RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-26_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 14.4877 0.367673 2 to 25 15.96 23.8783 0.877220 3 to 26 15.74 12.1632 0.209846 4 to 27 15.99 9.3428 0.071110 5 to 28 15.82 16.5880 0.517403 6 to 29 15.79 22.4307 0.831284 7 to 30 15.51 36.6484 0.996246 8 to 31 15.85 16.1108 0.484004 9 to 32 15.62 16.6866 0.524211 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.754606 Tough bday spacings test for dh-ranFile-2016-02-26_20:31: 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 39 80 95 98 69 60 28 7 7 5 (O-E)^2/E 0.9 0.2 0.6 0.1 0.0 1.1 1.2 0.1 4.2 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.518, p= 0.422 RESULTS OF GCD FOR dh-ranFile-2016-02-26_20:31 Euclid's algorithm: p-value, steps to gcd: 0.624095 p-value, dist. of gcd's: 0.723905 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-26_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.736 0.032 0.117 0.942 0.366 0.573 0.480 0.980 Bits 8 to 15---> 0.857 0.104 0.217 0.369 0.218 0.465 0.555 0.179 Bits 16 to 23---> 0.526 0.924 0.341 0.163 0.309 0.391 0.789 0.973 Bits 24 to 31---> 0.300 0.173 0.583 0.489 0.199 0.153 0.616 0.733 KS test for the above 32 p values: 0.386 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-26_20:31, p-values for 5 runs: 0.3913, 0.4922, 0.4452, 0.2992, 0.6135 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-26_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5095 5134.0 0.296 0.501 r= 30 23089 23103.0 0.009 0.510 r= 31 11598 11551.5 0.187 0.697 chi-square = 0.697 with df = 3; p-value = 0.126 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-26_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 237 211.4 3.095 3.095 r= 30 5139 5134.0 0.005 3.100 r= 31 22966 23103.0 0.813 3.913 r= 32 11658 11551.5 0.981 4.895 chi-square = 4.895 with df = 3; p-value = 0.820 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-26_20:31 b-rank test for bits 1 to 8, p=0.91659 b-rank test for bits 2 to 9, p=0.99103 b-rank test for bits 3 to 10, p=0.52950 b-rank test for bits 4 to 11, p=0.39129 b-rank test for bits 5 to 12, p=0.38011 b-rank test for bits 6 to 13, p=0.82755 b-rank test for bits 7 to 14, p=0.76071 b-rank test for bits 8 to 15, p=0.74190 b-rank test for bits 9 to 16, p=0.41122 b-rank test for bits 10 to 17, p=0.99094 b-rank test for bits 11 to 18, p=0.07182 b-rank test for bits 12 to 19, p=0.31472 b-rank test for bits 13 to 20, p=0.66988 b-rank test for bits 14 to 21, p=0.82385 b-rank test for bits 15 to 22, p=0.77450 b-rank test for bits 16 to 23, p=0.12543 b-rank test for bits 17 to 24, p=0.43076 b-rank test for bits 18 to 25, p=0.56268 b-rank test for bits 19 to 26, p=0.91853 b-rank test for bits 20 to 27, p=0.72344 b-rank test for bits 21 to 28, p=0.97000 b-rank test for bits 22 to 29, p=0.89065 b-rank test for bits 23 to 30, p=0.97280 b-rank test for bits 24 to 31, p=0.75552 b-rank test for bits 25 to 32, p=0.89344 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 = 0.002768 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-26_20:31 (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 141927 0.04 0.516466 2 141901 -0.02 0.492236 3 141847 -0.15 0.442106 4 141801 -0.25 0.400093 5 141552 -0.83 0.201892 6 141887 -0.05 0.479196 7 141602 -0.72 0.236360 8 142145 0.55 0.709057 9 141417 -1.15 0.125009 10 141907 -0.01 0.497828 11 141707 -0.47 0.318202 