RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-16_12:31 (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 7.7236 0.027895 2 to 25 15.86 28.6732 0.962339 3 to 26 15.95 34.1287 0.991919 4 to 27 15.52 17.9446 0.607658 5 to 28 15.43 21.7709 0.806308 6 to 29 15.75 18.2107 0.624335 7 to 30 15.69 12.8298 0.252499 8 to 31 15.67 17.0054 0.546001 9 to 32 15.66 19.8262 0.716783 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.278483 Tough bday spacings test for dh-ranFile-2015-12-16_12:31: 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 41 78 94 81 91 54 34 14 3 4 (O-E)^2/E 1.1 0.5 0.3 0.1 2.8 2.1 0.1 0.6 0.1 2.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.719, p= 0.534 RESULTS OF GCD FOR dh-ranFile-2015-12-16_12:31 Euclid's algorithm: p-value, steps to gcd: 0.066121 p-value, dist. of gcd's: 0.484827 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-16_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.029 0.280 0.547 0.388 0.285 0.746 0.189 0.400 Bits 8 to 15---> 0.812 0.107 0.498 0.031 0.951 0.891 0.476 0.262 Bits 16 to 23---> 0.786 0.340 0.117 0.383 0.060 0.777 0.740 0.017 Bits 24 to 31---> 0.183 0.261 0.219 0.371 0.691 0.093 0.772 0.475 KS test for the above 32 p values: 0.866 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-16_12:31, p-values for 5 runs: 0.7443, 0.2427, 0.4781, 0.2556, 0.0456 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-16_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5121 5134.0 0.033 2.236 r= 30 22989 23103.0 0.563 2.799 r= 31 11657 11551.5 0.963 3.762 chi-square = 3.762 with df = 3; p-value = 0.712 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-16_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 184 211.4 3.556 3.556 r= 30 5114 5134.0 0.078 3.634 r= 31 23185 23103.0 0.291 3.924 r= 32 11517 11551.5 0.103 4.028 chi-square = 4.028 with df = 3; p-value = 0.742 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-16_12:31 b-rank test for bits 1 to 8, p=0.98816 b-rank test for bits 2 to 9, p=0.03976 b-rank test for bits 3 to 10, p=0.36910 b-rank test for bits 4 to 11, p=0.46128 b-rank test for bits 5 to 12, p=0.71162 b-rank test for bits 6 to 13, p=0.85409 b-rank test for bits 7 to 14, p=0.55734 b-rank test for bits 8 to 15, p=0.87712 b-rank test for bits 9 to 16, p=0.71057 b-rank test for bits 10 to 17, p=0.16619 b-rank test for bits 11 to 18, p=0.43829 b-rank test for bits 12 to 19, p=0.95973 b-rank test for bits 13 to 20, p=0.15624 b-rank test for bits 14 to 21, p=0.09084 b-rank test for bits 15 to 22, p=0.27474 b-rank test for bits 16 to 23, p=0.46532 b-rank test for bits 17 to 24, p=0.51799 b-rank test for bits 18 to 25, p=0.95939 b-rank test for bits 19 to 26, p=0.31364 b-rank test for bits 20 to 27, p=0.53275 b-rank test for bits 21 to 28, p=0.83307 b-rank test for bits 22 to 29, p=0.34917 b-rank test for bits 23 to 30, p=0.52307 b-rank test for bits 24 to 31, p=0.60019 b-rank test for bits 25 to 32, p=0.09205 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 = 0.947143 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-16_12:31 (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 141293 -1.44 0.074930 2 141463 -1.04 0.148514 3 142082 0.40 0.656686 4 142104 0.45 0.675387 5 141466 -1.04 0.150144 6 142018 0.25 0.600214 7 142420 1.19 0.883596 8 142474 1.32 0.906469 9 142032 0.29 0.612795 10 142037 0.30 0.617261 11 142062 0.36 