RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-08_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 10.8959 0.138075 2 to 25 15.75 13.3103 0.284820 3 to 26 16.07 18.2101 0.624296 4 to 27 15.81 15.8949 0.468699 5 to 28 15.64 16.5284 0.513268 6 to 29 15.89 18.6913 0.653463 7 to 30 15.72 11.7799 0.186722 8 to 31 15.86 14.0672 0.337660 9 to 32 15.87 14.8086 0.390737 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.273592 Tough bday spacings test for dh-ranFile-2015-07-08_07:31: 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 12 37 75 97 98 74 56 28 17 2 4 (O-E)^2/E 0.9 0.0 0.0 0.0 0.0 0.2 0.3 0.1 0.3 3.2 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.072, p= 0.114 RESULTS OF GCD FOR dh-ranFile-2015-07-08_07:31 Euclid's algorithm: p-value, steps to gcd: 0.039546 p-value, dist. of gcd's: 0.944800 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-08_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.275 0.478 0.901 0.390 0.810 0.555 0.365 0.770 Bits 8 to 15---> 0.086 0.469 0.946 0.321 0.975 0.841 0.434 0.766 Bits 16 to 23---> 0.848 0.936 0.324 0.275 0.053 0.263 0.773 0.307 Bits 24 to 31---> 0.927 0.690 0.960 0.075 0.170 0.672 0.802 0.736 KS test for the above 32 p values: 0.750 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-08_07:31, p-values for 5 runs: 0.9991, 0.6639, 0.3274, 0.0848, 0.1440 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-08_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5147 5134.0 0.033 1.157 r= 30 23147 23103.0 0.084 1.241 r= 31 11510 11551.5 0.149 1.390 chi-square = 1.390 with df = 3; p-value = 0.292 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-08_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 191 211.4 1.972 1.972 r= 30 5015 5134.0 2.759 4.731 r= 31 22975 23103.0 0.710 5.440 r= 32 11819 11551.5 6.193 11.634 chi-square = 11.634 with df = 3; p-value = 0.991 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-08_07:31 b-rank test for bits 1 to 8, p=0.15861 b-rank test for bits 2 to 9, p=0.54521 b-rank test for bits 3 to 10, p=0.82383 b-rank test for bits 4 to 11, p=0.64212 b-rank test for bits 5 to 12, p=0.91205 b-rank test for bits 6 to 13, p=0.38805 b-rank test for bits 7 to 14, p=0.51203 b-rank test for bits 8 to 15, p=0.80510 b-rank test for bits 9 to 16, p=0.94345 b-rank test for bits 10 to 17, p=0.94873 b-rank test for bits 11 to 18, p=0.48225 b-rank test for bits 12 to 19, p=0.03247 b-rank test for bits 13 to 20, p=0.17283 b-rank test for bits 14 to 21, p=0.20712 b-rank test for bits 15 to 22, p=0.78091 b-rank test for bits 16 to 23, p=0.97453 b-rank test for bits 17 to 24, p=0.60676 b-rank test for bits 18 to 25, p=0.85356 b-rank test for bits 19 to 26, p=0.10766 b-rank test for bits 20 to 27, p=0.26696 b-rank test for bits 21 to 28, p=0.37460 b-rank test for bits 22 to 29, p=0.78035 b-rank test for bits 23 to 30, p=0.33102 b-rank test for bits 24 to 31, p=0.22803 b-rank test for bits 25 to 32, p=0.38192 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 = 0.894204 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-08_07:31 (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 142376 1.09 0.862221 2 142091 0.42 0.664386 3 141832 -0.18 0.428310 4 141555 -0.83 0.203871 5 141318 -1.38 0.083545 6 142029 0.28 0.610109 7 141351 -1.30 0.096030 8 141624 -0.67 0.252495 9 141596 -0.73 0.232060 10 142083 0.41 0.657545 11 141567 -0.80 