RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-15_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 32.0830 0.985306 2 to 25 15.74 14.1991 0.347038 3 to 26 15.32 26.0951 0.927255 4 to 27 15.34 27.4458 0.948154 5 to 28 15.78 17.6800 0.590705 6 to 29 15.69 14.5827 0.374486 7 to 30 15.63 17.6861 0.591103 8 to 31 15.80 18.3272 0.631513 9 to 32 15.84 11.6898 0.181453 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.248743 Tough bday spacings test for dh-ranFile-2018-04-15_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 15 51 71 89 100 68 54 27 19 5 1 (O-E)^2/E 3.7 5.6 0.1 0.8 0.1 1.3 0.1 0.3 1.1 0.4 2.3 Birthday Spacings: Sum(O-E)^2/E= 15.749, p= 0.893 RESULTS OF GCD FOR dh-ranFile-2018-04-15_13:31 Euclid's algorithm: p-value, steps to gcd: 0.932649 p-value, dist. of gcd's: 0.797353 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-15_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.374 0.419 0.033 0.637 0.355 0.181 0.033 0.252 Bits 8 to 15---> 0.041 0.923 0.355 0.038 0.762 0.802 0.922 0.976 Bits 16 to 23---> 0.872 0.275 0.265 0.520 0.525 0.318 0.155 0.458 Bits 24 to 31---> 0.164 0.163 0.192 0.530 0.411 0.719 0.240 0.227 KS test for the above 32 p values: 0.892 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-15_13:31, p-values for 5 runs: 0.1338, 0.0487, 0.7169, 0.9783, 0.9372 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-15_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5157 5134.0 0.103 0.195 r= 30 23074 23103.0 0.037 0.232 r= 31 11562 11551.5 0.010 0.241 chi-square = 0.241 with df = 3; p-value = 0.029 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-15_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5007 5134.0 3.142 3.337 r= 31 23201 23103.0 0.415 3.752 r= 32 11587 11551.5 0.109 3.861 chi-square = 3.861 with df = 3; p-value = 0.723 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-15_13:31 b-rank test for bits 1 to 8, p=0.01970 b-rank test for bits 2 to 9, p=0.88645 b-rank test for bits 3 to 10, p=0.58088 b-rank test for bits 4 to 11, p=0.47129 b-rank test for bits 5 to 12, p=0.05630 b-rank test for bits 6 to 13, p=0.01109 b-rank test for bits 7 to 14, p=0.61168 b-rank test for bits 8 to 15, p=0.81107 b-rank test for bits 9 to 16, p=0.75508 b-rank test for bits 10 to 17, p=0.79974 b-rank test for bits 11 to 18, p=0.03585 b-rank test for bits 12 to 19, p=0.50481 b-rank test for bits 13 to 20, p=0.27631 b-rank test for bits 14 to 21, p=0.33241 b-rank test for bits 15 to 22, p=0.17173 b-rank test for bits 16 to 23, p=0.65144 b-rank test for bits 17 to 24, p=0.32960 b-rank test for bits 18 to 25, p=0.86902 b-rank test for bits 19 to 26, p=0.18339 b-rank test for bits 20 to 27, p=0.36902 b-rank test for bits 21 to 28, p=0.73062 b-rank test for bits 22 to 29, p=0.04269 b-rank test for bits 23 to 30, p=0.73376 b-rank test for bits 24 to 31, p=0.53335 b-rank test for bits 25 to 32, p=0.26808 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 = 0.349167 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-15_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 142228 0.74 0.771730 2 142054 0.34 0.632324 3 141444 -1.09 0.138470 4 142087 0.42 0.660972 5 141828 -0.19 0.424645 6 142309 0.93 0.824799 7 141878 -0.07 0.470823 8 142050 0.33 0.628797 9 141680 -0.54 0.296042 10 141892 -0.04 0.483851 11 142178 0.63 0.734911 12 141811 -0.23 0.409146 13 141430 -1.12 