RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-14_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 13.5548 0.301675 2 to 25 15.95 18.8975 0.665555 3 to 26 15.73 19.6538 0.707680 4 to 27 15.89 11.6148 0.177122 5 to 28 15.87 14.9143 0.398344 6 to 29 15.62 17.5225 0.580452 7 to 30 15.85 15.2093 0.419593 8 to 31 15.47 19.8837 0.719779 9 to 32 15.23 28.1824 0.957148 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.753263 Tough bday spacings test for dh-ranFile-2015-08-14_20:31: 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 40 85 88 94 75 53 31 10 12 1 (O-E)^2/E 0.4 0.3 1.9 1.0 0.1 0.1 0.0 0.1 1.6 4.4 2.3 Birthday Spacings: Sum(O-E)^2/E= 12.150, p= 0.725 RESULTS OF GCD FOR dh-ranFile-2015-08-14_20:31 Euclid's algorithm: p-value, steps to gcd: 0.692945 p-value, dist. of gcd's: 0.235040 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-14_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.661 0.840 0.956 0.902 0.325 0.297 0.035 0.592 Bits 8 to 15---> 0.842 0.274 0.991 0.531 0.475 0.485 0.054 0.515 Bits 16 to 23---> 0.978 0.684 0.296 0.823 0.774 0.661 0.832 0.221 Bits 24 to 31---> 0.608 0.487 0.193 0.842 0.011 0.226 0.143 0.524 KS test for the above 32 p values: 0.185 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-14_20:31, p-values for 5 runs: 0.8055, 0.5575, 0.6057, 0.5971, 0.4126 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-14_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5011 5134.0 2.947 3.003 r= 30 23141 23103.0 0.062 3.065 r= 31 11640 11551.5 0.678 3.743 chi-square = 3.743 with df = 3; p-value = 0.709 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-14_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 240 211.4 3.864 3.864 r= 30 5061 5134.0 1.038 4.902 r= 31 23110 23103.0 0.002 4.904 r= 32 11589 11551.5 0.122 5.026 chi-square = 5.026 with df = 3; p-value = 0.830 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-14_20:31 b-rank test for bits 1 to 8, p=0.59376 b-rank test for bits 2 to 9, p=0.79238 b-rank test for bits 3 to 10, p=0.73037 b-rank test for bits 4 to 11, p=0.87734 b-rank test for bits 5 to 12, p=0.83120 b-rank test for bits 6 to 13, p=0.92932 b-rank test for bits 7 to 14, p=0.50968 b-rank test for bits 8 to 15, p=0.25166 b-rank test for bits 9 to 16, p=0.37728 b-rank test for bits 10 to 17, p=0.25827 b-rank test for bits 11 to 18, p=0.31127 b-rank test for bits 12 to 19, p=0.42849 b-rank test for bits 13 to 20, p=0.28597 b-rank test for bits 14 to 21, p=0.39763 b-rank test for bits 15 to 22, p=0.09943 b-rank test for bits 16 to 23, p=0.41693 b-rank test for bits 17 to 24, p=0.56950 b-rank test for bits 18 to 25, p=0.48179 b-rank test for bits 19 to 26, p=0.85517 b-rank test for bits 20 to 27, p=0.37262 b-rank test for bits 21 to 28, p=0.87489 b-rank test for bits 22 to 29, p=0.88996 b-rank test for bits 23 to 30, p=0.75994 b-rank test for bits 24 to 31, p=0.17088 b-rank test for bits 25 to 32, p=0.20952 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 = 0.560600 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-14_20:31 (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 141422 -1.14 0.127431 2 141606 -0.71 0.239251 3 142139 0.54 0.704232 4 141830 -0.19 0.426477 5 141777 -0.31 0.378591 6 142010 0.24 0.592977 7 141649 -0.61 0.271512 8 142531 1.45 0.926819 9 141441 -1.09 0.136927 10 141733 -0.41 0.340175 11 142143 0.55 0.707453 12 142544 1.48 