RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-04-29_04:31 (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 12.9682 0.261690 2 to 25 15.67 16.1126 0.484135 3 to 26 15.60 18.1820 0.622553 4 to 27 15.69 26.8855 0.940231 5 to 28 15.58 22.4548 0.832144 6 to 29 15.72 14.7462 0.386240 7 to 30 15.77 19.6487 0.707412 8 to 31 15.51 14.4978 0.368393 9 to 32 15.78 21.1686 0.781159 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.491060 Tough bday spacings test for dh-ranFile-2017-04-29_04:31: 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 17 33 75 99 91 81 50 34 11 5 4 (O-E)^2/E 6.7 0.4 0.0 0.0 0.5 0.1 0.1 0.6 1.0 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.791, p= 0.541 RESULTS OF GCD FOR dh-ranFile-2017-04-29_04:31 Euclid's algorithm: p-value, steps to gcd: 0.382423 p-value, dist. of gcd's: 0.662059 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-04-29_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.458 0.958 0.582 0.846 0.341 0.760 0.002 0.271 Bits 8 to 15---> 0.515 0.023 0.002 0.251 0.563 0.914 0.920 0.274 Bits 16 to 23---> 0.602 0.484 0.637 0.611 0.106 0.196 0.403 0.437 Bits 24 to 31---> 0.866 0.083 0.767 0.644 0.790 0.664 0.150 0.242 KS test for the above 32 p values: 0.296 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-04-29_04:31, p-values for 5 runs: 0.8684, 0.5686, 0.2619, 0.9465, 0.4755 Rank test for binary matrices (31x31) for dh-ranFile-2017-04-29_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5198 5134.0 0.798 1.146 r= 30 23097 23103.0 0.002 1.148 r= 31 11485 11551.5 0.383 1.531 chi-square = 1.531 with df = 3; p-value = 0.325 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-04-29_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5074 5134.0 0.701 0.702 r= 31 23107 23103.0 0.001 0.703 r= 32 11608 11551.5 0.276 0.979 chi-square = 0.979 with df = 3; p-value = 0.194 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-04-29_04:31 b-rank test for bits 1 to 8, p=0.39067 b-rank test for bits 2 to 9, p=0.59208 b-rank test for bits 3 to 10, p=0.90686 b-rank test for bits 4 to 11, p=0.43735 b-rank test for bits 5 to 12, p=0.03279 b-rank test for bits 6 to 13, p=0.35510 b-rank test for bits 7 to 14, p=0.19955 b-rank test for bits 8 to 15, p=0.54284 b-rank test for bits 9 to 16, p=0.70935 b-rank test for bits 10 to 17, p=0.68681 b-rank test for bits 11 to 18, p=0.92390 b-rank test for bits 12 to 19, p=0.96922 b-rank test for bits 13 to 20, p=0.56152 b-rank test for bits 14 to 21, p=0.15051 b-rank test for bits 15 to 22, p=0.40443 b-rank test for bits 16 to 23, p=0.06324 b-rank test for bits 17 to 24, p=0.02306 b-rank test for bits 18 to 25, p=0.78020 b-rank test for bits 19 to 26, p=0.48830 b-rank test for bits 20 to 27, p=0.42050 b-rank test for bits 21 to 28, p=0.20962 b-rank test for bits 22 to 29, p=0.07728 b-rank test for bits 23 to 30, p=0.74176 b-rank test for bits 24 to 31, p=0.72763 b-rank test for bits 25 to 32, p=0.87366 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 = 0.986946 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-04-29_04:31 (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 141675 -0.55 0.292018 2 142189 0.65 0.743262 3 141057 -1.99 0.023217 4 141923 0.03 0.512740 5 141804 -0.25 0.402803 6 142112 0.47 0.682082 7 142325 0.97 0.834274 8 141784 -0.29 0.384827 9 141065 -1.97 0.024263 10 141628 -0.66 0.255490 11 142798 2.08 0.981068 12 