RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-17_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.93 20.1141 0.731564 2 to 25 15.92 14.0679 0.337713 3 to 26 15.79 17.4445 0.575333 4 to 27 15.74 21.1459 0.780168 5 to 28 15.58 22.5111 0.834145 6 to 29 15.42 26.3478 0.931647 7 to 30 15.69 17.0835 0.551280 8 to 31 15.98 12.2295 0.213955 9 to 32 15.51 30.1846 0.974956 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.181417 Tough bday spacings test for dh-ranFile-2015-06-17_18:31: 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 43 67 112 107 63 51 28 11 5 6 (O-E)^2/E 0.5 1.1 0.5 2.1 0.9 2.9 0.0 0.1 1.0 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.530, p= 0.605 RESULTS OF GCD FOR dh-ranFile-2015-06-17_18:31 Euclid's algorithm: p-value, steps to gcd: 0.494330 p-value, dist. of gcd's: 0.868608 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-17_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.907 0.808 0.885 0.349 0.636 0.627 0.416 0.508 Bits 8 to 15---> 0.515 0.722 0.947 0.207 0.151 0.245 0.041 0.961 Bits 16 to 23---> 0.200 0.157 0.513 0.432 0.460 0.811 0.992 0.073 Bits 24 to 31---> 0.493 0.971 0.104 0.266 0.691 0.073 0.472 0.630 KS test for the above 32 p values: 0.060 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-17_18:31, p-values for 5 runs: 0.4490, 0.4553, 0.7077, 0.3807, 0.0835 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-17_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5118 5134.0 0.050 1.198 r= 30 23135 23103.0 0.044 1.243 r= 31 11520 11551.5 0.086 1.329 chi-square = 1.329 with df = 3; p-value = 0.278 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-17_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5118 5134.0 0.050 1.174 r= 31 23167 23103.0 0.177 1.351 r= 32 11519 11551.5 0.092 1.443 chi-square = 1.443 with df = 3; p-value = 0.304 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-17_18:31 b-rank test for bits 1 to 8, p=0.71340 b-rank test for bits 2 to 9, p=0.90783 b-rank test for bits 3 to 10, p=0.57074 b-rank test for bits 4 to 11, p=0.46961 b-rank test for bits 5 to 12, p=0.38661 b-rank test for bits 6 to 13, p=0.17524 b-rank test for bits 7 to 14, p=0.42066 b-rank test for bits 8 to 15, p=0.12733 b-rank test for bits 9 to 16, p=0.81633 b-rank test for bits 10 to 17, p=0.17833 b-rank test for bits 11 to 18, p=0.13114 b-rank test for bits 12 to 19, p=0.85057 b-rank test for bits 13 to 20, p=0.58232 b-rank test for bits 14 to 21, p=0.95554 b-rank test for bits 15 to 22, p=0.11024 b-rank test for bits 16 to 23, p=0.05014 b-rank test for bits 17 to 24, p=0.39704 b-rank test for bits 18 to 25, p=0.94187 b-rank test for bits 19 to 26, p=0.28694 b-rank test for bits 20 to 27, p=0.66864 b-rank test for bits 21 to 28, p=0.06962 b-rank test for bits 22 to 29, p=0.13405 b-rank test for bits 23 to 30, p=0.30008 b-rank test for bits 24 to 31, p=0.05620 b-rank test for bits 25 to 32, p=0.32136 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 = 0.269610 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-17_18:31 (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 141684 -0.53 0.299280 2 141724 -0.43 0.332502 3 142174 0.62 0.731840 4 142863 2.23 0.987066 5 142160 0.59 0.720954 6 141558 -0.82 0.205862 7 141527 -0.89 0.185850 8 141314 -1.39 0.082119 9 141981 0.17 0.566493 10 142671 1.78 0.962430 11 142018 0.25 0.600214 12 