RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-04-26_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 31.1901 0.981065 2 to 25 15.46 31.8528 0.984306 3 to 26 15.72 14.5945 0.375340 4 to 27 15.57 12.3711 0.222838 5 to 28 15.74 18.1591 0.621129 6 to 29 15.94 11.5595 0.173952 7 to 30 16.17 16.7141 0.526106 8 to 31 15.84 19.5857 0.704036 9 to 32 15.76 15.2439 0.422080 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.483935 Tough bday spacings test for dh-ranFile-2017-04-26_10:31: 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 10 33 62 82 103 80 58 32 26 8 6 (O-E)^2/E 0.1 0.4 1.7 2.5 0.3 0.0 0.7 0.2 8.3 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 15.365, p= 0.881 RESULTS OF GCD FOR dh-ranFile-2017-04-26_10:31 Euclid's algorithm: p-value, steps to gcd: 0.095222 p-value, dist. of gcd's: 0.262745 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-04-26_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.025 0.520 0.212 0.380 0.644 0.524 0.342 0.961 Bits 8 to 15---> 0.634 0.039 0.244 0.174 0.758 0.093 0.520 0.678 Bits 16 to 23---> 0.518 0.218 0.007 0.203 0.937 0.010 0.810 0.965 Bits 24 to 31---> 0.666 0.754 0.772 0.053 0.674 0.289 0.212 0.855 KS test for the above 32 p values: 0.559 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-04-26_10:31, p-values for 5 runs: 0.6329, 0.2402, 0.5542, 0.9086, 0.4530 Rank test for binary matrices (31x31) for dh-ranFile-2017-04-26_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5131 5134.0 0.002 0.003 r= 30 22975 23103.0 0.710 0.712 r= 31 11683 11551.5 1.496 2.209 chi-square = 2.209 with df = 3; p-value = 0.470 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-04-26_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5125 5134.0 0.016 0.028 r= 31 23135 23103.0 0.044 0.072 r= 32 11527 11551.5 0.052 0.124 chi-square = 0.124 with df = 3; p-value = 0.011 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-04-26_10:31 b-rank test for bits 1 to 8, p=0.68163 b-rank test for bits 2 to 9, p=0.68911 b-rank test for bits 3 to 10, p=0.95162 b-rank test for bits 4 to 11, p=0.99573 b-rank test for bits 5 to 12, p=0.20365 b-rank test for bits 6 to 13, p=0.46677 b-rank test for bits 7 to 14, p=0.87795 b-rank test for bits 8 to 15, p=0.73810 b-rank test for bits 9 to 16, p=0.38284 b-rank test for bits 10 to 17, p=0.83700 b-rank test for bits 11 to 18, p=0.84800 b-rank test for bits 12 to 19, p=0.06212 b-rank test for bits 13 to 20, p=0.28991 b-rank test for bits 14 to 21, p=0.69029 b-rank test for bits 15 to 22, p=0.21040 b-rank test for bits 16 to 23, p=0.92993 b-rank test for bits 17 to 24, p=0.81734 b-rank test for bits 18 to 25, p=0.67998 b-rank test for bits 19 to 26, p=0.65113 b-rank test for bits 20 to 27, p=0.06513 b-rank test for bits 21 to 28, p=0.28363 b-rank test for bits 22 to 29, p=0.15782 b-rank test for bits 23 to 30, p=0.17274 b-rank test for bits 24 to 31, p=0.20920 b-rank test for bits 25 to 32, p=0.34562 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 = 0.717950 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-04-26_10:31 (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 141887 -0.05 0.479196 2 141481 -1.00 0.158469 3 142270 0.84 0.800298 4 142460 1.29 0.900885 5 142504 1.39 0.917647 6 141508 -0.94 0.174203 7 141991 0.19 0.575666 8 141870 -0.09 0.463392 9 142075 0.39 0.650651 10 142449 1.26 0.896330 11 141451 -1.07 0.142115 12 142300 