RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-31_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.06 13.7556 0.315680 2 to 25 15.91 17.7370 0.594387 3 to 26 15.62 21.2106 0.782991 4 to 27 15.92 21.1592 0.780750 5 to 28 15.86 15.9301 0.471204 6 to 29 15.80 14.6069 0.376229 7 to 30 15.55 19.7600 0.713309 8 to 31 15.71 19.2890 0.687805 9 to 32 15.89 24.4286 0.891752 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.230001 Tough bday spacings test for dh-ranFile-2015-10-31_15:31: 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 5 36 67 111 95 79 52 32 14 6 3 (O-E)^2/E 1.9 0.0 0.5 1.8 0.1 0.0 0.0 0.2 0.1 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.889, p= 0.102 RESULTS OF GCD FOR dh-ranFile-2015-10-31_15:31 Euclid's algorithm: p-value, steps to gcd: 0.769587 p-value, dist. of gcd's: 0.695323 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-31_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.187 0.517 0.261 0.196 0.386 0.011 0.634 0.107 Bits 8 to 15---> 0.475 0.512 0.810 0.307 0.851 0.998 0.777 0.310 Bits 16 to 23---> 0.424 0.438 0.476 0.030 0.776 0.831 0.545 0.201 Bits 24 to 31---> 0.334 0.816 0.232 0.248 0.939 0.428 0.953 0.983 KS test for the above 32 p values: 0.196 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-31_15:31, p-values for 5 runs: 0.5410, 0.1832, 0.2435, 0.2470, 0.5003 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-31_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5059 5134.0 1.096 1.825 r= 30 23144 23103.0 0.073 1.898 r= 31 11598 11551.5 0.187 2.085 chi-square = 2.085 with df = 3; p-value = 0.445 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-31_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5127 5134.0 0.010 0.070 r= 31 23126 23103.0 0.023 0.093 r= 32 11532 11551.5 0.033 0.126 chi-square = 0.126 with df = 3; p-value = 0.011 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-31_15:31 b-rank test for bits 1 to 8, p=0.08062 b-rank test for bits 2 to 9, p=0.55335 b-rank test for bits 3 to 10, p=0.63537 b-rank test for bits 4 to 11, p=0.79015 b-rank test for bits 5 to 12, p=0.94418 b-rank test for bits 6 to 13, p=0.74383 b-rank test for bits 7 to 14, p=0.19560 b-rank test for bits 8 to 15, p=0.39161 b-rank test for bits 9 to 16, p=0.74498 b-rank test for bits 10 to 17, p=0.00467 b-rank test for bits 11 to 18, p=0.75460 b-rank test for bits 12 to 19, p=0.10270 b-rank test for bits 13 to 20, p=0.96188 b-rank test for bits 14 to 21, p=0.33030 b-rank test for bits 15 to 22, p=0.59774 b-rank test for bits 16 to 23, p=0.08379 b-rank test for bits 17 to 24, p=0.46055 b-rank test for bits 18 to 25, p=0.87637 b-rank test for bits 19 to 26, p=0.98841 b-rank test for bits 20 to 27, p=0.59343 b-rank test for bits 21 to 28, p=0.58937 b-rank test for bits 22 to 29, p=0.39943 b-rank test for bits 23 to 30, p=0.66128 b-rank test for bits 24 to 31, p=0.36827 b-rank test for bits 25 to 32, p=0.45644 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 = 0.815584 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-31_15:31 (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 142534 1.46 0.927788 2 141711 -0.46 0.321543 3 142053 0.34 0.631443 4 142583 1.57 0.942256 5 141607 -0.71 0.239976 6 142079 0.40 0.654104 7 141682 -0.53 0.297659 8 141979 0.16 0.564654 9 142306 0.93 0.822985 10 141846 -0.15 0.441184 11 142065 0.36 0.641965 12 141768 -0.33 0.370621 