RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-07_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 28.8611 0.964171 2 to 25 15.89 15.1642 0.416347 3 to 26 15.75 10.7039 0.128462 4 to 27 15.86 16.9422 0.541712 5 to 28 16.08 6.7399 0.013327 6 to 29 15.52 26.7065 0.937485 7 to 30 15.48 29.3671 0.968713 8 to 31 15.82 17.1226 0.553912 9 to 32 15.59 21.1244 0.779224 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.252698 Tough bday spacings test for dh-ranFile-2016-05-07_08:31: 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 5 31 71 98 115 73 52 31 15 6 3 (O-E)^2/E 1.9 0.9 0.1 0.0 3.1 0.3 0.0 0.1 0.0 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 6.622, p= 0.239 RESULTS OF GCD FOR dh-ranFile-2016-05-07_08:31 Euclid's algorithm: p-value, steps to gcd: 0.749723 p-value, dist. of gcd's: 0.656205 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-07_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.776 0.358 0.962 0.653 0.561 0.718 0.666 0.354 Bits 8 to 15---> 0.793 0.009 0.443 0.747 0.869 0.152 0.747 0.994 Bits 16 to 23---> 0.691 0.813 0.119 0.874 0.720 0.270 0.418 0.580 Bits 24 to 31---> 0.163 0.520 0.682 0.182 0.446 0.604 0.719 0.450 KS test for the above 32 p values: 0.767 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-07_08:31, p-values for 5 runs: 0.1500, 0.2660, 0.8589, 0.5245, 0.5250 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-07_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5297 5134.0 5.174 5.704 r= 30 22888 23103.0 2.002 7.706 r= 31 11593 11551.5 0.149 7.855 chi-square = 7.855 with df = 3; p-value = 0.951 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-07_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5223 5134.0 1.542 1.574 r= 31 22975 23103.0 0.710 2.284 r= 32 11588 11551.5 0.115 2.399 chi-square = 2.399 with df = 3; p-value = 0.506 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-07_08:31 b-rank test for bits 1 to 8, p=0.52137 b-rank test for bits 2 to 9, p=0.07246 b-rank test for bits 3 to 10, p=0.32804 b-rank test for bits 4 to 11, p=0.64165 b-rank test for bits 5 to 12, p=0.81059 b-rank test for bits 6 to 13, p=0.29762 b-rank test for bits 7 to 14, p=0.31938 b-rank test for bits 8 to 15, p=0.24159 b-rank test for bits 9 to 16, p=0.35813 b-rank test for bits 10 to 17, p=0.55101 b-rank test for bits 11 to 18, p=0.60632 b-rank test for bits 12 to 19, p=0.15530 b-rank test for bits 13 to 20, p=0.91875 b-rank test for bits 14 to 21, p=0.88067 b-rank test for bits 15 to 22, p=0.98286 b-rank test for bits 16 to 23, p=0.73557 b-rank test for bits 17 to 24, p=0.95746 b-rank test for bits 18 to 25, p=0.89283 b-rank test for bits 19 to 26, p=0.37418 b-rank test for bits 20 to 27, p=0.63653 b-rank test for bits 21 to 28, p=0.17651 b-rank test for bits 22 to 29, p=0.30227 b-rank test for bits 23 to 30, p=0.61438 b-rank test for bits 24 to 31, p=0.16749 b-rank test for bits 25 to 32, p=0.30455 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 = 0.817592 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-07_08:31 (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 141787 -0.29 0.387509 2 141362 -1.28 0.100482 3 142766 2.00 0.977334 4 141297 -1.43 0.076261 5 142125 0.50 0.692835 6 141754 -0.36 0.358332 7 142145 0.55 0.709057 8 141688 -0.52 0.302534 9 142164 0.60 0.724086 10 142365 1.06 0.856483 11 141662 -0.58 0.281675 12 141292 -1.44 0.074600 