0.91 0.819321 13 141608 -0.70 0.240703 14 142530 1.45 0.926494 15 141186 -1.69 0.045512 16 142748 1.96 0.974973 17 141126 -1.83 0.033609 18 141160 -1.75 0.039993 19 142644 1.72 0.956966 20 141991 0.19 0.575666 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-04-26_10:31 Bits used No. missing words z-score p-value 23 to 32 141766 -0.4942 0.310568 22 to 31 141872 -0.1287 0.448788 21 to 30 141728 -0.6253 0.265895 20 to 29 141949 0.1368 0.554403 19 to 28 141725 -0.6356 0.262512 18 to 27 141655 -0.8770 0.190243 17 to 26 142085 0.6058 0.727663 16 to 25 142093 0.6333 0.736746 15 to 24 142351 1.5230 0.936121 14 to 23 142105 0.6747 0.750075 13 to 22 141578 -1.1425 0.126620 12 to 21 142044 0.4644 0.678812 11 to 20 141962 0.1816 0.572060 10 to 19 141242 -2.3011 0.010692 9 to 18 141947 0.1299 0.551676 8 to 17 141892 -0.0598 0.476174 7 to 16 142070 0.5540 0.710222 6 to 15 142090 0.6230 0.733358 5 to 14 142375 1.6058 0.945837 4 to 13 141876 -0.1149 0.454250 3 to 12 141400 -1.7563 0.039518 2 to 11 142151 0.8333 0.797675 1 to 10 141768 -0.4873 0.313007 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-04-26_10:31 Bits used No. missing words z-score p-value 28 to 32 142340 1.4599 0.927841 27 to 31 141639 -0.9164 0.179736 26 to 30 141736 -0.5876 0.278414 25 to 29 142041 0.4463 0.672324 24 to 28 142210 1.0192 0.845951 23 to 27 142085 0.5955 0.724243 22 to 26 141515 -1.3367 0.090658 21 to 25 142230 1.0870 0.861485 20 to 24 141678 -0.7842 0.216470 19 to 23 141799 -0.3740 0.354202 18 to 22 141516 -1.3333 0.091213 17 to 21 142000 0.3074 0.620714 16 to 20 141855 -0.1842 0.426940 15 to 19 142232 1.0938 0.862978 14 to 18 141989 0.2701 0.606446 13 to 17 142338 1.4531 0.926905 12 to 16 142048 0.4701 0.680847 11 to 15 142017 0.3650 0.642438 10 to 14 141869 -0.1367 0.445629 9 to 13 141697 -0.7198 0.235836 8 to 12 141768 -0.4791 0.315939 7 to 11 141660 -0.8452 0.199003 6 to 10 141821 -0.2994 0.382308 5 to 9 141755 -0.5232 0.300434 4 to 8 142199 0.9819 0.836933 3 to 7 141702 -0.7028 0.241086 2 to 6 141703 -0.6994 0.242144 1 to 5 141430 -1.6248 0.052098 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-04-26_10:31 Bits used No. missing words z-score p-value 31 to 32 142109 0.5890 0.722068 30 to 31 141864 -0.1337 0.446813 29 to 30 142115 0.6067 0.727974 28 to 29 141745 -0.4847 0.313927 27 to 28 141812 -0.2871 0.387014 26 to 27 141798 -0.3284 0.371302 25 to 26 142216 0.9046 0.817170 24 to 25 141970 0.1790 0.571018 23 to 24 141948 0.1141 0.545409 22 to 23 141744 -0.4877 0.312882 21 to 22 141701 -0.6145 0.269428 20 to 21 141608 -0.8889 0.187034 19 to 20 141750 -0.4700 0.319178 18 to 19 141595 -0.9272 0.176904 17 to 18 142076 0.4917 0.688517 16 to 17 141604 -0.9007 0.183880 15 to 16 141580 -0.9715 0.165656 14 to 15 142124 0.6332 0.736713 13 to 14 141673 -0.6971 0.242858 12 to 13 142253 1.0138 0.844655 11 to 12 141830 -0.2340 0.407488 10 to 11 141515 -1.1632 0.122371 9 to 10 141615 -0.8682 0.192634 8 to 9 141161 -2.2075 0.013641 7 to 8 141431 -1.4110 0.079122 6 to 7 142361 1.3324 0.908629 5 to 6 141314 -1.7561 0.039533 4 to 5 141293 -1.8181 0.034526 3 to 4 141642 -0.7886 0.215178 2 to 3 142330 1.2409 0.892681 1 to 2 141633 -0.8151 0.207498 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-04-26_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2504.68 0.066 0.526409 Test results for specific bytes for dh-ranFile-2017-04-26_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2557.66 