RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-01_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 15.96 34.3745 0.992491 2 to 25 15.51 23.1023 0.854051 3 to 26 15.55 27.4129 0.947717 4 to 27 15.76 17.6146 0.586462 5 to 28 15.32 28.7591 0.963187 6 to 29 15.66 30.0584 0.974073 7 to 30 15.72 23.6635 0.871130 8 to 31 15.53 18.5754 0.646558 9 to 32 15.64 21.1164 0.778871 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000164 Tough bday spacings test for dh-ranFile-2016-06-01_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 41 68 89 107 79 48 34 15 7 4 (O-E)^2/E 0.1 0.5 0.4 0.8 0.9 0.0 0.3 0.6 0.0 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.663, p= 0.039 RESULTS OF GCD FOR dh-ranFile-2016-06-01_16:31 Euclid's algorithm: p-value, steps to gcd: 0.114818 p-value, dist. of gcd's: 0.736923 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-01_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.455 0.900 0.834 0.259 0.777 0.276 0.953 0.978 Bits 8 to 15---> 0.315 0.314 0.154 0.119 0.868 0.161 0.011 0.474 Bits 16 to 23---> 0.563 0.379 0.673 0.964 0.945 0.228 0.715 0.275 Bits 24 to 31---> 0.875 0.515 0.465 0.731 0.112 0.997 0.996 0.714 KS test for the above 32 p values: 0.844 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-01_16:31, p-values for 5 runs: 0.1923, 0.6021, 0.5738, 0.3060, 0.8695 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-01_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5149 5134.0 0.044 0.056 r= 30 22984 23103.0 0.613 0.669 r= 31 11654 11551.5 0.909 1.578 chi-square = 1.578 with df = 3; p-value = 0.336 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-01_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 248 211.4 6.330 6.330 r= 30 5089 5134.0 0.395 6.724 r= 31 22916 23103.0 1.514 8.239 r= 32 11747 11551.5 3.308 11.547 chi-square = 11.547 with df = 3; p-value = 0.991 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-01_16:31 b-rank test for bits 1 to 8, p=0.59103 b-rank test for bits 2 to 9, p=0.70609 b-rank test for bits 3 to 10, p=0.01366 b-rank test for bits 4 to 11, p=0.99422 b-rank test for bits 5 to 12, p=0.60907 b-rank test for bits 6 to 13, p=0.94548 b-rank test for bits 7 to 14, p=0.99326 b-rank test for bits 8 to 15, p=0.77009 b-rank test for bits 9 to 16, p=0.50991 b-rank test for bits 10 to 17, p=0.48567 b-rank test for bits 11 to 18, p=0.17337 b-rank test for bits 12 to 19, p=0.15346 b-rank test for bits 13 to 20, p=0.88234 b-rank test for bits 14 to 21, p=0.36565 b-rank test for bits 15 to 22, p=0.68098 b-rank test for bits 16 to 23, p=0.94176 b-rank test for bits 17 to 24, p=0.97421 b-rank test for bits 18 to 25, p=0.71530 b-rank test for bits 19 to 26, p=0.01938 b-rank test for bits 20 to 27, p=0.27753 b-rank test for bits 21 to 28, p=0.24877 b-rank test for bits 22 to 29, p=0.34604 b-rank test for bits 23 to 30, p=0.17209 b-rank test for bits 24 to 31, p=0.58678 b-rank test for bits 25 to 32, p=0.85209 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 = 0.260561 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-01_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 141846 -0.15 0.441184 2 142533 1.46 0.927466 3 142480 1.33 0.908790 4 142321 0.96 0.831936 5 141850 -0.14 0.444875 6 142677 1.79 0.963563 7 142607 1.63 0.948457 8 141344 -1.32 0.093273 9 142214 0.71 0.761720 10 142250 0.80 0.786972 11 141795 -0.27 0.394686 12 142137 