RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-29_17:31 (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 16.0783 0.481708 2 to 25 15.70 12.9654 0.261498 3 to 26 15.69 18.2064 0.624067 4 to 27 15.90 25.6180 0.918293 5 to 28 16.20 15.2881 0.425258 6 to 29 16.14 11.1483 0.151247 7 to 30 15.87 9.3738 0.072200 8 to 31 16.22 15.5554 0.444458 9 to 32 15.95 13.4383 0.293611 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.537315 Tough bday spacings test for dh-ranFile-2016-08-29_17:31: 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 9 32 71 106 102 79 54 25 15 4 3 (O-E)^2/E 0.0 0.6 0.1 0.7 0.2 0.0 0.1 0.8 0.0 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 3.715, p= 0.041 RESULTS OF GCD FOR dh-ranFile-2016-08-29_17:31 Euclid's algorithm: p-value, steps to gcd: 0.183532 p-value, dist. of gcd's: 0.377403 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-29_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.950 0.943 0.959 0.784 0.465 0.059 0.303 0.779 Bits 8 to 15---> 0.748 0.460 0.365 0.742 0.582 0.728 0.505 0.357 Bits 16 to 23---> 0.324 0.085 0.335 0.055 0.006 0.425 0.291 0.201 Bits 24 to 31---> 0.856 0.449 0.625 0.500 0.229 0.794 0.856 0.155 KS test for the above 32 p values: 0.014 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-29_17:31, p-values for 5 runs: 0.9141, 0.7523, 0.4214, 0.8216, 0.2240 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-29_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5166 5134.0 0.199 0.292 r= 30 23045 23103.0 0.146 0.437 r= 31 11582 11551.5 0.080 0.518 chi-square = 0.518 with df = 3; p-value = 0.085 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-29_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5227 5134.0 1.684 2.833 r= 31 22965 23103.0 0.825 3.658 r= 32 11581 11551.5 0.075 3.733 chi-square = 3.733 with df = 3; p-value = 0.708 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-29_17:31 b-rank test for bits 1 to 8, p=0.30223 b-rank test for bits 2 to 9, p=0.36833 b-rank test for bits 3 to 10, p=0.46609 b-rank test for bits 4 to 11, p=0.46267 b-rank test for bits 5 to 12, p=0.40433 b-rank test for bits 6 to 13, p=0.13850 b-rank test for bits 7 to 14, p=0.65794 b-rank test for bits 8 to 15, p=0.90284 b-rank test for bits 9 to 16, p=0.49964 b-rank test for bits 10 to 17, p=0.98547 b-rank test for bits 11 to 18, p=0.29063 b-rank test for bits 12 to 19, p=0.86215 b-rank test for bits 13 to 20, p=0.67659 b-rank test for bits 14 to 21, p=0.86815 b-rank test for bits 15 to 22, p=0.08983 b-rank test for bits 16 to 23, p=0.36319 b-rank test for bits 17 to 24, p=0.65512 b-rank test for bits 18 to 25, p=0.63992 b-rank test for bits 19 to 26, p=0.74038 b-rank test for bits 20 to 27, p=0.31890 b-rank test for bits 21 to 28, p=0.39638 b-rank test for bits 22 to 29, p=0.76013 b-rank test for bits 23 to 30, p=0.17143 b-rank test for bits 24 to 31, p=0.61182 b-rank test for bits 25 to 32, p=0.27365 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 = 0.675344 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-29_17:31 (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 142172 0.61 0.730298 2 143150 2.90 0.998127 3 141964 0.13 0.550820 4 141551 -0.84 0.201235 5 141431 -1.12 0.131870 6 142168 0.60 0.727201 7 141448 -1.08 0.140545 8 141327 -1.36 0.086823 9 141568 -0.80 0.212580 10 142261 0.82 0.794364 11 141975 0.15 0.560972 12 141778 -0.31 