 to 26, p=0.92371 b-rank test for bits 20 to 27, p=0.69083 b-rank test for bits 21 to 28, p=0.33241 b-rank test for bits 22 to 29, p=0.29477 b-rank test for bits 23 to 30, p=0.76948 b-rank test for bits 24 to 31, p=0.43087 b-rank test for bits 25 to 32, p=0.06596 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 = 0.910146 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-09_15:31 (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 141417 -1.15 0.125009 2 141683 -0.53 0.298469 3 141410 -1.17 0.121674 4 142449 1.26 0.896330 5 142074 0.38 0.649786 6 141264 -1.51 0.065805 7 141085 -1.93 0.027052 8 142266 0.83 0.797674 9 142016 0.25 0.598408 10 141867 -0.10 0.460608 11 141916 0.02 0.506217 12 142070 0.38 0.646317 13 142175 0.62 0.732610 14 141412 -1.16 0.122621 15 142851 2.20 0.986102 16 141622 -0.67 0.251005 17 142407 1.16 0.877541 18 142431 1.22 0.888550 19 142120 0.49 0.688718 20 142417 1.19 0.882217 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-09_15:31 Bits used No. missing words z-score p-value 23 to 32 142130 0.7609 0.776651 22 to 31 141437 -1.6287 0.051686 21 to 30 141584 -1.1218 0.130968 20 to 29 141959 0.1713 0.567997 19 to 28 141737 -0.5942 0.276175 18 to 27 141655 -0.8770 0.190243 17 to 26 141567 -1.1804 0.118911 16 to 25 141806 -0.3563 0.360804 15 to 24 141921 0.0402 0.516050 14 to 23 141539 -1.2770 0.100801 13 to 22 141621 -0.9942 0.160053 12 to 21 142376 1.6092 0.946214 11 to 20 142235 1.1230 0.869281 10 to 19 141567 -1.1804 0.118911 9 to 18 142594 2.3609 0.990885 8 to 17 141528 -1.3149 0.094267 7 to 16 141687 -0.7667 0.221643 6 to 15 142104 0.6713 0.748978 5 to 14 142397 1.6816 0.953679 4 to 13 141776 -0.4598 0.322845 3 to 12 142035 0.4333 0.667618 2 to 11 141818 -0.3149 0.376407 1 to 10 142035 0.4333 0.667618 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-09_15:31 Bits used No. missing words z-score p-value 28 to 32 141510 -1.3537 0.087922 27 to 31 142251 1.1582 0.876610 26 to 30 141484 -1.4418 0.074680 25 to 29 141991 0.2768 0.609051 24 to 28 141628 -0.9537 0.170128 23 to 27 142151 0.8192 0.793670 22 to 26 141844 -0.2215 0.412368 21 to 25 141368 -1.8350 0.033252 20 to 24 141787 -0.4147 0.339189 19 to 23 141609 -1.0181 0.154323 18 to 22 141507 -1.3638 0.086310 17 to 21 142398 1.6565 0.951191 16 to 20 142029 0.4057 0.657504 15 to 19 142009 0.3379 0.632267 14 to 18 141523 -1.3096 0.095167 13 to 17 141628 -0.9537 0.170128 12 to 16 141722 -0.6350 0.262709 11 to 15 141844 -0.2215 0.412368 10 to 14 141662 -0.8384 0.200901 9 to 13 141731 -0.6045 0.272753 8 to 12 141335 -1.9469 0.025774 7 to 11 142204 0.9989 0.841074 6 to 10 141759 -0.5096 0.305168 5 to 9 141672 -0.8045 0.210552 4 to 8 141983 0.2497 0.598602 3 to 7 141985 0.2565 0.601221 2 to 6 141646 -0.8926 0.186024 1 to 5 141379 -1.7977 0.036110 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-09_15:31 Bits used No. missing words z-score p-value 31 to 32 141102 -2.3815 0.008621 30 to 31 141783 -0.3727 0.354703 29 to 30 141512 -1.1721 0.120586 28 to 29 141859 -0.1485 0.440988 27 to 28 141794 -0.3402 0.366851 26 to 27 141367 -1.5998 0.054822 25 to 26 142015 0.3117 0.622370 24 to 25 142001 0.2704 0.606579 23 to 24 141871 -0.1131 0.454988 22 to 23 141961 0.1524 0.560572 21 to 22 141521 -1.1455 0.125998 20 to 21 141871 -0.1131 0.454988 19 to 20 141766 -0.4228 0.336220 18 to 19 141999 0.2645 0.604308 17 to 18 141958 0.1436 0.557080 16 to 17 141617 -0.8623 0.194253 15 to 16 142386 1.4061 0.920154 14 to 15 141843 -0.1957 0.422437 13 to 14 141704 -0.6057 0.272359 12 to 13 141210 -2.0629 0.019560 11 to 12 141380 -1.5614 0.059209 10 to 11 141974 0.1908 0.575646 9 to 10 141916 0.0197 