RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.89 18.3813 0.634822 2 to 25 15.49 26.8704 0.940004 3 to 26 15.79 20.1186 0.731790 4 to 27 16.03 10.4275 0.115268 5 to 28 15.91 9.7226 0.085163 6 to 29 15.69 16.0453 0.479374 7 to 30 15.78 14.9089 0.397960 8 to 31 16.05 23.6534 0.870837 9 to 32 15.92 10.3007 0.109469 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.907390 Tough bday spacings test for dh-ranFile-2018-06-26_23:31: 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 26 75 83 108 90 56 28 14 6 6 (O-E)^2/E 0.1 3.1 0.0 2.2 1.1 1.8 0.3 0.1 0.1 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.795, p= 0.541 RESULTS OF GCD FOR dh-ranFile-2018-06-26_23:31 Euclid's algorithm: p-value, steps to gcd: 0.939332 p-value, dist. of gcd's: 0.188091 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.210 0.437 0.475 0.200 0.026 0.556 0.681 0.671 Bits 8 to 15---> 0.891 0.106 0.953 0.199 0.736 0.006 0.507 0.764 Bits 16 to 23---> 0.041 0.637 0.578 0.400 0.328 0.276 0.385 0.343 Bits 24 to 31---> 0.202 0.267 0.600 0.884 0.175 0.121 0.412 0.992 KS test for the above 32 p values: 0.566 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_23:31, p-values for 5 runs: 0.9448, 0.3733, 0.0768, 0.8028, 0.5656 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5145 5134.0 0.024 0.079 r= 30 23051 23103.0 0.117 0.196 r= 31 11596 11551.5 0.171 0.367 chi-square = 0.367 with df = 3; p-value = 0.053 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5075 5134.0 0.678 0.706 r= 31 23097 23103.0 0.002 0.708 r= 32 11619 11551.5 0.394 1.102 chi-square = 1.102 with df = 3; p-value = 0.223 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_23:31 b-rank test for bits 1 to 8, p=0.70230 b-rank test for bits 2 to 9, p=0.39863 b-rank test for bits 3 to 10, p=0.74813 b-rank test for bits 4 to 11, p=0.59674 b-rank test for bits 5 to 12, p=0.53570 b-rank test for bits 6 to 13, p=0.05534 b-rank test for bits 7 to 14, p=0.10666 b-rank test for bits 8 to 15, p=0.25401 b-rank test for bits 9 to 16, p=0.27758 b-rank test for bits 10 to 17, p=0.59559 b-rank test for bits 11 to 18, p=0.36318 b-rank test for bits 12 to 19, p=0.95579 b-rank test for bits 13 to 20, p=0.21284 b-rank test for bits 14 to 21, p=0.62246 b-rank test for bits 15 to 22, p=0.91068 b-rank test for bits 16 to 23, p=0.52649 b-rank test for bits 17 to 24, p=0.71310 b-rank test for bits 18 to 25, p=0.26182 b-rank test for bits 19 to 26, p=0.83391 b-rank test for bits 20 to 27, p=0.30407 b-rank test for bits 21 to 28, p=0.13534 b-rank test for bits 22 to 29, p=0.78840 b-rank test for bits 23 to 30, p=0.82070 b-rank test for bits 24 to 31, p=0.55650 b-rank test for bits 25 to 32, p=0.91881 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 = 0.920201 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_23:31 (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 142020 0.26 0.602018 2 141946 0.09 0.534139 3 142076 0.39 0.651516 4 141286 -1.46 0.072644 5 142049 0.33 0.627913 6 141470 -1.03 0.152335 7 141704 -0.48 0.315705 8 142101 0.45 0.672861 9 142074 0.38 0.649786 10 142091 0.42 0.664386 11 142190 0.66 0.744014 12 142648 1.73 0.957814 13 142186 0.65 0.740998 14 141499 -0.96 0.168851 15 141469 -1.03 0.151785 16 141378 -1.24 0.107224 17 142159 0.58 0.720168 18 141603 -0.72 0.237081 