0.379480 13 142723 1.90 0.971355 14 141783 -0.30 0.383935 15 141905 -0.01 0.495964 16 142129 0.51 0.696111 17 141056 -1.99 0.023089 18 142325 0.97 0.834274 19 141625 -0.66 0.253242 20 141907 -0.01 0.497828 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-29_17:31 Bits used No. missing words z-score p-value 23 to 32 141506 -1.3908 0.082144 22 to 31 141941 0.1092 0.543481 21 to 30 142191 0.9713 0.834295 20 to 29 141667 -0.8356 0.201684 19 to 28 141615 -1.0149 0.155069 18 to 27 141970 0.2092 0.582857 17 to 26 142135 0.7782 0.781766 16 to 25 141492 -1.4391 0.075066 15 to 24 142136 0.7816 0.782781 14 to 23 142195 0.9851 0.837705 13 to 22 141439 -1.6218 0.052420 12 to 21 142543 2.1851 0.985558 11 to 20 142044 0.4644 0.678812 10 to 19 142263 1.2196 0.888683 9 to 18 141556 -1.2184 0.111540 8 to 17 141980 0.2437 0.596264 7 to 16 142446 1.8506 0.967885 6 to 15 141366 -1.8736 0.030496 5 to 14 141778 -0.4529 0.325324 4 to 13 141481 -1.4770 0.069838 3 to 12 142036 0.4368 0.668869 2 to 11 141492 -1.4391 0.075066 1 to 10 141612 -1.0253 0.152617 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-29_17:31 Bits used No. missing words z-score p-value 28 to 32 142235 1.1040 0.865196 27 to 31 141864 -0.1537 0.438939 26 to 30 142257 1.1785 0.880710 25 to 29 141740 -0.5740 0.282984 24 to 28 141503 -1.3774 0.084196 23 to 27 142426 1.7514 0.960064 22 to 26 141627 -0.9571 0.169271 21 to 25 141861 -0.1638 0.434932 20 to 24 141991 0.2768 0.609051 19 to 23 141753 -0.5299 0.298080 18 to 22 141838 -0.2418 0.404469 17 to 21 141751 -0.5367 0.295733 16 to 20 141795 -0.3876 0.349171 15 to 19 141638 -0.9198 0.178848 14 to 18 142156 0.8362 0.798470 13 to 17 142079 0.5752 0.717406 12 to 16 141729 -0.6113 0.270504 11 to 15 141992 0.2802 0.610352 10 to 14 141509 -1.3571 0.087383 9 to 13 141805 -0.3537 0.361797 8 to 12 141796 -0.3842 0.350426 7 to 11 141702 -0.7028 0.241086 6 to 10 141928 0.0633 0.525232 5 to 9 142434 1.7785 0.962343 4 to 8 141971 0.2091 0.582796 3 to 7 141999 0.3040 0.619423 2 to 6 141445 -1.5740 0.057744 1 to 5 141991 0.2768 0.609051 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-29_17:31 Bits used No. missing words z-score p-value 31 to 32 141996 0.2557 0.600895 30 to 31 141743 -0.4906 0.311837 29 to 30 141683 -0.6676 0.252182 28 to 29 142429 1.5329 0.937356 27 to 28 142208 0.8810 0.810850 26 to 27 141976 0.1967 0.577956 25 to 26 142109 0.5890 0.722068 24 to 25 142305 1.1672 0.878429 23 to 24 141555 -1.0452 0.147960 22 to 23 142323 1.2203 0.888818 21 to 22 142066 0.4622 0.678014 20 to 21 141956 0.1377 0.554749 19 to 20 141590 -0.9420 0.173102 18 to 19 142071 0.4769 0.683284 17 to 18 141425 -1.4287 0.076545 16 to 17 141414 -1.4612 0.071987 15 to 16 142010 0.2970 0.616752 14 to 15 142079 0.5005 0.691639 13 to 14 141894 -0.0452 0.481966 12 to 13 141632 -0.8181 0.206655 11 to 12 142027 0.3471 0.635745 10 to 11 141670 -0.7060 0.240098 9 to 10 141990 0.2380 0.594046 8 to 9 142236 0.9636 0.832384 7 to 8 142093 0.5418 0.706022 6 to 7 141555 -1.0452 0.147960 5 to 6 141708 -0.5939 0.276292 4 to 5 141803 -0.3137 0.376891 3 to 4 141776 -0.3933 0.347048 2 to 3 142190 0.8279 0.796146 1 to 2 142130 0.6509 0.742459 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-29_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2502.06 0.029 0.511605 Test results for specific bytes for dh-ranFile-2016-08-29_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2556.42 