RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-09_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 12.7111 0.244700 2 to 25 15.91 26.7260 0.937789 3 to 26 15.98 12.5373 0.233430 4 to 27 15.59 11.3637 0.162956 5 to 28 15.97 13.9201 0.327251 6 to 29 16.07 17.0931 0.551925 7 to 30 15.71 11.6085 0.176759 8 to 31 15.98 15.3814 0.431968 9 to 32 15.78 12.2580 0.215730 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.139424 Tough bday spacings test for dh-ranFile-2018-04-09_17:31: 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 12 47 61 92 110 81 47 32 8 6 4 (O-E)^2/E 0.9 2.9 2.1 0.3 1.6 0.1 0.5 0.2 3.2 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.766, p= 0.699 RESULTS OF GCD FOR dh-ranFile-2018-04-09_17:31 Euclid's algorithm: p-value, steps to gcd: 0.018673 p-value, dist. of gcd's: 0.332888 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-09_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.413 0.366 0.455 0.285 0.138 0.169 0.242 0.082 Bits 8 to 15---> 0.829 0.737 0.031 0.509 0.039 0.385 0.438 0.782 Bits 16 to 23---> 0.326 0.448 0.382 0.634 0.437 0.074 0.387 0.669 Bits 24 to 31---> 0.935 0.729 0.848 0.831 0.461 0.101 0.388 0.587 KS test for the above 32 p values: 0.714 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-09_17:31, p-values for 5 runs: 0.4792, 0.7624, 0.9514, 0.6903, 0.7671 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-09_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 231 211.4 1.814 1.814 r= 29 5096 5134.0 0.281 2.095 r= 30 23177 23103.0 0.237 2.332 r= 31 11496 11551.5 0.267 2.599 chi-square = 2.599 with df = 3; p-value = 0.542 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-09_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5163 5134.0 0.164 0.512 r= 31 23180 23103.0 0.256 0.768 r= 32 11437 11551.5 1.135 1.904 chi-square = 1.904 with df = 3; p-value = 0.407 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-09_17:31 b-rank test for bits 1 to 8, p=0.83926 b-rank test for bits 2 to 9, p=0.69388 b-rank test for bits 3 to 10, p=0.17716 b-rank test for bits 4 to 11, p=0.27048 b-rank test for bits 5 to 12, p=0.86580 b-rank test for bits 6 to 13, p=0.39204 b-rank test for bits 7 to 14, p=0.62901 b-rank test for bits 8 to 15, p=0.38756 b-rank test for bits 9 to 16, p=0.56651 b-rank test for bits 10 to 17, p=0.39759 b-rank test for bits 11 to 18, p=0.25977 b-rank test for bits 12 to 19, p=0.58462 b-rank test for bits 13 to 20, p=0.13765 b-rank test for bits 14 to 21, p=0.46331 b-rank test for bits 15 to 22, p=0.31738 b-rank test for bits 16 to 23, p=0.23172 b-rank test for bits 17 to 24, p=0.12768 b-rank test for bits 18 to 25, p=0.90750 b-rank test for bits 19 to 26, p=0.12134 b-rank test for bits 20 to 27, p=0.45489 b-rank test for bits 21 to 28, p=0.46157 b-rank test for bits 22 to 29, p=0.46157 b-rank test for bits 23 to 30, p=0.44278 b-rank test for bits 24 to 31, p=0.43613 b-rank test for bits 25 to 32, p=0.43305 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 = 0.134594 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-09_17:31 (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 141823 -0.20 0.420073 2 143032 2.62 0.995643 3 142165 0.60 0.724866 4 142422 1.20 0.884508 5 141449 -1.08 0.141067 6 141755 -0.36 0.359205 7 141729 -0.42 0.336756 8 142521 1.43 0.923517 9 142789 2.06 0.980075 10 142192 0.66 0.745516 11 141860 -0.12 0.454121 12 