RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-09_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 17.8458 0.601367 2 to 25 15.52 21.2848 0.786193 3 to 26 15.71 17.6933 0.591567 4 to 27 15.65 22.0923 0.818806 5 to 28 15.84 17.6134 0.586390 6 to 29 15.63 18.4425 0.638546 7 to 30 15.75 5.9976 0.006798 8 to 31 15.62 15.3295 0.428242 9 to 32 15.93 19.5396 0.701545 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.235324 Tough bday spacings test for dh-ranFile-2015-10-09_05:31: 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 46 66 97 90 95 39 25 19 9 4 (O-E)^2/E 0.1 2.4 0.7 0.0 0.6 3.6 3.3 0.8 1.1 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 13.493, p= 0.803 RESULTS OF GCD FOR dh-ranFile-2015-10-09_05:31 Euclid's algorithm: p-value, steps to gcd: 0.185949 p-value, dist. of gcd's: 0.690788 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-09_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.425 0.383 0.390 0.830 0.444 0.424 0.419 0.835 Bits 8 to 15---> 0.285 0.053 0.885 0.915 0.068 0.071 0.436 0.360 Bits 16 to 23---> 0.907 0.140 0.008 0.247 0.240 0.949 0.477 0.518 Bits 24 to 31---> 0.828 0.556 0.033 0.862 0.006 0.067 0.192 0.609 KS test for the above 32 p values: 0.836 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-09_05:31, p-values for 5 runs: 0.5043, 0.7007, 0.7396, 0.5798, 0.3108 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-09_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5065 5134.0 0.928 2.561 r= 30 23161 23103.0 0.145 2.706 r= 31 11544 11551.5 0.005 2.711 chi-square = 2.711 with df = 3; p-value = 0.562 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-09_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5091 5134.0 0.360 0.565 r= 31 23033 23103.0 0.212 0.778 r= 32 11658 11551.5 0.981 1.759 chi-square = 1.759 with df = 3; p-value = 0.376 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-09_05:31 b-rank test for bits 1 to 8, p=0.39928 b-rank test for bits 2 to 9, p=0.04799 b-rank test for bits 3 to 10, p=0.44897 b-rank test for bits 4 to 11, p=0.79163 b-rank test for bits 5 to 12, p=0.82553 b-rank test for bits 6 to 13, p=0.20328 b-rank test for bits 7 to 14, p=0.36639 b-rank test for bits 8 to 15, p=0.02458 b-rank test for bits 9 to 16, p=0.36087 b-rank test for bits 10 to 17, p=0.64551 b-rank test for bits 11 to 18, p=0.90022 b-rank test for bits 12 to 19, p=0.78036 b-rank test for bits 13 to 20, p=0.52389 b-rank test for bits 14 to 21, p=0.06990 b-rank test for bits 15 to 22, p=0.59875 b-rank test for bits 16 to 23, p=0.38802 b-rank test for bits 17 to 24, p=0.73766 b-rank test for bits 18 to 25, p=0.36803 b-rank test for bits 19 to 26, p=0.81465 b-rank test for bits 20 to 27, p=0.04651 b-rank test for bits 21 to 28, p=0.35902 b-rank test for bits 22 to 29, p=0.62250 b-rank test for bits 23 to 30, p=0.18353 b-rank test for bits 24 to 31, p=0.11006 b-rank test for bits 25 to 32, p=0.64630 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 = 0.525142 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-09_05:31 (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 141507 -0.94 0.173603 2 141556 -0.83 0.204533 3 142371 1.08 0.859632 4 141709 -0.47 0.319871 5 141439 -1.10 0.135905 6 141678 -0.54 0.294429 7 142154 0.57 0.716223 8 142177 0.63 0.734145 9 142241 0.77 0.780809 10 140916 -2.32 0.010147 11 141362 -1.28 0.100482 12 141211 -1.63 0.051381 