0.930946 13 142296 0.90 0.816852 14 141485 -0.99 0.160739 15 142141 0.54 0.705844 16 141892 -0.04 0.483851 17 141908 -0.00 0.498760 18 142395 1.13 0.871759 19 141498 -0.96 0.168263 20 141952 0.10 0.539707 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-14_20:31 Bits used No. missing words z-score p-value 23 to 32 142106 0.6782 0.751169 22 to 31 141720 -0.6529 0.256923 21 to 30 141860 -0.1701 0.432464 20 to 29 142131 0.7644 0.777679 19 to 28 141608 -1.0391 0.149386 18 to 27 142278 1.2713 0.898185 17 to 26 142011 0.3506 0.637051 16 to 25 141763 -0.5046 0.306925 15 to 24 141821 -0.3046 0.380341 14 to 23 142103 0.6678 0.747878 13 to 22 142291 1.3161 0.905930 12 to 21 141164 -2.5701 0.005083 11 to 20 141782 -0.4391 0.330306 10 to 19 141887 -0.0770 0.469312 9 to 18 141861 -0.1667 0.433821 8 to 17 141822 -0.3011 0.381655 7 to 16 142044 0.4644 0.678812 6 to 15 141570 -1.1701 0.120980 5 to 14 141502 -1.4046 0.080072 4 to 13 141941 0.1092 0.543481 3 to 12 141571 -1.1667 0.121675 2 to 11 142203 1.0127 0.844388 1 to 10 142259 1.2058 0.886045 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-14_20:31 Bits used No. missing words z-score p-value 28 to 32 141801 -0.3672 0.356727 27 to 31 142124 0.7277 0.766600 26 to 30 141866 -0.1469 0.441613 25 to 29 141790 -0.4045 0.342919 24 to 28 142077 0.5684 0.715109 23 to 27 142230 1.0870 0.861485 22 to 26 142112 0.6870 0.753964 21 to 25 141832 -0.2621 0.396609 20 to 24 141946 0.1243 0.549463 19 to 23 141750 -0.5401 0.294564 18 to 22 141756 -0.5198 0.301615 17 to 21 141932 0.0768 0.530628 16 to 20 141194 -2.4248 0.007657 15 to 19 141660 -0.8452 0.199003 14 to 18 142113 0.6904 0.755031 13 to 17 141404 -1.7130 0.043358 12 to 16 142288 1.2836 0.900364 11 to 15 142410 1.6972 0.955169 10 to 14 142258 1.1819 0.881384 9 to 13 141368 -1.8350 0.033252 8 to 12 142292 1.2972 0.902717 7 to 11 142097 0.6362 0.737667 6 to 10 142232 1.0938 0.862978 5 to 9 142390 1.6294 0.948385 4 to 8 141905 -0.0147 0.494145 3 to 7 142286 1.2768 0.899172 2 to 6 141215 -2.3537 0.009295 1 to 5 141824 -0.2893 0.386193 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-14_20:31 Bits used No. missing words z-score p-value 31 to 32 141635 -0.8092 0.209191 30 to 31 142382 1.3943 0.918388 29 to 30 142543 1.8692 0.969205 28 to 29 142375 1.3737 0.915226 27 to 28 141872 -0.1101 0.456158 26 to 27 142214 0.8987 0.815602 25 to 26 142066 0.4622 0.678014 24 to 25 141474 -1.2842 0.099543 23 to 24 141827 -0.2429 0.404056 22 to 23 142346 1.2881 0.901147 21 to 22 141976 0.1967 0.577956 20 to 21 141717 -0.5673 0.285240 19 to 20 142348 1.2940 0.902169 18 to 19 141771 -0.4081 0.341617 17 to 18 141032 -2.5880 0.004827 16 to 17 142017 0.3176 0.624610 15 to 16 141971 0.1819 0.572176 14 to 15 141999 0.2645 0.604308 13 to 14 141869 -0.1190 0.452651 12 to 13 142076 0.4917 0.688517 11 to 12 141533 -1.1101 0.133474 10 to 11 141429 -1.4169 0.078256 9 to 10 142204 0.8692 0.807640 8 to 9 141642 -0.7886 0.215178 7 to 8 141468 -1.3019 0.096482 6 to 7 141612 -0.8771 0.190222 5 to 6 142541 1.8633 0.968792 4 to 5 141589 -0.9449 0.172348 3 to 4 141615 -0.8682 0.192634 2 to 3 141624 -0.8417 0.199983 1 to 2 141886 -0.0688 0.472566 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-14_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2617.61 1.663 0.951866 Test results for specific bytes for dh-ranFile-2015-08-14_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2452.54 -0.671 0.251029 2 to 9 2539.71 0.562 0.712794 3 to 10 2482.13 -0.253 0.400268 4 to 11 2489.07 -0.155 0.438563 5 to 12 2641.48 2.001 0.977298 6 to 13 2398.91 -1.430 0.076410 7 to 14 2590.05 1.273 0.898579 8 to 15 2511.24 0.159 0.563138 9 to 16 2466.53 -0.473 0.317975 10 to 17 2510.57 0.149 0.559386 11 to 18 2424.65 -1.066 0.143308 12 to 19 2495.99 -0.057 0.477380 13 to 20 2580.85 1.143 0.873560 14 to 21 2676.64 2.498 0.993757 15 to 22 2510.22 0.145 0.557463 16 to 23 2600.23 1.418 0.921833 17 to 24 2541.89 0.592 0.723204 18 to 25 2473.36 -0.377 0.353175 19 to 26 2459.05 -0.579 0.281254 20 to 27 2603.68 1.466 0.928706 21 to 28 2462.24 -0.534 0.296648 22 to 29 2393.09 -1.512 0.065282 23 to 30 2378.28 -1.721 0.042596 24 to 31 2596.51 1.365 0.913858 25 to 32 2449.39 -0.716 0.237100 CDPARK for dh-ranFile-2015-08-14_20:31: 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 3556 1.5068 0.934075 3526 0.1370 0.554479 3572 2.2374 0.987371 3499 -1.0959 0.136563 3557 1.5525 0.939730 3547 1.0959 0.863437 3518 -0.2283 0.409702 3492 -1.4155 0.078457 3523 0.0000 0.500000 3543 0.9132 0.819442 Square side=100, avg. no. parked=3533.30 sample std.=24.76 p-value of the KSTEST for those 10 p-values: 0.172657 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-14_20:31 0.1422,0.7239,0.9623,0.3073,0.4492,0.8729,0.6797,0.1081,0.8974,0.1524, The KS test for those 10 p-values: 0.821148 The 3DSPHERES test for dh-ranFile-2015-08-14_20:31 sample no r^3 equiv. uni. 1 60.573 0.867226 2 12.148 0.332975 3 7.921 0.232051 4 69.509 0.901427 5 41.149 0.746308 6 23.427 0.542001 7 46.702 0.789178 8 41.068 0.745618 9 27.801 0.604136 10 19.102 0.470974 11 12.373 0.337971 12 22.129 0.521758 13 4.168 0.129715 14 92.502 0.954197 15 6.227 0.187429 16 45.520 0.780703 17 11.679 0.322476 18 15.459 0.402672 19 40.573 0.741387 20 39.071 0.728113 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.403568 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-14_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.8 -0.5 -0.5 -0.6 -1.1 1.1 0.1 -1.6 0.2 -0.9 0.6 0.6 -0.4 -0.3 1.0 2.1 0.7 0.1 1.1 -2.3 -0.5 -0.2 -0.6 -2.5 0.4 -1.1 1.0 0.1 -0.1 0.6 0.9 0.4 1.5 0.4 -1.6 0.5 -0.4 -0.7 3.1 2.0 -1.1 Chi-square with 42 degrees of freedom:52.996663 z-score=1.199834, p-value=0.881007 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-14_20:31 Test no p-value 1 0.384549 2 0.004740 3 0.310820 4 0.353807 5 0.224878 6 0.699108 7 0.330361 8 0.016883 9 0.772627 10 0.053810 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.039101 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-14_20:31: (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 66586 0.10 66859 0.55 3 25000.00 25072 0.21 24808 1.47 4 6666.67 6713 0.32 6606 0.55 5 1388.89 1344 1.45 1462 3.85 6 238.10 244 0.15 243 0.10 7 34.72 35 0.00 17 9.04 8 4.96 5 0.00 4 0.19 p=0.10230 p=0.98490 Number of rngs required: 688300, p-value: 0.453 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-14_20:31 No. of wins: Observed Expected 98586 98585.9 z-score= 0.001, pvalue=0.50025 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66623 66666.7 0.029 0.029 2 37455 37654.3 1.055 1.084 3 26859 26954.7 0.340 1.424 4 19520 19313.5 2.209 3.632 5 13673 13851.4 2.298 5.931 6 9883 9943.5 0.369 6.299 7 7306 7145.0 3.627 9.926 8 5257 5139.1 2.706 12.632 9 3773 3699.9 1.446 14.078 10 2647 2666.3 0.140 14.217 11 1954 1923.3 0.489 