RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-20_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 29.2127 0.967385 2 to 25 15.51 21.0992 0.778117 3 to 26 16.04 24.6362 0.896845 4 to 27 15.58 22.6488 0.838962 5 to 28 15.89 23.3428 0.861579 6 to 29 15.48 26.1783 0.928728 7 to 30 15.69 26.3940 0.932425 8 to 31 15.76 17.0323 0.547819 9 to 32 15.87 17.1552 0.556101 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.001131 Tough bday spacings test for dh-ranFile-2018-03-20_15:31: 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 8 38 75 88 100 79 54 35 17 3 3 (O-E)^2/E 0.1 0.1 0.0 1.0 0.1 0.0 0.1 0.9 0.3 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.807, p= 0.096 RESULTS OF GCD FOR dh-ranFile-2018-03-20_15:31 Euclid's algorithm: p-value, steps to gcd: 0.104052 p-value, dist. of gcd's: 0.473072 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-20_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.676 0.618 0.702 0.559 0.745 0.215 0.035 0.234 Bits 8 to 15---> 0.085 0.010 0.319 0.502 0.078 0.660 0.070 0.621 Bits 16 to 23---> 0.293 0.582 0.097 0.739 0.782 0.534 0.999 0.978 Bits 24 to 31---> 0.375 0.414 0.124 0.092 0.643 0.364 0.254 0.801 KS test for the above 32 p values: 0.673 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-20_15:31, p-values for 5 runs: 0.4595, 0.7651, 0.5804, 0.5428, 0.7381 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-20_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5156 5134.0 0.094 0.095 r= 30 22947 23103.0 1.054 1.149 r= 31 11686 11551.5 1.565 2.715 chi-square = 2.715 with df = 3; p-value = 0.562 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-20_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5029 5134.0 2.148 2.483 r= 31 23214 23103.0 0.533 3.016 r= 32 11554 11551.5 0.001 3.016 chi-square = 3.016 with df = 3; p-value = 0.611 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-20_15:31 b-rank test for bits 1 to 8, p=0.78597 b-rank test for bits 2 to 9, p=0.13240 b-rank test for bits 3 to 10, p=0.33754 b-rank test for bits 4 to 11, p=0.83176 b-rank test for bits 5 to 12, p=0.66159 b-rank test for bits 6 to 13, p=0.38054 b-rank test for bits 7 to 14, p=0.88276 b-rank test for bits 8 to 15, p=0.33453 b-rank test for bits 9 to 16, p=0.63832 b-rank test for bits 10 to 17, p=0.73239 b-rank test for bits 11 to 18, p=0.79764 b-rank test for bits 12 to 19, p=0.53887 b-rank test for bits 13 to 20, p=0.36384 b-rank test for bits 14 to 21, p=0.22418 b-rank test for bits 15 to 22, p=0.28599 b-rank test for bits 16 to 23, p=0.52561 b-rank test for bits 17 to 24, p=0.00733 b-rank test for bits 18 to 25, p=0.06019 b-rank test for bits 19 to 26, p=0.34355 b-rank test for bits 20 to 27, p=0.66059 b-rank test for bits 21 to 28, p=0.66422 b-rank test for bits 22 to 29, p=0.84805 b-rank test for bits 23 to 30, p=0.76688 b-rank test for bits 24 to 31, p=0.95350 b-rank test for bits 25 to 32, p=0.29980 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 = 0.809529 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-20_15:31 (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 142144 0.55 0.708255 2 141814 -0.22 0.411871 3 141355 -1.30 0.097632 4 142816 2.12 0.982929 5 141566 -0.80 0.211227 6 142086 0.41 0.660116 7 141487 -0.99 0.161882 8 142297 0.91 0.817471 9 142122 0.50 0.690368 10 142012 0.24 0.594790 11 142055 0.34 0.633204 12 141408 -1.17 0.120733 