RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-25_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 30.7979 0.978867 2 to 25 16.19 19.1357 0.679199 3 to 26 16.06 11.3807 0.163894 4 to 27 15.84 15.2849 0.425031 5 to 28 15.93 21.7229 0.804388 6 to 29 15.59 23.6074 0.869499 7 to 30 15.76 31.7370 0.983780 8 to 31 15.86 18.1352 0.619639 9 to 32 15.70 16.9061 0.539257 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.095739 Tough bday spacings test for dh-ranFile-2015-10-25_11:31: 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 16 28 70 99 97 83 61 28 8 7 3 (O-E)^2/E 5.1 2.0 0.1 0.0 0.0 0.3 1.5 0.1 3.2 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.728, p= 0.761 RESULTS OF GCD FOR dh-ranFile-2015-10-25_11:31 Euclid's algorithm: p-value, steps to gcd: 0.464486 p-value, dist. of gcd's: 0.392616 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-25_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.114 0.949 0.096 0.743 0.971 0.602 0.142 0.656 Bits 8 to 15---> 0.051 0.692 0.332 0.757 0.720 0.069 0.561 0.932 Bits 16 to 23---> 0.609 0.337 0.951 0.505 0.726 0.546 0.489 0.648 Bits 24 to 31---> 0.912 0.329 0.714 0.349 0.420 0.324 0.260 0.407 KS test for the above 32 p values: 0.243 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-25_11:31, p-values for 5 runs: 0.8447, 0.3295, 0.1299, 0.2150, 0.0525 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5046 5134.0 1.509 1.928 r= 30 23201 23103.0 0.415 2.344 r= 31 11551 11551.5 0.000 2.344 chi-square = 2.344 with df = 3; p-value = 0.496 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5123 5134.0 0.024 0.640 r= 31 23209 23103.0 0.486 1.126 r= 32 11468 11551.5 0.604 1.730 chi-square = 1.730 with df = 3; p-value = 0.370 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-25_11:31 b-rank test for bits 1 to 8, p=0.09919 b-rank test for bits 2 to 9, p=0.41623 b-rank test for bits 3 to 10, p=0.16419 b-rank test for bits 4 to 11, p=0.00619 b-rank test for bits 5 to 12, p=0.33620 b-rank test for bits 6 to 13, p=0.37942 b-rank test for bits 7 to 14, p=0.68187 b-rank test for bits 8 to 15, p=0.56510 b-rank test for bits 9 to 16, p=0.77464 b-rank test for bits 10 to 17, p=0.95321 b-rank test for bits 11 to 18, p=0.14544 b-rank test for bits 12 to 19, p=0.20268 b-rank test for bits 13 to 20, p=0.08264 b-rank test for bits 14 to 21, p=0.54259 b-rank test for bits 15 to 22, p=0.86480 b-rank test for bits 16 to 23, p=0.43763 b-rank test for bits 17 to 24, p=0.21284 b-rank test for bits 18 to 25, p=0.72331 b-rank test for bits 19 to 26, p=0.77256 b-rank test for bits 20 to 27, p=0.81913 b-rank test for bits 21 to 28, p=0.75890 b-rank test for bits 22 to 29, p=0.99271 b-rank test for bits 23 to 30, p=0.07667 b-rank test for bits 24 to 31, p=0.23806 b-rank test for bits 25 to 32, p=0.76372 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 = 0.871595 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-25_11:31 (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 141610 -0.70 0.242161 2 142266 0.83 0.797674 3 141997 0.20 0.581150 4 142939 2.41 0.991931 5 141730 -0.42 0.337610 6 143374 3.42 0.999689 7 141885 -0.06 0.477334 8 142564 1.53 0.936942 9 142286 0.88 0.810589 10 141969 0.14 0.555439 11 141985 0.18 0.570167 12 142647 1.72 0.957603 13 142441 1.24 0.892922 14 141892 -0.04 0.483851 15 142241 0.77 0.780809 