RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 22.9145 0.847944 2 to 25 15.85 21.7191 0.804234 3 to 26 15.83 19.7441 0.712471 4 to 27 15.96 12.4529 0.228027 5 to 28 15.92 13.8672 0.323520 6 to 29 15.56 30.8349 0.979085 7 to 30 15.47 19.9709 0.724281 8 to 31 15.73 14.2788 0.352723 9 to 32 15.67 17.5929 0.585055 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.381814 Tough bday spacings test for dh-ranFile-2018-07-02_22:31: 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 32 70 82 107 87 55 38 13 5 3 (O-E)^2/E 0.1 0.6 0.1 2.5 0.9 1.0 0.2 2.3 0.2 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.636, p= 0.433 RESULTS OF GCD FOR dh-ranFile-2018-07-02_22:31 Euclid's algorithm: p-value, steps to gcd: 0.333413 p-value, dist. of gcd's: 0.753811 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.223 0.112 0.379 0.561 0.575 0.398 0.513 0.850 Bits 8 to 15---> 0.398 0.265 0.414 0.487 0.878 0.062 0.500 0.526 Bits 16 to 23---> 0.121 0.450 0.391 0.908 0.711 0.469 0.799 0.250 Bits 24 to 31---> 0.579 0.200 0.598 0.389 0.780 0.557 0.492 0.407 KS test for the above 32 p values: 0.856 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_22:31, p-values for 5 runs: 0.2541, 0.2059, 0.5445, 0.1544, 0.1317 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5155 5134.0 0.086 1.521 r= 30 23180 23103.0 0.256 1.777 r= 31 11471 11551.5 0.561 2.338 chi-square = 2.338 with df = 3; p-value = 0.495 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5198 5134.0 0.798 1.946 r= 31 23089 23103.0 0.009 1.955 r= 32 11486 11551.5 0.372 2.326 chi-square = 2.326 with df = 3; p-value = 0.492 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_22:31 b-rank test for bits 1 to 8, p=0.14027 b-rank test for bits 2 to 9, p=0.78379 b-rank test for bits 3 to 10, p=0.27105 b-rank test for bits 4 to 11, p=0.37875 b-rank test for bits 5 to 12, p=0.07204 b-rank test for bits 6 to 13, p=0.30888 b-rank test for bits 7 to 14, p=0.00432 b-rank test for bits 8 to 15, p=0.65838 b-rank test for bits 9 to 16, p=0.58227 b-rank test for bits 10 to 17, p=0.43865 b-rank test for bits 11 to 18, p=0.36646 b-rank test for bits 12 to 19, p=0.60548 b-rank test for bits 13 to 20, p=0.78304 b-rank test for bits 14 to 21, p=0.37201 b-rank test for bits 15 to 22, p=0.14092 b-rank test for bits 16 to 23, p=0.81742 b-rank test for bits 17 to 24, p=0.53294 b-rank test for bits 18 to 25, p=0.37065 b-rank test for bits 19 to 26, p=0.67326 b-rank test for bits 20 to 27, p=0.47642 b-rank test for bits 21 to 28, p=0.62784 b-rank test for bits 22 to 29, p=0.36106 b-rank test for bits 23 to 30, p=0.46226 b-rank test for bits 24 to 31, p=0.06654 b-rank test for bits 25 to 32, p=0.16411 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 = 0.159549 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_22:31 (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 141956 0.11 0.543415 2 142513 1.41 0.920796 3 142362 1.06 0.854890 4 141514 -0.92 0.177830 5 142264 0.83 0.796354 6 141100 -1.89 0.029315 7 141588 -0.75 0.226395 8 141614 -0.69 0.245090 9 142597 1.61 0.945941 10 141171 -1.73 0.042257 11 141136 -1.81 0.035393 12 141749 -0.37 0.353978 13 142084 0.41 0.658403 14 141963 0.13 0.549895 15 141611 -0.70 0.242891 16 141404 -1.18 0.118865 17 143257 3.15 0.999180 18 140903 -2.35 0.009356 