RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-14_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 15.84 10.8237 0.134419 2 to 25 15.80 18.2303 0.625546 3 to 26 15.68 24.7550 0.899671 4 to 27 15.75 17.1662 0.556836 5 to 28 15.64 16.0995 0.483208 6 to 29 15.70 20.0807 0.729877 7 to 30 15.84 27.0838 0.943149 8 to 31 15.83 28.7937 0.963523 9 to 32 15.65 21.9493 0.813322 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.090952 Tough bday spacings test for dh-ranFile-2016-04-14_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 3 49 75 95 96 70 50 35 20 5 2 (O-E)^2/E 4.1 4.2 0.0 0.1 0.0 0.8 0.1 0.9 1.8 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.515, p= 0.804 RESULTS OF GCD FOR dh-ranFile-2016-04-14_18:31 Euclid's algorithm: p-value, steps to gcd: 0.006465 p-value, dist. of gcd's: 0.383530 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-14_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.796 0.744 0.048 0.975 0.523 0.829 0.711 0.535 Bits 8 to 15---> 0.579 0.666 0.933 0.817 0.829 0.444 0.188 0.711 Bits 16 to 23---> 0.047 0.514 0.510 0.724 0.100 0.361 0.903 0.290 Bits 24 to 31---> 0.226 0.759 0.622 0.692 0.367 0.205 0.338 0.309 KS test for the above 32 p values: 0.365 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-14_18:31, p-values for 5 runs: 0.0011, 0.4512, 0.2656, 0.4201, 0.6571 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-14_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 234 211.4 2.412 2.412 r= 29 5219 5134.0 1.407 3.819 r= 30 22967 23103.0 0.801 4.620 r= 31 11580 11551.5 0.070 4.690 chi-square = 4.690 with df = 3; p-value = 0.804 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-14_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5193 5134.0 0.678 0.705 r= 31 23095 23103.0 0.003 0.708 r= 32 11503 11551.5 0.204 0.912 chi-square = 0.912 with df = 3; p-value = 0.177 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-14_18:31 b-rank test for bits 1 to 8, p=0.91703 b-rank test for bits 2 to 9, p=0.23422 b-rank test for bits 3 to 10, p=0.26431 b-rank test for bits 4 to 11, p=0.93470 b-rank test for bits 5 to 12, p=0.59208 b-rank test for bits 6 to 13, p=0.50100 b-rank test for bits 7 to 14, p=0.14021 b-rank test for bits 8 to 15, p=0.96006 b-rank test for bits 9 to 16, p=0.88062 b-rank test for bits 10 to 17, p=0.12291 b-rank test for bits 11 to 18, p=0.93956 b-rank test for bits 12 to 19, p=0.99300 b-rank test for bits 13 to 20, p=0.11063 b-rank test for bits 14 to 21, p=0.19108 b-rank test for bits 15 to 22, p=0.05020 b-rank test for bits 16 to 23, p=0.55734 b-rank test for bits 17 to 24, p=0.09619 b-rank test for bits 18 to 25, p=0.24130 b-rank test for bits 19 to 26, p=0.32720 b-rank test for bits 20 to 27, p=0.54340 b-rank test for bits 21 to 28, p=0.39385 b-rank test for bits 22 to 29, p=0.09758 b-rank test for bits 23 to 30, p=0.47945 b-rank test for bits 24 to 31, p=0.42004 b-rank test for bits 25 to 32, p=0.28801 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 = 0.262711 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-14_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 141927 0.04 0.516466 2 142068 0.37 0.644579 3 141905 -0.01 0.495964 4 141590 -0.75 0.227804 5 141711 -0.46 0.321543 6 142001 0.21 0.584798 7 142645 1.72 0.957180 8 141688 -0.52 0.302534 9 142486 1.35 0.911068 10 142898 2.31 0.989555 11 141681 -0.53 0.296850 12 