RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-22_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 31.8186 0.984152 2 to 25 16.02 23.2487 0.858673 3 to 26 16.07 20.4708 0.749138 4 to 27 15.84 15.6227 0.449280 5 to 28 15.70 16.7983 0.531889 6 to 29 15.84 12.0856 0.205076 7 to 30 15.67 21.7660 0.806112 8 to 31 15.47 25.1135 0.907803 9 to 32 15.72 12.6432 0.240276 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.255406 Tough bday spacings test for dh-ranFile-2016-02-22_05:31: 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 37 68 86 117 78 48 33 14 10 1 (O-E)^2/E 0.1 0.0 0.4 1.4 3.8 0.0 0.3 0.4 0.1 1.7 2.3 Birthday Spacings: Sum(O-E)^2/E= 10.514, p= 0.603 RESULTS OF GCD FOR dh-ranFile-2016-02-22_05:31 Euclid's algorithm: p-value, steps to gcd: 0.186209 p-value, dist. of gcd's: 0.986443 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-22_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.040 0.708 0.904 0.902 0.492 0.776 0.211 0.448 Bits 8 to 15---> 0.972 0.492 0.367 0.045 0.637 0.446 0.439 0.228 Bits 16 to 23---> 0.428 0.337 0.149 0.966 0.380 0.224 0.007 0.830 Bits 24 to 31---> 0.488 0.307 0.971 0.083 0.936 0.757 0.700 0.074 KS test for the above 32 p values: 0.179 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-22_05:31, p-values for 5 runs: 0.3373, 0.4194, 0.6992, 0.1749, 0.8407 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-22_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 262 211.4 12.102 12.102 r= 29 5135 5134.0 0.000 12.102 r= 30 23185 23103.0 0.291 12.393 r= 31 11418 11551.5 1.543 13.936 chi-square = 13.936 with df = 3; p-value = 0.997 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-22_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5331 5134.0 7.558 7.590 r= 31 22839 23103.0 3.018 10.608 r= 32 11616 11551.5 0.360 10.968 chi-square = 10.968 with df = 3; p-value = 0.988 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-22_05:31 b-rank test for bits 1 to 8, p=0.00395 b-rank test for bits 2 to 9, p=0.16477 b-rank test for bits 3 to 10, p=0.99763 b-rank test for bits 4 to 11, p=0.29308 b-rank test for bits 5 to 12, p=0.67941 b-rank test for bits 6 to 13, p=0.15161 b-rank test for bits 7 to 14, p=0.68675 b-rank test for bits 8 to 15, p=0.97492 b-rank test for bits 9 to 16, p=0.24373 b-rank test for bits 10 to 17, p=0.45449 b-rank test for bits 11 to 18, p=0.30639 b-rank test for bits 12 to 19, p=0.56316 b-rank test for bits 13 to 20, p=0.33251 b-rank test for bits 14 to 21, p=0.23411 b-rank test for bits 15 to 22, p=0.51003 b-rank test for bits 16 to 23, p=0.67788 b-rank test for bits 17 to 24, p=0.93145 b-rank test for bits 18 to 25, p=0.53261 b-rank test for bits 19 to 26, p=0.49172 b-rank test for bits 20 to 27, p=0.67259 b-rank test for bits 21 to 28, p=0.92538 b-rank test for bits 22 to 29, p=0.53959 b-rank test for bits 23 to 30, p=0.57257 b-rank test for bits 24 to 31, p=0.25002 b-rank test for bits 25 to 32, p=0.61718 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 = 0.588863 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-22_05:31 (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 141848 -0.14 0.443029 2 141978 0.16 0.563734 3 142539 1.47 0.929380 4 141508 -0.94 0.174203 5 141866 -0.10 0.459681 6 141888 -0.05 0.480126 7 142121 0.49 0.689543 8 141991 0.19 0.575666 9 141107 -1.87 0.030424 10 141728 -0.42 0.335904 11 141811 -0.23 0.409146 12 141898 -0.03 0.489440 13 142309 0.93 0.824799 14 142115 