RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-28_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.14 13.0663 0.268266 2 to 25 16.06 20.5236 0.751671 3 to 26 15.58 17.0942 0.551997 4 to 27 15.76 19.4633 0.697403 5 to 28 15.87 19.7225 0.711333 6 to 29 15.78 20.3897 0.745215 7 to 30 15.96 19.7440 0.712466 8 to 31 15.86 17.4687 0.576928 9 to 32 15.69 14.2990 0.354163 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.166982 Tough bday spacings test for dh-ranFile-2016-01-28_22:31: 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 10 49 74 100 90 62 57 29 17 7 5 (O-E)^2/E 0.1 4.2 0.0 0.1 0.6 3.3 0.5 0.0 0.3 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.275, p= 0.494 RESULTS OF GCD FOR dh-ranFile-2016-01-28_22:31 Euclid's algorithm: p-value, steps to gcd: 0.205263 p-value, dist. of gcd's: 0.114045 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-28_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.137 0.647 0.275 0.895 0.139 0.534 0.630 0.926 Bits 8 to 15---> 0.184 0.815 0.622 0.619 0.103 0.528 0.230 0.824 Bits 16 to 23---> 0.495 0.185 0.236 0.779 0.989 0.687 0.929 0.806 Bits 24 to 31---> 0.216 0.387 0.861 0.115 0.800 0.676 0.223 0.574 KS test for the above 32 p values: 0.383 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-28_22:31, p-values for 5 runs: 0.9021, 0.2744, 0.4344, 0.7249, 0.1502 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-28_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5043 5134.0 1.613 1.669 r= 30 23010 23103.0 0.375 2.043 r= 31 11739 11551.5 3.043 5.086 chi-square = 5.086 with df = 3; p-value = 0.834 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-28_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5057 5134.0 1.155 1.183 r= 31 23165 23103.0 0.166 1.349 r= 32 11569 11551.5 0.026 1.375 chi-square = 1.375 with df = 3; p-value = 0.289 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-28_22:31 b-rank test for bits 1 to 8, p=0.92899 b-rank test for bits 2 to 9, p=0.20199 b-rank test for bits 3 to 10, p=0.07769 b-rank test for bits 4 to 11, p=0.21350 b-rank test for bits 5 to 12, p=0.47391 b-rank test for bits 6 to 13, p=0.70416 b-rank test for bits 7 to 14, p=0.41933 b-rank test for bits 8 to 15, p=0.00031 b-rank test for bits 9 to 16, p=0.41857 b-rank test for bits 10 to 17, p=0.14066 b-rank test for bits 11 to 18, p=0.76458 b-rank test for bits 12 to 19, p=0.00215 b-rank test for bits 13 to 20, p=0.27188 b-rank test for bits 14 to 21, p=0.57685 b-rank test for bits 15 to 22, p=0.69762 b-rank test for bits 16 to 23, p=0.13024 b-rank test for bits 17 to 24, p=0.67499 b-rank test for bits 18 to 25, p=0.48492 b-rank test for bits 19 to 26, p=0.04950 b-rank test for bits 20 to 27, p=0.56116 b-rank test for bits 21 to 28, p=0.84884 b-rank test for bits 22 to 29, p=0.76960 b-rank test for bits 23 to 30, p=0.09152 b-rank test for bits 24 to 31, p=0.54408 b-rank test for bits 25 to 32, p=0.72136 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 = 0.191928 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-28_22:31 (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 142408 1.17 0.878014 2 141942 0.08 0.530422 3 141426 -1.13 0.129391 4 142620 1.66 0.951587 5 141997 0.20 0.581150 6 142036 0.30 0.616369 7 142362 1.06 0.854890 8 141650 -0.61 0.272287 9 142151 0.56 0.713844 10 142311 0.94 0.826001 11 142507 1.40 0.918707 12 142373 1.08 0.860672 