RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.89 10.4930 0.118326 2 to 25 15.94 12.7827 0.249391 3 to 26 15.63 17.4009 0.572456 4 to 27 15.81 24.2626 0.887526 5 to 28 15.88 13.8707 0.323767 6 to 29 15.60 22.8065 0.844343 7 to 30 15.78 13.7440 0.314868 8 to 31 15.76 24.9399 0.903937 9 to 32 15.87 17.1871 0.558238 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.888911 Tough bday spacings test for dh-ranFile-2018-06-25_10:31: 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 37 78 95 88 85 56 30 11 8 4 (O-E)^2/E 0.1 0.0 0.3 0.1 1.0 0.6 0.3 0.0 1.0 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.690, p= 0.040 RESULTS OF GCD FOR dh-ranFile-2018-06-25_10:31 Euclid's algorithm: p-value, steps to gcd: 0.209236 p-value, dist. of gcd's: 0.129372 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.545 0.441 0.569 0.982 0.964 0.166 0.920 0.356 Bits 8 to 15---> 0.952 0.640 0.948 0.078 0.416 0.980 0.987 0.251 Bits 16 to 23---> 0.368 0.306 0.735 0.162 0.779 0.541 0.450 0.583 Bits 24 to 31---> 0.282 0.653 0.900 0.177 0.013 0.941 0.190 0.084 KS test for the above 32 p values: 0.795 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_10:31, p-values for 5 runs: 0.8687, 0.1998, 0.4869, 0.5077, 0.3378 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5054 5134.0 1.247 1.777 r= 30 23147 23103.0 0.084 1.860 r= 31 11577 11551.5 0.056 1.916 chi-square = 1.916 with df = 3; p-value = 0.410 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 195 211.4 1.275 1.275 r= 30 5076 5134.0 0.655 1.930 r= 31 23282 23103.0 1.386 3.317 r= 32 11447 11551.5 0.946 4.262 chi-square = 4.262 with df = 3; p-value = 0.766 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_10:31 b-rank test for bits 1 to 8, p=0.60729 b-rank test for bits 2 to 9, p=0.26548 b-rank test for bits 3 to 10, p=0.93568 b-rank test for bits 4 to 11, p=0.20765 b-rank test for bits 5 to 12, p=0.02033 b-rank test for bits 6 to 13, p=0.54579 b-rank test for bits 7 to 14, p=0.95022 b-rank test for bits 8 to 15, p=0.50025 b-rank test for bits 9 to 16, p=0.53326 b-rank test for bits 10 to 17, p=0.86434 b-rank test for bits 11 to 18, p=0.56472 b-rank test for bits 12 to 19, p=0.48327 b-rank test for bits 13 to 20, p=0.91741 b-rank test for bits 14 to 21, p=0.71961 b-rank test for bits 15 to 22, p=0.09272 b-rank test for bits 16 to 23, p=0.61483 b-rank test for bits 17 to 24, p=0.82443 b-rank test for bits 18 to 25, p=0.31099 b-rank test for bits 19 to 26, p=0.06583 b-rank test for bits 20 to 27, p=0.62586 b-rank test for bits 21 to 28, p=0.31199 b-rank test for bits 22 to 29, p=0.86586 b-rank test for bits 23 to 30, p=0.35412 b-rank test for bits 24 to 31, p=0.86052 b-rank test for bits 25 to 32, p=0.52479 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 = 0.705598 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_10:31 (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 142397 1.14 0.872735 2 142226 0.74 0.770315 3 141886 -0.05 0.478265 4 141690 -0.51 0.304167 5 141594 -0.74 0.230637 6 141815 -0.22 0.412781 7 142831 2.15 0.984358 8 142229 0.75 0.772436 9 141256 -1.53 0.063446 10 141318 -1.38 0.083545 11 142261 0.82 0.794364 12 142561 1.52 0.936070 13 141866 -0.10 0.459681 14 142479 1.33 0.908406 15 141573 -0.79 0.215987 16 141713 -0.46 0.323219 17 142933 2.39 0.991616 