RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-07_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 13.8626 0.323196 2 to 25 15.58 17.7177 0.593146 3 to 26 15.78 16.9748 0.543922 4 to 27 15.90 36.7379 0.996349 5 to 28 15.83 9.7912 0.087862 6 to 29 15.68 14.1250 0.341767 7 to 30 15.81 9.3277 0.070584 8 to 31 15.75 23.2636 0.859137 9 to 32 15.69 20.1284 0.732287 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.863186 Tough bday spacings test for dh-ranFile-2016-06-07_02:31: 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 31 77 103 92 89 65 19 11 2 5 (O-E)^2/E 1.1 0.9 0.2 0.3 0.3 1.5 3.2 3.9 1.0 3.2 0.2 Birthday Spacings: Sum(O-E)^2/E= 15.813, p= 0.895 RESULTS OF GCD FOR dh-ranFile-2016-06-07_02:31 Euclid's algorithm: p-value, steps to gcd: 0.718022 p-value, dist. of gcd's: 0.755321 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-07_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.639 0.746 0.682 0.114 0.609 0.956 0.484 0.570 Bits 8 to 15---> 0.486 0.021 0.387 0.714 0.317 0.660 0.459 0.339 Bits 16 to 23---> 0.671 0.061 0.204 0.192 0.239 0.139 0.564 0.025 Bits 24 to 31---> 0.238 0.491 0.659 0.821 0.053 0.116 0.778 0.191 KS test for the above 32 p values: 0.799 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-07_02:31, p-values for 5 runs: 0.2321, 0.6277, 0.9330, 0.5721, 0.3464 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-07_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5168 5134.0 0.225 2.428 r= 30 23049 23103.0 0.126 2.555 r= 31 11550 11551.5 0.000 2.555 chi-square = 2.555 with df = 3; p-value = 0.535 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-07_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5066 5134.0 0.901 1.535 r= 31 22965 23103.0 0.825 2.360 r= 32 11746 11551.5 3.274 5.634 chi-square = 5.634 with df = 3; p-value = 0.869 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-07_02:31 b-rank test for bits 1 to 8, p=0.41427 b-rank test for bits 2 to 9, p=0.63284 b-rank test for bits 3 to 10, p=0.16758 b-rank test for bits 4 to 11, p=0.14950 b-rank test for bits 5 to 12, p=0.44509 b-rank test for bits 6 to 13, p=0.35844 b-rank test for bits 7 to 14, p=0.10549 b-rank test for bits 8 to 15, p=0.28636 b-rank test for bits 9 to 16, p=0.56200 b-rank test for bits 10 to 17, p=0.63729 b-rank test for bits 11 to 18, p=0.18327 b-rank test for bits 12 to 19, p=0.64979 b-rank test for bits 13 to 20, p=0.64220 b-rank test for bits 14 to 21, p=0.88605 b-rank test for bits 15 to 22, p=0.56733 b-rank test for bits 16 to 23, p=0.31155 b-rank test for bits 17 to 24, p=0.31457 b-rank test for bits 18 to 25, p=0.94997 b-rank test for bits 19 to 26, p=0.87666 b-rank test for bits 20 to 27, p=0.01754 b-rank test for bits 21 to 28, p=0.26020 b-rank test for bits 22 to 29, p=0.65916 b-rank test for bits 23 to 30, p=0.30282 b-rank test for bits 24 to 31, p=0.42724 b-rank test for bits 25 to 32, p=0.53514 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 = 0.455453 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-07_02:31 (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 141761 -0.35 0.364459 2 141336 -1.34 0.090195 3 141852 -0.13 0.446722 4 141906 -0.01 0.496896 5 142459 1.28 0.900477 6 142091 0.42 0.664386 7 142642 1.71 0.956537 8 142219 0.72 0.765322 9 142010 0.24 0.592977 10 142388 1.12 0.868299 11 142391 1.13 0.869790 12 141824 -0.20 0.420987 13 141757 -0.36 0.360954 14 141807 -0.24 0.405518 15 142163 0.59 0.723305 16 141995 0.20 0.579324 17 141786 -0.29 0.386614 18 141920 0.02 0.509945 19 141618 -0.68 0.248038 20 142239 0.77 0.779426 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-07_02:31 Bits used No. missing words z-score p-value 23 to 32 142312 1.3885 0.917510 22 to 31 141928 0.0644 0.525666 21 to 30 141954 0.1540 0.561209 20 to 29 141902 -0.0253 0.489918 19 to 28 141506 -1.3908 0.082144 18 to 27 141534 -1.2942 0.097791 17 to 26 142071 0.5575 0.711401 16 to 25 141951 0.1437 0.557127 15 to 24 141845 -0.2218 0.412224 14 to 23 141686 -0.7701 0.220619 13 to 22 142148 0.8230 0.794746 12 to 21 141933 0.0816 0.532526 11 to 20 141320 -2.0322 0.021068 10 to 19 142253 1.1851 0.882005 9 to 18 142305 1.3644 0.913776 8 to 17 142346 1.5058 0.933935 7 to 16 141901 -0.0287 0.488542 6 to 15 141734 -0.6046 0.272727 5 to 14 141878 -0.1080 0.456984 4 to 13 141881 -0.0977 0.461089 3 to 12 141894 -0.0529 0.478921 2 to 11 142039 0.4471 0.672612 1 to 10 142447 1.8540 0.968133 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-07_02:31 Bits used No. missing words z-score p-value 28 to 32 142110 0.6802 0.751823 27 to 31 142290 1.2904 0.901545 26 to 30 142267 1.2124 0.887328 25 to 29 140966 -3.1977 0.000693 24 to 28 141514 -1.3401 0.090106 23 to 27 142339 1.4565 0.927374 22 to 26 141738 -0.5808 0.280695 21 to 25 141893 -0.0554 0.477928 20 to 24 141787 -0.4147 0.339189 19 to 23 141512 -1.3469 0.089009 18 to 22 142116 0.7006 0.758216 17 to 21 141335 -1.9469 0.025774 16 to 20 142325 1.4091 0.920590 15 to 19 141449 -1.5604 0.059328 14 to 18 141637 -0.9232 0.177964 13 to 17 142014 0.3548 0.638635 12 to 16 142111 0.6836 0.752895 11 to 15 141803 -0.3604 0.359259 10 to 14 141906 -0.0113 0.495497 9 to 13 141766 -0.4859 0.313532 8 to 12 142429 1.7616 0.960931 7 to 11 142244 1.1345 0.871702 6 to 10 142111 0.6836 0.752895 5 to 9 141940 0.1040 0.541402 4 to 8 142013 0.3514 0.637365 3 to 7 142199 0.9819 0.836933 2 to 6 142052 0.4836 0.685675 1 to 5 142555 2.1887 0.985691 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-07_02:31 Bits used No. missing words z-score p-value 31 to 32 142066 0.4622 0.678014 30 to 31 141998 0.2616 0.603171 29 to 30 141813 -0.2842 0.388144 28 to 29 141753 -0.4612 0.322345 27 to 28 141919 0.0285 0.511378 26 to 27 141562 -1.0246 0.152783 25 to 26 141886 -0.0688 0.472566 24 to 25 142271 1.0669 0.856985 23 to 24 142151 0.7129 0.762043 22 to 23 141434 -1.4022 0.080435 21 to 22 142190 0.8279 0.796146 20 to 21 141473 -1.2871 0.099028 19 to 20 141454 -1.3432 0.089611 18 to 19 142014 0.3088 0.621248 17 to 18 142311 1.1849 0.881965 16 to 17 141958 0.1436 0.557080 15 to 16 141751 -0.4671 0.320232 14 to 15 142107 0.5831 0.720086 13 to 14 142012 0.3029 0.619002 12 to 13 142135 0.6657 0.747196 11 to 12 142161 0.7424 0.771074 10 to 11 141755 -0.4553 0.324464 9 to 10 141726 -0.5408 0.294324 8 to 9 141797 -0.3314 0.370187 7 to 8 141766 -0.4228 0.336220 6 to 7 141962 0.1554 0.561735 5 to 6 141614 -0.8712 0.191828 4 to 5 141553 -1.0511 0.146602 3 to 4 142274 1.0757 0.858974 2 to 3 141914 0.0138 0.505496 1 to 2 141871 -0.1131 0.454988 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-07_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2592.86 1.313 0.905447 Test results for specific bytes for dh-ranFile-2016-06-07_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2502.73 