RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-12_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 22.7358 0.841949 2 to 25 15.81 17.9235 0.606316 3 to 26 15.78 43.1014 0.999536 4 to 27 15.87 19.5205 0.700515 5 to 28 15.84 4.6484 0.001397 6 to 29 15.79 17.2971 0.565577 7 to 30 15.87 16.4472 0.507617 8 to 31 15.58 19.9282 0.722081 9 to 32 15.76 15.2373 0.421608 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.167494 Tough bday spacings test for dh-ranFile-2016-09-12_16:31: 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 73 87 114 82 49 29 12 3 3 (O-E)^2/E 0.1 0.3 0.0 1.2 2.7 0.2 0.2 0.0 0.6 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.560, p= 0.328 RESULTS OF GCD FOR dh-ranFile-2016-09-12_16:31 Euclid's algorithm: p-value, steps to gcd: 0.491447 p-value, dist. of gcd's: 0.105151 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-12_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.560 0.238 0.049 0.079 0.044 0.879 0.532 0.950 Bits 8 to 15---> 0.038 0.189 0.074 0.252 0.223 0.598 0.206 0.410 Bits 16 to 23---> 0.546 0.414 0.738 0.895 0.088 0.124 0.222 0.149 Bits 24 to 31---> 0.657 0.946 0.766 0.279 0.371 0.669 0.051 0.275 KS test for the above 32 p values: 0.961 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-12_16:31, p-values for 5 runs: 0.8678, 0.9981, 0.6841, 0.3046, 0.9301 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-12_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5150 5134.0 0.050 1.174 r= 30 23080 23103.0 0.023 1.197 r= 31 11574 11551.5 0.044 1.241 chi-square = 1.241 with df = 3; p-value = 0.257 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-12_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5100 5134.0 0.225 0.373 r= 31 23273 23103.0 1.250 1.623 r= 32 11410 11551.5 1.734 3.357 chi-square = 3.357 with df = 3; p-value = 0.660 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-12_16:31 b-rank test for bits 1 to 8, p=0.01270 b-rank test for bits 2 to 9, p=0.11830 b-rank test for bits 3 to 10, p=0.30639 b-rank test for bits 4 to 11, p=0.28824 b-rank test for bits 5 to 12, p=0.37847 b-rank test for bits 6 to 13, p=0.91104 b-rank test for bits 7 to 14, p=0.46383 b-rank test for bits 8 to 15, p=0.05528 b-rank test for bits 9 to 16, p=0.24752 b-rank test for bits 10 to 17, p=0.76290 b-rank test for bits 11 to 18, p=0.17261 b-rank test for bits 12 to 19, p=0.84863 b-rank test for bits 13 to 20, p=0.68885 b-rank test for bits 14 to 21, p=0.63432 b-rank test for bits 15 to 22, p=0.23165 b-rank test for bits 16 to 23, p=0.54288 b-rank test for bits 17 to 24, p=0.93116 b-rank test for bits 18 to 25, p=0.03682 b-rank test for bits 19 to 26, p=0.55548 b-rank test for bits 20 to 27, p=0.24789 b-rank test for bits 21 to 28, p=0.27823 b-rank test for bits 22 to 29, p=0.10954 b-rank test for bits 23 to 30, p=0.64060 b-rank test for bits 24 to 31, p=0.82114 b-rank test for bits 25 to 32, p=0.84042 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 = 0.593419 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-12_16:31 (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 141969 0.14 0.555439 2 141976 0.16 0.561893 3 141293 -1.44 0.074930 4 140961 -2.22 0.013355 5 141443 -1.09 0.137954 6 141702 -0.48 0.314045 7 142177 0.63 0.734145 8 141953 0.10 0.540635 9 142064 0.36 0.641092 10 141415 -1.15 0.124050 11 142332 0.99 0.838313 12 142409 1.17 0.878486 13 141311 -1.40 0.081061 14 141754 -0.36 0.358332 15 142068 0.37 0.644579 16 141374 -1.25 0.105509 17 141696 -0.50 0.309089 18 141285 -1.46 0.072322 19 141988 0.18 0.572918 20 142217 0.72 0.763885 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-12_16:31 Bits used No. missing words z-score p-value 23 to 32 142049 0.4816 0.684962 22 to 31 141743 -0.5736 0.283136 21 to 30 142389 1.6540 0.950940 20 to 29 142167 0.8885 0.812869 19 to 28 141839 -0.2425 0.404190 18 to 27 141611 -1.0287 0.151805 17 to 26 141357 -1.9046 0.028417 16 to 25 141709 -0.6908 0.244848 15 to 24 141393 -1.7804 0.037501 14 to 23 141912 0.0092 0.503673 13 to 22 141782 -0.4391 0.330306 12 to 21 141977 0.2333 0.592253 11 to 20 142410 1.7264 0.957867 10 to 19 141578 -1.1425 0.126620 9 to 18 142249 1.1713 0.879256 8 to 17 141614 -1.0184 0.154249 7 to 16 142240 1.1402 0.872907 6 to 15 142366 1.5747 0.942340 5 to 14 141972 0.2161 0.585547 4 to 13 141850 -0.2046 0.418948 3 to 12 141933 0.0816 0.532526 2 to 11 142259 1.2058 0.886045 1 to 10 142189 0.9644 0.832572 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-12_16:31 Bits used No. missing words z-score p-value 28 to 32 142481 1.9379 0.973680 27 to 31 141784 -0.4248 0.335474 26 to 30 141451 -1.5537 0.060133 25 to 29 141688 -0.7503 0.226546 24 to 28 141963 0.1819 0.572182 23 to 27 141382 -1.7876 0.036924 22 to 26 141866 -0.1469 0.441613 21 to 25 142188 0.9446 0.827580 20 to 24 141705 -0.6926 0.244267 19 to 23 141981 0.2429 0.595978 18 to 22 141774 -0.4587 0.323208 17 to 21 141368 -1.8350 0.033252 16 to 20 141653 -0.8689 0.192447 15 to 19 141717 -0.6520 0.257212 14 to 18 141716 -0.6554 0.256119 13 to 17 141190 -2.4384 0.007376 12 to 16 142105 0.6633 0.746427 11 to 15 141987 0.2633 0.603836 10 to 14 141968 0.1989 0.578822 9 to 13 141733 -0.5977 0.275010 8 to 12 141705 -0.6926 0.244267 7 to 11 141773 -0.4621 0.321992 6 to 10 141839 -0.2384 0.405783 5 to 9 141652 -0.8723 0.191521 4 to 8 141650 -0.8791 0.189678 3 to 7 141503 -1.3774 0.084196 2 to 6 142147 0.8057 0.789781 1 to 5 141812 -0.3299 0.370726 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-12_16:31 Bits used No. missing words z-score p-value 31 to 32 141326 -1.7207 0.042649 30 to 31 141437 -1.3933 0.081764 29 to 30 141572 -0.9951 0.159850 28 to 29 141613 -0.8741 0.191024 27 to 28 142521 1.8043 0.964411 26 to 27 142179 0.7955 0.786835 25 to 26 141841 -0.2016 0.420129 24 to 25 141918 0.0256 0.510202 23 to 24 141724 -0.5467 0.292294 22 to 23 141387 -1.5408 0.061683 21 to 22 141670 -0.7060 0.240098 20 to 21 141330 -1.7089 0.043731 19 to 20 141660 -0.7355 0.231022 18 to 19 142230 0.9459 0.827908 17 to 18 142095 0.5477 0.708051 16 to 17 142042 0.3914 0.652233 15 to 16 141605 -0.8977 0.184665 14 to 15 141497 -1.2163 0.111933 13 to 14 141955 0.1347 0.553583 12 to 13 142138 0.6745 0.750017 11 to 12 142203 0.8663 0.806833 10 to 11 141694 -0.6352 0.262652 9 to 10 142164 0.7512 0.773746 8 to 9 142121 0.6244 0.733816 7 to 8 141917 0.0226 0.509025 6 to 7 141782 -0.3756 0.353605 5 to 6 142069 0.4710 0.681181 4 to 5 141852 -0.1691 0.432853 3 to 4 142184 0.8102 0.791098 2 to 3 142472 1.6598 0.951522 1 to 2 141700 -0.6175 0.268455 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-12_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2424.45 -1.068 0.142654 Test results for specific bytes for dh-ranFile-2016-09-12_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2506.01 