RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-13_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 9.5924 0.080174 2 to 25 15.59 18.6014 0.648112 3 to 26 15.94 16.5725 0.516328 4 to 27 15.63 27.8916 0.953779 5 to 28 15.66 20.3613 0.743833 6 to 29 15.87 14.1826 0.345860 7 to 30 15.72 23.7579 0.873835 8 to 31 15.65 19.7755 0.714126 9 to 32 15.87 11.2856 0.158662 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.906999 Tough bday spacings test for dh-ranFile-2016-03-13_11:31: 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 10 31 77 99 91 71 55 33 17 14 2 (O-E)^2/E 0.1 0.9 0.2 0.0 0.5 0.7 0.2 0.4 0.3 8.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 12.367, p= 0.739 RESULTS OF GCD FOR dh-ranFile-2016-03-13_11:31 Euclid's algorithm: p-value, steps to gcd: 0.763646 p-value, dist. of gcd's: 0.844770 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-13_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.919 0.496 0.113 0.268 0.787 0.990 0.420 0.917 Bits 8 to 15---> 0.785 0.977 0.501 0.628 0.916 0.652 0.696 0.665 Bits 16 to 23---> 0.894 0.121 0.959 0.208 0.023 0.566 0.590 0.256 Bits 24 to 31---> 0.274 0.196 0.445 0.092 0.885 0.691 0.380 0.134 KS test for the above 32 p values: 0.447 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-13_11:31, p-values for 5 runs: 0.0441, 0.0831, 0.5401, 0.3126, 0.6741 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-13_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 183 211.4 3.820 3.820 r= 29 5194 5134.0 0.701 4.521 r= 30 23075 23103.0 0.034 4.555 r= 31 11548 11551.5 0.001 4.556 chi-square = 4.556 with df = 3; p-value = 0.793 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-13_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5101 5134.0 0.212 0.647 r= 31 23269 23103.0 1.192 1.839 r= 32 11409 11551.5 1.758 3.597 chi-square = 3.597 with df = 3; p-value = 0.692 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-13_11:31 b-rank test for bits 1 to 8, p=0.78148 b-rank test for bits 2 to 9, p=0.38153 b-rank test for bits 3 to 10, p=0.27304 b-rank test for bits 4 to 11, p=0.61451 b-rank test for bits 5 to 12, p=0.81034 b-rank test for bits 6 to 13, p=0.41133 b-rank test for bits 7 to 14, p=0.24098 b-rank test for bits 8 to 15, p=0.99696 b-rank test for bits 9 to 16, p=0.85639 b-rank test for bits 10 to 17, p=0.95634 b-rank test for bits 11 to 18, p=0.03123 b-rank test for bits 12 to 19, p=0.09347 b-rank test for bits 13 to 20, p=0.05782 b-rank test for bits 14 to 21, p=0.17441 b-rank test for bits 15 to 22, p=0.22386 b-rank test for bits 16 to 23, p=0.84997 b-rank test for bits 17 to 24, p=0.42762 b-rank test for bits 18 to 25, p=0.07771 b-rank test for bits 19 to 26, p=0.18750 b-rank test for bits 20 to 27, p=0.01723 b-rank test for bits 21 to 28, p=0.50232 b-rank test for bits 22 to 29, p=0.48381 b-rank test for bits 23 to 30, p=0.44849 b-rank test for bits 24 to 31, p=0.27669 b-rank test for bits 25 to 32, p=0.22715 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 = 0.188489 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-13_11:31 (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 142020 0.26 0.602018 2 141615 -0.69 0.245825 3 141232 -1.58 0.056762 4 141315 -1.39 0.082474 5 141889 -0.05 0.481057 6 142647 1.72 0.957603 7 142539 1.47 0.929380 8 141666 -0.57 0.284838 9 142164 0.60 0.724086 10 142483 1.34 0.909934 11 142506 1.39 0.918355 