14.706 12 1432 1388.7 1.348 16.054 13 1042 1003.7 1.460 17.514 14 674 726.1 3.744 21.258 15 534 525.8 0.127 21.385 16 361 381.2 1.065 22.450 17 282 276.5 0.108 22.558 18 194 200.8 0.232 22.790 19 142 146.0 0.109 22.899 20 111 106.2 0.216 23.115 21 278 287.1 0.289 23.404 Chisq= 23.40 for 20 degrees of freedom, p= 0.73061 SUMMARY of craptest p-value for no. of wins: 0.500252 p-value for throws/game: 0.730609 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-14_20:31 No. of wins: Observed Expected 98546 98585.9 z-score=-0.178, pvalue=0.42926 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66693 66666.7 0.010 0.010 2 37867 37654.3 1.201 1.212 3 27087 26954.7 0.649 1.861 4 19141 19313.5 1.540 3.401 5 13615 13851.4 4.035 7.436 6 10195 9943.5 6.359 13.795 7 7024 7145.0 2.050 15.845 8 5099 5139.1 0.312 16.157 9 3765 3699.9 1.147 17.304 10 2564 2666.3 3.925 21.229 11 1958 1923.3 0.625 21.854 12 1344 1388.7 1.441 23.295 13 987 1003.7 0.278 23.574 14 711 726.1 0.316 23.889 15 533 525.8 0.098 23.987 16 403 381.2 1.253 25.239 17 307 276.5 3.355 28.595 18 210 200.8 0.419 29.013 19 125 146.0 3.016 32.030 20 107 106.2 0.006 32.036 21 265 287.1 1.703 33.739 Chisq= 33.74 for 20 degrees of freedom, p= 0.97205 SUMMARY of craptest p-value for no. of wins: 0.429255 p-value for throws/game: 0.972053 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0047,0.0048,0.0051,0.0077,0.0093,0.0106,0.0169,0.0333,0.0353,0.0391, 0.0426,0.0434,0.0535,0.0538,0.0653,0.0764,0.0783,0.0785,0.0801,0.0965, 0.0994,0.0995,0.1023,0.1081,0.1210,0.1217,0.1274,0.1297,0.1335,0.1366, 0.1369,0.1422,0.1426,0.1433,0.1494,0.1524,0.1607,0.1683,0.1709,0.1723, 0.1727,0.1771,0.1847,0.1874,0.1902,0.1926,0.1929,0.1990,0.2000,0.2092, 0.2095,0.2152,0.2205,0.2249,0.2260,0.2321,0.2350,0.2371,0.2393,0.2510, 0.2517,0.2569,0.2583,0.2715,0.2741,0.2813,0.2852,0.2860,0.2946,0.2965, 0.2966,0.2972,0.3016,0.3017,0.3069,0.3073,0.3108,0.3113,0.3180,0.3225, 0.3251,0.3303,0.3304,0.3330,0.3380,0.3402,0.3416,0.3429,0.3532,0.3538, 0.3567,0.3726,0.3773,0.3786,0.3803,0.3817,0.3845,0.3862,0.3966,0.3976, 0.3983,0.4003,0.4027,0.4036,0.4041,0.4097,0.4126,0.4169,0.4196,0.4265, 0.4285,0.4293,0.4325,0.4338,0.4386,0.4416,0.4492,0.4527,0.4528,0.4562, 0.4693,0.4710,0.4726,0.4754,0.4774,0.4818,0.4839,0.4850,0.4868,0.4941, 0.4988,0.5000,0.5003,0.5097,0.5149,0.5218,0.5237,0.5306,0.5311,0.5397, 0.5420,0.5435,0.5495,0.5545,0.5575,0.5575,0.5594,0.5606,0.5631,0.5695, 0.5722,0.5780,0.5805,0.5915,0.5930,0.5938,0.5971,0.6041,0.6043,0.6057, 0.6083,0.6246,0.6371,0.6605,0.6612,0.6656,0.6780,0.6788,0.6797,0.6837, 0.6885,0.6929,0.6991,0.7042,0.7058,0.7075,0.7077,0.7094,0.7128,0.7151, 0.7198,0.7232,0.7239,0.7249,0.7281,0.7304,0.7306,0.7377,0.7414,0.7456, 0.7463,0.7479,0.7512,0.7533,0.7540,0.7550,0.7599,0.7666,0.7726,0.7738, 0.7777,0.7807,0.7892,0.7924,0.8055,0.8076,0.8156,0.8169,0.8194,0.8211, 0.8228,0.8301,0.8312,0.8323,0.8398,0.8420,0.8421,0.8444,0.8552,0.8615, 0.8630,0.8634,0.8672,0.8718,0.8729,0.8736,0.8749,0.8773,0.8810,0.8814, 0.8860,0.8900,0.8974,0.8982,0.8986,0.8992,0.9004,0.9011,0.9014,0.9018, 0.9022,0.9027,0.9059,0.9139,0.9152,0.9184,0.9218,0.9268,0.9287,0.9293, 0.9309,0.9341,0.9397,0.9484,0.9519,0.9542,0.9552,0.9562,0.9571,0.9623, 0.9688,0.9692,0.9721,0.9773,0.9778,0.9849,0.9874,0.9912,0.9938, Overall p-value after applying KStest on 269 p-values = 0.248534 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.