RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-03-31_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.30 24.9146 0.903363 2 to 25 15.47 18.2869 0.629042 3 to 26 15.46 24.9389 0.903915 4 to 27 16.03 21.8711 0.810274 5 to 28 15.52 25.9231 0.924127 6 to 29 15.64 12.0882 0.205234 7 to 30 16.02 12.2460 0.214984 8 to 31 15.66 25.1266 0.908088 9 to 32 15.72 24.2987 0.888456 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.015302 Tough bday spacings test for dh-ranFile-2017-03-31_22:31: 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 34 74 114 102 76 46 28 8 5 4 (O-E)^2/E 0.0 0.2 0.0 2.7 0.2 0.1 0.7 0.1 3.2 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.574, p= 0.330 RESULTS OF GCD FOR dh-ranFile-2017-03-31_22:31 Euclid's algorithm: p-value, steps to gcd: 0.443314 p-value, dist. of gcd's: 0.365061 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-03-31_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.133 0.582 0.928 0.944 0.895 0.554 0.957 0.186 Bits 8 to 15---> 0.310 0.171 0.964 0.585 0.638 0.273 0.243 0.412 Bits 16 to 23---> 0.950 0.508 0.552 0.480 0.669 0.048 0.526 0.369 Bits 24 to 31---> 0.289 0.886 0.892 0.339 0.610 0.490 0.979 0.437 KS test for the above 32 p values: 0.776 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-03-31_22:31, p-values for 5 runs: 0.3636, 0.3860, 0.3960, 0.3388, 0.9748 Rank test for binary matrices (31x31) for dh-ranFile-2017-03-31_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 184 211.4 3.556 3.556 r= 29 5126 5134.0 0.012 3.568 r= 30 23143 23103.0 0.069 3.637 r= 31 11547 11551.5 0.002 3.639 chi-square = 3.639 with df = 3; p-value = 0.697 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-03-31_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5096 5134.0 0.281 1.287 r= 31 23074 23103.0 0.037 1.324 r= 32 11604 11551.5 0.238 1.562 chi-square = 1.562 with df = 3; p-value = 0.332 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-03-31_22:31 b-rank test for bits 1 to 8, p=0.40091 b-rank test for bits 2 to 9, p=0.76839 b-rank test for bits 3 to 10, p=0.65346 b-rank test for bits 4 to 11, p=0.66051 b-rank test for bits 5 to 12, p=0.31203 b-rank test for bits 6 to 13, p=0.81186 b-rank test for bits 7 to 14, p=0.99821 b-rank test for bits 8 to 15, p=0.91518 b-rank test for bits 9 to 16, p=0.90487 b-rank test for bits 10 to 17, p=0.88562 b-rank test for bits 11 to 18, p=0.77803 b-rank test for bits 12 to 19, p=0.98918 b-rank test for bits 13 to 20, p=0.24986 b-rank test for bits 14 to 21, p=0.26745 b-rank test for bits 15 to 22, p=0.53377 b-rank test for bits 16 to 23, p=0.38416 b-rank test for bits 17 to 24, p=0.63970 b-rank test for bits 18 to 25, p=0.17227 b-rank test for bits 19 to 26, p=0.06118 b-rank test for bits 20 to 27, p=0.48346 b-rank test for bits 21 to 28, p=0.80402 b-rank test for bits 22 to 29, p=0.65828 b-rank test for bits 23 to 30, p=0.65755 b-rank test for bits 24 to 31, p=0.49636 b-rank test for bits 25 to 32, p=0.85221 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 = 0.075830 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-03-31_22:31 (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 142202 0.68 0.752952 2 141848 -0.14 0.443029 3 142391 1.13 0.869790 4 142056 0.34 0.634083 5 140884 -2.40 0.008296 6 141670 -0.56 0.288019 7 141744 -0.39 0.349643 8 142024 0.27 0.605620 9 141963 0.13 0.549895 10 142461 1.29 0.901292 11 142654 