0.131372 14 141056 -1.99 0.023089 15 142201 0.68 0.752214 16 141722 -0.44 0.330807 17 142243 0.78 0.782188 18 142739 1.94 0.973718 19 141612 -0.69 0.243623 20 142520 1.43 0.923181 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-15_13:31 Bits used No. missing words z-score p-value 23 to 32 141883 -0.0908 0.463829 22 to 31 141653 -0.8839 0.188376 21 to 30 141674 -0.8115 0.208544 20 to 29 141715 -0.6701 0.251396 19 to 28 142357 1.5437 0.938668 18 to 27 141856 -0.1839 0.427047 17 to 26 142220 1.0713 0.857977 16 to 25 142071 0.5575 0.711401 15 to 24 141868 -0.1425 0.443336 14 to 23 142436 1.8161 0.965323 13 to 22 142225 1.0885 0.861817 12 to 21 141800 -0.3770 0.353087 11 to 20 142345 1.5023 0.933492 10 to 19 142096 0.6437 0.740112 9 to 18 142105 0.6747 0.750075 8 to 17 141930 0.0713 0.528411 7 to 16 141670 -0.8253 0.204608 6 to 15 141998 0.3058 0.620106 5 to 14 142041 0.4540 0.675098 4 to 13 142045 0.4678 0.680046 3 to 12 141627 -0.9736 0.165140 2 to 11 141408 -1.7287 0.041929 1 to 10 142362 1.5609 0.940730 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-15_13:31 Bits used No. missing words z-score p-value 28 to 32 141813 -0.3265 0.372007 27 to 31 141413 -1.6825 0.046238 26 to 30 142136 0.7684 0.778867 25 to 29 141835 -0.2520 0.400534 24 to 28 141659 -0.8486 0.198059 23 to 27 142135 0.7650 0.777859 22 to 26 141553 -1.2079 0.113543 21 to 25 141868 -0.1401 0.444290 20 to 24 141874 -0.1198 0.452336 19 to 23 141830 -0.2689 0.393998 18 to 22 141881 -0.0960 0.461747 17 to 21 141845 -0.2181 0.413688 16 to 20 141750 -0.5401 0.294564 15 to 19 141761 -0.5028 0.307548 14 to 18 141817 -0.3130 0.377147 13 to 17 141934 0.0836 0.533324 12 to 16 142082 0.5853 0.720834 11 to 15 141745 -0.5571 0.288746 10 to 14 141692 -0.7367 0.230649 9 to 13 141749 -0.5435 0.293396 8 to 12 141959 0.1684 0.566855 7 to 11 142262 1.1955 0.884053 6 to 10 142310 1.3582 0.912800 5 to 9 141570 -1.1503 0.125016 4 to 8 142363 1.5379 0.937959 3 to 7 142086 0.5989 0.725374 2 to 6 142048 0.4701 0.680847 1 to 5 142366 1.5480 0.939193 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-15_13:31 Bits used No. missing words z-score p-value 31 to 32 142042 0.3914 0.652233 30 to 31 141256 -1.9272 0.026976 29 to 30 141779 -0.3845 0.350321 28 to 29 141937 0.0816 0.532527 27 to 28 141560 -1.0305 0.151394 26 to 27 141070 -2.4759 0.006645 25 to 26 142117 0.6126 0.729928 24 to 25 141766 -0.4228 0.336220 23 to 24 142004 0.2793 0.609978 22 to 23 142198 0.8515 0.802764 21 to 22 142414 1.4887 0.931717 20 to 21 141652 -0.7591 0.223901 19 to 20 141919 0.0285 0.511378 18 to 19 141976 0.1967 0.577956 17 to 18 142065 0.4592 0.676956 16 to 17 141590 -0.9420 0.173102 15 to 16 141632 -0.8181 0.206655 14 to 15 141658 -0.7414 0.229230 13 to 14 141802 -0.3166 0.375771 12 to 13 141763 -0.4317 0.332997 11 to 12 141909 -0.0010 0.499612 10 to 11 141105 -2.3727 0.008830 9 to 10 141986 0.2262 0.589464 8 to 9 141752 -0.4641 0.321288 7 to 8 141946 0.1082 0.543070 6 to 7 141797 -0.3314 0.370187 5 to 6 142172 0.7748 0.780782 4 to 5 141948 0.1141 0.545409 3 to 4 141365 -1.6057 0.054171 2 to 3 141844 -0.1927 0.423592 1 to 2 141432 -1.4081 0.079558 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-15_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2459.08 -0.579 0.281388 Test results for specific bytes for dh-ranFile-2018-04-15_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2454.93 -0.637 0.261951 2 to 9 2484.74 -0.216 0.414580 3 to 10 2427.80 -1.021 0.153613 4 to 11 2486.71 -0.188 0.425459 5 to 12 2409.93 -1.274 0.101367 6 to 13 2470.45 -0.418 0.338018 7 to 14 2484.90 -0.214 0.415468 8 to 15 2545.43 0.642 0.739697 9 to 16 2520.78 0.294 0.615550 10 to 17 2411.99 -1.245 0.106637 11 to 18 2624.56 1.762 0.960931 12 to 19 2507.74 0.109 0.543582 13 to 20 2350.95 -2.108 0.017518 14 to 21 2503.98 0.056 0.522462 15 to 22 2530.44 0.431 0.666604 16 to 23 2484.39 -0.221 0.412627 17 to 24 2515.53 0.220 0.586936 18 to 25 2487.45 -0.177 0.429578 19 to 26 2512.92 0.183 0.572481 20 to 27 2577.33 1.094 0.862939 21 to 28 2481.36 -0.264 0.396028 22 to 29 2452.30 -0.675 0.249953 23 to 30 2565.24 0.923 0.821898 24 to 31 2541.56 0.588 0.721639 25 to 32 2614.34 1.617 0.947064 CDPARK for dh-ranFile-2018-04-15_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 3545 1.0046 0.842447 3529 0.2740 0.607947 3531 0.3653 0.642555 3508 -0.6849 0.246694 3501 -1.0046 0.157553 3566 1.9635 0.975204 3554 1.4155 0.921543 3563 1.8265 0.966111 3527 0.1826 0.572463 3503 -0.9132 0.180558 Square side=100, avg. no. parked=3532.70 sample std.=22.76 p-value of the KSTEST for those 10 p-values: 0.240280 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-15_13:31 0.4842,0.3520,0.4011,0.3933,0.8660,0.7579,0.8142,0.1812,0.2409,0.4013, The KS test for those 10 p-values: 0.616406 The 3DSPHERES test for dh-ranFile-2018-04-15_13:31 sample no r^3 equiv. uni. 1 68.112 0.896729 2 14.080 0.374588 3 14.394 0.381083 4 92.386 0.954020 5 27.219 0.596382 6 5.362 0.163670 7 11.555 0.319673 8 57.102 0.850938 9 31.767 0.653168 10 53.585 0.832399 11 2.843 0.090411 12 1.540 0.050034 13 38.873 0.726311 14 3.476 0.109403 15 37.939 0.717656 16 4.060 0.126567 17 13.289 0.357869 18 31.420 0.649123 19 50.581 0.814747 20 8.285 0.241315 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.966241 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-15_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 0.6 -0.4 0.6 1.1 -1.1 -0.0 1.6 1.4 -1.1 -0.3 1.2 -1.1 0.8 0.1 1.0 -0.4 -0.8 0.1 0.4 0.6 -1.2 -0.9 -0.3 1.5 -1.1 -0.8 0.9 -1.0 -1.0 1.0 -1.6 1.4 -1.5 -1.7 -0.2 0.2 0.1 0.4 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.417276 z-score=-0.281798, p-value=0.415043 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-15_13:31 Test no p-value 1 0.561158 2 0.028579 3 0.157468 4 0.624316 5 0.017353 6 0.367562 7 0.719310 8 0.965120 9 0.930386 10 0.061215 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.310287 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-15_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 66583 0.11 66787 0.22 3 25000.00 25040 0.06 24877 0.61 4 6666.67 6627 0.24 6710 0.28 5 1388.89 1471 4.85 1348 1.20 6 238.10 240 0.02 241 0.04 7 34.72 34 0.01 29 0.94 8 4.96 4 0.19 7 0.84 p=0.51555 p=0.34018 Number of rngs required: 689766, p-value: 0.945 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-15_13:31 No. of wins: Observed Expected 98914 98585.9 z-score= 1.468, pvalue=0.92890 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67200 66666.7 4.267 4.267 2 37271 37654.3 3.902 8.169 3 27197 26954.7 2.177 10.346 4 18966 19313.5 6.251 16.597 5 13675 13851.4 2.247 18.844 6 10106 9943.5 2.654 21.499 7 7150 7145.0 0.003 21.502 8 5212 5139.1 1.035 22.537 9 3614 3699.9 1.993 24.530 10 2675 2666.3 0.028 24.558 11 1980 1923.3 1.670 