RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-03_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.50 16.3631 0.501743 2 to 25 15.77 20.6900 0.759535 3 to 26 15.75 9.2605 0.068267 4 to 27 15.70 17.9943 0.610800 5 to 28 15.88 10.2655 0.107891 6 to 29 15.75 7.9917 0.033276 7 to 30 15.72 14.5082 0.369140 8 to 31 16.07 20.0349 0.727552 9 to 32 16.04 21.5148 0.795895 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.610376 Tough bday spacings test for dh-ranFile-2018-04-03_23:31: 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 36 69 110 93 87 48 25 16 6 1 (O-E)^2/E 0.0 0.0 0.2 1.6 0.2 1.0 0.3 0.8 0.1 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 6.582, p= 0.236 RESULTS OF GCD FOR dh-ranFile-2018-04-03_23:31 Euclid's algorithm: p-value, steps to gcd: 0.754524 p-value, dist. of gcd's: 0.022045 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-03_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.061 0.719 0.662 0.450 0.952 0.500 0.737 0.715 Bits 8 to 15---> 0.354 0.258 0.477 0.073 0.718 0.173 0.004 0.234 Bits 16 to 23---> 0.562 0.301 0.423 0.579 0.413 0.250 0.841 0.580 Bits 24 to 31---> 0.938 0.631 0.512 0.237 0.408 0.947 0.190 0.812 KS test for the above 32 p values: 0.110 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-03_23:31, p-values for 5 runs: 0.9911, 0.8284, 0.4094, 0.5088, 0.2149 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-03_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5143 5134.0 0.016 0.288 r= 30 23082 23103.0 0.019 0.307 r= 31 11556 11551.5 0.002 0.309 chi-square = 0.309 with df = 3; p-value = 0.042 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-03_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5166 5134.0 0.199 0.535 r= 31 23096 23103.0 0.002 0.537 r= 32 11535 11551.5 0.024 0.560 chi-square = 0.560 with df = 3; p-value = 0.095 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-03_23:31 b-rank test for bits 1 to 8, p=0.09843 b-rank test for bits 2 to 9, p=0.23360 b-rank test for bits 3 to 10, p=0.87922 b-rank test for bits 4 to 11, p=0.15639 b-rank test for bits 5 to 12, p=0.90931 b-rank test for bits 6 to 13, p=0.04031 b-rank test for bits 7 to 14, p=0.96510 b-rank test for bits 8 to 15, p=0.16949 b-rank test for bits 9 to 16, p=0.41482 b-rank test for bits 10 to 17, p=0.47111 b-rank test for bits 11 to 18, p=0.13691 b-rank test for bits 12 to 19, p=0.04778 b-rank test for bits 13 to 20, p=0.51422 b-rank test for bits 14 to 21, p=0.49492 b-rank test for bits 15 to 22, p=0.41471 b-rank test for bits 16 to 23, p=0.19470 b-rank test for bits 17 to 24, p=0.43274 b-rank test for bits 18 to 25, p=0.86980 b-rank test for bits 19 to 26, p=0.62040 b-rank test for bits 20 to 27, p=0.18439 b-rank test for bits 21 to 28, p=0.81231 b-rank test for bits 22 to 29, p=0.25258 b-rank test for bits 23 to 30, p=0.45554 b-rank test for bits 24 to 31, p=0.22725 b-rank test for bits 25 to 32, p=0.07967 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 = 0.116139 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-03_23:31 (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 142267 0.84 0.798332 2 141884 -0.06 0.476404 3 141717 -0.45 0.326583 4 141686 -0.52 0.300905 5 141482 -1.00 0.159034 6 141963 0.13 0.549895 7 141324 -1.37 0.085720 8 141788 -0.28 0.388404 9 142543 1.48 0.930635 10 141524 -0.90 0.183979 11 142710 1.87 0.969308 12 142268 0.84 0.798989 