RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.60 15.4745 0.438659 2 to 25 15.63 20.8946 0.768960 3 to 26 15.48 27.7235 0.951725 4 to 27 15.75 20.6112 0.755835 5 to 28 16.04 17.9694 0.609228 6 to 29 15.75 19.6803 0.709092 7 to 30 15.61 31.0620 0.980372 8 to 31 15.72 14.8266 0.392033 9 to 32 15.87 15.5518 0.444199 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.105166 Tough bday spacings test for dh-ranFile-2018-07-07_01:31: 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 7 42 69 102 90 74 60 27 16 7 6 (O-E)^2/E 0.5 0.8 0.2 0.2 0.6 0.2 1.2 0.3 0.1 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.040, p= 0.112 RESULTS OF GCD FOR dh-ranFile-2018-07-07_01:31 Euclid's algorithm: p-value, steps to gcd: 0.475883 p-value, dist. of gcd's: 0.357525 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.463 0.671 0.224 0.949 0.426 0.541 0.846 0.791 Bits 8 to 15---> 0.227 0.396 0.451 0.513 0.087 0.839 0.983 0.840 Bits 16 to 23---> 0.262 0.026 0.555 0.325 0.330 0.251 0.732 0.641 Bits 24 to 31---> 0.561 0.447 0.395 0.290 0.020 0.665 0.291 0.413 KS test for the above 32 p values: 0.380 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_01:31, p-values for 5 runs: 0.0612, 0.9272, 0.9337, 0.2950, 0.8635 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5187 5134.0 0.547 1.671 r= 30 23151 23103.0 0.100 1.771 r= 31 11466 11551.5 0.633 2.404 chi-square = 2.404 with df = 3; p-value = 0.507 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5100 5134.0 0.225 0.755 r= 31 23018 23103.0 0.313 1.068 r= 32 11660 11551.5 1.019 2.087 chi-square = 2.087 with df = 3; p-value = 0.445 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_01:31 b-rank test for bits 1 to 8, p=0.21657 b-rank test for bits 2 to 9, p=0.37660 b-rank test for bits 3 to 10, p=0.30045 b-rank test for bits 4 to 11, p=0.37672 b-rank test for bits 5 to 12, p=0.55548 b-rank test for bits 6 to 13, p=0.73388 b-rank test for bits 7 to 14, p=0.56233 b-rank test for bits 8 to 15, p=0.32674 b-rank test for bits 9 to 16, p=0.73268 b-rank test for bits 10 to 17, p=0.60793 b-rank test for bits 11 to 18, p=0.78635 b-rank test for bits 12 to 19, p=0.38873 b-rank test for bits 13 to 20, p=0.19001 b-rank test for bits 14 to 21, p=0.00245 b-rank test for bits 15 to 22, p=0.80239 b-rank test for bits 16 to 23, p=0.47894 b-rank test for bits 17 to 24, p=0.36451 b-rank test for bits 18 to 25, p=0.47709 b-rank test for bits 19 to 26, p=0.30320 b-rank test for bits 20 to 27, p=0.09419 b-rank test for bits 21 to 28, p=0.72818 b-rank test for bits 22 to 29, p=0.43765 b-rank test for bits 23 to 30, p=0.61642 b-rank test for bits 24 to 31, p=0.72080 b-rank test for bits 25 to 32, p=0.38450 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 = 0.193476 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_01:31 (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 141542 -0.86 0.195378 2 142065 0.36 0.641965 3 141525 -0.90 0.184602 4 141952 0.10 0.539707 5 141690 -0.51 0.304167 6 142793 2.06 0.980522 7 141535 -0.87 0.190895 8 142593 1.60 0.944907 9 142392 1.13 0.870284 10 141489 -0.98 0.163030 11 141729 -0.42 0.336756 12 141605 -0.71 0.238526 13 141809 -0.23 0.407331 14 141595 -0.73 0.231348 15 141750 -0.37 0.354847 16 142158 0.58 0.719381 17 141496 -0.97 0.167091 18 142411 1.17 