RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-16_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.10 15.5135 0.441457 2 to 25 15.72 30.7989 0.978873 3 to 26 15.75 15.7207 0.456288 4 to 27 16.15 13.2322 0.279493 5 to 28 15.97 12.5393 0.233558 6 to 29 15.78 13.6212 0.306291 7 to 30 15.65 15.9569 0.473105 8 to 31 15.80 11.2210 0.155153 9 to 32 15.74 15.7670 0.459591 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.256193 Tough bday spacings test for dh-ranFile-2016-03-16_05:31: 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 30 63 106 113 85 44 28 11 2 8 (O-E)^2/E 0.1 1.2 1.4 0.7 2.4 0.6 1.3 0.1 1.0 3.2 3.8 Birthday Spacings: Sum(O-E)^2/E= 15.830, p= 0.895 RESULTS OF GCD FOR dh-ranFile-2016-03-16_05:31 Euclid's algorithm: p-value, steps to gcd: 0.661111 p-value, dist. of gcd's: 0.831397 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-16_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.995 0.843 0.010 0.163 0.191 0.689 0.885 0.790 Bits 8 to 15---> 0.769 0.868 0.044 0.435 0.471 0.661 0.968 0.314 Bits 16 to 23---> 0.278 0.407 0.754 0.043 0.832 0.556 0.518 0.654 Bits 24 to 31---> 0.441 0.276 0.565 0.659 0.243 0.615 0.871 0.906 KS test for the above 32 p values: 0.466 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-16_05:31, p-values for 5 runs: 0.7446, 0.7964, 0.9612, 0.3075, 0.5732 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-16_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5134 5134.0 0.000 0.205 r= 30 23234 23103.0 0.742 0.947 r= 31 11414 11551.5 1.637 2.584 chi-square = 2.584 with df = 3; p-value = 0.540 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-16_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5245 5134.0 2.399 2.499 r= 31 23078 23103.0 0.027 2.526 r= 32 11461 11551.5 0.709 3.235 chi-square = 3.235 with df = 3; p-value = 0.643 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-16_05:31 b-rank test for bits 1 to 8, p=0.89451 b-rank test for bits 2 to 9, p=0.24075 b-rank test for bits 3 to 10, p=0.93900 b-rank test for bits 4 to 11, p=0.53275 b-rank test for bits 5 to 12, p=0.88739 b-rank test for bits 6 to 13, p=0.65485 b-rank test for bits 7 to 14, p=0.10107 b-rank test for bits 8 to 15, p=0.10966 b-rank test for bits 9 to 16, p=0.75076 b-rank test for bits 10 to 17, p=0.06297 b-rank test for bits 11 to 18, p=0.34985 b-rank test for bits 12 to 19, p=0.82914 b-rank test for bits 13 to 20, p=0.13055 b-rank test for bits 14 to 21, p=0.30604 b-rank test for bits 15 to 22, p=0.21140 b-rank test for bits 16 to 23, p=0.52663 b-rank test for bits 17 to 24, p=0.15482 b-rank test for bits 18 to 25, p=0.38577 b-rank test for bits 19 to 26, p=0.10968 b-rank test for bits 20 to 27, p=0.15188 b-rank test for bits 21 to 28, p=0.38779 b-rank test for bits 22 to 29, p=0.30591 b-rank test for bits 23 to 30, p=0.58772 b-rank test for bits 24 to 31, p=0.50465 b-rank test for bits 25 to 32, p=0.44269 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 = 0.265280 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-16_05:31 (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 141878 -0.07 0.470823 2 142656 1.74 0.959469 3 141505 -0.94 0.172407 4 142282 0.87 0.808048 5 142541 1.48 0.930010 6 142396 1.14 0.872247 7 141697 -0.50 0.309913 8 141711 -0.46 0.321543 9 142657 1.75 0.959672 10 142487 1.35 0.911443 11 142468 1.31 0.904105 12 142215 0.71 0.762443 13 142085 