19 142140 0.54 0.705039 20 142051 0.33 0.629680 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-26_23:31 Bits used No. missing words z-score p-value 23 to 32 142170 0.8989 0.815637 22 to 31 142301 1.3506 0.911586 21 to 30 142015 0.3644 0.642213 20 to 29 142140 0.7954 0.786814 19 to 28 142058 0.5127 0.695904 18 to 27 141722 -0.6460 0.259151 17 to 26 142041 0.4540 0.675098 16 to 25 142032 0.4230 0.663852 15 to 24 142321 1.4196 0.922131 14 to 23 141894 -0.0529 0.478921 13 to 22 141626 -0.9770 0.164285 12 to 21 141876 -0.1149 0.454250 11 to 20 141893 -0.0563 0.477547 10 to 19 141956 0.1609 0.563926 9 to 18 141774 -0.4667 0.320373 8 to 17 141754 -0.5356 0.296110 7 to 16 141969 0.2058 0.581510 6 to 15 141831 -0.2701 0.393540 5 to 14 141720 -0.6529 0.256923 4 to 13 142019 0.3782 0.647349 3 to 12 141659 -0.8632 0.194012 2 to 11 142295 1.3299 0.908224 1 to 10 141566 -1.1839 0.118227 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-26_23:31 Bits used No. missing words z-score p-value 28 to 32 141749 -0.5435 0.293396 27 to 31 141629 -0.9503 0.170987 26 to 30 141672 -0.8045 0.210552 25 to 29 141822 -0.2960 0.383602 24 to 28 141719 -0.6452 0.259403 23 to 27 141911 0.0057 0.502258 22 to 26 142230 1.0870 0.861485 21 to 25 141424 -1.6452 0.049966 20 to 24 141845 -0.2181 0.413688 19 to 23 141536 -1.2655 0.102842 18 to 22 141906 -0.0113 0.495497 17 to 21 141762 -0.4994 0.308741 16 to 20 142032 0.4158 0.661233 15 to 19 141858 -0.1740 0.430933 14 to 18 141773 -0.4621 0.321992 13 to 17 141387 -1.7706 0.038313 12 to 16 142046 0.4633 0.678421 11 to 15 141893 -0.0554 0.477928 10 to 14 141574 -1.1367 0.127829 9 to 13 141979 0.2362 0.593349 8 to 12 141911 0.0057 0.502258 7 to 11 142088 0.6057 0.727630 6 to 10 141673 -0.8011 0.211532 5 to 9 141804 -0.3571 0.360527 4 to 8 142251 1.1582 0.876610 3 to 7 142263 1.1989 0.884713 2 to 6 141931 0.0735 0.529279 1 to 5 141332 -1.9571 0.025171 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-26_23:31 Bits used No. missing words z-score p-value 31 to 32 142329 1.2380 0.892135 30 to 31 142069 0.4710 0.681181 29 to 30 141926 0.0492 0.519610 28 to 29 142231 0.9489 0.828659 27 to 28 142191 0.8309 0.796981 26 to 27 142185 0.8132 0.791944 25 to 26 141786 -0.3638 0.358002 24 to 25 141602 -0.9066 0.182315 23 to 24 141567 -1.0098 0.156290 22 to 23 141071 -2.4729 0.006700 21 to 22 141959 0.1465 0.558244 20 to 21 142135 0.6657 0.747196 19 to 20 142335 1.2557 0.895381 18 to 19 141839 -0.2075 0.417824 17 to 18 141525 -1.1337 0.128457 16 to 17 141739 -0.5024 0.307676 15 to 16 142119 0.6185 0.731876 14 to 15 141956 0.1377 0.554749 13 to 14 141074 -2.4641 0.006868 12 to 13 141327 -1.7178 0.042918 11 to 12 141655 -0.7502 0.226556 10 to 11 141941 0.0934 0.537216 9 to 10 142106 0.5801 0.719092 8 to 9 141511 -1.1750 0.119994 7 to 8 141403 -1.4936 0.067640 6 to 7 142023 0.3353 0.631304 5 to 6 141890 -0.0570 0.477264 4 to 5 141572 -0.9951 0.159850 3 to 4 141850 -0.1750 0.430534 2 to 3 141972 0.1849 0.573333 1 to 2 142318 1.2055 0.885998 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2413.02 -1.230 0.109323 Test results for specific bytes for dh-ranFile-2018-06-26_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.67 0.349 0.636400 2 to 9 2466.55 -0.473 0.318090 3 to 10 2513.57 0.192 0.576111 4 to 11 2488.34 -0.165 