19 141044 -2.02 0.021599 20 142165 0.60 0.724866 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-02_22:31 Bits used No. missing words z-score p-value 23 to 32 141732 -0.6115 0.270440 22 to 31 141546 -1.2529 0.105128 21 to 30 141790 -0.4115 0.340359 20 to 29 142244 1.1540 0.875757 19 to 28 142029 0.4127 0.660070 18 to 27 142148 0.8230 0.794746 17 to 26 142119 0.7230 0.765160 16 to 25 142365 1.5713 0.941941 15 to 24 141842 -0.2322 0.408202 14 to 23 142363 1.5644 0.941136 13 to 22 141661 -0.8563 0.195913 12 to 21 141757 -0.5253 0.299696 11 to 20 141903 -0.0218 0.491293 10 to 19 141843 -0.2287 0.409542 9 to 18 141683 -0.7804 0.217564 8 to 17 141823 -0.2977 0.382970 7 to 16 141922 0.0437 0.517424 6 to 15 142007 0.3368 0.631864 5 to 14 141692 -0.7494 0.226804 4 to 13 142172 0.9058 0.817468 3 to 12 141832 -0.2667 0.394867 2 to 11 141728 -0.6253 0.265895 1 to 10 141513 -1.3667 0.085867 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-02_22:31 Bits used No. missing words z-score p-value 28 to 32 141771 -0.4689 0.319565 27 to 31 141697 -0.7198 0.235836 26 to 30 142070 0.5446 0.707001 25 to 29 141813 -0.3265 0.372007 24 to 28 141968 0.1989 0.578822 23 to 27 141125 -2.6587 0.003922 22 to 26 142074 0.5582 0.711647 21 to 25 141591 -1.0791 0.140275 20 to 24 141773 -0.4621 0.321992 19 to 23 141534 -1.2723 0.101632 18 to 22 142286 1.2768 0.899172 17 to 21 141991 0.2768 0.609051 16 to 20 142103 0.6565 0.744252 15 to 19 141879 -0.1028 0.459056 14 to 18 141950 0.1379 0.554826 13 to 17 141831 -0.2655 0.395302 12 to 16 142253 1.1650 0.877987 11 to 15 141940 0.1040 0.541402 10 to 14 142198 0.9785 0.836097 9 to 13 141500 -1.3876 0.082636 8 to 12 141817 -0.3130 0.377147 7 to 11 142490 1.9684 0.975487 6 to 10 142166 0.8701 0.807868 5 to 9 141480 -1.4554 0.072785 4 to 8 141661 -0.8418 0.199951 3 to 7 141774 -0.4587 0.323208 2 to 6 142076 0.5650 0.713957 1 to 5 141553 -1.2079 0.113543 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-02_22:31 Bits used No. missing words z-score p-value 31 to 32 141615 -0.8682 0.192634 30 to 31 141721 -0.5555 0.289261 29 to 30 142378 1.3825 0.916592 28 to 29 141634 -0.8122 0.208343 27 to 28 142352 1.3058 0.904192 26 to 27 141458 -1.3314 0.091536 25 to 26 141899 -0.0305 0.487845 24 to 25 142563 1.9282 0.973087 23 to 24 141665 -0.7207 0.235536 22 to 23 142038 0.3796 0.647863 21 to 22 142368 1.3530 0.911974 20 to 21 141982 0.2144 0.584869 19 to 20 141673 -0.6971 0.242858 18 to 19 141629 -0.8269 0.204138 17 to 18 142101 0.5654 0.714099 16 to 17 141832 -0.2281 0.409780 15 to 16 141499 -1.2104 0.113060 14 to 15 141550 -1.0600 0.144579 13 to 14 141854 -0.1632 0.435174 12 to 13 141945 0.1052 0.541900 11 to 12 141731 -0.5260 0.299428 10 to 11 142155 0.7247 0.765679 9 to 10 141605 -0.8977 0.184665 8 to 9 142240 0.9754 0.835326 7 to 8 141761 -0.4376 0.330856 6 to 7 142150 0.7099 0.761130 5 to 6 141808 -0.2989 0.382505 4 to 5 142008 0.2911 0.614498 3 to 4 141370 -1.5909 0.055811 2 to 3 141999 0.2645 0.604308 1 to 2 142462 1.6303 0.948480 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2515.04 0.213 0.584221 Test results for specific bytes for dh-ranFile-2018-07-02_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2474.03 -0.367 0.356727 2 to 9 2528.16 0.398 0.654751 3 to 10 2456.09 -0.621 0.267305 4 to 11 2549.22 