RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-11_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.21 23.2637 0.859140 2 to 25 15.65 12.5390 0.233539 3 to 26 15.82 26.8314 0.939412 4 to 27 15.93 22.6061 0.837480 5 to 28 15.74 20.1974 0.735742 6 to 29 15.85 21.4706 0.794056 7 to 30 15.68 17.5573 0.582733 8 to 31 15.52 34.1597 0.991994 9 to 32 15.55 23.3303 0.861198 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.007693 Tough bday spacings test for dh-ranFile-2018-04-11_17:31: 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 35 85 110 88 61 56 33 11 7 8 (O-E)^2/E 1.1 0.1 1.9 1.6 1.0 3.8 0.3 0.4 1.0 0.0 3.8 Birthday Spacings: Sum(O-E)^2/E= 14.802, p= 0.861 RESULTS OF GCD FOR dh-ranFile-2018-04-11_17:31 Euclid's algorithm: p-value, steps to gcd: 0.219036 p-value, dist. of gcd's: 0.740734 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-11_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.374 0.672 0.882 0.854 0.599 0.874 0.669 0.442 Bits 8 to 15---> 0.913 0.053 0.262 0.950 0.420 0.157 0.176 0.869 Bits 16 to 23---> 0.577 0.849 0.146 0.901 0.334 0.546 0.905 0.125 Bits 24 to 31---> 0.470 0.014 0.753 0.393 0.585 0.944 0.887 0.265 KS test for the above 32 p values: 0.700 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-11_17:31, p-values for 5 runs: 0.0424, 0.7382, 0.4896, 0.7336, 0.9251 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-11_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5216 5134.0 1.309 2.161 r= 30 23066 23103.0 0.059 2.220 r= 31 11520 11551.5 0.086 2.306 chi-square = 2.306 with df = 3; p-value = 0.489 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-11_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 228 211.4 1.301 1.301 r= 30 5144 5134.0 0.019 1.320 r= 31 23068 23103.0 0.053 1.373 r= 32 11560 11551.5 0.006 1.379 chi-square = 1.379 with df = 3; p-value = 0.290 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-11_17:31 b-rank test for bits 1 to 8, p=0.98105 b-rank test for bits 2 to 9, p=0.57029 b-rank test for bits 3 to 10, p=0.38409 b-rank test for bits 4 to 11, p=0.51745 b-rank test for bits 5 to 12, p=0.98442 b-rank test for bits 6 to 13, p=0.77471 b-rank test for bits 7 to 14, p=0.66381 b-rank test for bits 8 to 15, p=0.93782 b-rank test for bits 9 to 16, p=0.93351 b-rank test for bits 10 to 17, p=0.43736 b-rank test for bits 11 to 18, p=0.21649 b-rank test for bits 12 to 19, p=0.00665 b-rank test for bits 13 to 20, p=0.55874 b-rank test for bits 14 to 21, p=0.63960 b-rank test for bits 15 to 22, p=0.89780 b-rank test for bits 16 to 23, p=0.58850 b-rank test for bits 17 to 24, p=0.59281 b-rank test for bits 18 to 25, p=0.00742 b-rank test for bits 19 to 26, p=0.14471 b-rank test for bits 20 to 27, p=0.17465 b-rank test for bits 21 to 28, p=0.15861 b-rank test for bits 22 to 29, p=0.52744 b-rank test for bits 23 to 30, p=0.61341 b-rank test for bits 24 to 31, p=0.00740 b-rank test for bits 25 to 32, p=0.76469 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 = 0.331534 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-11_17:31 (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 141990 0.19 0.574750 2 141859 -0.12 0.453195 3 142649 1.73 0.958024 4 141942 0.08 0.530422 5 141304 -1.41 0.078634 6 142114 0.48 0.683746 7 142076 0.39 0.651516 8 141779 -0.30 0.380370 9 141016 -2.09 0.018434 10 142346 1.02 0.846197 11 142509 1.40 0.919408 12 141506 -0.94 0.173004 13 142096 0.44 0.668634 14 141014 -2.09 0.018224 15 142704 1.86 0.968323 16 142109 0.47 0.679578 17 141635 -0.64 0.260775 18 140957 -2.23 0.013038 19 141922 0.03 0.511808 20 142631 1.69 0.954116 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-11_17:31 Bits used No. missing words z-score p-value 23 to 32 142451 1.8678 0.969107 22 to 31 141919 0.0333 0.513300 21 to 30 141196 -2.4598 0.006952 20 to 29 141697 -0.7322 0.232032 19 to 28 141946 0.1264 0.550312 18 to 27 141773 -0.4701 0.319141 17 to 26 141662 -0.8529 0.196868 16 to 25 141601 -1.0632 0.143844 15 to 24 141427 -1.6632 0.048136 14 to 23 141778 -0.4529 0.325324 13 to 22 141771 -0.4770 0.316681 12 to 21 142208 1.0299 0.848471 11 to 20 141882 -0.0942 0.462459 10 to 19 141452 -1.5770 0.057398 9 to 18 141761 -0.5115 0.304507 8 to 17 141964 0.1885 0.574764 7 to 16 142103 0.6678 0.747878 6 to 15 141863 -0.1598 0.436536 5 to 14 142738 2.8575 0.997865 4 to 13 142147 0.8196 0.793764 3 to 12 141625 -0.9804 0.163432 2 to 11 142097 0.6471 0.741229 1 to 10 141458 -1.5563 0.059817 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-11_17:31 Bits used No. missing words z-score p-value 28 to 32 141738 -0.5808 0.280695 27 to 31 141833 -0.2587 0.397916 26 to 30 141715 -0.6587 0.255030 25 to 29 141922 0.0429 0.517129 24 to 28 141930 0.0701 0.527930 23 to 27 141261 -2.1977 0.013984 22 to 26 142062 0.5175 0.697605 21 to 25 141220 -2.3367 0.009727 20 to 24 141733 -0.5977 0.275010 19 to 23 141581 -1.1130 0.132858 18 to 22 142287 1.2802 0.899769 17 to 21 142254 1.1684 0.878672 16 to 20 141701 -0.7062 0.240031 15 to 19 141523 -1.3096 0.095167 14 to 18 141644 -0.8994 0.184214 13 to 17 142494 1.9819 0.976257 12 to 16 142158 0.8429 0.800372 11 to 15 141602 -1.0418 0.148753 10 to 14 142231 1.0904 0.862233 9 to 13 141623 -0.9706 0.165871 8 to 12 141758 -0.5130 0.303982 7 to 11 142114 0.6938 0.756095 6 to 10 141739 -0.5774 0.281838 5 to 9 141751 -0.5367 0.295733 4 to 8 142274 1.2362 0.891802 3 to 7 141977 0.2294 0.590717 2 to 6 142267 1.2124 0.887328 1 to 5 141755 -0.5232 0.300434 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-11_17:31 Bits used No. missing words z-score p-value 31 to 32 141167 -2.1898 0.014271 30 to 31 141855 -0.1603 0.436336 29 to 30 142245 0.9902 0.838956 28 to 29 142678 2.2675 0.988319 27 to 28 141382 -1.5555 0.059908 26 to 27 141598 -0.9184 0.179211 25 to 26 142136 0.6686 0.748138 24 to 25 142069 0.4710 0.681181 23 to 24 141686 -0.6588 0.255015 22 to 23 141682 -0.6706 0.251241 21 to 22 142511 1.7748 0.962038 20 to 21 141709 -0.5909 0.277279 19 to 20 141233 -1.9951 0.023017 18 to 19 141564 -1.0187 0.154179 17 to 18 141720 -0.5585 0.288253 16 to 17 142234 0.9577 0.830900 15 to 16 141490 -1.2370 0.108051 14 to 15 141643 -0.7856 0.216041 13 to 14 141762 -0.4346 0.331926 12 to 13 141334 -1.6971 0.044835 11 to 12 141739 -0.5024 0.307676 10 to 11 141897 -0.0364 0.485493 9 to 10 141452 -1.3491 0.088660 8 to 9 141528 -1.1249 0.130323 7 to 8 141532 -1.1131 0.132840 6 to 7 141959 0.1465 0.558244 5 to 6 142131 0.6539 0.743410 4 to 5 141618 -0.8594 0.195065 3 to 4 141678 -0.6824 0.247496 2 to 3 142200 0.8574 0.804397 1 to 2 141712 -0.5821 0.280252 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-11_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2544.78 0.633 0.736736 Test results for specific bytes for dh-ranFile-2018-04-11_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2452.44 -0.673 0.250614 2 to 9 2599.29 1.404 0.919873 3 to 10 2570.90 1.003 0.841994 4 to 11 2410.26 -1.269 0.102212 5 to 12 2441.48 -0.828 0.203950 6 to 13 2516.46 0.233 0.592033 7 to 14 2466.03 -0.480 0.315454 8 to 15 2489.93 -0.142 0.443400 9 to 16 2483.01 -0.240 0.405045 10 to 17 2354.31 -2.060 0.019684 11 to 18 2482.77 -0.244 0.403731 12 to 19 2512.10 0.171 0.567916 13 to 20 2339.74 -2.266 0.011712 14 to 21 2611.03 1.570 0.941812 15 to 22 2460.66 -0.556 0.288977 16 to 23 2476.08 -0.338 0.367558 17 to 24 2453.07 -0.664 0.253429 18 to 25 2568.70 0.972 0.834357 19 to 26 2579.78 1.128 0.870395 20 to 27 2458.29 -0.590 0.277647 21 to 28 2456.74 -0.612 0.270351 22 to 29 2518.22 0.258 0.601643 23 to 30 2469.79 -0.427 0.334605 24 to 31 2590.38 1.278 0.899398 25 to 32 2474.05 -0.367 0.356798 CDPARK for dh-ranFile-2018-04-11_17:31: 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 3477 -2.1005 0.017844 3521 -0.0913 0.463617 3517 -0.2740 0.392053 3562 1.7808 0.962529 3523 0.0000 0.500000 3511 -0.5479 0.291865 3557 1.5525 0.939730 3530 0.3196 0.625377 3526 0.1370 0.554479 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3523.20 sample std.=22.93 p-value of the KSTEST for those 10 p-values: 0.834323 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-11_17:31 0.4891,0.7574,0.4028,0.4353,0.1319,0.3194,0.2038,0.6924,0.7360,0.8217, The KS test for those 10 p-values: 0.818284 The 3DSPHERES test for dh-ranFile-2018-04-11_17:31 sample no r^3 equiv. uni. 1 12.675 0.344590 2 21.294 0.508251 3 31.861 0.654243 4 11.355 0.315115 5 36.371 0.702509 6 9.916 0.281465 7 45.905 0.783498 8 6.497 0.194732 9 37.891 0.717203 10 20.665 0.497836 11 10.868 0.303900 12 1.040 0.034079 13 5.674 0.172336 14 20.937 0.502378 15 36.908 0.707781 16 13.441 0.361113 17 25.569 0.573568 18 24.159 0.553051 19 7.417 0.219048 20 27.307 0.597566 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.241709 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-11_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.8 0.2 -0.1 1.0 -0.7 1.4 0.9 0.7 -0.3 0.2 -1.0 1.3 0.9 1.2 1.1 -1.8 1.5 -1.3 -0.9 -0.1 -1.6 -1.9 -0.2 0.9 1.6 -1.1 0.5 1.5 -0.4 -1.2 -2.7 -0.2 -0.6 1.5 -0.9 -1.3 -1.2 -0.7 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:50.564976 z-score=0.934516, p-value=0.828761 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-11_17:31 Test no p-value 1 0.376454 2 0.148555 3 0.021562 4 0.301864 5 0.554084 6 0.085318 7 0.005489 8 0.882686 9 0.607344 10 0.246031 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.062390 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-11_17:31: (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 66616 0.04 66324 1.76 3 25000.00 25147 0.86 25288 3.32 4 6666.67 6606 0.55 6769 1.57 5 1388.89 1330 2.50 1387 0.00 6 238.10 263 2.61 195 7.80 7 34.72 31 0.40 30 0.64 8 4.96 6 0.22 6 0.22 p=0.69491 p=0.98204 Number of rngs required: 687845, p-value: 0.260 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-11_17:31 No. of wins: Observed Expected 98627 98585.9 z-score= 0.184, pvalue=0.57300 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66942 66666.7 1.137 1.137 2 37480 37654.3 0.807 1.944 3 26976 26954.7 0.017 1.961 4 19221 19313.5 0.443 2.404 5 13850 13851.4 0.000 2.404 6 9892 9943.5 0.267 2.671 7 7090 7145.0 0.424 3.095 8 5189 5139.1 0.485 3.580 9 3687 3699.9 0.045 3.624 10 2707 2666.3 0.621 