0.639344 12 141844 -0.15 0.439341 13 142367 1.07 0.857538 14 142238 0.77 0.778733 15 141666 -0.57 0.284838 16 142374 1.09 0.861189 17 141585 -0.76 0.224291 18 142171 0.61 0.729526 19 142659 1.75 0.960076 20 141937 0.06 0.525774 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-16_12:31 Bits used No. missing words z-score p-value 23 to 32 141649 -0.8977 0.184676 22 to 31 141911 0.0058 0.502297 21 to 30 141721 -0.6494 0.258036 20 to 29 142222 1.0782 0.859522 19 to 28 141606 -1.0460 0.147789 18 to 27 141927 0.0609 0.524293 17 to 26 142029 0.4127 0.660070 16 to 25 142154 0.8437 0.800579 15 to 24 142395 1.6747 0.953006 14 to 23 141804 -0.3632 0.358225 13 to 22 142347 1.5092 0.934377 12 to 21 142215 1.0540 0.854066 11 to 20 142015 0.3644 0.642213 10 to 19 141578 -1.1425 0.126620 9 to 18 141751 -0.5460 0.292545 8 to 17 141928 0.0644 0.525666 7 to 16 141820 -0.3080 0.379028 6 to 15 142168 0.8920 0.813794 5 to 14 142181 0.9368 0.825568 4 to 13 141845 -0.2218 0.412224 3 to 12 142358 1.5471 0.939085 2 to 11 142328 1.4437 0.925587 1 to 10 141997 0.3023 0.618792 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-16_12:31 Bits used No. missing words z-score p-value 28 to 32 141646 -0.8926 0.186024 27 to 31 142307 1.3480 0.911176 26 to 30 141919 0.0328 0.513075 25 to 29 142195 0.9684 0.833571 24 to 28 141836 -0.2486 0.401844 23 to 27 142203 0.9955 0.840251 22 to 26 141508 -1.3604 0.086845 21 to 25 142000 0.3074 0.620714 20 to 24 141482 -1.4486 0.073728 19 to 23 141891 -0.0621 0.475227 18 to 22 142280 1.2565 0.895534 17 to 21 142372 1.5684 0.941603 16 to 20 142238 1.1141 0.867390 15 to 19 142366 1.5480 0.939193 14 to 18 141884 -0.0859 0.465787 13 to 17 141968 0.1989 0.578822 12 to 16 141831 -0.2655 0.395302 11 to 15 141936 0.0904 0.536018 10 to 14 141574 -1.1367 0.127829 9 to 13 141613 -1.0045 0.157567 8 to 12 141761 -0.5028 0.307548 7 to 11 141534 -1.2723 0.101632 6 to 10 142404 1.6768 0.953214 5 to 9 141891 -0.0621 0.475227 4 to 8 142226 1.0735 0.858467 3 to 7 142014 0.3548 0.638635 2 to 6 141967 0.1955 0.577496 1 to 5 141805 -0.3537 0.361797 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-16_12:31 Bits used No. missing words z-score p-value 31 to 32 142039 0.3825 0.648958 30 to 31 142663 2.2232 0.986899 29 to 30 141812 -0.2871 0.387014 28 to 29 142259 1.0315 0.848841 27 to 28 142074 0.4858 0.686429 26 to 27 142179 0.7955 0.786835 25 to 26 141840 -0.2045 0.418976 24 to 25 141534 -1.1072 0.134111 23 to 24 141540 -1.0895 0.137974 22 to 23 141592 -0.9361 0.174617 21 to 22 141533 -1.1101 0.133474 20 to 21 142844 2.7571 0.997085 19 to 20 141937 0.0816 0.532527 18 to 19 141703 -0.6086 0.271381 17 to 18 142164 0.7512 0.773746 16 to 17 141488 -1.2429 0.106959 15 to 16 141788 -0.3579 0.360207 14 to 15 141281 -1.8535 0.031907 13 to 14 141921 0.0344 0.513731 12 to 13 142363 1.3383 0.909594 11 to 12 141343 -1.6706 0.047401 10 to 11 141919 0.0285 0.511378 9 to 10 142136 0.6686 0.748138 8 to 9 141783 -0.3727 0.354703 7 to 8 141736 -0.5113 0.304571 6 to 7 141869 -0.1190 0.452651 5 to 6 141939 0.0875 0.534872 4 to 5 141487 -1.2458 0.106417 3 to 4 142030 0.3560 0.639064 2 to 3 142589 2.0049 0.977515 1 to 2 141909 -0.0010 0.499612 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-16_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2424.30 -1.071 0.142172 Test results for specific bytes for dh-ranFile-2015-12-16_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2407.55 -1.307 0.095532 2 to 9 2556.12 0.794 0.786286 3 to 10 2546.43 0.657 0.744294 4 to 11 2525.38 0.359 0.640194 5 to 12 2501.97 0.028 0.511111 6 to 13 2493.93 -0.086 0.465820 7 to 14 2550.84 0.719 0.763904 8 to 15 2502.62 0.037 0.514791 9 to 16 2660.48 2.270 0.988383 10 to 17 2475.29 -0.349 0.363397 11 to 18 2729.21 3.242 0.999405 12 to 19 2445.85 -0.766 0.221912 13 to 20 2376.87 -1.741 0.040813 14 to 21 2449.38 -0.716 0.237025 15 to 22 2476.21 -0.336 0.368262 16 to 23 2301.90 -2.802 0.002543 17 to 24 2567.07 0.948 0.828562 18 to 25 2427.78 -1.021 0.153561 19 to 26 2464.50 -0.502 0.307793 20 to 27 2521.43 0.303 0.619084 21 to 28 2477.93 -0.312 0.377477 22 to 29 2356.82 -2.025 0.021439 23 to 30 2475.91 -0.341 0.366693 24 to 31 2432.52 -0.954 0.169952 25 to 32 2513.05 0.185 0.573210 CDPARK for dh-ranFile-2015-12-16_12:31: 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 3536 0.5936 0.723613 3527 0.1826 0.572463 3522 -0.0457 0.481790 3541 0.8219 0.794438 3527 0.1826 0.572463 3518 -0.2283 0.409702 3554 1.4155 0.921543 3541 0.8219 0.794438 3541 0.8219 0.794438 Square side=100, avg. no. parked=3532.80 sample std.=10.97 p-value of the KSTEST for those 10 p-values: 0.092163 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-16_12:31 0.9661,0.9357,0.7554,0.7890,0.1370,0.8818,0.9545,0.3084,0.9056,0.2150, The KS test for those 10 p-values: 0.022518 The 3DSPHERES test for dh-ranFile-2015-12-16_12:31 sample no r^3 equiv. uni. 1 8.078 0.236067 2 4.251 0.132113 3 59.800 0.863759 4 31.679 0.652139 5 9.310 0.266800 6 5.227 0.159904 7 13.171 0.355333 8 17.554 0.442967 9 148.364 0.992884 10 34.070 0.678796 11 38.692 0.724658 12 29.374 0.624357 13 1.243 0.040589 14 10.284 0.290209 15 27.299 0.597459 16 51.988 0.823236 17 5.529 0.168311 18 0.985 0.032290 19 35.760 0.696390 20 98.633 0.962663 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.946909 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-16_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 -0.8 -1.9 1.4 -1.2 -0.6 -0.9 1.3 1.3 1.6 -0.5 1.6 0.9 -0.8 -2.2 -0.6 1.3 -0.8 0.1 -0.8 -0.6 0.0 -1.2 1.5 1.6 0.7 -0.1 -0.8 0.2 1.0 -1.2 0.3 -0.5 -0.1 -0.8 -0.9 -0.4 0.1 -0.1 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:43.658205 z-score=0.180925, p-value=0.599164 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-16_12:31 Test no p-value 1 0.269600 2 0.681934 3 0.926793 4 0.099381 5 0.037123 6 0.519345 7 0.956110 8 0.017322 9 0.167706 10 0.065534 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.084711 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-16_12:31: (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 66436 0.80 66928 1.02 3 25000.00 25213 1.81 24738 2.75 4 6666.67 6651 0.04 6708 0.26 5 1388.89 1411 0.35 1375 0.14 6 238.10 247 0.33 220 1.38 7 34.72 37 0.15 27 1.72 8 4.96 4 0.19 3 0.77 p=0.27880 p=0.76420 Number of rngs required: 689156, p-value: 0.808 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-16_12:31 No. of wins: Observed Expected 98270 98585.9 z-score=-1.413, pvalue=0.07887 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66711 66666.7 0.029 0.029 2 37522 37654.3 0.465 0.494 3 27039 26954.7 0.263 0.758 4 19197 19313.5 0.702 1.460 5 13936 13851.4 0.516 1.977 6 9962 9943.5 0.034 2.011 7 7214 7145.0 0.666 2.677 8 5054 5139.1 1.408 4.085 9 3690 3699.9 0.026 4.111 10 2722 2666.3 1.164 5.275 11 