12 142434 1.23 0.889875 13 141823 -0.20 0.420073 14 142243 0.78 0.782188 15 142822 2.13 0.983513 16 141677 -0.54 0.293624 17 141697 -0.50 0.309913 18 141124 -1.83 0.033262 19 142194 0.67 0.747012 20 142450 1.26 0.896750 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-13_11:31 Bits used No. missing words z-score p-value 23 to 32 142346 1.5058 0.933935 22 to 31 142264 1.2230 0.889335 21 to 30 142443 1.8402 0.967134 20 to 29 141813 -0.3322 0.369880 19 to 28 142157 0.8540 0.803457 18 to 27 142059 0.5161 0.697109 17 to 26 142010 0.3471 0.635756 16 to 25 142304 1.3609 0.913232 15 to 24 141698 -0.7287 0.233085 14 to 23 141584 -1.1218 0.130968 13 to 22 141330 -1.9977 0.022875 12 to 21 142019 0.3782 0.647349 11 to 20 141940 0.1058 0.542113 10 to 19 141857 -0.1804 0.428400 9 to 18 142136 0.7816 0.782781 8 to 17 142408 1.7196 0.957243 7 to 16 141424 -1.6736 0.047109 6 to 15 141443 -1.6080 0.053914 5 to 14 142074 0.5678 0.714924 4 to 13 141510 -1.3770 0.084256 3 to 12 141853 -0.1942 0.422994 2 to 11 141745 -0.5667 0.285474 1 to 10 141423 -1.6770 0.046771 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-13_11:31 Bits used No. missing words z-score p-value 28 to 32 141843 -0.2248 0.411049 27 to 31 141763 -0.4960 0.309935 26 to 30 141746 -0.5537 0.289905 25 to 29 141926 0.0565 0.522532 24 to 28 142002 0.3141 0.623291 23 to 27 141361 -1.8587 0.031532 22 to 26 142022 0.3819 0.648744 21 to 25 141537 -1.2621 0.103450 20 to 24 141727 -0.6181 0.268265 19 to 23 141969 0.2023 0.580148 18 to 22 141903 -0.0215 0.491440 17 to 21 141715 -0.6587 0.255030 16 to 20 141998 0.3006 0.618131 15 to 19 142472 1.9074 0.971763 14 to 18 141820 -0.3028 0.381016 13 to 17 141143 -2.5977 0.004692 12 to 16 142170 0.8836 0.811551 11 to 15 142380 1.5955 0.944699 10 to 14 141473 -1.4791 0.069559 9 to 13 142055 0.4938 0.689275 8 to 12 141196 -2.4181 0.007802 7 to 11 141786 -0.4181 0.337949 6 to 10 141757 -0.5164 0.302797 5 to 9 142171 0.8870 0.812465 4 to 8 142517 2.0599 0.980296 3 to 7 141649 -0.8825 0.188760 2 to 6 141212 -2.3638 0.009044 1 to 5 141857 -0.1774 0.429601 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-13_11:31 Bits used No. missing words z-score p-value 31 to 32 141334 -1.6971 0.044835 30 to 31 141881 -0.0836 0.466699 29 to 30 141551 -1.0570 0.145251 28 to 29 142343 1.2793 0.899598 27 to 28 142042 0.3914 0.652233 26 to 27 141482 -1.2606 0.103734 25 to 26 142205 0.8722 0.808446 24 to 25 141607 -0.8918 0.186242 23 to 24 141885 -0.0718 0.471393 22 to 23 141879 -0.0895 0.464355 21 to 22 142035 0.3707 0.644573 20 to 21 141950 0.1200 0.547747 19 to 20 141632 -0.8181 0.206655 18 to 19 142222 0.9223 0.821822 17 to 18 141992 0.2439 0.596332 16 to 17 141850 -0.1750 0.430534 15 to 16 141499 -1.2104 0.113060 14 to 15 141703 -0.6086 0.271381 13 to 14 142209 0.8840 0.811647 12 to 13 141829 -0.2370 0.406343 11 to 12 142012 0.3029 0.619002 10 to 11 141805 -0.3078 0.379133 9 to 10 142010 0.2970 0.616752 8 to 9 141610 -0.8830 0.188624 7 to 8 141841 -0.2016 0.420129 6 to 7 142023 0.3353 0.631304 5 to 6 141861 -0.1426 0.443316 4 to 5 142343 1.2793 0.899598 3 to 4 142318 1.2055 0.885998 2 to 3 141355 -1.6352 0.051004 1 to 2 141577 -0.9803 0.163463 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-13_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2380.40 -1.691 0.045386 Test results for specific bytes for dh-ranFile-2016-03-13_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2550.75 