RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-16_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.20 15.8533 0.465742 2 to 25 15.99 10.8133 0.133897 3 to 26 15.66 32.4852 0.986911 4 to 27 15.35 29.7116 0.971499 5 to 28 15.84 18.7320 0.655870 6 to 29 15.57 26.2127 0.929328 7 to 30 15.72 28.4580 0.960137 8 to 31 15.75 20.9594 0.771887 9 to 32 15.61 14.9210 0.398828 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.024684 Tough bday spacings test for dh-ranFile-2018-03-16_21:31: 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 31 73 86 89 101 50 31 19 9 4 (O-E)^2/E 0.5 0.9 0.0 1.4 0.8 6.7 0.1 0.1 1.1 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.361, p= 0.738 RESULTS OF GCD FOR dh-ranFile-2018-03-16_21:31 Euclid's algorithm: p-value, steps to gcd: 0.678828 p-value, dist. of gcd's: 0.651325 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-16_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.544 0.750 0.578 0.597 0.333 0.564 0.276 0.714 Bits 8 to 15---> 0.843 0.523 0.397 0.917 0.670 0.115 0.858 0.055 Bits 16 to 23---> 0.748 0.671 0.577 0.752 0.990 0.712 0.018 0.453 Bits 24 to 31---> 0.953 0.268 0.823 0.647 0.996 0.302 0.441 0.083 KS test for the above 32 p values: 0.728 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-16_21:31, p-values for 5 runs: 0.5398, 0.1018, 0.3254, 0.5240, 0.5105 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-16_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5207 5134.0 1.038 1.767 r= 30 23126 23103.0 0.023 1.790 r= 31 11468 11551.5 0.604 2.394 chi-square = 2.394 with df = 3; p-value = 0.505 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-16_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5180 5134.0 0.412 0.511 r= 31 23139 23103.0 0.056 0.567 r= 32 11465 11551.5 0.648 1.215 chi-square = 1.215 with df = 3; p-value = 0.251 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-16_21:31 b-rank test for bits 1 to 8, p=0.21997 b-rank test for bits 2 to 9, p=0.11315 b-rank test for bits 3 to 10, p=0.12332 b-rank test for bits 4 to 11, p=0.78253 b-rank test for bits 5 to 12, p=0.04087 b-rank test for bits 6 to 13, p=0.46532 b-rank test for bits 7 to 14, p=0.22667 b-rank test for bits 8 to 15, p=0.09591 b-rank test for bits 9 to 16, p=0.18207 b-rank test for bits 10 to 17, p=0.93064 b-rank test for bits 11 to 18, p=0.98249 b-rank test for bits 12 to 19, p=0.35371 b-rank test for bits 13 to 20, p=0.48803 b-rank test for bits 14 to 21, p=0.27101 b-rank test for bits 15 to 22, p=0.31572 b-rank test for bits 16 to 23, p=0.12117 b-rank test for bits 17 to 24, p=0.24042 b-rank test for bits 18 to 25, p=0.20070 b-rank test for bits 19 to 26, p=0.04827 b-rank test for bits 20 to 27, p=0.85699 b-rank test for bits 21 to 28, p=0.68908 b-rank test for bits 22 to 29, p=0.83736 b-rank test for bits 23 to 30, p=0.09187 b-rank test for bits 24 to 31, p=0.60529 b-rank test for bits 25 to 32, p=0.44866 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 = 0.061205 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-16_21:31 (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 142140 0.54 0.705039 2 141500 -0.96 0.169441 3 140992 -2.14 0.016045 4 141833 -0.18 0.429228 5 141394 -1.20 0.114287 6 141158 -1.76 0.039592 7 141280 -1.47 0.070727 8 142835 2.16 0.984721 9 141753 -0.37 0.357460 10 141494 -0.97 0.165924 11 141711 -0.46 0.321543 12 141920 0.02 