RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-29_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 16.4130 0.505231 2 to 25 15.80 7.1839 0.018960 3 to 26 15.98 10.2104 0.105445 4 to 27 15.90 16.7880 0.531187 5 to 28 15.83 15.8837 0.467906 6 to 29 15.58 28.2156 0.957519 7 to 30 15.71 11.1882 0.153384 8 to 31 15.83 13.6641 0.309277 9 to 32 15.82 19.2402 0.685078 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.634135 Tough bday spacings test for dh-ranFile-2017-01-29_18:31: 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 6 38 65 110 103 82 47 22 16 10 1 (O-E)^2/E 1.1 0.1 0.9 1.6 0.3 0.2 0.5 2.0 0.1 1.7 2.3 Birthday Spacings: Sum(O-E)^2/E= 10.758, p= 0.623 RESULTS OF GCD FOR dh-ranFile-2017-01-29_18:31 Euclid's algorithm: p-value, steps to gcd: 0.742885 p-value, dist. of gcd's: 0.621574 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-29_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.189 0.355 0.622 0.251 0.378 0.216 0.269 0.361 Bits 8 to 15---> 0.732 0.673 0.371 0.951 0.108 0.444 0.878 0.976 Bits 16 to 23---> 0.060 0.306 0.642 0.456 0.953 0.103 0.689 0.870 Bits 24 to 31---> 0.892 0.748 0.123 0.230 0.928 0.847 0.658 0.415 KS test for the above 32 p values: 0.177 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-29_18:31, p-values for 5 runs: 0.5304, 0.2164, 0.5697, 0.6377, 0.3358 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-29_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5043 5134.0 1.613 2.248 r= 30 23093 23103.0 0.004 2.252 r= 31 11641 11551.5 0.693 2.945 chi-square = 2.945 with df = 3; p-value = 0.600 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-29_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5064 5134.0 0.955 1.054 r= 31 23133 23103.0 0.039 1.093 r= 32 11587 11551.5 0.109 1.202 chi-square = 1.202 with df = 3; p-value = 0.247 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-29_18:31 b-rank test for bits 1 to 8, p=0.63532 b-rank test for bits 2 to 9, p=0.23682 b-rank test for bits 3 to 10, p=0.01311 b-rank test for bits 4 to 11, p=0.33689 b-rank test for bits 5 to 12, p=0.30902 b-rank test for bits 6 to 13, p=0.80785 b-rank test for bits 7 to 14, p=0.80487 b-rank test for bits 8 to 15, p=0.96726 b-rank test for bits 9 to 16, p=0.87549 b-rank test for bits 10 to 17, p=0.91905 b-rank test for bits 11 to 18, p=0.85171 b-rank test for bits 12 to 19, p=0.77705 b-rank test for bits 13 to 20, p=0.55420 b-rank test for bits 14 to 21, p=0.17732 b-rank test for bits 15 to 22, p=0.15013 b-rank test for bits 16 to 23, p=0.31717 b-rank test for bits 17 to 24, p=0.52047 b-rank test for bits 18 to 25, p=0.58293 b-rank test for bits 19 to 26, p=0.12353 b-rank test for bits 20 to 27, p=0.27407 b-rank test for bits 21 to 28, p=0.99273 b-rank test for bits 22 to 29, p=0.84729 b-rank test for bits 23 to 30, p=0.56925 b-rank test for bits 24 to 31, p=0.31512 b-rank test for bits 25 to 32, p=0.75891 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 = 0.622806 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-29_18:31 (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 141784 -0.29 0.384827 2 142876 2.26 0.988045 3 142458 1.28 0.900068 4 142196 0.67 0.748504 5 141701 -0.49 0.313217 6 142402 1.15 0.875154 7 141800 -0.26 0.399190 8 141470 -1.03 0.152335 9 142202 0.68 0.752952 10 142128 0.51 0.695293 11 141472 -1.02 0.153438 12 142355 1.04 0.851128 13 