13 141932 0.05 0.521121 14 141637 -0.64 0.262295 15 142470 1.31 0.904898 16 142877 2.26 0.988118 17 141792 -0.27 0.391990 18 142232 0.75 0.774546 19 141728 -0.42 0.335904 20 141433 -1.11 0.132871 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-07_08:31 Bits used No. missing words z-score p-value 23 to 32 141643 -0.9184 0.179210 22 to 31 141893 -0.0563 0.477547 21 to 30 142015 0.3644 0.642213 20 to 29 141821 -0.3046 0.380341 19 to 28 141918 0.0299 0.511925 18 to 27 141671 -0.8218 0.205588 17 to 26 141580 -1.1356 0.128058 16 to 25 141800 -0.3770 0.353087 15 to 24 141760 -0.5149 0.303301 14 to 23 141691 -0.7529 0.225766 13 to 22 141536 -1.2873 0.098987 12 to 21 141685 -0.7736 0.219598 11 to 20 141850 -0.2046 0.418948 10 to 19 141986 0.2644 0.604256 9 to 18 141653 -0.8839 0.188376 8 to 17 141891 -0.0632 0.474801 7 to 16 141416 -1.7011 0.044459 6 to 15 141793 -0.4011 0.344159 5 to 14 141900 -0.0322 0.487167 4 to 13 141525 -1.3253 0.092540 3 to 12 142439 1.8264 0.966109 2 to 11 142025 0.3989 0.655003 1 to 10 142348 1.5127 0.934816 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-07_08:31 Bits used No. missing words z-score p-value 28 to 32 141988 0.2667 0.605141 27 to 31 142273 1.2328 0.891171 26 to 30 142229 1.0836 0.860735 25 to 29 141251 -2.2316 0.012820 24 to 28 142311 1.3616 0.913337 23 to 27 142330 1.4260 0.923066 22 to 26 142207 1.0091 0.843525 21 to 25 142190 0.9514 0.829305 20 to 24 141715 -0.6587 0.255030 19 to 23 141816 -0.3164 0.375860 18 to 22 142014 0.3548 0.638635 17 to 21 141989 0.2701 0.606446 16 to 20 142475 1.9175 0.972414 15 to 19 141744 -0.5604 0.287589 14 to 18 141786 -0.4181 0.337949 13 to 17 141979 0.2362 0.593349 12 to 16 142185 0.9345 0.824970 11 to 15 142290 1.2904 0.901545 10 to 14 142017 0.3650 0.642438 9 to 13 141794 -0.3909 0.347917 8 to 12 141923 0.0463 0.518480 7 to 11 141805 -0.3537 0.361797 6 to 10 141598 -1.0554 0.145631 5 to 9 142166 0.8701 0.807868 4 to 8 142238 1.1141 0.867390 3 to 7 142086 0.5989 0.725374 2 to 6 141873 -0.1232 0.450993 1 to 5 141953 0.1480 0.558842 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-07_08:31 Bits used No. missing words z-score p-value 31 to 32 142544 1.8722 0.969409 30 to 31 141890 -0.0570 0.477264 29 to 30 141652 -0.7591 0.223901 28 to 29 141156 -2.2222 0.013134 27 to 28 141529 -1.1219 0.130949 26 to 27 142588 2.0020 0.977356 25 to 26 142210 0.8869 0.812442 24 to 25 141622 -0.8476 0.198336 23 to 24 141731 -0.5260 0.299428 22 to 23 141879 -0.0895 0.464355 21 to 22 141860 -0.1455 0.442152 20 to 21 141543 -1.0806 0.139933 19 to 20 141633 -0.8151 0.207498 18 to 19 142118 0.6155 0.730903 17 to 18 142291 1.1259 0.869890 16 to 17 141654 -0.7532 0.225669 15 to 16 141756 -0.4523 0.325526 14 to 15 142532 1.8368 0.966879 13 to 14 141726 -0.5408 0.294324 12 to 13 141583 -0.9626 0.167868 11 to 12 142003 0.2763 0.608846 10 to 11 142342 1.2763 0.899078 9 to 10 141595 -0.9272 0.176904 8 to 9 142126 0.6391 0.738636 7 to 8 142070 0.4740 0.682233 6 to 7 141769 -0.4140 0.339454 5 to 6 141778 -0.3874 0.349229 4 to 5 141960 0.1495 0.559408 3 to 4 141938 0.0846 0.533699 2 to 3 142235 0.9607 0.831643 1 to 2 142175 0.7837 0.783388 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-07_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2536.37 0.514 0.696480 Test results for specific bytes for dh-ranFile-2016-05-07_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2517.88 