141843 -0.15 0.438420 13 141847 -0.15 0.442106 14 141435 -1.11 0.133877 15 142408 1.17 0.878014 16 141872 -0.09 0.465249 17 141414 -1.16 0.123572 18 142277 0.86 0.804841 19 141845 -0.15 0.440263 20 142174 0.62 0.731840 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-09_17:31 Bits used No. missing words z-score p-value 23 to 32 141659 -0.8632 0.194012 22 to 31 141628 -0.9701 0.165998 21 to 30 141508 -1.3839 0.083195 20 to 29 141971 0.2127 0.584202 19 to 28 141685 -0.7736 0.219598 18 to 27 141225 -2.3598 0.009143 17 to 26 141847 -0.2149 0.414911 16 to 25 142101 0.6609 0.745672 15 to 24 142223 1.0816 0.860289 14 to 23 141558 -1.2115 0.112855 13 to 22 141843 -0.2287 0.409542 12 to 21 142018 0.3747 0.646067 11 to 20 142293 1.3230 0.907082 10 to 19 142175 0.9161 0.820194 9 to 18 142354 1.5333 0.937405 8 to 17 142042 0.4575 0.676338 7 to 16 141957 0.1644 0.565284 6 to 15 141931 0.0747 0.529783 5 to 14 142045 0.4678 0.680046 4 to 13 142108 0.6851 0.753350 3 to 12 142022 0.3885 0.651183 2 to 11 141915 0.0196 0.507800 1 to 10 142161 0.8678 0.807256 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-09_17:31 Bits used No. missing words z-score p-value 28 to 32 141956 0.1582 0.562852 27 to 31 142359 1.5243 0.936284 26 to 30 142115 0.6972 0.757157 25 to 29 142110 0.6802 0.751823 24 to 28 142071 0.5480 0.708166 23 to 27 142034 0.4226 0.663710 22 to 26 142266 1.2091 0.886678 21 to 25 141658 -0.8520 0.197116 20 to 24 141574 -1.1367 0.127829 19 to 23 142121 0.7175 0.763475 18 to 22 141529 -1.2893 0.098655 17 to 21 141316 -2.0113 0.022148 16 to 20 142325 1.4091 0.920590 15 to 19 141644 -0.8994 0.184214 14 to 18 141750 -0.5401 0.294564 13 to 17 141844 -0.2215 0.412368 12 to 16 141859 -0.1706 0.432265 11 to 15 142053 0.4870 0.686877 10 to 14 142606 2.3616 0.990902 9 to 13 141936 0.0904 0.536018 8 to 12 141887 -0.0757 0.469831 7 to 11 142176 0.9040 0.816993 6 to 10 141532 -1.2791 0.100434 5 to 9 141675 -0.7943 0.213499 4 to 8 141712 -0.6689 0.251775 3 to 7 141855 -0.1842 0.426940 2 to 6 142346 1.4802 0.930595 1 to 5 141379 -1.7977 0.036110 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-09_17:31 Bits used No. missing words z-score p-value 31 to 32 142155 0.7247 0.765679 30 to 31 141534 -1.1072 0.134111 29 to 30 142152 0.7158 0.762955 28 to 29 141653 -0.7561 0.224784 27 to 28 141820 -0.2635 0.396079 26 to 27 141766 -0.4228 0.336220 25 to 26 142430 1.5359 0.937719 24 to 25 142465 1.6391 0.949408 23 to 24 142099 0.5595 0.712089 22 to 23 141550 -1.0600 0.144579 21 to 22 141840 -0.2045 0.418976 20 to 21 141537 -1.0983 0.136033 19 to 20 142412 1.4828 0.930937 18 to 19 142318 1.2055 0.885998 17 to 18 142356 1.3176 0.906183 16 to 17 142278 1.0875 0.861597 15 to 16 141671 -0.7030 0.241016 14 to 15 142001 0.2704 0.606579 13 to 14 142588 2.0020 0.977356 12 to 13 141763 -0.4317 0.332997 11 to 12 142138 0.6745 0.750017 10 to 11 141748 -0.4759 0.317073 9 to 10 141625 -0.8387 0.200810 8 to 9 141457 -1.3343 0.091052 7 to 8 141851 -0.1721 0.431693 6 to 7 141227 -2.0128 0.022069 5 to 6 142345 1.2852 0.900632 4 to 5 141574 -0.9892 0.161289 3 to 4 141547 -1.0688 0.142575 2 to 3 142129 0.6480 0.741506 1 to 2 142358 1.3235 0.907167 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-09_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2530.76 0.435 0.668235 Test results for specific bytes for dh-ranFile-2018-04-09_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2449.35 -0.716 0.236883 2 to 9 2501.73 0.024 0.509752 3 to 10 2628.97 1.824 0.965922 4 to 11 2435.10 -0.918 0.179364 5 to 12 2529.04 0.411 0.659343 6 to 13 2496.21 -0.054 0.478604 7 to 14 2587.86 1.242 0.892973 8 to 15 2551.74 0.732 0.767827 9 to 16 2513.74 0.194 0.577050 10 to 17 2421.76 -1.107 0.134249 11 to 18 2331.52 -2.383 0.008595 12 to 19 2539.10 0.553 0.709840 13 to 20 2498.81 -0.017 0.493267 14 to 21 2451.12 -0.691 0.244682 15 to 22 2471.43 -0.404 0.343070 16 to 23 2482.92 -0.241 0.404590 17 to 24 2560.31 0.853 0.803161 18 to 25 2454.91 -0.638 0.261823 19 to 26 2580.17 1.134 0.871555 20 to 27 2484.31 -0.222 0.412211 21 to 28 2532.83 0.464 0.678776 22 to 29 2630.11 1.840 0.967114 23 to 30 2497.85 -0.030 0.487875 24 to 31 2531.63 0.447 0.672684 25 to 32 2497.19 -0.040 0.484167 CDPARK for dh-ranFile-2018-04-09_17:31: 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 3497 -1.1872 0.117571 3480 -1.9635 0.024796 3537 0.6393 0.738676 3523 0.0000 0.500000 3551 1.2785 0.899470 3496 -1.2329 0.108811 3497 -1.1872 0.117571 3482 -1.8721 0.030593 3562 1.7808 0.962529 3537 0.6393 0.738676 Square side=100, avg. no. parked=3516.20 sample std.=28.01 p-value of the KSTEST for those 10 p-values: 0.146435 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-09_17:31 0.8409,0.1176,0.6617,0.8918,0.7295,0.2295,0.6545,0.8052,0.3150,0.7009, The KS test for those 10 p-values: 0.381614 The 3DSPHERES test for dh-ranFile-2018-04-09_17:31 sample no r^3 equiv. uni. 1 21.444 0.510710 2 22.969 0.534953 3 54.094 0.835219 4 36.573 0.704504 5 5.610 0.170562 6 1.071 0.035084 7 155.077 0.994311 8 42.901 0.760702 9 1.727 0.055932 10 19.327 0.474935 11 17.436 0.440764 12 5.249 0.160528 13 42.066 0.753946 14 54.168 0.835625 15 3.123 0.098857 16 3.420 0.107755 17 22.697 0.530731 18 3.349 0.105627 19 8.472 0.246027 20 22.564 0.528640 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.482257 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-09_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 -0.4 0.6 -0.7 0.3 0.6 0.5 1.0 -0.9 -0.6 1.1 0.3 0.6 0.9 -1.5 1.8 -1.8 0.3 -0.4 0.2 -1.0 0.6 -0.9 -0.6 1.7 -0.2 0.8 -0.1 0.0 0.2 -1.5 -2.4 0.5 -0.6 -1.0 -1.6 -1.7 -0.4 1.0 -0.6 1.0 0.8 Chi-square with 42 degrees of freedom:42.264991 z-score=0.028913, p-value=0.540477 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-09_17:31 Test no p-value 1 0.588923 2 0.159847 3 0.824688 4 0.011524 5 0.689426 6 0.038321 7 0.294960 8 0.255145 9 0.351107 10 0.723390 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.365855 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-09_17:31: (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 66550 0.20 66447 0.72 3 25000.00 25079 0.25 25254 2.58 4 6666.67 6670 0.00 6602 0.63 5 1388.89 1414 0.45 1407 0.24 6 238.10 249 0.50 245 0.20 7 34.72 31 0.40 37 0.15 8 4.96 6 0.22 7 0.84 p=0.08266 p=0.50109 Number of rngs required: 688300, p-value: 0.453 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-09_17:31 No. of wins: Observed Expected 98638 98585.9 z-score= 0.233, pvalue=0.59220 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66573 66666.7 0.132 0.132 2 37249 37654.3 4.363 4.495 3 26921 26954.7 0.042 4.537 4 19555 19313.5 3.021 7.558 5 13809 13851.4 0.130 7.687 6 10123 9943.5 3.239 10.926 7 7213 7145.0 0.647 11.573 8 5176 5139.1 0.265 11.838 9 3699 3699.9 0.000 11.838 10 2739 2666.3 1.982 13.821 11 1919 