26.228 12 1331 1388.7 2.401 28.629 13 981 1003.7 0.514 29.143 14 740 726.1 0.265 29.407 15 532 525.8 0.072 29.479 16 366 381.2 0.602 30.082 17 270 276.5 0.155 30.236 18 205 200.8 0.087 30.323 19 150 146.0 0.110 30.433 20 96 106.2 0.982 31.416 21 283 287.1 0.059 31.475 Chisq= 31.47 for 20 degrees of freedom, p= 0.95077 SUMMARY of craptest p-value for no. of wins: 0.928899 p-value for throws/game: 0.950774 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-15_13:31 No. of wins: Observed Expected 98683 98585.9 z-score= 0.434, pvalue=0.66803 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67044 66666.7 2.136 2.136 2 37664 37654.3 0.002 2.138 3 26924 26954.7 0.035 2.173 4 19247 19313.5 0.229 2.402 5 13663 13851.4 2.563 4.965 6 9990 9943.5 0.217 5.182 7 7147 7145.0 0.001 5.183 8 5110 5139.1 0.164 5.347 9 3752 3699.9 0.735 6.082 10 2577 2666.3 2.991 9.072 11 1869 1923.3 1.535 10.607 12 1394 1388.7 0.020 10.627 13 986 1003.7 0.313 10.940 14 732 726.1 0.047 10.987 15 518 525.8 0.117 11.104 16 376 381.2 0.070 11.173 17 290 276.5 0.655 11.828 18 198 200.8 0.040 11.868 19 140 146.0 0.245 12.114 20 112 106.2 0.315 12.429 21 267 287.1 1.409 13.838 Chisq= 13.84 for 20 degrees of freedom, p= 0.16138 SUMMARY of craptest p-value for no. of wins: 0.668028 p-value for throws/game: 0.161377 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0066,0.0088,0.0111,0.0174,0.0175,0.0197,0.0231,0.0270,0.0286,0.0293, 0.0326,0.0333,0.0359,0.0376,0.0411,0.0419,0.0427,0.0462,0.0487,0.0500, 0.0542,0.0563,0.0612,0.0796,0.0904,0.1014,0.1066,0.1094,0.1135,0.1250, 0.1266,0.1314,0.1338,0.1385,0.1514,0.1536,0.1546,0.1575,0.1576,0.1614, 0.1627,0.1637,0.1643,0.1651,0.1717,0.1731,0.1806,0.1812,0.1813,0.1815, 0.1834,0.1884,0.1924,0.1981,0.2046,0.2067,0.2085,0.2239,0.2273,0.2292, 0.2306,0.2399,0.2403,0.2409,0.2413,0.2436,0.2467,0.2487,0.2500,0.2514, 0.2521,0.2620,0.2652,0.2681,0.2751,0.2763,0.2814,0.2887,0.2934,0.2946, 0.2960,0.3075,0.3103,0.3178,0.3197,0.3213,0.3296,0.3308,0.3324,0.3330, 0.3362,0.3380,0.3402,0.3470,0.3492,0.3503,0.3520,0.3531,0.3547,0.3548, 0.3579,0.3676,0.3690,0.3702,0.3720,0.3736,0.3745,0.3746,0.3758,0.3771, 0.3811,0.3933,0.3940,0.3960,0.4005,0.4011,0.4013,0.4091,0.4113,0.4126, 0.4137,0.4146,0.4150,0.4155,0.4192,0.4236,0.4246,0.4255,0.4270,0.4296, 0.4433,0.4443,0.4523,0.4580,0.4617,0.4638,0.4708,0.4713,0.4839,0.4842, 0.4996,0.5048,0.5114,0.5156,0.5201,0.5225,0.5249,0.5284,0.5301,0.5325, 0.5333,0.5333,0.5431,0.5436,0.5454,0.5612,0.5669,0.5725,0.5725,0.5780, 0.5809,0.5869,0.5895,0.5907,0.5911,0.5964,0.6079,0.6100,0.6117,0.6156, 0.6164,0.6201,0.6243,0.6288,0.6315,0.6323,0.6369,0.6426,0.6491,0.6514, 0.6522,0.6532,0.6610,0.6666,0.6680,0.6751,0.6770,0.6800,0.6808,0.7114, 0.7169,0.7177,0.7188,0.7193,0.7208,0.7216,0.7232,0.7254,0.7263,0.7299, 0.7306,0.7338,0.7349,0.7397,0.7401,0.7501,0.7522,0.7551,0.7579,0.7625, 0.7717,0.7779,0.7789,0.7808,0.7822,0.7974,0.7997,0.8015,0.8028,0.8111, 0.8142,0.8147,0.8219,0.8248,0.8324,0.8424,0.8509,0.8580,0.8618,0.8629, 0.8660,0.8690,0.8715,0.8841,0.8864,0.8923,0.8929,0.8967,0.9128,0.9215, 0.9217,0.9226,0.9232,0.9273,0.9289,0.9304,0.9317,0.9326,0.9335,0.9372, 0.9380,0.9387,0.9392,0.9407,0.9447,0.9471,0.9482,0.9508,0.9540,0.9609, 0.9651,0.9653,0.9661,0.9662,0.9737,0.9752,0.9755,0.9783,0.9853, Overall p-value after applying KStest on 269 p-values = 0.669508 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.