0.48 0.684577 15 141848 -0.14 0.443029 16 141918 0.02 0.508081 17 141588 -0.75 0.226395 18 141485 -0.99 0.160739 19 141639 -0.63 0.263820 20 142590 1.59 0.944122 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-22_05:31 Bits used No. missing words z-score p-value 23 to 32 141805 -0.3598 0.359514 22 to 31 141893 -0.0563 0.477547 21 to 30 142302 1.3540 0.912137 20 to 29 141777 -0.4563 0.324083 19 to 28 142327 1.4402 0.925100 18 to 27 142596 2.3678 0.991054 17 to 26 142020 0.3816 0.648629 16 to 25 142237 1.1299 0.870740 15 to 24 141668 -0.8322 0.202656 14 to 23 141889 -0.0701 0.472056 13 to 22 141452 -1.5770 0.057398 12 to 21 141729 -0.6218 0.267028 11 to 20 142075 0.5713 0.716094 10 to 19 141634 -0.9494 0.171205 9 to 18 141579 -1.1391 0.127337 8 to 17 141903 -0.0218 0.491293 7 to 16 141482 -1.4736 0.070301 6 to 15 141875 -0.1184 0.452884 5 to 14 142346 1.5058 0.933935 4 to 13 142029 0.4127 0.660070 3 to 12 141700 -0.7218 0.235200 2 to 11 142413 1.7368 0.958788 1 to 10 141592 -1.0942 0.136925 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-22_05:31 Bits used No. missing words z-score p-value 28 to 32 142190 0.9514 0.829305 27 to 31 141733 -0.5977 0.275010 26 to 30 141621 -0.9774 0.164188 25 to 29 141818 -0.3096 0.378435 24 to 28 141508 -1.3604 0.086845 23 to 27 142013 0.3514 0.637365 22 to 26 141739 -0.5774 0.281838 21 to 25 142493 1.9785 0.976066 20 to 24 141770 -0.4723 0.318355 19 to 23 141449 -1.5604 0.059328 18 to 22 141984 0.2531 0.599912 17 to 21 141623 -0.9706 0.165871 16 to 20 141409 -1.6960 0.044940 15 to 19 141942 0.1107 0.544091 14 to 18 141887 -0.0757 0.469831 13 to 17 142318 1.3853 0.917023 12 to 16 141422 -1.6520 0.049271 11 to 15 142176 0.9040 0.816993 10 to 14 141665 -0.8282 0.203768 9 to 13 142097 0.6362 0.737667 8 to 12 142497 1.9921 0.976820 7 to 11 142134 0.7616 0.776849 6 to 10 142109 0.6768 0.750749 5 to 9 141320 -1.9977 0.022873 4 to 8 141670 -0.8113 0.208600 3 to 7 142437 1.7887 0.963169 2 to 6 141752 -0.5333 0.296905 1 to 5 141887 -0.0757 0.469831 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-22_05:31 Bits used No. missing words z-score p-value 31 to 32 141700 -0.6175 0.268455 30 to 31 141291 -1.8240 0.034077 29 to 30 141428 -1.4199 0.077825 28 to 29 142517 1.7925 0.963477 27 to 28 141675 -0.6912 0.244708 26 to 27 142387 1.4091 0.920591 25 to 26 141510 -1.1780 0.119405 24 to 25 141562 -1.0246 0.152783 23 to 24 142000 0.2675 0.605444 22 to 23 141962 0.1554 0.561735 21 to 22 142302 1.1583 0.876633 20 to 21 141910 0.0020 0.500789 19 to 20 141904 -0.0157 0.493728 18 to 19 142344 1.2822 0.900116 17 to 18 141664 -0.7237 0.234629 16 to 17 142284 1.1052 0.865468 15 to 16 141275 -1.8712 0.030660 14 to 15 141938 0.0846 0.533699 13 to 14 142256 1.0226 0.846758 12 to 13 142300 1.1524 0.875426 11 to 12 141757 -0.4494 0.326589 10 to 11 141187 -2.1308 0.016554 9 to 10 142187 0.8191 0.793631 8 to 9 141600 -0.9125 0.180759 7 to 8 141630 -0.8240 0.204975 6 to 7 142264 1.0462 0.852271 5 to 6 141812 -0.2871 0.387014 4 to 5 141903 -0.0187 0.492551 3 to 4 141737 -0.5083 0.305605 2 to 3 141680 -0.6765 0.249365 1 to 2 141721 -0.5555 0.289261 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-22_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2519.95 0.282 0.611075 Test results for specific bytes for dh-ranFile-2016-02-22_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2539.09 0.553 0.709807 2 to 9 2404.63 -1.349 0.088705 3 to 10 2552.28 0.739 0.770134 