RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-05_13:31 (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 19.5104 0.699964 2 to 25 15.71 22.2005 0.822870 3 to 26 15.67 13.3528 0.287734 4 to 27 15.61 28.8658 0.964216 5 to 28 16.04 8.4896 0.045072 6 to 29 16.04 24.0097 0.880828 7 to 30 15.75 18.2858 0.628968 8 to 31 16.07 9.7718 0.087093 9 to 32 15.85 19.3913 0.693460 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.580024 Tough bday spacings test for dh-ranFile-2016-01-05_13:31: 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 40 65 90 108 80 59 26 14 7 3 (O-E)^2/E 0.1 0.3 0.9 0.6 1.1 0.0 0.9 0.5 0.1 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.872, p= 0.100 RESULTS OF GCD FOR dh-ranFile-2016-01-05_13:31 Euclid's algorithm: p-value, steps to gcd: 0.962705 p-value, dist. of gcd's: 0.386095 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-05_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.197 0.379 0.909 0.966 0.390 0.687 0.765 0.284 Bits 8 to 15---> 0.800 0.331 0.854 0.441 0.006 0.822 0.636 0.337 Bits 16 to 23---> 0.992 0.619 0.236 0.965 0.208 0.279 0.197 0.890 Bits 24 to 31---> 0.566 0.323 0.284 0.483 0.887 0.337 0.152 0.059 KS test for the above 32 p values: 0.283 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-05_13:31, p-values for 5 runs: 0.3662, 0.5118, 0.6841, 0.9405, 0.1917 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-05_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5198 5134.0 0.798 1.217 r= 30 23211 23103.0 0.504 1.722 r= 31 11389 11551.5 2.287 4.008 chi-square = 4.008 with df = 3; p-value = 0.739 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-05_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5115 5134.0 0.070 0.265 r= 31 23169 23103.0 0.188 0.453 r= 32 11511 11551.5 0.142 0.596 chi-square = 0.596 with df = 3; p-value = 0.103 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-05_13:31 b-rank test for bits 1 to 8, p=0.87335 b-rank test for bits 2 to 9, p=0.42579 b-rank test for bits 3 to 10, p=0.02809 b-rank test for bits 4 to 11, p=0.92495 b-rank test for bits 5 to 12, p=0.47269 b-rank test for bits 6 to 13, p=0.91847 b-rank test for bits 7 to 14, p=0.19912 b-rank test for bits 8 to 15, p=0.60823 b-rank test for bits 9 to 16, p=0.25979 b-rank test for bits 10 to 17, p=0.00321 b-rank test for bits 11 to 18, p=0.65007 b-rank test for bits 12 to 19, p=0.09791 b-rank test for bits 13 to 20, p=0.58484 b-rank test for bits 14 to 21, p=0.61384 b-rank test for bits 15 to 22, p=0.28961 b-rank test for bits 16 to 23, p=0.27888 b-rank test for bits 17 to 24, p=0.24732 b-rank test for bits 18 to 25, p=0.58596 b-rank test for bits 19 to 26, p=0.87614 b-rank test for bits 20 to 27, p=0.95905 b-rank test for bits 21 to 28, p=0.37353 b-rank test for bits 22 to 29, p=0.59557 b-rank test for bits 23 to 30, p=0.64804 b-rank test for bits 24 to 31, p=0.05887 b-rank test for bits 25 to 32, p=0.28152 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 = 0.799614 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-05_13:31 (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 141958 0.11 0.545268 3 142197 0.67 0.749248 4 141675 -0.55 0.292018 5 142085 0.41 0.659260 6 143326 3.31 0.999533 7 141769 -0.33 0.371504 8 141884 -0.06 0.476404 9 141468 -1.03 0.151236 10 141762 -0.34 0.365337 11 141141 -1.80 0.036314 12 142994 2.53 0.994366 13 142597 1.61 