16 141720 -0.44 0.329114 17 142269 0.84 0.799644 18 142447 1.26 0.895485 19 142601 1.62 0.946958 20 142165 0.60 0.724866 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-25_11:31 Bits used No. missing words z-score p-value 23 to 32 141580 -1.1356 0.128058 22 to 31 141753 -0.5391 0.294920 21 to 30 141831 -0.2701 0.393540 20 to 29 142111 0.6954 0.756602 19 to 28 142190 0.9678 0.833435 18 to 27 141848 -0.2115 0.416255 17 to 26 142224 1.0851 0.861054 16 to 25 142114 0.7058 0.759831 15 to 24 141807 -0.3529 0.362096 14 to 23 142026 0.4023 0.656272 13 to 22 141921 0.0402 0.516050 12 to 21 141706 -0.7011 0.241609 11 to 20 141661 -0.8563 0.195913 10 to 19 142070 0.5540 0.710222 9 to 18 142254 1.1885 0.882685 8 to 17 141954 0.1540 0.561209 7 to 16 141524 -1.3287 0.091970 6 to 15 141274 -2.1908 0.014233 5 to 14 141853 -0.1942 0.422994 4 to 13 141979 0.2402 0.594928 3 to 12 141695 -0.7391 0.229933 2 to 11 141697 -0.7322 0.232032 1 to 10 141473 -1.5046 0.066215 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-25_11:31 Bits used No. missing words z-score p-value 28 to 32 141894 -0.0520 0.479278 27 to 31 142356 1.5141 0.935004 26 to 30 142039 0.4396 0.669872 25 to 29 141796 -0.3842 0.350426 24 to 28 141322 -1.9909 0.023243 23 to 27 141631 -0.9435 0.172715 22 to 26 141787 -0.4147 0.339189 21 to 25 141322 -1.9909 0.023243 20 to 24 141292 -2.0926 0.018190 19 to 23 142278 1.2497 0.894301 18 to 22 142261 1.1921 0.883389 17 to 21 142210 1.0192 0.845951 16 to 20 141842 -0.2282 0.409731 15 to 19 142191 0.9548 0.830164 14 to 18 142032 0.4158 0.661233 13 to 17 141994 0.2870 0.612950 12 to 16 141866 -0.1469 0.441613 11 to 15 142259 1.1853 0.882055 10 to 14 141614 -1.0011 0.158385 9 to 13 141788 -0.4113 0.340431 8 to 12 141882 -0.0926 0.463093 7 to 11 141750 -0.5401 0.294564 6 to 10 142271 1.2260 0.889901 5 to 9 141524 -1.3062 0.095742 4 to 8 141819 -0.3062 0.379725 3 to 7 141518 -1.3265 0.092330 2 to 6 141764 -0.4926 0.311132 1 to 5 142268 1.2158 0.887975 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-25_11:31 Bits used No. missing words z-score p-value 31 to 32 141735 -0.5142 0.303539 30 to 31 141951 0.1229 0.548915 29 to 30 141814 -0.2812 0.389275 28 to 29 141307 -1.7768 0.037802 27 to 28 141466 -1.3078 0.095478 26 to 27 141635 -0.8092 0.209191 25 to 26 141574 -0.9892 0.161289 24 to 25 141847 -0.1839 0.427060 23 to 24 141381 -1.5585 0.059558 22 to 23 142041 0.3884 0.651143 21 to 22 142676 2.2616 0.988138 20 to 21 142623 2.1052 0.982364 19 to 20 141717 -0.5673 0.285240 18 to 19 141989 0.2350 0.592901 17 to 18 142220 0.9164 0.820280 16 to 17 142054 0.4268 0.665221 15 to 16 142070 0.4740 0.682233 14 to 15 141921 0.0344 0.513731 13 to 14 141816 -0.2753 0.391539 12 to 13 141984 0.2203 0.587168 11 to 12 142179 0.7955 0.786835 10 to 11 141933 0.0698 0.527833 9 to 10 142100 0.5624 0.713095 8 to 9 141842 -0.1986 0.421283 7 to 8 141890 -0.0570 0.477264 6 to 7 140669 -3.6588 0.000127 5 to 6 141489 -1.2399 0.107504 4 to 5 142384 1.4002 0.919274 3 to 4 142243 0.9843 0.837510 2 to 3 141946 0.1082 0.543070 1 to 2 141802 -0.3166 0.375771 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2558.20 0.823 0.794765 Test results for specific bytes for dh-ranFile-2015-10-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2492.83 -0.101 0.459622 2 to 9 2477.72 -0.315 0.376350 3 to 10 2456.34 -0.617 0.268469 