0.879427 19 142239 0.77 0.779426 20 141548 -0.84 0.199271 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-07_01:31 Bits used No. missing words z-score p-value 23 to 32 141637 -0.9391 0.173848 22 to 31 142028 0.4092 0.658806 21 to 30 142137 0.7851 0.783793 20 to 29 141603 -1.0563 0.145413 19 to 28 141947 0.1299 0.551676 18 to 27 141357 -1.9046 0.028417 17 to 26 141312 -2.0598 0.019711 16 to 25 141657 -0.8701 0.192122 15 to 24 141767 -0.4908 0.311786 14 to 23 141694 -0.7425 0.228887 13 to 22 141487 -1.4563 0.072653 12 to 21 141977 0.2333 0.592253 11 to 20 141681 -0.7873 0.215540 10 to 19 142416 1.7471 0.959693 9 to 18 141636 -0.9425 0.172964 8 to 17 141785 -0.4287 0.334062 7 to 16 141813 -0.3322 0.369880 6 to 15 141831 -0.2701 0.393540 5 to 14 142134 0.7747 0.780749 4 to 13 142462 1.9058 0.971659 3 to 12 142145 0.8127 0.791792 2 to 11 142942 3.5609 0.999815 1 to 10 141791 -0.4080 0.341624 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-07_01:31 Bits used No. missing words z-score p-value 28 to 32 142224 1.0667 0.856941 27 to 31 141930 0.0701 0.527930 26 to 30 141946 0.1243 0.549463 25 to 29 142294 1.3040 0.903877 24 to 28 141849 -0.2045 0.418978 23 to 27 141343 -1.9198 0.027444 22 to 26 141871 -0.1299 0.448310 21 to 25 142087 0.6023 0.726503 20 to 24 141504 -1.3740 0.084721 19 to 23 142106 0.6667 0.747511 18 to 22 142173 0.8938 0.814285 17 to 21 142094 0.6260 0.734343 16 to 20 142198 0.9785 0.836097 15 to 19 141741 -0.5706 0.284132 14 to 18 142247 1.1446 0.873822 13 to 17 142239 1.1175 0.868115 12 to 16 141229 -2.3062 0.010550 11 to 15 141935 0.0870 0.534671 10 to 14 142166 0.8701 0.807868 9 to 13 142452 1.8396 0.967084 8 to 12 141797 -0.3808 0.351683 7 to 11 142044 0.4565 0.675988 6 to 10 142087 0.6023 0.726503 5 to 9 141913 0.0124 0.504963 4 to 8 142233 1.0972 0.863720 3 to 7 142145 0.7989 0.787820 2 to 6 142317 1.3819 0.916504 1 to 5 142114 0.6938 0.756095 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-07_01:31 Bits used No. missing words z-score p-value 31 to 32 142049 0.4120 0.659832 30 to 31 141167 -2.1898 0.014271 29 to 30 142001 0.2704 0.606579 28 to 29 142000 0.2675 0.605444 27 to 28 141339 -1.6824 0.046247 26 to 27 141504 -1.1957 0.115914 25 to 26 141468 -1.3019 0.096482 24 to 25 141559 -1.0334 0.150703 23 to 24 141680 -0.6765 0.249365 22 to 23 141383 -1.5526 0.060260 21 to 22 141721 -0.5555 0.289261 20 to 21 141326 -1.7207 0.042649 19 to 20 142190 0.8279 0.796146 18 to 19 142325 1.2262 0.889932 17 to 18 141467 -1.3048 0.095979 16 to 17 141955 0.1347 0.553583 15 to 16 142061 0.4474 0.672708 14 to 15 141851 -0.1721 0.431693 13 to 14 141987 0.2291 0.590610 12 to 13 141766 -0.4228 0.336220 11 to 12 141891 -0.0541 0.478439 10 to 11 141632 -0.8181 0.206655 9 to 10 142025 0.3412 0.633527 8 to 9 141680 -0.6765 0.249365 7 to 8 141775 -0.3963 0.345959 6 to 7 141708 -0.5939 0.276292 5 to 6 142633 2.1347 0.983608 4 to 5 142348 1.2940 0.902169 3 to 4 142420 1.5064 0.934018 2 to 3 141212 -2.0570 0.019842 1 to 2 141499 -1.2104 0.113060 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2520.22 0.286 0.612567 Test results for specific bytes for dh-ranFile-2018-07-07_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2545.99 0.650 0.742291 2 to 9 2521.64 0.306 0.620200 3 to 10 2567.79 0.959 0.831144 4 to 11 2503.42 