RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-15_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 15.73 25.9592 0.924792 2 to 25 15.79 6.5100 0.010950 3 to 26 15.75 21.2572 0.785004 4 to 27 15.55 17.0154 0.546676 5 to 28 15.88 13.4331 0.293254 6 to 29 15.49 17.0427 0.548526 7 to 30 15.48 15.2977 0.425951 8 to 31 15.47 33.9413 0.991456 9 to 32 15.45 20.1689 0.734320 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.504455 Tough bday spacings test for dh-ranFile-2015-11-15_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 11 33 62 104 101 71 51 31 19 11 6 (O-E)^2/E 0.4 0.4 1.7 0.4 0.1 0.7 0.0 0.1 1.1 2.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 8.674, p= 0.437 RESULTS OF GCD FOR dh-ranFile-2015-11-15_22:31 Euclid's algorithm: p-value, steps to gcd: 0.953427 p-value, dist. of gcd's: 0.222129 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-15_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.338 0.476 0.074 0.958 0.332 0.018 0.968 0.640 Bits 8 to 15---> 0.261 0.471 0.251 0.472 0.533 0.813 0.277 0.908 Bits 16 to 23---> 0.587 0.953 0.477 0.445 0.503 0.945 0.223 0.486 Bits 24 to 31---> 0.921 0.648 0.635 0.167 0.507 0.641 0.591 0.779 KS test for the above 32 p values: 0.607 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-15_22:31, p-values for 5 runs: 0.2603, 0.0137, 0.3261, 0.4949, 0.1520 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-15_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5109 5134.0 0.122 0.327 r= 30 23047 23103.0 0.136 0.463 r= 31 11626 11551.5 0.480 0.943 chi-square = 0.943 with df = 3; p-value = 0.185 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-15_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5149 5134.0 0.044 0.191 r= 31 23091 23103.0 0.006 0.197 r= 32 11543 11551.5 0.006 0.204 chi-square = 0.204 with df = 3; p-value = 0.023 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-15_22:31 b-rank test for bits 1 to 8, p=0.01282 b-rank test for bits 2 to 9, p=0.88427 b-rank test for bits 3 to 10, p=0.32261 b-rank test for bits 4 to 11, p=0.21211 b-rank test for bits 5 to 12, p=0.25330 b-rank test for bits 6 to 13, p=0.85639 b-rank test for bits 7 to 14, p=0.35034 b-rank test for bits 8 to 15, p=0.11690 b-rank test for bits 9 to 16, p=0.90272 b-rank test for bits 10 to 17, p=0.07086 b-rank test for bits 11 to 18, p=0.12334 b-rank test for bits 12 to 19, p=0.76053 b-rank test for bits 13 to 20, p=0.08106 b-rank test for bits 14 to 21, p=0.86297 b-rank test for bits 15 to 22, p=0.27694 b-rank test for bits 16 to 23, p=0.53510 b-rank test for bits 17 to 24, p=0.97918 b-rank test for bits 18 to 25, p=0.89794 b-rank test for bits 19 to 26, p=0.69200 b-rank test for bits 20 to 27, p=0.42054 b-rank test for bits 21 to 28, p=0.30826 b-rank test for bits 22 to 29, p=0.37588 b-rank test for bits 23 to 30, p=0.64549 b-rank test for bits 24 to 31, p=0.23674 b-rank test for bits 25 to 32, p=0.35961 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 = 0.615277 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-15_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 141905 -0.01 0.495964 2 142264 0.83 0.796354 3 141819 -0.21 0.416424 4 141811 -0.23 0.409146 5 142363 1.06 0.855422 6 140872 -2.42 0.007682 7 142613 1.64 0.949921 8 142338 1.00 0.841723 9 141883 -0.06 0.475473 10 142189 0.65 0.743262 11 142440 1.24 0.892491 12 142361 1.06 