0.798 0.787517 2 to 9 2403.07 -1.371 0.085212 3 to 10 2418.34 -1.155 0.124072 4 to 11 2567.76 0.958 0.831032 5 to 12 2387.45 -1.592 0.055725 6 to 13 2444.44 -0.786 0.216018 7 to 14 2568.22 0.965 0.832654 8 to 15 2609.00 1.542 0.938410 9 to 16 2548.54 0.686 0.753798 10 to 17 2536.12 0.511 0.695238 11 to 18 2549.96 0.707 0.760077 12 to 19 2597.69 1.382 0.916446 13 to 20 2490.22 -0.138 0.445017 14 to 21 2423.37 -1.084 0.139250 15 to 22 2582.59 1.168 0.878596 16 to 23 2505.11 0.072 0.528831 17 to 24 2575.09 1.062 0.855852 18 to 25 2462.99 -0.523 0.300342 19 to 26 2513.57 0.192 0.576078 20 to 27 2538.41 0.543 0.706509 21 to 28 2458.94 -0.581 0.280727 22 to 29 2474.53 -0.360 0.359341 23 to 30 2502.04 0.029 0.511531 24 to 31 2469.21 -0.435 0.331608 25 to 32 2501.26 0.018 0.507112 CDPARK for dh-ranFile-2016-08-29_17:31: 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 3534 0.5023 0.692266 3560 1.6895 0.954438 3534 0.5023 0.692266 3547 1.0959 0.863437 3523 0.0000 0.500000 3529 0.2740 0.607947 3518 -0.2283 0.409702 3506 -0.7763 0.218799 3522 -0.0457 0.481790 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3527.50 sample std.=16.66 p-value of the KSTEST for those 10 p-values: 0.775152 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-29_17:31 0.4272,0.9278,0.2515,0.0007,0.8074,0.9240,0.1727,0.5085,0.3338,0.4000, The KS test for those 10 p-values: 0.602145 The 3DSPHERES test for dh-ranFile-2016-08-29_17:31 sample no r^3 equiv. uni. 1 27.584 0.601262 2 27.765 0.603670 3 17.753 0.446660 4 28.960 0.619141 5 18.311 0.456846 6 13.139 0.354658 7 4.405 0.136560 8 65.217 0.886265 9 1.252 0.040874 10 7.773 0.228254 11 4.247 0.131988 12 3.231 0.102115 13 14.740 0.388200 14 22.422 0.526400 15 10.394 0.292819 16 24.756 0.561850 17 39.032 0.727755 18 4.571 0.141326 19 59.942 0.864403 20 6.093 0.183802 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.285638 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-29_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -1.3 0.5 0.5 -1.5 -1.6 -0.7 -0.5 0.3 -0.1 0.5 -0.1 -0.0 0.5 1.0 -1.4 -0.6 0.6 0.7 0.8 -0.1 1.2 -1.2 -2.2 -0.3 -0.8 0.8 1.4 -0.7 1.8 0.2 -0.1 -0.6 -0.1 1.1 0.0 0.5 1.3 -1.3 1.6 1.0 -1.1 Chi-square with 42 degrees of freedom:39.784695 z-score=-0.241710, p-value=0.431345 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-29_17:31 Test no p-value 1 0.178934 2 0.281187 3 0.411801 4 0.542550 5 0.057150 6 0.751535 7 0.048783 8 0.533272 9 0.001640 10 0.318772 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.047855 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-29_17:31: (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 66742 0.09 66961 1.30 3 25000.00 24799 1.62 24776 2.01 4 6666.67 6800 2.67 6585 1.00 5 1388.89 1394 0.02 1369 0.28 6 238.10 231 0.21 268 3.76 7 34.72 30 0.64 36 0.05 8 4.96 3 0.77 4 0.19 p=0.57839 p=0.80144 Number of rngs required: 688364, p-value: 0.482 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-29_17:31 No. of wins: Observed Expected 98685 98585.9 z-score= 0.443, pvalue=0.67127 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66753 66666.7 0.112 0.112 2 37790 37654.3 0.489 0.601 3 26878 26954.7 0.218 0.819 4 19215 19313.5 0.502 1.321 5 13882 13851.4 0.068 1.389 6 9870 9943.5 0.544 1.933 7 7215 7145.0 0.685 2.618 8 5203 5139.1 0.795 3.413 9 3601 3699.9 2.642 6.055 10 2637 2666.3 0.322 6.377 11 1899 