13 141900 -0.02 0.491304 14 141043 -2.02 0.021478 15 141229 -1.59 0.055967 16 141727 -0.43 0.335052 17 141464 -1.04 0.149056 18 142387 1.12 0.867800 19 142165 0.60 0.724866 20 141978 0.16 0.563734 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-31_15:31 Bits used No. missing words z-score p-value 23 to 32 142377 1.6127 0.946590 22 to 31 142025 0.3989 0.655003 21 to 30 141809 -0.3460 0.364684 20 to 29 142004 0.3264 0.627957 19 to 28 141137 -2.6632 0.003870 18 to 27 142098 0.6506 0.742343 17 to 26 141733 -0.6080 0.271582 16 to 25 141540 -1.2736 0.101411 15 to 24 141384 -1.8115 0.035033 14 to 23 142024 0.3954 0.653731 13 to 22 142389 1.6540 0.950940 12 to 21 142164 0.8782 0.810075 11 to 20 141238 -2.3149 0.010308 10 to 19 142172 0.9058 0.817468 9 to 18 141768 -0.4873 0.313007 8 to 17 141757 -0.5253 0.299696 7 to 16 141699 -0.7253 0.234141 6 to 15 141593 -1.0908 0.137682 5 to 14 142294 1.3264 0.907654 4 to 13 141969 0.2058 0.581510 3 to 12 141679 -0.7942 0.213528 2 to 11 142395 1.6747 0.953006 1 to 10 142227 1.0954 0.863332 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-31_15:31 Bits used No. missing words z-score p-value 28 to 32 141919 0.0328 0.513075 27 to 31 141792 -0.3977 0.345415 26 to 30 141859 -0.1706 0.432265 25 to 29 142008 0.3345 0.630989 24 to 28 141722 -0.6350 0.262709 23 to 27 141833 -0.2587 0.397916 22 to 26 142162 0.8565 0.804142 21 to 25 141626 -0.9604 0.168417 20 to 24 142291 1.2938 0.902132 19 to 23 141492 -1.4147 0.078581 18 to 22 141813 -0.3265 0.372007 17 to 21 141806 -0.3503 0.363068 16 to 20 141833 -0.2587 0.397916 15 to 19 142078 0.5718 0.716259 14 to 18 142096 0.6328 0.736561 13 to 17 141368 -1.8350 0.033252 12 to 16 141152 -2.5672 0.005126 11 to 15 142917 3.4158 0.999682 10 to 14 141866 -0.1469 0.441613 9 to 13 141801 -0.3672 0.356727 8 to 12 142398 1.6565 0.951191 7 to 11 142210 1.0192 0.845951 6 to 10 141682 -0.7706 0.220469 5 to 9 142114 0.6938 0.756095 4 to 8 141493 -1.4113 0.079080 3 to 7 141588 -1.0893 0.138021 2 to 6 141658 -0.8520 0.197116 1 to 5 142279 1.2531 0.894919 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-31_15:31 Bits used No. missing words z-score p-value 31 to 32 141650 -0.7650 0.222140 30 to 31 141986 0.2262 0.589464 29 to 30 141131 -2.2960 0.010839 28 to 29 142111 0.5949 0.724044 27 to 28 141917 0.0226 0.509025 26 to 27 142253 1.0138 0.844655 25 to 26 141313 -1.7591 0.039282 24 to 25 142320 1.2114 0.887132 23 to 24 141848 -0.1809 0.428217 22 to 23 142123 0.6303 0.735749 21 to 22 141988 0.2321 0.591756 20 to 21 141534 -1.1072 0.134111 19 to 20 141371 -1.5880 0.056144 18 to 19 141276 -1.8682 0.030865 17 to 18 141466 -1.3078 0.095478 16 to 17 142004 0.2793 0.609978 15 to 16 142261 1.0374 0.850219 14 to 15 141438 -1.3904 0.082211 13 to 14 142479 1.6804 0.953564 12 to 13 141555 -1.0452 0.147960 11 to 12 142590 2.0079 0.977672 10 to 11 141775 -0.3963 0.345959 9 to 10 141397 -1.5113 0.065356 8 to 9 142182 0.8043 0.789399 7 to 8 142389 1.4150 0.921459 6 to 7 141953 0.1288 0.551250 5 to 6 141812 -0.2871 0.387014 4 to 5 142115 0.6067 0.727974 3 to 4 141787 -0.3609 0.359104 2 to 3 141996 0.2557 0.600895 1 to 2 142101 0.5654 0.714099 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-31_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2503.28 0.046 0.518491 Test results for specific bytes for dh-ranFile-2015-10-31_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2426.38 -1.041 0.148900 2 to 9 2442.40 -0.815 0.207651 3 to 10 2620.90 1.710 0.956349 4 to 11 2526.94 0.381 0.648387 5 to 12 2483.30 -0.236 0.406668 6 to 13 2498.93 -0.015 0.493946 7 to 14 2346.62 -2.169 0.015036 8 to 15 2405.29 -1.339 0.090228 9 to 16 2519.64 0.278 0.609377 10 to 17 2370.40 -1.833 0.033412 11 to 18 2502.03 0.029 0.511445 12 to 19 2612.28 1.588 0.943839 13 to 20 2501.94 0.027 0.510919 14 to 21 2548.42 0.685 0.753231 15 to 22 2331.61 -2.381 0.008623 16 to 23 2641.07 1.995 0.976983 17 to 24 2508.88 0.126 0.549964 18 to 25 2614.29 1.616 0.946987 19 to 26 2495.96 -0.057 0.477196 20 to 27 2569.50 0.983 0.837160 21 to 28 2436.77 -0.894 0.185619 22 to 29 2590.59 1.281 0.899923 23 to 30 2390.28 -1.552 0.060376 24 to 31 2417.74 -1.163 0.122339 25 to 32 2445.07 -0.777 0.218621 CDPARK for dh-ranFile-2015-10-31_15:31: 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 3524 0.0457 0.518210 3525 0.0913 0.536383 3514 -0.4110 0.340551 3501 -1.0046 0.157553 3517 -0.2740 0.392053 3499 -1.0959 0.136563 3556 1.5068 0.934075 3540 0.7763 0.781201 3488 -1.5982 0.055002 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3517.20 sample std.=19.17 p-value of the KSTEST for those 10 p-values: 0.610430 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-31_15:31 0.5466,0.4380,0.3942,0.1080,0.9445,0.4675,0.2334,0.5331,0.3764,0.1385, The KS test for those 10 p-values: 0.389203 The 3DSPHERES test for dh-ranFile-2015-10-31_15:31 sample no r^3 equiv. uni. 1 6.436 0.193074 2 13.272 0.357513 3 3.730 0.116915 4 5.383 0.164269 5 55.148 0.840905 6 14.330 0.379776 7 4.268 0.132603 8 10.021 0.283962 9 0.563 0.018592 10 16.735 0.427552 11 16.500 0.423042 12 3.361 0.105986 13 3.333 0.105162 14 59.005 0.860102 15 13.237 0.356766 16 18.738 0.464519 17 31.027 0.644498 18 6.981 0.207610 19 98.700 0.962746 20 48.263 0.799869 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.130323 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-31_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -1.1 -1.9 0.0 -0.7 1.2 0.6 -0.0 1.0 -0.9 0.8 1.4 0.4 0.7 1.5 0.3 -0.4 -0.4 -2.0 1.3 -0.6 -1.5 -0.3 0.6 -1.9 -0.8 -0.1 0.3 -1.0 0.2 -0.2 0.0 -1.6 0.1 1.1 -0.5 -0.1 -0.8 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:34.946593 z-score=-0.769590, p-value=0.228569 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-31_15:31 Test no p-value 1 0.110338 2 0.517254 3 0.099612 4 0.352981 5 0.119169 6 0.869592 7 0.058431 8 0.999775 9 0.076566 10 0.954000 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.060141 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-31_15:31: (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 66743 0.09 66532 0.27 3 25000.00 24996 0.00 25010 0.00 4 6666.67 6600 0.67 6735 0.70 5 1388.89 1377 0.10 1444 2.19 6 238.10 233 0.11 243 0.10 7 34.72 45 3.04 26 2.19 8 4.96 5 0.00 9 3.29 p=0.32463 p=0.81156 Number of rngs required: 687703, p-value: 0.209 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-31_15:31 No. of wins: Observed Expected 98301 98585.9 z-score=-1.274, pvalue=0.10132 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66525 66666.7 0.301 0.301 2 37612 37654.3 0.048 0.349 3 27089 26954.7 0.669 1.017 4 19333 19313.5 0.020 1.037 5 13855 13851.4 0.001 1.038 6 9995 9943.5 0.266 1.304 7 7144 7145.0 0.000 1.305 8 5192 5139.1 0.545 1.850 9 3717 3699.9 0.079 1.929 10 2662 2666.3 0.007 1.936 11 1882 1923.3 