0.434509 5 to 12 2405.19 -1.341 0.089998 6 to 13 2525.43 0.360 0.640418 7 to 14 2553.38 0.755 0.774859 8 to 15 2545.74 0.647 0.741142 9 to 16 2383.13 -1.653 0.049180 10 to 17 2590.39 1.278 0.899441 11 to 18 2418.57 -1.152 0.124743 12 to 19 2436.91 -0.892 0.186124 13 to 20 2517.88 0.253 0.599798 14 to 21 2568.93 0.975 0.835171 15 to 22 2577.51 1.096 0.863488 16 to 23 2562.08 0.878 0.810027 17 to 24 2402.74 -1.375 0.084502 18 to 25 2552.68 0.745 0.771865 19 to 26 2490.87 -0.129 0.448613 20 to 27 2540.82 0.577 0.718108 21 to 28 2541.70 0.590 0.722308 22 to 29 2519.03 0.269 0.606105 23 to 30 2429.21 -1.001 0.158388 24 to 31 2392.84 -1.515 0.064835 25 to 32 2464.97 -0.495 0.310176 CDPARK for dh-ranFile-2018-06-26_23:31: 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 3535 0.5479 0.708135 3538 0.6849 0.753306 3545 1.0046 0.842447 3543 0.9132 0.819442 3546 1.0502 0.853193 3489 -1.5525 0.060270 3523 0.0000 0.500000 3531 0.3653 0.642555 3510 -0.5936 0.276387 3523 0.0000 0.500000 Square side=100, avg. no. parked=3528.30 sample std.=17.00 p-value of the KSTEST for those 10 p-values: 0.375028 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_23:31 0.3848,0.6397,0.4132,0.6899,0.3878,0.1547,0.6027,0.0279,0.5749,0.9610, The KS test for those 10 p-values: 0.856322 The 3DSPHERES test for dh-ranFile-2018-06-26_23:31 sample no r^3 equiv. uni. 1 26.786 0.590520 2 29.994 0.632050 3 3.360 0.105944 4 36.491 0.703697 5 26.983 0.593196 6 13.169 0.355307 7 8.017 0.234513 8 0.232 0.007717 9 7.882 0.231042 10 13.927 0.371373 11 20.996 0.503351 12 13.551 0.363450 13 29.406 0.624767 14 11.971 0.329026 15 24.435 0.557138 16 48.369 0.800569 17 20.213 0.490207 18 65.236 0.886340 19 53.480 0.831808 20 22.026 0.520112 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.511774 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 -0.4 0.2 2.0 0.1 -0.9 -0.5 -0.3 2.1 0.6 0.4 -1.2 -0.7 -1.7 -1.1 0.8 -1.0 1.3 0.2 -1.0 1.7 0.6 1.8 -0.7 0.3 0.8 0.1 0.3 -1.9 -0.1 -1.7 -1.4 -0.9 0.6 1.7 1.4 -2.0 0.9 -0.1 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:49.021714 z-score=0.766132, p-value=0.787864 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-26_23:31 Test no p-value 1 0.178825 2 0.316279 3 0.394146 4 0.319950 5 0.210670 6 0.363112 7 0.355419 8 0.041913 9 0.000451 10 0.814975 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.024567 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_23:31: (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 66547 0.21 66716 0.04 3 25000.00 25023 0.02 25057 0.13 4 6666.67 6693 0.10 6591 0.86 5 1388.89 1452 2.87 1378 0.09 6 238.10 241 0.04 224 0.83 7 34.72 38 0.31 31 0.40 8 4.96 5 0.00 2 1.77 p=0.26313 p=0.33823 Number of rngs required: 689545, p-value: 0.908 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_23:31 No. of wins: Observed Expected 99045 98585.9 z-score= 2.054, pvalue=0.97999 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66903 66666.7 0.838 0.838 2 37419 37654.3 1.471 2.308 3 26919 26954.7 0.047 2.356 4 19075 19313.5 2.944 5.300 5 13920 13851.4 0.340 5.640 6 10023 9943.5 0.635 6.275 7 7289 7145.0 2.901 9.176 8 5033 5139.1 2.189 11.365 9 3697 3699.9 0.002 11.367 10 2714 2666.3 0.853 12.221 11 1890 1923.3 0.578 12.798 12 1371 1388.7 0.227 13.025 13 1075 1003.7 5.063 18.088 14 785 726.1 