0.509945 13 142071 0.38 0.647186 14 142408 1.17 0.878014 15 141918 0.02 0.508081 16 141445 -1.08 0.138987 17 141993 0.20 0.577496 18 142696 1.84 0.966970 19 141542 -0.86 0.195378 20 141433 -1.11 0.132871 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-16_21:31 Bits used No. missing words z-score p-value 23 to 32 142370 1.5885 0.943915 22 to 31 142095 0.6402 0.738992 21 to 30 141927 0.0609 0.524293 20 to 29 141414 -1.7080 0.043815 19 to 28 141901 -0.0287 0.488542 18 to 27 141938 0.0989 0.539376 17 to 26 142290 1.3127 0.905350 16 to 25 142245 1.1575 0.876462 15 to 24 142285 1.2954 0.902411 14 to 23 142285 1.2954 0.902411 13 to 22 141803 -0.3667 0.356938 12 to 21 141772 -0.4736 0.317910 11 to 20 141933 0.0816 0.532526 10 to 19 141877 -0.1115 0.455617 9 to 18 142367 1.5782 0.942737 8 to 17 141509 -1.3804 0.083724 7 to 16 141730 -0.6184 0.268163 6 to 15 142142 0.8023 0.788813 5 to 14 142479 1.9644 0.975257 4 to 13 142335 1.4678 0.928924 3 to 12 141825 -0.2908 0.385605 2 to 11 141342 -1.9563 0.025214 1 to 10 142009 0.3437 0.634460 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-16_21:31 Bits used No. missing words z-score p-value 28 to 32 141306 -2.0452 0.020418 27 to 31 141315 -2.0147 0.021969 26 to 30 141750 -0.5401 0.294564 25 to 29 141919 0.0328 0.513075 24 to 28 142109 0.6768 0.750749 23 to 27 141946 0.1243 0.549463 22 to 26 141942 0.1107 0.544091 21 to 25 142019 0.3718 0.644965 20 to 24 142231 1.0904 0.862233 19 to 23 142036 0.4294 0.666180 18 to 22 140993 -3.1062 0.000948 17 to 21 141986 0.2599 0.602529 16 to 20 142117 0.7040 0.759273 15 to 19 141499 -1.3909 0.082120 14 to 18 141788 -0.4113 0.340431 13 to 17 142484 1.9480 0.974295 12 to 16 142238 1.1141 0.867390 11 to 15 141683 -0.7672 0.221475 10 to 14 141478 -1.4621 0.071852 9 to 13 142137 0.7718 0.779873 8 to 12 141889 -0.0689 0.472529 7 to 11 141411 -1.6893 0.045585 6 to 10 141566 -1.1638 0.122246 5 to 9 141537 -1.2621 0.103450 4 to 8 141639 -0.9164 0.179736 3 to 7 141771 -0.4689 0.319565 2 to 6 141699 -0.7130 0.237928 1 to 5 142191 0.9548 0.830164 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-16_21:31 Bits used No. missing words z-score p-value 31 to 32 141752 -0.4641 0.321288 30 to 31 142257 1.0256 0.847454 29 to 30 141728 -0.5349 0.296361 28 to 29 142047 0.4061 0.657668 27 to 28 142205 0.8722 0.808446 26 to 27 141515 -1.1632 0.122371 25 to 26 141554 -1.0482 0.147280 24 to 25 141812 -0.2871 0.387014 23 to 24 141834 -0.2222 0.412074 22 to 23 141956 0.1377 0.554749 21 to 22 141944 0.1023 0.540729 20 to 21 142107 0.5831 0.720086 19 to 20 141966 0.1672 0.566381 18 to 19 142349 1.2970 0.902678 17 to 18 141801 -0.3196 0.374652 16 to 17 142201 0.8604 0.805211 15 to 16 141876 -0.0983 0.460840 14 to 15 141987 0.2291 0.590610 13 to 14 142015 0.3117 0.622370 12 to 13 142034 0.3678 0.643473 11 to 12 142437 1.5565 0.940211 10 to 11 141891 -0.0541 0.478439 9 to 10 141714 -0.5762 0.282242 8 to 9 141784 -0.3697 0.355801 7 to 8 141721 -0.5555 0.289261 6 to 7 141623 -0.8446 0.199158 5 to 6 141660 -0.7355 0.231022 4 to 5 142431 1.5388 0.938080 3 to 4 141629 -0.8269 0.204138 2 to 3 141632 -0.8181 0.206655 1 to 2 142023 0.3353 0.631304 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-16_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2467.25 -0.463 0.321602 Test results for specific bytes for dh-ranFile-2018-03-16_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2555.71 