0.696 0.756825 5 to 12 2633.48 1.888 0.970468 6 to 13 2610.87 1.568 0.941549 7 to 14 2549.84 0.705 0.759559 8 to 15 2505.01 0.071 0.528252 9 to 16 2444.25 -0.788 0.215242 10 to 17 2467.61 -0.458 0.323452 11 to 18 2512.84 0.182 0.572036 12 to 19 2502.67 0.038 0.515040 13 to 20 2585.21 1.205 0.885903 14 to 21 2510.72 0.152 0.560233 15 to 22 2569.21 0.979 0.836142 16 to 23 2652.95 2.163 0.984732 17 to 24 2518.29 0.259 0.602063 18 to 25 2410.80 -1.262 0.103561 19 to 26 2436.85 -0.893 0.185894 20 to 27 2453.94 -0.651 0.257389 21 to 28 2601.52 1.436 0.924458 22 to 29 2584.07 1.189 0.882766 23 to 30 2602.43 1.449 0.926282 24 to 31 2614.81 1.624 0.947769 25 to 32 2600.93 1.427 0.923257 CDPARK for dh-ranFile-2018-07-02_22:31: 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 3546 1.0502 0.853193 3518 -0.2283 0.409702 3532 0.4110 0.659449 3526 0.1370 0.554479 3518 -0.2283 0.409702 3532 0.4110 0.659449 3546 1.0502 0.853193 3536 0.5936 0.723613 3519 -0.1826 0.427537 3528 0.2283 0.590298 Square side=100, avg. no. parked=3530.10 sample std.=9.92 p-value of the KSTEST for those 10 p-values: 0.148909 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_22:31 0.3920,0.3768,0.5637,0.3332,0.2053,0.0436,0.9367,0.8874,0.3364,0.8551, The KS test for those 10 p-values: 0.870026 The 3DSPHERES test for dh-ranFile-2018-07-02_22:31 sample no r^3 equiv. uni. 1 11.545 0.319434 2 27.783 0.603903 3 17.962 0.450495 4 31.239 0.647003 5 21.771 0.516006 6 17.047 0.433479 7 14.611 0.385559 8 34.128 0.679417 9 15.508 0.403649 10 44.951 0.776503 11 18.634 0.462662 12 44.986 0.776768 13 42.495 0.757436 14 31.421 0.649136 15 12.546 0.341770 16 23.001 0.535463 17 17.631 0.444394 18 8.404 0.244310 19 0.898 0.029488 20 1.156 0.037795 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.229217 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.6 0.0 -0.4 -0.3 -0.1 -1.5 0.5 -1.9 -0.8 -0.6 -2.0 1.1 0.1 0.5 0.5 1.6 2.8 -0.3 -0.8 -1.0 -1.7 -0.8 1.0 -1.2 0.3 1.5 1.2 -0.4 0.2 0.5 0.2 -1.7 -1.5 0.2 -0.9 0.5 0.5 -0.7 3.9 0.0 0.8 Chi-square with 42 degrees of freedom:59.300331 z-score=1.887621, p-value=0.959742 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-02_22:31 Test no p-value 1 0.120603 2 0.139237 3 0.116842 4 0.912736 5 0.052088 6 0.316511 7 0.289375 8 0.552361 9 0.240166 10 0.132488 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.019485 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_22:31: (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 66441 0.76 66718 0.04 3 25000.00 25169 1.14 24814 1.38 4 6666.67 6733 0.66 6780 1.93 5 1388.89 1391 0.00 1375 0.14 6 238.10 222 1.09 264 2.82 7 34.72 38 0.31 44 2.48 8 4.96 5 0.00 4 0.19 p=0.31895 p=0.82492 Number of rngs required: 687731, p-value: 0.219 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_22:31 No. of wins: Observed Expected 98769 98585.9 z-score= 0.819, pvalue=0.79364 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66746 66666.7 0.094 0.094 2 37699 37654.3 0.053 0.147 3 26700 26954.7 2.407 2.555 4 19269 19313.5 0.102 2.657 5 13731 13851.4 1.047 3.704 6 9971 9943.5 0.076 3.780 7 7274 7145.0 2.328 6.108 8 5186 5139.1 0.429 6.536 9 3693 3699.9 0.013 6.549 10 2577 2666.3 2.991 9.540 11 1967 1923.3 0.992 10.531 12 1464 1388.7 4.079 14.610 13 1039 1003.7 1.240 15.850 14 716 726.1 0.142 