0.039 0.515416 2 to 9 2407.61 -1.307 0.095684 3 to 10 2513.59 0.192 0.576200 4 to 11 2385.80 -1.615 0.053147 5 to 12 2510.88 0.154 0.561162 6 to 13 2434.95 -0.920 0.178802 7 to 14 2519.93 0.282 0.610987 8 to 15 2589.06 1.259 0.896073 9 to 16 2516.67 0.236 0.593177 10 to 17 2517.11 0.242 0.595591 11 to 18 2668.06 2.377 0.991267 12 to 19 2523.88 0.338 0.632197 13 to 20 2517.16 0.243 0.595871 14 to 21 2516.57 0.234 0.592643 15 to 22 2442.09 -0.819 0.206412 16 to 23 2363.33 -1.933 0.026634 17 to 24 2471.96 -0.397 0.345835 18 to 25 2383.10 -1.653 0.049139 19 to 26 2468.44 -0.446 0.327706 20 to 27 2467.19 -0.464 0.321344 21 to 28 2507.06 0.100 0.539793 22 to 29 2554.21 0.767 0.778350 23 to 30 2415.40 -1.196 0.115774 24 to 31 2440.59 -0.840 0.200411 25 to 32 2445.07 -0.777 0.218650 CDPARK for dh-ranFile-2016-06-07_02:31: 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 3523 0.0000 0.500000 3469 -2.4658 0.006836 3529 0.2740 0.607947 3552 1.3242 0.907282 3538 0.6849 0.753306 3508 -0.6849 0.246694 3518 -0.2283 0.409702 3514 -0.4110 0.340551 3546 1.0502 0.853193 3503 -0.9132 0.180558 Square side=100, avg. no. parked=3520.00 sample std.=22.78 p-value of the KSTEST for those 10 p-values: 0.971331 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-07_02:31 0.3329,0.9544,0.0138,0.7231,0.7610,0.2524,0.2723,0.6016,0.1880,0.1767, The KS test for those 10 p-values: 0.634558 The 3DSPHERES test for dh-ranFile-2016-06-07_02:31 sample no r^3 equiv. uni. 1 8.863 0.255779 2 78.165 0.926133 3 39.267 0.729887 4 17.222 0.436774 5 24.495 0.558022 6 17.041 0.433368 7 19.919 0.485189 8 27.498 0.600119 9 8.862 0.255763 10 24.810 0.562646 11 0.610 0.020112 12 9.579 0.273335 13 55.161 0.840976 14 10.515 0.295670 15 14.256 0.378231 16 68.432 0.897826 17 14.630 0.385953 18 1.181 0.038605 19 3.494 0.109942 20 40.188 0.738051 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.791956 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-07_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.4 0.9 -0.1 -0.7 0.6 0.6 -0.4 0.5 -0.6 -1.6 -0.1 0.4 -0.8 -0.5 0.2 0.7 0.8 0.4 0.9 -1.8 0.8 -1.2 -0.1 1.6 0.7 -0.1 -0.2 -1.0 0.2 1.9 0.8 0.4 -2.7 0.2 0.7 -1.7 0.5 0.4 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:35.804539 z-score=-0.675980, p-value=0.261524 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-07_02:31 Test no p-value 1 0.837943 2 0.105714 3 0.026615 4 0.564519 5 0.092469 6 0.173680 7 0.006048 8 0.403786 9 0.767447 10 0.998024 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.106359 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-07_02:31: (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 66921 0.97 66891 0.75 3 25000.00 24799 1.62 24832 1.13 4 6666.67 6568 1.46 6592 0.84 5 1388.89 1430 1.22 1377 0.10 6 238.10 254 1.06 265 3.04 7 34.72 24 3.31 38 0.31 8 4.96 3 0.77 4 0.19 p=0.89160 p=0.61568 Number of rngs required: 686953, p-value: 0.045 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-07_02:31 No. of wins: Observed Expected 98375 98585.9 z-score=-0.943, pvalue=0.17282 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66922 66666.7 0.978 0.978 2 37740 37654.3 0.195 1.173 3 26942 26954.7 0.006 1.179 4 18957 19313.5 6.579 7.758 5 13944 13851.4 0.619 8.377 6 9738 9943.5 4.249 12.626 7 7134 7145.0 0.017 12.643 8 5181 5139.1 0.342 12.985 9 3741 3699.9 0.457 13.442 10 2622 2666.3 0.736 14.178 11 1912 