12 141163 -1.74 0.040600 13 141775 -0.31 0.376816 14 142334 0.99 0.839455 15 141811 -0.23 0.409146 16 141968 0.14 0.554516 17 141828 -0.19 0.424645 18 141610 -0.70 0.242161 19 141744 -0.39 0.349643 20 141939 0.07 0.527634 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-26_20:31 Bits used No. missing words z-score p-value 23 to 32 141963 0.1851 0.573413 22 to 31 142149 0.8264 0.795725 21 to 30 142262 1.2161 0.888027 20 to 29 141533 -1.2977 0.097197 19 to 28 142054 0.4989 0.691062 18 to 27 141876 -0.1149 0.454250 17 to 26 141716 -0.6667 0.252496 16 to 25 142165 0.8816 0.811009 15 to 24 141973 0.2196 0.586890 14 to 23 142045 0.4678 0.680046 13 to 22 141984 0.2575 0.601597 12 to 21 142131 0.7644 0.777679 11 to 20 141938 0.0989 0.539376 10 to 19 141790 -0.4115 0.340359 9 to 18 141942 0.1127 0.544848 8 to 17 141753 -0.5391 0.294920 7 to 16 141975 0.2264 0.589574 6 to 15 142173 0.9092 0.818380 5 to 14 142043 0.4609 0.677576 4 to 13 141803 -0.3667 0.356938 3 to 12 141764 -0.5011 0.308137 2 to 11 141805 -0.3598 0.359514 1 to 10 141591 -1.0977 0.136170 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-26_20:31 Bits used No. missing words z-score p-value 28 to 32 142054 0.4904 0.688077 27 to 31 141461 -1.5198 0.064285 26 to 30 141754 -0.5265 0.299256 25 to 29 142108 0.6735 0.749672 24 to 28 142070 0.5446 0.707001 23 to 27 141497 -1.3977 0.081097 22 to 26 141853 -0.1909 0.424283 21 to 25 141927 0.0599 0.523882 20 to 24 141500 -1.3876 0.082636 19 to 23 142169 0.8802 0.810635 18 to 22 141511 -1.3503 0.088465 17 to 21 142081 0.5819 0.719694 16 to 20 142005 0.3243 0.627147 15 to 19 142391 1.6328 0.948742 14 to 18 141824 -0.2893 0.386193 13 to 17 142495 1.9853 0.976446 12 to 16 142068 0.5379 0.704665 11 to 15 142016 0.3616 0.641172 10 to 14 141496 -1.4011 0.080589 9 to 13 142176 0.9040 0.816993 8 to 12 141868 -0.1401 0.444290 7 to 11 141770 -0.4723 0.318355 6 to 10 141742 -0.5672 0.285282 5 to 9 142088 0.6057 0.727630 4 to 8 142023 0.3853 0.650001 3 to 7 142097 0.6362 0.737667 2 to 6 142267 1.2124 0.887328 1 to 5 141940 0.1040 0.541402 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-26_20:31 Bits used No. missing words z-score p-value 31 to 32 141734 -0.5172 0.302509 30 to 31 141883 -0.0777 0.469045 29 to 30 141598 -0.9184 0.179211 28 to 29 141822 -0.2576 0.398354 27 to 28 142119 0.6185 0.731876 26 to 27 141755 -0.4553 0.324464 25 to 26 141280 -1.8564 0.031696 24 to 25 141365 -1.6057 0.054171 23 to 24 142051 0.4179 0.661992 22 to 23 141939 0.0875 0.534872 21 to 22 142380 1.3884 0.917493 20 to 21 142172 0.7748 0.780782 19 to 20 141731 -0.5260 0.299428 18 to 19 142230 0.9459 0.827908 17 to 18 141772 -0.4051 0.342701 16 to 17 141710 -0.5880 0.278268 15 to 16 142230 0.9459 0.827908 14 to 15 141835 -0.2193 0.413223 13 to 14 141804 -0.3107 0.378011 12 to 13 142068 0.4681 0.680127 11 to 12 141878 -0.0924 0.463183 10 to 11 141550 -1.0600 0.144579 9 to 10 141765 -0.4258 0.335144 8 to 9 141667 -0.7148 0.237355 7 to 8 141718 -0.5644 0.286243 6 to 7 141784 -0.3697 0.355801 5 to 6 142167 0.7601 0.776399 4 to 5 141673 -0.6971 0.242858 3 to 4 142365 1.3442 0.910552 2 to 3 141551 -1.0570 0.145251 1 to 2 141666 -0.7178 0.236444 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-26_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2417.33 -1.169 0.121174 Test results for specific bytes for dh-ranFile-2016-02-26_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2493.93 -0.086 0.465776 2 to 9 2559.21 0.837 0.798811 3 to 10 2463.35 -0.518 0.302129 4 to 11 2519.02 0.269 0.606006 5 to 12 2456.26 -0.619 0.268109 6 to 13 2463.07 -0.522 0.300717 7 to 14 2477.31 -0.321 0.374144 8 to 15 2520.34 0.288 0.613187 9 to 16 2352.88 -2.081 0.018738 10 to 17 2588.66 1.254 0.895048 11 to 18 2509.93 0.140 0.555831 12 to 19 2512.03 0.170 0.567558 13 to 20 2542.70 0.604 0.727049 14 to 21 2621.72 1.721 0.957404 15 to 22 2503.73 0.053 0.521046 16 to 23 2698.82 2.812 0.997536 17 to 24 2450.58 -0.699 0.242324 18 to 25 2446.25 -0.760 0.223577 19 to 26 2468.06 -0.452 0.325751 20 to 27 2534.23 0.484 0.685821 21 to 28 2459.11 -0.578 0.281563 22 to 29 2599.88 1.413 0.921106 23 to 30 2467.40 -0.461 0.322404 24 to 31 2369.37 -1.847 0.032346 25 to 32 2581.15 1.148 0.874427 CDPARK for dh-ranFile-2016-02-26_20:31: 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 3545 1.0046 0.842447 3487 -1.6438 0.050105 3530 0.3196 0.625377 3480 -1.9635 0.024796 3485 -1.7352 0.041356 3508 -0.6849 0.246694 3505 -0.8219 0.205562 3506 -0.7763 0.218799 3511 -0.5479 0.291865 3529 0.2740 0.607947 Square side=100, avg. no. parked=3508.60 sample std.=20.17 p-value of the KSTEST for those 10 p-values: 0.048403 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-26_20:31 0.0817,0.9119,0.0016,0.8967,0.4164,0.0552,0.6830,0.6159,0.0224,0.5860, The KS test for those 10 p-values: 0.132158 The 3DSPHERES test for dh-ranFile-2016-02-26_20:31 sample no r^3 equiv. uni. 1 10.319 0.291059 2 14.364 0.380468 3 31.374 0.648585 4 2.859 0.090890 5 21.777 0.516109 6 33.187 0.669198 7 38.097 0.719142 8 2.760 0.087899 9 10.322 0.291112 10 43.164 0.762784 11 3.632 0.114016 12 7.890 0.231254 13 12.809 0.347525 14 20.919 0.502080 15 4.559 0.140970 16 27.868 0.605031 17 1.385 0.045103 18 77.751 0.925108 19 82.187 0.935401 20 66.407 0.890692 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.873659 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-26_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.4 0.0 -0.5 -0.4 -1.0 0.4 0.1 -2.1 0.4 0.2 -0.4 0.0 1.7 -0.8 0.2 0.2 -1.6 0.1 -1.0 0.4 -0.9 0.1 1.2 0.4 2.2 1.5 -1.0 1.0 0.6 2.0 -0.1 -0.5 -0.5 -1.9 -1.4 -0.7 0.1 -1.8 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:41.308024 z-score=-0.075501, p-value=0.498804 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-26_20:31 Test no p-value 1 0.252781 2 0.363232 3 0.260135 4 0.139403 5 0.002458 6 0.836529 7 0.993498 8 0.141112 9 0.000516 10 0.193604 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009738 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-26_20:31: (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 66926 1.01 66687 0.01 3 25000.00 24777 1.99 24907 0.35 4 6666.67 6602 0.63 6741 0.83 5 1388.89 1397 0.05 1378 0.09 6 238.10 255 1.20 255 1.20 7 34.72 37 0.15 26 2.19 8 4.96 5 0.00 5 0.00 p=0.45912 p=0.41149 Number of rngs required: 688247, p-value: 0.429 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-26_20:31 No. of wins: Observed Expected 98868 98585.9 z-score= 1.262, pvalue=0.89651 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66757 66666.7 0.122 0.122 2 37644 37654.3 0.003 0.125 3 27036 26954.7 0.245 0.370 4 19239 19313.5 0.287 0.657 5 13863 13851.4 0.010 0.667 6 9820 9943.5 1.535 2.202 7 7094 7145.0 0.364 2.566 8 5109 5139.1 0.176 2.742 9 3732 3699.9 0.279 3.021 10 2761 2666.3 3.364 6.385 