13 141971 0.14 0.557285 14 142066 0.37 0.642837 15 142630 1.68 0.953891 16 142277 0.86 0.804841 17 141474 -1.02 0.154547 18 142254 0.81 0.789678 19 141604 -0.71 0.237803 20 141379 -1.24 0.107656 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-20_15:31 Bits used No. missing words z-score p-value 23 to 32 142148 0.8230 0.794746 22 to 31 141661 -0.8563 0.195913 21 to 30 141975 0.2264 0.589574 20 to 29 142124 0.7402 0.770423 19 to 28 142079 0.5851 0.720749 18 to 27 141864 -0.1563 0.437894 17 to 26 141712 -0.6804 0.248110 16 to 25 142383 1.6333 0.948802 15 to 24 141794 -0.3977 0.345430 14 to 23 141694 -0.7425 0.228887 13 to 22 142285 1.2954 0.902411 12 to 21 142338 1.4782 0.930319 11 to 20 141791 -0.4080 0.341624 10 to 19 141471 -1.5115 0.065333 9 to 18 142148 0.8230 0.794746 8 to 17 141956 0.1609 0.563926 7 to 16 141819 -0.3115 0.377717 6 to 15 141425 -1.6701 0.047449 5 to 14 142170 0.8989 0.815637 4 to 13 141670 -0.8253 0.204608 3 to 12 142389 1.6540 0.950940 2 to 11 142896 3.4023 0.999666 1 to 10 142166 0.8851 0.811940 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-20_15:31 Bits used No. missing words z-score p-value 28 to 32 141781 -0.4350 0.331775 27 to 31 141853 -0.1909 0.424283 26 to 30 141995 0.2904 0.614248 25 to 29 142206 1.0057 0.842711 24 to 28 142159 0.8463 0.801318 23 to 27 142028 0.4023 0.656258 22 to 26 141544 -1.2384 0.107783 21 to 25 141835 -0.2520 0.400534 20 to 24 141639 -0.9164 0.179736 19 to 23 142093 0.6226 0.733230 18 to 22 141850 -0.2011 0.420303 17 to 21 142387 1.6192 0.947300 16 to 20 141909 -0.0011 0.499554 15 to 19 141805 -0.3537 0.361797 14 to 18 141860 -0.1672 0.433598 13 to 17 142200 0.9853 0.837767 12 to 16 141906 -0.0113 0.495497 11 to 15 141689 -0.7469 0.227568 10 to 14 141440 -1.5909 0.055811 9 to 13 141937 0.0938 0.537365 8 to 12 141714 -0.6621 0.253942 7 to 11 141834 -0.2554 0.399224 6 to 10 141748 -0.5469 0.292230 5 to 9 142374 1.5752 0.942389 4 to 8 142146 0.8023 0.788802 3 to 7 141932 0.0768 0.530628 2 to 6 142263 1.1989 0.884713 1 to 5 142030 0.4091 0.658749 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-20_15:31 Bits used No. missing words z-score p-value 31 to 32 141833 -0.2252 0.410927 30 to 31 141517 -1.1573 0.123572 29 to 30 142002 0.2734 0.607713 28 to 29 142233 0.9548 0.830155 27 to 28 141743 -0.4906 0.311837 26 to 27 142142 0.6863 0.753751 25 to 26 141757 -0.4494 0.326589 24 to 25 141789 -0.3550 0.361311 23 to 24 141921 0.0344 0.513731 22 to 23 141796 -0.3343 0.369074 21 to 22 141952 0.1259 0.550083 20 to 21 141907 -0.0069 0.497258 19 to 20 141801 -0.3196 0.374652 18 to 19 141988 0.2321 0.591756 17 to 18 142274 1.0757 0.858974 16 to 17 142280 1.0934 0.862896 15 to 16 141999 0.2645 0.604308 14 to 15 141871 -0.1131 0.454988 13 to 14 141716 -0.5703 0.284239 12 to 13 141785 -0.3668 0.356901 11 to 12 141489 -1.2399 0.107504 10 to 11 142183 0.8073 0.790249 9 to 10 142049 0.4120 0.659832 8 to 9 142317 1.2026 0.885428 7 to 8 142194 0.8397 0.799471 6 to 7 142012 0.3029 0.619002 5 to 6 141440 -1.3845 0.083110 4 to 5 142164 0.7512 0.773746 3 to 4 142368 1.3530 0.911974 2 to 3 142044 0.3973 0.654411 1 to 2 141873 -0.1072 0.457328 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-20_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2546.36 0.656 0.743986 Test results for specific bytes for dh-ranFile-2018-03-20_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2475.44 -0.347 0.364148 2 to 9 2398.72 -1.432 0.076023 3 to 10 2507.92 0.112 0.544582 4 to 11 2487.47 -0.177 0.429680 5 to 12 2506.56 0.093 0.536984 6 to 13 2558.45 0.827 0.795753 7 to 14 2643.54 2.030 0.978817 8 to 15 2527.08 0.383 0.649106 9 to 16 2597.84 1.384 0.916760 10 to 17 2448.19 -0.733 0.231889 11 to 18 2497.82 -0.031 0.487683 12 to 19 2429.84 -0.992 0.160548 13 to 20 2507.02 0.099 0.539519 14 to 21 2472.63 -0.387 0.349361 15 to 22 2346.75 -2.167 0.015107 16 to 23 2541.70 0.590 0.722331 17 to 24 2571.98 1.018 0.845647 18 to 25 2594.92 1.342 0.910260 19 to 26 2456.62 -0.613 0.269800 20 to 27 2502.65 0.037 0.514920 21 to 28 2421.09 -1.116 0.132214 22 to 29 2564.35 0.910 0.818606 23 to 30 2476.69 -0.330 0.370840 24 to 31 2340.80 -2.251 0.012178 25 to 32 2492.80 -0.102 0.459424 CDPARK for dh-ranFile-2018-03-20_15:31: 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 3543 0.9132 0.819442 3503 -0.9132 0.180558 3525 0.0913 0.536383 3509 -0.6393 0.261324 3558 1.5982 0.944998 3503 -0.9132 0.180558 3519 -0.1826 0.427537 3587 2.9224 0.998263 3520 -0.1370 0.445521 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3527.90 sample std.=25.74 p-value of the KSTEST for those 10 p-values: 0.529428 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-20_15:31 0.7007,0.1407,0.5521,0.3031,0.9370,0.5710,0.8621,0.6154,0.2174,0.1492, The KS test for those 10 p-values: 0.972987 The 3DSPHERES test for dh-ranFile-2018-03-20_15:31 sample no r^3 equiv. uni. 1 10.403 0.293020 2 42.554 0.757916 3 59.151 0.860779 4 15.002 0.393515 5 10.510 0.295539 6 27.244 0.596722 7 48.533 0.801662 8 76.331 0.921476 9 27.841 0.604670 10 46.414 0.787141 11 47.070 0.791747 12 18.537 0.460923 13 4.566 0.141173 14 4.787 0.147497 15 4.781 0.147326 16 43.447 0.765014 17 9.312 0.266856 18 50.173 0.812210 19 20.215 0.490253 20 55.110 0.840705 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.387819 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-20_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 -0.4 -0.7 0.3 2.1 0.4 -0.1 1.1 0.9 0.1 -0.8 0.4 -0.4 1.4 0.7 1.4 -1.4 0.5 -0.2 0.5 -1.6 0.2 0.3 -3.0 0.4 -1.3 -1.3 0.0 -1.1 0.4 -1.1 1.6 0.3 1.5 0.1 0.5 -0.4 0.5 0.4 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:43.496944 z-score=0.163330, p-value=0.592522 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-20_15:31 Test no p-value 1 0.808809 2 0.100077 3 0.753997 4 0.153282 5 0.237904 6 0.040914 7 0.310255 8 0.271605 9 0.585022 10 0.456352 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.301000 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-20_15:31: (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 66609 0.05 66486 0.49 3 25000.00 24894 0.45 25161 1.04 4 6666.67 6810 3.08 6637 0.13 5 1388.89 1423 0.84 1421 0.74 6 238.10 218 1.70 251 0.70 7 34.72 38 0.31 35 0.00 8 4.96 7 0.84 8 1.86 p=0.70283 p=0.45179 Number of rngs required: 688161, p-value: 0.390 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-20_15:31 No. of wins: Observed Expected 98499 98585.9 z-score=-0.388, pvalue=0.34883 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66622 66666.7 0.030 0.030 2 37561 37654.3 0.231 0.261 3 27074 26954.7 0.528 0.789 4 19329 19313.5 0.013 0.801 5 13820 13851.4 0.071 0.873 6 9844 9943.5 0.997 1.869 7 7149 7145.0 0.002 1.871 8 5117 5139.1 0.095 1.966 9 3846 3699.9 5.772 7.738 10 2617 2666.3 0.911 8.650 11 1925 