1.74 0.959060 12 141834 -0.18 0.430145 13 141419 -1.15 0.125974 14 141733 -0.41 0.340175 15 142060 0.35 0.637593 16 141796 -0.26 0.395586 17 141822 -0.20 0.419160 18 141581 -0.77 0.221503 19 141928 0.04 0.517397 20 142199 0.68 0.750733 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-03-31_22:31 Bits used No. missing words z-score p-value 23 to 32 141226 -2.3563 0.009229 22 to 31 141771 -0.4770 0.316681 21 to 30 142294 1.3264 0.907654 20 to 29 141233 -2.3322 0.009846 19 to 28 141614 -1.0184 0.154249 18 to 27 141902 -0.0253 0.489918 17 to 26 141951 0.1437 0.557127 16 to 25 141570 -1.1701 0.120980 15 to 24 142237 1.1299 0.870740 14 to 23 142051 0.4885 0.687408 13 to 22 141553 -1.2287 0.109588 12 to 21 141749 -0.5529 0.290179 11 to 20 141202 -2.4391 0.007363 10 to 19 142112 0.6989 0.757681 9 to 18 141852 -0.1977 0.421644 8 to 17 142361 1.5575 0.940322 7 to 16 142551 2.2127 0.986539 6 to 15 141824 -0.2942 0.384287 5 to 14 142024 0.3954 0.653731 4 to 13 141886 -0.0804 0.467940 3 to 12 141446 -1.5977 0.055056 2 to 11 142114 0.7058 0.759831 1 to 10 141976 0.2299 0.590914 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-03-31_22:31 Bits used No. missing words z-score p-value 28 to 32 141405 -1.7096 0.043671 27 to 31 141825 -0.2859 0.387491 26 to 30 141960 0.1718 0.568188 25 to 29 142158 0.8429 0.800372 24 to 28 142110 0.6802 0.751823 23 to 27 142284 1.2701 0.897970 22 to 26 141623 -0.9706 0.165871 21 to 25 141962 0.1785 0.570852 20 to 24 141639 -0.9164 0.179736 19 to 23 141914 0.0158 0.506315 18 to 22 142106 0.6667 0.747511 17 to 21 141761 -0.5028 0.307548 16 to 20 141988 0.2667 0.605141 15 to 19 141626 -0.9604 0.168417 14 to 18 142148 0.8091 0.790757 13 to 17 141856 -0.1808 0.428270 12 to 16 142127 0.7379 0.769702 11 to 15 141954 0.1514 0.560179 10 to 14 141400 -1.7265 0.042125 9 to 13 141530 -1.2859 0.099245 8 to 12 141782 -0.4316 0.333006 7 to 11 142096 0.6328 0.736561 6 to 10 142060 0.5107 0.695236 5 to 9 142150 0.8158 0.792702 4 to 8 142401 1.6667 0.952211 3 to 7 141886 -0.0791 0.468483 2 to 6 141748 -0.5469 0.292230 1 to 5 142165 0.8667 0.806941 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-03-31_22:31 Bits used No. missing words z-score p-value 31 to 32 141885 -0.0718 0.471393 30 to 31 142559 1.9164 0.972345 29 to 30 141403 -1.4936 0.067640 28 to 29 141963 0.1583 0.562897 27 to 28 142001 0.2704 0.606579 26 to 27 141437 -1.3933 0.081764 25 to 26 141999 0.2645 0.604308 24 to 25 141928 0.0551 0.521960 23 to 24 141757 -0.4494 0.326589 22 to 23 141876 -0.0983 0.460840 21 to 22 142099 0.5595 0.712089 20 to 21 141329 -1.7119 0.043459 19 to 20 141702 -0.6116 0.270404 18 to 19 141931 0.0639 0.525484 17 to 18 142022 0.3324 0.630191 16 to 17 141850 -0.1750 0.430534 15 to 16 141609 -0.8859 0.187828 14 to 15 142076 0.4917 0.688517 13 to 14 142046 0.4032 0.656583 12 to 13 141452 -1.3491 0.088660 11 to 12 142464 1.6362 0.949101 10 to 11 142085 0.5182 0.697841 9 to 10 141620 -0.8535 0.196696 8 to 9 142130 0.6509 0.742459 7 to 8 142339 1.2675 0.897505 6 to 7 141781 -0.3786 0.352509 5 to 6 142185 0.8132 0.791944 4 to 5 141741 -0.4965 0.309754 3 to 4 142099 0.5595 0.712089 2 to 3 141881 -0.0836 0.466699 1 to 2 142282 1.0993 0.864186 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-03-31_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2435.13 -0.917 0.179471 Test results for specific bytes for