141955 0.11 0.542489 13 142087 0.42 0.660972 14 142046 0.32 0.625259 15 141581 -0.77 0.221503 16 142056 0.34 0.634083 17 141968 0.14 0.554516 18 142656 1.74 0.959469 19 141105 -1.88 0.030103 20 141973 0.15 0.559129 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-17_18:31 Bits used No. missing words z-score p-value 23 to 32 141115 -2.7391 0.003081 22 to 31 141609 -1.0356 0.150190 21 to 30 141384 -1.8115 0.035033 20 to 29 141884 -0.0873 0.465199 19 to 28 142287 1.3023 0.903595 18 to 27 142025 0.3989 0.655003 17 to 26 141567 -1.1804 0.118911 16 to 25 141724 -0.6391 0.261389 15 to 24 141945 0.1230 0.548947 14 to 23 141419 -1.6908 0.045438 13 to 22 141642 -0.9218 0.178309 12 to 21 141680 -0.7908 0.214532 11 to 20 141854 -0.1908 0.424344 10 to 19 142182 0.9402 0.826453 9 to 18 141975 0.2264 0.589574 8 to 17 142287 1.3023 0.903595 7 to 16 142259 1.2058 0.886045 6 to 15 141969 0.2058 0.581510 5 to 14 141694 -0.7425 0.228887 4 to 13 141747 -0.5598 0.287822 3 to 12 141805 -0.3598 0.359514 2 to 11 142133 0.7713 0.779728 1 to 10 142204 1.0161 0.845210 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-17_18:31 Bits used No. missing words z-score p-value 28 to 32 142048 0.4701 0.680847 27 to 31 141651 -0.8757 0.190598 26 to 30 142176 0.9040 0.816993 25 to 29 142134 0.7616 0.776849 24 to 28 141846 -0.2147 0.415009 23 to 27 141763 -0.4960 0.309935 22 to 26 141950 0.1379 0.554826 21 to 25 141542 -1.2452 0.106532 20 to 24 142181 0.9209 0.821453 19 to 23 142487 1.9582 0.974897 18 to 22 142290 1.2904 0.901545 17 to 21 141814 -0.3232 0.373290 16 to 20 141798 -0.3774 0.352942 15 to 19 141690 -0.7435 0.228592 14 to 18 141606 -1.0282 0.151919 13 to 17 142421 1.7345 0.958583 12 to 16 141834 -0.2554 0.399224 11 to 15 141820 -0.3028 0.381016 10 to 14 141898 -0.0384 0.484682 9 to 13 141939 0.1006 0.540057 8 to 12 141567 -1.1604 0.122935 7 to 11 141633 -0.9367 0.174453 6 to 10 141728 -0.6147 0.269384 5 to 9 142002 0.3141 0.623291 4 to 8 141669 -0.8147 0.207628 3 to 7 142445 1.8158 0.965302 2 to 6 142029 0.4057 0.657504 1 to 5 141744 -0.5604 0.287589 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-17_18:31 Bits used No. missing words z-score p-value 31 to 32 141511 -1.1750 0.119994 30 to 31 141511 -1.1750 0.119994 29 to 30 142375 1.3737 0.915226 28 to 29 142289 1.1200 0.868637 27 to 28 141738 -0.5054 0.306640 26 to 27 141366 -1.6027 0.054496 25 to 26 142022 0.3324 0.630191 24 to 25 141815 -0.2783 0.390407 23 to 24 141635 -0.8092 0.209191 22 to 23 141496 -1.2193 0.111372 21 to 22 141401 -1.4995 0.066872 20 to 21 141632 -0.8181 0.206655 19 to 20 142555 1.9046 0.971586 18 to 19 142330 1.2409 0.892681 17 to 18 141916 0.0197 0.507849 16 to 17 141829 -0.2370 0.406343 15 to 16 141492 -1.2311 0.109150 14 to 15 141765 -0.4258 0.335144 13 to 14 141640 -0.7945 0.213457 12 to 13 142369 1.3560 0.912444 11 to 12 141856 -0.1573 0.437498 10 to 11 141887 -0.0659 0.473741 9 to 10 142181 0.8014 0.788546 8 to 9 141606 -0.8948 0.185453 7 to 8 141735 -0.5142 0.303539 6 to 7 141805 -0.3078 0.379133 5 to 6 141624 -0.8417 0.199983 4 to 5 141855 -0.1603 0.436336 3 to 4 141887 -0.0659 0.473741 2 to 3 141881 -0.0836 0.466699 1 to 2 141716 -0.5703 0.284239 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-17_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2556.60 0.800 0.788276 Test results for specific bytes for