141940 0.07 0.528563 14 141321 -1.37 0.084627 15 142340 1.01 0.842850 16 141285 -1.46 0.072322 17 141948 0.09 0.535996 18 141645 -0.62 0.268422 19 141200 -1.66 0.048728 20 140948 -2.25 0.012349 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-29_18:31 Bits used No. missing words z-score p-value 23 to 32 142218 1.0644 0.856422 22 to 31 141818 -0.3149 0.376407 21 to 30 142076 0.5747 0.717261 20 to 29 141755 -0.5322 0.297303 19 to 28 142007 0.3368 0.631864 18 to 27 141832 -0.2667 0.394867 17 to 26 142097 0.6471 0.741229 16 to 25 141928 0.0644 0.525666 15 to 24 142185 0.9506 0.829093 14 to 23 142032 0.4230 0.663852 13 to 22 141747 -0.5598 0.287822 12 to 21 141370 -1.8598 0.031460 11 to 20 141696 -0.7356 0.230981 10 to 19 141901 -0.0287 0.488542 9 to 18 141653 -0.8839 0.188376 8 to 17 141199 -2.4494 0.007154 7 to 16 141660 -0.8598 0.194961 6 to 15 141947 0.1299 0.551676 5 to 14 142022 0.3885 0.651183 4 to 13 141994 0.2920 0.614844 3 to 12 141418 -1.6942 0.045110 2 to 11 142332 1.4575 0.927508 1 to 10 141810 -0.3425 0.365981 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-29_18:31 Bits used No. missing words z-score p-value 28 to 32 142375 1.5785 0.942779 27 to 31 141990 0.2735 0.607749 26 to 30 141788 -0.4113 0.340431 25 to 29 141554 -1.2045 0.114197 24 to 28 141595 -1.0655 0.143319 23 to 27 142196 0.9718 0.834416 22 to 26 142009 0.3379 0.632267 21 to 25 142160 0.8497 0.802262 20 to 24 141578 -1.1232 0.130686 19 to 23 141355 -1.8791 0.030116 18 to 22 142079 0.5752 0.717406 17 to 21 141517 -1.3299 0.091770 16 to 20 142341 1.4633 0.928306 15 to 19 142142 0.7887 0.784860 14 to 18 142260 1.1887 0.882723 13 to 17 142218 1.0463 0.852298 12 to 16 142110 0.6802 0.751823 11 to 15 142203 0.9955 0.840251 10 to 14 141697 -0.7198 0.235836 9 to 13 141400 -1.7265 0.042125 8 to 12 141552 -1.2113 0.112893 7 to 11 142499 1.9989 0.977189 6 to 10 141798 -0.3774 0.352942 5 to 9 141838 -0.2418 0.404469 4 to 8 141610 -1.0147 0.155130 3 to 7 142153 0.8260 0.795598 2 to 6 142250 1.1548 0.875917 1 to 5 141698 -0.7164 0.236881 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-29_18:31 Bits used No. missing words z-score p-value 31 to 32 142306 1.1701 0.879023 30 to 31 141743 -0.4906 0.311837 29 to 30 141969 0.1760 0.569860 28 to 29 142123 0.6303 0.735749 27 to 28 142138 0.6745 0.750017 26 to 27 141857 -0.1544 0.438661 25 to 26 141668 -0.7119 0.238267 24 to 25 142105 0.5772 0.718097 23 to 24 141542 -1.0836 0.139278 22 to 23 141715 -0.5732 0.283240 21 to 22 142318 1.2055 0.885998 20 to 21 141908 -0.0039 0.498435 19 to 20 141729 -0.5319 0.297381 18 to 19 142036 0.3737 0.645671 17 to 18 142058 0.4386 0.669508 16 to 17 142030 0.3560 0.639064 15 to 16 142019 0.3235 0.626846 14 to 15 141662 -0.7296 0.232821 13 to 14 142188 0.8220 0.794472 12 to 13 141954 0.1318 0.552417 11 to 12 141975 0.1937 0.576801 10 to 11 141964 0.1613 0.564059 9 to 10 141899 -0.0305 0.487845 8 to 9 141247 -1.9538 0.025364 7 to 8 142085 0.5182 0.697841 6 to 7 142548 1.8840 0.970216 5 to 6 141561 -1.0275 0.152087 4 to 5 141866 -0.1278 0.449147 3 to 4 142671 2.2468 0.987674 2 to 3 141925 0.0462 0.518434 1 to 2 141781 -0.3786 0.352509 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-29_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2444.61 -0.783 0.216728 Test results for specific bytes for dh-ranFile-2017-01-29_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2489.24 -0.152 0.439534 2 to 9 2543.76 0.619 0.732008 3 to 10 2596.78 1.369 0.914440 4 to 11 2540.67 0.575 0.717393 5 to 12 2531.11 0.440 0.669998 6 to 13 2526.42 0.374 0.645651 7 to 14 2418.76 -1.149 0.125302 8 to 15 2535.06 0.496 0.689987 9 to 16 2571.20 1.007 0.843009 10 to 17 2493.76 -0.088 0.464841 11 to 18 2628.52 1.818 0.965435 12 to 19 2394.25 -1.496 0.067384 13 to 20 2546.84 0.662 0.746127 14 to 21 2433.52 -0.940 0.173559 15 to 22 2368.33 -1.862 0.031296 16 to 23 2496.42 -0.051 0.479825 17 to 24 2495.08 -0.070 0.472284 18 to 25 2498.78 -0.017 0.493123 19 to 26 2385.26 -1.623 0.052338 20 to 27 2379.13 -1.709 0.043694 21 to 28 2466.29 -0.477 0.316787 22 to 29 2585.10 1.203 0.885595 23 to 30 2606.31 1.503 0.933631 24 to 31 2505.49 0.078 0.530933 25 to 32 2479.25 -0.293 0.384612 CDPARK for dh-ranFile-2017-01-29_18:31: 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 3548 1.1416 0.873180 3520 -0.1370 0.445521 3544 0.9589 0.831196 3499 -1.0959 0.136563 3506 -0.7763 0.218799 3524 0.0457 0.518210 3514 -0.4110 0.340551 3534 0.5023 0.692266 3537 0.6393 0.738676 3504 -0.8676 0.192812 Square side=100, avg. no. parked=3523.00 sample std.=16.43 p-value of the KSTEST for those 10 p-values: 0.965545 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-29_18:31 0.7606,0.8647,0.5732,0.9763,0.8560,0.9814,0.6825,0.0717,0.8513,0.1407, The KS test for those 10 p-values: 0.041351 The 3DSPHERES test for dh-ranFile-2017-01-29_18:31 sample no r^3 equiv. uni. 1 34.672 0.685177 2 10.933 0.305403 3 24.160 0.553066 4 21.954 0.518965 5 7.048 0.209373 6 11.403 0.316213 7 17.535 0.442623 8 53.800 0.833593 9 68.875 0.899323 10 27.606 0.601554 11 161.738 0.995444 12 7.115 0.211151 13 67.280 0.893826 14 23.063 0.536412 15 48.954 0.804422 16 9.070 0.260918 17 28.914 0.618560 18 12.931 0.350154 19 42.862 0.760391 20 16.788 0.428565 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.388665 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-29_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.6 0.9 0.4 -1.4 -1.7 0.3 -0.5 -2.6 0.6 -1.9 -0.1 1.2 0.9 1.0 2.6 0.1 -1.2 -1.0 0.0 0.5 0.4 -0.5 0.6 -0.8 -1.5 -0.5 -0.2 1.0 -0.7 1.4 -0.6 -0.1 -0.2 -0.3 -0.2 0.5 0.9 -1.3 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:41.282295 z-score=-0.078308, p-value=0.497672 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-29_18:31 Test no p-value 1 0.055050 2 0.306923 3 0.000724 4 0.021896 5 0.148594 6 0.012023 7 0.314253 8 0.022343 9 0.764237 10 0.834919 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000432 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-29_18:31: (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 66637 0.01 67007 1.74 3 25000.00 25010 0.00 24777 1.99 4 6666.67 6718 0.40 6552 1.97 5 1388.89 1349 1.15 1383 0.02 6 238.10 244 0.15 248 0.41 7 34.72 34 0.01 27 1.72 8 4.96 7 0.84 5 0.00 p=0.13814 p=0.75091 Number of rngs required: 687210, p-value: 0.082 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-29_18:31 No. of wins: Observed Expected 98301 98585.9 z-score=-1.274, pvalue=0.10132 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66570 66666.7 0.140 0.140 2 37659 37654.3 0.001 0.141 3 27144 26954.7 1.329 1.470 4 19214 19313.5 0.512 1.982 5 13858 13851.4 0.003 1.985 6 9872 9943.5 0.515 2.500 7 7127 7145.0 0.045 2.545 8 5187 5139.1 0.447 2.992 9 3686 3699.9 0.052 3.044 10 2696 2666.3 0.331 3.375 