13 141688 -0.52 0.302534 14 141928 0.04 0.517397 15 141917 0.02 0.507149 16 142298 0.91 0.818089 17 141947 0.09 0.535067 18 141875 -0.08 0.468035 19 142269 0.84 0.799644 20 141683 -0.53 0.298469 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-09_05:31 Bits used No. missing words z-score p-value 23 to 32 142162 0.8713 0.808198 22 to 31 141866 -0.1494 0.440614 21 to 30 141348 -1.9356 0.026457 20 to 29 141670 -0.8253 0.204608 19 to 28 141412 -1.7149 0.043179 18 to 27 141864 -0.1563 0.437894 17 to 26 141238 -2.3149 0.010308 16 to 25 141788 -0.4184 0.337835 15 to 24 141950 0.1402 0.555765 14 to 23 141195 -2.4632 0.006885 13 to 22 141824 -0.2942 0.384287 12 to 21 141627 -0.9736 0.165140 11 to 20 141368 -1.8667 0.030975 10 to 19 141773 -0.4701 0.319141 9 to 18 142088 0.6161 0.731087 8 to 17 141006 -3.1149 0.000920 7 to 16 141975 0.2264 0.589574 6 to 15 142006 0.3333 0.630563 5 to 14 142352 1.5264 0.936551 4 to 13 142436 1.8161 0.965323 3 to 12 142085 0.6058 0.727663 2 to 11 141765 -0.4977 0.309351 1 to 10 141869 -0.1391 0.444698 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-09_05:31 Bits used No. missing words z-score p-value 28 to 32 141774 -0.4587 0.323208 27 to 31 142356 1.5141 0.935004 26 to 30 141927 0.0599 0.523882 25 to 29 142015 0.3582 0.639905 24 to 28 142207 1.0091 0.843525 23 to 27 142006 0.3277 0.628429 22 to 26 141898 -0.0384 0.484682 21 to 25 141454 -1.5435 0.061356 20 to 24 141772 -0.4655 0.320778 19 to 23 142036 0.4294 0.666180 18 to 22 142193 0.9616 0.831873 17 to 21 141602 -1.0418 0.148753 16 to 20 142052 0.4836 0.685675 15 to 19 142008 0.3345 0.630989 14 to 18 142202 0.9921 0.839426 13 to 17 141722 -0.6350 0.262709 12 to 16 141163 -2.5299 0.005704 11 to 15 141540 -1.2520 0.105291 10 to 14 142515 2.0531 0.979969 9 to 13 141562 -1.1774 0.119520 8 to 12 141864 -0.1537 0.438939 7 to 11 142312 1.3650 0.913871 6 to 10 142286 1.2768 0.899172 5 to 9 142077 0.5684 0.715109 4 to 8 141304 -2.0520 0.020086 3 to 7 142384 1.6091 0.946197 2 to 6 141432 -1.6181 0.052824 1 to 5 142234 1.1006 0.864459 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-09_05:31 Bits used No. missing words z-score p-value 31 to 32 142355 1.3147 0.905688 30 to 31 142071 0.4769 0.683284 29 to 30 142347 1.2911 0.901659 28 to 29 141807 -0.3019 0.381380 27 to 28 142397 1.4386 0.924862 26 to 27 141903 -0.0187 0.492551 25 to 26 142209 0.8840 0.811647 24 to 25 141874 -0.1042 0.458498 23 to 24 142212 0.8928 0.814026 22 to 23 141944 0.1023 0.540729 21 to 22 142341 1.2734 0.898555 20 to 21 142061 0.4474 0.672708 19 to 20 141586 -0.9538 0.170099 18 to 19 141930 0.0610 0.524310 17 to 18 141753 -0.4612 0.322345 16 to 17 142247 0.9961 0.840394 15 to 16 142107 0.5831 0.720086 14 to 15 141950 0.1200 0.547747 13 to 14 141920 0.0315 0.512555 12 to 13 141339 -1.6824 0.046247 11 to 12 141925 0.0462 0.518434 10 to 11 142071 0.4769 0.683284 9 to 10 142254 1.0167 0.845358 8 to 9 142258 1.0285 0.848149 7 to 8 142696 2.3206 0.989845 6 to 7 141860 -0.1455 0.442152 5 to 6 141427 -1.4228 0.077397 4 to 5 142339 1.2675 0.897505 3 to 4 141858 -0.1514 0.439824 2 to 3 141923 0.0403 0.516083 1 to 2 142182 0.8043 0.789399 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-09_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2579.47 1.124 0.869473 Test results for specific bytes for dh-ranFile-2015-10-09_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2427.67 -1.023 0.153185 2 to 9 2552.25 0.739 0.770006 3 to 10 2549.48 0.700 0.757980 4 to 11 2443.69 -0.796 0.212935 5 to 12 2618.02 1.669 0.952453 6 to 13 2572.85 1.030 0.848547 7 to 14 2437.13 -0.889 0.186968 8 to 15 2394.24 -1.496 0.067367 9 to 16 2525.80 0.365 0.642370 10 to 17 2571.04 1.005 0.842477 11 to 18 2553.78 0.761 0.776545 12 to 19 2484.55 -0.218 0.413548 13 to 20 2555.42 0.784 0.783402 14 to 21 2566.61 0.942 0.826895 15 to 22 2502.28 0.032 0.512837 16 to 23 2443.23 -0.803 0.211036 17 to 24 2519.55 0.276 0.608900 18 to 25 2509.89 0.140 0.555623 19 to 26 2508.61 0.122 0.548474 20 to 27 2467.35 -0.462 0.322133 21 to 28 2520.17 0.285 0.612269 22 to 29 2507.50 0.106 0.542263 23 to 30 2667.19 2.364 0.990971 24 to 31 2328.72 -2.422 0.007713 25 to 32 2438.00 -0.877 0.190309 CDPARK for dh-ranFile-2015-10-09_05:31: 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 3500 -1.0502 0.146807 3498 -1.1416 0.126820 3536 0.5936 0.723613 3494 -1.3242 0.092718 3512 -0.5023 0.307734 3538 0.6849 0.753306 3537 0.6393 0.738676 3559 1.6438 0.949895 3536 0.5936 0.723613 3478 -2.0548 0.019949 Square side=100, avg. no. parked=3518.80 sample std.=24.53 p-value of the KSTEST for those 10 p-values: 0.468876 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-09_05:31 0.9217,0.3736,0.7211,0.7966,0.8152,0.4416,0.1847,0.8388,0.8413,0.0235, The KS test for those 10 p-values: 0.327551 The 3DSPHERES test for dh-ranFile-2015-10-09_05:31 sample no r^3 equiv. uni. 1 54.411 0.836951 2 25.213 0.568478 3 50.987 0.817237 4 53.236 0.830438 5 32.253 0.658741 6 23.531 0.543588 7 4.231 0.131546 8 4.492 0.139057 9 6.431 0.192945 10 12.942 0.350392 11 1.654 0.053626 12 39.712 0.733862 13 14.682 0.386999 14 84.868 0.940923 15 99.040 0.963165 16 147.198 0.992602 17 6.706 0.200310 18 3.853 0.120524 19 1.423 0.046335 20 62.077 0.873715 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.535189 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-09_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 0.1 -0.5 -1.0 -1.4 -2.0 0.4 -0.0 1.2 -0.2 0.6 0.2 -0.0 1.5 -0.1 -0.8 0.2 -1.5 -1.4 0.7 -0.5 0.6 -1.6 1.4 2.6 0.8 0.6 -0.5 -0.8 -0.1 -1.0 -1.1 -0.9 0.9 0.2 -0.5 1.1 0.5 1.5 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:42.519793 z-score=0.056714, p-value=0.551411 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-09_05:31 Test no p-value 1 0.647237 2 0.683999 3 0.664890 4 0.527904 5 0.806812 6 0.597896 7 0.149873 8 0.676051 9 0.048298 10 0.999459 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.246433 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-09_05:31: (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 66481 0.52 66719 0.04 3 25000.00 25142 0.81 24933 0.18 4 6666.67 6745 0.92 6747 0.97 5 1388.89 1358 0.69 1320 3.42 6 238.10 233 0.11 225 0.72 7 34.72 36 0.05 42 1.53 8 4.96 4 0.19 13 13.03 p=0.22612 p=0.99710 Number of rngs required: 688132, p-value: 0.378 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-09_05:31 No. of wins: Observed Expected 98288 98585.9 z-score=-1.332, pvalue=0.09140 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66460 66666.7 0.641 0.641 2 37688 37654.3 0.030 0.671 3 26824 26954.7 0.634 1.305 4 19438 19313.5 0.803 2.108 5 13826 13851.4 0.047 2.155 6 9901 9943.5 0.182 2.337 7 7187 7145.0 0.247 2.583 8 5166 5139.1 0.141 2.724 9 3775 3699.9 1.526 4.250 10 2678 2666.3 0.051 4.301 11 1934 