0.53 0.702616 13 142117 0.49 0.686236 14 142162 0.59 0.722522 15 141612 -0.69 0.243623 16 141783 -0.30 0.383935 17 142377 1.09 0.862734 18 142299 0.91 0.818706 19 141222 -1.61 0.054147 20 141834 -0.18 0.430145 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-01_16:31 Bits used No. missing words z-score p-value 23 to 32 141904 -0.0184 0.492668 22 to 31 141957 0.1644 0.565284 21 to 30 142163 0.8747 0.809138 20 to 29 142074 0.5678 0.714924 19 to 28 141684 -0.7770 0.218579 18 to 27 141688 -0.7632 0.222670 17 to 26 141917 0.0264 0.510550 16 to 25 142117 0.7161 0.763036 15 to 24 141900 -0.0322 0.487167 14 to 23 141680 -0.7908 0.214532 13 to 22 142207 1.0264 0.847660 12 to 21 141857 -0.1804 0.428400 11 to 20 142009 0.3437 0.634460 10 to 19 142037 0.4402 0.670119 9 to 18 142324 1.4299 0.923627 8 to 17 142242 1.1471 0.874338 7 to 16 141203 -2.4356 0.007433 6 to 15 142051 0.4885 0.687408 5 to 14 142486 1.9885 0.976623 4 to 13 141994 0.2920 0.614844 3 to 12 141359 -1.8977 0.028868 2 to 11 141607 -1.0425 0.148586 1 to 10 141289 -2.1391 0.016215 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-01_16:31 Bits used No. missing words z-score p-value 28 to 32 142079 0.5752 0.717406 27 to 31 142088 0.6057 0.727630 26 to 30 142040 0.4429 0.671099 25 to 29 141295 -2.0825 0.018650 24 to 28 141858 -0.1740 0.430933 23 to 27 141462 -1.5164 0.064713 22 to 26 141702 -0.7028 0.241086 21 to 25 142220 1.0531 0.853857 20 to 24 142231 1.0904 0.862233 19 to 23 141688 -0.7503 0.226546 18 to 22 142054 0.4904 0.688077 17 to 21 141910 0.0023 0.500906 16 to 20 141969 0.2023 0.580148 15 to 19 142114 0.6938 0.756095 14 to 18 141790 -0.4045 0.342919 13 to 17 141423 -1.6486 0.049617 12 to 16 142042 0.4497 0.673547 11 to 15 141582 -1.1096 0.133587 10 to 14 141716 -0.6554 0.256119 9 to 13 141877 -0.1096 0.456366 8 to 12 141493 -1.4113 0.079080 7 to 11 142404 1.6768 0.953214 6 to 10 141809 -0.3401 0.366890 5 to 9 141451 -1.5537 0.060133 4 to 8 142300 1.3243 0.907299 3 to 7 141665 -0.8282 0.203768 2 to 6 141405 -1.7096 0.043671 1 to 5 141791 -0.4011 0.344166 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-01_16:31 Bits used No. missing words z-score p-value 31 to 32 141682 -0.6706 0.251241 30 to 31 142116 0.6096 0.728952 29 to 30 141714 -0.5762 0.282242 28 to 29 141938 0.0846 0.533699 27 to 28 141379 -1.5644 0.058862 26 to 27 141903 -0.0187 0.492551 25 to 26 141919 0.0285 0.511378 24 to 25 141634 -0.8122 0.208343 23 to 24 141793 -0.3432 0.365740 22 to 23 142259 1.0315 0.848841 21 to 22 141582 -0.9656 0.167128 20 to 21 142060 0.4445 0.671643 19 to 20 141782 -0.3756 0.353605 18 to 19 142255 1.0197 0.846059 17 to 18 142190 0.8279 0.796146 16 to 17 142374 1.3707 0.914767 15 to 16 141725 -0.5437 0.293308 14 to 15 142662 2.2203 0.986800 13 to 14 141638 -0.8004 0.211744 12 to 13 141956 0.1377 0.554749 11 to 12 142201 0.8604 0.805211 10 to 11 142535 1.8456 0.967527 9 to 10 142217 0.9076 0.817950 8 to 9 141889 -0.0600 0.476090 7 to 8 141656 -0.7473 0.227445 6 to 7 141924 0.0433 0.517259 5 to 6 141916 0.0197 0.507849 4 to 5 141156 -2.2222 0.013134 3 to 4 141989 0.2350 0.592901 2 to 3 141098 -2.3933 0.008349 1 to 2 141618 -0.8594 0.195065 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-01_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2414.97 -1.202 0.114595 Test results for specific bytes for dh-ranFile-2016-06-01_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2494.51 -0.078 0.469041 2 to 9 2523.33 0.330 0.629270 3 to 10 2536.27 0.513 0.695985 4 to 11 2502.28 0.032 0.512849 5 to 12 2583.47 1.180 0.881091 6 to 13 2492.47 -0.106 0.457600 7 to 14 2484.29 -0.222 0.412086 8 to 15 2316.03 -2.602 0.004638 9 to 16 2427.98 -1.019 0.154215 10 to 17 2467.59 -0.458 0.323375 11 to 18 2377.13 -1.738 0.041138 12 to 19 2452.30 -0.675 0.249970 13 to 20 2609.80 1.553 0.939763 14 to 21 2547.01 0.665 0.746901 15 to 22 2349.53 -2.128 0.016668 16 to 23 2412.44 -1.238 0.107799 17 to 24 2616.00 1.640 0.949547 18 to 25 2501.49 0.021 0.508378 19 to 26 2373.63 -1.787 0.036958 20 to 27 2505.71 0.081 0.532154 21 to 28 2448.00 -0.735 0.231065 22 to 29 2616.03 1.641 0.949596 23 to 30 2528.65 0.405 0.657303 24 to 31 2352.26 -2.089 0.018339 25 to 32 2446.07 -0.763 0.222833 CDPARK for dh-ranFile-2016-06-01_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 3518 -0.2283 0.409702 3514 -0.4110 0.340551 3497 -1.1872 0.117571 3495 -1.2785 0.100530 3539 0.7306 0.767486 3507 -0.7306 0.232514 3523 0.0000 0.500000 3557 1.5525 0.939730 3515 -0.3653 0.357445 3526 0.1370 0.554479 Square side=100, avg. no. parked=3519.10 sample std.=17.76 p-value of the KSTEST for those 10 p-values: 0.708760 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-01_16:31 0.7437,0.0492,0.3641,0.9406,0.7046,0.2362,0.4286,0.1986,0.0402,0.0736, The KS test for those 10 p-values: 0.238931 The 3DSPHERES test for dh-ranFile-2016-06-01_16:31 sample no r^3 equiv. uni. 1 14.788 0.389164 2 11.580 0.320238 3 99.819 0.964110 4 37.306 0.711638 5 12.192 0.333952 6 0.769 0.025321 7 32.724 0.664053 8 23.553 0.543926 9 37.857 0.716887 10 13.586 0.364188 11 11.131 0.309973 12 4.111 0.128056 13 23.460 0.542506 14 11.149 0.310388 15 79.891 0.930262 16 39.056 0.727979 17 14.645 0.386241 18 5.503 0.167579 19 37.988 0.718119 20 8.387 0.243881 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.714781 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-01_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.4 0.5 1.6 0.3 -1.3 1.1 -1.5 -0.7 1.3 -1.0 -1.7 1.5 0.0 0.6 0.2 1.1 -0.2 0.7 -0.1 -0.8 -0.3 -2.2 0.5 0.4 -1.1 -1.2 1.7 1.5 -0.6 1.6 0.5 1.0 -1.0 -0.1 -0.5 2.1 0.5 -0.7 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:45.020779 z-score=0.329594, p-value=0.653359 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-01_16:31 Test no p-value 1 0.007513 2 0.433418 3 0.266216 4 0.015690 5 0.929217 6 0.242416 7 0.167393 8 0.247699 9 0.951782 10 0.081686 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.034211 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-01_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 66677 0.00 66615 0.04 3 25000.00 25072 0.21 25151 0.91 4 6666.67 6556 1.84 6479 5.28 5 1388.89 1461 3.74 1465 4.17 6 238.10 198 6.75 243 0.10 7 34.72 30 0.64 35 0.00 8 4.96 5 0.00 11 7.36 p=0.95980 p=0.99342 Number of rngs required: 687670, p-value: 0.198 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-01_16:31 No. of wins: Observed Expected 98864 98585.9 z-score= 1.244, pvalue=0.89325 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66520 66666.7 0.323 0.323 2 37717 37654.3 0.104 0.427 3 27037 26954.7 0.251 0.678 4 19279 19313.5 0.061 0.740 5 14067 13851.4 3.355 4.095 6 9947 9943.5 0.001 4.096 7 7093 7145.0 0.379 4.475 8 5057 5139.1 1.311 5.786 9 3742 3699.9 0.480 6.265 10 2694 2666.3 0.288 6.553 11 1860 1923.3 