RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-28_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 15.75 27.0705 0.942958 2 to 25 15.77 22.5439 0.835303 3 to 26 15.75 17.1080 0.552925 4 to 27 16.03 17.6115 0.586261 5 to 28 15.87 18.7930 0.659456 6 to 29 15.66 14.3851 0.360320 7 to 30 15.78 13.4727 0.295986 8 to 31 15.69 15.6644 0.452264 9 to 32 15.63 19.6201 0.705881 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.405197 Tough bday spacings test for dh-ranFile-2018-03-28_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 28 75 98 95 74 60 30 16 11 7 (O-E)^2/E 1.1 2.0 0.0 0.0 0.1 0.2 1.2 0.0 0.1 2.9 2.1 Birthday Spacings: Sum(O-E)^2/E= 9.765, p= 0.539 RESULTS OF GCD FOR dh-ranFile-2018-03-28_12:31 Euclid's algorithm: p-value, steps to gcd: 0.527341 p-value, dist. of gcd's: 0.732249 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-28_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.359 0.706 0.911 0.830 0.146 0.871 0.722 0.091 Bits 8 to 15---> 0.530 0.673 0.860 0.285 0.143 0.200 0.606 0.613 Bits 16 to 23---> 0.327 0.062 0.131 0.706 0.790 0.474 0.279 0.576 Bits 24 to 31---> 0.806 0.477 0.037 0.461 0.023 0.597 0.751 0.494 KS test for the above 32 p values: 0.174 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-28_12:31, p-values for 5 runs: 0.9257, 0.0096, 0.3512, 0.4531, 0.5578 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-28_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5161 5134.0 0.142 1.442 r= 30 23217 23103.0 0.562 2.004 r= 31 11394 11551.5 2.148 4.153 chi-square = 4.153 with df = 3; p-value = 0.755 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-28_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5178 5134.0 0.377 0.408 r= 31 23007 23103.0 0.399 0.808 r= 32 11601 11551.5 0.212 1.020 chi-square = 1.020 with df = 3; p-value = 0.204 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-28_12:31 b-rank test for bits 1 to 8, p=0.06494 b-rank test for bits 2 to 9, p=0.63499 b-rank test for bits 3 to 10, p=0.61947 b-rank test for bits 4 to 11, p=0.21987 b-rank test for bits 5 to 12, p=0.59954 b-rank test for bits 6 to 13, p=0.67366 b-rank test for bits 7 to 14, p=0.43020 b-rank test for bits 8 to 15, p=0.66315 b-rank test for bits 9 to 16, p=0.42714 b-rank test for bits 10 to 17, p=0.06092 b-rank test for bits 11 to 18, p=0.03926 b-rank test for bits 12 to 19, p=0.79725 b-rank test for bits 13 to 20, p=0.44807 b-rank test for bits 14 to 21, p=0.68483 b-rank test for bits 15 to 22, p=0.65738 b-rank test for bits 16 to 23, p=0.03556 b-rank test for bits 17 to 24, p=0.91022 b-rank test for bits 18 to 25, p=0.71414 b-rank test for bits 19 to 26, p=0.03742 b-rank test for bits 20 to 27, p=0.71494 b-rank test for bits 21 to 28, p=0.47779 b-rank test for bits 22 to 29, p=0.28044 b-rank test for bits 23 to 30, p=0.19368 b-rank test for bits 24 to 31, p=0.19354 b-rank test for bits 25 to 32, p=0.61826 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 = 0.254418 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-28_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 140984 -2.16 0.015310 2 141729 -0.42 0.336756 3 141583 -0.76 0.222895 4 141581 -0.77 0.221503 5 142692 1.83 0.966275 6 141807 -0.24 0.405518 7 141285 -1.46 0.072322 8 142125 0.50 0.692835 9 141930 0.05 0.519259 10 142215 0.71 0.762443 11 141371 -1.26 0.104236 12 141895 -0.03 0.486645 13 141702 -0.48 0.314045 14 141945 0.08 0.533210 15 142469 1.31 0.904502 16 141947 0.09 0.535067 17 141272 -1.49 0.068232 18 141038 -2.04 0.020884 19 142179 0.63 0.735676 20 141837 -0.17 0.432900 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-28_12:31 Bits used No. missing words z-score p-value 23 to 32 142230 1.1058 0.865585 22 to 31 142300 1.3471 0.911032 21 to 30 141482 -1.4736 0.070301 20 to 29 141577 -1.1460 0.125905 19 to 28 141467 -1.5253 0.063595 18 to 27 141591 -1.0977 0.136170 17 to 26 141724 -0.6391 0.261389 16 to 25 142031 0.4196 0.662594 15 to 24 141748 -0.5563 0.288999 14 to 23 142186 0.9540 0.829967 13 to 22 142078 0.5816 0.719589 12 to 21 142346 1.5058 0.933935 11 to 20 142377 1.6127 0.946590 10 to 19 141957 0.1644 0.565284 9 to 18 142270 1.2437 0.893193 8 to 17 142022 0.3885 0.651183 7 to 16 141771 -0.4770 0.316681 6 to 15 141811 -0.3391 0.367279 5 to 14 142039 0.4471 0.672612 4 to 13 141512 -1.3701 0.085327 3 to 12 142052 0.4920 0.688628 2 to 11 142670 2.6230 0.995642 1 to 10 142323 1.4264 0.923131 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-28_12:31 Bits used No. missing words z-score p-value 28 to 32 142081 0.5819 0.719694 27 to 31 142053 0.4870 0.686877 26 to 30 142078 0.5718 0.716259 25 to 29 142000 0.3074 0.620714 24 to 28 141806 -0.3503 0.363068 23 to 27 141797 -0.3808 0.351683 22 to 26 141709 -0.6791 0.248542 21 to 25 141535 -1.2689 0.102236 20 to 24 142078 0.5718 0.716259 19 to 23 141552 -1.2113 0.112893 18 to 22 141966 0.1921 0.576169 17 to 21 141631 -0.9435 0.172715 16 to 20 141914 0.0158 0.506315 15 to 19 141684 -0.7638 0.222484 14 to 18 141634 -0.9333 0.175327 13 to 17 141416 -1.6723 0.047232 12 to 16 141672 -0.8045 0.210552 11 to 15 141920 0.0362 0.514426 10 to 14 141670 -0.8113 0.208600 9 to 13 141741 -0.5706 0.284132 8 to 12 141998 0.3006 0.618131 7 to 11 141712 -0.6689 0.251775 6 to 10 141529 -1.2893 0.098655 5 to 9 141969 0.2023 0.580148 4 to 8 141711 -0.6723 0.250695 3 to 7 141847 -0.2113 0.416331 2 to 6 141703 -0.6994 0.242144 1 to 5 141455 -1.5401 0.061768 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-28_12:31 Bits used No. missing words z-score p-value 31 to 32 142212 0.8928 0.814026 30 to 31 141527 -1.1278 0.129699 29 to 30 142070 0.4740 0.682233 28 to 29 141816 -0.2753 0.391539 27 to 28 141979 0.2055 0.581416 26 to 27 141834 -0.2222 0.412074 25 to 26 142309 1.1790 0.880794 24 to 25 142535 1.8456 0.967527 23 to 24 142470 1.6539 0.950925 22 to 23 142380 1.3884 0.917493 21 to 22 142245 0.9902 0.838956 20 to 21 141633 -0.8151 0.207498 19 to 20 141566 -1.0128 0.155584 18 to 19 142072 0.4799 0.684334 17 to 18 142101 0.5654 0.714099 16 to 17 141430 -1.4140 0.078688 15 to 16 141777 -0.3904 0.348137 14 to 15 141235 -1.9892 0.023341 13 to 14 141598 -0.9184 0.179211 12 to 13 142106 0.5801 0.719092 11 to 12 141805 -0.3078 0.379133 10 to 11 141969 0.1760 0.569860 9 to 10 141753 -0.4612 0.322345 8 to 9 142078 0.4976 0.690600 7 to 8 141975 0.1937 0.576801 6 to 7 141754 -0.4582 0.323404 5 to 6 142177 0.7896 0.785116 4 to 5 142070 0.4740 0.682233 3 to 4 142218 0.9105 0.818729 2 to 3 141764 -0.4287 0.334070 1 to 2 142781 2.5713 0.994934 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-28_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2444.87 -0.780 0.217799 Test results for specific bytes for dh-ranFile-2018-03-28_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2611.57 