0.718 0.763515 2 to 9 2463.69 -0.514 0.303783 3 to 10 2534.19 0.483 0.685615 4 to 11 2471.75 -0.399 0.344773 5 to 12 2362.87 -1.939 0.026231 6 to 13 2521.35 0.302 0.618668 7 to 14 2384.91 -1.628 0.051796 8 to 15 2417.82 -1.162 0.122589 9 to 16 2385.65 -1.617 0.052919 10 to 17 2484.96 -0.213 0.415792 11 to 18 2608.01 1.528 0.936684 12 to 19 2469.71 -0.428 0.334200 13 to 20 2405.59 -1.335 0.090912 14 to 21 2447.48 -0.743 0.228830 15 to 22 2398.49 -1.436 0.075566 16 to 23 2511.23 0.159 0.563102 17 to 24 2565.01 0.919 0.821036 18 to 25 2529.50 0.417 0.661713 19 to 26 2656.74 2.217 0.986676 20 to 27 2551.56 0.729 0.767038 21 to 28 2464.40 -0.503 0.307336 22 to 29 2577.15 1.091 0.862369 23 to 30 2469.09 -0.437 0.331009 24 to 31 2516.03 0.227 0.589653 25 to 32 2563.49 0.898 0.815361 CDPARK for dh-ranFile-2016-03-13_11:31: 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 3557 1.5525 0.939730 3522 -0.0457 0.481790 3520 -0.1370 0.445521 3541 0.8219 0.794438 3573 2.2831 0.988788 3525 0.0913 0.536383 3531 0.3653 0.642555 3556 1.5068 0.934075 3551 1.2785 0.899470 3531 0.3653 0.642555 Square side=100, avg. no. parked=3540.70 sample std.=16.92 p-value of the KSTEST for those 10 p-values: 0.015666 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-13_11:31 0.7989,0.8562,0.6471,0.3804,0.8807,0.5934,0.0646,0.9762,0.2975,0.0535, The KS test for those 10 p-values: 0.712599 The 3DSPHERES test for dh-ranFile-2016-03-13_11:31 sample no r^3 equiv. uni. 1 15.828 0.409973 2 37.958 0.717835 3 35.491 0.693653 4 29.077 0.620632 5 10.447 0.294057 6 128.716 0.986302 7 30.407 0.637074 8 6.687 0.199806 9 31.536 0.650477 10 47.013 0.791347 11 93.869 0.956238 12 46.386 0.786945 13 2.799 0.089081 14 19.436 0.476837 15 1.159 0.037912 16 6.875 0.204795 17 10.693 0.299824 18 22.929 0.534338 19 16.446 0.422016 20 1.371 0.044665 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.985518 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-13_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.8 0.6 -0.5 -0.4 1.1 2.1 -0.1 0.0 -0.3 0.9 -0.5 -1.6 -0.2 1.4 0.1 -0.3 0.8 0.5 0.6 0.4 -1.9 -1.2 -1.9 0.9 -0.5 1.4 0.3 0.1 0.1 0.2 -1.0 0.0 -1.2 1.0 1.0 1.8 -0.4 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:33.950564 z-score=-0.878265, p-value=0.192814 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-13_11:31 Test no p-value 1 0.447291 2 0.048436 3 0.914771 4 0.958554 5 0.075939 6 0.201126 7 0.163052 8 0.680910 9 0.648215 10 0.003484 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.227718 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-13_11:31: (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 66477 0.54 66570 0.14 3 25000.00 25008 0.00 24987 0.01 4 6666.67 6810 3.08 6711 0.29 5 1388.89 1449 2.60 1456 3.24 6 238.10 210 3.32 235 0.04 7 34.72 40 0.80 34 0.01 8 4.96 5 0.00 6 0.22 p=0.88910 p=0.31759 Number of rngs required: 688138, p-value: 0.380 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-13_11:31 No. of wins: Observed Expected 98600 98585.9 z-score= 0.063, pvalue=0.52522 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66966 66666.7 1.344 1.344 2 37618 37654.3 0.035 1.379 3 26891 26954.7 0.151 1.530 4 19445 19313.5 0.896 2.426 5 13624 13851.4 3.734 6.159 6 9866 9943.5 0.605 6.764 7 6981 7145.0 3.765 10.530 8 5115 5139.1 0.113 10.642 9 3717 3699.9 0.079 10.722 10 2685 2666.3 0.131 10.853 11 1952 