dh-ranFile-2017-03-31_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2521.91 0.310 0.621645 2 to 9 2426.60 -1.038 0.149613 3 to 10 2579.47 1.124 0.869458 4 to 11 2477.95 -0.312 0.377610 5 to 12 2520.30 0.287 0.612996 6 to 13 2426.19 -1.044 0.148272 7 to 14 2450.77 -0.696 0.243161 8 to 15 2474.07 -0.367 0.356895 9 to 16 2570.56 0.998 0.840833 10 to 17 2513.43 0.190 0.575311 11 to 18 2541.78 0.591 0.722670 12 to 19 2498.97 -0.015 0.494177 13 to 20 2451.38 -0.688 0.245842 14 to 21 2552.58 0.744 0.771451 15 to 22 2425.88 -1.048 0.147285 16 to 23 2377.09 -1.738 0.041086 17 to 24 2488.21 -0.167 0.433782 18 to 25 2532.62 0.461 0.677735 19 to 26 2598.76 1.397 0.918753 20 to 27 2389.92 -1.557 0.059758 21 to 28 2426.55 -1.039 0.149468 22 to 29 2373.63 -1.787 0.036956 23 to 30 2511.60 0.164 0.565131 24 to 31 2379.88 -1.699 0.044681 25 to 32 2459.26 -0.576 0.282251 CDPARK for dh-ranFile-2017-03-31_22:31: 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 3539 0.7306 0.767486 3481 -1.9178 0.027568 3508 -0.6849 0.246694 3526 0.1370 0.554479 3521 -0.0913 0.463617 3510 -0.5936 0.276387 3548 1.1416 0.873180 3521 -0.0913 0.463617 3515 -0.3653 0.357445 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3519.00 sample std.=17.22 p-value of the KSTEST for those 10 p-values: 0.651611 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-03-31_22:31 0.9535,0.2917,0.6726,0.7095,0.1920,0.0604,0.6585,0.2027,0.6861,0.3653, The KS test for those 10 p-values: 0.912941 The 3DSPHERES test for dh-ranFile-2017-03-31_22:31 sample no r^3 equiv. uni. 1 3.518 0.110664 2 0.006 0.000212 3 100.111 0.964458 4 62.604 0.875916 5 14.526 0.383808 6 36.628 0.705049 7 20.315 0.491941 8 16.258 0.418385 9 8.577 0.248651 10 23.806 0.547755 11 46.264 0.786079 12 41.719 0.751081 13 2.769 0.088174 14 11.834 0.325951 15 45.961 0.783902 16 88.061 0.946889 17 73.506 0.913724 18 8.797 0.254141 19 5.204 0.159261 20 100.779 0.965240 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.512816 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-03-31_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.6 0.8 0.1 0.5 -1.1 2.5 1.1 1.5 0.2 -2.4 -0.1 0.7 -0.2 -1.1 1.1 -0.9 -0.3 0.6 0.8 -1.6 0.0 0.6 -1.0 0.9 -0.8 0.0 -0.6 2.2 0.8 1.0 0.2 0.0 -0.8 0.4 -1.2 0.8 -0.4 -0.1 1.6 -1.0 1.8 Chi-square with 42 degrees of freedom:44.859254 z-score=0.311970, p-value=0.647128 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-03-31_22:31 Test no p-value 1 0.116629 2 0.219290 3 0.903841 4 0.148795 5 0.092340 6 0.916077 7 0.871880 8 0.277725 9 0.022354 10 0.324038 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.133820 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-03-31_22:31: (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 66537 0.25 66837 0.44 3 25000.00 25096 0.37 24892 0.47 4 6666.67 6647 0.06 6644 0.08 5 1388.89 1454 3.05 1349 1.15 6 238.10 226 0.61 227 0.52 7 34.72 33 0.09 46 3.66 8 4.96 6 0.22 4 0.19 p=0.41043 p=0.62962 Number of rngs required: 687426, p-value: 0.128 RESULTS OF CRAPS TEST for dh-ranFile-2017-03-31_22:31 No. of wins: Observed Expected 98521 98585.9 z-score=-0.290, pvalue=0.38588 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66898 66666.7 0.803 0.803 2 37434 37654.3 1.289 2.092 3 27246 26954.7 3.147 5.239 4 19312 19313.5 0.000 5.239 5 13827 13851.4 0.043 5.282 6 10026 9943.5 0.684 5.966 7 7042 7145.0 1.486 7.452 8 5014 5139.1 3.044 10.496 9 3651 3699.9 0.645 11.141 10 2563 2666.3 4.002 