0.41 0.659260 14 142465 1.30 0.902907 15 141978 0.16 0.563734 16 141562 -0.81 0.208534 17 141406 -1.18 0.119797 18 142850 2.20 0.986019 19 141807 -0.24 0.405518 20 141858 -0.12 0.452269 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-16_05:31 Bits used No. missing words z-score p-value 23 to 32 142051 0.4885 0.687408 22 to 31 142239 1.1368 0.872188 21 to 30 141452 -1.5770 0.057398 20 to 29 141950 0.1402 0.555765 19 to 28 142397 1.6816 0.953679 18 to 27 141822 -0.3011 0.381655 17 to 26 141688 -0.7632 0.222670 16 to 25 141371 -1.8563 0.031705 15 to 24 141436 -1.6322 0.051322 14 to 23 141279 -2.1736 0.014869 13 to 22 141486 -1.4598 0.072178 12 to 21 141969 0.2058 0.581510 11 to 20 141780 -0.4460 0.327811 10 to 19 142095 0.6402 0.738992 9 to 18 142099 0.6540 0.743455 8 to 17 141922 0.0437 0.517424 7 to 16 141516 -1.3563 0.087500 6 to 15 142234 1.1196 0.868548 5 to 14 141740 -0.5839 0.279645 4 to 13 141741 -0.5804 0.280806 3 to 12 141570 -1.1701 0.120980 2 to 11 141651 -0.8908 0.186520 1 to 10 142103 0.6678 0.747878 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-16_05:31 Bits used No. missing words z-score p-value 28 to 32 141598 -1.0554 0.145631 27 to 31 141610 -1.0147 0.155130 26 to 30 142061 0.5141 0.696421 25 to 29 142168 0.8768 0.809715 24 to 28 142201 0.9887 0.838598 23 to 27 141712 -0.6689 0.251775 22 to 26 141693 -0.7333 0.231681 21 to 25 141833 -0.2587 0.397916 20 to 24 142174 0.8972 0.815190 19 to 23 141724 -0.6282 0.264924 18 to 22 141729 -0.6113 0.270504 17 to 21 142149 0.8124 0.791731 16 to 20 142079 0.5752 0.717406 15 to 19 142115 0.6972 0.757157 14 to 18 141749 -0.5435 0.293396 13 to 17 141736 -0.5876 0.278414 12 to 16 142113 0.6904 0.755031 11 to 15 142441 1.8023 0.964249 10 to 14 141686 -0.7571 0.224510 9 to 13 141176 -2.4859 0.006462 8 to 12 142553 2.1819 0.985443 7 to 11 141883 -0.0893 0.464440 6 to 10 141604 -1.0350 0.150331 5 to 9 141873 -0.1232 0.450993 4 to 8 141655 -0.8621 0.194306 3 to 7 141494 -1.4079 0.079581 2 to 6 141324 -1.9842 0.023618 1 to 5 141816 -0.3164 0.375860 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-16_05:31 Bits used No. missing words z-score p-value 31 to 32 141696 -0.6293 0.264579 30 to 31 142189 0.8250 0.795310 29 to 30 141822 -0.2576 0.398354 28 to 29 142006 0.2852 0.612240 27 to 28 141465 -1.3107 0.094978 26 to 27 141719 -0.5614 0.287247 25 to 26 142301 1.1554 0.876030 24 to 25 142357 1.3206 0.906676 23 to 24 142049 0.4120 0.659832 22 to 23 140975 -2.7561 0.002924 21 to 22 141937 0.0816 0.532527 20 to 21 141709 -0.5909 0.277279 19 to 20 141719 -0.5614 0.287247 18 to 19 142383 1.3973 0.918832 17 to 18 141913 0.0108 0.504319 16 to 17 141895 -0.0423 0.483141 15 to 16 141836 -0.2163 0.414372 14 to 15 141630 -0.8240 0.204975 13 to 14 141759 -0.4435 0.328720 12 to 13 142582 1.9843 0.976388 11 to 12 141819 -0.2665 0.394942 10 to 11 141383 -1.5526 0.060260 9 to 10 141700 -0.6175 0.268455 8 to 9 141604 -0.9007 0.183880 7 to 8 142218 0.9105 0.818729 6 to 7 141689 -0.6499 0.257865 5 to 6 141729 -0.5319 0.297381 4 to 5 141775 -0.3963 0.345959 3 to 4 141655 -0.7502 0.226556 2 to 3 141836 -0.2163 0.414372 1 to 2 142051 0.4179 0.661992 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-16_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2518.01 0.255 0.600511 Test results for specific bytes for dh-ranFile-2016-03-16_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2444.62 -0.783 0.216776 2 to 9 2488.99 -0.156 0.438140 3 to 10 2509.97 0.141 0.556059 4 to 11 2394.37 -1.494 0.067608 5 to 12 2424.76 -1.064 0.143664 6 to 13 2438.94 -0.864 0.193927 7 to 14 2429.49 -0.997 0.159347 8 to 15 2457.93 -0.595 0.275947 9 to 16 2538.86 0.550 0.708676 10 to 17 2630.36 1.844 0.967375 11 to 18 2467.17 -0.464 0.321244 12 to 19 2624.54 1.761 0.960899 13 to 20 2456.00 -0.622 0.266878 14 to 21 2535.13 0.497 0.690338 15 to 22 2536.46 0.516 0.696928 16 to 23 2443.60 -0.798 0.212532 17 to 24 2477.19 -0.323 0.373512 18 to 25 2498.73 -0.018 0.492860 19 to 26 2472.26 -0.392 0.347410 20 to 27 2514.93 0.211 0.583613 21 to 28 2385.68 -1.617 0.052972 22 to 29 2476.89 -0.327 0.371914 23 to 30 2464.48 -0.502 0.307740 24 to 31 2527.72 0.392 0.652456 25 to 32 2524.39 0.345 0.634929 CDPARK for dh-ranFile-2016-03-16_05:31: 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 3502 -0.9589 0.168804 3512 -0.5023 0.307734 3505 -0.8219 0.205562 3567 2.0091 0.977738 3522 -0.0457 0.481790 3553 1.3699 0.914635 3528 0.2283 0.590298 3499 -1.0959 0.136563 3523 0.0000 0.500000 3535 0.5479 0.708135 Square side=100, avg. no. parked=3524.60 sample std.=21.08 p-value of the KSTEST for those 10 p-values: 0.946525 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-16_05:31 0.6119,0.8254,0.5518,0.4491,0.8813,0.2203,0.4075,0.3467,0.2456,0.5517, The KS test for those 10 p-values: 0.646370 The 3DSPHERES test for dh-ranFile-2016-03-16_05:31 sample no r^3 equiv. uni. 1 10.770 0.301614 2 58.336 0.856946 3 12.141 0.332825 4 18.883 0.467099 5 51.168 0.818340 6 22.300 0.524470 7 91.635 0.952854 8 86.669 0.944367 9 48.245 0.799747 10 55.223 0.841302 11 9.232 0.264890 12 37.944 0.717704 13 13.301 0.358123 14 7.694 0.226221 15 26.252 0.583159 16 25.884 0.578020 17 20.287 0.491479 18 24.841 0.563091 19 19.693 0.481305 20 27.510 0.600280 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.182273 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-16_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 0.6 -1.3 -0.9 0.8 0.7 -1.6 -0.9 1.6 -0.9 0.8 -1.1 -0.7 -1.0 1.1 2.0 0.3 -0.5 1.8 -0.2 -1.0 -0.5 -1.3 0.3 -0.4 1.2 0.2 -1.9 0.4 -0.9 -0.7 1.6 1.7 -0.4 -0.1 -0.5 -0.7 -0.4 0.4 -1.3 1.0 0.8 Chi-square with 42 degrees of freedom:44.235061 z-score=0.243865, p-value=0.622546 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-16_05:31 Test no p-value 1 0.346219 2 0.012273 3 0.632100 4 0.015722 5 0.057434 6 0.517871 7 0.034906 8 0.043235 9 0.825887 10 0.079441 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001118 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-16_05:31: (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 66861 0.57 66787 0.22 3 25000.00 24823 1.25 25020 0.02 4 6666.67 6681 0.03 6481 5.17 5 1388.89 1365 0.41 1440 1.88 6 238.10 235 0.04 230 0.28 7 34.72 34 0.01 36 0.05 8 4.96 0 4.96 5 0.00 p=0.70397 p=0.73173 Number of rngs required: 688299, p-value: 0.452 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-16_05:31 No. of wins: Observed Expected 98743 98585.9 z-score= 0.703, pvalue=0.75892 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66862 66666.7 0.572 0.572 2 37368 37654.3 2.177 2.749 3 27097 26954.7 0.751 3.500 4 19299 19313.5 0.011 3.511 5 13676 13851.4 2.222 5.733 6 10181 9943.5 5.671 11.403 7 7063 7145.0 0.942 12.345 8 5111 5139.1 0.153 12.498 9 3731 3699.9 0.262 12.760 10 2666 2666.3 0.000 12.760 11 1893 