4 to 11 2536.63 0.518 0.697783 5 to 12 2603.10 1.458 0.927588 6 to 13 2564.53 0.913 0.819272 7 to 14 2434.79 -0.922 0.178225 8 to 15 2530.41 0.430 0.666430 9 to 16 2614.39 1.618 0.947140 10 to 17 2566.45 0.940 0.826321 11 to 18 2544.47 0.629 0.735301 12 to 19 2455.09 -0.635 0.262663 13 to 20 2463.15 -0.521 0.301155 14 to 21 2513.07 0.185 0.573326 15 to 22 2476.95 -0.326 0.372213 16 to 23 2544.70 0.632 0.736343 17 to 24 2466.57 -0.473 0.318163 18 to 25 2454.97 -0.637 0.262115 19 to 26 2427.58 -1.024 0.152863 20 to 27 2451.33 -0.688 0.245643 21 to 28 2450.04 -0.707 0.239907 22 to 29 2497.01 -0.042 0.483143 23 to 30 2400.77 -1.403 0.080271 24 to 31 2476.94 -0.326 0.372185 25 to 32 2425.00 -1.061 0.144425 CDPARK for dh-ranFile-2015-10-25_11:31: 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 3512 -0.5023 0.307734 3527 0.1826 0.572463 3568 2.0548 0.980051 3531 0.3653 0.642555 3520 -0.1370 0.445521 3561 1.7352 0.958644 3511 -0.5479 0.291865 3482 -1.8721 0.030593 3554 1.4155 0.921543 3529 0.2740 0.607947 Square side=100, avg. no. parked=3529.50 sample std.=24.65 p-value of the KSTEST for those 10 p-values: 0.472531 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-25_11:31 0.9089,0.2184,0.2201,0.0355,0.4540,0.3398,0.0915,0.5672,0.2437,0.5755, The KS test for those 10 p-values: 0.241593 The 3DSPHERES test for dh-ranFile-2015-10-25_11:31 sample no r^3 equiv. uni. 1 123.888 0.983911 2 3.165 0.100130 3 0.875 0.028748 4 24.746 0.561711 5 57.374 0.852284 6 17.603 0.443872 7 20.031 0.487119 8 6.788 0.202496 9 17.364 0.439428 10 8.344 0.242793 11 92.069 0.953532 12 8.739 0.252712 13 51.480 0.820215 14 54.278 0.836224 15 73.359 0.913298 16 42.787 0.759792 17 33.942 0.677418 18 37.213 0.710739 19 0.140 0.004661 20 6.571 0.196697 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.799412 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-25_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.6 -0.4 0.0 0.3 -0.1 -2.4 1.2 -0.7 1.7 -1.3 -2.6 -0.2 -0.5 -0.4 -0.2 0.7 -1.2 3.1 0.1 1.3 1.0 0.6 -1.5 -0.6 0.9 0.7 -1.3 -1.9 -0.4 0.9 -1.1 1.1 0.8 -0.4 0.1 0.0 -0.7 0.5 -0.7 -0.6 1.0 0.8 Chi-square with 42 degrees of freedom:53.060791 z-score=1.206831, p-value=0.882194 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-25_11:31 Test no p-value 1 0.000901 2 0.357173 3 0.333046 4 0.408223 5 0.090407 6 0.092275 7 0.016730 8 0.027718 9 0.684840 10 0.088365 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000517 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-25_11:31: (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 66647 0.01 66547 0.21 3 25000.00 25176 1.24 25023 0.02 4 6666.67 6542 2.33 6715 0.35 5 1388.89 1389 0.00 1426 0.99 6 238.10 210 3.32 248 0.41 7 34.72 29 0.94 36 0.05 8 4.96 6 0.22 4 0.19 p=0.76567 p=0.10190 Number of rngs required: 687657, p-value: 0.194 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-25_11:31 No. of wins: Observed Expected 98415 98585.9 z-score=-0.764, pvalue=0.22238 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66453 66666.7 0.685 0.685 2 37592 37654.3 0.103 0.788 3 27308 26954.7 4.630 5.418 4 19232 19313.5 0.344 5.761 5 13783 13851.4 0.338 6.099 6 9934 9943.5 0.009 6.109 7 7173 7145.0 0.110 6.218 8 5149 5139.1 0.019 6.237 9 3694 3699.9 0.009 6.247 10 2711 2666.3 0.749 6.996 11 1963 1923.3 0.818 7.814 12 1355 1388.7 0.820 8.634 13 