13 142210 0.70 0.758816 14 141362 -1.28 0.100482 15 141398 -1.19 0.116103 16 141549 -0.84 0.199924 17 141484 -0.99 0.160169 18 142375 1.09 0.861706 19 142601 1.62 0.946958 20 141646 -0.62 0.269193 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-28_22:31 Bits used No. missing words z-score p-value 23 to 32 141905 -0.0149 0.494044 22 to 31 142108 0.6851 0.753350 21 to 30 141630 -0.9632 0.167722 20 to 29 141675 -0.8080 0.209535 19 to 28 141685 -0.7736 0.219598 18 to 27 142350 1.5196 0.935688 17 to 26 142224 1.0851 0.861054 16 to 25 141592 -1.0942 0.136925 15 to 24 141825 -0.2908 0.385605 14 to 23 141939 0.1023 0.540745 13 to 22 141570 -1.1701 0.120980 12 to 21 141948 0.1333 0.553040 11 to 20 142263 1.2196 0.888683 10 to 19 141778 -0.4529 0.325324 9 to 18 141997 0.3023 0.618792 8 to 17 142034 0.4299 0.666365 7 to 16 141912 0.0092 0.503673 6 to 15 141668 -0.8322 0.202656 5 to 14 142061 0.5230 0.699513 4 to 13 141558 -1.2115 0.112855 3 to 12 142384 1.6368 0.949163 2 to 11 142316 1.4023 0.919589 1 to 10 141781 -0.4425 0.329058 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-28_22:31 Bits used No. missing words z-score p-value 28 to 32 142009 0.3379 0.632267 27 to 31 141909 -0.0011 0.499554 26 to 30 142094 0.6260 0.734343 25 to 29 141989 0.2701 0.606446 24 to 28 142073 0.5548 0.710489 23 to 27 141832 -0.2621 0.396609 22 to 26 141494 -1.4079 0.079581 21 to 25 141919 0.0328 0.513075 20 to 24 141898 -0.0384 0.484682 19 to 23 141906 -0.0113 0.495497 18 to 22 142181 0.9209 0.821453 17 to 21 142035 0.4260 0.664946 16 to 20 142443 1.8091 0.964778 15 to 19 142261 1.1921 0.883389 14 to 18 142089 0.6091 0.728755 13 to 17 142147 0.8057 0.789781 12 to 16 142186 0.9379 0.825843 11 to 15 141883 -0.0893 0.464440 10 to 14 142229 1.0836 0.860735 9 to 13 142090 0.6124 0.729877 8 to 12 142633 2.4531 0.992919 7 to 11 141810 -0.3367 0.368167 6 to 10 141440 -1.5909 0.055811 5 to 9 141883 -0.0893 0.464440 4 to 8 141882 -0.0926 0.463093 3 to 7 141970 0.2057 0.581472 2 to 6 141883 -0.0893 0.464440 1 to 5 141337 -1.9401 0.026184 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-28_22:31 Bits used No. missing words z-score p-value 31 to 32 142131 0.6539 0.743410 30 to 31 141379 -1.5644 0.058862 29 to 30 142210 0.8869 0.812442 28 to 29 141952 0.1259 0.550083 27 to 28 142366 1.3471 0.911027 26 to 27 142291 1.1259 0.869890 25 to 26 142170 0.7689 0.779035 24 to 25 141480 -1.2665 0.102674 23 to 24 142400 1.4474 0.926108 22 to 23 142014 0.3088 0.621248 21 to 22 142439 1.5624 0.940909 20 to 21 141962 0.1554 0.561735 19 to 20 141621 -0.8505 0.197515 18 to 19 141763 -0.4317 0.332997 17 to 18 141299 -1.8004 0.035900 16 to 17 141462 -1.3196 0.093491 15 to 16 142350 1.2999 0.903184 14 to 15 141647 -0.7738 0.219514 13 to 14 141593 -0.9331 0.175377 12 to 13 141933 0.0698 0.527833 11 to 12 141520 -1.1485 0.125388 10 to 11 141732 -0.5231 0.300453 9 to 10 141873 -0.1072 0.457328 8 to 9 141657 -0.7443 0.228337 7 to 8 141577 -0.9803 0.163463 6 to 7 141685 -0.6617 0.254069 5 to 6 141811 -0.2901 0.385886 4 to 5 141848 -0.1809 0.428217 3 to 4 142216 0.9046 0.817170 2 to 3 141862 -0.1396 0.444482 1 to 2 141948 0.1141 0.545409 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-28_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2533.25 0.470 0.680893 Test results for specific bytes for dh-ranFile-2016-01-28_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2624.35 