0.253 0.599808 2 to 9 2478.85 -0.299 0.382408 3 to 10 2427.83 -1.021 0.153709 4 to 11 2511.26 0.159 0.563250 5 to 12 2446.56 -0.756 0.224911 6 to 13 2419.04 -1.145 0.126130 7 to 14 2424.40 -1.069 0.142497 8 to 15 2542.26 0.598 0.724965 9 to 16 2639.22 1.969 0.975519 10 to 17 2577.82 1.101 0.864445 11 to 18 2409.14 -1.285 0.099402 12 to 19 2489.47 -0.149 0.440795 13 to 20 2479.17 -0.295 0.384150 14 to 21 2549.62 0.702 0.758583 15 to 22 2382.87 -1.656 0.048816 16 to 23 2520.72 0.293 0.615240 17 to 24 2533.96 0.480 0.684506 18 to 25 2504.94 0.070 0.527843 19 to 26 2558.15 0.822 0.794576 20 to 27 2423.49 -1.082 0.139616 21 to 28 2471.90 -0.397 0.345520 22 to 29 2642.17 2.011 0.977815 23 to 30 2617.40 1.660 0.951578 24 to 31 2576.04 1.075 0.858907 25 to 32 2478.15 -0.309 0.378650 CDPARK for dh-ranFile-2016-05-07_08:31: 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 3541 0.8219 0.794438 3542 0.8676 0.807188 3514 -0.4110 0.340551 3561 1.7352 0.958644 3563 1.8265 0.966111 3530 0.3196 0.625377 3521 -0.0913 0.463617 3544 0.9589 0.831196 3505 -0.8219 0.205562 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3531.70 sample std.=21.45 p-value of the KSTEST for those 10 p-values: 0.343892 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-07_08:31 0.0662,0.6905,0.7357,0.7844,0.4472,0.4429,0.1652,0.4750,0.6362,0.7327, The KS test for those 10 p-values: 0.630854 The 3DSPHERES test for dh-ranFile-2016-05-07_08:31 sample no r^3 equiv. uni. 1 3.030 0.096054 2 3.783 0.118470 3 17.429 0.440638 4 3.412 0.107517 5 42.156 0.754680 6 44.621 0.774031 7 73.378 0.913355 8 1.738 0.056285 9 62.674 0.876206 10 48.834 0.803641 11 11.843 0.326164 12 45.383 0.779702 13 5.864 0.177539 14 18.362 0.457772 15 50.589 0.814799 16 25.224 0.568637 17 7.647 0.225015 18 8.050 0.235348 19 48.946 0.804369 20 17.517 0.442276 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.765543 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-07_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.4 0.0 1.4 -0.1 0.1 -2.2 0.0 0.7 -1.0 0.2 -0.4 0.1 0.7 -0.2 0.2 0.3 -0.1 1.2 0.3 -2.5 -1.0 1.9 0.7 1.0 -1.5 0.1 -0.4 -1.0 -0.0 1.4 0.5 -0.1 -0.2 -0.7 1.2 -0.1 0.5 -0.1 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:34.399083 z-score=-0.829328, p-value=0.208559 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-07_08:31 Test no p-value 1 0.030344 2 0.902228 3 0.071589 4 0.211966 5 0.303050 6 0.057822 7 0.850544 8 0.240032 9 0.081948 10 0.334439 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.025626 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-07_08:31: (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 66470 0.58 66758 0.13 3 25000.00 25224 2.01 25006 0.00 4 6666.67 6598 0.71 6634 0.16 5 1388.89 1406 0.21 1334 2.17 6 238.10 259 1.84 222 1.09 7 34.72 36 0.05 38 0.31 8 4.96 6 0.22 7 0.84 p=0.53127 p=0.41624 Number of rngs required: 687339, p-value: 0.108 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-07_08:31 No. of wins: Observed Expected 98602 98585.9 z-score= 0.072, pvalue=0.52878 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66662 66666.7 0.000 0.000 2 37598 37654.3 0.084 0.085 3 27254 26954.7 3.323 3.407 4 19391 19313.5 0.311 3.719 5 13819 13851.4 0.076 3.794 6 10094 9943.5 2.277 6.071 7 6971 7145.0 4.239 10.310 8 5066 5139.1 1.039 11.349 9 3699 3699.9 0.000 11.349 10 2673 2666.3 0.017 11.366 11 1841 1923.3 