11 1935 1923.3 0.071 3.446 12 1384 1388.7 0.016 3.462 13 1031 1003.7 0.742 4.204 14 717 726.1 0.115 4.319 15 501 525.8 1.173 5.492 16 383 381.2 0.009 5.501 17 288 276.5 0.475 5.976 18 184 200.8 1.410 7.386 19 152 146.0 0.248 7.634 20 117 106.2 1.095 8.729 21 295 287.1 0.217 8.946 Chisq= 8.95 for 20 degrees of freedom, p= 0.01647 SUMMARY of craptest p-value for no. of wins: 0.101322 p-value for throws/game: 0.016473 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-29_18:31 No. of wins: Observed Expected 98213 98585.9 z-score=-1.668, pvalue=0.04769 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66414 66666.7 0.958 0.958 2 37897 37654.3 1.564 2.522 3 26989 26954.7 0.044 2.565 4 19206 19313.5 0.598 3.163 5 13859 13851.4 0.004 3.167 6 10029 9943.5 0.734 3.902 7 7183 7145.0 0.202 4.104 8 5179 5139.1 0.310 4.414 9 3707 3699.9 0.014 4.428 10 2670 2666.3 0.005 4.433 11 1901 1923.3 0.259 4.692 12 1376 1388.7 0.117 4.809 13 1008 1003.7 0.018 4.827 14 718 726.1 0.091 4.918 15 523 525.8 0.015 4.934 16 376 381.2 0.070 5.003 17 250 276.5 2.547 7.550 18 205 200.8 0.087 7.637 19 117 146.0 5.755 13.392 20 112 106.2 0.315 13.707 21 281 287.1 0.130 13.837 Chisq= 13.84 for 20 degrees of freedom, p= 0.16132 SUMMARY of craptest p-value for no. of wins: 0.047694 p-value for throws/game: 0.161325 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0007,0.0072,0.0120,0.0123,0.0131,0.0165,0.0190,0.0219,0.0223, 0.0254,0.0301,0.0313,0.0315,0.0414,0.0421,0.0437,0.0451,0.0477,0.0487, 0.0523,0.0550,0.0598,0.0674,0.0717,0.0723,0.0821,0.0846,0.0918,0.1013, 0.1026,0.1054,0.1076,0.1129,0.1142,0.1229,0.1235,0.1253,0.1307,0.1366, 0.1381,0.1393,0.1407,0.1433,0.1486,0.1501,0.1521,0.1523,0.1534,0.1534, 0.1551,0.1613,0.1736,0.1769,0.1773,0.1884,0.1893,0.1928,0.1950,0.2094, 0.2112,0.2156,0.2164,0.2167,0.2188,0.2304,0.2310,0.2328,0.2358,0.2368, 0.2369,0.2383,0.2474,0.2506,0.2609,0.2684,0.2689,0.2741,0.2832,0.2878, 0.2973,0.2974,0.3054,0.3061,0.3069,0.3090,0.3093,0.3118,0.3132,0.3143, 0.3151,0.3162,0.3168,0.3172,0.3358,0.3369,0.3404,0.3406,0.3502,0.3525, 0.3529,0.3554,0.3607,0.3660,0.3712,0.3764,0.3781,0.3846,0.3848,0.3887, 0.3949,0.3992,0.4045,0.4150,0.4286,0.4387,0.4395,0.4426,0.4435,0.4455, 0.4491,0.4563,0.4648,0.4679,0.4723,0.4798,0.4878,0.4885,0.4931,0.4977, 0.4984,0.5052,0.5182,0.5184,0.5190,0.5205,0.5257,0.5286,0.5304,0.5309, 0.5312,0.5360,0.5364,0.5517,0.5524,0.5531,0.5542,0.5641,0.5692,0.5697, 0.5699,0.5732,0.5768,0.5829,0.5999,0.6016,0.6077,0.6148,0.6186,0.6216, 0.6217,0.6228,0.6233,0.6268,0.6319,0.6323,0.6341,0.6353,0.6377,0.6391, 0.6424,0.6457,0.6457,0.6512,0.6581,0.6639,0.6695,0.6700,0.6726,0.6825, 0.6851,0.6852,0.6894,0.6900,0.6923,0.6953,0.6978,0.7173,0.7174,0.7174, 0.7181,0.7320,0.7321,0.7357,0.7387,0.7412,0.7429,0.7461,0.7480,0.7485, 0.7500,0.7509,0.7518,0.7530,0.7589,0.7604,0.7606,0.7642,0.7771,0.7849, 0.7945,0.7956,0.8023,0.8044,0.8049,0.8078,0.8291,0.8312,0.8336,0.8344, 0.8349,0.8403,0.8428,0.8430,0.8465,0.8473,0.8511,0.8513,0.8517,0.8523, 0.8560,0.8564,0.8647,0.8703,0.8732,0.8752,0.8755,0.8759,0.8785,0.8790, 0.8827,0.8856,0.8860,0.8921,0.8938,0.8993,0.9001,0.9144,0.9191,0.9275, 0.9282,0.9283,0.9336,0.9428,0.9512,0.9528,0.9575,0.9654,0.9655,0.9673, 0.9702,0.9755,0.9763,0.9772,0.9814,0.9877,0.9880,0.9927,0.9954, Overall p-value after applying KStest on 269 p-values = 0.777851 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.