RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-26_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 23.3598 0.862102 2 to 25 15.70 21.5690 0.798131 3 to 26 15.74 7.7621 0.028627 4 to 27 15.66 13.2513 0.280792 5 to 28 15.69 11.8268 0.189488 6 to 29 15.66 11.1808 0.152990 7 to 30 15.63 24.3622 0.890077 8 to 31 15.69 14.3003 0.354256 9 to 32 15.94 8.2798 0.039808 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.259503 Tough bday spacings test for dh-ranFile-2016-03-26_08:31: 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 6 36 72 111 105 83 52 23 7 5 0 (O-E)^2/E 1.1 0.0 0.0 1.8 0.5 0.3 0.0 1.5 4.2 0.4 4.1 Birthday Spacings: Sum(O-E)^2/E= 13.964, p= 0.825 RESULTS OF GCD FOR dh-ranFile-2016-03-26_08:31 Euclid's algorithm: p-value, steps to gcd: 0.002089 p-value, dist. of gcd's: 0.591985 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-26_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.348 0.933 0.642 0.749 0.092 0.718 0.710 0.697 Bits 8 to 15---> 0.457 0.106 0.724 0.401 0.118 0.378 0.973 0.748 Bits 16 to 23---> 0.301 0.597 0.365 0.745 0.300 0.496 0.597 0.585 Bits 24 to 31---> 0.517 0.032 0.025 0.310 0.852 0.115 0.824 0.718 KS test for the above 32 p values: 0.229 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-26_08:31, p-values for 5 runs: 0.5707, 0.4302, 0.0259, 0.0568, 0.4632 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-26_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5267 5134.0 3.445 3.584 r= 30 22946 23103.0 1.068 4.651 r= 31 11581 11551.5 0.075 4.727 chi-square = 4.727 with df = 3; p-value = 0.807 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-26_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5088 5134.0 0.412 1.537 r= 31 23200 23103.0 0.407 1.944 r= 32 11516 11551.5 0.109 2.053 chi-square = 2.053 with df = 3; p-value = 0.438 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-26_08:31 b-rank test for bits 1 to 8, p=0.20852 b-rank test for bits 2 to 9, p=0.67097 b-rank test for bits 3 to 10, p=0.47665 b-rank test for bits 4 to 11, p=0.62105 b-rank test for bits 5 to 12, p=0.37925 b-rank test for bits 6 to 13, p=0.36243 b-rank test for bits 7 to 14, p=0.40851 b-rank test for bits 8 to 15, p=0.25223 b-rank test for bits 9 to 16, p=0.44774 b-rank test for bits 10 to 17, p=0.46053 b-rank test for bits 11 to 18, p=0.18064 b-rank test for bits 12 to 19, p=0.08074 b-rank test for bits 13 to 20, p=0.47665 b-rank test for bits 14 to 21, p=0.94895 b-rank test for bits 15 to 22, p=0.01153 b-rank test for bits 16 to 23, p=0.57697 b-rank test for bits 17 to 24, p=0.53959 b-rank test for bits 18 to 25, p=0.23951 b-rank test for bits 19 to 26, p=0.11635 b-rank test for bits 20 to 27, p=0.25039 b-rank test for bits 21 to 28, p=0.32484 b-rank test for bits 22 to 29, p=0.61038 b-rank test for bits 23 to 30, p=0.15442 b-rank test for bits 24 to 31, p=0.60584 b-rank test for bits 25 to 32, p=0.57072 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 = 0.063732 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-26_08:31 (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 142277 0.86 0.804841 2 142272 0.85 0.801603 3 142400 1.15 0.874190 4 141842 -0.16 0.437499 5 142127 0.51 0.694475 6 141653 -0.60 0.274619 7 141543 -0.86 0.196023 8 141004 -2.12 0.017204 9 141463 -1.04 0.148514 10 142350 1.03 0.848402 11 141548 -0.84 0.199271 12 142746 1.95 0.974699 13 141686 -0.52 0.300905 14 142185 0.64 0.740241 15 142008 0.23 0.591163 16 141684 -0.53 0.299280 17 141971 0.14 0.557285 18 141913 0.01 0.503421 19 141985 0.18 0.570167 20 142255 0.81 0.790351 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-26_08:31 Bits used No. missing words z-score p-value 23 to 32 141879 -0.1046 0.458352 22 to 31 141752 -0.5425 0.293731 21 to 30 141889 -0.0701 0.472056 20 to 29 141920 0.0368 0.514675 19 to 28 141808 -0.3494 0.363389 18 to 27 141749 -0.5529 0.290179 17 to 26 141711 -0.6839 0.247020 16 to 25 142051 0.4885 0.687408 15 to 24 142365 1.5713 0.941941 14 to 23 142189 0.9644 0.832572 13 to 22 142616 2.4368 0.992591 12 to 21 142278 1.2713 0.898185 11 to 20 142648 2.5471 0.994569 10 to 19 142210 1.0368 0.850084 9 to 18 141933 0.0816 0.532526 8 to 17 142031 0.4196 0.662594 7 to 16 142242 1.1471 0.874338 6 to 15 141696 -0.7356 0.230981 5 to 14 142271 1.2471 0.893827 4 to 13 142185 0.9506 0.829093 3 to 12 141552 -1.2322 0.108942 2 to 11 141567 -1.1804 0.118911 1 to 10 142218 1.0644 0.856422 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-26_08:31 Bits used No. missing words z-score p-value 28 to 32 142129 0.7446 0.771757 27 to 31 141682 -0.7706 0.220469 26 to 30 141641 -0.9096 0.181519 25 to 29 142052 0.4836 0.685675 24 to 28 141828 -0.2757 0.391391 23 to 27 141669 -0.8147 0.207628 22 to 26 142033 0.4192 0.662473 21 to 25 142117 0.7040 0.759273 20 to 24 142387 1.6192 0.947300 19 to 23 141962 0.1785 0.570852 18 to 22 142031 0.4124 0.659992 17 to 21 142079 0.5752 0.717406 16 to 20 141909 -0.0011 0.499554 15 to 19 142091 0.6158 0.730997 14 to 18 142007 0.3311 0.629710 13 to 17 141863 -0.1571 0.437602 12 to 16 141912 0.0091 0.503611 11 to 15 142200 0.9853 0.837767 10 to 14 141588 -1.0893 0.138021 9 to 13 141654 -0.8655 0.193375 8 to 12 142363 1.5379 0.937959 7 to 11 141837 -0.2452 0.403156 6 to 10 142344 1.4735 0.929686 5 to 9 142096 0.6328 0.736561 4 to 8 141669 -0.8147 0.207628 3 to 7 141983 0.2497 0.598602 2 to 6 141567 -1.1604 0.122935 1 to 5 142043 0.4531 0.674768 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-26_08:31 Bits used No. missing words z-score p-value 31 to 32 141676 -0.6883 0.245635 30 to 31 141775 -0.3963 0.345959 29 to 30 141637 -0.8033 0.210891 28 to 29 141659 -0.7384 0.230125 27 to 28 141094 -2.4051 0.008084 26 to 27 141584 -0.9597 0.168609 25 to 26 142212 0.8928 0.814026 24 to 25 142171 0.7719 0.779910 23 to 24 142012 0.3029 0.619002 22 to 23 141154 -2.2281 0.012937 21 to 22 142087 0.5241 0.699896 20 to 21 142074 0.4858 0.686429 19 to 20 140950 -2.8299 0.002328 18 to 19 141431 -1.4110 0.079122 17 to 18 142673 2.2527 0.987861 16 to 17 141997 0.2586 0.602033 15 to 16 141611 -0.8800 0.189422 14 to 15 142045 0.4002 0.655498 13 to 14 142377 1.3796 0.916139 12 to 13 141887 -0.0659 0.473741 11 to 12 142481 1.6863 0.954135 10 to 11 142929 3.0079 0.998685 9 to 10 141827 -0.2429 0.404056 8 to 9 142191 0.8309 0.796981 7 to 8 141946 0.1082 0.543070 6 to 7 141038 -2.5703 0.005081 5 to 6 142431 1.5388 0.938080 4 to 5 142097 0.5536 0.710073 3 to 4 141883 -0.0777 0.469045 2 to 3 141495 -1.2222 0.110814 1 to 2 141821 -0.2606 0.397216 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-26_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2372.50 -1.803 0.035684 Test results for specific bytes for dh-ranFile-2016-03-26_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2428.13 -1.016 0.154705 2 to 9 2423.33 -1.084 0.139120 3 to 10 2477.70 -0.315 0.376216 4 to 11 2368.68 -1.857 0.031649 5 to 12 2485.41 -0.206 0.418248 6 to 13 2593.88 1.328 0.907858 7 to 14 2452.83 -0.667 0.252349 8 to 15 2597.93 1.385 0.916972 9 to 16 2552.70 0.745 0.771943 10 to 17 2652.36 2.155 0.984406 11 to 18 2586.92 1.229 0.890516 12 to 19 2670.93 2.417 0.992182 13 to 20 2605.20 1.488 0.931601 14 to 21 2509.02 0.128 0.550735 15 to 22 2480.97 -0.269 0.393912 16 to 23 2490.76 -0.131 0.448043 17 to 24 2493.69 -0.089 0.464421 18 to 25 2332.69 -2.366 0.008988 19 to 26 2424.45 -1.068 0.142676 20 to 27 2602.65 1.452 0.926701 21 to 28 2409.37 -1.282 0.099983 22 to 29 2504.64 0.066 0.526171 23 to 30 2501.09 0.015 0.506127 24 to 31 2457.70 -0.598 0.274843 25 to 32 2435.97 -0.905 0.182611 CDPARK for dh-ranFile-2016-03-26_08:31: 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 3521 -0.0913 0.463617 3553 1.3699 0.914635 3505 -0.8219 0.205562 3499 -1.0959 0.136563 3542 0.8676 0.807188 3519 -0.1826 0.427537 3524 0.0457 0.518210 3515 -0.3653 0.357445 3544 0.9589 0.831196 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3523.70 sample std.=16.57 p-value of the KSTEST for those 10 p-values: 0.873019 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-26_08:31 0.8329,0.7159,0.1871,0.4378,0.4999,0.1192,0.4678,0.2797,0.2477,0.1325, The KS test for those 10 p-values: 0.347127 The 3DSPHERES test for dh-ranFile-2016-03-26_08:31 sample no r^3 equiv. uni. 1 14.502 0.383312 2 31.723 0.652648 3 9.811 0.278950 4 64.860 0.884905 5 1.579 0.051284 6 101.257 0.965790 7 0.793 0.026091 8 19.715 0.481689 9 0.307 0.010188 10 142.087 0.991228 11 22.738 0.531359 12 157.654 0.994779 13 9.175 0.263484 14 3.159 0.099935 15 86.497 0.944047 16 35.742 0.696206 17 7.265 0.215065 18 18.827 0.466116 19 10.042 0.284463 20 5.500 0.167498 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.255462 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-26_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 3.0 -1.6 -0.5 0.4 0.9 -2.4 -0.7 0.3 0.4 0.4 -2.3 -1.5 0.4 -0.4 0.1 1.0 -1.7 0.4 0.5 0.8 0.7 0.6 1.2 0.2 -0.0 0.0 -0.5 0.9 -0.6 -0.7 0.8 0.2 0.3 0.3 -0.7 -1.4 -0.4 0.9 1.0 1.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:46.060987 z-score=0.443090, p-value=0.692102 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-26_08:31 Test no p-value 1 0.449218 2 0.181555 3 0.331222 4 0.339322 5 0.085808 6 0.561355 7 0.012253 8 0.079531 9 0.200312 10 0.005800 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002620 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-26_08:31: (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 66650 0.00 66952 1.22 3 25000.00 25066 0.17 24840 1.02 4 6666.67 6664 0.00 6542 2.33 5 1388.89 1359 0.64 1415 0.49 6 238.10 221 1.23 217 1.87 7 34.72 34 0.01 31 0.40 8 4.96 5 0.00 2 1.77 p=0.08642 p=0.83205 Number of rngs required: 688111, p-value: 0.368 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-26_08:31 No. of wins: Observed Expected 98300 98585.9 z-score=-1.279, pvalue=0.10053 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66544 66666.7 0.226 0.226 2 38012 37654.3 3.398 3.623 3 26732 26954.7 1.840 5.464 4 19349 19313.5 0.065 5.529 5 13905 13851.4 0.207 5.736 6 10008 9943.5 0.418 6.154 7 7032 7145.0 1.788 7.942 8 5106 5139.1 0.213 8.155 9 3635 3699.9 1.137 9.292 10 2694 2666.3 0.288 9.580 11 1940 1923.3 