RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-21_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.58 17.5435 0.581831 2 to 25 15.62 26.7853 0.938707 3 to 26 15.82 17.1550 0.556086 4 to 27 15.44 24.4850 0.893155 5 to 28 15.78 16.5461 0.514493 6 to 29 15.71 17.2829 0.564633 7 to 30 15.76 14.8260 0.391985 8 to 31 15.81 12.6854 0.243018 9 to 32 15.63 24.7680 0.899976 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.264399 Tough bday spacings test for dh-ranFile-2016-04-21_03:31: 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 3 39 67 96 103 88 48 27 10 14 5 (O-E)^2/E 4.1 0.2 0.5 0.0 0.3 1.2 0.3 0.3 1.6 8.2 0.2 Birthday Spacings: Sum(O-E)^2/E= 17.030, p= 0.926 RESULTS OF GCD FOR dh-ranFile-2016-04-21_03:31 Euclid's algorithm: p-value, steps to gcd: 0.172036 p-value, dist. of gcd's: 0.848686 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-21_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.279 0.422 0.429 0.920 0.779 0.060 0.731 0.543 Bits 8 to 15---> 0.056 0.498 0.620 0.876 0.307 0.382 0.404 0.266 Bits 16 to 23---> 0.803 0.858 0.733 0.807 0.741 0.294 0.445 0.301 Bits 24 to 31---> 0.933 0.296 0.285 0.147 0.935 0.010 0.769 0.178 KS test for the above 32 p values: 0.123 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-21_03:31, p-values for 5 runs: 0.9812, 0.2608, 0.8543, 0.3791, 0.7584 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-21_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5105 5134.0 0.164 0.499 r= 30 23142 23103.0 0.066 0.565 r= 31 11550 11551.5 0.000 0.565 chi-square = 0.565 with df = 3; p-value = 0.096 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-21_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5114 5134.0 0.078 0.608 r= 31 23202 23103.0 0.424 1.031 r= 32 11462 11551.5 0.694 1.725 chi-square = 1.725 with df = 3; p-value = 0.369 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-21_03:31 b-rank test for bits 1 to 8, p=0.77305 b-rank test for bits 2 to 9, p=0.31866 b-rank test for bits 3 to 10, p=0.50629 b-rank test for bits 4 to 11, p=0.97754 b-rank test for bits 5 to 12, p=0.99870 b-rank test for bits 6 to 13, p=0.56545 b-rank test for bits 7 to 14, p=0.40683 b-rank test for bits 8 to 15, p=0.78473 b-rank test for bits 9 to 16, p=0.02968 b-rank test for bits 10 to 17, p=0.07115 b-rank test for bits 11 to 18, p=0.29214 b-rank test for bits 12 to 19, p=0.53010 b-rank test for bits 13 to 20, p=0.38629 b-rank test for bits 14 to 21, p=0.74376 b-rank test for bits 15 to 22, p=0.43282 b-rank test for bits 16 to 23, p=0.82516 b-rank test for bits 17 to 24, p=0.07978 b-rank test for bits 18 to 25, p=0.08792 b-rank test for bits 19 to 26, p=0.70757 b-rank test for bits 20 to 27, p=0.38642 b-rank test for bits 21 to 28, p=0.52644 b-rank test for bits 22 to 29, p=0.02823 b-rank test for bits 23 to 30, p=0.73712 b-rank test for bits 24 to 31, p=0.37731 b-rank test for bits 25 to 32, p=0.54661 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 = 0.675150 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-21_03:31 (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 141891 -0.04 0.482920 2 141122 -1.84 0.032917 3 141611 -0.70 0.242891 4 141284 -1.46 0.072001 5 142601 1.62 0.946958 6 141818 -0.21 0.415512 7 141783 -0.30 0.383935 8 141655 -0.59 0.276180 9 141636 -0.64 0.261535 10 141680 -0.54 0.296042 11 141044 -2.02 0.021599 12 141780 -0.30 0.381260 13 