972 1003.7 1.002 9.636 14 726 726.1 0.000 9.636 15 563 525.8 2.627 12.263 16 364 381.2 0.772 13.035 17 265 276.5 0.482 13.516 18 207 200.8 0.190 13.706 19 161 146.0 1.544 15.250 20 99 106.2 0.490 15.740 21 296 287.1 0.275 16.015 Chisq= 16.02 for 20 degrees of freedom, p= 0.28432 SUMMARY of craptest p-value for no. of wins: 0.222380 p-value for throws/game: 0.284323 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-25_11:31 No. of wins: Observed Expected 98939 98585.9 z-score= 1.579, pvalue=0.94288 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66972 66666.7 1.398 1.398 2 37896 37654.3 1.551 2.950 3 26745 26954.7 1.632 4.582 4 19169 19313.5 1.081 5.662 5 13919 13851.4 0.330 5.992 6 9917 9943.5 0.071 6.063 7 6969 7145.0 4.337 10.399 8 5100 5139.1 0.297 10.696 9 3687 3699.9 0.045 10.741 10 2668 2666.3 0.001 10.742 11 1930 1923.3 0.023 10.765 12 1385 1388.7 0.010 10.775 13 1006 1003.7 0.005 10.781 14 700 726.1 0.941 11.722 15 557 525.8 1.847 13.569 16 391 381.2 0.255 13.823 17 278 276.5 0.008 13.831 18 216 200.8 1.146 14.977 19 139 146.0 0.334 15.311 20 112 106.2 0.315 15.626 21 244 287.1 6.474 22.100 Chisq= 22.10 for 20 degrees of freedom, p= 0.66489 SUMMARY of craptest p-value for no. of wins: 0.942884 p-value for throws/game: 0.664893 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0005,0.0009,0.0047,0.0062,0.0142,0.0167,0.0182,0.0232,0.0232, 0.0277,0.0287,0.0306,0.0355,0.0378,0.0513,0.0525,0.0596,0.0662,0.0689, 0.0767,0.0803,0.0826,0.0884,0.0904,0.0915,0.0920,0.0923,0.0923,0.0955, 0.0957,0.0957,0.0958,0.0992,0.1001,0.1019,0.1075,0.1137,0.1281,0.1299, 0.1418,0.1444,0.1454,0.1529,0.1584,0.1613,0.1639,0.1642,0.1727,0.1782, 0.1941,0.1959,0.1967,0.2025,0.2027,0.2092,0.2128,0.2150,0.2184,0.2201, 0.2224,0.2299,0.2320,0.2381,0.2399,0.2416,0.2416,0.2422,0.2428,0.2429, 0.2437,0.2456,0.2527,0.2601,0.2621,0.2627,0.2685,0.2843,0.2852,0.2919, 0.2946,0.2949,0.3012,0.3035,0.3077,0.3111,0.3182,0.3240,0.3291,0.3293, 0.3295,0.3316,0.3330,0.3362,0.3366,0.3376,0.3392,0.3398,0.3404,0.3488, 0.3504,0.3572,0.3621,0.3697,0.3722,0.3722,0.3758,0.3764,0.3794,0.3797, 0.3893,0.3915,0.3926,0.3935,0.4071,0.4082,0.4097,0.4162,0.4163,0.4197, 0.4213,0.4230,0.4250,0.4271,0.4376,0.4394,0.4416,0.4439,0.4455,0.4540, 0.4596,0.4631,0.4645,0.4725,0.4773,0.4773,0.4793,0.4831,0.4839,0.4871, 0.4895,0.4958,0.5048,0.5137,0.5160,0.5278,0.5393,0.5426,0.5431,0.5459, 0.5489,0.5554,0.5605,0.5612,0.5617,0.5651,0.5672,0.5702,0.5725,0.5733, 0.5755,0.5812,0.5872,0.5929,0.5949,0.6020,0.6079,0.6085,0.6130,0.6196, 0.6426,0.6481,0.6511,0.6555,0.6563,0.6612,0.6649,0.6652,0.6664,0.6699, 0.6774,0.6792,0.6819,0.6822,0.6848,0.6915,0.6978,0.7102,0.7107,0.7131, 0.7143,0.7201,0.7233,0.7249,0.7260,0.7353,0.7363,0.7430,0.7566,0.7567, 0.7589,0.7598,0.7598,0.7607,0.7637,0.7657,0.7726,0.7746,0.7808,0.7868, 0.7948,0.7977,0.7994,0.7996,0.8044,0.8106,0.8191,0.8193,0.8202,0.8203, 0.8263,0.8302,0.8334,0.8362,0.8375,0.8447,0.8460,0.8523,0.8611,0.8648, 0.8695,0.8716,0.8821,0.8822,0.8827,0.8834,0.8880,0.8899,0.8929,0.8943, 0.8955,0.9089,0.9122,0.9133,0.9193,0.9215,0.9276,0.9318,0.9350,0.9369, 0.9429,0.9470,0.9471,0.9493,0.9505,0.9532,0.9535,0.9576,0.9586,0.9706, 0.9789,0.9801,0.9824,0.9838,0.9839,0.9881,0.9919,0.9927,0.9997, Overall p-value after applying KStest on 269 p-values = 0.813660 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.