13 141982 0.17 0.567412 14 142486 1.35 0.911068 15 141305 -1.41 0.078977 16 142502 1.38 0.916934 17 141959 0.12 0.546194 18 142396 1.14 0.872247 19 142028 0.28 0.609212 20 142190 0.66 0.744014 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-03_23:31 Bits used No. missing words z-score p-value 23 to 32 141939 0.1023 0.540745 22 to 31 142026 0.4023 0.656272 21 to 30 142157 0.8540 0.803457 20 to 29 142034 0.4299 0.666365 19 to 28 142412 1.7333 0.958483 18 to 27 142197 0.9920 0.839393 17 to 26 141753 -0.5391 0.294920 16 to 25 141722 -0.6460 0.259151 15 to 24 142491 2.0058 0.977559 14 to 23 141544 -1.2598 0.103878 13 to 22 141775 -0.4632 0.321608 12 to 21 142011 0.3506 0.637051 11 to 20 141484 -1.4667 0.071235 10 to 19 141909 -0.0011 0.499546 9 to 18 141912 0.0092 0.503673 8 to 17 142081 0.5920 0.723063 7 to 16 142138 0.7885 0.784803 6 to 15 141344 -1.9494 0.025623 5 to 14 141653 -0.8839 0.188376 4 to 13 142212 1.0437 0.851686 3 to 12 141697 -0.7322 0.232032 2 to 11 142054 0.4989 0.691062 1 to 10 141637 -0.9391 0.173848 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-03_23:31 Bits used No. missing words z-score p-value 28 to 32 141668 -0.8181 0.206659 27 to 31 141813 -0.3265 0.372007 26 to 30 141885 -0.0825 0.467135 25 to 29 141948 0.1311 0.552146 24 to 28 141967 0.1955 0.577496 23 to 27 141358 -1.8689 0.030817 22 to 26 142444 1.8124 0.965041 21 to 25 142282 1.2633 0.896757 20 to 24 141729 -0.6113 0.270504 19 to 23 142282 1.2633 0.896757 18 to 22 141873 -0.1232 0.450993 17 to 21 141957 0.1616 0.564187 16 to 20 141479 -1.4587 0.072318 15 to 19 142090 0.6124 0.729877 14 to 18 142354 1.5074 0.934140 13 to 17 142138 0.7752 0.780875 12 to 16 141816 -0.3164 0.375860 11 to 15 141857 -0.1774 0.429601 10 to 14 141926 0.0565 0.522532 9 to 13 141595 -1.0655 0.143319 8 to 12 142185 0.9345 0.824970 7 to 11 142200 0.9853 0.837767 6 to 10 142003 0.3175 0.624578 5 to 9 141563 -1.1740 0.120198 4 to 8 141949 0.1345 0.553486 3 to 7 142098 0.6396 0.738770 2 to 6 142221 1.0565 0.854632 1 to 5 142016 0.3616 0.641172 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-03_23:31 Bits used No. missing words z-score p-value 31 to 32 141765 -0.4258 0.335144 30 to 31 142522 1.8073 0.964641 29 to 30 142561 1.9223 0.972718 28 to 29 141988 0.2321 0.591756 27 to 28 142019 0.3235 0.626846 26 to 27 141516 -1.1603 0.122970 25 to 26 142122 0.6273 0.734784 24 to 25 142294 1.1347 0.871754 23 to 24 142005 0.2822 0.611110 22 to 23 141225 -2.0187 0.021761 21 to 22 141814 -0.2812 0.389275 20 to 21 142020 0.3265 0.627962 19 to 20 141684 -0.6647 0.253124 18 to 19 142254 1.0167 0.845358 17 to 18 141540 -1.0895 0.137974 16 to 17 142409 1.4740 0.929753 15 to 16 141393 -1.5231 0.063867 14 to 15 141970 0.1790 0.571018 13 to 14 141436 -1.3963 0.081319 12 to 13 141507 -1.1868 0.117650 11 to 12 142385 1.4032 0.919715 10 to 11 142649 2.1819 0.985442 9 to 10 141939 0.0875 0.534872 8 to 9 142449 1.5919 0.944302 7 to 8 141901 -0.0246 0.490198 6 to 7 142018 0.3206 0.625728 5 to 6 141695 -0.6322 0.263614 4 to 5 142255 1.0197 0.846059 3 to 4 141849 -0.1780 0.429375 2 to 3 141383 -1.5526 0.060260 1 to 2 142706 2.3501 0.990615 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-03_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.66 -0.868 0.192823 Test results for specific bytes for dh-ranFile-2018-04-03_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2576.91 