142347 1.02 0.846750 14 142343 1.01 0.844529 15 141872 -0.09 0.465249 16 141839 -0.16 0.434739 17 142023 0.27 0.604720 18 141562 -0.81 0.208534 19 141834 -0.18 0.430145 20 141670 -0.56 0.288019 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-21_03:31 Bits used No. missing words z-score p-value 23 to 32 141781 -0.4425 0.329058 22 to 31 141902 -0.0253 0.489918 21 to 30 141637 -0.9391 0.173848 20 to 29 141628 -0.9701 0.165998 19 to 28 141787 -0.4218 0.336575 18 to 27 141538 -1.2804 0.100194 17 to 26 141916 0.0230 0.509175 16 to 25 142405 1.7092 0.956294 15 to 24 141881 -0.0977 0.461089 14 to 23 141619 -1.0011 0.158380 13 to 22 141715 -0.6701 0.251396 12 to 21 142214 1.0506 0.853276 11 to 20 142284 1.2920 0.901815 10 to 19 141203 -2.4356 0.007433 9 to 18 141743 -0.5736 0.283136 8 to 17 142233 1.1161 0.867811 7 to 16 141932 0.0782 0.531155 6 to 15 141792 -0.4046 0.342891 5 to 14 142094 0.6368 0.737870 4 to 13 141924 0.0506 0.520172 3 to 12 141874 -0.1218 0.451518 2 to 11 141827 -0.2839 0.388245 1 to 10 141876 -0.1149 0.454250 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-21_03:31 Bits used No. missing words z-score p-value 28 to 32 142080 0.5785 0.718551 27 to 31 142227 1.0768 0.859226 26 to 30 142097 0.6362 0.737667 25 to 29 142307 1.3480 0.911176 24 to 28 141678 -0.7842 0.216470 23 to 27 141845 -0.2181 0.413688 22 to 26 142005 0.3243 0.627147 21 to 25 142482 1.9413 0.973886 20 to 24 141580 -1.1164 0.132131 19 to 23 141901 -0.0282 0.488737 18 to 22 141950 0.1379 0.554826 17 to 21 141996 0.2938 0.615543 16 to 20 141567 -1.1604 0.122935 15 to 19 142588 2.3006 0.989292 14 to 18 141805 -0.3537 0.361797 13 to 17 142041 0.4463 0.672324 12 to 16 142753 2.8599 0.997881 11 to 15 142011 0.3446 0.634819 10 to 14 141830 -0.2689 0.393998 9 to 13 142490 1.9684 0.975487 8 to 12 141943 0.1141 0.545435 7 to 11 141967 0.1955 0.577496 6 to 10 141771 -0.4689 0.319565 5 to 9 141764 -0.4926 0.311132 4 to 8 141983 0.2497 0.598602 3 to 7 142175 0.9006 0.816093 2 to 6 142152 0.8226 0.794635 1 to 5 141393 -1.7503 0.040036 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-21_03:31 Bits used No. missing words z-score p-value 31 to 32 141882 -0.0806 0.467872 30 to 31 142092 0.5388 0.705005 29 to 30 141968 0.1731 0.568701 28 to 29 142031 0.3589 0.640168 27 to 28 142180 0.7984 0.787691 26 to 27 142026 0.3442 0.634637 25 to 26 142273 1.0728 0.858314 24 to 25 141295 -1.8122 0.034979 23 to 24 142502 1.7483 0.959793 22 to 23 142324 1.2232 0.889376 21 to 22 142010 0.2970 0.616752 20 to 21 141851 -0.1721 0.431693 19 to 20 141980 0.2085 0.582568 18 to 19 142224 0.9282 0.823356 17 to 18 141779 -0.3845 0.350321 16 to 17 141799 -0.3255 0.372418 15 to 16 141582 -0.9656 0.167128 14 to 15 141866 -0.1278 0.449147 13 to 14 141994 0.2498 0.598615 12 to 13 141709 -0.5909 0.277279 11 to 12 142655 2.1996 0.986083 10 to 11 142595 2.0226 0.978444 9 to 10 141944 0.1023 0.540729 8 to 9 142146 0.6981 0.757456 7 to 8 141614 -0.8712 0.191828 6 to 7 142042 0.3914 0.652233 5 to 6 141840 -0.2045 0.418976 4 to 5 142237 0.9666 0.833123 3 to 4 141864 -0.1337 0.446813 2 to 3 142051 0.4179 0.661992 1 to 2 141538 -1.0954 0.136678 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-21_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2427.38 -1.027 0.152207 Test results for specific bytes for dh-ranFile-2016-04-21_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2549.36 