1.578 0.942694 2 to 9 2546.35 0.655 0.743914 3 to 10 2582.51 1.167 0.878364 4 to 11 2423.75 -1.078 0.140440 5 to 12 2652.13 2.151 0.984279 6 to 13 2662.17 2.293 0.989088 7 to 14 2533.83 0.478 0.683840 8 to 15 2553.06 0.750 0.773504 9 to 16 2492.92 -0.100 0.460135 10 to 17 2492.01 -0.113 0.455000 11 to 18 2551.17 0.724 0.765350 12 to 19 2420.26 -1.128 0.129721 13 to 20 2506.88 0.097 0.538735 14 to 21 2443.73 -0.796 0.213079 15 to 22 2541.89 0.592 0.723233 16 to 23 2369.88 -1.840 0.032876 17 to 24 2485.79 -0.201 0.420344 18 to 25 2527.69 0.392 0.652338 19 to 26 2522.70 0.321 0.625896 20 to 27 2337.74 -2.295 0.010875 21 to 28 2520.55 0.291 0.614311 22 to 29 2483.04 -0.240 0.405206 23 to 30 2505.98 0.085 0.533714 24 to 31 2390.71 -1.546 0.061108 25 to 32 2418.04 -1.159 0.123219 CDPARK for dh-ranFile-2018-03-28_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 3512 -0.5023 0.307734 3520 -0.1370 0.445521 3529 0.2740 0.607947 3529 0.2740 0.607947 3559 1.6438 0.949895 3534 0.5023 0.692266 3484 -1.7808 0.037471 3567 2.0091 0.977738 3541 0.8219 0.794438 3554 1.4155 0.921543 Square side=100, avg. no. parked=3532.90 sample std.=23.20 p-value of the KSTEST for those 10 p-values: 0.205582 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-28_12:31 0.6331,0.3448,0.5786,0.9406,0.3360,0.9705,0.8685,0.9495,0.5383,0.5230, The KS test for those 10 p-values: 0.076423 The 3DSPHERES test for dh-ranFile-2018-03-28_12:31 sample no r^3 equiv. uni. 1 34.921 0.687775 2 10.131 0.286580 3 44.843 0.775699 4 19.588 0.479479 5 32.902 0.666040 6 27.827 0.604482 7 44.051 0.769698 8 0.849 0.027894 9 5.236 0.160140 10 3.801 0.118998 11 13.724 0.367110 12 6.190 0.186444 13 147.704 0.992726 14 8.802 0.254272 15 2.596 0.082887 16 5.254 0.160658 17 38.844 0.726046 18 28.595 0.614476 19 2.859 0.090905 20 24.282 0.554870 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.410260 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-28_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.6 1.6 0.2 -1.6 -1.5 2.4 -0.1 1.0 -0.6 2.0 -0.7 0.3 0.9 -2.3 -0.8 1.5 -0.8 -0.7 1.5 -0.9 1.0 0.6 -0.2 -0.9 -0.8 -0.4 0.7 -0.7 0.5 -0.5 -0.5 -1.1 2.2 0.6 -0.9 1.5 0.5 0.4 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:47.210558 z-score=0.568519, p-value=0.731935 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-28_12:31 Test no p-value 1 0.301562 2 0.023261 3 0.519436 4 0.114744 5 0.401357 6 0.059247 7 0.091683 8 0.255704 9 0.266731 10 0.763572 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.024462 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-28_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 66667 0.00 66753 0.11 3 25000.00 25051 0.10 24925 0.23 4 6666.67 6608 0.52 6671 0.00 5 1388.89 1390 0.00 1364 0.45 6 238.10 237 0.01 231 0.21 7 34.72 39 0.53 52 8.60 8 4.96 7 0.84 3 0.77 p=0.07965 p=0.89016 Number of rngs required: 688095, p-value: 0.361 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-28_12:31 No. of wins: Observed Expected 98688 98585.9 z-score= 0.457, pvalue=0.67611 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66755 66666.7 0.117 0.117 2 37630 37654.3 0.016 0.133 3 26872 26954.7 0.254 0.387 4 19145 19313.5 1.469 1.856 5 13899 13851.4 0.163 2.020 6 10015 9943.5 0.514 2.533 7 7279 7145.0 2.512 5.045 8 5111 5139.1 0.153 5.199 9 3716 3699.9 0.070 5.269 10 2674 2666.3 0.022 5.291 11 1879 1923.3 1.022 