1.759 0.960680 2 to 9 2430.69 -0.980 0.163493 3 to 10 2635.23 1.913 0.972094 4 to 11 2686.50 2.637 0.995824 5 to 12 2441.95 -0.821 0.205837 6 to 13 2482.89 -0.242 0.404374 7 to 14 2444.47 -0.785 0.216117 8 to 15 2501.29 0.018 0.507294 9 to 16 2609.19 1.544 0.938725 10 to 17 2515.79 0.223 0.588349 11 to 18 2480.19 -0.280 0.389704 12 to 19 2557.53 0.814 0.792057 13 to 20 2579.92 1.130 0.870820 14 to 21 2423.98 -1.075 0.141160 15 to 22 2450.01 -0.707 0.239803 16 to 23 2477.96 -0.312 0.377649 17 to 24 2542.80 0.605 0.727518 18 to 25 2437.35 -0.886 0.187801 19 to 26 2474.74 -0.357 0.360485 20 to 27 2584.15 1.190 0.882995 21 to 28 2424.48 -1.068 0.142764 22 to 29 2582.65 1.169 0.878772 23 to 30 2449.93 -0.708 0.239439 24 to 31 2478.73 -0.301 0.381762 25 to 32 2562.54 0.884 0.811784 CDPARK for dh-ranFile-2016-01-28_22:31: 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 3503 -0.9132 0.180558 3491 -1.4612 0.071982 3522 -0.0457 0.481790 3509 -0.6393 0.261324 3523 0.0000 0.500000 3554 1.4155 0.921543 3524 0.0457 0.518210 3485 -1.7352 0.041356 3571 2.1918 0.985802 3551 1.2785 0.899470 Square side=100, avg. no. parked=3523.30 sample std.=26.67 p-value of the KSTEST for those 10 p-values: 0.649860 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-28_22:31 0.5793,0.9659,0.8605,0.0601,0.8359,0.2381,0.0220,0.6384,0.2860,0.8620, The KS test for those 10 p-values: 0.625450 The 3DSPHERES test for dh-ranFile-2016-01-28_22:31 sample no r^3 equiv. uni. 1 61.812 0.872595 2 9.679 0.275762 3 33.932 0.677306 4 51.416 0.819834 5 58.826 0.859265 6 31.083 0.645158 7 0.858 0.028190 8 64.352 0.882941 9 15.337 0.400253 10 10.631 0.298380 11 156.819 0.994632 12 68.263 0.897248 13 0.990 0.032465 14 8.133 0.237462 15 22.774 0.531931 16 3.270 0.103281 17 14.331 0.379790 18 74.410 0.916285 19 55.099 0.840648 20 8.160 0.238135 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.423060 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-28_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.7 -0.4 -0.5 -0.9 1.5 -2.4 -0.5 -1.0 -1.4 0.3 -0.7 1.0 1.4 0.1 -0.1 0.8 1.0 -0.2 -0.5 1.0 -0.5 0.1 -0.7 1.1 -1.2 -0.4 0.3 -0.9 0.1 -1.9 -1.2 -1.3 0.5 -0.8 -0.1 0.3 0.8 -1.2 -0.1 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:39.049979 z-score=-0.321874, p-value=0.398790 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-28_22:31 Test no p-value 1 0.275643 2 0.011462 3 0.498500 4 0.747831 5 0.034050 6 0.449527 7 0.440433 8 0.073124 9 0.334650 10 0.553961 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.100729 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-28_22:31: (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 66964 1.33 66705 0.02 3 25000.00 24733 2.85 24993 0.00 4 6666.67 6676 0.01 6687 0.06 5 1388.89 1340 1.72 1328 2.67 6 238.10 250 0.60 249 0.50 7 34.72 32 0.21 37 0.15 8 4.96 4 0.19 0 4.96 p=0.67035 p=0.78741 Number of rngs required: 688445, p-value: 0.519 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-28_22:31 No. of wins: Observed Expected 98358 98585.9 z-score=-1.019, pvalue=0.15407 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66561 66666.7 0.167 0.167 2 37754 37654.3 0.264 0.431 3 26969 26954.7 0.008 0.439 4 19526 19313.5 2.339 2.778 5 13859 13851.4 0.004 2.782 6 9877 9943.5 0.445 3.227 7 7195 7145.0 0.350 3.577 8 5125 5139.1 0.039 3.615 9 3667 3699.9 0.292 3.907 10 2681 2666.3 0.081 3.988 11 1862 