dh-ranFile-2015-06-17_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2488.05 -0.169 0.432872 2 to 9 2521.79 0.308 0.621037 3 to 10 2392.42 -1.521 0.064071 4 to 11 2490.73 -0.131 0.447862 5 to 12 2514.31 0.202 0.580210 6 to 13 2480.46 -0.276 0.391126 7 to 14 2548.57 0.687 0.753904 8 to 15 2535.09 0.496 0.690123 9 to 16 2441.52 -0.827 0.204105 10 to 17 2454.90 -0.638 0.261797 11 to 18 2444.19 -0.789 0.214963 12 to 19 2487.45 -0.178 0.429555 13 to 20 2567.72 0.958 0.830879 14 to 21 2564.45 0.911 0.818963 15 to 22 2600.72 1.424 0.922836 16 to 23 2567.05 0.948 0.828476 17 to 24 2446.76 -0.753 0.225735 18 to 25 2578.26 1.107 0.865814 19 to 26 2529.67 0.420 0.662601 20 to 27 2565.69 0.929 0.823540 21 to 28 2465.16 -0.493 0.311129 22 to 29 2374.03 -1.781 0.037418 23 to 30 2551.08 0.722 0.764973 24 to 31 2386.23 -1.609 0.053808 25 to 32 2565.96 0.933 0.824550 CDPARK for dh-ranFile-2015-06-17_18:31: 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 3511 -0.5479 0.291865 3494 -1.3242 0.092718 3530 0.3196 0.625377 3527 0.1826 0.572463 3541 0.8219 0.794438 3518 -0.2283 0.409702 3526 0.1370 0.554479 3536 0.5936 0.723613 3532 0.4110 0.659449 3504 -0.8676 0.192812 Square side=100, avg. no. parked=3521.90 sample std.=14.17 p-value of the KSTEST for those 10 p-values: 0.732335 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-17_18:31 0.8558,0.9904,0.6137,0.8933,0.7779,0.5765,0.5187,0.7314,0.9699,0.8896, The KS test for those 10 p-values: 0.002738 The 3DSPHERES test for dh-ranFile-2015-06-17_18:31 sample no r^3 equiv. uni. 1 7.937 0.232455 2 61.295 0.870384 3 4.971 0.152712 4 105.715 0.970514 5 14.836 0.390146 6 20.015 0.486831 7 3.179 0.100533 8 3.604 0.113187 9 17.305 0.438329 10 76.510 0.921945 11 29.962 0.631649 12 5.363 0.163712 13 4.622 0.142796 14 12.404 0.338650 15 11.616 0.321047 16 14.286 0.378853 17 68.358 0.897573 18 5.524 0.168181 19 7.400 0.218598 20 41.597 0.750067 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.301723 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-17_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 2.2 -0.6 -1.0 0.6 0.1 0.1 -0.2 0.5 -1.5 -1.2 0.6 -0.3 1.8 0.8 -0.1 -0.1 0.2 -1.0 0.4 -0.4 -0.8 1.4 -1.5 -0.7 -1.0 1.3 -0.2 1.1 1.4 0.1 -1.3 0.3 0.1 0.8 -1.0 0.0 0.8 1.3 -0.7 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:35.903043 z-score=-0.665232, p-value=0.265422 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-17_18:31 Test no p-value 1 0.483881 2 0.003822 3 0.081427 4 0.047983 5 0.028505 6 0.332667 7 0.830522 8 0.419546 9 0.173141 10 0.440019 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015450 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-17_18:31: (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 66888 0.73 66767 0.15 3 25000.00 24877 0.61 24807 1.49 4 6666.67 6553 1.94 6709 0.27 5 1388.89 1397 0.05 1437 1.67 6 238.10 249 0.50 232 0.16 7 34.72 32 0.21 41 1.14 8 4.96 3 0.77 6 0.22 p=0.43192 p=0.46720 Number of rngs required: 689036, p-value: 0.768 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-17_18:31 No. of wins: Observed Expected 98739 98585.9 z-score= 0.685, pvalue=0.75331 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66633 66666.7 0.017 0.017 2 37832 37654.3 0.838 0.855 3 27107 26954.7 0.860 1.716 4 19355 19313.5 0.089 1.805 5 13848 13851.4 0.001 1.806 6 9837 9943.5 1.142 2.947 7 7040 7145.0 1.544 4.491 8 5054 5139.1 1.408 5.899 