RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-26_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 19.8802 0.719599 2 to 25 15.63 24.0631 0.882269 3 to 26 15.98 17.6046 0.585814 4 to 27 15.79 25.0781 0.907026 5 to 28 16.03 16.0047 0.476497 6 to 29 16.05 17.4981 0.578856 7 to 30 15.90 9.5623 0.079045 8 to 31 16.09 21.8961 0.811251 9 to 32 15.58 18.2778 0.628478 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.247855 Tough bday spacings test for dh-ranFile-2015-09-26_07:31: 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 39 79 117 83 79 45 30 9 6 6 (O-E)^2/E 0.5 0.2 0.4 3.8 2.2 0.0 1.0 0.0 2.3 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.420, p= 0.674 RESULTS OF GCD FOR dh-ranFile-2015-09-26_07:31 Euclid's algorithm: p-value, steps to gcd: 0.100308 p-value, dist. of gcd's: 0.721649 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-26_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.773 0.764 0.565 0.994 0.968 0.241 0.641 0.577 Bits 8 to 15---> 0.896 0.241 0.140 0.225 0.101 0.848 0.969 0.553 Bits 16 to 23---> 0.193 0.487 0.304 0.818 0.236 0.709 0.976 0.226 Bits 24 to 31---> 0.533 0.447 0.821 0.277 0.904 0.265 0.396 0.815 KS test for the above 32 p values: 0.744 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-26_07:31, p-values for 5 runs: 0.0606, 0.3104, 0.4146, 0.6969, 0.0689 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-26_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5141 5134.0 0.010 0.281 r= 30 22991 23103.0 0.543 0.825 r= 31 11649 11551.5 0.823 1.647 chi-square = 1.647 with df = 3; p-value = 0.351 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-26_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 237 211.4 3.095 3.095 r= 30 5076 5134.0 0.655 3.751 r= 31 23125 23103.0 0.021 3.772 r= 32 11562 11551.5 0.010 3.781 chi-square = 3.781 with df = 3; p-value = 0.714 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-26_07:31 b-rank test for bits 1 to 8, p=0.31323 b-rank test for bits 2 to 9, p=0.55228 b-rank test for bits 3 to 10, p=0.56499 b-rank test for bits 4 to 11, p=0.88539 b-rank test for bits 5 to 12, p=0.48616 b-rank test for bits 6 to 13, p=0.96677 b-rank test for bits 7 to 14, p=0.90401 b-rank test for bits 8 to 15, p=0.16768 b-rank test for bits 9 to 16, p=0.47417 b-rank test for bits 10 to 17, p=0.17835 b-rank test for bits 11 to 18, p=0.79925 b-rank test for bits 12 to 19, p=0.63923 b-rank test for bits 13 to 20, p=0.12059 b-rank test for bits 14 to 21, p=0.60584 b-rank test for bits 15 to 22, p=0.37396 b-rank test for bits 16 to 23, p=0.26768 b-rank test for bits 17 to 24, p=0.57770 b-rank test for bits 18 to 25, p=0.41596 b-rank test for bits 19 to 26, p=0.91603 b-rank test for bits 20 to 27, p=0.39299 b-rank test for bits 21 to 28, p=0.26066 b-rank test for bits 22 to 29, p=0.06217 b-rank test for bits 23 to 30, p=0.33660 b-rank test for bits 24 to 31, p=0.64404 b-rank test for bits 25 to 32, p=0.91449 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 = 0.849895 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-26_07:31 (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 141764 -0.34 0.367095 2 142001 0.21 0.584798 3 141965 0.13 0.551745 4 141087 -1.92 0.027345 5 142078 0.39 0.653242 6 141636 -0.64 0.261535 7 141329 -1.36 0.087564 8 141567 -0.80 0.211903 9 142153 0.57 0.715431 10 142447 1.26 0.895485 11 142207 0.70 0.756626 12 141679 -0.54 0.295235 13 141748 -0.38 0.353109 14 141840 -0.16 0.435658 15 140541 -3.20 0.000694 16 141301 -1.42 0.077610 17 142122 0.50 0.690368 18 142329 0.98 0.836590 19 141691 -0.51 0.304985 20 142218 0.72 0.764604 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-26_07:31 Bits used No. missing words z-score p-value 23 to 32 141995 0.2954 0.616161 22 to 31 142070 0.5540 0.710222 21 to 30 141833 -0.2632 0.396196 20 to 29 141907 -0.0080 0.496795 19 to 28 141458 -1.5563 0.059817 18 to 27 142182 0.9402 0.826453 17 to 26 141791 -0.4080 0.341624 16 to 25 141861 -0.1667 0.433821 15 to 24 141334 -1.9839 0.023634 14 to 23 141940 0.1058 0.542113 13 to 22 141865 -0.1529 0.439254 12 to 21 142123 0.7368 0.769376 11 to 20 141759 -0.5184 0.302097 10 to 19 142374 1.6023 0.945457 9 to 18 141670 -0.8253 0.204608 8 to 17 141483 -1.4701 0.070767 7 to 16 141383 -1.8149 0.034767 6 to 15 142161 0.8678 0.807256 5 to 14 141806 -0.3563 0.360804 4 to 13 141946 0.1264 0.550312 3 to 12 142008 0.3402 0.633163 2 to 11 142341 1.4885 0.931693 1 to 10 142170 0.8989 0.815637 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-26_07:31 Bits used No. missing words z-score p-value 28 to 32 142151 0.8192 0.793670 27 to 31 141980 0.2396 0.594664 26 to 30 141855 -0.1842 0.426940 25 to 29 141894 -0.0520 0.479278 24 to 28 141527 -1.2960 0.097482 23 to 27 141689 -0.7469 0.227568 22 to 26 141611 -1.0113 0.155939 21 to 25 142229 1.0836 0.860735 20 to 24 142219 1.0497 0.853079 19 to 23 142036 0.4294 0.666180 18 to 22 141867 -0.1435 0.442951 17 to 21 141560 -1.1842 0.118173 16 to 20 141827 -0.2791 0.390090 15 to 19 141886 -0.0791 0.468483 14 to 18 141870 -0.1333 0.446969 13 to 17 141795 -0.3876 0.349171 12 to 16 141720 -0.6418 0.260503 11 to 15 141904 -0.0181 0.492792 10 to 14 141770 -0.4723 0.318355 9 to 13 142112 0.6870 0.753964 8 to 12 141666 -0.8248 0.204729 7 to 11 141283 -2.1232 0.016871 6 to 10 141593 -1.0723 0.141792 5 to 9 141832 -0.2621 0.396609 4 to 8 142188 0.9446 0.827580 3 to 7 142363 1.5379 0.937959 2 to 6 141690 -0.7435 0.228592 1 to 5 142032 0.4158 0.661233 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-26_07:31 Bits used No. missing words z-score p-value 31 to 32 142130 0.6509 0.742459 30 to 31 141817 -0.2724 0.392673 29 to 30 141824 -0.2517 0.400632 28 to 29 141405 -1.4877 0.068415 27 to 28 141962 0.1554 0.561735 26 to 27 142361 1.3324 0.908629 25 to 26 141536 -1.1013 0.135390 24 to 25 142557 1.9105 0.971968 23 to 24 142388 1.4120 0.921026 22 to 23 141681 -0.6735 0.250302 21 to 22 141419 -1.4464 0.074032 20 to 21 141962 0.1554 0.561735 19 to 20 141720 -0.5585 0.288253 18 to 19 142233 0.9548 0.830155 17 to 18 141897 -0.0364 0.485493 16 to 17 141314 -1.7561 0.039533 15 to 16 142455 1.6096 0.946262 14 to 15 141829 -0.2370 0.406343 13 to 14 142086 0.5212 0.698869 12 to 13 141780 -0.3815 0.351415 11 to 12 141755 -0.4553 0.324464 10 to 11 142122 0.6273 0.734784 9 to 10 141598 -0.9184 0.179211 8 to 9 141265 -1.9007 0.028672 7 to 8 142556 1.9076 0.971777 6 to 7 141744 -0.4877 0.312882 5 to 6 141403 -1.4936 0.067640 4 to 5 141673 -0.6971 0.242858 3 to 4 142384 1.4002 0.919274 2 to 3 142129 0.6480 0.741506 1 to 2 141692 -0.6411 0.260732 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-26_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2504.04 0.057 0.522803 Test results for specific bytes for dh-ranFile-2015-09-26_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2551.46 