0.788 0.784622 2 to 9 2406.43 -1.323 0.092869 3 to 10 2384.35 -1.635 0.050973 4 to 11 2460.74 -0.555 0.289383 5 to 12 2528.07 0.397 0.654317 6 to 13 2413.65 -1.221 0.111016 7 to 14 2402.28 -1.382 0.083494 8 to 15 2423.34 -1.084 0.139160 9 to 16 2620.08 1.698 0.955266 10 to 17 2536.04 0.510 0.694872 11 to 18 2430.26 -0.986 0.161987 12 to 19 2487.30 -0.180 0.428724 13 to 20 2418.40 -1.154 0.124260 14 to 21 2391.99 -1.527 0.063321 15 to 22 2533.38 0.472 0.681549 16 to 23 2385.96 -1.613 0.053395 17 to 24 2451.42 -0.687 0.246024 18 to 25 2552.55 0.743 0.771322 19 to 26 2600.56 1.422 0.922514 20 to 27 2492.65 -0.104 0.458595 21 to 28 2573.79 1.043 0.851637 22 to 29 2491.96 -0.114 0.454737 23 to 30 2649.85 2.119 0.982965 24 to 31 2334.33 -2.343 0.009568 25 to 32 2361.64 -1.957 0.025187 CDPARK for dh-ranFile-2018-03-16_21:31: 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 3530 0.3196 0.625377 3516 -0.3196 0.374623 3560 1.6895 0.954438 3478 -2.0548 0.019949 3511 -0.5479 0.291865 3561 1.7352 0.958644 3523 0.0000 0.500000 3528 0.2283 0.590298 3542 0.8676 0.807188 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3525.70 sample std.=23.70 p-value of the KSTEST for those 10 p-values: 0.870369 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-16_21:31 0.8685,0.6040,0.1709,0.0810,0.7501,0.3664,0.5902,0.1310,0.9187,0.7766, The KS test for those 10 p-values: 0.939217 The 3DSPHERES test for dh-ranFile-2018-03-16_21:31 sample no r^3 equiv. uni. 1 19.304 0.474531 2 58.556 0.857991 3 18.610 0.462234 4 38.553 0.723378 5 22.500 0.527638 6 55.888 0.844782 7 91.728 0.953000 8 1.373 0.044750 9 14.738 0.388146 10 10.609 0.297858 11 29.978 0.631857 12 91.828 0.953156 13 0.952 0.031238 14 5.619 0.170810 15 5.883 0.178072 16 13.104 0.353901 17 29.259 0.622922 18 54.184 0.835710 19 47.064 0.791708 20 9.139 0.262603 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.989388 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-16_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.4 0.6 -1.0 0.0 -0.8 -1.2 0.1 -0.5 0.2 -0.6 1.3 1.0 -0.8 1.1 0.5 -0.3 0.9 0.2 0.1 -1.2 -0.8 -0.4 0.5 -1.0 0.0 0.4 0.1 -0.2 -1.4 -0.9 0.5 -0.4 -0.1 -0.5 0.7 1.1 -1.2 0.4 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:22.668143 z-score=-2.109279, p-value=0.006440 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-16_21:31 Test no p-value 1 0.783705 2 0.747835 3 0.179730 4 0.182246 5 0.268351 6 0.904319 7 0.802677 8 0.732795 9 0.119458 10 0.002879 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.433293 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-16_21:31: (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 66523 0.31 66738 0.08 3 25000.00 25129 0.67 24982 0.01 4 6666.67 6734 0.68 6646 0.06 5 1388.89 1327 2.76 1361 0.56 6 238.10 243 0.10 228 0.43 7 34.72 38 0.31 41 1.14 8 4.96 5 0.00 3 0.77 p=0.43347 p=0.19769 Number of rngs required: 687616, p-value: 0.181 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-16_21:31 No. of wins: Observed Expected 98427 98585.9 z-score=-0.711, pvalue=0.23869 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66907 66666.7 0.866 0.866 2 37673 37654.3 0.009 0.876 3 26675 26954.7 2.903 3.779 4 19419 19313.5 0.577 4.355 5 13813 13851.4 0.107 4.462 6 9897 9943.5 0.218 4.680 7 7212 7145.0 0.628 5.308 8 5253 5139.1 2.526 7.833 9 3650 3699.9 0.672 8.505 10 2656 2666.3 0.040 8.545 11 1917 