0.698 0.757439 2 to 9 2482.11 -0.253 0.400150 3 to 10 2502.77 0.039 0.515623 4 to 11 2447.90 -0.737 0.230626 5 to 12 2440.71 -0.838 0.200879 6 to 13 2454.44 -0.644 0.259702 7 to 14 2599.88 1.413 0.921111 8 to 15 2579.22 1.120 0.868710 9 to 16 2453.85 -0.653 0.257003 10 to 17 2539.56 0.559 0.712076 11 to 18 2407.10 -1.314 0.094450 12 to 19 2518.61 0.263 0.603803 13 to 20 2459.74 -0.569 0.284534 14 to 21 2509.62 0.136 0.554101 15 to 22 2508.05 0.114 0.545294 16 to 23 2531.50 0.445 0.672010 17 to 24 2522.67 0.321 0.625733 18 to 25 2529.03 0.411 0.659320 19 to 26 2467.57 -0.459 0.323231 20 to 27 2538.88 0.550 0.708784 21 to 28 2526.44 0.374 0.645753 22 to 29 2434.99 -0.919 0.178965 23 to 30 2475.15 -0.351 0.362634 24 to 31 2601.19 1.431 0.923782 25 to 32 2532.10 0.454 0.675047 CDPARK for dh-ranFile-2016-04-21_03:31: 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 3513 -0.4566 0.323972 3532 0.4110 0.659449 3519 -0.1826 0.427537 3540 0.7763 0.781201 3502 -0.9589 0.168804 3533 0.4566 0.676028 3560 1.6895 0.954438 3485 -1.7352 0.041356 3532 0.4110 0.659449 3543 0.9132 0.819442 Square side=100, avg. no. parked=3525.90 sample std.=20.58 p-value of the KSTEST for those 10 p-values: 0.866064 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-21_03:31 0.8507,0.0336,0.4947,0.6789,0.1642,0.4613,0.8253,0.0328,0.8866,0.2859, The KS test for those 10 p-values: 0.763629 The 3DSPHERES test for dh-ranFile-2016-04-21_03:31 sample no r^3 equiv. uni. 1 70.364 0.904198 2 40.787 0.743231 3 26.415 0.585420 4 15.164 0.396778 5 2.665 0.084999 6 22.997 0.535397 7 4.903 0.150768 8 59.814 0.863824 9 27.371 0.598431 10 19.102 0.470980 11 21.267 0.507818 12 11.614 0.321004 13 61.733 0.872262 14 6.253 0.188150 15 20.500 0.495061 16 57.487 0.852840 17 11.780 0.324747 18 37.507 0.713561 19 56.177 0.846272 20 136.503 0.989434 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.448592 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-21_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.5 0.6 -2.2 0.4 0.1 1.0 2.3 1.7 0.0 -0.1 1.3 0.8 -0.2 1.8 0.2 -0.4 0.2 -0.5 -1.4 -0.6 -0.1 0.0 -1.8 -0.9 -0.7 -1.3 -0.8 0.2 1.2 -0.1 -0.6 1.8 -0.3 0.1 0.6 2.8 -0.4 -1.2 -0.1 -0.6 2.0 -0.1 Chi-square with 42 degrees of freedom:51.657650 z-score=1.053736, p-value=0.854024 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-21_03:31 Test no p-value 1 0.108263 2 0.622101 3 0.191258 4 0.752480 5 0.559779 6 0.000255 7 0.916129 8 0.019620 9 0.151233 10 0.529319 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.117858 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-21_03:31: (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 66700 0.02 66617 0.04 3 25000.00 24933 0.18 24889 0.49 4 6666.67 6716 0.37 6818 3.44 5 1388.89 1390 0.00 1376 0.12 6 238.10 228 0.43 255 1.20 7 34.72 28 1.30 37 0.15 8 4.96 4 0.19 7 0.84 p=0.12892 p=0.60675 Number of rngs required: 687649, p-value: 0.192 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-21_03:31 No. of wins: Observed Expected 99157 98585.9 z-score= 2.554, pvalue=0.99468 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66981 66666.7 1.482 1.482 2 37368 37654.3 2.177 3.659 3 27067 26954.7 0.468 4.127 4 19126 19313.5 1.820 5.946 5 13756 13851.4 0.657 6.604 6 9920 9943.5 0.056 6.659 7 7026 7145.0 1.983 8.642 8 5260 5139.1 2.846 11.488 9 3868 3699.9 7.641 19.128 10 2661 2666.3 0.011 19.139 11 1981 1923.3 