2.085 8.638 12 1407 1388.7 0.240 8.879 13 1016 1003.7 0.150 9.029 14 712 726.1 0.275 9.304 15 477 525.8 4.536 13.840 16 405 381.2 1.492 15.332 17 261 276.5 0.873 16.205 18 185 200.8 1.248 17.453 19 146 146.0 0.000 17.453 20 107 106.2 0.006 17.459 21 271 287.1 0.904 18.363 Chisq= 18.36 for 20 degrees of freedom, p= 0.43651 SUMMARY of craptest p-value for no. of wins: 0.893252 p-value for throws/game: 0.436506 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-01_16:31 No. of wins: Observed Expected 98409 98585.9 z-score=-0.791, pvalue=0.21447 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66474 66666.7 0.557 0.557 2 37738 37654.3 0.186 0.743 3 27332 26954.7 5.280 6.023 4 19156 19313.5 1.284 7.307 5 13724 13851.4 1.172 8.479 6 10021 9943.5 0.603 9.082 7 7009 7145.0 2.590 11.672 8 5222 5139.1 1.338 13.010 9 3698 3699.9 0.001 13.011 10 2682 2666.3 0.092 13.104 11 1844 1923.3 3.272 16.376 12 1453 1388.7 2.973 19.349 13 980 1003.7 0.560 19.909 14 717 726.1 0.115 20.024 15 540 525.8 0.382 20.406 16 375 381.2 0.099 20.505 17 294 276.5 1.102 21.608 18 209 200.8 0.332 21.940 19 137 146.0 0.553 22.493 20 113 106.2 0.433 22.926 21 282 287.1 0.091 23.017 Chisq= 23.02 for 20 degrees of freedom, p= 0.71206 SUMMARY of craptest p-value for no. of wins: 0.214468 p-value for throws/game: 0.712062 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0046,0.0074,0.0075,0.0083,0.0111,0.0131,0.0137,0.0157,0.0162, 0.0167,0.0183,0.0186,0.0194,0.0253,0.0289,0.0342,0.0370,0.0387,0.0402, 0.0411,0.0437,0.0492,0.0496,0.0541,0.0589,0.0601,0.0647,0.0736,0.0791, 0.0817,0.0933,0.1005,0.1078,0.1121,0.1146,0.1148,0.1176,0.1187,0.1281, 0.1336,0.1486,0.1535,0.1537,0.1542,0.1605,0.1671,0.1674,0.1676,0.1721, 0.1734,0.1923,0.1951,0.1983,0.1986,0.2038,0.2083,0.2117,0.2145,0.2145, 0.2186,0.2227,0.2228,0.2265,0.2274,0.2284,0.2311,0.2325,0.2362,0.2389, 0.2411,0.2424,0.2436,0.2439,0.2477,0.2488,0.2500,0.2512,0.2561,0.2587, 0.2606,0.2662,0.2747,0.2759,0.2775,0.2822,0.2933,0.3060,0.3100,0.3104, 0.3140,0.3149,0.3202,0.3234,0.3340,0.3356,0.3406,0.3429,0.3442,0.3460, 0.3536,0.3574,0.3641,0.3642,0.3656,0.3657,0.3669,0.3786,0.3839,0.3862, 0.3892,0.3947,0.4097,0.4121,0.4284,0.4286,0.4301,0.4309,0.4334,0.4365, 0.4412,0.4449,0.4549,0.4564,0.4576,0.4652,0.4690,0.4742,0.4761,0.4857, 0.4872,0.4926,0.4927,0.5000,0.5009,0.5078,0.5084,0.5099,0.5106,0.5114, 0.5128,0.5151,0.5173,0.5322,0.5337,0.5425,0.5439,0.5545,0.5547,0.5635, 0.5653,0.5738,0.5801,0.5865,0.5868,0.5910,0.5929,0.6021,0.6091,0.6148, 0.6293,0.6345,0.6466,0.6534,0.6573,0.6641,0.6701,0.6711,0.6716,0.6732, 0.6735,0.6810,0.6862,0.6874,0.6881,0.6960,0.7026,0.7046,0.7061,0.7088, 0.7116,0.7121,0.7137,0.7148,0.7149,0.7150,0.7153,0.7169,0.7174,0.7181, 0.7225,0.7276,0.7280,0.7290,0.7305,0.7369,0.7437,0.7469,0.7561,0.7617, 0.7630,0.7675,0.7701,0.7768,0.7789,0.7870,0.7961,0.8052,0.8091,0.8180, 0.8187,0.8319,0.8343,0.8441,0.8461,0.8477,0.8488,0.8521,0.8539,0.8541, 0.8622,0.8627,0.8680,0.8695,0.8711,0.8743,0.8746,0.8811,0.8823,0.8933, 0.9003,0.9073,0.9088,0.9148,0.9236,0.9275,0.9292,0.9303,0.9397,0.9398, 0.9406,0.9418,0.9445,0.9455,0.9477,0.9485,0.9495,0.9496,0.9518,0.9529, 0.9532,0.9598,0.9632,0.9636,0.9641,0.9642,0.9675,0.9741,0.9742,0.9766, 0.9781,0.9868,0.9909,0.9925,0.9933,0.9934,0.9942,0.9959,0.9972, Overall p-value after applying KStest on 269 p-values = 0.100097 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.