1923.3 0.021 8.566 12 1277 1388.7 8.991 17.557 13 1044 1003.7 1.617 19.174 14 731 726.1 0.033 19.206 15 515 525.8 0.223 19.429 16 388 381.2 0.123 19.552 17 295 276.5 1.232 20.785 18 199 200.8 0.017 20.802 19 103 146.0 12.657 33.458 20 111 106.2 0.216 33.674 21 265 287.1 1.703 35.377 Chisq= 35.38 for 20 degrees of freedom, p= 0.98181 SUMMARY of craptest p-value for no. of wins: 0.238695 p-value for throws/game: 0.981813 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-16_21:31 No. of wins: Observed Expected 98768 98585.9 z-score= 0.815, pvalue=0.79236 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66882 66666.7 0.696 0.696 2 37479 37654.3 0.816 1.512 3 27030 26954.7 0.210 1.722 4 19285 19313.5 0.042 1.764 5 13928 13851.4 0.423 2.187 6 9858 9943.5 0.736 2.923 7 7168 7145.0 0.074 2.997 8 5167 5139.1 0.152 3.149 9 3591 3699.9 3.203 6.352 10 2705 2666.3 0.562 6.914 11 1898 1923.3 0.334 7.247 12 1395 1388.7 0.028 7.276 13 981 1003.7 0.514 7.790 14 748 726.1 0.658 8.448 15 510 525.8 0.477 8.925 16 384 381.2 0.021 8.946 17 278 276.5 0.008 8.954 18 199 200.8 0.017 8.970 19 132 146.0 1.340 10.310 20 90 106.2 2.475 12.786 21 292 287.1 0.083 12.869 Chisq= 12.87 for 20 degrees of freedom, p= 0.11705 SUMMARY of craptest p-value for no. of wins: 0.792362 p-value for throws/game: 0.117052 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0029,0.0064,0.0096,0.0160,0.0179,0.0199,0.0204,0.0220,0.0247, 0.0252,0.0252,0.0312,0.0396,0.0409,0.0438,0.0448,0.0456,0.0483,0.0510, 0.0534,0.0551,0.0612,0.0633,0.0707,0.0719,0.0810,0.0821,0.0830,0.0835, 0.0837,0.0919,0.0929,0.0959,0.1018,0.1035,0.1110,0.1132,0.1143,0.1153, 0.1171,0.1195,0.1212,0.1222,0.1224,0.1233,0.1243,0.1310,0.1329,0.1339, 0.1390,0.1392,0.1473,0.1620,0.1659,0.1694,0.1708,0.1709,0.1781,0.1797, 0.1797,0.1812,0.1821,0.1822,0.1954,0.1977,0.1992,0.2007,0.2041,0.2067, 0.2200,0.2215,0.2267,0.2310,0.2379,0.2387,0.2404,0.2460,0.2467,0.2507, 0.2626,0.2682,0.2683,0.2684,0.2710,0.2756,0.2822,0.2893,0.2894,0.2919, 0.2946,0.2964,0.2979,0.3021,0.3157,0.3179,0.3196,0.3213,0.3215,0.3216, 0.3254,0.3334,0.3404,0.3537,0.3539,0.3558,0.3569,0.3575,0.3664,0.3746, 0.3747,0.3856,0.3870,0.3881,0.3965,0.3988,0.4121,0.4287,0.4292,0.4333, 0.4335,0.4414,0.4487,0.4526,0.4547,0.4556,0.4586,0.4608,0.4622,0.4653, 0.4657,0.4725,0.4745,0.4784,0.4880,0.4885,0.5000,0.5052,0.5081,0.5099, 0.5105,0.5131,0.5228,0.5240,0.5243,0.5276,0.5325,0.5394,0.5398,0.5407, 0.5441,0.5443,0.5495,0.5547,0.5642,0.5664,0.5771,0.5775,0.5780,0.5902, 0.5903,0.5906,0.5967,0.6025,0.6040,0.6053,0.6224,0.6229,0.6254,0.6313, 0.6319,0.6345,0.6435,0.6450,0.6467,0.6472,0.6513,0.6543,0.6559,0.6577, 0.6662,0.6701,0.6712,0.6788,0.6815,0.6891,0.6949,0.7050,0.7125,0.7136, 0.7201,0.7234,0.7279,0.7328,0.7384,0.7390,0.7478,0.7485,0.7497,0.7501, 0.7507,0.7523,0.7593,0.7713,0.7719,0.7766,0.7799,0.7825,0.7837,0.7846, 0.7888,0.7917,0.7924,0.8027,0.8052,0.8072,0.8084,0.8229,0.8302,0.8357, 0.8374,0.8429,0.8448,0.8475,0.8516,0.8570,0.8580,0.8584,0.8622,0.8674, 0.8685,0.8704,0.8765,0.8780,0.9024,0.9024,0.9027,0.9043,0.9054,0.9169, 0.9187,0.9225,0.9289,0.9293,0.9306,0.9381,0.9392,0.9402,0.9427,0.9439, 0.9530,0.9532,0.9533,0.9544,0.9553,0.9586,0.9601,0.9670,0.9715,0.9743, 0.9753,0.9818,0.9825,0.9830,0.9847,0.9869,0.9894,0.9896,0.9957, Overall p-value after applying KStest on 269 p-values = 0.245990 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.