4.246 11 1902 1923.3 0.237 4.482 12 1376 1388.7 0.117 4.599 13 1003 1003.7 0.001 4.600 14 744 726.1 0.439 5.039 15 551 525.8 1.204 6.243 16 385 381.2 0.039 6.282 17 279 276.5 0.022 6.304 18 205 200.8 0.087 6.391 19 161 146.0 1.544 7.935 20 98 106.2 0.635 8.570 21 262 287.1 2.197 10.767 Chisq= 10.77 for 20 degrees of freedom, p= 0.04796 SUMMARY of craptest p-value for no. of wins: 0.572997 p-value for throws/game: 0.047963 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-11_17:31 No. of wins: Observed Expected 98365 98585.9 z-score=-0.988, pvalue=0.16162 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66824 66666.7 0.371 0.371 2 37545 37654.3 0.317 0.689 3 26847 26954.7 0.431 1.119 4 19366 19313.5 0.143 1.262 5 13862 13851.4 0.008 1.270 6 9819 9943.5 1.560 2.830 7 7165 7145.0 0.056 2.886 8 5245 5139.1 2.183 5.069 9 3661 3699.9 0.408 5.478 10 2638 2666.3 0.300 5.778 11 1956 1923.3 0.555 6.333 12 1393 1388.7 0.013 6.346 13 1023 1003.7 0.371 6.717 14 713 726.1 0.238 6.954 15 548 525.8 0.934 7.889 16 355 381.2 1.794 9.683 17 272 276.5 0.075 9.757 18 194 200.8 0.232 9.990 19 144 146.0 0.027 10.017 20 116 106.2 0.901 10.918 21 314 287.1 2.518 13.436 Chisq= 13.44 for 20 degrees of freedom, p= 0.14208 SUMMARY of craptest p-value for no. of wins: 0.161623 p-value for throws/game: 0.142078 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0055,0.0067,0.0070,0.0074,0.0074,0.0077,0.0097,0.0117,0.0130,0.0140, 0.0140,0.0143,0.0178,0.0182,0.0184,0.0197,0.0216,0.0230,0.0341,0.0424, 0.0448,0.0480,0.0481,0.0532,0.0574,0.0598,0.0599,0.0624,0.0786,0.0853, 0.0887,0.0952,0.1022,0.1081,0.1253,0.1303,0.1319,0.1328,0.1329,0.1421, 0.1438,0.1447,0.1457,0.1486,0.1488,0.1542,0.1571,0.1586,0.1616,0.1634, 0.1659,0.1723,0.1730,0.1746,0.1758,0.1792,0.1842,0.1947,0.1951,0.1969, 0.2038,0.2040,0.2160,0.2165,0.2190,0.2190,0.2320,0.2335,0.2400,0.2417, 0.2460,0.2467,0.2475,0.2506,0.2512,0.2534,0.2550,0.2550,0.2598,0.2608, 0.2615,0.2648,0.2704,0.2750,0.2773,0.2776,0.2803,0.2807,0.2815,0.2818, 0.2883,0.2890,0.2896,0.2919,0.2957,0.3004,0.3019,0.3039,0.3040,0.3045, 0.3077,0.3151,0.3155,0.3167,0.3191,0.3194,0.3253,0.3315,0.3319,0.3338, 0.3346,0.3446,0.3568,0.3611,0.3676,0.3737,0.3765,0.3804,0.3841,0.3921, 0.3931,0.3979,0.4028,0.4037,0.4050,0.4196,0.4353,0.4363,0.4365,0.4374, 0.4417,0.4434,0.4532,0.4625,0.4636,0.4696,0.4855,0.4887,0.4891,0.4896, 0.4978,0.5000,0.5024,0.5083,0.5118,0.5133,0.5171,0.5174,0.5274,0.5279, 0.5304,0.5463,0.5503,0.5531,0.5541,0.5545,0.5582,0.5587,0.5679,0.5703, 0.5730,0.5736,0.5748,0.5748,0.5767,0.5827,0.5845,0.5885,0.5907,0.5920, 0.5928,0.5976,0.5993,0.6016,0.6073,0.6134,0.6254,0.6396,0.6515,0.6542, 0.6638,0.6686,0.6688,0.6722,0.6796,0.6812,0.6837,0.6924,0.6949,0.6976, 0.6997,0.7025,0.7078,0.7172,0.7336,0.7357,0.7360,0.7367,0.7382,0.7407, 0.7412,0.7434,0.7479,0.7481,0.7529,0.7561,0.7574,0.7647,0.7747,0.7835, 0.7938,0.7941,0.8004,0.8044,0.8183,0.8217,0.8288,0.8309,0.8343,0.8344, 0.8375,0.8390,0.8420,0.8462,0.8485,0.8486,0.8543,0.8591,0.8606,0.8612, 0.8622,0.8687,0.8704,0.8735,0.8787,0.8820,0.8827,0.8873,0.8874,0.8918, 0.8978,0.8994,0.8998,0.9008,0.9047,0.9130,0.9194,0.9199,0.9251,0.9335, 0.9378,0.9394,0.9397,0.9418,0.9436,0.9500,0.9541,0.9580,0.9620,0.9625, 0.9683,0.9691,0.9763,0.9810,0.9820,0.9844,0.9883,0.9920,0.9979, Overall p-value after applying KStest on 269 p-values = 0.128410 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.