3.524 14.890 12 1373 1388.7 0.178 15.068 13 974 1003.7 0.880 15.948 14 769 726.1 2.530 18.478 15 493 525.8 2.050 20.528 16 362 381.2 0.962 21.490 17 270 276.5 0.155 21.645 18 179 200.8 2.373 24.018 19 143 146.0 0.061 24.079 20 96 106.2 0.982 25.061 21 273 287.1 0.694 25.755 Chisq= 25.76 for 20 degrees of freedom, p= 0.82594 SUMMARY of craptest p-value for no. of wins: 0.528776 p-value for throws/game: 0.825945 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-07_08:31 No. of wins: Observed Expected 98773 98585.9 z-score= 0.837, pvalue=0.79871 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66630 66666.7 0.020 0.020 2 37446 37654.3 1.153 1.173 3 26720 26954.7 2.044 3.217 4 19375 19313.5 0.196 3.413 5 13927 13851.4 0.412 3.825 6 9873 9943.5 0.500 4.326 7 7219 7145.0 0.766 5.092 8 5200 5139.1 0.722 5.814 9 3739 3699.9 0.414 6.228 10 2783 2666.3 5.108 11.336 11 1910 1923.3 0.092 11.428 12 1395 1388.7 0.028 11.457 13 1088 1003.7 7.078 18.534 14 757 726.1 1.311 19.846 15 555 525.8 1.618 21.463 16 356 381.2 1.660 23.123 17 283 276.5 0.151 23.274 18 181 200.8 1.958 25.232 19 141 146.0 0.170 25.402 20 104 106.2 0.046 25.448 21 318 287.1 3.323 28.771 Chisq= 28.77 for 20 degrees of freedom, p= 0.90762 SUMMARY of craptest p-value for no. of wins: 0.798705 p-value for throws/game: 0.907625 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0093,0.0128,0.0131,0.0133,0.0256,0.0303,0.0445,0.0488,0.0563,0.0578, 0.0662,0.0716,0.0725,0.0746,0.0763,0.0819,0.0925,0.0961,0.0990,0.0994, 0.1005,0.1075,0.1080,0.1088,0.1185,0.1194,0.1261,0.1281,0.1285,0.1309, 0.1329,0.1396,0.1399,0.1425,0.1456,0.1500,0.1519,0.1537,0.1553,0.1626, 0.1652,0.1675,0.1679,0.1765,0.1769,0.1775,0.1792,0.1820,0.1884,0.1983, 0.2056,0.2056,0.2075,0.2086,0.2120,0.2196,0.2239,0.2249,0.2250,0.2257, 0.2258,0.2353,0.2394,0.2400,0.2416,0.2527,0.2550,0.2623,0.2660,0.2701, 0.2817,0.2876,0.2943,0.2976,0.2994,0.3023,0.3025,0.3031,0.3033,0.3046, 0.3194,0.3255,0.3262,0.3280,0.3344,0.3359,0.3379,0.3395,0.3406,0.3439, 0.3442,0.3455,0.3479,0.3492,0.3531,0.3539,0.3581,0.3581,0.3583,0.3618, 0.3742,0.3759,0.3787,0.3803,0.3824,0.3841,0.3875,0.3920,0.4162,0.4163, 0.4185,0.4189,0.4406,0.4408,0.4422,0.4423,0.4429,0.4433,0.4457,0.4472, 0.4504,0.4510,0.4578,0.4636,0.4644,0.4748,0.4750,0.4773,0.4775,0.4872, 0.5062,0.5119,0.5185,0.5195,0.5211,0.5214,0.5245,0.5250,0.5278,0.5288, 0.5313,0.5337,0.5417,0.5510,0.5539,0.5588,0.5594,0.5607,0.5633,0.5686, 0.5800,0.5933,0.5998,0.6040,0.6043,0.6051,0.6063,0.6064,0.6088,0.6144, 0.6152,0.6254,0.6309,0.6362,0.6365,0.6386,0.6416,0.6422,0.6424,0.6528, 0.6550,0.6562,0.6655,0.6822,0.6824,0.6845,0.6905,0.6909,0.6928,0.6965, 0.7091,0.7183,0.7192,0.7201,0.7241,0.7250,0.7254,0.7309,0.7327,0.7356, 0.7357,0.7386,0.7467,0.7474,0.7497,0.7547,0.7586,0.7655,0.7666,0.7740, 0.7745,0.7757,0.7792,0.7797,0.7834,0.7844,0.7935,0.7944,0.7946,0.7987, 0.8036,0.8044,0.8072,0.8079,0.8106,0.8124,0.8129,0.8148,0.8176,0.8250, 0.8259,0.8293,0.8312,0.8316,0.8435,0.8505,0.8565,0.8589,0.8589,0.8607, 0.8644,0.8674,0.8692,0.8699,0.8738,0.8762,0.8807,0.8912,0.8928,0.8991, 0.9015,0.9022,0.9049,0.9076,0.9133,0.9134,0.9187,0.9231,0.9348,0.9375, 0.9509,0.9516,0.9575,0.9586,0.9619,0.9642,0.9661,0.9661,0.9669,0.9687, 0.9694,0.9724,0.9755,0.9773,0.9774,0.9778,0.9829,0.9881,0.9935, Overall p-value after applying KStest on 269 p-values = 0.569228 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.