1.088 0.861639 2 to 9 2498.03 -0.028 0.488914 3 to 10 2582.90 1.172 0.879477 4 to 11 2548.72 0.689 0.754604 5 to 12 2525.66 0.363 0.641667 6 to 13 2512.72 0.180 0.571390 7 to 14 2427.14 -1.030 0.151400 8 to 15 2491.29 -0.123 0.451010 9 to 16 2618.75 1.679 0.953466 10 to 17 2531.99 0.452 0.674504 11 to 18 2490.04 -0.141 0.443992 12 to 19 2477.12 -0.324 0.373141 13 to 20 2457.63 -0.599 0.274505 14 to 21 2516.62 0.235 0.592911 15 to 22 2518.71 0.265 0.604324 16 to 23 2600.71 1.424 0.922818 17 to 24 2505.34 0.076 0.530112 18 to 25 2551.75 0.732 0.767852 19 to 26 2524.79 0.351 0.637046 20 to 27 2428.23 -1.015 0.155045 21 to 28 2548.74 0.689 0.754669 22 to 29 2569.61 0.984 0.837543 23 to 30 2424.33 -1.070 0.142267 24 to 31 2477.05 -0.324 0.372781 25 to 32 2431.30 -0.972 0.165619 CDPARK for dh-ranFile-2018-04-03_23:31: 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 3574 2.3288 0.990064 3513 -0.4566 0.323972 3538 0.6849 0.753306 3488 -1.5982 0.055002 3534 0.5023 0.692266 3561 1.7352 0.958644 3489 -1.5525 0.060270 3523 0.0000 0.500000 3547 1.0959 0.863437 3490 -1.5068 0.065925 Square side=100, avg. no. parked=3525.70 sample std.=29.09 p-value of the KSTEST for those 10 p-values: 0.342523 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-03_23:31 0.0839,0.1028,0.4960,0.9401,0.2209,0.9439,0.0826,0.7534,0.0437,0.7371, The KS test for those 10 p-values: 0.259260 The 3DSPHERES test for dh-ranFile-2018-04-03_23:31 sample no r^3 equiv. uni. 1 4.293 0.133338 2 28.579 0.614280 3 36.157 0.700374 4 12.008 0.329848 5 13.544 0.363309 6 87.558 0.945992 7 16.991 0.432415 8 5.323 0.162596 9 4.778 0.147226 10 53.029 0.829266 11 59.687 0.863246 12 6.712 0.200464 13 48.703 0.802777 14 26.020 0.579926 15 15.372 0.400937 16 10.765 0.301514 17 25.959 0.579081 18 14.436 0.381960 19 7.961 0.233064 20 8.082 0.236152 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.577889 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-03_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 -0.1 -0.5 -0.7 0.6 1.0 -2.1 -0.8 -0.4 0.9 -1.0 -2.6 -0.8 0.1 -1.1 0.4 0.9 1.8 -0.0 1.3 0.3 1.3 0.1 0.7 -2.3 0.4 1.1 -1.2 -0.0 -0.4 -0.9 0.4 -0.8 -0.6 0.6 -0.7 0.2 -0.4 -0.1 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:39.519886 z-score=-0.270603, p-value=0.419592 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-03_23:31 Test no p-value 1 0.721287 2 0.744615 3 0.903941 4 0.015711 5 0.681115 6 0.022513 7 0.044126 8 0.729213 9 0.844704 10 0.127821 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.134701 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-03_23:31: (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 66754 0.11 66747 0.10 3 25000.00 24992 0.00 24944 0.13 4 6666.67 6584 1.03 6612 0.45 5 1388.89 1409 0.29 1441 1.96 6 238.10 217 1.87 217 1.87 7 34.72 38 0.31 35 0.00 8 4.96 5 0.00 3 0.77 p=0.27105 p=0.49051 Number of rngs required: 687120, p-value: 0.067 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-03_23:31 No. of wins: Observed Expected 98625 98585.9 z-score= 0.175, pvalue=0.56949 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66604 66666.7 0.059 0.059 2 37873 37654.3 1.270 1.329 3 26744 26954.7 1.648 2.976 4 19202 19313.5 0.643 3.620 5 13893 13851.4 0.125 3.744 6 10029 9943.5 0.734 4.479 7 7077 7145.0 0.648 5.127 8 5215 5139.1 1.122 6.248 9 3821 3699.9 3.966 10.214 10 2631 2666.3 0.467 10.682 11 1870 1923.3 1.479 