0.945941 14 142475 1.32 0.906859 15 141477 -1.01 0.156220 16 142436 1.23 0.890752 17 141969 0.14 0.555439 18 142013 0.24 0.595695 19 141439 -1.10 0.135905 20 141684 -0.53 0.299280 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-05_13:31 Bits used No. missing words z-score p-value 23 to 32 142121 0.7299 0.767273 22 to 31 141821 -0.3046 0.380341 21 to 30 141554 -1.2253 0.110236 20 to 29 141807 -0.3529 0.362096 19 to 28 141604 -1.0529 0.146202 18 to 27 141552 -1.2322 0.108942 17 to 26 141752 -0.5425 0.293731 16 to 25 141421 -1.6839 0.046101 15 to 24 142097 0.6471 0.741229 14 to 23 142165 0.8816 0.811009 13 to 22 142244 1.1540 0.875757 12 to 21 142050 0.4851 0.686186 11 to 20 141926 0.0575 0.522920 10 to 19 142178 0.9264 0.822894 9 to 18 141688 -0.7632 0.222670 8 to 17 141425 -1.6701 0.047449 7 to 16 141956 0.1609 0.563926 6 to 15 142252 1.1816 0.881322 5 to 14 141621 -0.9942 0.160053 4 to 13 141374 -1.8460 0.032449 3 to 12 141366 -1.8736 0.030496 2 to 11 141834 -0.2598 0.397525 1 to 10 141809 -0.3460 0.364684 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-05_13:31 Bits used No. missing words z-score p-value 28 to 32 142494 1.9819 0.976257 27 to 31 142224 1.0667 0.856941 26 to 30 141532 -1.2791 0.100434 25 to 29 141856 -0.1808 0.428270 24 to 28 141611 -1.0113 0.155939 23 to 27 141915 0.0192 0.507667 22 to 26 141765 -0.4893 0.312331 21 to 25 141542 -1.2452 0.106532 20 to 24 141532 -1.2791 0.100434 19 to 23 141715 -0.6587 0.255030 18 to 22 141930 0.0701 0.527930 17 to 21 141552 -1.2113 0.112893 16 to 20 140871 -3.5198 0.000216 15 to 19 142219 1.0497 0.853079 14 to 18 141589 -1.0859 0.138770 13 to 17 141342 -1.9232 0.027230 12 to 16 141265 -2.1842 0.014475 11 to 15 141758 -0.5130 0.303982 10 to 14 141714 -0.6621 0.253942 9 to 13 141548 -1.2248 0.110316 8 to 12 142244 1.1345 0.871702 7 to 11 141597 -1.0587 0.144858 6 to 10 142015 0.3582 0.639905 5 to 9 141391 -1.7571 0.039455 4 to 8 141987 0.2633 0.603836 3 to 7 141756 -0.5198 0.301615 2 to 6 141859 -0.1706 0.432265 1 to 5 141979 0.2362 0.593349 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-05_13:31 Bits used No. missing words z-score p-value 31 to 32 142187 0.8191 0.793631 30 to 31 142145 0.6952 0.756532 29 to 30 142394 1.4297 0.923599 28 to 29 142028 0.3501 0.636853 27 to 28 142184 0.8102 0.791098 26 to 27 142296 1.1406 0.872986 25 to 26 142501 1.7453 0.959537 24 to 25 142134 0.6627 0.746253 23 to 24 141939 0.0875 0.534872 22 to 23 142266 1.0521 0.853629 21 to 22 142811 2.6598 0.996091 20 to 21 142025 0.3412 0.633527 19 to 20 141809 -0.2960 0.383631 18 to 19 141552 -1.0541 0.145925 17 to 18 141692 -0.6411 0.260732 16 to 17 142463 1.6332 0.948791 15 to 16 141988 0.2321 0.591756 14 to 15 141689 -0.6499 0.257865 13 to 14 142180 0.7984 0.787691 12 to 13 142122 0.6273 0.734784 11 to 12 142400 1.4474 0.926108 10 to 11 142324 1.2232 0.889376 9 to 10 141889 -0.0600 0.476090 8 to 9 141769 -0.4140 0.339454 7 to 8 141743 -0.4906 0.311837 6 to 7 141891 -0.0541 0.478439 5 to 6 142287 1.1141 0.867376 4 to 5 141284 -1.8446 0.032546 3 to 4 142112 0.5978 0.725029 2 to 3 141279 -1.8594 0.031487 1 to 2 141972 0.1849 0.573333 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-05_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2434.66 -0.924 0.177713 Test results for specific bytes for dh-ranFile-2016-01-05_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2556.54 