142577 1.56 0.940617 13 141839 -0.16 0.434739 14 142215 0.71 0.762443 15 141807 -0.24 0.405518 16 142129 0.51 0.696111 17 141784 -0.29 0.384827 18 142127 0.51 0.694475 19 141199 -1.66 0.048492 20 141633 -0.65 0.259259 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-14_18:31 Bits used No. missing words z-score p-value 23 to 32 142062 0.5264 0.700712 22 to 31 141875 -0.1184 0.452884 21 to 30 141589 -1.1046 0.134669 20 to 29 142379 1.6196 0.947336 19 to 28 142097 0.6471 0.741229 18 to 27 141774 -0.4667 0.320373 17 to 26 141477 -1.4908 0.068008 16 to 25 142472 1.9402 0.973825 15 to 24 142283 1.2885 0.901217 14 to 23 142238 1.1333 0.871465 13 to 22 141969 0.2058 0.581510 12 to 21 141757 -0.5253 0.299696 11 to 20 141718 -0.6598 0.254704 10 to 19 141838 -0.2460 0.402855 9 to 18 142346 1.5058 0.933935 8 to 17 142078 0.5816 0.719589 7 to 16 141751 -0.5460 0.292545 6 to 15 141982 0.2506 0.598933 5 to 14 141763 -0.5046 0.306925 4 to 13 142479 1.9644 0.975257 3 to 12 141911 0.0058 0.502297 2 to 11 142418 1.7540 0.960288 1 to 10 142041 0.4540 0.675098 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-14_18:31 Bits used No. missing words z-score p-value 28 to 32 141667 -0.8215 0.205693 27 to 31 142531 2.1074 0.982457 26 to 30 141805 -0.3537 0.361797 25 to 29 141290 -2.0994 0.017890 24 to 28 141421 -1.6554 0.048926 23 to 27 141261 -2.1977 0.013984 22 to 26 141875 -0.1164 0.453679 21 to 25 141880 -0.0994 0.460401 20 to 24 141248 -2.2418 0.012487 19 to 23 142065 0.5277 0.701145 18 to 22 141713 -0.6655 0.252857 17 to 21 142129 0.7446 0.771757 16 to 20 141820 -0.3028 0.381016 15 to 19 142220 1.0531 0.853857 14 to 18 142086 0.5989 0.725374 13 to 17 141845 -0.2181 0.413688 12 to 16 142267 1.2124 0.887328 11 to 15 141922 0.0429 0.517129 10 to 14 141743 -0.5638 0.286435 9 to 13 141837 -0.2452 0.403156 8 to 12 142287 1.2802 0.899769 7 to 11 141893 -0.0554 0.477928 6 to 10 141949 0.1345 0.553486 5 to 9 141978 0.2328 0.592034 4 to 8 142244 1.1345 0.871702 3 to 7 142128 0.7413 0.770730 2 to 6 142231 1.0904 0.862233 1 to 5 142365 1.5446 0.938784 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-14_18:31 Bits used No. missing words z-score p-value 31 to 32 141874 -0.1042 0.458498 30 to 31 141516 -1.1603 0.122970 29 to 30 142169 0.7660 0.778158 28 to 29 142103 0.5713 0.716101 27 to 28 141666 -0.7178 0.236444 26 to 27 142337 1.2616 0.896447 25 to 26 142279 1.0905 0.862247 24 to 25 142582 1.9843 0.976388 23 to 24 141724 -0.5467 0.292294 22 to 23 141721 -0.5555 0.289261 21 to 22 141427 -1.4228 0.077397 20 to 21 141512 -1.1721 0.120586 19 to 20 141981 0.2114 0.583719 18 to 19 141539 -1.0924 0.137325 17 to 18 142467 1.6450 0.950020 16 to 17 142090 0.5329 0.702966 15 to 16 142039 0.3825 0.648958 14 to 15 141772 -0.4051 0.342701 13 to 14 142155 0.7247 0.765679 12 to 13 141964 0.1613 0.564059 11 to 12 142133 0.6598 0.745307 10 to 11 141993 0.2468 0.597474 9 to 10 142587 1.9990 0.977197 8 to 9 141727 -0.5378 0.295342 7 to 8 141781 -0.3786 0.352509 6 to 7 142029 0.3530 0.637959 5 to 6 142267 1.0551 0.854304 4 to 5 141723 -0.5496 0.291281 3 to 4 142160 0.7394 0.770180 2 to 3 142530 1.8309 0.966441 1 to 2 142447 1.5860 0.943636 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-14_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2442.81 -0.809 0.209337 Test results for specific bytes for dh-ranFile-2016-04-14_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2528.93 