0.888 2.824 12 1293 1388.7 6.600 9.424 13 1003 1003.7 0.001 9.425 14 718 726.1 0.091 9.516 15 539 525.8 0.330 9.846 16 414 381.2 2.831 12.677 17 302 276.5 2.344 15.021 18 195 200.8 0.169 15.190 19 133 146.0 1.155 16.345 20 111 106.2 0.216 16.561 21 286 287.1 0.004 16.565 Chisq= 16.56 for 20 degrees of freedom, p= 0.31898 SUMMARY of craptest p-value for no. of wins: 0.101322 p-value for throws/game: 0.318984 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-31_15:31 No. of wins: Observed Expected 98757 98585.9 z-score= 0.765, pvalue=0.77800 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67003 66666.7 1.697 1.697 2 37416 37654.3 1.508 3.205 3 26992 26954.7 0.052 3.257 4 19377 19313.5 0.209 3.466 5 13935 13851.4 0.504 3.970 6 9743 9943.5 4.045 8.015 7 7227 7145.0 0.940 8.955 8 5040 5139.1 1.910 10.865 9 3681 3699.9 0.096 10.961 10 2656 2666.3 0.040 11.001 11 1925 1923.3 0.001 11.002 12 1374 1388.7 0.156 11.159 13 972 1003.7 1.002 12.161 14 731 726.1 0.033 12.194 15 533 525.8 0.098 12.291 16 375 381.2 0.099 12.390 17 258 276.5 1.243 13.633 18 203 200.8 0.023 13.657 19 157 146.0 0.831 14.488 20 123 106.2 2.652 17.140 21 279 287.1 0.229 17.370 Chisq= 17.37 for 20 degrees of freedom, p= 0.37115 SUMMARY of craptest p-value for no. of wins: 0.777996 p-value for throws/game: 0.371149 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0039,0.0047,0.0051,0.0086,0.0103,0.0106,0.0108,0.0115,0.0150,0.0186, 0.0215,0.0299,0.0309,0.0333,0.0334,0.0350,0.0393,0.0550,0.0560,0.0561, 0.0584,0.0601,0.0604,0.0654,0.0766,0.0786,0.0791,0.0806,0.0822,0.0838, 0.0902,0.0955,0.0996,0.1013,0.1014,0.1015,0.1027,0.1052,0.1060,0.1068, 0.1080,0.1103,0.1169,0.1192,0.1223,0.1303,0.1326,0.1341,0.1366,0.1377, 0.1380,0.1385,0.1480,0.1489,0.1491,0.1576,0.1643,0.1684,0.1832,0.1856, 0.1869,0.1931,0.1956,0.1957,0.1961,0.1971,0.2008,0.2076,0.2077,0.2092, 0.2135,0.2186,0.2205,0.2221,0.2286,0.2300,0.2317,0.2334,0.2341,0.2400, 0.2435,0.2467,0.2470,0.2480,0.2611,0.2627,0.2716,0.2840,0.2977,0.2997, 0.3069,0.3101,0.3130,0.3157,0.3190,0.3215,0.3246,0.3303,0.3345,0.3351, 0.3406,0.3454,0.3460,0.3530,0.3567,0.3568,0.3575,0.3591,0.3631,0.3647, 0.3683,0.3706,0.3711,0.3720,0.3762,0.3764,0.3798,0.3860,0.3870,0.3892, 0.3916,0.3921,0.3942,0.3979,0.3979,0.3994,0.4067,0.4230,0.4240,0.4276, 0.4279,0.4282,0.4323,0.4380,0.4383,0.4412,0.4416,0.4450,0.4564,0.4605, 0.4645,0.4675,0.4712,0.4748,0.4764,0.4772,0.4913,0.4939,0.5003,0.5090, 0.5109,0.5114,0.5123,0.5131,0.5171,0.5173,0.5182,0.5185,0.5331,0.5364, 0.5410,0.5446,0.5466,0.5500,0.5513,0.5534,0.5637,0.5647,0.5815,0.5894, 0.5895,0.5918,0.5934,0.5944,0.5977,0.6009,0.6094,0.6100,0.6104,0.6280, 0.6310,0.6314,0.6341,0.6354,0.6420,0.6445,0.6484,0.6537,0.6541,0.6550, 0.6613,0.6878,0.6953,0.7133,0.7141,0.7163,0.7240,0.7249,0.7280,0.7357, 0.7366,0.7423,0.7438,0.7450,0.7532,0.7546,0.7561,0.7696,0.7758,0.7767, 0.7780,0.7807,0.7812,0.7830,0.7894,0.7902,0.7999,0.8041,0.8098,0.8101, 0.8116,0.8156,0.8162,0.8175,0.8230,0.8313,0.8372,0.8409,0.8447,0.8460, 0.8502,0.8507,0.8601,0.8633,0.8678,0.8696,0.8764,0.8871,0.8918,0.8949, 0.8999,0.9021,0.9077,0.9215,0.9278,0.9341,0.9387,0.9423,0.9438,0.9442, 0.9445,0.9466,0.9470,0.9509,0.9512,0.9530,0.9535,0.9536,0.9540,0.9563, 0.9619,0.9627,0.9770,0.9777,0.9826,0.9884,0.9980,0.9997,0.9998, Overall p-value after applying KStest on 269 p-values = 0.071263 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.