1923.3 0.427 11.280 12 1449 1388.7 2.615 13.895 13 993 1003.7 0.114 14.010 14 714 726.1 0.203 14.213 15 527 525.8 0.003 14.215 16 418 381.2 3.563 17.778 17 266 276.5 0.402 18.179 18 213 200.8 0.737 18.917 19 144 146.0 0.027 18.944 20 113 106.2 0.433 19.377 21 303 287.1 0.879 20.256 Chisq= 20.26 for 20 degrees of freedom, p= 0.55799 SUMMARY of craptest p-value for no. of wins: 0.525216 p-value for throws/game: 0.557990 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-13_11:31 No. of wins: Observed Expected 98912 98585.9 z-score= 1.459, pvalue=0.92768 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66367 66666.7 1.347 1.347 2 37605 37654.3 0.065 1.412 3 27076 26954.7 0.546 1.957 4 19358 19313.5 0.103 2.060 5 13956 13851.4 0.790 2.849 6 10036 9943.5 0.860 3.709 7 7233 7145.0 1.083 4.792 8 5029 5139.1 2.358 7.150 9 3694 3699.9 0.009 7.159 10 2566 2666.3 3.773 10.932 11 1870 1923.3 1.479 12.411 12 1450 1388.7 2.702 15.113 13 1070 1003.7 4.377 19.490 14 727 726.1 0.001 19.492 15 536 525.8 0.196 19.688 16 384 381.2 0.021 19.709 17 278 276.5 0.008 19.717 18 234 200.8 5.479 25.196 19 138 146.0 0.437 25.632 20 110 106.2 0.135 25.767 21 283 287.1 0.059 25.826 Chisq= 25.83 for 20 degrees of freedom, p= 0.82837 SUMMARY of craptest p-value for no. of wins: 0.927675 p-value for throws/game: 0.828366 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0047,0.0078,0.0090,0.0157,0.0172,0.0229,0.0231,0.0262,0.0312, 0.0315,0.0333,0.0379,0.0441,0.0447,0.0448,0.0454,0.0468,0.0471,0.0484, 0.0510,0.0518,0.0529,0.0535,0.0539,0.0568,0.0578,0.0646,0.0696,0.0756, 0.0759,0.0777,0.0802,0.0825,0.0831,0.0843,0.0891,0.0909,0.0917,0.0935, 0.1035,0.1037,0.1127,0.1131,0.1206,0.1226,0.1310,0.1343,0.1453,0.1587, 0.1631,0.1635,0.1744,0.1862,0.1875,0.1885,0.1886,0.1888,0.1928,0.1965, 0.1998,0.2011,0.2048,0.2067,0.2079,0.2239,0.2271,0.2277,0.2288,0.2331, 0.2410,0.2458,0.2550,0.2561,0.2682,0.2683,0.2714,0.2730,0.2740,0.2767, 0.2848,0.2855,0.2899,0.2936,0.2941,0.2975,0.2998,0.3028,0.3038,0.3073, 0.3099,0.3099,0.3126,0.3176,0.3310,0.3342,0.3379,0.3448,0.3459,0.3699, 0.3791,0.3796,0.3802,0.3804,0.3810,0.3815,0.4063,0.4100,0.4110,0.4113, 0.4158,0.4201,0.4201,0.4204,0.4220,0.4230,0.4276,0.4284,0.4296,0.4305, 0.4433,0.4448,0.4455,0.4473,0.4473,0.4485,0.4644,0.4667,0.4714,0.4768, 0.4811,0.4818,0.4838,0.4914,0.4961,0.5006,0.5023,0.5163,0.5225,0.5252, 0.5343,0.5364,0.5401,0.5421,0.5477,0.5580,0.5631,0.5660,0.5801,0.5897, 0.5898,0.5934,0.5963,0.6020,0.6145,0.6168,0.6181,0.6187,0.6190,0.6206, 0.6233,0.6277,0.6313,0.6358,0.6371,0.6426,0.6426,0.6446,0.6471,0.6473, 0.6481,0.6482,0.6487,0.6505,0.6516,0.6522,0.6617,0.6653,0.6741,0.6809, 0.6856,0.6893,0.6912,0.6916,0.6937,0.6963,0.6971,0.7126,0.7141,0.7149, 0.7178,0.7241,0.7388,0.7438,0.7470,0.7635,0.7636,0.7670,0.7815,0.7822, 0.7828,0.7850,0.7869,0.7874,0.7913,0.7926,0.7944,0.7989,0.8035,0.8084, 0.8103,0.8116,0.8116,0.8125,0.8154,0.8210,0.8218,0.8284,0.8448,0.8500, 0.8562,0.8564,0.8624,0.8738,0.8807,0.8851,0.8860,0.8891,0.8893,0.8899, 0.8935,0.8967,0.8995,0.8996,0.8996,0.9070,0.9099,0.9132,0.9148,0.9161, 0.9175,0.9184,0.9185,0.9277,0.9294,0.9339,0.9341,0.9367,0.9397,0.9447, 0.9538,0.9562,0.9563,0.9572,0.9576,0.9586,0.9591,0.9671,0.9718,0.9762, 0.9772,0.9803,0.9835,0.9855,0.9863,0.9867,0.9888,0.9902,0.9970, Overall p-value after applying KStest on 269 p-values = 0.208261 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.