1938 1923.3 0.112 5.387 12 1348 1388.7 1.195 6.582 13 1026 1003.7 0.495 7.077 14 722 726.1 0.024 7.101 15 510 525.8 0.477 7.577 16 383 381.2 0.009 7.586 17 290 276.5 0.655 8.242 18 212 200.8 0.621 8.863 19 148 146.0 0.028 8.891 20 86 106.2 3.847 12.738 21 290 287.1 0.029 12.767 Chisq= 12.77 for 20 degrees of freedom, p= 0.11285 SUMMARY of craptest p-value for no. of wins: 0.078871 p-value for throws/game: 0.112850 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-16_12:31 No. of wins: Observed Expected 98413 98585.9 z-score=-0.773, pvalue=0.21972 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66608 66666.7 0.052 0.052 2 37718 37654.3 0.108 0.159 3 27054 26954.7 0.366 0.525 4 19264 19313.5 0.127 0.652 5 13750 13851.4 0.743 1.394 6 10015 9943.5 0.514 1.908 7 7210 7145.0 0.591 2.499 8 5084 5139.1 0.590 3.089 9 3674 3699.9 0.181 3.270 10 2650 2666.3 0.100 3.369 11 1953 1923.3 0.458 3.827 12 1339 1388.7 1.782 5.608 13 998 1003.7 0.033 5.641 14 766 726.1 2.188 7.829 15 530 525.8 0.033 7.862 16 369 381.2 0.387 8.249 17 256 276.5 1.526 9.775 18 216 200.8 1.146 10.921 19 153 146.0 0.337 11.258 20 102 106.2 0.167 11.425 21 291 287.1 0.053 11.478 Chisq= 11.48 for 20 degrees of freedom, p= 0.06712 SUMMARY of craptest p-value for no. of wins: 0.219724 p-value for throws/game: 0.067118 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0025,0.0173,0.0174,0.0214,0.0225,0.0279,0.0288,0.0311,0.0319,0.0323, 0.0371,0.0398,0.0406,0.0408,0.0456,0.0474,0.0598,0.0655,0.0661,0.0671, 0.0737,0.0749,0.0789,0.0847,0.0868,0.0908,0.0920,0.0922,0.0927,0.0955, 0.0994,0.1016,0.1064,0.1070,0.1070,0.1128,0.1174,0.1266,0.1278,0.1321, 0.1335,0.1341,0.1370,0.1380,0.1422,0.1478,0.1485,0.1501,0.1536,0.1562, 0.1576,0.1599,0.1662,0.1677,0.1683,0.1700,0.1746,0.1834,0.1847,0.1860, 0.1893,0.2150,0.2189,0.2197,0.2219,0.2243,0.2361,0.2370,0.2427,0.2525, 0.2556,0.2580,0.2608,0.2624,0.2668,0.2696,0.2714,0.2747,0.2785,0.2788, 0.2802,0.2848,0.2849,0.2902,0.2925,0.3046,0.3075,0.3078,0.3084,0.3136, 0.3404,0.3492,0.3547,0.3553,0.3582,0.3602,0.3618,0.3634,0.3667,0.3683, 0.3691,0.3706,0.3775,0.3790,0.3832,0.3870,0.3881,0.3953,0.4001,0.4018, 0.4097,0.4122,0.4190,0.4383,0.4393,0.4430,0.4527,0.4613,0.4636,0.4653, 0.4658,0.4658,0.4749,0.4752,0.4752,0.4762,0.4781,0.4818,0.4848,0.4982, 0.4996,0.5023,0.5111,0.5114,0.5131,0.5137,0.5148,0.5180,0.5193,0.5231, 0.5243,0.5257,0.5258,0.5325,0.5327,0.5345,0.5349,0.5360,0.5460,0.5466, 0.5573,0.5725,0.5725,0.5732,0.5775,0.5788,0.5975,0.5992,0.6002,0.6002, 0.6077,0.6128,0.6173,0.6188,0.6191,0.6207,0.6243,0.6244,0.6386,0.6391, 0.6393,0.6402,0.6422,0.6490,0.6521,0.6567,0.6601,0.6754,0.6788,0.6819, 0.6864,0.6912,0.6964,0.7106,0.7116,0.7117,0.7168,0.7236,0.7247,0.7295, 0.7402,0.7415,0.7443,0.7443,0.7458,0.7481,0.7554,0.7639,0.7642,0.7720, 0.7737,0.7769,0.7787,0.7857,0.7863,0.7868,0.7890,0.7944,0.7944,0.7944, 0.8006,0.8063,0.8081,0.8120,0.8138,0.8232,0.8256,0.8286,0.8331,0.8336, 0.8403,0.8488,0.8541,0.8541,0.8575,0.8585,0.8595,0.8612,0.8638,0.8657, 0.8674,0.8771,0.8818,0.8836,0.8912,0.8955,0.9056,0.9065,0.9096,0.9112, 0.9215,0.9256,0.9268,0.9344,0.9357,0.9391,0.9392,0.9416,0.9469,0.9471, 0.9508,0.9530,0.9532,0.9545,0.9561,0.9594,0.9597,0.9601,0.9623,0.9627, 0.9661,0.9775,0.9869,0.9882,0.9884,0.9919,0.9929,0.9971,0.9994, Overall p-value after applying KStest on 269 p-values = 0.642919 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.