1.729 20.868 12 1346 1388.7 1.315 22.184 13 963 1003.7 1.652 23.835 14 751 726.1 0.851 24.686 15 503 525.8 0.992 25.678 16 383 381.2 0.009 25.687 17 276 276.5 0.001 25.688 18 220 200.8 1.830 27.518 19 124 146.0 3.311 30.829 20 113 106.2 0.433 31.262 21 307 287.1 1.377 32.639 Chisq= 32.64 for 20 degrees of freedom, p= 0.96306 SUMMARY of craptest p-value for no. of wins: 0.994683 p-value for throws/game: 0.963056 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-21_03:31 No. of wins: Observed Expected 99002 98585.9 z-score= 1.861, pvalue=0.96864 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66498 66666.7 0.427 0.427 2 37747 37654.3 0.228 0.655 3 26607 26954.7 4.486 5.141 4 19704 19313.5 7.897 13.038 5 13991 13851.4 1.407 14.444 6 9918 9943.5 0.066 14.510 7 7176 7145.0 0.134 14.644 8 4996 5139.1 3.983 18.627 9 3614 3699.9 1.993 20.620 10 2676 2666.3 0.035 20.655 11 1938 1923.3 0.112 20.767 12 1420 1388.7 0.704 21.471 13 1072 1003.7 4.646 26.117 14 749 726.1 0.720 26.836 15 542 525.8 0.497 27.333 16 347 381.2 3.060 30.393 17 274 276.5 0.023 30.416 18 202 200.8 0.007 30.423 19 133 146.0 1.155 31.578 20 87 106.2 3.476 35.054 21 309 287.1 1.668 36.722 Chisq= 36.72 for 20 degrees of freedom, p= 0.98737 SUMMARY of craptest p-value for no. of wins: 0.968644 p-value for throws/game: 0.987369 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0074,0.0098,0.0196,0.0216,0.0282,0.0297,0.0328,0.0329,0.0336, 0.0350,0.0400,0.0414,0.0557,0.0601,0.0711,0.0720,0.0798,0.0850,0.0879, 0.0944,0.0956,0.1002,0.1083,0.1179,0.1229,0.1235,0.1289,0.1321,0.1367, 0.1466,0.1508,0.1512,0.1522,0.1584,0.1642,0.1660,0.1671,0.1688,0.1720, 0.1738,0.1781,0.1790,0.1882,0.1913,0.1916,0.1918,0.2009,0.2085,0.2165, 0.2306,0.2429,0.2430,0.2514,0.2570,0.2597,0.2608,0.2615,0.2644,0.2659, 0.2762,0.2773,0.2793,0.2831,0.2845,0.2845,0.2859,0.2880,0.2921,0.2941, 0.2960,0.2965,0.3012,0.3069,0.3111,0.3187,0.3196,0.3210,0.3232,0.3240, 0.3247,0.3291,0.3366,0.3429,0.3503,0.3618,0.3626,0.3687,0.3724,0.3773, 0.3791,0.3813,0.3823,0.3839,0.3863,0.3864,0.3882,0.3920,0.3940,0.3968, 0.4002,0.4041,0.4068,0.4137,0.4155,0.4190,0.4222,0.4275,0.4285,0.4301, 0.4317,0.4328,0.4347,0.4447,0.4468,0.4486,0.4491,0.4515,0.4542,0.4611, 0.4613,0.4652,0.4679,0.4710,0.4829,0.4887,0.4899,0.4947,0.4951,0.4978, 0.5063,0.5078,0.5092,0.5145,0.5156,0.5202,0.5264,0.5293,0.5301,0.5312, 0.5354,0.5407,0.5433,0.5453,0.5454,0.5466,0.5541,0.5548,0.5561,0.5598, 0.5646,0.5655,0.5687,0.5775,0.5818,0.5826,0.5854,0.5984,0.5986,0.5986, 0.6038,0.6047,0.6067,0.6155,0.6168,0.6204,0.6221,0.6257,0.6271,0.6346, 0.6348,0.6402,0.6458,0.6522,0.6593,0.6594,0.6594,0.6620,0.6720,0.6723, 0.6750,0.6752,0.6760,0.6789,0.7050,0.7076,0.7088,0.7121,0.7136,0.7186, 0.7306,0.7330,0.7371,0.7377,0.7379,0.7411,0.7432,0.7438,0.7525,0.7574, 0.7575,0.7584,0.7636,0.7689,0.7731,0.7787,0.7812,0.7847,0.7877,0.7946, 0.8026,0.8067,0.8161,0.8194,0.8234,0.8252,0.8253,0.8331,0.8445,0.8463, 0.8467,0.8487,0.8507,0.8528,0.8533,0.8540,0.8543,0.8580,0.8583,0.8592, 0.8638,0.8661,0.8678,0.8687,0.8723,0.8757,0.8866,0.8894,0.8932,0.9000, 0.9018,0.9042,0.9112,0.9161,0.9196,0.9211,0.9238,0.9263,0.9327,0.9346, 0.9387,0.9470,0.9544,0.9563,0.9598,0.9631,0.9686,0.9739,0.9755,0.9775, 0.9784,0.9812,0.9861,0.9874,0.9893,0.9894,0.9947,0.9979,0.9987, Overall p-value after applying KStest on 269 p-values = 0.435516 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.