18 142241 0.77 0.780809 19 141724 -0.43 0.332502 20 141697 -0.50 0.309913 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-25_10:31 Bits used No. missing words z-score p-value 23 to 32 142458 1.8920 0.970752 22 to 31 142016 0.3678 0.643499 21 to 30 142220 1.0713 0.857977 20 to 29 141991 0.2816 0.610883 19 to 28 141889 -0.0701 0.472056 18 to 27 142175 0.9161 0.820194 17 to 26 141482 -1.4736 0.070301 16 to 25 141953 0.1506 0.559849 15 to 24 141744 -0.5701 0.284304 14 to 23 141940 0.1058 0.542113 13 to 22 142152 0.8368 0.798646 12 to 21 142008 0.3402 0.633163 11 to 20 141555 -1.2218 0.110886 10 to 19 141686 -0.7701 0.220619 9 to 18 141841 -0.2356 0.406864 8 to 17 141292 -2.1287 0.016639 7 to 16 142081 0.5920 0.723063 6 to 15 141944 0.1196 0.547581 5 to 14 141592 -1.0942 0.136925 4 to 13 142098 0.6506 0.742343 3 to 12 142273 1.2540 0.895085 2 to 11 142170 0.8989 0.815637 1 to 10 141748 -0.5563 0.288999 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-25_10:31 Bits used No. missing words z-score p-value 28 to 32 141487 -1.4316 0.076125 27 to 31 141930 0.0701 0.527930 26 to 30 141551 -1.2147 0.112244 25 to 29 142133 0.7582 0.775835 24 to 28 141640 -0.9130 0.180626 23 to 27 141741 -0.5706 0.284132 22 to 26 141890 -0.0655 0.473878 21 to 25 141989 0.2701 0.606446 20 to 24 141506 -1.3672 0.085778 19 to 23 141542 -1.2452 0.106532 18 to 22 142023 0.3853 0.650001 17 to 21 142321 1.3955 0.918566 16 to 20 142055 0.4938 0.689275 15 to 19 142281 1.2599 0.896147 14 to 18 141735 -0.5909 0.277277 13 to 17 141829 -0.2723 0.392694 12 to 16 142152 0.8226 0.794635 11 to 15 142447 1.8226 0.965819 10 to 14 141960 0.1718 0.568188 9 to 13 141679 -0.7808 0.217466 8 to 12 141699 -0.7130 0.237928 7 to 11 141822 -0.2960 0.383602 6 to 10 141627 -0.9571 0.169271 5 to 9 141722 -0.6350 0.262709 4 to 8 141914 0.0158 0.506315 3 to 7 142393 1.6396 0.949452 2 to 6 142267 1.2124 0.887328 1 to 5 141827 -0.2791 0.390090 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-25_10:31 Bits used No. missing words z-score p-value 31 to 32 141562 -1.0246 0.152783 30 to 31 141985 0.2232 0.588316 29 to 30 141520 -1.1485 0.125388 28 to 29 142293 1.1318 0.871134 27 to 28 141583 -0.9626 0.167868 26 to 27 141792 -0.3461 0.364632 25 to 26 142367 1.3501 0.911501 24 to 25 142112 0.5978 0.725029 23 to 24 141763 -0.4317 0.332997 22 to 23 141620 -0.8535 0.196696 21 to 22 142451 1.5978 0.944961 20 to 21 142247 0.9961 0.840394 19 to 20 141825 -0.2488 0.401773 18 to 19 141292 -1.8210 0.034301 17 to 18 141966 0.1672 0.566381 16 to 17 141539 -1.0924 0.137325 15 to 16 141481 -1.2635 0.103203 14 to 15 141882 -0.0806 0.467872 13 to 14 141257 -1.9243 0.027160 12 to 13 141045 -2.5496 0.005392 11 to 12 141875 -0.1013 0.459669 10 to 11 141894 -0.0452 0.481966 9 to 10 141819 -0.2665 0.394942 8 to 9 141528 -1.1249 0.130323 7 to 8 142212 0.8928 0.814026 6 to 7 142119 0.6185 0.731876 5 to 6 142398 1.4415 0.925279 4 to 5 142396 1.4356 0.924443 3 to 4 141891 -0.0541 0.478439 2 to 3 141746 -0.4818 0.314974 1 to 2 142195 0.8427 0.800298 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2470.24 -0.421 0.336916 Test results for specific bytes for dh-ranFile-2018-06-25_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2578.69 1.113 0.867100 2 to 9 2432.73 -0.951 0.170725 3 to 10 2534.34 0.486 0.686383 4 