0.211903 12 142080 0.40 0.654966 13 141646 -0.62 0.269193 14 141375 -1.25 0.105936 15 141931 0.05 0.520190 16 142327 0.98 0.835434 17 141553 -0.83 0.202550 18 141926 0.04 0.515534 19 141515 -0.92 0.178439 20 141966 0.13 0.552669 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-08_07:31 Bits used No. missing words z-score p-value 23 to 32 141497 -1.4218 0.077538 22 to 31 141941 0.1092 0.543481 21 to 30 141722 -0.6460 0.259151 20 to 29 142507 2.0609 0.980345 19 to 28 141465 -1.5322 0.062740 18 to 27 141904 -0.0184 0.492668 17 to 26 142027 0.4058 0.657540 16 to 25 141799 -0.3804 0.351806 15 to 24 141640 -0.9287 0.176516 14 to 23 141697 -0.7322 0.232032 13 to 22 142004 0.3264 0.627957 12 to 21 141993 0.2885 0.613525 11 to 20 141542 -1.2667 0.102639 10 to 19 142196 0.9885 0.838550 9 to 18 142642 2.5264 0.994239 8 to 17 142021 0.3851 0.649907 7 to 16 141551 -1.2356 0.108300 6 to 15 142356 1.5402 0.938249 5 to 14 141961 0.1782 0.570706 4 to 13 142009 0.3437 0.634460 3 to 12 141800 -0.3770 0.353087 2 to 11 142278 1.2713 0.898185 1 to 10 142248 1.1678 0.878562 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-08_07:31 Bits used No. missing words z-score p-value 28 to 32 141971 0.2091 0.582796 27 to 31 142157 0.8396 0.799422 26 to 30 141940 0.1040 0.541402 25 to 29 142223 1.0633 0.856174 24 to 28 141884 -0.0859 0.465787 23 to 27 142245 1.1379 0.872411 22 to 26 142307 1.3480 0.911176 21 to 25 141841 -0.2316 0.408414 20 to 24 141998 0.3006 0.618131 19 to 23 142104 0.6599 0.745341 18 to 22 141929 0.0667 0.526581 17 to 21 141480 -1.4554 0.072785 16 to 20 141951 0.1413 0.556166 15 to 19 141792 -0.3977 0.345415 14 to 18 141311 -2.0282 0.021268 13 to 17 141509 -1.3571 0.087383 12 to 16 141851 -0.1977 0.421629 11 to 15 141923 0.0463 0.518480 10 to 14 141926 0.0565 0.522532 9 to 13 141911 0.0057 0.502258 8 to 12 142377 1.5853 0.943553 7 to 11 141979 0.2362 0.593349 6 to 10 141805 -0.3537 0.361797 5 to 9 141917 0.0260 0.510371 4 to 8 141950 0.1379 0.554826 3 to 7 141568 -1.1571 0.123626 2 to 6 142301 1.3277 0.907861 1 to 5 142157 0.8396 0.799422 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-08_07:31 Bits used No. missing words z-score p-value 31 to 32 142069 0.4710 0.681181 30 to 31 142020 0.3265 0.627962 29 to 30 141513 -1.1691 0.121179 28 to 29 142124 0.6332 0.736713 27 to 28 141932 0.0669 0.526659 26 to 27 142255 1.0197 0.846059 25 to 26 142120 0.6214 0.732847 24 to 25 142510 1.7719 0.961793 23 to 24 142427 1.5271 0.936626 22 to 23 141598 -0.9184 0.179211 21 to 22 142370 1.3589 0.912912 20 to 21 141742 -0.4936 0.310795 19 to 20 142012 0.3029 0.619002 18 to 19 142205 0.8722 0.808446 17 to 18 142265 1.0492 0.852951 16 to 17 141694 -0.6352 0.262652 15 to 16 142020 0.3265 0.627962 14 to 15 142339 1.2675 0.897505 13 to 14 141681 -0.6735 0.250302 12 to 13 141544 -1.0777 0.140591 11 to 12 142467 1.6450 0.950020 10 to 11 142500 1.7424 0.959280 9 to 10 142126 0.6391 0.738636 8 to 9 142295 1.1377 0.872371 7 to 8 141813 -0.2842 0.388144 6 to 7 141570 -1.0010 0.158420 5 to 6 142036 0.3737 0.645671 4 to 5 141559 -1.0334 0.150703 3 to 4 142000 0.2675 0.605444 2 to 3 141954 0.1318 0.552417 1 to 2 141645 -0.7797 0.217774 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-08_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2390.25 -1.552 0.060316 Test results for specific bytes for dh-ranFile-2015-07-08_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2513.19 