0.409 0.658762 2 to 9 2511.90 0.168 0.566849 3 to 10 2345.63 -2.183 0.014514 4 to 11 2485.09 -0.211 0.416519 5 to 12 2549.85 0.705 0.759569 6 to 13 2612.40 1.590 0.944033 7 to 14 2523.83 0.337 0.631956 8 to 15 2284.53 -3.047 0.001155 9 to 16 2505.45 0.077 0.530736 10 to 17 2407.43 -1.309 0.095252 11 to 18 2374.85 -1.770 0.038373 12 to 19 2466.23 -0.478 0.316488 13 to 20 2583.24 1.177 0.880440 14 to 21 2344.46 -2.200 0.013914 15 to 22 2478.30 -0.307 0.379454 16 to 23 2457.83 -0.596 0.275455 17 to 24 2493.49 -0.092 0.463321 18 to 25 2484.66 -0.217 0.414106 19 to 26 2545.25 0.640 0.738872 20 to 27 2406.92 -1.316 0.094033 21 to 28 2481.28 -0.265 0.395611 22 to 29 2492.04 -0.113 0.455207 23 to 30 2555.06 0.779 0.781896 24 to 31 2437.65 -0.882 0.188952 25 to 32 2562.94 0.890 0.813284 CDPARK for dh-ranFile-2016-04-14_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 3522 -0.0457 0.481790 3567 2.0091 0.977738 3550 1.2329 0.891189 3530 0.3196 0.625377 3517 -0.2740 0.392053 3506 -0.7763 0.218799 3506 -0.7763 0.218799 3509 -0.6393 0.261324 3521 -0.0913 0.463617 3547 1.0959 0.863437 Square side=100, avg. no. parked=3527.50 sample std.=19.75 p-value of the KSTEST for those 10 p-values: 0.752657 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-14_18:31 0.6624,0.4177,0.6034,0.8975,0.8193,0.8176,0.2299,0.1219,0.9463,0.8759, The KS test for those 10 p-values: 0.194707 The 3DSPHERES test for dh-ranFile-2016-04-14_18:31 sample no r^3 equiv. uni. 1 11.486 0.318093 2 14.943 0.392323 3 58.155 0.856080 4 2.909 0.092418 5 3.514 0.110540 6 25.336 0.570247 7 33.566 0.673353 8 29.222 0.622459 9 71.515 0.907803 10 6.688 0.199831 11 10.138 0.286768 12 42.402 0.756685 13 2.463 0.078828 14 30.993 0.644098 15 44.362 0.772071 16 10.504 0.295404 17 13.485 0.362051 18 20.337 0.492315 19 17.364 0.439437 20 15.753 0.408496 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.717319 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-14_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 0.8 -0.5 -1.2 -1.0 -0.5 0.7 -0.4 -0.5 1.1 1.4 1.2 -0.6 0.6 1.7 -1.0 0.3 -0.7 0.1 -0.6 -0.1 -1.0 -0.7 -1.5 0.9 0.3 -1.5 0.5 0.9 -1.1 -0.6 0.0 1.3 -0.4 1.0 -0.7 0.2 -0.8 0.4 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:29.933025 z-score=-1.316615, p-value=0.081579 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-14_18:31 Test no p-value 1 0.008347 2 0.014465 3 0.073449 4 0.228963 5 0.011163 6 0.392635 7 0.390038 8 0.141184 9 0.246722 10 0.398575 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000356 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-14_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 66421 0.91 66913 0.91 3 25000.00 24998 0.00 24864 0.74 4 6666.67 6908 8.74 6600 0.67 5 1388.89 1409 0.29 1330 2.50 6 238.10 217 1.87 245 0.20 7 34.72 42 1.53 43 1.97 8 4.96 4 0.19 4 0.19 p=0.96444 p=0.69498 Number of rngs required: 688000, p-value: 0.321 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-14_18:31 No. of wins: Observed Expected 98374 98585.9 z-score=-0.948, pvalue=0.17168 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66981 66666.7 1.482 1.482 2 37366 37654.3 2.208 3.690 3 26760 26954.7 1.407 5.097 4 19484 19313.5 1.506 6.602 5 13761 13851.4 0.590 7.193 6 9933 9943.5 0.011 7.204 7 7161 7145.0 0.036 7.240 8 5205 5139.1 0.846 8.085 9 3703 3699.9 0.003 8.088 10 2676 2666.3 0.035 8.123 11 1900 