142313 0.94 0.827199 13 141497 -0.96 0.167676 14 141891 -0.04 0.482920 15 141887 -0.05 0.479196 16 141240 -1.56 0.058926 17 141452 -1.07 0.142641 18 141470 -1.03 0.152335 19 142368 1.07 0.858063 20 142400 1.15 0.874190 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-04-29_04:31 Bits used No. missing words z-score p-value 23 to 32 141923 0.0471 0.518798 22 to 31 142299 1.3437 0.910476 21 to 30 141983 0.2540 0.600266 20 to 29 141944 0.1196 0.547581 19 to 28 142064 0.5333 0.703103 18 to 27 142064 0.5333 0.703103 17 to 26 141864 -0.1563 0.437894 16 to 25 142007 0.3368 0.631864 15 to 24 141839 -0.2425 0.404190 14 to 23 142163 0.8747 0.809138 13 to 22 142334 1.4644 0.928455 12 to 21 141925 0.0540 0.521546 11 to 20 141598 -1.0736 0.141512 10 to 19 142223 1.0816 0.860289 9 to 18 141583 -1.1253 0.130236 8 to 17 141947 0.1299 0.551676 7 to 16 141650 -0.8942 0.185596 6 to 15 141854 -0.1908 0.424344 5 to 14 142185 0.9506 0.829093 4 to 13 141953 0.1506 0.559849 3 to 12 141972 0.2161 0.585547 2 to 11 141886 -0.0804 0.467940 1 to 10 141717 -0.6632 0.253599 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-04-29_04:31 Bits used No. missing words z-score p-value 28 to 32 141795 -0.3876 0.349171 27 to 31 141895 -0.0486 0.480629 26 to 30 142096 0.6328 0.736561 25 to 29 141558 -1.1909 0.116837 24 to 28 141299 -2.0689 0.019277 23 to 27 141921 0.0396 0.515778 22 to 26 142299 1.3209 0.906735 21 to 25 142457 1.8565 0.968309 20 to 24 141421 -1.6554 0.048926 19 to 23 141470 -1.4893 0.068210 18 to 22 141775 -0.4554 0.324427 17 to 21 141663 -0.8350 0.201854 16 to 20 141854 -0.1876 0.425611 15 to 19 141642 -0.9062 0.182414 14 to 18 141547 -1.2282 0.109679 13 to 17 141657 -0.8554 0.196177 12 to 16 141508 -1.3604 0.086845 11 to 15 142077 0.5684 0.715109 10 to 14 142087 0.6023 0.726503 9 to 13 142117 0.7040 0.759273 8 to 12 142416 1.7175 0.957058 7 to 11 141826 -0.2825 0.388790 6 to 10 141759 -0.5096 0.305168 5 to 9 141989 0.2701 0.606446 4 to 8 142017 0.3650 0.642438 3 to 7 142156 0.8362 0.798470 2 to 6 142056 0.4972 0.690471 1 to 5 141390 -1.7604 0.039167 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-04-29_04:31 Bits used No. missing words z-score p-value 31 to 32 141869 -0.1190 0.452651 30 to 31 141249 -1.9479 0.025715 29 to 30 141770 -0.4110 0.340535 28 to 29 141477 -1.2753 0.101100 27 to 28 141943 0.0993 0.539559 26 to 27 141475 -1.2812 0.100060 25 to 26 141804 -0.3107 0.378011 24 to 25 142039 0.3825 0.648958 23 to 24 142030 0.3560 0.639064 22 to 23 142177 0.7896 0.785116 21 to 22 141618 -0.8594 0.195065 20 to 21 141729 -0.5319 0.297381 19 to 20 141781 -0.3786 0.352509 18 to 19 141579 -0.9744 0.164923 17 to 18 141598 -0.9184 0.179211 16 to 17 141664 -0.7237 0.234629 15 to 16 141544 -1.0777 0.140591 14 to 15 142156 0.7276 0.766583 13 to 14 141745 -0.4847 0.313927 12 to 13 141714 -0.5762 0.282242 11 to 12 142475 1.6686 0.952406 10 to 11 141653 -0.7561 0.224784 9 to 10 141763 -0.4317 0.332997 8 to 9 141926 0.0492 0.519610 7 to 8 142108 0.5860 0.721078 6 to 7 142253 1.0138 0.844655 5 to 6 142227 0.9371 0.825641 4 to 5 142382 1.3943 0.918388 3 to 4 142044 0.3973 0.654411 2 to 3 141928 0.0551 0.521960 1 to 2 142022 0.3324 0.630191 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-04-29_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2466.83 -0.469 0.319479 Test results for specific bytes for dh-ranFile-2017-04-29_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2471.87 -0.398 0.345369 2 to 9 2438.23 -0.874 0.191169 3 to 10 2571.98 1.018 0.845640 4 to 11 2593.52 1.323 0.907006 5 to 12 2645.30 2.055 0.980055 6 to 13 2551.17 0.724 0.765378 7 to 14 2553.61 0.758 0.775825 8 to 15 2439.15 -0.861 0.194755 9 to 16 2729.85 3.251 0.999424 10 to 17 2456.65 -0.613 0.269933 11 to 18 2449.50 -0.714 0.237572 12 to 19 2545.61 0.645 0.740521 13 to 20 2349.32 -2.131 0.016550 14 to 21 2424.63 -1.066 0.143221 15 to 22 2463.48 -0.516 0.302767 16 to 23 2548.66 0.688 0.754306 17 to 24 2427.55 -1.025 0.152793 18 to 25 2470.48 -0.418 0.338154 19 to 26 2467.28 -0.463 0.321767 20 to 27 2409.29 -1.283 0.099771 21 to 28 2462.32 -0.533 0.297059 22 to 29 2460.47 -0.559 0.288070 23 to 30 2482.75 -0.244 0.403632 24 to 31 2488.46 -0.163 0.435165 25 to 32 2600.02 1.414 0.921385 CDPARK for dh-ranFile-2017-04-29_04:31: 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 3519 -0.1826 0.427537 3517 -0.2740 0.392053 3528 0.2283 0.590298 3519 -0.1826 0.427537 3528 0.2283 0.590298 3516 -0.3196 0.374623 3560 1.6895 0.954438 3560 1.6895 0.954438 3514 -0.4110 0.340551 3527 0.1826 0.572463 Square side=100, avg. no. parked=3528.80 sample std.=16.33 p-value of the KSTEST for those 10 p-values: 0.255326 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-04-29_04:31 0.8699,0.9781,0.4802,0.4359,0.7244,0.0815,0.4518,0.9845,0.6549,0.3752, The KS test for those 10 p-values: 0.308356 The 3DSPHERES test for dh-ranFile-2017-04-29_04:31 sample no r^3 equiv. uni. 1 22.545 0.528340 2 0.789 0.025946 3 4.836 0.148869 4 23.585 0.544405 5 7.392 0.218386 6 1.073 0.035140 7 125.889 0.984949 8 47.640 0.795663 9 50.529 0.814427 10 69.010 0.899776 11 5.117 0.156819 12 29.916 0.631090 13 19.637 0.480340 14 4.102 0.127806 15 16.780 0.428416 16 25.063 0.566307 17 19.235 0.473329 18 61.978 0.873302 19 13.466 0.361647 20 101.964 0.966586 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.940000 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-04-29_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 -0.8 -1.0 -0.6 0.0 1.2 -0.4 0.5 0.2 -0.8 1.7 -0.9 0.7 0.7 0.5 0.5 0.7 -0.5 0.1 -0.7 -0.1 -1.4 0.3 -1.4 -0.5 0.4 0.1 -0.6 -0.4 -0.0 -0.7 0.2 -0.1 -1.2 0.8 0.5 -0.7 0.9 0.4 0.9 -1.0 1.8 Chi-square with 42 degrees of freedom:27.048017 z-score=-1.631395, p-value=0.035641 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-04-29_04:31 Test no p-value 1 0.329061 2 0.640701 3 0.066409 4 0.791857 5 0.002581 6 0.431981 7 0.610932 8 0.669867 9 0.056819 10 0.724496 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.321884 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-04-29_04:31: (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 66894 0.78 66756 0.12 3 25000.00 24795 1.68 24797 1.65 4 6666.67 6660 0.01 6696 0.13 5 1388.89 1388 0.00 1485 6.65 6 238.10 230 0.28 220 1.38 7 34.72 29 0.94 43 1.97 8 4.96 3 0.77 2 1.77 p=0.38472 p=0.96638 Number of rngs required: 687206, p-value: 0.081 RESULTS OF CRAPS TEST for dh-ranFile-2017-04-29_04:31 No. of wins: Observed Expected 98456 98585.9 z-score=-0.581, pvalue=0.28069 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66793 66666.7 0.239 0.239 2 37810 37654.3 0.644 0.883 3 27086 26954.7 0.639 1.522 4 19238 19313.5 0.295 1.817 5 13847 13851.4 0.001 1.819 6 9618 9943.5 10.658 12.477 7 7146 7145.0 0.000 12.477 8 5080 5139.1 0.679 13.156 9 3595 3699.9 2.972 16.128 10 2763 2666.3 3.507 