1923.3 0.001 8.651 12 1351 1388.7 1.026 9.677 13 1072 1003.7 4.646 14.322 14 746 726.1 0.543 14.865 15 541 525.8 0.437 15.303 16 402 381.2 1.140 16.443 17 267 276.5 0.329 16.772 18 215 200.8 1.000 17.772 19 133 146.0 1.155 18.927 20 96 106.2 0.982 19.909 21 273 287.1 0.694 20.603 Chisq= 20.60 for 20 degrees of freedom, p= 0.57919 SUMMARY of craptest p-value for no. of wins: 0.348830 p-value for throws/game: 0.579194 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-20_15:31 No. of wins: Observed Expected 98661 98585.9 z-score= 0.336, pvalue=0.63159 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66582 66666.7 0.108 0.108 2 37720 37654.3 0.115 0.222 3 26828 26954.7 0.596 0.818 4 19371 19313.5 0.171 0.989 5 13720 13851.4 1.247 2.236 6 10040 9943.5 0.936 3.172 7 7219 7145.0 0.766 3.938 8 5099 5139.1 0.312 4.250 9 3794 3699.9 2.395 6.645 10 2664 2666.3 0.002 6.647 11 1989 1923.3 2.242 8.890 12 1364 1388.7 0.441 9.330 13 980 1003.7 0.560 9.891 14 696 726.1 1.251 11.142 15 527 525.8 0.003 11.144 16 369 381.2 0.387 11.532 17 273 276.5 0.045 11.577 18 218 200.8 1.468 13.045 19 137 146.0 0.553 13.598 20 104 106.2 0.046 13.644 21 306 287.1 1.242 14.886 Chisq= 14.89 for 20 degrees of freedom, p= 0.21713 SUMMARY of craptest p-value for no. of wins: 0.631593 p-value for throws/game: 0.217128 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0073,0.0096,0.0122,0.0151,0.0346,0.0409,0.0474,0.0558,0.0602, 0.0653,0.0696,0.0760,0.0780,0.0831,0.0854,0.0919,0.0963,0.0966,0.0976, 0.1001,0.1041,0.1075,0.1077,0.1078,0.1207,0.1236,0.1242,0.1322,0.1324, 0.1407,0.1412,0.1473,0.1475,0.1492,0.1533,0.1545,0.1605,0.1619,0.1797, 0.1806,0.1806,0.1959,0.2046,0.2112,0.2145,0.2171,0.2174,0.2242,0.2276, 0.2289,0.2319,0.2345,0.2378,0.2379,0.2481,0.2539,0.2542,0.2613,0.2669, 0.2698,0.2716,0.2842,0.2860,0.2922,0.2930,0.2934,0.2955,0.2998,0.3010, 0.3031,0.3077,0.3103,0.3118,0.3192,0.3266,0.3318,0.3345,0.3375,0.3416, 0.3435,0.3454,0.3488,0.3494,0.3569,0.3613,0.3618,0.3638,0.3641,0.3645, 0.3691,0.3708,0.3747,0.3752,0.3777,0.3805,0.3878,0.3903,0.3935,0.3992, 0.4005,0.4109,0.4119,0.4139,0.4203,0.4243,0.4275,0.4297,0.4336,0.4379, 0.4455,0.4518,0.4550,0.4564,0.4573,0.4594,0.4595,0.4609,0.4731,0.4877, 0.4903,0.4955,0.4973,0.4996,0.5025,0.5137,0.5149,0.5256,0.5294,0.5306, 0.5337,0.5364,0.5370,0.5374,0.5389,0.5395,0.5428,0.5446,0.5478,0.5501, 0.5521,0.5561,0.5573,0.5595,0.5622,0.5639,0.5710,0.5792,0.5804,0.5825, 0.5850,0.5896,0.5918,0.5925,0.5948,0.5967,0.6043,0.6047,0.6077,0.6109, 0.6142,0.6154,0.6181,0.6190,0.6208,0.6316,0.6332,0.6383,0.6428,0.6432, 0.6491,0.6544,0.6563,0.6587,0.6598,0.6601,0.6601,0.6606,0.6616,0.6642, 0.6728,0.6759,0.6904,0.7007,0.7018,0.7028,0.7083,0.7207,0.7223,0.7324, 0.7332,0.7381,0.7385,0.7440,0.7450,0.7538,0.7540,0.7579,0.7650,0.7651, 0.7669,0.7704,0.7737,0.7781,0.7822,0.7860,0.7871,0.7888,0.7897,0.7902, 0.7917,0.7947,0.7947,0.7958,0.7976,0.7995,0.8012,0.8013,0.8017,0.8048, 0.8088,0.8095,0.8119,0.8122,0.8156,0.8175,0.8186,0.8194,0.8302,0.8318, 0.8378,0.8390,0.8407,0.8427,0.8456,0.8480,0.8590,0.8608,0.8616,0.8621, 0.8629,0.8828,0.8847,0.8854,0.8968,0.9024,0.9103,0.9120,0.9168,0.9215, 0.9287,0.9303,0.9324,0.9370,0.9424,0.9450,0.9473,0.9488,0.9509,0.9535, 0.9539,0.9674,0.9730,0.9777,0.9788,0.9829,0.9983,0.9991,0.9997, Overall p-value after applying KStest on 269 p-values = 0.232802 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.