0.854357 13 142007 0.23 0.590255 14 141333 -1.35 0.089060 15 142414 1.18 0.880828 16 142254 0.81 0.789678 17 141082 -1.93 0.026617 18 141976 0.16 0.561893 19 141614 -0.69 0.245090 20 141276 -1.48 0.069471 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-15_22:31 Bits used No. missing words z-score p-value 23 to 32 141984 0.2575 0.601597 22 to 31 142645 2.5368 0.994406 21 to 30 142350 1.5196 0.935688 20 to 29 142130 0.7609 0.776651 19 to 28 141440 -1.6184 0.052790 18 to 27 142086 0.6092 0.728806 17 to 26 141849 -0.2080 0.417601 16 to 25 141817 -0.3184 0.375099 15 to 24 142030 0.4161 0.661333 14 to 23 141870 -0.1356 0.446061 13 to 22 142204 1.0161 0.845210 12 to 21 141632 -0.9563 0.169458 11 to 20 141561 -1.2011 0.114849 10 to 19 142028 0.4092 0.658806 9 to 18 142348 1.5127 0.934816 8 to 17 142003 0.3230 0.626652 7 to 16 141747 -0.5598 0.287822 6 to 15 142357 1.5437 0.938668 5 to 14 142215 1.0540 0.854066 4 to 13 142224 1.0851 0.861054 3 to 12 142226 1.0920 0.862576 2 to 11 142278 1.2713 0.898185 1 to 10 142128 0.7540 0.774586 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-15_22:31 Bits used No. missing words z-score p-value 28 to 32 141723 -0.6316 0.263815 27 to 31 142085 0.5955 0.724243 26 to 30 141901 -0.0282 0.488737 25 to 29 141951 0.1413 0.556166 24 to 28 141775 -0.4554 0.324427 23 to 27 141869 -0.1367 0.445629 22 to 26 142266 1.2091 0.886678 21 to 25 141729 -0.6113 0.270504 20 to 24 141790 -0.4045 0.342919 19 to 23 141370 -1.8282 0.033757 18 to 22 141683 -0.7672 0.221475 17 to 21 141900 -0.0316 0.487385 16 to 20 141806 -0.3503 0.363068 15 to 19 141366 -1.8418 0.032752 14 to 18 141710 -0.6757 0.249617 13 to 17 141686 -0.7571 0.224510 12 to 16 142309 1.3548 0.912262 11 to 15 141932 0.0768 0.530628 10 to 14 142390 1.6294 0.948385 9 to 13 142177 0.9074 0.817891 8 to 12 141981 0.2429 0.595978 7 to 11 142175 0.9006 0.816093 6 to 10 141898 -0.0384 0.484682 5 to 9 141531 -1.2825 0.099838 4 to 8 141561 -1.1808 0.118845 3 to 7 142173 0.8938 0.814285 2 to 6 141974 0.2192 0.586761 1 to 5 141520 -1.3198 0.093457 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-15_22:31 Bits used No. missing words z-score p-value 31 to 32 141668 -0.7119 0.238267 30 to 31 142198 0.8515 0.802764 29 to 30 142166 0.7571 0.775517 28 to 29 141693 -0.6381 0.261691 27 to 28 141682 -0.6706 0.251241 26 to 27 141442 -1.3786 0.084016 25 to 26 141459 -1.3284 0.092022 24 to 25 142101 0.5654 0.714099 23 to 24 142150 0.7099 0.761130 22 to 23 142300 1.1524 0.875426 21 to 22 141768 -0.4169 0.338375 20 to 21 141331 -1.7060 0.044005 19 to 20 142039 0.3825 0.648958 18 to 19 141693 -0.6381 0.261691 17 to 18 141842 -0.1986 0.421283 16 to 17 142237 0.9666 0.833123 15 to 16 142117 0.6126 0.729928 14 to 15 141623 -0.8446 0.199158 13 to 14 142495 1.7276 0.957974 12 to 13 141452 -1.3491 0.088660 11 to 12 142167 0.7601 0.776399 10 to 11 142236 0.9636 0.832384 9 to 10 141186 -2.1337 0.016433 8 to 9 141836 -0.2163 0.414372 7 to 8 142200 0.8574 0.804397 6 to 7 142132 0.6568 0.744359 5 to 6 141969 0.1760 0.569860 4 to 5 142096 0.5506 0.709063 3 to 4 142040 0.3855 0.650051 2 to 3 141950 0.1200 0.547747 1 to 2 142351 1.3029 0.903689 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-15_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2400.11 -1.413 0.078887 Test results for specific bytes for dh-ranFile-2015-11-15_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2576.64 