0.815 0.792579 2 to 9 2528.44 0.402 0.656215 3 to 10 2389.14 -1.568 0.058461 4 to 11 2599.77 1.411 0.920871 5 to 12 2558.77 0.831 0.797047 6 to 13 2403.13 -1.370 0.085362 7 to 14 2541.10 0.581 0.719468 8 to 15 2429.54 -0.996 0.159513 9 to 16 2541.18 0.582 0.719841 10 to 17 2500.16 0.002 0.500887 11 to 18 2508.14 0.115 0.545818 12 to 19 2563.57 0.899 0.815666 13 to 20 2463.57 -0.515 0.303187 14 to 21 2493.85 -0.087 0.465328 15 to 22 2492.45 -0.107 0.457463 16 to 23 2560.84 0.860 0.805211 17 to 24 2559.42 0.840 0.799623 18 to 25 2514.97 0.212 0.583856 19 to 26 2537.82 0.535 0.703639 20 to 27 2490.94 -0.128 0.449003 21 to 28 2530.32 0.429 0.665970 22 to 29 2502.05 0.029 0.511545 23 to 30 2449.08 -0.720 0.235710 24 to 31 2460.50 -0.559 0.288233 25 to 32 2395.33 -1.480 0.069410 CDPARK for dh-ranFile-2017-04-26_10:31: 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 3553 1.3699 0.914635 3514 -0.4110 0.340551 3481 -1.9178 0.027568 3526 0.1370 0.554479 3558 1.5982 0.944998 3514 -0.4110 0.340551 3549 1.1872 0.882429 3508 -0.6849 0.246694 3537 0.6393 0.738676 3541 0.8219 0.794438 Square side=100, avg. no. parked=3528.10 sample std.=22.85 p-value of the KSTEST for those 10 p-values: 0.571252 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-04-26_10:31 0.4387,0.1396,0.2290,0.8397,0.4481,0.8849,0.8377,0.6680,0.9703,0.8671, The KS test for those 10 p-values: 0.206596 The 3DSPHERES test for dh-ranFile-2017-04-26_10:31 sample no r^3 equiv. uni. 1 105.826 0.970623 2 28.052 0.607441 3 21.765 0.515920 4 4.227 0.131427 5 2.872 0.091284 6 34.438 0.682706 7 38.641 0.724184 8 18.509 0.460413 9 54.557 0.837741 10 93.626 0.955881 11 34.718 0.685657 12 77.128 0.923537 13 3.527 0.110920 14 77.398 0.924220 15 30.303 0.635819 16 155.836 0.994453 17 42.382 0.756520 18 59.101 0.860550 19 28.260 0.610152 20 26.101 0.581060 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.020516 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-04-26_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -0.1 -0.4 -0.3 0.1 0.2 -0.5 -0.7 -0.5 -0.2 0.6 0.0 -0.5 1.5 1.2 -0.1 -0.3 -1.5 0.9 1.4 -0.6 -1.5 0.1 0.6 -0.1 -1.8 2.1 -1.8 0.3 0.7 -1.1 -1.7 -0.2 0.3 0.6 -0.2 -0.1 -1.2 -0.7 0.1 2.0 -1.1 Chi-square with 42 degrees of freedom:37.453449 z-score=-0.496069, p-value=0.329355 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-04-26_10:31 Test no p-value 1 0.659910 2 0.021411 3 0.634672 4 0.245257 5 0.007385 6 0.328363 7 0.934525 8 0.348185 9 0.941710 10 0.530177 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.554782 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-04-26_10:31: (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 66592 0.08 66616 0.04 3 25000.00 25141 0.80 25062 0.15 4 6666.67 6627 0.24 6634 0.16 5 1388.89 1380 0.06 1416 0.53 6 238.10 227 0.52 232 0.16 7 34.72 26 2.19 34 0.01 8 4.96 6 0.22 5 0.00 p=0.33645 p=0.01647 Number of rngs required: 687792, p-value: 0.240 RESULTS OF CRAPS TEST for dh-ranFile-2017-04-26_10:31 No. of wins: Observed Expected 98532 98585.9 z-score=-0.241, pvalue=0.40482 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66456 66666.7 0.666 0.666 2 37512 37654.3 0.538 1.204 3 27087 26954.7 0.649 1.853 4 19395 19313.5 0.344 2.197 5 13863 13851.4 0.010 2.207 6 10024 9943.5 0.651 2.858 7 7316 7145.0 4.091 6.949 8 5104 5139.1 0.239 7.188 9 3630 3699.9 1.319 8.507 10 2714 2666.3 0.853 9.361 11 2034 