RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-11_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 18.5221 0.643358 2 to 25 15.55 17.1732 0.557306 3 to 26 15.81 19.3253 0.689817 4 to 27 15.69 9.4909 0.076408 5 to 28 15.75 25.0872 0.907226 6 to 29 15.80 13.4156 0.292046 7 to 30 15.27 23.0235 0.851514 8 to 31 15.78 14.5078 0.369112 9 to 32 15.93 16.2183 0.491585 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.939007 Tough bday spacings test for dh-ranFile-2017-01-11_04:31: 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 8 42 70 100 96 85 56 20 13 7 3 (O-E)^2/E 0.1 0.8 0.1 0.1 0.0 0.6 0.3 3.2 0.2 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.803, p= 0.168 RESULTS OF GCD FOR dh-ranFile-2017-01-11_04:31 Euclid's algorithm: p-value, steps to gcd: 0.003636 p-value, dist. of gcd's: 0.606413 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-11_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.842 0.375 0.568 0.678 0.344 0.434 0.869 0.005 Bits 8 to 15---> 0.138 0.064 0.991 0.286 0.552 0.501 0.990 0.602 Bits 16 to 23---> 0.443 0.380 0.127 0.037 0.240 0.291 0.421 0.318 Bits 24 to 31---> 0.199 0.829 0.865 0.550 0.350 0.223 0.980 0.877 KS test for the above 32 p values: 0.346 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-11_04:31, p-values for 5 runs: 0.5016, 0.6103, 0.3972, 0.5597, 0.9604 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-11_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5145 5134.0 0.024 0.051 r= 30 22900 23103.0 1.785 1.836 r= 31 11746 11551.5 3.274 5.110 chi-square = 5.110 with df = 3; p-value = 0.836 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-11_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5172 5134.0 0.281 0.916 r= 31 22987 23103.0 0.583 1.499 r= 32 11618 11551.5 0.383 1.881 chi-square = 1.881 with df = 3; p-value = 0.403 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-11_04:31 b-rank test for bits 1 to 8, p=0.26537 b-rank test for bits 2 to 9, p=0.21777 b-rank test for bits 3 to 10, p=0.75220 b-rank test for bits 4 to 11, p=0.84194 b-rank test for bits 5 to 12, p=0.81646 b-rank test for bits 6 to 13, p=0.14547 b-rank test for bits 7 to 14, p=0.66215 b-rank test for bits 8 to 15, p=0.32605 b-rank test for bits 9 to 16, p=0.99995 b-rank test for bits 10 to 17, p=0.21119 b-rank test for bits 11 to 18, p=0.31721 b-rank test for bits 12 to 19, p=0.30080 b-rank test for bits 13 to 20, p=0.47429 b-rank test for bits 14 to 21, p=0.70738 b-rank test for bits 15 to 22, p=0.60555 b-rank test for bits 16 to 23, p=0.75038 b-rank test for bits 17 to 24, p=0.13710 b-rank test for bits 18 to 25, p=0.64165 b-rank test for bits 19 to 26, p=0.40760 b-rank test for bits 20 to 27, p=0.46532 b-rank test for bits 21 to 28, p=0.22036 b-rank test for bits 22 to 29, p=0.25188 b-rank test for bits 23 to 30, p=0.54976 b-rank test for bits 24 to 31, p=0.52197 b-rank test for bits 25 to 32, p=0.45067 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 = 0.345352 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-11_04:31 (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 141675 -0.55 0.292018 2 141726 -0.43 0.334201 3 142075 0.39 0.650651 4 142480 1.33 0.908790 5 141642 -0.62 0.266116 6 140803 -2.58 0.004871 7 142547 1.49 0.931873 8 142486 1.35 0.911068 9 141583 -0.76 0.222895 10 142305 0.92 0.822377 11 141701 -0.49 0.313217 12 142150 0.56 0.713049 