1.084 0.860770 2 to 9 2524.75 0.350 0.636814 3 to 10 2503.42 0.048 0.519303 4 to 11 2407.80 -1.304 0.096136 5 to 12 2501.22 0.017 0.506872 6 to 13 2602.49 1.449 0.926396 7 to 14 2556.23 0.795 0.786753 8 to 15 2503.29 0.046 0.518533 9 to 16 2654.71 2.188 0.985663 10 to 17 2560.45 0.855 0.803690 11 to 18 2438.90 -0.864 0.193774 12 to 19 2614.27 1.616 0.946948 13 to 20 2619.41 1.689 0.954364 14 to 21 2517.33 0.245 0.596792 15 to 22 2463.82 -0.512 0.304419 16 to 23 2454.09 -0.649 0.258090 17 to 24 2364.03 -1.923 0.027242 18 to 25 2544.27 0.626 0.734373 19 to 26 2464.23 -0.506 0.306490 20 to 27 2423.06 -1.088 0.138272 21 to 28 2470.97 -0.411 0.340690 22 to 29 2440.39 -0.843 0.199610 23 to 30 2528.82 0.408 0.658231 24 to 31 2532.86 0.465 0.678908 25 to 32 2456.66 -0.613 0.269950 CDPARK for dh-ranFile-2015-11-15_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 3572 2.2374 0.987371 3513 -0.4566 0.323972 3529 0.2740 0.607947 3512 -0.5023 0.307734 3530 0.3196 0.625377 3492 -1.4155 0.078457 3537 0.6393 0.738676 3561 1.7352 0.958644 3542 0.8676 0.807188 3498 -1.1416 0.126820 Square side=100, avg. no. parked=3528.60 sample std.=24.45 p-value of the KSTEST for those 10 p-values: 0.703519 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-15_22:31 0.1827,0.7480,0.1616,0.0916,0.8921,0.2532,0.7518,0.6260,0.7969,0.3774, The KS test for those 10 p-values: 0.913328 The 3DSPHERES test for dh-ranFile-2015-11-15_22:31 sample no r^3 equiv. uni. 1 146.056 0.992315 2 69.574 0.901640 3 50.548 0.814546 4 28.996 0.619607 5 4.268 0.132622 6 17.056 0.433639 7 33.036 0.667530 8 8.471 0.246015 9 12.211 0.334380 10 5.052 0.154997 11 122.780 0.983305 12 28.502 0.613289 13 17.942 0.450120 14 41.762 0.751440 15 5.820 0.176334 16 69.103 0.900085 17 64.531 0.883637 18 21.702 0.514908 19 42.496 0.757450 20 4.104 0.127855 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.385898 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-15_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 2.3 -1.6 1.1 -0.6 0.3 -0.9 -0.4 0.7 0.8 1.4 1.3 1.0 1.0 -2.0 -0.8 0.8 0.5 -2.8 -1.6 -1.4 0.6 0.2 0.5 1.1 1.0 0.2 0.9 -0.5 1.6 0.2 -0.5 -1.0 -0.6 0.4 2.1 -1.0 -0.4 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:49.659822 z-score=0.835755, p-value=0.805527 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-15_22:31 Test no p-value 1 0.008067 2 0.125692 3 0.010744 4 0.079225 5 0.436718 6 0.089728 7 0.884381 8 0.704017 9 0.086836 10 0.010298 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000401 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-15_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 66723 0.05 66581 0.11 3 25000.00 24781 1.92 24864 0.74 4 6666.67 6770 1.60 6802 2.75 5 1388.89 1435 1.53 1471 4.85 6 238.10 253 0.93 238 0.00 7 34.72 33 0.09 41 1.14 8 4.96 4 0.19 2 1.77 p=0.60983 p=0.92196 Number of rngs required: 689515, p-value: 0.902 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-15_22:31 No. of wins: Observed Expected 98827 98585.9 z-score= 1.079, pvalue=0.85960 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66896 66666.7 0.789 0.789 2 37149 37654.3 6.781 7.570 3 27036 26954.7 0.245 7.815 4 19300 19313.5 0.009 7.825 5 13984 13851.4 1.269 9.094 6 9780 9943.5 2.690 11.784 7 7139 7145.0 0.005 11.789 8 5152 5139.1 0.033 11.821 9 3711 3699.9 0.034 11.855 10 2708 2666.3 0.652 12.507 11 1952 1923.3 