15.143 11 1892 1923.3 0.510 15.653 12 1387 1388.7 0.002 15.655 13 1010 1003.7 0.039 15.695 14 738 726.1 0.194 15.889 15 573 525.8 4.230 20.119 16 369 381.2 0.387 20.506 17 280 276.5 0.043 20.549 18 198 200.8 0.040 20.589 19 140 146.0 0.245 20.835 20 96 106.2 0.982 21.817 21 304 287.1 0.993 22.810 Chisq= 22.81 for 20 degrees of freedom, p= 0.70179 SUMMARY of craptest p-value for no. of wins: 0.385875 p-value for throws/game: 0.701792 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-03-31_22:31 No. of wins: Observed Expected 98349 98585.9 z-score=-1.059, pvalue=0.14472 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66949 66666.7 1.196 1.196 2 37561 37654.3 0.231 1.427 3 26867 26954.7 0.286 1.713 4 19387 19313.5 0.280 1.993 5 13695 13851.4 1.766 3.759 6 9954 9943.5 0.011 3.770 7 7173 7145.0 0.110 3.879 8 5135 5139.1 0.003 3.883 9 3768 3699.9 1.255 5.137 10 2680 2666.3 0.070 5.208 11 1933 1923.3 0.049 5.256 12 1357 1388.7 0.725 5.982 13 923 1003.7 6.491 12.473 14 710 726.1 0.359 12.831 15 536 525.8 0.196 13.028 16 387 381.2 0.090 13.118 17 254 276.5 1.837 14.955 18 193 200.8 0.305 15.260 19 168 146.0 3.320 18.580 20 87 106.2 3.476 22.056 21 283 287.1 0.059 22.115 Chisq= 22.12 for 20 degrees of freedom, p= 0.66572 SUMMARY of craptest p-value for no. of wins: 0.144716 p-value for throws/game: 0.665716 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0074,0.0083,0.0092,0.0098,0.0153,0.0224,0.0276,0.0370,0.0411, 0.0421,0.0435,0.0437,0.0447,0.0479,0.0551,0.0598,0.0604,0.0612,0.0676, 0.0758,0.0818,0.0882,0.0887,0.0923,0.0992,0.1096,0.1107,0.1166,0.1210, 0.1260,0.1284,0.1328,0.1338,0.1447,0.1473,0.1483,0.1488,0.1495,0.1496, 0.1542,0.1593,0.1659,0.1684,0.1710,0.1723,0.1795,0.1797,0.1863,0.1878, 0.1920,0.1967,0.2027,0.2052,0.2150,0.2193,0.2215,0.2431,0.2432,0.2458, 0.2467,0.2487,0.2499,0.2541,0.2674,0.2704,0.2734,0.2764,0.2777,0.2823, 0.2880,0.2885,0.2902,0.2917,0.2922,0.3075,0.3098,0.3105,0.3120,0.3167, 0.3240,0.3260,0.3266,0.3296,0.3320,0.3330,0.3388,0.3394,0.3402,0.3496, 0.3525,0.3569,0.3574,0.3636,0.3651,0.3653,0.3694,0.3776,0.3838,0.3842, 0.3843,0.3859,0.3860,0.3875,0.3956,0.3960,0.4009,0.4104,0.4124,0.4184, 0.4192,0.4216,0.4283,0.4301,0.4305,0.4338,0.4374,0.4430,0.4433,0.4608, 0.4636,0.4636,0.4636,0.4667,0.4679,0.4685,0.4714,0.4800,0.4835,0.4896, 0.4899,0.4919,0.4942,0.4964,0.5063,0.5084,0.5128,0.5174,0.5220,0.5255, 0.5263,0.5338,0.5478,0.5499,0.5518,0.5541,0.5545,0.5571,0.5602,0.5629, 0.5651,0.5682,0.5709,0.5753,0.5825,0.5845,0.5909,0.6043,0.6051,0.6056, 0.6066,0.6104,0.6130,0.6216,0.6290,0.6296,0.6302,0.6341,0.6376,0.6376, 0.6397,0.6471,0.6516,0.6535,0.6537,0.6566,0.6575,0.6583,0.6585,0.6605, 0.6657,0.6694,0.6726,0.6777,0.6861,0.6874,0.6885,0.6952,0.6968,0.6978, 0.7018,0.7050,0.7095,0.7121,0.7121,0.7227,0.7366,0.7425,0.7475,0.7507, 0.7511,0.7518,0.7530,0.7577,0.7598,0.7675,0.7684,0.7697,0.7715,0.7758, 0.7780,0.7839,0.7861,0.7908,0.7919,0.7927,0.8004,0.8040,0.8069,0.8103, 0.8119,0.8408,0.8522,0.8642,0.8695,0.8698,0.8707,0.8719,0.8732,0.8759, 0.8856,0.8859,0.8885,0.8916,0.8946,0.8975,0.8980,0.9013,0.9034,0.9038, 0.9039,0.9049,0.9077,0.9081,0.9129,0.9137,0.9152,0.9161,0.9188,0.9241, 0.9276,0.9403,0.9440,0.9469,0.9491,0.9504,0.9522,0.9535,0.9569,0.9591, 0.9642,0.9645,0.9652,0.9723,0.9748,0.9793,0.9865,0.9892,0.9982, Overall p-value after applying KStest on 269 p-values = 0.941226 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.