13 141967 0.13 0.553593 14 141555 -0.83 0.203871 15 141470 -1.03 0.152335 16 141854 -0.13 0.448570 17 141298 -1.43 0.076597 18 141805 -0.24 0.403708 19 141712 -0.46 0.322381 20 142080 0.40 0.654966 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-11_04:31 Bits used No. missing words z-score p-value 23 to 32 141926 0.0575 0.522920 22 to 31 142017 0.3713 0.644784 21 to 30 142224 1.0851 0.861054 20 to 29 141760 -0.5149 0.303301 19 to 28 141739 -0.5873 0.278486 18 to 27 141524 -1.3287 0.091970 17 to 26 142084 0.6023 0.726516 16 to 25 142164 0.8782 0.810075 15 to 24 141557 -1.2149 0.112196 14 to 23 141833 -0.2632 0.396196 13 to 22 141490 -1.4460 0.074093 12 to 21 141838 -0.2460 0.402855 11 to 20 141643 -0.9184 0.179210 10 to 19 141897 -0.0425 0.483043 9 to 18 142179 0.9299 0.823788 8 to 17 142053 0.4954 0.689846 7 to 16 141780 -0.4460 0.327811 6 to 15 142170 0.8989 0.815637 5 to 14 142146 0.8161 0.792780 4 to 13 141846 -0.2184 0.413567 3 to 12 141967 0.1989 0.578815 2 to 11 141754 -0.5356 0.296110 1 to 10 141633 -0.9529 0.170330 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-11_04:31 Bits used No. missing words z-score p-value 28 to 32 141562 -1.1774 0.119520 27 to 31 141826 -0.2825 0.388790 26 to 30 142164 0.8633 0.806011 25 to 29 141873 -0.1232 0.450993 24 to 28 141776 -0.4520 0.325647 23 to 27 142046 0.4633 0.678421 22 to 26 142153 0.8260 0.795598 21 to 25 141776 -0.4520 0.325647 20 to 24 141691 -0.7401 0.229619 19 to 23 141918 0.0294 0.511723 18 to 22 141466 -1.5028 0.066444 17 to 21 141903 -0.0215 0.491440 16 to 20 141659 -0.8486 0.198059 15 to 19 142395 1.6463 0.950153 14 to 18 142115 0.6972 0.757157 13 to 17 142063 0.5209 0.698787 12 to 16 141700 -0.7096 0.238978 11 to 15 141980 0.2396 0.594664 10 to 14 141242 -2.2621 0.011845 9 to 13 141690 -0.7435 0.228592 8 to 12 142411 1.7006 0.955489 7 to 11 142013 0.3514 0.637365 6 to 10 141856 -0.1808 0.428270 5 to 9 142371 1.5650 0.941207 4 to 8 141866 -0.1469 0.441613 3 to 7 142088 0.6057 0.727630 2 to 6 142023 0.3853 0.650001 1 to 5 142095 0.6294 0.735453 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-11_04:31 Bits used No. missing words z-score p-value 31 to 32 141553 -1.0511 0.146602 30 to 31 141911 0.0049 0.501965 29 to 30 141810 -0.2930 0.384758 28 to 29 141687 -0.6558 0.255963 27 to 28 142068 0.4681 0.680127 26 to 27 142062 0.4504 0.673772 25 to 26 142275 1.0787 0.859633 24 to 25 141561 -1.0275 0.152087 23 to 24 141443 -1.3756 0.084472 22 to 23 142014 0.3088 0.621248 21 to 22 141916 0.0197 0.507849 20 to 21 141830 -0.2340 0.407488 19 to 20 142799 2.6244 0.995660 18 to 19 142219 0.9135 0.819505 17 to 18 141757 -0.4494 0.326589 16 to 17 141774 -0.3992 0.344872 15 to 16 141972 0.1849 0.573333 14 to 15 141814 -0.2812 0.389275 13 to 14 142467 1.6450 0.950020 12 to 13 141654 -0.7532 0.225669 11 to 12 141306 -1.7797 0.037560 10 to 11 142209 0.8840 0.811647 9 to 10 141657 -0.7443 0.228337 8 to 9 141952 0.1259 0.550083 7 to 8 142341 1.2734 0.898555 6 to 7 141598 -0.9184 0.179211 5 to 6 141948 0.1141 0.545409 4 to 5 142438 1.5595 0.940561 3 to 4 141850 -0.1750 0.430534 2 to 3 141527 -1.1278 0.129699 1 to 2 142145 0.6952 0.756532 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-11_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2485.42 -0.206 0.418294 Test results for specific bytes for dh-ranFile-2017-01-11_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2431.78 -0.965 0.167338 2 to 9 2631.37 1.858 0.968407 3 to 10 2415.04 -1.202 0.114775 4 to 11 2465.07 -0.494 0.310649 5 to 12 2386.25 -1.609 0.053852 6 to 13 2442.41 -0.814 0.207704 7 to 14 2463.86 -0.511 0.304620 8 to 15 2443.37 -0.801 0.211606 9 to 16 2408.89 -1.288 0.098789 10 to 17 2584.85 1.200 0.884911 11 to 18 2480.66 -0.274 0.392219 12 to 19 2438.34 -0.872 0.191591 13 to 20 2504.27 0.060 0.524080 14 to 21 2451.44 -0.687 0.246133 15 to 22 2542.60 0.602 0.726578 16 to 23 2505.52 0.078 0.531137 17 to 24 2476.67 -0.330 0.370747 18 to 25 2495.71 -0.061 0.475827 19 to 26 2495.43 -0.065 0.474212 20 to 27 2524.56 0.347 0.635814 21 to 28 2494.99 -0.071 0.471731 22 to 29 2476.75 -0.329 0.371156 23 to 30 2551.51 0.728 0.766816 24 to 31 2516.02 0.227 0.589602 25 to 32 2383.86 -1.642 0.050253 CDPARK for dh-ranFile-2017-01-11_04:31: 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 3541 0.8219 0.794438 3510 -0.5936 0.276387 3534 0.5023 0.692266 3531 0.3653 0.642555 3521 -0.0913 0.463617 3560 1.6895 0.954438 3490 -1.5068 0.065925 3515 -0.3653 0.357445 3546 1.0502 0.853193 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3527.00 sample std.=18.91 p-value of the KSTEST for those 10 p-values: 0.907163 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-11_04:31 0.4913,0.4601,0.8837,0.0115,0.4306,0.3810,0.5114,0.5711,0.8075,0.3332, The KS test for those 10 p-values: 0.540556 The 3DSPHERES test for dh-ranFile-2017-01-11_04:31 sample no r^3 equiv. uni. 1 76.429 0.921733 2 62.185 0.874171 3 12.691 0.344945 4 0.620 0.020446 5 20.670 0.497924 6 50.974 0.817156 7 37.479 0.713297 8 4.501 0.139317 9 16.258 0.418370 10 4.609 0.142413 11 9.138 0.262572 12 9.556 0.272789 13 7.557 0.222679 14 9.586 0.273506 15 68.101 0.896690 16 4.325 0.134258 17 0.864 0.028381 18 10.989 0.306706 19 29.281 0.623200 20 10.781 0.301870 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.221545 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-11_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 1.3 -1.4 1.9 0.5 0.4 -0.0 2.0 0.5 0.5 2.2 -0.2 0.2 1.4 -0.9 -1.5 1.5 -1.6 0.2 -1.2 -1.1 -0.1 -1.3 -0.5 1.3 0.9 0.7 -1.5 -0.2 -0.4 0.3 -1.5 -1.0 1.0 0.1 0.7 0.2 1.3 0.4 -0.6 1.0 0.8 Chi-square with 42 degrees of freedom:49.353488 z-score=0.802331, p-value=0.797181 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-11_04:31 Test no p-value 1 0.373727 2 0.087430 3 0.037555 4 0.144380 5 0.027243 6 0.335764 7 0.805117 8 0.984618 9 0.038335 10 0.014085 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003216 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-11_04:31: (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 66744 0.09 66785 0.21 3 25000.00 24896 0.43 24913 0.30 4 6666.67 6734 0.68 6714 0.34 5 1388.89 1349 1.15 1301 5.56 6 238.10 230 0.28 246 0.26 7 34.72 40 0.80 38 0.31 8 4.96 6 0.22 2 1.77 p=0.27531 p=0.81182 Number of rngs required: 687639, p-value: 0.188 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-11_04:31 No. of wins: Observed Expected 98446 98585.9 z-score=-0.626, pvalue=0.26581 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66718 66666.7 0.040 0.040 2 37981 37654.3 2.834 2.874 3 26748 26954.7 1.586 4.459 4 19089 19313.5 2.609 7.068 5 13843 13851.4 0.005 7.073 6 9953 9943.5 0.009 7.082 7 7258 7145.0 1.786 8.868 8 5123 5139.1 0.050 8.919 9 3645 3699.9 0.814 9.732 10 2724 2666.3 1.249 10.981 11 1910 1923.3 