1923.3 1.956 5.944 12 1319 1388.7 3.502 9.446 13 985 1003.7 0.349 9.795 14 706 726.1 0.559 10.354 15 543 525.8 0.560 10.914 16 401 381.2 1.034 11.948 17 243 276.5 4.068 16.016 18 174 200.8 3.584 19.600 19 149 146.0 0.062 19.662 20 109 106.2 0.073 19.735 21 295 287.1 0.217 19.952 Chisq= 19.95 for 20 degrees of freedom, p= 0.53905 SUMMARY of craptest p-value for no. of wins: 0.154074 p-value for throws/game: 0.539049 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-28_22:31 No. of wins: Observed Expected 98554 98585.9 z-score=-0.142, pvalue=0.44335 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66644 66666.7 0.008 0.008 2 37444 37654.3 1.175 1.182 3 27055 26954.7 0.373 1.555 4 19240 19313.5 0.279 1.835 5 14023 13851.4 2.125 3.960 6 9894 9943.5 0.247 4.207 7 7300 7145.0 3.361 7.568 8 5206 5139.1 0.872 8.440 9 3644 3699.9 0.844 9.284 10 2693 2666.3 0.267 9.551 11 1921 1923.3 0.003 9.554 12 1354 1388.7 0.869 10.423 13 989 1003.7 0.216 10.639 14 770 726.1 2.649 13.288 15 479 525.8 4.172 17.459 16 360 381.2 1.174 18.633 17 259 276.5 1.112 19.746 18 189 200.8 0.697 20.442 19 151 146.0 0.172 20.615 20 100 106.2 0.364 20.978 21 285 287.1 0.016 20.994 Chisq= 20.99 for 20 degrees of freedom, p= 0.60251 SUMMARY of craptest p-value for no. of wins: 0.443346 p-value for throws/game: 0.602512 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0021,0.0115,0.0220,0.0262,0.0282,0.0325,0.0340,0.0359,0.0414, 0.0495,0.0558,0.0589,0.0601,0.0720,0.0731,0.0777,0.0796,0.0915,0.0935, 0.1005,0.1007,0.1027,0.1028,0.1033,0.1129,0.1140,0.1149,0.1161,0.1210, 0.1254,0.1294,0.1302,0.1369,0.1374,0.1388,0.1407,0.1412,0.1428,0.1502, 0.1541,0.1602,0.1635,0.1635,0.1670,0.1677,0.1754,0.1806,0.1836,0.1850, 0.1878,0.1919,0.1975,0.1999,0.2020,0.2027,0.2053,0.2058,0.2095,0.2135, 0.2159,0.2161,0.2195,0.2196,0.2226,0.2283,0.2302,0.2357,0.2375,0.2381, 0.2381,0.2394,0.2398,0.2541,0.2613,0.2683,0.2692,0.2719,0.2723,0.2744, 0.2747,0.2756,0.2758,0.2860,0.2887,0.2984,0.3005,0.3253,0.3291,0.3330, 0.3346,0.3542,0.3605,0.3682,0.3776,0.3798,0.3818,0.3832,0.3856,0.3859, 0.3869,0.3897,0.3966,0.3988,0.4003,0.4044,0.4186,0.4193,0.4231,0.4282, 0.4344,0.4404,0.4433,0.4445,0.4495,0.4573,0.4631,0.4644,0.4644,0.4644, 0.4739,0.4818,0.4847,0.4849,0.4938,0.4940,0.4950,0.4955,0.4985,0.4996, 0.5000,0.5037,0.5073,0.5131,0.5182,0.5193,0.5277,0.5278,0.5304,0.5319, 0.5340,0.5390,0.5407,0.5441,0.5454,0.5501,0.5520,0.5530,0.5540,0.5612, 0.5617,0.5735,0.5768,0.5769,0.5793,0.5812,0.5815,0.5883,0.6025,0.6064, 0.6164,0.6188,0.6190,0.6212,0.6218,0.6255,0.6297,0.6323,0.6384,0.6452, 0.6467,0.6499,0.6649,0.6664,0.6704,0.6750,0.6759,0.6773,0.6809,0.6873, 0.6974,0.6976,0.6995,0.7042,0.7105,0.7113,0.7125,0.7138,0.7214,0.7249, 0.7275,0.7288,0.7299,0.7343,0.7434,0.7452,0.7478,0.7517,0.7533,0.7588, 0.7646,0.7696,0.7790,0.7794,0.7874,0.7898,0.7921,0.7998,0.8063,0.8118, 0.8124,0.8149,0.8172,0.8198,0.8215,0.8235,0.8258,0.8260,0.8344,0.8359, 0.8406,0.8488,0.8549,0.8593,0.8605,0.8607,0.8607,0.8607,0.8611,0.8617, 0.8620,0.8699,0.8708,0.8726,0.8780,0.8788,0.8829,0.8830,0.8834,0.8887, 0.8953,0.8972,0.8995,0.9021,0.9032,0.9110,0.9163,0.9187,0.9196,0.9215, 0.9260,0.9261,0.9289,0.9290,0.9357,0.9387,0.9409,0.9470,0.9492,0.9516, 0.9607,0.9648,0.9659,0.9721,0.9858,0.9893,0.9929,0.9946,0.9958, Overall p-value after applying KStest on 269 p-values = 0.770247 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.