4.771 22.859 15 520 525.8 0.065 22.923 16 357 381.2 1.530 24.454 17 284 276.5 0.201 24.655 18 189 200.8 0.697 25.352 19 132 146.0 1.340 26.691 20 109 106.2 0.073 26.764 21 296 287.1 0.275 27.039 Chisq= 27.04 for 20 degrees of freedom, p= 0.86584 SUMMARY of craptest p-value for no. of wins: 0.979990 p-value for throws/game: 0.865841 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_23:31 No. of wins: Observed Expected 98682 98585.9 z-score= 0.430, pvalue=0.66640 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66801 66666.7 0.271 0.271 2 37939 37654.3 2.152 2.423 3 26807 26954.7 0.810 3.233 4 19203 19313.5 0.632 3.864 5 13802 13851.4 0.176 4.041 6 9810 9943.5 1.793 5.834 7 7150 7145.0 0.003 5.838 8 5222 5139.1 1.338 7.176 9 3673 3699.9 0.195 7.371 10 2615 2666.3 0.987 8.358 11 1975 1923.3 1.388 9.746 12 1375 1388.7 0.136 9.882 13 1030 1003.7 0.688 10.570 14 694 726.1 1.423 11.993 15 518 525.8 0.117 12.110 16 357 381.2 1.530 13.640 17 269 276.5 0.206 13.845 18 219 200.8 1.644 15.489 19 152 146.0 0.248 15.737 20 98 106.2 0.635 16.373 21 291 287.1 0.053 16.425 Chisq= 16.43 for 20 degrees of freedom, p= 0.31009 SUMMARY of craptest p-value for no. of wins: 0.666402 p-value for throws/game: 0.310088 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0064,0.0067,0.0069,0.0077,0.0246,0.0252,0.0259,0.0279,0.0383, 0.0409,0.0419,0.0429,0.0492,0.0500,0.0531,0.0553,0.0603,0.0648,0.0676, 0.0726,0.0768,0.0845,0.0852,0.0900,0.1028,0.1059,0.1061,0.1067,0.1072, 0.1093,0.1095,0.1153,0.1182,0.1200,0.1214,0.1247,0.1278,0.1285,0.1353, 0.1518,0.1523,0.1547,0.1563,0.1584,0.1599,0.1643,0.1689,0.1710,0.1753, 0.1788,0.1823,0.1861,0.1881,0.1940,0.1988,0.2002,0.2019,0.2096,0.2106, 0.2107,0.2115,0.2128,0.2233,0.2266,0.2310,0.2345,0.2371,0.2540,0.2569, 0.2592,0.2594,0.2618,0.2631,0.2674,0.2756,0.2764,0.2776,0.2934,0.2961, 0.3041,0.3077,0.3087,0.3101,0.3102,0.3157,0.3163,0.3181,0.3200,0.3204, 0.3220,0.3281,0.3290,0.3382,0.3427,0.3553,0.3554,0.3580,0.3605,0.3631, 0.3632,0.3635,0.3714,0.3733,0.3750,0.3836,0.3848,0.3855,0.3878,0.3935, 0.3941,0.3980,0.3986,0.3997,0.4116,0.4132,0.4137,0.4178,0.4305,0.4309, 0.4345,0.4366,0.4486,0.4542,0.4751,0.4773,0.4775,0.4779,0.4789,0.4794, 0.4902,0.4955,0.5000,0.5000,0.5023,0.5023,0.5034,0.5067,0.5118,0.5196, 0.5201,0.5265,0.5293,0.5341,0.5357,0.5372,0.5413,0.5547,0.5559,0.5565, 0.5571,0.5582,0.5639,0.5656,0.5656,0.5733,0.5749,0.5761,0.5779,0.5815, 0.5905,0.5932,0.5933,0.5956,0.5967,0.5998,0.5998,0.6020,0.6027,0.6061, 0.6225,0.6248,0.6279,0.6297,0.6313,0.6320,0.6348,0.6364,0.6367,0.6397, 0.6404,0.6422,0.6426,0.6473,0.6498,0.6515,0.6612,0.6639,0.6644,0.6664, 0.6712,0.6729,0.6751,0.6784,0.6812,0.6812,0.6899,0.6959,0.7023,0.7037, 0.7050,0.7081,0.7131,0.7181,0.7191,0.7202,0.7223,0.7276,0.7318,0.7319, 0.7362,0.7410,0.7411,0.7440,0.7472,0.7481,0.7533,0.7640,0.7719,0.7749, 0.7868,0.7879,0.7884,0.7919,0.7970,0.8006,0.8028,0.8100,0.8150,0.8156, 0.8194,0.8207,0.8287,0.8318,0.8339,0.8352,0.8424,0.8532,0.8563,0.8615, 0.8635,0.8658,0.8708,0.8766,0.8838,0.8847,0.8860,0.8863,0.8910,0.8921, 0.8954,0.8994,0.9074,0.9082,0.9082,0.9107,0.9116,0.9188,0.9202,0.9221, 0.9393,0.9400,0.9448,0.9532,0.9558,0.9578,0.9610,0.9800,0.9918, Overall p-value after applying KStest on 269 p-values = 0.286341 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.