0.187 0.574006 2 to 9 2454.19 -0.648 0.258557 3 to 10 2478.90 -0.298 0.382702 4 to 11 2589.30 1.263 0.896682 5 to 12 2541.95 0.593 0.723498 6 to 13 2556.76 0.803 0.788911 7 to 14 2614.08 1.613 0.946661 8 to 15 2465.87 -0.483 0.314662 9 to 16 2453.40 -0.659 0.254929 10 to 17 2446.37 -0.758 0.224094 11 to 18 2505.23 0.074 0.529500 12 to 19 2479.90 -0.284 0.388119 13 to 20 2550.52 0.714 0.762538 14 to 21 2562.84 0.889 0.812918 15 to 22 2413.43 -1.224 0.110430 16 to 23 2463.59 -0.515 0.303283 17 to 24 2603.61 1.465 0.928582 18 to 25 2456.87 -0.610 0.270961 19 to 26 2453.69 -0.655 0.256276 20 to 27 2515.13 0.214 0.584718 21 to 28 2640.72 1.990 0.976712 22 to 29 2440.56 -0.841 0.200298 23 to 30 2520.79 0.294 0.615626 24 to 31 2610.40 1.561 0.940774 25 to 32 2514.49 0.205 0.581156 CDPARK for dh-ranFile-2015-07-08_07:31: 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 3547 1.0959 0.863437 3553 1.3699 0.914635 3561 1.7352 0.958644 3582 2.6941 0.996471 3507 -0.7306 0.232514 3508 -0.6849 0.246694 3525 0.0913 0.536383 3516 -0.3196 0.374623 3586 2.8767 0.997991 3548 1.1416 0.873180 Square side=100, avg. no. parked=3543.30 sample std.=27.22 p-value of the KSTEST for those 10 p-values: 0.006029 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-08_07:31 0.7236,0.1693,0.1960,0.5070,0.4560,0.8634,0.0072,0.5414,0.6427,0.5294, The KS test for those 10 p-values: 0.706073 The 3DSPHERES test for dh-ranFile-2015-07-08_07:31 sample no r^3 equiv. uni. 1 1.173 0.038342 2 32.578 0.662412 3 32.584 0.662478 4 17.095 0.434374 5 32.298 0.659250 6 0.397 0.013135 7 0.490 0.016211 8 34.973 0.688315 9 9.557 0.272816 10 11.013 0.307262 11 7.601 0.223825 12 74.442 0.916374 13 1.009 0.033070 14 11.545 0.319437 15 20.350 0.492536 16 46.677 0.789002 17 22.203 0.522930 18 12.350 0.337463 19 29.241 0.622692 20 17.659 0.444916 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.210488 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-08_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 2.2 0.6 0.5 -0.4 -1.2 -1.6 0.7 -0.8 0.5 -0.2 0.5 -0.1 0.0 -1.2 0.5 -0.8 0.0 -0.2 -1.3 1.4 1.0 -0.2 1.3 0.5 0.7 -0.1 -1.3 -0.1 1.2 -2.2 0.6 0.1 0.9 1.7 -1.6 -0.5 0.8 -0.8 -0.7 3.1 0.0 -1.1 Chi-square with 42 degrees of freedom:48.787176 z-score=0.740542, p-value=0.781104 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-08_07:31 Test no p-value 1 0.314935 2 0.009928 3 0.618421 4 0.000526 5 0.302761 6 0.048270 7 0.198242 8 0.037400 9 0.894186 10 0.624369 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009956 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-08_07:31: (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 66883 0.70 66688 0.01 3 25000.00 24818 1.32 25064 0.16 4 6666.67 6640 0.11 6605 0.57 5 1388.89 1369 0.28 1369 0.28 6 238.10 248 0.41 233 0.11 7 34.72 35 0.00 35 0.00 8 4.96 6 0.22 5 0.00 p=0.19756 p=0.02015 Number of rngs required: 688174, p-value: 0.396 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-08_07:31 No. of wins: Observed Expected 98602 98585.9 z-score= 0.072, pvalue=0.52878 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66374 66666.7 1.285 1.285 2 37759 37654.3 0.291 1.576 3 26938 26954.7 0.010 1.586 4 19393 19313.5 0.328 1.914 5 13863 13851.4 0.010 1.923 6 9948 9943.5 0.002 1.925 7 7032 7145.0 1.788 3.713 8 5235 5139.1 1.791 5.504 9 3669 3699.9 0.257 5.761 10 2643 2666.3 0.204 5.965 11 