6.313 12 1381 1388.7 0.043 6.356 13 1014 1003.7 0.105 6.461 14 728 726.1 0.005 6.466 15 494 525.8 1.927 8.394 16 379 381.2 0.012 8.406 17 264 276.5 0.569 8.974 18 195 200.8 0.169 9.144 19 146 146.0 0.000 9.144 20 110 106.2 0.135 9.278 21 314 287.1 2.518 11.796 Chisq= 11.80 for 20 degrees of freedom, p= 0.07708 SUMMARY of craptest p-value for no. of wins: 0.676106 p-value for throws/game: 0.077083 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-28_12:31 No. of wins: Observed Expected 98301 98585.9 z-score=-1.274, pvalue=0.10132 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66513 66666.7 0.354 0.354 2 37370 37654.3 2.147 2.501 3 26966 26954.7 0.005 2.506 4 19529 19313.5 2.405 4.911 5 13865 13851.4 0.013 4.924 6 10068 9943.5 1.558 6.482 7 7273 7145.0 2.292 8.774 8 5092 5139.1 0.431 9.206 9 3740 3699.9 0.435 9.641 10 2584 2666.3 2.540 12.181 11 1927 1923.3 0.007 12.188 12 1379 1388.7 0.068 12.256 13 961 1003.7 1.818 14.074 14 752 726.1 0.921 14.995 15 550 525.8 1.110 16.106 16 410 381.2 2.184 18.289 17 291 276.5 0.756 19.045 18 176 200.8 3.070 22.115 19 155 146.0 0.557 22.672 20 105 106.2 0.014 22.686 21 294 287.1 0.165 22.851 Chisq= 22.85 for 20 degrees of freedom, p= 0.70383 SUMMARY of craptest p-value for no. of wins: 0.101322 p-value for throws/game: 0.703833 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0096,0.0109,0.0153,0.0209,0.0233,0.0233,0.0233,0.0245,0.0279,0.0329, 0.0356,0.0373,0.0374,0.0375,0.0393,0.0472,0.0592,0.0609,0.0611,0.0616, 0.0618,0.0636,0.0649,0.0682,0.0703,0.0723,0.0764,0.0771,0.0787,0.0797, 0.0829,0.0853,0.0909,0.0915,0.0917,0.0987,0.1013,0.1022,0.1042,0.1129, 0.1147,0.1190,0.1232,0.1259,0.1297,0.1297,0.1307,0.1362,0.1404,0.1427, 0.1463,0.1556,0.1601,0.1607,0.1727,0.1737,0.1753,0.1792,0.1864,0.1935, 0.1937,0.2002,0.2035,0.2056,0.2075,0.2086,0.2106,0.2131,0.2178,0.2199, 0.2215,0.2225,0.2229,0.2421,0.2485,0.2507,0.2518,0.2543,0.2544,0.2557, 0.2614,0.2667,0.2788,0.2804,0.2841,0.2847,0.2866,0.2890,0.2960,0.3016, 0.3077,0.3140,0.3167,0.3223,0.3234,0.3274,0.3341,0.3360,0.3368,0.3448, 0.3481,0.3512,0.3517,0.3593,0.3603,0.3614,0.3631,0.3671,0.3673,0.3791, 0.3915,0.4014,0.4052,0.4052,0.4055,0.4103,0.4121,0.4163,0.4203,0.4271, 0.4302,0.4329,0.4455,0.4481,0.4523,0.4531,0.4550,0.4601,0.4612,0.4744, 0.4769,0.4778,0.4795,0.4866,0.4944,0.5063,0.5144,0.5193,0.5194,0.5230, 0.5273,0.5300,0.5332,0.5337,0.5351,0.5383,0.5387,0.5387,0.5529,0.5549, 0.5578,0.5653,0.5699,0.5762,0.5763,0.5768,0.5786,0.5801,0.5814,0.5863, 0.5975,0.5995,0.6045,0.6062,0.6079,0.6079,0.6125,0.6143,0.6145,0.6181, 0.6183,0.6195,0.6207,0.6259,0.6331,0.6350,0.6512,0.6523,0.6574,0.6595, 0.6626,0.6631,0.6660,0.6726,0.6732,0.6737,0.6761,0.6822,0.6822,0.6838, 0.6843,0.6848,0.6869,0.6878,0.6886,0.6906,0.6923,0.6928,0.7038,0.7057, 0.7059,0.7060,0.7141,0.7141,0.7149,0.7163,0.7163,0.7191,0.7196,0.7197, 0.7221,0.7232,0.7260,0.7319,0.7322,0.7357,0.7439,0.7509,0.7545,0.7624, 0.7636,0.7654,0.7697,0.7735,0.7757,0.7851,0.7899,0.7944,0.7973,0.8063, 0.8140,0.8187,0.8298,0.8300,0.8353,0.8390,0.8598,0.8656,0.8685,0.8713, 0.8784,0.8808,0.8902,0.8932,0.9045,0.9102,0.9110,0.9111,0.9175,0.9215, 0.9231,0.9257,0.9339,0.9406,0.9427,0.9430,0.9466,0.9495,0.9499,0.9509, 0.9663,0.9675,0.9705,0.9777,0.9843,0.9891,0.9927,0.9949,0.9956, Overall p-value after applying KStest on 269 p-values = 0.199262 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.