0.800 0.788009 2 to 9 2431.02 -0.976 0.164655 3 to 10 2538.70 0.547 0.707894 4 to 11 2411.50 -1.252 0.105360 5 to 12 2344.66 -2.197 0.014016 6 to 13 2443.50 -0.799 0.212143 7 to 14 2408.44 -1.295 0.097682 8 to 15 2583.60 1.182 0.881443 9 to 16 2688.54 2.666 0.996167 10 to 17 2481.50 -0.262 0.396818 11 to 18 2478.78 -0.300 0.382054 12 to 19 2561.51 0.870 0.807833 13 to 20 2444.83 -0.780 0.217638 14 to 21 2502.49 0.035 0.514027 15 to 22 2510.05 0.142 0.556503 16 to 23 2441.13 -0.833 0.202552 17 to 24 2454.42 -0.645 0.259610 18 to 25 2521.91 0.310 0.621669 19 to 26 2543.33 0.613 0.729990 20 to 27 2334.79 -2.336 0.009734 21 to 28 2473.49 -0.375 0.353847 22 to 29 2598.29 1.390 0.917745 23 to 30 2534.20 0.484 0.685686 24 to 31 2604.83 1.482 0.930895 25 to 32 2395.83 -1.473 0.070358 CDPARK for dh-ranFile-2016-01-05_13:31: 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 3518 -0.2283 0.409702 3541 0.8219 0.794438 3488 -1.5982 0.055002 3528 0.2283 0.590298 3513 -0.4566 0.323972 3519 -0.1826 0.427537 3511 -0.5479 0.291865 3490 -1.5068 0.065925 3505 -0.8219 0.205562 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3512.70 sample std.=15.14 p-value of the KSTEST for those 10 p-values: 0.149601 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-05_13:31 0.7800,0.2052,0.8855,0.8855,0.1808,0.8210,0.6457,0.2260,0.1863,0.6300, The KS test for those 10 p-values: 0.573019 The 3DSPHERES test for dh-ranFile-2016-01-05_13:31 sample no r^3 equiv. uni. 1 29.608 0.627282 2 44.201 0.770850 3 41.207 0.746794 4 68.324 0.897455 5 44.860 0.775830 6 13.338 0.358917 7 21.430 0.510477 8 6.710 0.200429 9 9.182 0.263659 10 15.733 0.408109 11 16.004 0.413441 12 4.352 0.135040 13 153.556 0.994015 14 99.150 0.963300 15 25.928 0.578642 16 136.572 0.989458 17 20.572 0.496279 18 0.096 0.003199 19 18.397 0.458405 20 25.964 0.579150 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.407867 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-05_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 1.1 0.6 -0.7 -0.1 0.1 1.3 -0.2 -1.2 0.7 2.2 0.5 0.5 0.7 -0.3 -0.2 -1.4 -0.6 -0.5 1.3 1.3 -0.6 0.7 -1.2 -1.5 -1.4 0.2 -0.4 -0.4 -1.4 -0.5 0.8 -0.4 0.2 -1.4 -1.6 -0.4 -2.0 0.4 3.1 1.0 1.8 Chi-square with 42 degrees of freedom:53.277473 z-score=1.230473, p-value=0.886136 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-05_13:31 Test no p-value 1 0.874559 2 0.015813 3 0.135201 4 0.259391 5 0.547244 6 0.800885 7 0.373674 8 0.248989 9 0.632666 10 0.844414 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.957035 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-05_13:31: (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 66613 0.04 66982 1.49 3 25000.00 24951 0.10 24766 2.19 4 6666.67 6776 1.79 6596 0.75 5 1388.89 1368 0.31 1376 0.12 6 238.10 253 0.93 240 0.02 7 34.72 35 0.00 39 0.53 8 4.96 3 0.77 0 4.96 p=0.31740 p=0.87758 Number of rngs required: 688866, p-value: 0.703 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-05_13:31 No. of wins: Observed Expected 98372 98585.9 z-score=-0.957, pvalue=0.16941 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66507 66666.7 0.382 0.382 2 37802 37654.3 0.579 0.962 3 26954 26954.7 0.000 0.962 4 19188 19313.5 0.815 1.777 5 13836 13851.4 0.017 1.794 6 9817 9943.5 1.610 3.404 7 7254 7145.0 1.662 5.066 8 5106 5139.1 0.213 5.279 9 3722 3699.9 0.132 5.412 10 2749 2666.3 2.565 7.977 11 1971 