1923.3 0.010 13.831 12 1412 1388.7 0.390 14.220 13 985 1003.7 0.349 14.569 14 708 726.1 0.453 15.022 15 496 525.8 1.693 16.715 16 394 381.2 0.433 17.148 17 279 276.5 0.022 17.170 18 193 200.8 0.305 17.476 19 147 146.0 0.007 17.483 20 98 106.2 0.635 18.118 21 312 287.1 2.157 20.275 Chisq= 20.28 for 20 degrees of freedom, p= 0.55915 SUMMARY of craptest p-value for no. of wins: 0.592200 p-value for throws/game: 0.559152 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-09_17:31 No. of wins: Observed Expected 98242 98585.9 z-score=-1.538, pvalue=0.06203 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66909 66666.7 0.881 0.881 2 37418 37654.3 1.483 2.364 3 26783 26954.7 1.094 3.458 4 19472 19313.5 1.301 4.760 5 13670 13851.4 2.376 7.136 6 9871 9943.5 0.529 7.665 7 7237 7145.0 1.184 8.849 8 5138 5139.1 0.000 8.849 9 3739 3699.9 0.414 9.263 10 2652 2666.3 0.077 9.340 11 1938 1923.3 0.112 9.452 12 1419 1388.7 0.659 10.111 13 991 1003.7 0.161 10.272 14 734 726.1 0.085 10.357 15 546 525.8 0.773 11.130 16 388 381.2 0.123 11.253 17 292 276.5 0.864 12.118 18 218 200.8 1.468 13.586 19 144 146.0 0.027 13.613 20 121 106.2 2.058 15.671 21 320 287.1 3.767 19.437 Chisq= 19.44 for 20 degrees of freedom, p= 0.50643 SUMMARY of craptest p-value for no. of wins: 0.062032 p-value for throws/game: 0.506426 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0086,0.0091,0.0115,0.0187,0.0221,0.0221,0.0248,0.0306,0.0315,0.0351, 0.0361,0.0383,0.0390,0.0559,0.0620,0.0735,0.0816,0.0827,0.0832,0.0911, 0.0987,0.0989,0.1004,0.1008,0.1056,0.1078,0.1088,0.1129,0.1176,0.1176, 0.1176,0.1213,0.1236,0.1277,0.1278,0.1339,0.1341,0.1342,0.1346,0.1360, 0.1376,0.1384,0.1394,0.1411,0.1426,0.1446,0.1464,0.1598,0.1605,0.1613, 0.1630,0.1660,0.1686,0.1706,0.1768,0.1772,0.1794,0.1842,0.1940,0.1971, 0.2008,0.2135,0.2157,0.2196,0.2248,0.2295,0.2317,0.2334,0.2369,0.2410, 0.2417,0.2447,0.2447,0.2460,0.2518,0.2551,0.2598,0.2618,0.2705,0.2846, 0.2946,0.2950,0.3150,0.3171,0.3174,0.3263,0.3273,0.3329,0.3330,0.3362, 0.3368,0.3431,0.3511,0.3592,0.3658,0.3659,0.3816,0.3818,0.3851,0.3868, 0.3876,0.3882,0.3920,0.3961,0.3976,0.4046,0.4074,0.4095,0.4122,0.4124, 0.4127,0.4149,0.4190,0.4201,0.4269,0.4317,0.4320,0.4323,0.4331,0.4361, 0.4366,0.4379,0.4384,0.4403,0.4408,0.4421,0.4428,0.4481,0.4528,0.4541, 0.4549,0.4550,0.4607,0.4616,0.4616,0.4633,0.4652,0.4698,0.4749,0.4786, 0.4792,0.4823,0.4842,0.4879,0.4933,0.5000,0.5011,0.5064,0.5078,0.5088, 0.5098,0.5107,0.5286,0.5298,0.5307,0.5350,0.5360,0.5405,0.5423,0.5519, 0.5592,0.5629,0.5653,0.5665,0.5771,0.5842,0.5846,0.5868,0.5889,0.5922, 0.6066,0.6290,0.6340,0.6461,0.6512,0.6545,0.6593,0.6617,0.6637,0.6682, 0.6691,0.6727,0.6763,0.6788,0.6800,0.6869,0.6894,0.6903,0.6939,0.6990, 0.7009,0.7045,0.7082,0.7098,0.7121,0.7144,0.7234,0.7249,0.7289,0.7295, 0.7318,0.7374,0.7387,0.7387,0.7415,0.7455,0.7457,0.7500,0.7518,0.7533, 0.7539,0.7572,0.7607,0.7624,0.7630,0.7635,0.7657,0.7671,0.7678,0.7818, 0.8032,0.8048,0.8052,0.8073,0.8170,0.8202,0.8247,0.8290,0.8310,0.8352, 0.8356,0.8393,0.8409,0.8480,0.8603,0.8616,0.8658,0.8716,0.8780,0.8845, 0.8860,0.8867,0.8918,0.8930,0.8995,0.9006,0.9062,0.9071,0.9072,0.9075, 0.9206,0.9235,0.9306,0.9309,0.9354,0.9363,0.9374,0.9377,0.9378,0.9494, 0.9514,0.9625,0.9659,0.9671,0.9774,0.9801,0.9909,0.9943,0.9956, Overall p-value after applying KStest on 269 p-values = 0.531955 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.