to 11 2597.12 1.374 0.915206 5 to 12 2515.71 0.222 0.587928 6 to 13 2550.80 0.718 0.763749 7 to 14 2497.82 -0.031 0.487678 8 to 15 2594.19 1.332 0.908571 9 to 16 2529.67 0.420 0.662603 10 to 17 2594.50 1.336 0.909288 11 to 18 2479.00 -0.297 0.383256 12 to 19 2314.09 -2.629 0.004280 13 to 20 2535.68 0.505 0.693091 14 to 21 2474.74 -0.357 0.360438 15 to 22 2486.25 -0.194 0.422908 16 to 23 2442.73 -0.810 0.209010 17 to 24 2608.90 1.540 0.938231 18 to 25 2438.55 -0.869 0.192420 19 to 26 2498.85 -0.016 0.493503 20 to 27 2433.52 -0.940 0.173573 21 to 28 2425.83 -1.049 0.147103 22 to 29 2410.07 -1.272 0.101718 23 to 30 2466.39 -0.475 0.317295 24 to 31 2549.02 0.693 0.755903 25 to 32 2522.17 0.314 0.623086 CDPARK for dh-ranFile-2018-06-25_10:31: 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 3545 1.0046 0.842447 3563 1.8265 0.966111 3545 1.0046 0.842447 3557 1.5525 0.939730 3542 0.8676 0.807188 3506 -0.7763 0.218799 3533 0.4566 0.676028 3520 -0.1370 0.445521 3511 -0.5479 0.291865 3578 2.5114 0.993988 Square side=100, avg. no. parked=3540.00 sample std.=21.82 p-value of the KSTEST for those 10 p-values: 0.025169 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_10:31 0.2272,0.3281,0.2400,0.5890,0.6923,0.4169,0.1237,0.8643,0.2555,0.6928, The KS test for those 10 p-values: 0.646919 The 3DSPHERES test for dh-ranFile-2018-06-25_10:31 sample no r^3 equiv. uni. 1 17.482 0.441638 2 31.580 0.650996 3 26.513 0.586777 4 63.175 0.878257 5 21.795 0.516399 6 35.355 0.692259 7 32.830 0.665233 8 51.889 0.822651 9 24.997 0.565357 10 8.175 0.238539 11 67.862 0.895866 12 0.845 0.027762 13 79.104 0.928410 14 87.917 0.946634 15 14.219 0.377466 16 52.004 0.823328 17 18.223 0.455244 18 2.433 0.077901 19 63.989 0.881514 20 4.075 0.127023 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.348750 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 1.8 0.6 -0.5 -0.6 -0.7 1.0 -0.7 -0.0 -0.7 0.6 -0.4 -2.1 0.2 0.9 -0.3 0.5 -1.0 1.7 -1.5 2.3 -1.5 0.3 0.2 0.8 -0.2 -0.2 -0.1 0.1 1.2 0.6 0.1 0.0 0.6 0.4 0.0 1.5 0.9 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:35.849039 z-score=-0.671125, p-value=0.263282 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-25_10:31 Test no p-value 1 0.040601 2 0.997782 3 0.064854 4 0.778221 5 0.019926 6 0.059215 7 0.281420 8 0.586563 9 0.245349 10 0.710441 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.074001 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_10:31: (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 66243 2.69 66545 0.22 3 25000.00 25195 1.52 25031 0.04 4 6666.67 6850 5.04 6748 0.99 5 1388.89 1421 0.74 1417 0.57 6 238.10 242 0.06 227 0.52 7 34.72 43 1.97 29 0.94 8 4.96 5 0.00 2 1.77 p=0.93884 p=0.46226 Number of rngs required: 688947, p-value: 0.735 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_10:31 No. of wins: Observed Expected 99109 98585.9 z-score= 2.340, pvalue=0.99035 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66754 66666.7 0.114 0.114 2 37731 37654.3 0.156 0.271 3 26770 26954.7 1.266 1.537 4 19225 19313.5 0.405 1.942 5 13968 13851.4 0.981 2.923 6 9993 9943.5 0.246 3.169 7 7155 7145.0 0.014 3.183 8 5117 5139.1 0.095 3.278 9 3571 3699.9 4.488 7.766 10 2674 2666.3 0.022 7.788 11 1940 1923.3 0.144 7.933 12 1371 1388.7 0.227 8.159 13 1021 1003.7 0.298 8.457 14 718 726.1 