0.728 0.766629 2 to 9 2546.00 0.651 0.742350 3 to 10 2468.87 -0.440 0.329874 4 to 11 2447.21 -0.747 0.227671 5 to 12 2479.74 -0.287 0.387219 6 to 13 2381.84 -1.671 0.047353 7 to 14 2525.83 0.365 0.642546 8 to 15 2474.57 -0.360 0.359542 9 to 16 2392.26 -1.524 0.063795 10 to 17 2532.23 0.456 0.675719 11 to 18 2566.98 0.947 0.828235 12 to 19 2484.48 -0.219 0.413158 13 to 20 2430.73 -0.980 0.163651 14 to 21 2416.22 -1.185 0.118051 15 to 22 2542.30 0.598 0.725164 16 to 23 2435.42 -0.913 0.180540 17 to 24 2508.87 0.125 0.549887 18 to 25 2466.98 -0.467 0.320274 19 to 26 2518.14 0.257 0.601257 20 to 27 2466.52 -0.473 0.317936 21 to 28 2374.94 -1.769 0.038479 22 to 29 2341.95 -2.235 0.012705 23 to 30 2428.88 -1.006 0.157262 24 to 31 2545.81 0.648 0.741478 25 to 32 2463.45 -0.517 0.302624 CDPARK for dh-ranFile-2015-09-26_07:31: 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 3521 -0.0913 0.463617 3541 0.8219 0.794438 3516 -0.3196 0.374623 3534 0.5023 0.692266 3553 1.3699 0.914635 3475 -2.1918 0.014198 3513 -0.4566 0.323972 3549 1.1872 0.882429 3530 0.3196 0.625377 3534 0.5023 0.692266 Square side=100, avg. no. parked=3526.60 sample std.=21.26 p-value of the KSTEST for those 10 p-values: 0.578552 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-26_07:31 0.3294,0.5620,0.2007,0.2741,0.9550,0.6933,0.0951,0.8966,0.7843,0.6673, The KS test for those 10 p-values: 0.956924 The 3DSPHERES test for dh-ranFile-2015-09-26_07:31 sample no r^3 equiv. uni. 1 46.132 0.785130 2 57.099 0.850925 3 28.847 0.617707 4 71.204 0.906843 5 63.896 0.881147 6 39.151 0.728835 7 109.587 0.974084 8 59.793 0.863728 9 5.389 0.164410 10 15.222 0.397944 11 143.480 0.991626 12 72.575 0.911004 13 12.655 0.344148 14 20.323 0.492083 15 4.608 0.142375 16 80.440 0.931528 17 19.760 0.482452 18 31.994 0.655780 19 21.611 0.513429 20 2.707 0.086283 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.044990 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-26_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.6 0.9 -0.1 -1.1 -1.3 0.5 -0.7 -0.2 -1.6 -0.7 0.2 1.5 0.8 0.5 0.6 -0.4 -1.3 0.9 -0.6 0.4 -0.5 -1.3 0.9 1.2 -0.6 1.5 -0.9 -0.8 1.2 -0.9 -0.3 0.7 1.7 -0.7 -1.4 0.5 0.5 -1.3 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:34.457298 z-score=-0.822976, p-value=0.210646 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-26_07:31 Test no p-value 1 0.225565 2 0.246640 3 0.574791 4 0.023559 5 0.121423 6 0.287324 7 0.156082 8 0.040303 9 0.122499 10 0.255930 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001433 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-26_07:31: (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 66735 0.07 66602 0.06 3 25000.00 25019 0.01 25040 0.06 4 6666.67 6581 1.10 6648 0.05 5 1388.89 1368 0.31 1415 0.49 6 238.10 254 1.06 261 2.20 7 34.72 35 0.00 29 0.94 8 4.96 7 0.84 4 0.19 p=0.24321 p=0.32352 Number of rngs required: 690443, p-value: 0.992 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-26_07:31 No. of wins: Observed Expected 98249 98585.9 z-score=-1.507, pvalue=0.06595 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66619 66666.7 0.034 0.034 2 37735 37654.3 0.173 0.207 3 26973 26954.7 0.012 0.219 4 19295 19313.5 0.018 0.237 5 13793 13851.4 0.246 0.483 6 9888 9943.5 0.310 0.794 7 7137 7145.0 0.009 0.803 8 5264 5139.1 3.037 3.840 9 3694 3699.9 0.009 3.849 10 2688 2666.3 0.177 