0.507849 8 to 9 142065 0.4592 0.676956 7 to 8 141648 -0.7709 0.220388 6 to 7 142107 0.5831 0.720086 5 to 6 142099 0.5595 0.712089 4 to 5 142028 0.3501 0.636853 3 to 4 141757 -0.4494 0.326589 2 to 3 141576 -0.9833 0.162736 1 to 2 141831 -0.2311 0.408633 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-09_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2495.95 -0.057 0.477135 Test results for specific bytes for dh-ranFile-2016-12-09_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2564.55 0.913 0.819360 2 to 9 2393.92 -1.500 0.066773 3 to 10 2461.88 -0.539 0.294891 4 to 11 2678.67 2.527 0.994245 5 to 12 2360.36 -1.975 0.024145 6 to 13 2531.63 0.447 0.672693 7 to 14 2486.44 -0.192 0.423968 8 to 15 2439.71 -0.853 0.196949 9 to 16 2479.83 -0.285 0.387738 10 to 17 2545.95 0.650 0.742102 11 to 18 2629.32 1.829 0.966287 12 to 19 2488.31 -0.165 0.434341 13 to 20 2558.53 0.828 0.796081 14 to 21 2443.77 -0.795 0.213246 15 to 22 2632.74 1.877 0.969759 16 to 23 2523.97 0.339 0.632694 17 to 24 2562.96 0.890 0.813366 18 to 25 2577.14 1.091 0.862340 19 to 26 2587.00 1.230 0.890732 20 to 27 2411.06 -1.258 0.104238 21 to 28 2489.35 -0.151 0.440119 22 to 29 2527.45 0.388 0.651092 23 to 30 2419.68 -1.136 0.128012 24 to 31 2521.68 0.307 0.620406 25 to 32 2393.18 -1.511 0.065435 CDPARK for dh-ranFile-2016-12-09_15:31: 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 3524 0.0457 0.518210 3521 -0.0913 0.463617 3524 0.0457 0.518210 3517 -0.2740 0.392053 3522 -0.0457 0.481790 3519 -0.1826 0.427537 3499 -1.0959 0.136563 3544 0.9589 0.831196 3530 0.3196 0.625377 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3521.90 sample std.=10.62 p-value of the KSTEST for those 10 p-values: 0.233191 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-09_15:31 0.0527,0.3202,0.7744,0.5776,0.5742,0.2666,0.9142,0.9659,0.6544,0.5534, The KS test for those 10 p-values: 0.782591 The 3DSPHERES test for dh-ranFile-2016-12-09_15:31 sample no r^3 equiv. uni. 1 36.478 0.703568 2 31.220 0.646777 3 7.743 0.227485 4 3.567 0.112093 5 0.933 0.030630 6 6.663 0.199165 7 1.504 0.048902 8 66.653 0.891582 9 170.340 0.996580 10 45.869 0.783241 11 57.655 0.853663 12 1.350 0.043989 13 0.885 0.029078 14 10.568 0.296899 15 2.495 0.079808 16 5.836 0.176785 17 21.263 0.507751 18 22.693 0.530658 19 1.588 0.051563 20 37.519 0.713677 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.044839 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-09_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.4 -0.4 1.7 0.6 1.1 -1.8 0.4 -0.7 0.3 0.6 2.0 0.1 -0.3 -0.5 -1.3 0.1 -0.6 0.9 0.8 -0.4 -0.1 0.1 0.5 0.0 0.1 -0.3 -1.1 -0.7 -0.1 -0.3 0.0 -1.2 -0.4 -0.8 -0.2 1.1 -1.2 1.5 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:27.050814 z-score=-1.631090, p-value=0.035673 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-09_15:31 Test no p-value 1 0.002709 2 0.947899 3 0.081745 4 0.706851 5 0.493921 6 0.005069 7 0.840816 8 0.158829 9 0.028864 10 0.482458 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.031419 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-09_15:31: (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 66416 0.94 66692 0.01 3 25000.00 25150 0.90 25053 0.11 4 6666.67 6710 0.28 6601 0.65 5 1388.89 1413 0.42 1392 0.01 6 238.10 268 3.76 228 0.43 7 34.72 40 0.80 30 0.64 8 4.96 2 1.77 3 0.77 p=0.81887 p=0.14520 Number of rngs required: 688312, p-value: 0.458 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-09_15:31 No. of wins: Observed Expected 98526 98585.9 z-score=-0.268, pvalue=0.39446 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66501 66666.7 0.412 0.412 2 37598 37654.3 