0.091 8.548 15 557 525.8 1.847 10.395 16 411 381.2 2.338 12.733 17 293 276.5 0.980 13.713 18 212 200.8 0.621 14.334 19 145 146.0 0.007 14.341 20 102 106.2 0.167 14.508 21 272 287.1 0.796 15.304 Chisq= 15.30 for 20 degrees of freedom, p= 0.24121 SUMMARY of craptest p-value for no. of wins: 0.990353 p-value for throws/game: 0.241215 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_10:31 No. of wins: Observed Expected 98418 98585.9 z-score=-0.751, pvalue=0.22640 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66556 66666.7 0.184 0.184 2 37611 37654.3 0.050 0.234 3 27300 26954.7 4.423 4.656 4 19390 19313.5 0.303 4.959 5 13759 13851.4 0.617 5.576 6 9842 9943.5 1.037 6.613 7 6930 7145.0 6.471 13.084 8 5205 5139.1 0.846 13.930 9 3795 3699.9 2.446 16.376 10 2697 2666.3 0.354 16.730 11 1843 1923.3 3.355 20.085 12 1385 1388.7 0.010 20.095 13 999 1003.7 0.022 20.117 14 764 726.1 1.974 22.091 15 537 525.8 0.237 22.328 16 385 381.2 0.039 22.367 17 286 276.5 0.324 22.690 18 200 200.8 0.003 22.694 19 155 146.0 0.557 23.251 20 80 106.2 6.470 29.721 21 281 287.1 0.130 29.851 Chisq= 29.85 for 20 degrees of freedom, p= 0.92770 SUMMARY of craptest p-value for no. of wins: 0.226398 p-value for throws/game: 0.927696 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0054,0.0125,0.0166,0.0199,0.0203,0.0252,0.0272,0.0278,0.0343, 0.0397,0.0406,0.0592,0.0634,0.0649,0.0658,0.0703,0.0740,0.0761,0.0779, 0.0781,0.0835,0.0838,0.0858,0.0927,0.1017,0.1032,0.1065,0.1109,0.1122, 0.1183,0.1237,0.1254,0.1270,0.1294,0.1303,0.1369,0.1373,0.1471,0.1528, 0.1619,0.1660,0.1679,0.1693,0.1707,0.1736,0.1771,0.1806,0.1902,0.1924, 0.1967,0.1998,0.2076,0.2090,0.2092,0.2160,0.2175,0.2188,0.2206,0.2264, 0.2272,0.2306,0.2379,0.2385,0.2400,0.2412,0.2453,0.2494,0.2507,0.2555, 0.2627,0.2633,0.2655,0.2773,0.2814,0.2823,0.2841,0.2843,0.2890,0.2919, 0.3042,0.3063,0.3099,0.3110,0.3120,0.3149,0.3150,0.3173,0.3232,0.3238, 0.3281,0.3325,0.3330,0.3369,0.3378,0.3487,0.3541,0.3561,0.3604,0.3646, 0.3677,0.3775,0.3833,0.3836,0.3901,0.3927,0.3949,0.4018,0.4069,0.4101, 0.4128,0.4162,0.4169,0.4229,0.4414,0.4416,0.4455,0.4505,0.4552,0.4597, 0.4597,0.4623,0.4679,0.4721,0.4739,0.4783,0.4784,0.4820,0.4833,0.4869, 0.4877,0.4935,0.5002,0.5063,0.5077,0.5164,0.5248,0.5279,0.5333,0.5407, 0.5421,0.5448,0.5458,0.5476,0.5582,0.5598,0.5647,0.5654,0.5664,0.5682, 0.5687,0.5725,0.5829,0.5866,0.5868,0.5879,0.5883,0.5890,0.6064,0.6073, 0.6109,0.6148,0.6231,0.6259,0.6332,0.6397,0.6435,0.6469,0.6500,0.6510, 0.6527,0.6626,0.6652,0.6760,0.6864,0.6893,0.6923,0.6923,0.6928,0.6931, 0.7056,0.7104,0.7196,0.7231,0.7250,0.7319,0.7348,0.7349,0.7423,0.7559, 0.7637,0.7655,0.7703,0.7724,0.7758,0.7782,0.7792,0.7808,0.7944,0.7946, 0.7947,0.7986,0.8003,0.8072,0.8140,0.8156,0.8202,0.8227,0.8233,0.8244, 0.8404,0.8424,0.8424,0.8443,0.8580,0.8605,0.8643,0.8643,0.8659,0.8671, 0.8687,0.8711,0.8727,0.8783,0.8815,0.8873,0.8875,0.8889,0.8951,0.8959, 0.8961,0.8997,0.9039,0.9084,0.9086,0.9093,0.9115,0.9152,0.9174,0.9186, 0.9203,0.9244,0.9253,0.9277,0.9284,0.9357,0.9361,0.9382,0.9388,0.9397, 0.9415,0.9450,0.9466,0.9476,0.9495,0.9502,0.9521,0.9636,0.9658,0.9661, 0.9708,0.9796,0.9819,0.9844,0.9867,0.9904,0.9916,0.9940,0.9978, Overall p-value after applying KStest on 269 p-values = 0.284120 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.