0.085 0.533847 2 to 9 2518.71 0.265 0.604345 3 to 10 2511.64 0.165 0.565375 4 to 11 2469.24 -0.435 0.331798 5 to 12 2553.61 0.758 0.775838 6 to 13 2318.16 -2.572 0.005062 7 to 14 2407.45 -1.309 0.095289 8 to 15 2453.08 -0.663 0.253507 9 to 16 2450.52 -0.700 0.242029 10 to 17 2512.36 0.175 0.569392 11 to 18 2473.59 -0.373 0.354395 12 to 19 2360.74 -1.969 0.024450 13 to 20 2494.27 -0.081 0.467699 14 to 21 2559.46 0.841 0.799799 15 to 22 2477.67 -0.316 0.376062 16 to 23 2497.25 -0.039 0.484494 17 to 24 2403.83 -1.360 0.086898 18 to 25 2523.33 0.330 0.629295 19 to 26 2461.21 -0.549 0.291626 20 to 27 2575.52 1.068 0.857231 21 to 28 2549.91 0.706 0.759867 22 to 29 2502.60 0.037 0.514682 23 to 30 2357.30 -2.018 0.021794 24 to 31 2509.52 0.135 0.553559 25 to 32 2497.27 -0.039 0.484609 CDPARK for dh-ranFile-2016-09-12_16:31: 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 3584 2.7854 0.997327 3541 0.8219 0.794438 3518 -0.2283 0.409702 3517 -0.2740 0.392053 3531 0.3653 0.642555 3527 0.1826 0.572463 3470 -2.4201 0.007758 3543 0.9132 0.819442 3509 -0.6393 0.261324 3525 0.0913 0.536383 Square side=100, avg. no. parked=3526.50 sample std.=27.34 p-value of the KSTEST for those 10 p-values: 0.640222 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-12_16:31 0.6458,0.2510,0.4308,0.6818,0.1682,0.3890,0.2349,0.9358,0.6721,0.5258, The KS test for those 10 p-values: 0.803983 The 3DSPHERES test for dh-ranFile-2016-09-12_16:31 sample no r^3 equiv. uni. 1 5.365 0.163749 2 18.447 0.459312 3 7.209 0.213602 4 57.050 0.850680 5 91.775 0.953074 6 59.922 0.864313 7 102.139 0.966781 8 123.054 0.983457 9 73.115 0.912592 10 5.407 0.164919 11 11.225 0.312135 12 26.662 0.588821 13 34.460 0.682936 14 90.349 0.950789 15 11.063 0.308417 16 12.574 0.342375 17 10.855 0.303607 18 6.990 0.207840 19 17.002 0.432622 20 2.532 0.080927 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.295049 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-12_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 1.1 1.6 0.7 -0.3 0.9 -2.1 0.2 1.1 -1.4 -0.9 -1.8 0.5 -0.5 1.6 1.6 1.0 1.6 -1.7 1.6 -0.4 -1.4 -1.8 -1.5 1.6 -0.9 0.1 -0.3 0.1 -0.7 0.3 1.4 -0.4 -0.4 1.0 0.0 1.8 -1.6 0.4 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:53.530018 z-score=1.258028, p-value=0.890599 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-12_16:31 Test no p-value 1 0.610434 2 0.061123 3 0.033609 4 0.259471 5 0.736386 6 0.745643 7 0.791887 8 0.006753 9 0.129895 10 0.817943 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.175899 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-12_16:31: (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 66674 0.00 66598 0.07 3 25000.00 25020 0.02 25009 0.00 4 6666.67 6650 0.04 6698 0.15 5 1388.89 1378 0.09 1397 0.05 6 238.10 238 0.00 260 2.02 7 34.72 28 1.30 36 0.05 8 4.96 11 7.36 1 3.16 p=0.81484 p=0.51765 Number of rngs required: 688610, p-value: 0.594 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-12_16:31 No. of wins: Observed Expected 98558 98585.9 z-score=-0.125, pvalue=0.45042 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66568 66666.7 0.146 0.146 2 37797 37654.3 0.541 0.687 3 26899 26954.7 0.115 0.802 4 19456 19313.5 1.052 1.854 5 13805 13851.4 0.156 2.009 6 9900 9943.5 0.191 2.200 7 7086 7145.0 0.488 2.688 8 5259 5139.1 2.799 5.486 9 3722 3699.9 0.132 5.619 10 2635 2666.3 0.367 5.986 11 1882 1923.3 