1923.3 1.182 9.158 12 1400 1388.7 0.091 9.250 13 1011 1003.7 0.053 9.302 14 798 726.1 7.111 16.414 15 531 525.8 0.051 16.464 16 381 381.2 0.000 16.465 17 263 276.5 0.663 17.127 18 187 200.8 0.952 18.080 19 143 146.0 0.061 18.141 20 116 106.2 0.901 19.042 21 264 287.1 1.861 20.903 Chisq= 20.90 for 20 degrees of freedom, p= 0.59714 SUMMARY of craptest p-value for no. of wins: 0.169410 p-value for throws/game: 0.597137 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-05_13:31 No. of wins: Observed Expected 98421 98585.9 z-score=-0.737, pvalue=0.23046 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66554 66666.7 0.190 0.190 2 37813 37654.3 0.669 0.859 3 26916 26954.7 0.056 0.915 4 19271 19313.5 0.093 1.008 5 13957 13851.4 0.805 1.813 6 9784 9943.5 2.560 4.373 7 7186 7145.0 0.235 4.608 8 5098 5139.1 0.328 4.936 9 3689 3699.9 0.032 4.968 10 2741 2666.3 2.093 7.061 11 1938 1923.3 0.112 7.173 12 1375 1388.7 0.136 7.309 13 1028 1003.7 0.588 7.896 14 750 726.1 0.784 8.680 15 514 525.8 0.266 8.947 16 389 381.2 0.162 9.108 17 282 276.5 0.108 9.216 18 195 200.8 0.169 9.385 19 127 146.0 2.469 11.854 20 101 106.2 0.256 12.110 21 292 287.1 0.083 12.193 Chisq= 12.19 for 20 degrees of freedom, p= 0.09074 SUMMARY of craptest p-value for no. of wins: 0.230457 p-value for throws/game: 0.090740 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0032,0.0032,0.0056,0.0097,0.0140,0.0145,0.0158,0.0272,0.0281, 0.0305,0.0315,0.0324,0.0325,0.0363,0.0395,0.0451,0.0461,0.0474,0.0550, 0.0587,0.0589,0.0659,0.0704,0.0871,0.0907,0.0977,0.0979,0.1004,0.1004, 0.1005,0.1026,0.1054,0.1065,0.1089,0.1102,0.1103,0.1129,0.1350,0.1352, 0.1359,0.1388,0.1449,0.1459,0.1462,0.1496,0.1512,0.1522,0.1559,0.1562, 0.1601,0.1647,0.1694,0.1777,0.1808,0.1863,0.1917,0.1967,0.1972,0.1991, 0.2004,0.2026,0.2052,0.2056,0.2083,0.2121,0.2176,0.2227,0.2260,0.2305, 0.2362,0.2473,0.2490,0.2539,0.2550,0.2579,0.2594,0.2596,0.2598,0.2607, 0.2637,0.2786,0.2789,0.2815,0.2827,0.2836,0.2836,0.2877,0.2896,0.2919, 0.2920,0.2920,0.2937,0.2993,0.3016,0.3040,0.3118,0.3123,0.3174,0.3228, 0.3240,0.3308,0.3367,0.3375,0.3395,0.3406,0.3538,0.3589,0.3621,0.3647, 0.3653,0.3662,0.3715,0.3735,0.3737,0.3790,0.3803,0.3821,0.3836,0.3861, 0.3903,0.3968,0.3975,0.4079,0.4081,0.4097,0.4134,0.4258,0.4275,0.4283, 0.4323,0.4413,0.4584,0.4727,0.4761,0.4764,0.4784,0.4832,0.4963,0.5077, 0.5105,0.5118,0.5140,0.5229,0.5279,0.5349,0.5453,0.5472,0.5554,0.5565, 0.5639,0.5658,0.5730,0.5733,0.5786,0.5791,0.5800,0.5848,0.5860,0.5903, 0.5918,0.5933,0.5956,0.5957,0.5971,0.6038,0.6082,0.6138,0.6193,0.6217, 0.6273,0.6290,0.6300,0.6327,0.6335,0.6364,0.6369,0.6399,0.6457,0.6480, 0.6501,0.6593,0.6841,0.6857,0.6862,0.6866,0.6935,0.7000,0.7032,0.7079, 0.7250,0.7300,0.7348,0.7394,0.7412,0.7463,0.7468,0.7492,0.7565,0.7654, 0.7673,0.7708,0.7758,0.7800,0.7877,0.7880,0.7911,0.7936,0.7944,0.7996, 0.8000,0.8009,0.8078,0.8110,0.8210,0.8216,0.8229,0.8229,0.8444,0.8531, 0.8536,0.8541,0.8569,0.8674,0.8717,0.8730,0.8734,0.8746,0.8758,0.8761, 0.8776,0.8808,0.8813,0.8814,0.8855,0.8855,0.8861,0.8865,0.8894,0.8897, 0.8908,0.8975,0.9069,0.9086,0.9177,0.9185,0.9236,0.9249,0.9261,0.9309, 0.9405,0.9459,0.9488,0.9570,0.9591,0.9595,0.9627,0.9633,0.9642,0.9645, 0.9655,0.9763,0.9895,0.9917,0.9940,0.9944,0.9961,0.9962,0.9995, Overall p-value after applying KStest on 269 p-values = 0.300731 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.