1923.3 0.478 13.239 12 1389 1388.7 0.000 13.239 13 940 1003.7 4.045 17.283 14 768 726.1 2.413 19.696 15 521 525.8 0.044 19.741 16 399 381.2 0.836 20.577 17 290 276.5 0.655 21.232 18 185 200.8 1.248 22.480 19 148 146.0 0.028 22.508 20 104 106.2 0.046 22.554 21 309 287.1 1.668 24.222 Chisq= 24.22 for 20 degrees of freedom, p= 0.76717 SUMMARY of craptest p-value for no. of wins: 0.758919 p-value for throws/game: 0.767172 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-16_05:31 No. of wins: Observed Expected 98668 98585.9 z-score= 0.367, pvalue=0.64333 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66833 66666.7 0.415 0.415 2 37482 37654.3 0.789 1.204 3 27008 26954.7 0.105 1.309 4 19185 19313.5 0.854 2.163 5 13787 13851.4 0.300 2.463 6 9957 9943.5 0.018 2.481 7 7268 7145.0 2.117 4.598 8 5190 5139.1 0.505 5.102 9 3755 3699.9 0.822 5.924 10 2742 2666.3 2.149 8.073 11 1960 1923.3 0.699 8.773 12 1359 1388.7 0.637 9.409 13 966 1003.7 1.417 10.827 14 672 726.1 4.037 14.863 15 497 525.8 1.581 16.445 16 355 381.2 1.794 18.239 17 285 276.5 0.259 18.498 18 196 200.8 0.116 18.614 19 132 146.0 1.340 19.953 20 94 106.2 1.405 21.358 21 277 287.1 0.356 21.715 Chisq= 21.71 for 20 degrees of freedom, p= 0.64380 SUMMARY of craptest p-value for no. of wins: 0.643334 p-value for throws/game: 0.643799 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0029,0.0065,0.0097,0.0123,0.0149,0.0157,0.0236,0.0317,0.0349, 0.0428,0.0432,0.0439,0.0513,0.0530,0.0574,0.0574,0.0603,0.0630,0.0676, 0.0722,0.0794,0.0796,0.0875,0.0950,0.1011,0.1097,0.1097,0.1198,0.1210, 0.1306,0.1366,0.1437,0.1456,0.1503,0.1519,0.1548,0.1551,0.1552,0.1593, 0.1632,0.1688,0.1724,0.1823,0.1839,0.1865,0.1908,0.1939,0.1943,0.2050, 0.2056,0.2085,0.2114,0.2125,0.2168,0.2203,0.2227,0.2245,0.2262,0.2266, 0.2317,0.2336,0.2407,0.2426,0.2456,0.2518,0.2562,0.2579,0.2646,0.2649, 0.2649,0.2653,0.2669,0.2685,0.2705,0.2755,0.2759,0.2773,0.2779,0.2784, 0.2795,0.2796,0.2808,0.2872,0.2872,0.2934,0.2974,0.3016,0.3059,0.3060, 0.3063,0.3075,0.3077,0.3077,0.3099,0.3138,0.3212,0.3215,0.3278,0.3287, 0.3328,0.3460,0.3462,0.3467,0.3474,0.3499,0.3581,0.3719,0.3735,0.3759, 0.3817,0.3858,0.3878,0.3949,0.3979,0.3984,0.4055,0.4075,0.4075,0.4144, 0.4144,0.4346,0.4381,0.4412,0.4415,0.4427,0.4491,0.4510,0.4523,0.4524, 0.4563,0.4596,0.4644,0.4658,0.4671,0.4708,0.4708,0.4731,0.4813,0.4818, 0.4831,0.4915,0.4929,0.5000,0.5043,0.5047,0.5174,0.5179,0.5181,0.5245, 0.5266,0.5325,0.5327,0.5398,0.5517,0.5518,0.5557,0.5558,0.5561,0.5631, 0.5637,0.5646,0.5732,0.5780,0.5815,0.5832,0.5836,0.5877,0.5903,0.6003, 0.6005,0.6119,0.6122,0.6151,0.6225,0.6321,0.6349,0.6432,0.6433,0.6438, 0.6464,0.6525,0.6536,0.6549,0.6592,0.6593,0.6598,0.6610,0.6611,0.6620, 0.6874,0.6886,0.6903,0.6964,0.6969,0.7040,0.7081,0.7087,0.7174,0.7177, 0.7317,0.7390,0.7435,0.7446,0.7479,0.7508,0.7535,0.7550,0.7572,0.7589, 0.7624,0.7672,0.7693,0.7902,0.7917,0.7953,0.7964,0.7997,0.8080,0.8097, 0.8152,0.8183,0.8187,0.8254,0.8259,0.8291,0.8314,0.8321,0.8386,0.8413, 0.8425,0.8569,0.8680,0.8685,0.8707,0.8722,0.8722,0.8760,0.8813,0.8849, 0.8874,0.8945,0.8954,0.9029,0.9041,0.9063,0.9067,0.9114,0.9146,0.9188, 0.9300,0.9390,0.9444,0.9465,0.9529,0.9537,0.9595,0.9597,0.9609,0.9612, 0.9642,0.9674,0.9678,0.9764,0.9777,0.9789,0.9854,0.9860,0.9946, Overall p-value after applying KStest on 269 p-values = 0.621751 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.