0.084 0.496 3 27254 26954.7 3.323 3.819 4 19326 19313.5 0.008 3.827 5 13907 13851.4 0.223 4.050 6 9803 9943.5 1.986 6.036 7 7156 7145.0 0.017 6.053 8 5026 5139.1 2.488 8.541 9 3806 3699.9 3.045 11.586 10 2632 2666.3 0.441 12.027 11 1813 1923.3 6.329 18.356 12 1416 1388.7 0.535 18.891 13 1069 1003.7 4.246 23.137 14 726 726.1 0.000 23.137 15 539 525.8 0.330 23.467 16 416 381.2 3.186 26.653 17 268 276.5 0.264 26.917 18 203 200.8 0.023 26.940 19 161 146.0 1.544 28.485 20 112 106.2 0.315 28.800 21 268 287.1 1.272 30.072 Chisq= 30.07 for 20 degrees of freedom, p= 0.93131 SUMMARY of craptest p-value for no. of wins: 0.394456 p-value for throws/game: 0.931306 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-09_15:31 No. of wins: Observed Expected 98459 98585.9 z-score=-0.567, pvalue=0.28523 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66465 66666.7 0.610 0.610 2 37934 37654.3 2.077 2.687 3 26861 26954.7 0.326 3.013 4 19574 19313.5 3.515 6.528 5 13865 13851.4 0.013 6.541 6 10028 9943.5 0.717 7.259 7 7162 7145.0 0.040 7.299 8 5074 5139.1 0.824 8.123 9 3656 3699.9 0.520 8.643 10 2614 2666.3 1.026 9.669 11 1864 1923.3 1.830 11.499 12 1374 1388.7 0.156 11.655 13 989 1003.7 0.216 11.871 14 701 726.1 0.870 12.741 15 485 525.8 3.171 15.913 16 345 381.2 3.429 19.341 17 276 276.5 0.001 19.343 18 176 200.8 3.070 22.412 19 146 146.0 0.000 22.412 20 108 106.2 0.030 22.442 21 303 287.1 0.879 23.321 Chisq= 23.32 for 20 degrees of freedom, p= 0.72671 SUMMARY of craptest p-value for no. of wins: 0.285226 p-value for throws/game: 0.726709 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0051,0.0083,0.0086,0.0196,0.0241,0.0258,0.0271,0.0289,0.0289, 0.0291,0.0306,0.0314,0.0333,0.0357,0.0361,0.0440,0.0448,0.0489,0.0500, 0.0516,0.0517,0.0527,0.0548,0.0592,0.0654,0.0658,0.0659,0.0660,0.0668, 0.0747,0.0798,0.0817,0.0863,0.0879,0.0918,0.0943,0.0950,0.0952,0.0984, 0.1008,0.1042,0.1054,0.1121,0.1189,0.1189,0.1206,0.1217,0.1226,0.1250, 0.1260,0.1280,0.1310,0.1320,0.1341,0.1366,0.1452,0.1543,0.1588,0.1601, 0.1627,0.1701,0.1701,0.1768,0.1860,0.1902,0.1943,0.1969,0.1992,0.2009, 0.2106,0.2132,0.2204,0.2216,0.2275,0.2332,0.2495,0.2510,0.2516,0.2533, 0.2545,0.2627,0.2666,0.2724,0.2728,0.2762,0.2845,0.2852,0.2948,0.2949, 0.2949,0.2969,0.2985,0.2995,0.3052,0.3087,0.3121,0.3124,0.3202,0.3228, 0.3243,0.3266,0.3324,0.3362,0.3392,0.3435,0.3547,0.3594,0.3608,0.3669, 0.3764,0.3838,0.3877,0.3921,0.3928,0.3945,0.4062,0.4086,0.4124,0.4124, 0.4224,0.4240,0.4275,0.4275,0.4309,0.4343,0.4382,0.4401,0.4410,0.4435, 0.4550,0.4550,0.4565,0.4583,0.4606,0.4636,0.4667,0.4720,0.4732,0.4771, 0.4818,0.4825,0.4837,0.4869,0.4939,0.4957,0.5042,0.5062,0.5071,0.5078, 0.5078,0.5114,0.5160,0.5182,0.5182,0.5189,0.5307,0.5336,0.5419,0.5534, 0.5571,0.5592,0.5606,0.5637,0.5680,0.5742,0.5756,0.5776,0.5789,0.5984, 0.5986,0.6012,0.6043,0.6066,0.6091,0.6116,0.6204,0.6224,0.6254,0.6323, 0.6323,0.6327,0.6369,0.6463,0.6468,0.6486,0.6491,0.6498,0.6511,0.6544, 0.6575,0.6658,0.6676,0.6676,0.6727,0.6770,0.6887,0.6908,0.7036,0.7069, 0.7121,0.7137,0.7201,0.7267,0.7301,0.7326,0.7421,0.7446,0.7490,0.7549, 0.7648,0.7695,0.7744,0.7767,0.7821,0.7826,0.7832,0.7937,0.7961,0.7977, 0.8111,0.8115,0.8134,0.8173,0.8177,0.8189,0.8194,0.8312,0.8408,0.8411, 0.8443,0.8537,0.8623,0.8693,0.8766,0.8775,0.8822,0.8874,0.8886,0.8907, 0.8916,0.8963,0.9101,0.9130,0.9142,0.9202,0.9237,0.9258,0.9299,0.9313, 0.9462,0.9479,0.9512,0.9536,0.9537,0.9556,0.9579,0.9581,0.9659,0.9663, 0.9698,0.9757,0.9844,0.9861,0.9883,0.9909,0.9920,0.9942,0.9966, Overall p-value after applying KStest on 269 p-values = 0.061305 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.