RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-04-25_06:31 (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 17.5268 0.580738 2 to 25 15.94 32.2087 0.985826 3 to 26 15.88 12.4286 0.226484 4 to 27 15.74 21.6907 0.803092 5 to 28 15.67 13.1872 0.276434 6 to 29 15.63 22.4318 0.831320 7 to 30 15.42 28.2181 0.957547 8 to 31 15.73 25.5601 0.917142 9 to 32 15.67 20.1457 0.733156 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.042897 Tough bday spacings test for dh-ranFile-2017-04-25_06:31: 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 10 37 70 99 96 83 62 23 13 6 1 (O-E)^2/E 0.1 0.0 0.1 0.0 0.0 0.3 1.9 1.5 0.2 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 6.604, p= 0.238 RESULTS OF GCD FOR dh-ranFile-2017-04-25_06:31 Euclid's algorithm: p-value, steps to gcd: 0.776109 p-value, dist. of gcd's: 0.869960 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-04-25_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.040 0.455 0.970 0.104 0.259 0.177 0.723 0.703 Bits 8 to 15---> 0.339 0.274 0.504 0.127 0.681 0.126 0.779 0.205 Bits 16 to 23---> 0.507 0.078 0.451 0.881 0.653 0.047 0.715 0.495 Bits 24 to 31---> 0.315 0.591 0.464 0.246 0.327 0.653 0.339 0.091 KS test for the above 32 p values: 0.844 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-04-25_06:31, p-values for 5 runs: 0.8132, 0.2843, 0.3884, 0.5084, 0.4965 Rank test for binary matrices (31x31) for dh-ranFile-2017-04-25_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5137 5134.0 0.002 0.029 r= 30 23121 23103.0 0.014 0.043 r= 31 11533 11551.5 0.030 0.073 chi-square = 0.073 with df = 3; p-value = 0.005 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-04-25_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5204 5134.0 0.954 0.986 r= 31 23170 23103.0 0.194 1.180 r= 32 11412 11551.5 1.685 2.865 chi-square = 2.865 with df = 3; p-value = 0.587 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-04-25_06:31 b-rank test for bits 1 to 8, p=0.56802 b-rank test for bits 2 to 9, p=0.52826 b-rank test for bits 3 to 10, p=0.05149 b-rank test for bits 4 to 11, p=0.06157 b-rank test for bits 5 to 12, p=0.69901 b-rank test for bits 6 to 13, p=0.52527 b-rank test for bits 7 to 14, p=0.29541 b-rank test for bits 8 to 15, p=0.12571 b-rank test for bits 9 to 16, p=0.01673 b-rank test for bits 10 to 17, p=0.52561 b-rank test for bits 11 to 18, p=0.22638 b-rank test for bits 12 to 19, p=0.36530 b-rank test for bits 13 to 20, p=0.27981 b-rank test for bits 14 to 21, p=0.19169 b-rank test for bits 15 to 22, p=0.96947 b-rank test for bits 16 to 23, p=0.70157 b-rank test for bits 17 to 24, p=0.41138 b-rank test for bits 18 to 25, p=0.73388 b-rank test for bits 19 to 26, p=0.29180 b-rank test for bits 20 to 27, p=0.80817 b-rank test for bits 21 to 28, p=0.06979 b-rank test for bits 22 to 29, p=0.60692 b-rank test for bits 23 to 30, p=0.06745 b-rank test for bits 24 to 31, p=0.22582 b-rank test for bits 25 to 32, p=0.61578 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 = 0.123740 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-04-25_06:31 (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 142246 0.79 0.784246 2 141628 -0.66 0.255490 3 141723 -0.44 0.331654 4 142534 1.46 0.927788 5 141253 -1.53 0.062579 6 141261 -1.51 0.064913 7 141535 -0.87 0.190895 8 142048 0.32 0.627029 9 142379 1.10 0.863758 10 141763 -0.34 0.366216 11 142088 0.42 0.661827 