0.048 0.519288 5 to 12 2594.43 1.335 0.909130 6 to 13 2416.22 -1.185 0.118036 7 to 14 2445.51 -0.771 0.220473 8 to 15 2611.88 1.582 0.943207 9 to 16 2407.10 -1.314 0.094455 10 to 17 2581.34 1.150 0.875006 11 to 18 2494.57 -0.077 0.469374 12 to 19 2469.84 -0.426 0.334884 13 to 20 2474.42 -0.362 0.358792 14 to 21 2379.91 -1.698 0.044725 15 to 22 2449.73 -0.711 0.238560 16 to 23 2529.10 0.411 0.659642 17 to 24 2422.42 -1.097 0.136293 18 to 25 2459.70 -0.570 0.284352 19 to 26 2510.85 0.153 0.560963 20 to 27 2484.12 -0.225 0.411175 21 to 28 2434.20 -0.931 0.176029 22 to 29 2616.41 1.646 0.950145 23 to 30 2622.28 1.729 0.958118 24 to 31 2512.71 0.180 0.571307 25 to 32 2528.65 0.405 0.657314 CDPARK for dh-ranFile-2018-07-07_01:31: 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 3567 2.0091 0.977738 3491 -1.4612 0.071982 3527 0.1826 0.572463 3534 0.5023 0.692266 3558 1.5982 0.944998 3553 1.3699 0.914635 3529 0.2740 0.607947 3470 -2.4201 0.007758 3549 1.1872 0.882429 3523 0.0000 0.500000 Square side=100, avg. no. parked=3530.10 sample std.=28.70 p-value of the KSTEST for those 10 p-values: 0.142996 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_01:31 0.2423,0.8165,0.6835,0.2734,0.4512,0.0799,0.6444,0.5751,0.0556,0.7942, The KS test for those 10 p-values: 0.885369 The 3DSPHERES test for dh-ranFile-2018-07-07_01:31 sample no r^3 equiv. uni. 1 51.801 0.822132 2 3.222 0.101841 3 12.972 0.351043 4 54.824 0.839177 5 8.231 0.239943 6 14.484 0.382940 7 27.511 0.600293 8 153.971 0.994097 9 11.228 0.312212 10 43.189 0.762988 11 28.162 0.608873 12 97.542 0.961280 13 18.402 0.458490 14 2.096 0.067489 15 12.896 0.349400 16 25.475 0.572232 17 61.537 0.871425 18 52.676 0.827244 19 6.693 0.199974 20 76.754 0.922576 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.550088 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 -1.6 -0.1 -0.3 -1.4 1.3 -1.1 0.1 -0.6 -0.8 1.3 -0.9 -0.3 0.5 0.5 1.4 -0.8 2.8 -0.3 -0.2 -0.4 -0.4 -0.5 1.6 -2.3 -2.8 -0.8 0.0 0.9 0.2 -1.2 -0.3 -0.2 -0.6 0.2 1.7 -0.4 -0.4 -0.1 2.4 0.0 -0.1 Chi-square with 42 degrees of freedom:52.857489 z-score=1.184649, p-value=0.878399 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-07_01:31 Test no p-value 1 0.306414 2 0.106727 3 0.003608 4 0.314649 5 0.724620 6 0.690618 7 0.249743 8 0.524003 9 0.204026 10 0.635247 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.245681 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_01:31: (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 66596 0.07 66797 0.25 3 25000.00 25026 0.03 24890 0.48 4 6666.67 6697 0.14 6686 0.06 5 1388.89 1406 0.21 1338 1.86 6 238.10 224 0.83 248 0.41 7 34.72 47 4.34 35 0.00 8 4.96 3 0.77 5 0.00 p=0.62040 p=0.20051 Number of rngs required: 688213, p-value: 0.413 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_01:31 No. of wins: Observed Expected 98580 98585.9 z-score=-0.026, pvalue=0.48955 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66950 66666.7 1.204 1.204 2 37647 37654.3 0.001 1.206 3 26782 26954.7 1.107 2.313 4 19335 19313.5 0.024 2.337 5 13811 13851.4 0.118 2.454 6 10081 9943.5 1.900 4.355 7 7085 7145.0 0.504 4.859 8 5074 5139.1 0.824 5.683 9 3689 3699.9 0.032 5.715 10 2622 2666.3 0.736 6.451 11 1954 1923.3 0.489 6.940 12 1353 1388.7 0.920 7.860 13 1007 1003.7 0.011 7.870 14 730 726.1 