1923.3 6.368 15.729 12 1380 1388.7 0.055 15.784 13 968 1003.7 1.271 17.055 14 698 726.1 1.091 18.145 15 511 525.8 0.419 18.564 16 366 381.2 0.602 19.166 17 255 276.5 1.678 20.844 18 187 200.8 0.952 21.796 19 145 146.0 0.007 21.803 20 97 106.2 0.800 22.603 21 258 287.1 2.952 25.555 Chisq= 25.55 for 20 degrees of freedom, p= 0.81897 SUMMARY of craptest p-value for no. of wins: 0.404821 p-value for throws/game: 0.818975 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-04-26_10:31 No. of wins: Observed Expected 98552 98585.9 z-score=-0.151, pvalue=0.43982 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66651 66666.7 0.004 0.004 2 37907 37654.3 1.696 1.699 3 27036 26954.7 0.245 1.944 4 19195 19313.5 0.727 2.671 5 13755 13851.4 0.671 3.342 6 10001 9943.5 0.332 3.674 7 6990 7145.0 3.364 7.038 8 5162 5139.1 0.102 7.140 9 3644 3699.9 0.844 7.983 10 2680 2666.3 0.070 8.054 11 1873 1923.3 1.317 9.371 12 1402 1388.7 0.127 9.498 13 1035 1003.7 0.975 10.473 14 705 726.1 0.615 11.088 15 537 525.8 0.237 11.325 16 361 381.2 1.065 12.390 17 310 276.5 4.049 16.439 18 213 200.8 0.737 17.177 19 149 146.0 0.062 17.239 20 103 106.2 0.097 17.336 21 291 287.1 0.053 17.389 Chisq= 17.39 for 20 degrees of freedom, p= 0.37240 SUMMARY of craptest p-value for no. of wins: 0.439816 p-value for throws/game: 0.372399 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0074,0.0075,0.0097,0.0107,0.0112,0.0136,0.0165,0.0205,0.0214,0.0250, 0.0276,0.0336,0.0345,0.0386,0.0395,0.0395,0.0400,0.0455,0.0521,0.0529, 0.0585,0.0621,0.0651,0.0694,0.0791,0.0854,0.0907,0.0912,0.0913,0.0932, 0.0952,0.1109,0.1224,0.1266,0.1314,0.1396,0.1421,0.1578,0.1585,0.1595, 0.1657,0.1727,0.1740,0.1742,0.1745,0.1769,0.1797,0.1839,0.1870,0.1902, 0.1926,0.1990,0.2033,0.2037,0.2066,0.2075,0.2092,0.2104,0.2122,0.2125, 0.2152,0.2165,0.2183,0.2228,0.2290,0.2357,0.2358,0.2402,0.2403,0.2407, 0.2411,0.2421,0.2429,0.2443,0.2453,0.2467,0.2625,0.2627,0.2659,0.2694, 0.2784,0.2836,0.2882,0.2887,0.2899,0.3004,0.3032,0.3106,0.3129,0.3130, 0.3139,0.3159,0.3192,0.3284,0.3294,0.3364,0.3406,0.3406,0.3419,0.3456, 0.3482,0.3542,0.3713,0.3724,0.3753,0.3804,0.3823,0.3828,0.3870,0.4048, 0.4075,0.4221,0.4269,0.4387,0.4398,0.4456,0.4468,0.4481,0.4488,0.4490, 0.4530,0.4542,0.4575,0.4604,0.4634,0.4653,0.4668,0.4698,0.4762,0.4792, 0.4839,0.5009,0.5115,0.5159,0.5176,0.5195,0.5198,0.5244,0.5261,0.5264, 0.5302,0.5454,0.5458,0.5517,0.5542,0.5544,0.5545,0.5548,0.5591,0.5710, 0.5713,0.5721,0.5757,0.5757,0.5811,0.5839,0.6064,0.6074,0.6102,0.6207, 0.6211,0.6329,0.6341,0.6347,0.6358,0.6424,0.6442,0.6507,0.6511,0.6562, 0.6599,0.6660,0.6664,0.6680,0.6723,0.6735,0.6784,0.6788,0.6800,0.6808, 0.6816,0.6827,0.6857,0.6885,0.6891,0.6903,0.7036,0.7040,0.7102,0.7180, 0.7195,0.7198,0.7221,0.7242,0.7242,0.7277,0.7280,0.7334,0.7367,0.7367, 0.7381,0.7387,0.7501,0.7537,0.7565,0.7577,0.7716,0.7926,0.7944,0.7970, 0.7977,0.7996,0.8003,0.8052,0.8096,0.8157,0.8172,0.8173,0.8190,0.8193, 0.8369,0.8370,0.8377,0.8377,0.8397,0.8447,0.8460,0.8480,0.8548,0.8605, 0.8615,0.8630,0.8671,0.8780,0.8807,0.8824,0.8849,0.8927,0.8963,0.9009, 0.9086,0.9086,0.9146,0.9176,0.9209,0.9235,0.9242,0.9265,0.9269,0.9278, 0.9299,0.9345,0.9361,0.9367,0.9417,0.9450,0.9458,0.9516,0.9559,0.9570, 0.9608,0.9647,0.9703,0.9706,0.9750,0.9811,0.9843,0.9945,0.9957, Overall p-value after applying KStest on 269 p-values = 0.856725 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.