19.635 11 1954 1923.3 0.489 20.124 12 1382 1388.7 0.033 20.157 13 992 1003.7 0.137 20.294 14 755 726.1 1.147 21.441 15 541 525.8 0.437 21.878 16 388 381.2 0.123 22.001 17 256 276.5 1.526 23.527 18 194 200.8 0.232 23.759 19 159 146.0 1.160 24.919 20 105 106.2 0.014 24.933 21 298 287.1 0.413 25.346 Chisq= 25.35 for 20 degrees of freedom, p= 0.81149 SUMMARY of craptest p-value for no. of wins: 0.280687 p-value for throws/game: 0.811486 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-04-29_04:31 No. of wins: Observed Expected 98747 98585.9 z-score= 0.721, pvalue=0.76446 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66701 66666.7 0.018 0.018 2 37745 37654.3 0.218 0.236 3 26917 26954.7 0.053 0.289 4 19299 19313.5 0.011 0.300 5 13898 13851.4 0.157 0.456 6 9857 9943.5 0.753 1.210 7 7059 7145.0 1.036 2.245 8 5084 5139.1 0.590 2.835 9 3739 3699.9 0.414 3.249 10 2651 2666.3 0.088 3.337 11 1937 1923.3 0.097 3.434 12 1425 1388.7 0.947 4.381 13 1034 1003.7 0.914 5.295 14 735 726.1 0.108 5.403 15 537 525.8 0.237 5.640 16 382 381.2 0.002 5.642 17 278 276.5 0.008 5.650 18 194 200.8 0.232 5.882 19 134 146.0 0.984 6.866 20 108 106.2 0.030 6.896 21 286 287.1 0.004 6.900 Chisq= 6.90 for 20 degrees of freedom, p= 0.00300 SUMMARY of craptest p-value for no. of wins: 0.764459 p-value for throws/game: 0.003000 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0017,0.0026,0.0030,0.0165,0.0193,0.0227,0.0231,0.0232,0.0243, 0.0257,0.0259,0.0328,0.0351,0.0356,0.0392,0.0489,0.0568,0.0589,0.0632, 0.0664,0.0682,0.0773,0.0814,0.0815,0.0833,0.0868,0.0998,0.1001,0.1011, 0.1060,0.1097,0.1168,0.1278,0.1302,0.1406,0.1415,0.1426,0.1432,0.1489, 0.1498,0.1505,0.1523,0.1528,0.1568,0.1649,0.1677,0.1792,0.1824,0.1856, 0.1912,0.1937,0.1948,0.1951,0.1961,0.1962,0.1996,0.2019,0.2096,0.2184, 0.2248,0.2346,0.2376,0.2420,0.2514,0.2536,0.2553,0.2555,0.2617,0.2619, 0.2699,0.2705,0.2739,0.2807,0.2822,0.2881,0.2920,0.2955,0.2971,0.2974, 0.3028,0.3052,0.3084,0.3139,0.3195,0.3218,0.3219,0.3244,0.3248,0.3291, 0.3330,0.3382,0.3405,0.3406,0.3406,0.3454,0.3492,0.3525,0.3551,0.3616, 0.3684,0.3746,0.3752,0.3780,0.3824,0.3847,0.3848,0.3862,0.3888,0.3907, 0.3921,0.4028,0.4032,0.4036,0.4042,0.4044,0.4205,0.4243,0.4256,0.4275, 0.4275,0.4284,0.4320,0.4352,0.4359,0.4371,0.4373,0.4379,0.4518,0.4527, 0.4576,0.4679,0.4733,0.4755,0.4792,0.4802,0.4803,0.4806,0.4829,0.4837, 0.4841,0.4883,0.4911,0.5127,0.5149,0.5158,0.5188,0.5196,0.5215,0.5220, 0.5283,0.5396,0.5410,0.5428,0.5444,0.5476,0.5517,0.5598,0.5615,0.5635, 0.5663,0.5686,0.5725,0.5825,0.5855,0.5903,0.5903,0.5921,0.6003,0.6025, 0.6064,0.6109,0.6112,0.6226,0.6302,0.6311,0.6319,0.6372,0.6391,0.6407, 0.6424,0.6443,0.6490,0.6544,0.6549,0.6621,0.6644,0.6699,0.6821,0.6868, 0.6905,0.7031,0.7031,0.7074,0.7094,0.7151,0.7211,0.7244,0.7245,0.7265, 0.7276,0.7366,0.7405,0.7418,0.7433,0.7543,0.7593,0.7604,0.7645,0.7654, 0.7666,0.7667,0.7758,0.7802,0.7812,0.7851,0.7900,0.7919,0.7957,0.7985, 0.8091,0.8115,0.8144,0.8256,0.8272,0.8291,0.8321,0.8343,0.8447,0.8456, 0.8457,0.8581,0.8603,0.8657,0.8684,0.8699,0.8733,0.8737,0.8742,0.8998, 0.9067,0.9069,0.9070,0.9105,0.9138,0.9184,0.9203,0.9214,0.9239,0.9285, 0.9400,0.9402,0.9465,0.9524,0.9544,0.9544,0.9571,0.9575,0.9664,0.9666, 0.9683,0.9692,0.9781,0.9801,0.9811,0.9845,0.9849,0.9869,0.9994, Overall p-value after applying KStest on 269 p-values = 0.819224 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.