1923.3 0.283 8.406 12 1418 1388.7 0.616 9.023 13 1042 1003.7 1.460 10.483 14 704 726.1 0.675 11.158 15 530 525.8 0.033 11.191 16 396 381.2 0.579 11.770 17 251 276.5 2.359 14.128 18 198 200.8 0.040 14.168 19 153 146.0 0.337 14.505 20 98 106.2 0.635 15.141 21 280 287.1 0.176 15.317 Chisq= 15.32 for 20 degrees of freedom, p= 0.24201 SUMMARY of craptest p-value for no. of wins: 0.171678 p-value for throws/game: 0.242012 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-14_18:31 No. of wins: Observed Expected 98249 98585.9 z-score=-1.507, pvalue=0.06595 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66501 66666.7 0.412 0.412 2 37782 37654.3 0.433 0.845 3 27064 26954.7 0.443 1.288 4 19262 19313.5 0.137 1.425 5 13931 13851.4 0.457 1.882 6 10126 9943.5 3.348 5.230 7 7063 7145.0 0.942 6.172 8 5151 5139.1 0.028 6.199 9 3646 3699.9 0.784 6.983 10 2585 2666.3 2.479 9.462 11 1813 1923.3 6.329 15.791 12 1326 1388.7 2.834 18.626 13 1032 1003.7 0.797 19.423 14 765 726.1 2.080 21.502 15 507 525.8 0.675 22.177 16 410 381.2 2.184 24.361 17 272 276.5 0.075 24.435 18 202 200.8 0.007 24.442 19 162 146.0 1.757 26.199 20 109 106.2 0.073 26.272 21 291 287.1 0.053 26.325 Chisq= 26.32 for 20 degrees of freedom, p= 0.84464 SUMMARY of craptest p-value for no. of wins: 0.065953 p-value for throws/game: 0.844640 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0011,0.0012,0.0065,0.0083,0.0112,0.0125,0.0139,0.0140,0.0145, 0.0145,0.0179,0.0384,0.0468,0.0477,0.0485,0.0489,0.0502,0.0660,0.0680, 0.0734,0.0774,0.0788,0.0816,0.0910,0.0924,0.0940,0.0953,0.0962,0.0976, 0.0996,0.1105,0.1106,0.1206,0.1219,0.1229,0.1230,0.1344,0.1347,0.1373, 0.1402,0.1412,0.1717,0.1775,0.1885,0.1890,0.1911,0.1947,0.1998,0.2046, 0.2057,0.2093,0.2188,0.2188,0.2257,0.2278,0.2290,0.2299,0.2342,0.2364, 0.2413,0.2420,0.2467,0.2529,0.2547,0.2593,0.2613,0.2627,0.2643,0.2656, 0.2755,0.2864,0.2868,0.2880,0.2893,0.2900,0.2913,0.2923,0.2925,0.2953, 0.2954,0.2969,0.2997,0.3025,0.3069,0.3090,0.3165,0.3181,0.3204,0.3212, 0.3215,0.3272,0.3375,0.3427,0.3525,0.3608,0.3618,0.3621,0.3653,0.3667, 0.3795,0.3810,0.3835,0.3848,0.3900,0.3921,0.3923,0.3926,0.3938,0.3956, 0.3986,0.4029,0.4032,0.4055,0.4085,0.4137,0.4141,0.4165,0.4177,0.4200, 0.4201,0.4347,0.4394,0.4444,0.4512,0.4529,0.4537,0.4552,0.4585,0.4604, 0.4633,0.4636,0.4779,0.4795,0.4818,0.4832,0.4923,0.4960,0.5010,0.5023, 0.5102,0.5142,0.5165,0.5171,0.5228,0.5307,0.5352,0.5434,0.5535,0.5568, 0.5573,0.5641,0.5668,0.5702,0.5785,0.5815,0.5837,0.5848,0.5920,0.5921, 0.5975,0.5989,0.6034,0.6221,0.6225,0.6254,0.6255,0.6320,0.6380,0.6441, 0.6446,0.6490,0.6571,0.6588,0.6624,0.6657,0.6734,0.6751,0.6915,0.6945, 0.6950,0.6961,0.7007,0.7011,0.7030,0.7106,0.7112,0.7161,0.7173,0.7196, 0.7237,0.7254,0.7299,0.7389,0.7412,0.7443,0.7453,0.7527,0.7567,0.7592, 0.7596,0.7624,0.7657,0.7702,0.7707,0.7718,0.7721,0.7782,0.7819,0.7960, 0.8037,0.8041,0.8133,0.8133,0.8175,0.8176,0.8193,0.8286,0.8293,0.8446, 0.8539,0.8543,0.8561,0.8622,0.8622,0.8634,0.8715,0.8717,0.8759,0.8804, 0.8806,0.8873,0.8912,0.8964,0.8975,0.8997,0.8998,0.9012,0.9028,0.9078, 0.9111,0.9170,0.9330,0.9339,0.9347,0.9388,0.9396,0.9406,0.9431,0.9436, 0.9440,0.9463,0.9473,0.9500,0.9572,0.9601,0.9603,0.9635,0.9644,0.9664, 0.9738,0.9749,0.9753,0.9764,0.9772,0.9777,0.9825,0.9896,0.9930, Overall p-value after applying KStest on 269 p-values = 0.620479 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.