12.160 12 1439 1388.7 1.819 13.979 13 1036 1003.7 1.038 15.018 14 709 726.1 0.405 15.422 15 466 525.8 6.809 22.231 16 390 381.2 0.205 22.437 17 279 276.5 0.022 22.459 18 195 200.8 0.169 22.628 19 126 146.0 2.736 25.364 20 109 106.2 0.073 25.437 21 292 287.1 0.083 25.520 Chisq= 25.52 for 20 degrees of freedom, p= 0.81773 SUMMARY of craptest p-value for no. of wins: 0.569485 p-value for throws/game: 0.817733 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-03_23:31 No. of wins: Observed Expected 98777 98585.9 z-score= 0.855, pvalue=0.80370 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66833 66666.7 0.415 0.415 2 37404 37654.3 1.664 2.079 3 27079 26954.7 0.573 2.652 4 19199 19313.5 0.678 3.330 5 13888 13851.4 0.097 3.427 6 9996 9943.5 0.277 3.704 7 7174 7145.0 0.117 3.821 8 5049 5139.1 1.579 5.400 9 3759 3699.9 0.945 6.345 10 2663 2666.3 0.004 6.349 11 1896 1923.3 0.388 6.737 12 1428 1388.7 1.110 7.847 13 966 1003.7 1.417 9.264 14 769 726.1 2.530 11.794 15 497 525.8 1.581 13.376 16 381 381.2 0.000 13.376 17 287 276.5 0.396 13.771 18 193 200.8 0.305 14.077 19 150 146.0 0.110 14.187 20 110 106.2 0.135 14.322 21 279 287.1 0.229 14.551 Chisq= 14.55 for 20 degrees of freedom, p= 0.19851 SUMMARY of craptest p-value for no. of wins: 0.803696 p-value for throws/game: 0.198511 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0039,0.0157,0.0218,0.0220,0.0225,0.0256,0.0308,0.0333,0.0403,0.0416, 0.0437,0.0441,0.0478,0.0550,0.0603,0.0603,0.0610,0.0639,0.0659,0.0670, 0.0683,0.0712,0.0723,0.0727,0.0790,0.0797,0.0813,0.0826,0.0839,0.0857, 0.0945,0.0984,0.1028,0.1039,0.1079,0.1097,0.1161,0.1177,0.1202,0.1230, 0.1278,0.1333,0.1347,0.1369,0.1380,0.1423,0.1433,0.1472,0.1514,0.1550, 0.1564,0.1590,0.1626,0.1656,0.1695,0.1725,0.1738,0.1840,0.1844,0.1884, 0.1897,0.1928,0.1947,0.1985,0.2005,0.2067,0.2149,0.2209,0.2272,0.2320, 0.2331,0.2336,0.2343,0.2357,0.2362,0.2371,0.2498,0.2526,0.2531,0.2577, 0.2592,0.2593,0.2636,0.2705,0.2711,0.2745,0.2949,0.3007,0.3009,0.3015, 0.3216,0.3240,0.3266,0.3298,0.3351,0.3425,0.3543,0.3633,0.3691,0.3720, 0.3728,0.3731,0.3759,0.3820,0.3884,0.3893,0.4009,0.4084,0.4094,0.4132, 0.4147,0.4148,0.4196,0.4225,0.4294,0.4296,0.4324,0.4327,0.4440,0.4501, 0.4510,0.4510,0.4555,0.4671,0.4711,0.4764,0.4769,0.4889,0.4902,0.4905, 0.4949,0.4960,0.4995,0.5000,0.5005,0.5017,0.5037,0.5088,0.5117,0.5142, 0.5225,0.5301,0.5349,0.5407,0.5462,0.5499,0.5521,0.5535,0.5621,0.5642, 0.5674,0.5695,0.5710,0.5714,0.5775,0.5779,0.5790,0.5791,0.5799,0.5804, 0.5918,0.5929,0.6043,0.6092,0.6104,0.6108,0.6111,0.6143,0.6204,0.6246, 0.6257,0.6268,0.6280,0.6306,0.6370,0.6371,0.6412,0.6417,0.6563,0.6617, 0.6664,0.6745,0.6811,0.6911,0.6923,0.7004,0.7154,0.7176,0.7191,0.7213, 0.7231,0.7276,0.7292,0.7299,0.7348,0.7371,0.7373,0.7388,0.7440,0.7446, 0.7533,0.7534,0.7545,0.7546,0.7547,0.7595,0.7679,0.7809,0.7848,0.7959, 0.7983,0.7990,0.8028,0.8035,0.8037,0.8117,0.8123,0.8177,0.8250,0.8284, 0.8293,0.8375,0.8378,0.8394,0.8411,0.8447,0.8454,0.8461,0.8517,0.8546, 0.8616,0.8632,0.8634,0.8698,0.8718,0.8722,0.8792,0.8795,0.8968,0.8968, 0.9039,0.9093,0.9111,0.9169,0.9197,0.9228,0.9298,0.9306,0.9341,0.9384, 0.9401,0.9439,0.9443,0.9460,0.9466,0.9515,0.9535,0.9585,0.9586,0.9646, 0.9650,0.9651,0.9693,0.9727,0.9776,0.9854,0.9901,0.9906,0.9911, Overall p-value after applying KStest on 269 p-values = 0.702994 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.