0.427 12.934 12 1438 1388.7 1.747 14.682 13 1043 1003.7 1.538 16.219 14 805 726.1 8.564 24.783 15 513 525.8 0.313 25.097 16 380 381.2 0.003 25.100 17 260 276.5 0.989 26.089 18 206 200.8 0.133 26.222 19 146 146.0 0.000 26.222 20 114 106.2 0.571 26.793 21 288 287.1 0.003 26.796 Chisq= 26.80 for 20 degrees of freedom, p= 0.85889 SUMMARY of craptest p-value for no. of wins: 0.859600 p-value for throws/game: 0.858892 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-15_22:31 No. of wins: Observed Expected 98746 98585.9 z-score= 0.716, pvalue=0.76308 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66592 66666.7 0.084 0.084 2 37676 37654.3 0.012 0.096 3 26812 26954.7 0.756 0.852 4 19432 19313.5 0.728 1.579 5 14043 13851.4 2.650 4.229 6 9963 9943.5 0.038 4.267 7 7174 7145.0 0.117 4.385 8 5063 5139.1 1.126 5.511 9 3728 3699.9 0.214 5.725 10 2648 2666.3 0.126 5.850 11 1870 1923.3 1.479 7.329 12 1419 1388.7 0.659 7.988 13 996 1003.7 0.059 8.048 14 731 726.1 0.033 8.080 15 489 525.8 2.580 10.661 16 371 381.2 0.270 10.931 17 272 276.5 0.075 11.005 18 212 200.8 0.621 11.627 19 130 146.0 1.750 13.377 20 115 106.2 0.727 14.104 21 264 287.1 1.861 15.964 Chisq= 15.96 for 20 degrees of freedom, p= 0.28116 SUMMARY of craptest p-value for no. of wins: 0.763080 p-value for throws/game: 0.281163 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0077,0.0081,0.0103,0.0107,0.0109,0.0128,0.0137,0.0164,0.0184, 0.0230,0.0266,0.0272,0.0328,0.0338,0.0440,0.0528,0.0695,0.0709,0.0744, 0.0785,0.0789,0.0792,0.0811,0.0840,0.0868,0.0887,0.0891,0.0897,0.0916, 0.0920,0.0935,0.0961,0.0998,0.1148,0.1169,0.1188,0.1233,0.1257,0.1268, 0.1279,0.1326,0.1383,0.1520,0.1550,0.1616,0.1671,0.1695,0.1763,0.1827, 0.1849,0.1938,0.1992,0.1996,0.2121,0.2215,0.2221,0.2234,0.2245,0.2367, 0.2383,0.2451,0.2460,0.2496,0.2505,0.2512,0.2532,0.2533,0.2581,0.2603, 0.2614,0.2617,0.2617,0.2638,0.2699,0.2705,0.2769,0.2771,0.2812,0.2878, 0.2933,0.3044,0.3065,0.3077,0.3083,0.3226,0.3240,0.3244,0.3261,0.3320, 0.3344,0.3378,0.3384,0.3407,0.3429,0.3503,0.3596,0.3631,0.3751,0.3759, 0.3774,0.3859,0.4091,0.4144,0.4164,0.4176,0.4205,0.4213,0.4260,0.4336, 0.4367,0.4367,0.4452,0.4456,0.4461,0.4501,0.4713,0.4715,0.4755,0.4757, 0.4770,0.4847,0.4860,0.4874,0.4887,0.4949,0.4960,0.5031,0.5045,0.5069, 0.5069,0.5149,0.5185,0.5193,0.5306,0.5330,0.5351,0.5467,0.5477,0.5485, 0.5562,0.5619,0.5699,0.5868,0.5871,0.5903,0.5909,0.5960,0.5968,0.6016, 0.6070,0.6079,0.6098,0.6133,0.6153,0.6196,0.6254,0.6260,0.6267,0.6345, 0.6368,0.6396,0.6414,0.6455,0.6477,0.6490,0.6501,0.6582,0.6588,0.6613, 0.6675,0.6789,0.6920,0.7035,0.7040,0.7091,0.7141,0.7242,0.7288,0.7299, 0.7343,0.7344,0.7387,0.7433,0.7444,0.7480,0.7514,0.7518,0.7574,0.7605, 0.7611,0.7631,0.7746,0.7755,0.7764,0.7767,0.7791,0.7850,0.7868,0.7897, 0.7964,0.7969,0.8028,0.8037,0.8044,0.8055,0.8072,0.8133,0.8143,0.8145, 0.8161,0.8179,0.8324,0.8331,0.8417,0.8452,0.8541,0.8544,0.8554,0.8564, 0.8589,0.8596,0.8608,0.8611,0.8626,0.8630,0.8754,0.8808,0.8836,0.8843, 0.8844,0.8867,0.8921,0.8925,0.8979,0.8982,0.9001,0.9016,0.9022,0.9027, 0.9037,0.9083,0.9123,0.9133,0.9206,0.9220,0.9248,0.9264,0.9348,0.9357, 0.9387,0.9450,0.9469,0.9484,0.9499,0.9531,0.9534,0.9544,0.9576,0.9580, 0.9586,0.9675,0.9792,0.9833,0.9857,0.9874,0.9915,0.9923,0.9944, Overall p-value after applying KStest on 269 p-values = 0.199851 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.