0.144 9.725 12 1393 1388.7 0.013 9.738 13 1015 1003.7 0.127 9.864 14 684 726.1 2.446 12.310 15 525 525.8 0.001 12.311 16 392 381.2 0.309 12.620 17 281 276.5 0.072 12.692 18 198 200.8 0.040 12.732 19 141 146.0 0.170 12.902 20 107 106.2 0.006 12.908 21 307 287.1 1.377 14.285 Chisq= 14.29 for 20 degrees of freedom, p= 0.18426 SUMMARY of craptest p-value for no. of wins: 0.100532 p-value for throws/game: 0.184263 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-26_08:31 No. of wins: Observed Expected 98558 98585.9 z-score=-0.125, pvalue=0.45042 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66615 66666.7 0.040 0.040 2 37371 37654.3 2.132 2.172 3 27001 26954.7 0.079 2.251 4 19362 19313.5 0.122 2.373 5 13871 13851.4 0.028 2.401 6 9976 9943.5 0.106 2.507 7 7229 7145.0 0.987 3.494 8 5170 5139.1 0.186 3.680 9 3669 3699.9 0.257 3.937 10 2749 2666.3 2.565 6.503 11 1910 1923.3 0.092 6.595 12 1397 1388.7 0.049 6.644 13 1017 1003.7 0.176 6.820 14 752 726.1 0.921 7.741 15 500 525.8 1.269 9.010 16 386 381.2 0.062 9.072 17 286 276.5 0.324 9.396 18 210 200.8 0.419 9.814 19 122 146.0 3.940 13.755 20 105 106.2 0.014 13.769 21 302 287.1 0.772 14.541 Chisq= 14.54 for 20 degrees of freedom, p= 0.19793 SUMMARY of craptest p-value for no. of wins: 0.450420 p-value for throws/game: 0.197933 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0021,0.0023,0.0026,0.0051,0.0058,0.0081,0.0090,0.0102,0.0115,0.0123, 0.0129,0.0172,0.0246,0.0259,0.0261,0.0286,0.0316,0.0320,0.0357,0.0398, 0.0513,0.0568,0.0637,0.0791,0.0795,0.0807,0.0858,0.0864,0.0918,0.0999, 0.1000,0.1005,0.1063,0.1089,0.1108,0.1153,0.1164,0.1176,0.1189,0.1192, 0.1229,0.1325,0.1366,0.1380,0.1391,0.1427,0.1485,0.1530,0.1544,0.1547, 0.1675,0.1686,0.1806,0.1815,0.1816,0.1826,0.1843,0.1871,0.1894,0.1895, 0.1934,0.1960,0.1979,0.1993,0.2003,0.2056,0.2076,0.2076,0.2085,0.2109, 0.2151,0.2205,0.2294,0.2301,0.2310,0.2395,0.2456,0.2470,0.2477,0.2504, 0.2522,0.2523,0.2555,0.2595,0.2635,0.2746,0.2748,0.2789,0.2797,0.2808, 0.2845,0.2902,0.2937,0.2993,0.2999,0.3009,0.3012,0.3096,0.3248,0.3312, 0.3393,0.3460,0.3471,0.3479,0.3543,0.3574,0.3574,0.3624,0.3634,0.3649, 0.3684,0.3762,0.3775,0.3793,0.3833,0.3914,0.3939,0.3972,0.4008,0.4032, 0.4041,0.4085,0.4182,0.4275,0.4302,0.4375,0.4376,0.4378,0.4385,0.4477, 0.4480,0.4492,0.4504,0.4571,0.4584,0.4605,0.4632,0.4636,0.4644,0.4661, 0.4678,0.4690,0.4721,0.4737,0.4766,0.4766,0.4817,0.4956,0.4996,0.4999, 0.5034,0.5036,0.5061,0.5147,0.5171,0.5182,0.5262,0.5314,0.5325,0.5396, 0.5431,0.5507,0.5573,0.5614,0.5702,0.5707,0.5707,0.5709,0.5770,0.5847, 0.5912,0.5920,0.5969,0.5972,0.5986,0.6020,0.6058,0.6104,0.6190,0.6210, 0.6297,0.6415,0.6526,0.6555,0.6600,0.6625,0.6626,0.6710,0.6748,0.6857, 0.6864,0.6874,0.6921,0.6945,0.6962,0.6967,0.6999,0.7099,0.7101,0.7159, 0.7174,0.7181,0.7183,0.7243,0.7310,0.7366,0.7402,0.7446,0.7477,0.7489, 0.7593,0.7718,0.7719,0.7799,0.7904,0.7970,0.7981,0.8016,0.8048,0.8070, 0.8072,0.8140,0.8241,0.8254,0.8291,0.8312,0.8320,0.8326,0.8329,0.8378, 0.8484,0.8501,0.8521,0.8564,0.8621,0.8730,0.8742,0.8743,0.8849,0.8901, 0.8905,0.8938,0.8982,0.9079,0.9146,0.9161,0.9170,0.9267,0.9297,0.9316, 0.9335,0.9380,0.9381,0.9419,0.9440,0.9473,0.9489,0.9541,0.9658,0.9732, 0.9747,0.9844,0.9879,0.9912,0.9922,0.9926,0.9946,0.9948,0.9987, Overall p-value after applying KStest on 269 p-values = 0.107969 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.