0.021 7.891 15 498 525.8 1.474 9.364 16 372 381.2 0.220 9.584 17 258 276.5 1.243 10.827 18 209 200.8 0.332 11.159 19 144 146.0 0.027 11.186 20 101 106.2 0.256 11.442 21 298 287.1 0.413 11.855 Chisq= 11.86 for 20 degrees of freedom, p= 0.07903 SUMMARY of craptest p-value for no. of wins: 0.489548 p-value for throws/game: 0.079030 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_01:31 No. of wins: Observed Expected 98416 98585.9 z-score=-0.760, pvalue=0.22371 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66788 66666.7 0.221 0.221 2 37679 37654.3 0.016 0.237 3 27001 26954.7 0.079 0.316 4 19165 19313.5 1.141 1.458 5 13812 13851.4 0.112 1.570 6 9920 9943.5 0.056 1.626 7 7094 7145.0 0.364 1.990 8 5147 5139.1 0.012 2.002 9 3775 3699.9 1.526 3.528 10 2652 2666.3 0.077 3.605 11 1916 1923.3 0.028 3.633 12 1395 1388.7 0.028 3.661 13 1006 1003.7 0.005 3.666 14 714 726.1 0.203 3.869 15 541 525.8 0.437 4.306 16 392 381.2 0.309 4.615 17 289 276.5 0.561 5.177 18 187 200.8 0.952 6.129 19 140 146.0 0.245 6.374 20 107 106.2 0.006 6.380 21 280 287.1 0.176 6.556 Chisq= 6.56 for 20 degrees of freedom, p= 0.00209 SUMMARY of craptest p-value for no. of wins: 0.223715 p-value for throws/game: 0.002094 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0021,0.0024,0.0036,0.0078,0.0105,0.0143,0.0197,0.0198,0.0199,0.0262, 0.0274,0.0284,0.0426,0.0447,0.0462,0.0556,0.0603,0.0612,0.0675,0.0720, 0.0727,0.0790,0.0799,0.0847,0.0873,0.0942,0.0945,0.0960,0.0965,0.1018, 0.1052,0.1067,0.1115,0.1131,0.1159,0.1180,0.1363,0.1430,0.1454,0.1507, 0.1630,0.1671,0.1730,0.1738,0.1760,0.1846,0.1900,0.1909,0.1921,0.1935, 0.1954,0.1993,0.2000,0.2005,0.2040,0.2067,0.2155,0.2166,0.2205,0.2237, 0.2244,0.2270,0.2289,0.2313,0.2385,0.2386,0.2399,0.2423,0.2457,0.2494, 0.2494,0.2497,0.2513,0.2623,0.2734,0.2763,0.2841,0.2844,0.2893,0.2899, 0.2911,0.2950,0.3005,0.3032,0.3042,0.3064,0.3118,0.3122,0.3146,0.3245, 0.3267,0.3297,0.3341,0.3349,0.3362,0.3368,0.3416,0.3460,0.3494,0.3510, 0.3517,0.3548,0.3575,0.3588,0.3645,0.3699,0.3766,0.3767,0.3800,0.3829, 0.3845,0.3887,0.3920,0.3935,0.3949,0.3960,0.4073,0.4112,0.4131,0.4135, 0.4190,0.4255,0.4317,0.4377,0.4387,0.4442,0.4454,0.4473,0.4483,0.4511, 0.4512,0.4585,0.4635,0.4694,0.4759,0.4771,0.4784,0.4789,0.4895,0.5000, 0.5050,0.5071,0.5132,0.5193,0.5240,0.5279,0.5347,0.5397,0.5406,0.5495, 0.5501,0.5517,0.5536,0.5548,0.5555,0.5608,0.5610,0.5623,0.5713,0.5722, 0.5725,0.5751,0.5906,0.5923,0.6003,0.6054,0.6066,0.6079,0.6079,0.6089, 0.6092,0.6126,0.6164,0.6202,0.6204,0.6335,0.6352,0.6406,0.6420,0.6444, 0.6573,0.6588,0.6596,0.6598,0.6649,0.6711,0.6727,0.6760,0.6835,0.6906, 0.6923,0.7091,0.7194,0.7208,0.7246,0.7265,0.7265,0.7282,0.7320,0.7327, 0.7339,0.7343,0.7423,0.7475,0.7558,0.7561,0.7630,0.7690,0.7794,0.7807, 0.7838,0.7863,0.7878,0.7908,0.7918,0.7942,0.7961,0.8024,0.8079,0.8143, 0.8165,0.8221,0.8272,0.8311,0.8361,0.8387,0.8392,0.8398,0.8459,0.8569, 0.8635,0.8637,0.8681,0.8703,0.8714,0.8738,0.8750,0.8784,0.8794,0.8824, 0.8854,0.8899,0.9022,0.9039,0.9091,0.9146,0.9165,0.9226,0.9272,0.9337, 0.9340,0.9432,0.9449,0.9450,0.9493,0.9501,0.9517,0.9581,0.9597,0.9613, 0.9671,0.9717,0.9777,0.9804,0.9805,0.9832,0.9836,0.9941,0.9998, Overall p-value after applying KStest on 269 p-values = 0.934233 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.