0.888 6.874 12 1383 1388.7 0.024 6.898 13 963 1003.7 1.652 8.550 14 695 726.1 1.335 9.885 15 544 525.8 0.627 10.513 16 385 381.2 0.039 10.551 17 267 276.5 0.329 10.880 18 200 200.8 0.003 10.884 19 157 146.0 0.831 11.715 20 117 106.2 1.095 12.810 21 280 287.1 0.176 12.986 Chisq= 12.99 for 20 degrees of freedom, p= 0.12204 SUMMARY of craptest p-value for no. of wins: 0.450420 p-value for throws/game: 0.122035 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-12_16:31 No. of wins: Observed Expected 98649 98585.9 z-score= 0.282, pvalue=0.61118 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66842 66666.7 0.461 0.461 2 37562 37654.3 0.226 0.687 3 26970 26954.7 0.009 0.696 4 19372 19313.5 0.177 0.874 5 13709 13851.4 1.464 2.338 6 9926 9943.5 0.031 2.369 7 7176 7145.0 0.134 2.503 8 5083 5139.1 0.612 3.115 9 3713 3699.9 0.047 3.162 10 2699 2666.3 0.401 3.563 11 1968 1923.3 1.038 4.600 12 1466 1388.7 4.298 8.898 13 919 1003.7 7.150 16.048 14 679 726.1 3.060 19.109 15 531 525.8 0.051 19.160 16 384 381.2 0.021 19.181 17 309 276.5 3.810 22.991 18 168 200.8 5.367 28.358 19 145 146.0 0.007 28.364 20 108 106.2 0.030 28.394 21 271 287.1 0.904 29.299 Chisq= 29.30 for 20 degrees of freedom, p= 0.91796 SUMMARY of craptest p-value for no. of wins: 0.611184 p-value for throws/game: 0.917960 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0014,0.0051,0.0068,0.0074,0.0078,0.0127,0.0134,0.0218,0.0245,0.0284, 0.0333,0.0336,0.0368,0.0369,0.0375,0.0377,0.0426,0.0437,0.0441,0.0492, 0.0513,0.0553,0.0601,0.0611,0.0617,0.0723,0.0738,0.0749,0.0789,0.0809, 0.0811,0.0818,0.0842,0.0869,0.0877,0.0953,0.1052,0.1055,0.1095,0.1119, 0.1183,0.1220,0.1239,0.1241,0.1266,0.1299,0.1380,0.1427,0.1492,0.1518, 0.1542,0.1599,0.1637,0.1649,0.1675,0.1682,0.1726,0.1759,0.1847,0.1892, 0.1897,0.1910,0.1915,0.1924,0.2065,0.2078,0.2136,0.2223,0.2229,0.2265, 0.2310,0.2316,0.2349,0.2382,0.2401,0.2420,0.2443,0.2443,0.2448,0.2475, 0.2479,0.2510,0.2517,0.2535,0.2561,0.2568,0.2572,0.2595,0.2613,0.2627, 0.2685,0.2750,0.2752,0.2782,0.2786,0.2831,0.2882,0.2916,0.2923,0.2950, 0.3036,0.3046,0.3064,0.3084,0.3091,0.3121,0.3140,0.3220,0.3232,0.3283, 0.3303,0.3318,0.3355,0.3424,0.3536,0.3544,0.3583,0.3707,0.3714,0.3761, 0.3785,0.3890,0.3921,0.4042,0.4058,0.4097,0.4099,0.4144,0.4189,0.4201, 0.4216,0.4308,0.4326,0.4329,0.4416,0.4504,0.4593,0.4638,0.4677,0.4845, 0.4846,0.4914,0.5037,0.5076,0.5090,0.5102,0.5147,0.5176,0.5258,0.5324, 0.5325,0.5338,0.5364,0.5406,0.5429,0.5459,0.5536,0.5536,0.5554,0.5555, 0.5604,0.5619,0.5654,0.5656,0.5694,0.5722,0.5725,0.5729,0.5788,0.5855, 0.5888,0.5923,0.5934,0.5941,0.5960,0.5977,0.6038,0.6043,0.6063,0.6104, 0.6112,0.6293,0.6343,0.6402,0.6406,0.6411,0.6426,0.6446,0.6458,0.6522, 0.6566,0.6602,0.6690,0.6721,0.6812,0.6818,0.6829,0.6841,0.6850,0.6888, 0.7005,0.7081,0.7221,0.7338,0.7341,0.7364,0.7380,0.7456,0.7464,0.7500, 0.7599,0.7629,0.7639,0.7660,0.7737,0.7758,0.7868,0.7898,0.7911,0.7919, 0.7944,0.7998,0.8040,0.8068,0.8129,0.8148,0.8179,0.8194,0.8211,0.8276, 0.8279,0.8326,0.8383,0.8404,0.8419,0.8486,0.8507,0.8572,0.8643,0.8678, 0.8729,0.8785,0.8793,0.8794,0.8860,0.8906,0.8951,0.9110,0.9126,0.9180, 0.9301,0.9312,0.9358,0.9423,0.9458,0.9499,0.9508,0.9509,0.9515,0.9531, 0.9579,0.9612,0.9644,0.9668,0.9737,0.9835,0.9973,0.9981,0.9995, Overall p-value after applying KStest on 269 p-values = 0.043027 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.