9 3629 3699.9 1.357 7.257 10 2685 2666.3 0.131 7.388 11 1961 1923.3 0.738 8.126 12 1381 1388.7 0.043 8.169 13 983 1003.7 0.428 8.596 14 749 726.1 0.720 9.316 15 507 525.8 0.675 9.991 16 358 381.2 1.406 11.397 17 270 276.5 0.155 11.552 18 216 200.8 1.146 12.697 19 154 146.0 0.440 13.138 20 103 106.2 0.097 13.235 21 298 287.1 0.413 13.648 Chisq= 13.65 for 20 degrees of freedom, p= 0.15210 SUMMARY of craptest p-value for no. of wins: 0.753308 p-value for throws/game: 0.152097 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-17_18:31 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 66660 66666.7 0.001 0.001 2 37544 37654.3 0.323 0.324 3 27033 26954.7 0.227 0.551 4 19411 19313.5 0.493 1.044 5 13909 13851.4 0.239 1.283 6 9887 9943.5 0.322 1.605 7 7088 7145.0 0.455 2.060 8 5112 5139.1 0.143 2.202 9 3724 3699.9 0.157 2.360 10 2685 2666.3 0.131 2.491 11 1943 1923.3 0.201 2.692 12 1336 1388.7 2.003 4.695 13 1036 1003.7 1.038 5.734 14 717 726.1 0.115 5.849 15 543 525.8 0.560 6.409 16 368 381.2 0.454 6.863 17 251 276.5 2.359 9.221 18 186 200.8 1.095 10.316 19 147 146.0 0.007 10.323 20 123 106.2 2.652 12.976 21 297 287.1 0.340 13.316 Chisq= 13.32 for 20 degrees of freedom, p= 0.13659 SUMMARY of craptest p-value for no. of wins: 0.238695 p-value for throws/game: 0.136594 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0031,0.0038,0.0155,0.0285,0.0301,0.0350,0.0374,0.0410,0.0454, 0.0480,0.0501,0.0538,0.0545,0.0562,0.0604,0.0641,0.0669,0.0696,0.0731, 0.0731,0.0814,0.0821,0.0835,0.0927,0.1005,0.1037,0.1065,0.1091,0.1102, 0.1114,0.1132,0.1189,0.1200,0.1200,0.1229,0.1273,0.1311,0.1340,0.1366, 0.1428,0.1502,0.1512,0.1519,0.1521,0.1527,0.1566,0.1637,0.1682,0.1731, 0.1745,0.1752,0.1783,0.1783,0.1814,0.1855,0.1858,0.1906,0.1928,0.1998, 0.2000,0.2041,0.2059,0.2067,0.2068,0.2076,0.2092,0.2135,0.2140,0.2145, 0.2150,0.2186,0.2215,0.2257,0.2286,0.2289,0.2325,0.2387,0.2448,0.2614, 0.2618,0.2654,0.2665,0.2694,0.2696,0.2776,0.2842,0.2869,0.2876,0.2878, 0.2919,0.2993,0.3001,0.3017,0.3035,0.3045,0.3066,0.3099,0.3111,0.3210, 0.3214,0.3325,0.3327,0.3351,0.3377,0.3386,0.3489,0.3529,0.3595,0.3733, 0.3789,0.3791,0.3807,0.3810,0.3866,0.3901,0.3904,0.3911,0.3970,0.3992, 0.4063,0.4097,0.4150,0.4158,0.4195,0.4207,0.4243,0.4296,0.4318,0.4319, 0.4329,0.4363,0.4375,0.4383,0.4400,0.4479,0.4490,0.4553,0.4604,0.4652, 0.4667,0.4672,0.4696,0.4717,0.4737,0.4737,0.4839,0.4847,0.4868,0.4925, 0.4943,0.5078,0.5078,0.5126,0.5147,0.5187,0.5401,0.5425,0.5489,0.5513, 0.5545,0.5545,0.5548,0.5591,0.5665,0.5707,0.5725,0.5753,0.5765,0.5802, 0.5815,0.5823,0.5896,0.6002,0.6047,0.6137,0.6210,0.6233,0.6253,0.6254, 0.6271,0.6301,0.6302,0.6316,0.6341,0.6361,0.6550,0.6575,0.6594,0.6610, 0.6626,0.6686,0.6808,0.6901,0.6909,0.7077,0.7134,0.7210,0.7219,0.7236, 0.7314,0.7316,0.7318,0.7323,0.7501,0.7533,0.7539,0.7650,0.7676,0.7768, 0.7779,0.7797,0.7802,0.7883,0.7885,0.7944,0.8081,0.8109,0.8163,0.8170, 0.8190,0.8215,0.8235,0.8246,0.8265,0.8285,0.8305,0.8309,0.8341,0.8452, 0.8506,0.8558,0.8658,0.8686,0.8686,0.8704,0.8848,0.8860,0.8896,0.8927, 0.8933,0.8976,0.9015,0.9036,0.9036,0.9071,0.9078,0.9124,0.9152,0.9219, 0.9228,0.9316,0.9419,0.9471,0.9555,0.9586,0.9595,0.9611,0.9624,0.9653, 0.9699,0.9705,0.9711,0.9716,0.9749,0.9750,0.9871,0.9904,0.9916, Overall p-value after applying KStest on 269 p-values = 0.186546 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.