1923.3 0.308 6.685 12 1401 1388.7 0.108 6.793 13 955 1003.7 2.364 9.157 14 732 726.1 0.047 9.204 15 521 525.8 0.044 9.249 16 382 381.2 0.002 9.251 17 289 276.5 0.561 9.812 18 217 200.8 1.302 11.114 19 157 146.0 0.831 11.945 20 106 106.2 0.000 11.946 21 297 287.1 0.340 12.286 Chisq= 12.29 for 20 degrees of freedom, p= 0.09413 SUMMARY of craptest p-value for no. of wins: 0.671268 p-value for throws/game: 0.094128 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-29_17:31 No. of wins: Observed Expected 98629 98585.9 z-score= 0.193, pvalue=0.57650 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66593 66666.7 0.081 0.081 2 37677 37654.3 0.014 0.095 3 26961 26954.7 0.001 0.097 4 19418 19313.5 0.566 0.662 5 13794 13851.4 0.238 0.900 6 9864 9943.5 0.636 1.537 7 7157 7145.0 0.020 1.557 8 5192 5139.1 0.545 2.102 9 3740 3699.9 0.435 2.537 10 2686 2666.3 0.146 2.683 11 1800 1923.3 7.908 10.591 12 1368 1388.7 0.310 10.901 13 1021 1003.7 0.298 11.198 14 735 726.1 0.108 11.307 15 493 525.8 2.050 13.357 16 393 381.2 0.368 13.725 17 288 276.5 0.475 14.200 18 207 200.8 0.190 14.390 19 174 146.0 5.376 19.766 20 118 106.2 1.308 21.074 21 321 287.1 3.999 25.073 Chisq= 25.07 for 20 degrees of freedom, p= 0.80135 SUMMARY of craptest p-value for no. of wins: 0.576502 p-value for throws/game: 0.801353 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0016,0.0063,0.0144,0.0231,0.0305,0.0407,0.0409,0.0479,0.0488, 0.0524,0.0555,0.0557,0.0572,0.0577,0.0594,0.0698,0.0720,0.0722,0.0751, 0.0751,0.0765,0.0821,0.0842,0.0847,0.0851,0.0852,0.0868,0.0874,0.0898, 0.0941,0.1021,0.1115,0.1241,0.1319,0.1320,0.1366,0.1385,0.1392,0.1405, 0.1413,0.1480,0.1480,0.1512,0.1526,0.1551,0.1554,0.1688,0.1693,0.1714, 0.1727,0.1731,0.1788,0.1789,0.1835,0.1838,0.2005,0.2012,0.2017,0.2067, 0.2126,0.2160,0.2188,0.2240,0.2283,0.2288,0.2401,0.2411,0.2515,0.2522, 0.2532,0.2615,0.2705,0.2736,0.2763,0.2807,0.2812,0.2830,0.2856,0.2906, 0.2912,0.2928,0.2936,0.2957,0.2981,0.3003,0.3022,0.3033,0.3118,0.3188, 0.3189,0.3242,0.3253,0.3316,0.3338,0.3351,0.3470,0.3492,0.3504,0.3547, 0.3573,0.3593,0.3618,0.3632,0.3653,0.3683,0.3769,0.3774,0.3795,0.3839, 0.3882,0.3964,0.4000,0.4043,0.4045,0.4097,0.4118,0.4214,0.4246,0.4253, 0.4272,0.4313,0.4349,0.4389,0.4445,0.4450,0.4467,0.4488,0.4568,0.4603, 0.4627,0.4646,0.4661,0.4817,0.4818,0.4820,0.4821,0.4960,0.4978,0.4996, 0.4999,0.5000,0.5050,0.5071,0.5085,0.5115,0.5116,0.5252,0.5264,0.5288, 0.5333,0.5373,0.5426,0.5435,0.5508,0.5547,0.5610,0.5618,0.5761,0.5765, 0.5780,0.5784,0.5816,0.5828,0.5829,0.5940,0.5963,0.6009,0.6013,0.6021, 0.6037,0.6079,0.6091,0.6091,0.6104,0.6118,0.6168,0.6191,0.6194,0.6241, 0.6250,0.6357,0.6399,0.6551,0.6579,0.6689,0.6713,0.6753,0.6766,0.6780, 0.6788,0.6833,0.6916,0.6923,0.6923,0.6952,0.6961,0.7060,0.7065,0.7082, 0.7174,0.7221,0.7272,0.7278,0.7281,0.7303,0.7404,0.7421,0.7425,0.7485, 0.7515,0.7523,0.7538,0.7601,0.7601,0.7752,0.7788,0.7818,0.7828,0.7839, 0.7875,0.7944,0.7944,0.7961,0.7985,0.8014,0.8014,0.8074,0.8108,0.8216, 0.8310,0.8324,0.8327,0.8343,0.8343,0.8377,0.8559,0.8559,0.8562,0.8622, 0.8634,0.8644,0.8652,0.8682,0.8784,0.8786,0.8807,0.8863,0.8887,0.8888, 0.9028,0.9141,0.9164,0.9183,0.9240,0.9278,0.9374,0.9384,0.9432,0.9502, 0.9544,0.9585,0.9601,0.9623,0.9679,0.9714,0.9855,0.9856,0.9981, Overall p-value after applying KStest on 269 p-values = 0.391422 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.