1923.3 0.067 14.245 12 1465 1388.7 4.188 18.432 13 1025 1003.7 0.451 18.884 14 754 726.1 1.069 19.953 15 519 525.8 0.089 20.041 16 399 381.2 0.836 20.877 17 263 276.5 0.663 21.540 18 186 200.8 1.095 22.635 19 161 146.0 1.544 24.180 20 109 106.2 0.073 24.253 21 286 287.1 0.004 24.257 Chisq= 24.26 for 20 degrees of freedom, p= 0.76866 SUMMARY of craptest p-value for no. of wins: 0.172819 p-value for throws/game: 0.768658 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-07_02:31 No. of wins: Observed Expected 98764 98585.9 z-score= 0.797, pvalue=0.78720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66467 66666.7 0.598 0.598 2 37764 37654.3 0.319 0.917 3 27008 26954.7 0.105 1.023 4 19187 19313.5 0.828 1.851 5 13834 13851.4 0.022 1.873 6 9985 9943.5 0.173 2.046 7 7111 7145.0 0.162 2.208 8 5212 5139.1 1.035 3.242 9 3675 3699.9 0.167 3.410 10 2704 2666.3 0.533 3.943 11 2003 1923.3 3.300 7.243 12 1414 1388.7 0.459 7.702 13 1012 1003.7 0.068 7.771 14 727 726.1 0.001 7.772 15 516 525.8 0.184 7.956 16 382 381.2 0.002 7.958 17 257 276.5 1.381 9.338 18 204 200.8 0.050 9.388 19 178 146.0 7.021 16.410 20 93 106.2 1.644 18.054 21 267 287.1 1.409 19.463 Chisq= 19.46 for 20 degrees of freedom, p= 0.50806 SUMMARY of craptest p-value for no. of wins: 0.787203 p-value for throws/game: 0.508059 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0060,0.0068,0.0138,0.0175,0.0201,0.0210,0.0211,0.0253,0.0258, 0.0266,0.0266,0.0386,0.0445,0.0491,0.0526,0.0531,0.0593,0.0610,0.0706, 0.0804,0.0821,0.0879,0.0890,0.0896,0.0901,0.0902,0.0925,0.0957,0.0978, 0.0990,0.1055,0.1057,0.1064,0.1099,0.1140,0.1158,0.1165,0.1390,0.1466, 0.1495,0.1528,0.1676,0.1728,0.1737,0.1767,0.1780,0.1788,0.1806,0.1833, 0.1880,0.1906,0.1916,0.1918,0.2004,0.2044,0.2064,0.2186,0.2206,0.2321, 0.2381,0.2393,0.2467,0.2480,0.2524,0.2558,0.2558,0.2602,0.2615,0.2723, 0.2727,0.2733,0.2807,0.2864,0.2943,0.2957,0.3028,0.3115,0.3135,0.3146, 0.3170,0.3202,0.3213,0.3223,0.3232,0.3245,0.3277,0.3329,0.3362,0.3392, 0.3392,0.3406,0.3418,0.3458,0.3464,0.3584,0.3593,0.3610,0.3645,0.3702, 0.3782,0.3860,0.3866,0.3871,0.3881,0.4038,0.4055,0.4097,0.4122,0.4143, 0.4210,0.4272,0.4334,0.4368,0.4451,0.4467,0.4550,0.4555,0.4570,0.4589, 0.4611,0.4726,0.4779,0.4789,0.4835,0.4852,0.4857,0.4885,0.4899,0.4909, 0.4955,0.4969,0.5000,0.5055,0.5081,0.5099,0.5114,0.5154,0.5257,0.5325, 0.5345,0.5351,0.5398,0.5414,0.5439,0.5571,0.5571,0.5580,0.5612,0.5612, 0.5617,0.5620,0.5626,0.5635,0.5645,0.5673,0.5702,0.5721,0.5762,0.5793, 0.5926,0.5930,0.5931,0.5932,0.5956,0.5959,0.6001,0.6016,0.6032,0.6079, 0.6089,0.6110,0.6157,0.6190,0.6212,0.6277,0.6322,0.6328,0.6346,0.6373, 0.6374,0.6386,0.6388,0.6422,0.6498,0.6591,0.6592,0.6596,0.6644,0.6714, 0.6726,0.6780,0.6817,0.6857,0.7114,0.7137,0.7180,0.7201,0.7231,0.7233, 0.7299,0.7323,0.7381,0.7464,0.7472,0.7518,0.7529,0.7529,0.7533,0.7553, 0.7582,0.7610,0.7620,0.7653,0.7674,0.7687,0.7711,0.7779,0.7783,0.7794, 0.7872,0.7920,0.7947,0.7961,0.7990,0.8211,0.8369,0.8379,0.8410,0.8532, 0.8570,0.8590,0.8591,0.8632,0.8683,0.8692,0.8698,0.8717,0.8767,0.8820, 0.8820,0.8860,0.8873,0.8916,0.8949,0.8961,0.8978,0.9005,0.9015,0.9054, 0.9073,0.9138,0.9175,0.9206,0.9261,0.9274,0.9330,0.9339,0.9500,0.9544, 0.9555,0.9565,0.9609,0.9681,0.9713,0.9857,0.9913,0.9963,0.9980, Overall p-value after applying KStest on 269 p-values = 0.747482 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.