4.026 11 1970 1923.3 1.133 5.158 12 1375 1388.7 0.136 5.294 13 988 1003.7 0.246 5.540 14 698 726.1 1.091 6.631 15 513 525.8 0.313 6.944 16 365 381.2 0.684 7.628 17 269 276.5 0.206 7.834 18 210 200.8 0.419 8.253 19 139 146.0 0.334 8.587 20 90 106.2 2.475 11.062 21 297 287.1 0.340 11.403 Chisq= 11.40 for 20 degrees of freedom, p= 0.06489 SUMMARY of craptest p-value for no. of wins: 0.065953 p-value for throws/game: 0.064892 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-26_07:31 No. of wins: Observed Expected 98703 98585.9 z-score= 0.524, pvalue=0.69983 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67094 66666.7 2.739 2.739 2 37289 37654.3 3.544 6.284 3 27048 26954.7 0.323 6.606 4 19134 19313.5 1.668 8.274 5 13964 13851.4 0.915 9.189 6 9873 9943.5 0.500 9.689 7 7154 7145.0 0.011 9.701 8 5121 5139.1 0.064 9.764 9 3688 3699.9 0.038 9.802 10 2676 2666.3 0.035 9.837 11 1969 1923.3 1.084 10.922 12 1375 1388.7 0.136 11.058 13 1006 1003.7 0.005 11.063 14 732 726.1 0.047 11.110 15 496 525.8 1.693 12.803 16 372 381.2 0.220 13.023 17 295 276.5 1.232 14.255 18 190 200.8 0.584 14.839 19 152 146.0 0.248 15.087 20 85 106.2 4.237 19.325 21 287 287.1 0.000 19.325 Chisq= 19.32 for 20 degrees of freedom, p= 0.49918 SUMMARY of craptest p-value for no. of wins: 0.699835 p-value for throws/game: 0.499184 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0014,0.0127,0.0142,0.0169,0.0236,0.0236,0.0273,0.0287,0.0348, 0.0385,0.0395,0.0403,0.0450,0.0474,0.0598,0.0606,0.0622,0.0638,0.0649, 0.0660,0.0676,0.0684,0.0689,0.0708,0.0740,0.0776,0.0790,0.0863,0.0876, 0.0951,0.0975,0.1003,0.1013,0.1181,0.1182,0.1206,0.1214,0.1225,0.1354, 0.1405,0.1418,0.1424,0.1559,0.1561,0.1573,0.1637,0.1644,0.1677,0.1783, 0.1792,0.1805,0.1927,0.2007,0.2046,0.2047,0.2106,0.2119,0.2254,0.2256, 0.2263,0.2276,0.2277,0.2286,0.2362,0.2409,0.2414,0.2429,0.2432,0.2466, 0.2479,0.2503,0.2559,0.2605,0.2607,0.2607,0.2615,0.2648,0.2677,0.2741, 0.2767,0.2873,0.2883,0.2952,0.3021,0.3026,0.3042,0.3050,0.3104,0.3129, 0.3132,0.3179,0.3184,0.3203,0.3235,0.3240,0.3245,0.3294,0.3299,0.3366, 0.3416,0.3441,0.3492,0.3513,0.3514,0.3531,0.3595,0.3608,0.3671,0.3740, 0.3746,0.3872,0.3901,0.3927,0.3930,0.3958,0.3962,0.3966,0.3979,0.4006, 0.4063,0.4132,0.4146,0.4160,0.4269,0.4338,0.4357,0.4393,0.4430,0.4469, 0.4470,0.4636,0.4685,0.4742,0.4765,0.4793,0.4825,0.4855,0.4862,0.4866, 0.4921,0.4928,0.4968,0.4992,0.5134,0.5228,0.5325,0.5421,0.5499,0.5503, 0.5517,0.5523,0.5534,0.5617,0.5617,0.5620,0.5650,0.5654,0.5748,0.5766, 0.5777,0.5786,0.5789,0.5848,0.5858,0.5947,0.6013,0.6058,0.6162,0.6177, 0.6254,0.6285,0.6332,0.6392,0.6411,0.6425,0.6440,0.6532,0.6558,0.6612, 0.6662,0.6673,0.6742,0.6757,0.6904,0.6923,0.6923,0.6933,0.6969,0.6989, 0.6998,0.7091,0.7102,0.7139,0.7154,0.7196,0.7216,0.7252,0.7288,0.7348, 0.7415,0.7415,0.7423,0.7425,0.7441,0.7540,0.7566,0.7643,0.7646,0.7666, 0.7694,0.7727,0.7843,0.7851,0.7937,0.7944,0.7993,0.8073,0.8113,0.8148, 0.8156,0.8177,0.8214,0.8265,0.8276,0.8282,0.8302,0.8366,0.8476,0.8499, 0.8509,0.8531,0.8607,0.8637,0.8811,0.8823,0.8824,0.8854,0.8955,0.8963, 0.8966,0.9035,0.9040,0.9068,0.9070,0.9086,0.9110,0.9145,0.9146,0.9160, 0.9193,0.9210,0.9315,0.9317,0.9380,0.9455,0.9463,0.9550,0.9569,0.9668, 0.9680,0.9686,0.9718,0.9720,0.9741,0.9760,0.9916,0.9924,0.9941, Overall p-value after applying KStest on 269 p-values = 0.770079 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.