15.992 15 546 525.8 0.773 16.765 16 369 381.2 0.387 17.153 17 288 276.5 0.475 17.628 18 222 200.8 2.232 19.859 19 160 146.0 1.346 21.205 20 101 106.2 0.256 21.461 21 282 287.1 0.091 21.552 Chisq= 21.55 for 20 degrees of freedom, p= 0.63469 SUMMARY of craptest p-value for no. of wins: 0.793640 p-value for throws/game: 0.634688 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_22:31 No. of wins: Observed Expected 98595 98585.9 z-score= 0.041, pvalue=0.51631 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66739 66666.7 0.078 0.078 2 37674 37654.3 0.010 0.089 3 26804 26954.7 0.843 0.932 4 19207 19313.5 0.587 1.519 5 13911 13851.4 0.256 1.775 6 9910 9943.5 0.113 1.888 7 7128 7145.0 0.041 1.929 8 5229 5139.1 1.574 3.502 9 3751 3699.9 0.707 4.209 10 2637 2666.3 0.322 4.531 11 1926 1923.3 0.004 4.535 12 1452 1388.7 2.882 7.416 13 1027 1003.7 0.540 7.956 14 703 726.1 0.737 8.694 15 532 525.8 0.072 8.766 16 370 381.2 0.326 9.092 17 282 276.5 0.108 9.200 18 198 200.8 0.040 9.240 19 140 146.0 0.245 9.485 20 82 106.2 5.521 15.006 21 298 287.1 0.413 15.419 Chisq= 15.42 for 20 degrees of freedom, p= 0.24803 SUMMARY of craptest p-value for no. of wins: 0.516307 p-value for throws/game: 0.248026 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0039,0.0043,0.0094,0.0195,0.0216,0.0293,0.0295,0.0354,0.0378,0.0423, 0.0436,0.0521,0.0558,0.0620,0.0665,0.0720,0.0728,0.0826,0.0859,0.0915, 0.1016,0.1036,0.1051,0.1118,0.1131,0.1135,0.1168,0.1189,0.1206,0.1211, 0.1317,0.1325,0.1392,0.1403,0.1403,0.1409,0.1446,0.1489,0.1544,0.1595, 0.1641,0.1778,0.1847,0.1859,0.1926,0.1959,0.1997,0.2000,0.2041,0.2053, 0.2059,0.2083,0.2152,0.2176,0.2188,0.2234,0.2264,0.2268,0.2280,0.2292, 0.2355,0.2358,0.2402,0.2429,0.2429,0.2443,0.2451,0.2480,0.2495,0.2541, 0.2574,0.2647,0.2659,0.2673,0.2704,0.2710,0.2893,0.2894,0.2994,0.2997, 0.3089,0.3165,0.3190,0.3194,0.3196,0.3220,0.3232,0.3235,0.3235,0.3309, 0.3332,0.3334,0.3364,0.3404,0.3418,0.3527,0.3540,0.3567,0.3611,0.3665, 0.3706,0.3720,0.3720,0.3768,0.3771,0.3788,0.3790,0.3818,0.3825,0.3830, 0.3856,0.3894,0.3907,0.3920,0.3949,0.3953,0.3982,0.3985,0.4036,0.4067, 0.4082,0.4095,0.4097,0.4097,0.4098,0.4139,0.4275,0.4331,0.4335,0.4352, 0.4387,0.4444,0.4501,0.4505,0.4591,0.4623,0.4627,0.4689,0.4764,0.4868, 0.4878,0.4913,0.4923,0.4925,0.4948,0.4998,0.5131,0.5150,0.5160,0.5163, 0.5174,0.5255,0.5283,0.5329,0.5355,0.5414,0.5419,0.5434,0.5445,0.5499, 0.5524,0.5545,0.5548,0.5574,0.5602,0.5605,0.5637,0.5720,0.5747,0.5787, 0.5788,0.5823,0.5842,0.5849,0.5851,0.5903,0.5976,0.6021,0.6039,0.6043, 0.6055,0.6091,0.6145,0.6278,0.6319,0.6347,0.6470,0.6479,0.6491,0.6548, 0.6584,0.6584,0.6594,0.6594,0.6601,0.6733,0.6794,0.7070,0.7111,0.7116, 0.7125,0.7140,0.7141,0.7236,0.7243,0.7249,0.7443,0.7538,0.7568,0.7574, 0.7596,0.7611,0.7652,0.7657,0.7765,0.7768,0.7803,0.7830,0.7838,0.7936, 0.7947,0.7964,0.7992,0.8042,0.8079,0.8174,0.8175,0.8249,0.8353,0.8361, 0.8361,0.8479,0.8501,0.8532,0.8532,0.8549,0.8551,0.8557,0.8700,0.8758, 0.8780,0.8784,0.8828,0.8859,0.8874,0.8992,0.9042,0.9083,0.9120,0.9127, 0.9166,0.9208,0.9233,0.9245,0.9263,0.9367,0.9411,0.9415,0.9419,0.9459, 0.9478,0.9485,0.9597,0.9705,0.9731,0.9755,0.9791,0.9847,0.9992, Overall p-value after applying KStest on 269 p-values = 0.235249 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.