2007 1923.3 3.640 9.605 12 1403 1388.7 0.146 9.751 13 1053 1003.7 2.420 12.171 14 738 726.1 0.194 12.365 15 533 525.8 0.098 12.463 16 398 381.2 0.745 13.208 17 300 276.5 1.990 15.198 18 200 200.8 0.003 15.201 19 147 146.0 0.007 15.208 20 112 106.2 0.315 15.523 21 255 287.1 3.592 19.115 Chisq= 19.12 for 20 degrees of freedom, p= 0.48566 SUMMARY of craptest p-value for no. of wins: 0.528776 p-value for throws/game: 0.485663 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-08_07:31 No. of wins: Observed Expected 98785 98585.9 z-score= 0.891, pvalue=0.81345 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66714 66666.7 0.034 0.034 2 37778 37654.3 0.406 0.440 3 26864 26954.7 0.305 0.745 4 19299 19313.5 0.011 0.756 5 13912 13851.4 0.265 1.021 6 9870 9943.5 0.544 1.565 7 7153 7145.0 0.009 1.574 8 5094 5139.1 0.395 1.969 9 3579 3699.9 3.948 5.918 10 2691 2666.3 0.229 6.146 11 1883 1923.3 0.846 6.992 12 1473 1388.7 5.112 12.104 13 991 1003.7 0.161 12.265 14 663 726.1 5.490 17.756 15 558 525.8 1.967 19.723 16 403 381.2 1.253 20.976 17 282 276.5 0.108 21.083 18 209 200.8 0.332 21.416 19 161 146.0 1.544 22.960 20 111 106.2 0.216 23.176 21 312 287.1 2.157 25.333 Chisq= 25.33 for 20 degrees of freedom, p= 0.81101 SUMMARY of craptest p-value for no. of wins: 0.813449 p-value for throws/game: 0.811009 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0060,0.0072,0.0099,0.0100,0.0131,0.0162,0.0201,0.0213,0.0325, 0.0331,0.0374,0.0383,0.0395,0.0483,0.0525,0.0603,0.0627,0.0728,0.0750, 0.0775,0.0835,0.0848,0.0863,0.0874,0.0960,0.1026,0.1059,0.1077,0.1083, 0.1104,0.1137,0.1212,0.1236,0.1381,0.1406,0.1440,0.1507,0.1584,0.1586, 0.1693,0.1702,0.1728,0.1765,0.1784,0.1792,0.1867,0.1960,0.1976,0.1982, 0.2003,0.2026,0.2039,0.2071,0.2105,0.2119,0.2178,0.2238,0.2241,0.2280, 0.2320,0.2321,0.2325,0.2467,0.2503,0.2525,0.2549,0.2563,0.2586,0.2592, 0.2627,0.2632,0.2670,0.2692,0.2710,0.2728,0.2736,0.2751,0.2751,0.2848, 0.2921,0.3028,0.3033,0.3073,0.3075,0.3108,0.3147,0.3149,0.3194,0.3210, 0.3241,0.3274,0.3310,0.3375,0.3377,0.3454,0.3518,0.3531,0.3618,0.3648, 0.3746,0.3746,0.3819,0.3827,0.3881,0.3881,0.3881,0.3895,0.3907,0.3961, 0.4084,0.4216,0.4283,0.4340,0.4344,0.4449,0.4560,0.4658,0.4685,0.4687, 0.4784,0.4823,0.4857,0.4925,0.4927,0.5023,0.5070,0.5104,0.5120,0.5133, 0.5155,0.5185,0.5202,0.5225,0.5229,0.5266,0.5267,0.5288,0.5294,0.5295, 0.5364,0.5414,0.5414,0.5435,0.5452,0.5524,0.5527,0.5548,0.5553,0.5562, 0.5707,0.5740,0.5812,0.5828,0.5847,0.5933,0.6054,0.6068,0.6101,0.6135, 0.6156,0.6181,0.6184,0.6190,0.6227,0.6243,0.6244,0.6280,0.6280,0.6280, 0.6345,0.6421,0.6427,0.6457,0.6499,0.6535,0.6550,0.6575,0.6575,0.6592, 0.6624,0.6625,0.6639,0.6644,0.6723,0.6812,0.6883,0.6895,0.7061,0.7235, 0.7236,0.7328,0.7356,0.7367,0.7386,0.7453,0.7496,0.7625,0.7656,0.7699, 0.7725,0.7804,0.7809,0.7811,0.7889,0.7890,0.7994,0.7994,0.8022,0.8051, 0.8084,0.8097,0.8110,0.8129,0.8134,0.8238,0.8354,0.8386,0.8413,0.8461, 0.8477,0.8530,0.8536,0.8562,0.8622,0.8634,0.8634,0.8724,0.8724,0.8732, 0.8786,0.8942,0.8942,0.8967,0.8975,0.8982,0.9013,0.9079,0.9112,0.9120, 0.9129,0.9146,0.9164,0.9266,0.9286,0.9360,0.9366,0.9382,0.9408,0.9435, 0.9436,0.9448,0.9459,0.9467,0.9487,0.9500,0.9586,0.9593,0.9596,0.9618, 0.9745,0.9750,0.9767,0.9803,0.9913,0.9942,0.9965,0.9980,0.9991, Overall p-value after applying KStest on 269 p-values = 0.743661 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.