12 141947 0.09 0.535067 13 142078 0.39 0.653242 14 141984 0.17 0.569249 15 141658 -0.59 0.278528 16 142593 1.60 0.944907 17 141812 -0.23 0.410054 18 141800 -0.26 0.399190 19 141210 -1.63 0.051135 20 141816 -0.22 0.413691 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-04-25_06:31 Bits used No. missing words z-score p-value 23 to 32 141654 -0.8804 0.189308 22 to 31 141722 -0.6460 0.259151 21 to 30 141972 0.2161 0.585547 20 to 29 142001 0.3161 0.624038 19 to 28 142279 1.2747 0.898797 18 to 27 141908 -0.0046 0.498170 17 to 26 141734 -0.6046 0.272727 16 to 25 142078 0.5816 0.719589 15 to 24 141790 -0.4115 0.340359 14 to 23 142005 0.3299 0.629261 13 to 22 142253 1.1851 0.882005 12 to 21 141932 0.0782 0.531155 11 to 20 142052 0.4920 0.688628 10 to 19 142051 0.4885 0.687408 9 to 18 141844 -0.2253 0.410882 8 to 17 141677 -0.8011 0.211526 7 to 16 142407 1.7161 0.956928 6 to 15 142168 0.8920 0.813794 5 to 14 141867 -0.1460 0.441974 4 to 13 141660 -0.8598 0.194961 3 to 12 142198 0.9954 0.840233 2 to 11 142163 0.8747 0.809138 1 to 10 141973 0.2196 0.586890 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-04-25_06:31 Bits used No. missing words z-score p-value 28 to 32 141530 -1.2859 0.099245 27 to 31 142229 1.0836 0.860735 26 to 30 141828 -0.2757 0.391391 25 to 29 141221 -2.3333 0.009816 24 to 28 141651 -0.8757 0.190598 23 to 27 141263 -2.1909 0.014228 22 to 26 141758 -0.5130 0.303982 21 to 25 141875 -0.1164 0.453679 20 to 24 141715 -0.6587 0.255030 19 to 23 141774 -0.4587 0.323208 18 to 22 142532 2.1107 0.982603 17 to 21 141972 0.2124 0.584118 16 to 20 142974 3.6091 0.999846 15 to 19 141558 -1.1909 0.116837 14 to 18 142254 1.1684 0.878672 13 to 17 142405 1.6802 0.953544 12 to 16 141872 -0.1265 0.449651 11 to 15 142223 1.0633 0.856174 10 to 14 142597 2.3311 0.990126 9 to 13 141916 0.0226 0.509019 8 to 12 142266 1.2091 0.886678 7 to 11 142284 1.2701 0.897970 6 to 10 142395 1.6463 0.950153 5 to 9 142163 0.8599 0.805077 4 to 8 142057 0.5006 0.691665 3 to 7 142354 1.5074 0.934140 2 to 6 141958 0.1650 0.565521 1 to 5 142271 1.2260 0.889901 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-04-25_06:31 Bits used No. missing words z-score p-value 31 to 32 142119 0.6185 0.731876 30 to 31 142103 0.5713 0.716101 29 to 30 142341 1.2734 0.898555 28 to 29 141823 -0.2547 0.399493 27 to 28 142536 1.8486 0.967741 26 to 27 141532 -1.1131 0.132840 25 to 26 142250 1.0049 0.842534 24 to 25 142102 0.5683 0.715101 23 to 24 142246 0.9931 0.839676 22 to 23 141782 -0.3756 0.353605 21 to 22 142709 2.3589 0.990836 20 to 21 141951 0.1229 0.548915 19 to 20 141821 -0.2606 0.397216 18 to 19 141541 -1.0865 0.138625 17 to 18 142188 0.8220 0.794472 16 to 17 141348 -1.6558 0.048877 15 to 16 142105 0.5772 0.718097 14 to 15 142066 0.4622 0.678014 13 to 14 142278 1.0875 0.861597 12 to 13 142002 0.2734 0.607713 11 to 12 142254 1.0167 0.845358 10 to 11 142664 2.2262 0.986998 9 to 10 142000 0.2675 0.605444 8 to 9 141815 -0.2783 0.390407 7 to 8 142277 1.0846 0.860944 6 to 7 141731 -0.5260 0.299428 5 to 6 142142 0.6863 0.753751 4 to 5 141596 -0.9243 0.177671 3 to 4 141794 -0.3402 0.366851 2 to 3 141720 -0.5585 0.288253 1 to 2 142436 1.5536 0.939860 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-04-25_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2537.18 0.526 0.700474 Test results for specific bytes for dh-ranFile-2017-04-25_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2378.84 -1.713 0.043316 2 to 9 2627.51 1.803 0.964330 3 to 10 2476.55 -0.332 0.370077 4 to 11 2348.82 -2.138 0.016260 5 to 12 2488.76 -0.159 0.436858 6 to 13 2576.10 1.076 0.859096 7 to 14 2388.84 -1.572 0.057963 8 to 15 2438.50 -0.870 0.192234 9 to 16 2579.31 1.122 0.868982 10 to 17 2556.84 0.804 0.789241 11 to 18 2433.25 -0.944 0.172577 12 to 19 2558.20 0.823 0.794784 13 to 20 2465.01 -0.495 0.310371 14 to 21 2650.77 2.132 0.983504 15 to 22 2611.20 1.573 0.942089 16 to 23 2571.94 1.017 0.845524 17 to 24 2603.08 1.458 0.927549 18 to 25 2574.48 1.053 0.853904 19 to 26 2549.81 0.704 0.759405 20 to 27 2434.11 -0.932 0.175730 21 to 28 2468.64 -0.443 0.328723 22 to 29 2472.03 -0.396 0.346226 23 to 30 2416.91 -1.175 0.119972 24 to 31 2506.70 0.095 0.537762 25 to 32 2568.74 0.972 0.834505 CDPARK for dh-ranFile-2017-04-25_06:31: 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 3586 2.8767 0.997991 3541 0.8219 0.794438 3529 0.2740 0.607947 3555 1.4612 0.928018 3538 0.6849 0.753306 3539 0.7306 0.767486 3481 -1.9178 0.027568 3543 0.9132 0.819442 3574 2.3288 0.990064 3538 0.6849 0.753306 Square side=100, avg. no. parked=3542.40 sample std.=26.57 p-value of the KSTEST for those 10 p-values: 0.003420 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-04-25_06:31 0.9254,0.8195,0.7816,0.8335,0.1858,0.1989,0.9572,0.3991,0.7750,0.8473, The KS test for those 10 p-values: 0.055612 The 3DSPHERES test for dh-ranFile-2017-04-25_06:31 sample no r^3 equiv. uni. 1 4.342 0.134757 2 47.667 0.795847 3 69.255 0.900590 4 0.840 0.027615 5 20.900 0.501762 6 6.490 0.194546 7 6.678 0.199569 8 17.961 0.450468 9 4.368 0.135494 10 6.801 0.202835 11 0.491 0.016220 12 69.421 0.901138 13 52.024 0.823450 14 5.747 0.174338 15 8.249 0.240415 16 73.232 0.912933 17 5.189 0.158824 18 43.268 0.763609 19 3.240 0.102383 20 9.023 0.259754 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.058676 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-04-25_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.6 0.0 1.3 -0.6 1.0 -1.9 -0.4 0.2 0.2 -0.7 -0.0 -0.1 1.1 0.3 -0.9 -0.8 -0.4 -0.7 0.2 1.7 0.1 1.0 -1.1 -1.2 0.4 0.9 0.8 1.0 1.1 0.8 -1.5 1.2 -2.2 -0.3 0.0 0.5 -0.4 -0.1 -1.3 0.0 1.8 Chi-square with 42 degrees of freedom:36.137021 z-score=-0.639703, p-value=0.274768 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-04-25_06:31 Test no p-value 1 0.039443 2 0.001774 3 0.965515 4 0.903580 5 0.472386 6 0.983528 7 0.637467 8 0.077614 9 0.740368 10 0.217647 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.197799 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-04-25_06:31: (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 66674 0.00 66673 0.00 3 25000.00 24987 0.01 25027 0.03 4 6666.67 6683 0.04 6650 0.04 5 1388.89 1379 0.07 1369 0.28 6 238.10 245 0.20 241 0.04 7 34.72 27 1.72 35 0.00 8 4.96 4 0.19 4 0.19 p=0.10166 p=0.00327 Number of rngs required: 688049, p-value: 0.342 RESULTS OF CRAPS TEST for dh-ranFile-2017-04-25_06:31 No. of wins: Observed Expected 98749 98585.9 z-score= 0.730, pvalue=0.76720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66396 66666.7 1.099 1.099 2 38063 37654.3 4.436 5.534 3 26724 26954.7 1.975 7.510 4 19316 19313.5 0.000 7.510 5 13944 13851.4 0.619 8.129 6 9921 9943.5 0.051 8.180 7 7229 7145.0 0.987 9.167 8 5013 5139.1 3.093 12.260 9 3691 3699.9 0.021 12.281 10 2735 2666.3 1.770 14.051 11 1918 