0.092 11.073 12 1361 1388.7 0.554 11.628 13 1008 1003.7 0.018 11.646 14 747 726.1 0.599 12.245 15 547 525.8 0.852 13.097 16 375 381.2 0.099 13.196 17 257 276.5 1.381 14.577 18 191 200.8 0.481 15.058 19 137 146.0 0.553 15.611 20 98 106.2 0.635 16.246 21 287 287.1 0.000 16.246 Chisq= 16.25 for 20 degrees of freedom, p= 0.29876 SUMMARY of craptest p-value for no. of wins: 0.265812 p-value for throws/game: 0.298764 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-11_04:31 No. of wins: Observed Expected 98538 98585.9 z-score=-0.214, pvalue=0.41525 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66545 66666.7 0.222 0.222 2 37755 37654.3 0.269 0.491 3 27021 26954.7 0.163 0.654 4 19510 19313.5 2.000 2.654 5 13904 13851.4 0.200 2.854 6 9792 9943.5 2.310 5.163 7 7143 7145.0 0.001 5.164 8 5159 5139.1 0.077 5.241 9 3637 3699.9 1.068 6.309 10 2680 2666.3 0.070 6.380 11 1883 1923.3 0.846 7.225 12 1368 1388.7 0.310 7.535 13 1016 1003.7 0.150 7.685 14 709 726.1 0.405 8.090 15 486 525.8 3.018 11.108 16 385 381.2 0.039 11.147 17 287 276.5 0.396 11.543 18 179 200.8 2.373 13.915 19 164 146.0 2.223 16.139 20 108 106.2 0.030 16.169 21 269 287.1 1.143 17.311 Chisq= 17.31 for 20 degrees of freedom, p= 0.36733 SUMMARY of craptest p-value for no. of wins: 0.415253 p-value for throws/game: 0.367333 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0032,0.0036,0.0047,0.0049,0.0115,0.0118,0.0141,0.0204,0.0272,0.0284, 0.0374,0.0376,0.0376,0.0383,0.0503,0.0539,0.0640,0.0659,0.0664,0.0741, 0.0764,0.0766,0.0845,0.0874,0.0920,0.0988,0.1122,0.1148,0.1195,0.1274, 0.1297,0.1343,0.1371,0.1380,0.1393,0.1424,0.1444,0.1455,0.1466,0.1521, 0.1523,0.1673,0.1685,0.1703,0.1792,0.1792,0.1884,0.1916,0.1981,0.1992, 0.2039,0.2077,0.2112,0.2116,0.2178,0.2204,0.2215,0.2227,0.2229,0.2232, 0.2257,0.2283,0.2286,0.2296,0.2390,0.2403,0.2461,0.2519,0.2560,0.2626, 0.2654,0.2658,0.2661,0.2728,0.2735,0.2753,0.2764,0.2785,0.2862,0.2910, 0.2920,0.2920,0.2961,0.2988,0.3008,0.3019,0.3033,0.3046,0.3067,0.3106, 0.3132,0.3172,0.3180,0.3224,0.3256,0.3256,0.3261,0.3266,0.3278,0.3332, 0.3342,0.3358,0.3444,0.3449,0.3449,0.3454,0.3464,0.3497,0.3574,0.3673, 0.3691,0.3707,0.3712,0.3737,0.3754,0.3803,0.3810,0.3848,0.3888,0.3893, 0.3922,0.3962,0.3972,0.4025,0.4029,0.4037,0.4075,0.4076,0.4136,0.4153, 0.4183,0.4184,0.4215,0.4283,0.4305,0.4306,0.4337,0.4416,0.4426,0.4486, 0.4507,0.4510,0.4601,0.4636,0.4653,0.4717,0.4742,0.4743,0.4758,0.4818, 0.4830,0.4913,0.4914,0.4916,0.4979,0.5013,0.5016,0.5020,0.5078,0.5114, 0.5117,0.5220,0.5229,0.5241,0.5311,0.5406,0.5454,0.5498,0.5500,0.5501, 0.5524,0.5536,0.5573,0.5597,0.5682,0.5711,0.5733,0.5788,0.5896,0.5947, 0.6016,0.6056,0.6064,0.6103,0.6212,0.6232,0.6358,0.6374,0.6417,0.6426, 0.6434,0.6448,0.6500,0.6507,0.6550,0.6621,0.6738,0.6778,0.6784,0.6801, 0.6898,0.6898,0.6923,0.6988,0.7074,0.7130,0.7133,0.7265,0.7266,0.7276, 0.7355,0.7504,0.7522,0.7565,0.7572,0.7668,0.7928,0.7944,0.7956,0.7972, 0.8051,0.8060,0.8075,0.8101,0.8116,0.8118,0.8156,0.8165,0.8172,0.8195, 0.8224,0.8238,0.8287,0.8361,0.8417,0.8419,0.8515,0.8532,0.8596,0.8611, 0.8646,0.8690,0.8742,0.8767,0.8837,0.8849,0.8967,0.8986,0.9072,0.9072, 0.9088,0.9111,0.9217,0.9319,0.9390,0.9406,0.9412,0.9500,0.9502,0.9544, 0.9555,0.9604,0.9684,0.9798,0.9846,0.9896,0.9914,0.9957,0.9999, Overall p-value after applying KStest on 269 p-values = 0.051230 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.