11 1925 1923.3 0.001 6.387 12 1379 1388.7 0.068 6.455 13 962 1003.7 1.734 8.189 14 707 726.1 0.505 8.693 15 530 525.8 0.033 8.726 16 406 381.2 1.620 10.346 17 254 276.5 1.837 12.183 18 215 200.8 1.000 13.183 19 147 146.0 0.007 13.190 20 98 106.2 0.635 13.826 21 322 287.1 4.239 18.064 Chisq= 18.06 for 20 degrees of freedom, p= 0.41684 SUMMARY of craptest p-value for no. of wins: 0.896508 p-value for throws/game: 0.416835 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-26_20:31 No. of wins: Observed Expected 98439 98585.9 z-score=-0.657, pvalue=0.25564 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66733 66666.7 0.066 0.066 2 37507 37654.3 0.576 0.642 3 26969 26954.7 0.008 0.650 4 19358 19313.5 0.103 0.753 5 13983 13851.4 1.250 2.003 6 9994 9943.5 0.256 2.259 7 7110 7145.0 0.172 2.430 8 5114 5139.1 0.122 2.553 9 3559 3699.9 5.363 7.916 10 2661 2666.3 0.011 7.926 11 1926 1923.3 0.004 7.930 12 1377 1388.7 0.099 8.029 13 980 1003.7 0.560 8.590 14 710 726.1 0.359 8.948 15 557 525.8 1.847 10.795 16 419 381.2 3.759 14.554 17 318 276.5 6.216 20.770 18 190 200.8 0.584 21.354 19 151 146.0 0.172 21.526 20 104 106.2 0.046 21.572 21 280 287.1 0.176 21.749 Chisq= 21.75 for 20 degrees of freedom, p= 0.64570 SUMMARY of craptest p-value for no. of wins: 0.255643 p-value for throws/game: 0.645700 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0016,0.0025,0.0028,0.0097,0.0187,0.0224,0.0248,0.0317,0.0317, 0.0323,0.0406,0.0414,0.0451,0.0484,0.0501,0.0542,0.0552,0.0643,0.0711, 0.0718,0.0806,0.0811,0.0817,0.0826,0.0879,0.0885,0.0909,0.0972,0.1038, 0.1140,0.1171,0.1212,0.1250,0.1254,0.1261,0.1322,0.1362,0.1394,0.1410, 0.1411,0.1446,0.1453,0.1531,0.1628,0.1729,0.1786,0.1792,0.1936,0.1989, 0.2019,0.2056,0.2098,0.2165,0.2176,0.2188,0.2236,0.2313,0.2364,0.2364, 0.2374,0.2422,0.2423,0.2429,0.2467,0.2525,0.2528,0.2556,0.2601,0.2681, 0.2783,0.2816,0.2853,0.2862,0.2911,0.2911,0.2919,0.2949,0.2992,0.2993, 0.2994,0.3003,0.3007,0.3021,0.3025,0.3081,0.3094,0.3147,0.3182,0.3184, 0.3224,0.3245,0.3258,0.3351,0.3404,0.3412,0.3427,0.3475,0.3496,0.3558, 0.3569,0.3595,0.3632,0.3662,0.3677,0.3690,0.3741,0.3768,0.3780,0.3801, 0.3805,0.3862,0.3864,0.3905,0.3913,0.3913,0.3984,0.4001,0.4091,0.4112, 0.4115,0.4132,0.4164,0.4168,0.4216,0.4243,0.4246,0.4288,0.4308,0.4421, 0.4443,0.4452,0.4542,0.4591,0.4632,0.4655,0.4658,0.4690,0.4792,0.4804, 0.4840,0.4895,0.4922,0.4922,0.4978,0.4988,0.5021,0.5161,0.5165,0.5174, 0.5210,0.5239,0.5242,0.5265,0.5276,0.5295,0.5349,0.5394,0.5414,0.5448, 0.5545,0.5546,0.5558,0.5627,0.5676,0.5733,0.5734,0.5832,0.5860,0.5869, 0.5896,0.6016,0.6050,0.6060,0.6079,0.6132,0.6135,0.6158,0.6159,0.6241, 0.6254,0.6271,0.6412,0.6457,0.6486,0.6500,0.6620,0.6692,0.6699,0.6776, 0.6800,0.6801,0.6830,0.6858,0.6881,0.6911,0.7047,0.7070,0.7091,0.7191, 0.7197,0.7234,0.7239,0.7270,0.7276,0.7319,0.7326,0.7363,0.7377,0.7419, 0.7497,0.7546,0.7555,0.7607,0.7628,0.7745,0.7764,0.7777,0.7808,0.7893, 0.7957,0.7988,0.8106,0.8110,0.8170,0.8184,0.8203,0.8238,0.8276,0.8279, 0.8279,0.8313,0.8365,0.8395,0.8424,0.8565,0.8737,0.8744,0.8772,0.8873, 0.8880,0.8906,0.8907,0.8934,0.8950,0.8965,0.8967,0.9106,0.9119,0.9166, 0.9175,0.9185,0.9211,0.9244,0.9251,0.9354,0.9418,0.9487,0.9574,0.9700, 0.9728,0.9731,0.9764,0.9802,0.9909,0.9910,0.9935,0.9962,0.9975, Overall p-value after applying KStest on 269 p-values = 0.388249 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.