1923.3 0.015 14.066 12 1444 1388.7 2.199 16.265 13 1037 1003.7 1.104 17.368 14 704 726.1 0.675 18.044 15 468 525.8 6.361 24.405 16 386 381.2 0.062 24.466 17 282 276.5 0.108 24.574 18 190 200.8 0.584 25.158 19 133 146.0 1.155 26.313 20 109 106.2 0.073 26.386 21 297 287.1 0.340 26.727 Chisq= 26.73 for 20 degrees of freedom, p= 0.85687 SUMMARY of craptest p-value for no. of wins: 0.767202 p-value for throws/game: 0.856868 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-04-25_06:31 No. of wins: Observed Expected 98541 98585.9 z-score=-0.201, pvalue=0.42049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66675 66666.7 0.001 0.001 2 37870 37654.3 1.235 1.236 3 26929 26954.7 0.025 1.261 4 19388 19313.5 0.288 1.549 5 13675 13851.4 2.247 3.796 6 9918 9943.5 0.066 3.861 7 7159 7145.0 0.027 3.889 8 5019 5139.1 2.805 6.694 9 3667 3699.9 0.292 6.986 10 2648 2666.3 0.126 7.112 11 1946 1923.3 0.267 7.379 12 1371 1388.7 0.227 7.605 13 1005 1003.7 0.002 7.607 14 731 726.1 0.033 7.640 15 570 525.8 3.709 11.349 16 427 381.2 5.515 16.864 17 279 276.5 0.022 16.886 18 185 200.8 1.248 18.134 19 145 146.0 0.007 18.140 20 105 106.2 0.014 18.154 21 288 287.1 0.003 18.157 Chisq= 18.16 for 20 degrees of freedom, p= 0.42294 SUMMARY of craptest p-value for no. of wins: 0.420492 p-value for throws/game: 0.422937 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0033,0.0034,0.0051,0.0098,0.0142,0.0162,0.0163,0.0167,0.0276, 0.0276,0.0394,0.0403,0.0429,0.0433,0.0474,0.0489,0.0511,0.0515,0.0556, 0.0580,0.0587,0.0616,0.0626,0.0649,0.0675,0.0698,0.0776,0.0779,0.0912, 0.0992,0.1017,0.1024,0.1039,0.1168,0.1200,0.1237,0.1256,0.1257,0.1270, 0.1328,0.1348,0.1355,0.1386,0.1588,0.1726,0.1743,0.1757,0.1766,0.1777, 0.1858,0.1893,0.1906,0.1909,0.1917,0.1922,0.1945,0.1950,0.1978,0.1989, 0.1996,0.2028,0.2054,0.2115,0.2176,0.2258,0.2264,0.2265,0.2378,0.2404, 0.2455,0.2550,0.2555,0.2592,0.2592,0.2598,0.2727,0.2739,0.2748,0.2764, 0.2785,0.2798,0.2843,0.2883,0.2918,0.2954,0.2994,0.3040,0.3104,0.3151, 0.3232,0.3274,0.3287,0.3317,0.3389,0.3392,0.3404,0.3417,0.3462,0.3536, 0.3653,0.3662,0.3669,0.3701,0.3884,0.3904,0.3914,0.3972,0.3991,0.3992, 0.3995,0.4101,0.4109,0.4114,0.4137,0.4205,0.4229,0.4369,0.4420,0.4497, 0.4505,0.4508,0.4537,0.4550,0.4640,0.4724,0.4948,0.4965,0.4982,0.5018, 0.5037,0.5073,0.5084,0.5090,0.5253,0.5256,0.5283,0.5312,0.5351,0.5378, 0.5489,0.5655,0.5680,0.5692,0.5807,0.5841,0.5855,0.5869,0.5871,0.5906, 0.6054,0.6069,0.6077,0.6079,0.6158,0.6240,0.6270,0.6293,0.6375,0.6530, 0.6532,0.6534,0.6618,0.6780,0.6809,0.6874,0.6886,0.6917,0.6990,0.7005, 0.7016,0.7033,0.7151,0.7155,0.7161,0.7181,0.7196,0.7233,0.7319,0.7332, 0.7339,0.7404,0.7533,0.7533,0.7538,0.7594,0.7636,0.7672,0.7675,0.7750, 0.7761,0.7794,0.7816,0.7842,0.7892,0.7944,0.7945,0.7948,0.7958,0.8031, 0.8051,0.8082,0.8091,0.8132,0.8138,0.8194,0.8195,0.8234,0.8313,0.8335, 0.8345,0.8397,0.8402,0.8425,0.8444,0.8454,0.8455,0.8473,0.8539,0.8562, 0.8569,0.8591,0.8607,0.8609,0.8616,0.8638,0.8690,0.8700,0.8787,0.8806, 0.8820,0.8867,0.8899,0.8980,0.8986,0.8988,0.9006,0.9011,0.9036,0.9129, 0.9171,0.9254,0.9275,0.9278,0.9280,0.9341,0.9399,0.9421,0.9449,0.9502, 0.9535,0.9569,0.9572,0.9575,0.9643,0.9655,0.9677,0.9695,0.9702,0.9826, 0.9835,0.9835,0.9858,0.9870,0.9901,0.9901,0.9908,0.9980,0.9998, Overall p-value after applying KStest on 269 p-values = 0.088937 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.