1923.3 0.059 4.361 12 1407 1388.7 0.240 4.601 13 1005 1003.7 0.002 4.602 14 764 726.1 1.974 6.576 15 540 525.8 0.382 6.958 16 409 381.2 2.035 8.993 17 276 276.5 0.001 8.994 18 199 200.8 0.017 9.010 19 146 146.0 0.000 9.010 20 106 106.2 0.000 9.011 21 271 287.1 0.904 9.915 Chisq= 9.92 for 20 degrees of freedom, p= 0.03032 SUMMARY of craptest p-value for no. of wins: 0.091398 p-value for throws/game: 0.030316 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-09_05:31 No. of wins: Observed Expected 98631 98585.9 z-score= 0.202, pvalue=0.58000 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66403 66666.7 1.043 1.043 2 37524 37654.3 0.451 1.494 3 26967 26954.7 0.006 1.499 4 19692 19313.5 7.419 8.919 5 13935 13851.4 0.504 9.423 6 9867 9943.5 0.589 10.012 7 7183 7145.0 0.202 10.214 8 5151 5139.1 0.028 10.242 9 3737 3699.9 0.373 10.614 10 2722 2666.3 1.164 11.778 11 1864 1923.3 1.830 13.608 12 1405 1388.7 0.190 13.799 13 955 1003.7 2.364 16.163 14 717 726.1 0.115 16.278 15 510 525.8 0.477 16.755 16 391 381.2 0.255 17.009 17 248 276.5 2.945 19.955 18 224 200.8 2.673 22.628 19 140 146.0 0.245 22.873 20 113 106.2 0.433 23.307 21 252 287.1 4.294 27.601 Chisq= 27.60 for 20 degrees of freedom, p= 0.88082 SUMMARY of craptest p-value for no. of wins: 0.580002 p-value for throws/game: 0.880818 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0057,0.0057,0.0068,0.0069,0.0077,0.0084,0.0101,0.0103,0.0199, 0.0201,0.0235,0.0246,0.0265,0.0303,0.0310,0.0334,0.0432,0.0462,0.0463, 0.0465,0.0480,0.0483,0.0514,0.0528,0.0530,0.0536,0.0614,0.0669,0.0674, 0.0684,0.0699,0.0707,0.0774,0.0914,0.0927,0.1005,0.1053,0.1101,0.1195, 0.1205,0.1268,0.1315,0.1359,0.1391,0.1399,0.1468,0.1488,0.1499,0.1532, 0.1651,0.1701,0.1736,0.1835,0.1847,0.1859,0.1870,0.1903,0.1923,0.1929, 0.2003,0.2033,0.2045,0.2046,0.2110,0.2129,0.2261,0.2353,0.2398,0.2464, 0.2467,0.2627,0.2853,0.2944,0.2985,0.3025,0.3077,0.3094,0.3108,0.3191, 0.3199,0.3208,0.3221,0.3223,0.3232,0.3276,0.3378,0.3504,0.3590,0.3596, 0.3609,0.3664,0.3680,0.3736,0.3761,0.3775,0.3814,0.3830,0.3843,0.3870, 0.3880,0.3900,0.3993,0.4135,0.4190,0.4239,0.4251,0.4282,0.4356,0.4379, 0.4389,0.4398,0.4406,0.4416,0.4422,0.4442,0.4447,0.4490,0.4585,0.4680, 0.4689,0.4772,0.4847,0.4926,0.5043,0.5071,0.5126,0.5128,0.5161,0.5174, 0.5180,0.5184,0.5239,0.5239,0.5243,0.5251,0.5279,0.5351,0.5352,0.5407, 0.5423,0.5436,0.5477,0.5485,0.5514,0.5556,0.5558,0.5558,0.5617,0.5685, 0.5798,0.5800,0.5864,0.5896,0.5916,0.5979,0.5988,0.6014,0.6089,0.6090, 0.6123,0.6225,0.6284,0.6306,0.6310,0.6385,0.6399,0.6424,0.6455,0.6463, 0.6472,0.6587,0.6649,0.6662,0.6727,0.6761,0.6833,0.6833,0.6840,0.6857, 0.6908,0.7007,0.7015,0.7151,0.7162,0.7201,0.7211,0.7236,0.7236,0.7277, 0.7311,0.7339,0.7341,0.7377,0.7387,0.7396,0.7533,0.7580,0.7700,0.7765, 0.7804,0.7808,0.7834,0.7862,0.7894,0.7916,0.7966,0.7996,0.8026,0.8068, 0.8082,0.8116,0.8140,0.8146,0.8152,0.8172,0.8181,0.8188,0.8255,0.8269, 0.8279,0.8299,0.8304,0.8319,0.8345,0.8361,0.8370,0.8388,0.8394,0.8404, 0.8413,0.8425,0.8435,0.8454,0.8481,0.8485,0.8596,0.8619,0.8645,0.8695, 0.8737,0.8808,0.8848,0.8975,0.8986,0.8992,0.9002,0.9017,0.9057,0.9073, 0.9139,0.9147,0.9217,0.9249,0.9350,0.9366,0.9409,0.9462,0.9492,0.9499, 0.9525,0.9632,0.9653,0.9800,0.9898,0.9910,0.9926,0.9971,0.9995, Overall p-value after applying KStest on 269 p-values = 0.224374 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.