4 to 11 2398.89 -1.430 0.076381 5 to 12 2498.59 -0.020 0.492053 6 to 13 2419.37 -1.140 0.127084 7 to 14 2626.00 1.782 0.962620 8 to 15 2479.90 -0.284 0.388092 9 to 16 2591.94 1.300 0.903231 10 to 17 2692.99 2.729 0.996826 11 to 18 2407.38 -1.310 0.095120 12 to 19 2561.33 0.867 0.807110 13 to 20 2610.65 1.565 0.941188 14 to 21 2538.97 0.551 0.709217 15 to 22 2434.48 -0.927 0.177052 16 to 23 2396.77 -1.460 0.072156 17 to 24 2488.32 -0.165 0.434412 18 to 25 2466.44 -0.475 0.317548 19 to 26 2646.36 2.070 0.980767 20 to 27 2502.05 0.029 0.511571 21 to 28 2471.92 -0.397 0.345626 22 to 29 2583.54 1.181 0.881274 23 to 30 2431.99 -0.962 0.168064 24 to 31 2474.96 -0.354 0.361601 25 to 32 2642.59 2.017 0.978130 CDPARK for dh-ranFile-2016-02-22_05:31: 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 3530 0.3196 0.625377 3516 -0.3196 0.374623 3523 0.0000 0.500000 3491 -1.4612 0.071982 3548 1.1416 0.873180 3523 0.0000 0.500000 3546 1.0502 0.853193 3522 -0.0457 0.481790 3509 -0.6393 0.261324 3555 1.4612 0.928018 Square side=100, avg. no. parked=3526.30 sample std.=18.41 p-value of the KSTEST for those 10 p-values: 0.842686 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-22_05:31 0.6873,0.0751,0.6301,0.8848,0.9565,0.8102,0.3518,0.7532,0.3851,0.0330, The KS test for those 10 p-values: 0.742395 The 3DSPHERES test for dh-ranFile-2016-02-22_05:31 sample no r^3 equiv. uni. 1 13.515 0.362699 2 15.616 0.405800 3 29.357 0.624152 4 4.499 0.139276 5 121.950 0.982837 6 13.693 0.366470 7 10.494 0.295179 8 31.733 0.652771 9 0.995 0.032636 10 4.624 0.142836 11 38.405 0.722013 12 6.695 0.200032 13 5.728 0.173810 14 5.223 0.159775 15 25.258 0.569118 16 5.136 0.157360 17 17.174 0.435869 18 31.502 0.650086 19 41.515 0.749384 20 39.198 0.729264 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.349070 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-22_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 1.3 0.0 0.1 1.0 -0.0 1.0 0.4 1.2 0.4 0.2 1.1 0.9 0.2 0.2 -1.4 -0.9 -0.3 -0.5 -0.4 0.2 -1.2 -0.2 0.9 -0.1 0.1 0.2 0.9 -0.4 0.0 -1.0 0.6 -0.9 -2.2 -1.0 0.0 0.2 0.1 0.4 -1.3 0.0 0.8 Chi-square with 42 degrees of freedom:25.809408 z-score=-1.766538, p-value=0.023372 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-22_05:31 Test no p-value 1 0.682161 2 0.013711 3 0.124951 4 0.251530 5 0.011000 6 0.272430 7 0.820042 8 0.009897 9 0.219913 10 0.832329 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015337 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-22_05:31: (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 66522 0.31 66587 0.10 3 25000.00 25231 2.13 24954 0.08 4 6666.67 6652 0.03 6750 1.04 5 1388.89 1306 4.95 1442 2.03 6 238.10 251 0.70 235 0.04 7 34.72 33 0.09 26 2.19 8 4.96 4 0.19 5 0.00 p=0.78963 p=0.51648 Number of rngs required: 687945, p-value: 0.299 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-22_05:31 No. of wins: Observed Expected 98776 98585.9 z-score= 0.850, pvalue=0.80246 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66877 66666.7 0.664 0.664 2 37605 37654.3 0.065 0.728 3 27177 26954.7 1.833 2.561 4 19528 19313.5 2.383 4.944 5 13605 13851.4 4.384 9.328 6 9674 9943.5 7.307 16.635 7 7152 7145.0 0.007 16.641 8 5032 5139.1 2.231 18.872 9 3757 3699.9 0.882 19.755 10 2638 2666.3 0.300 20.055 11 1908 1923.3 0.122 20.177 12 1390 1388.7 0.001 20.178 13 1021 1003.7 0.298 20.476 14 724 726.1 0.006 20.482 15 505 525.8 0.826 21.308 16 414 381.2 2.831 24.139 17 255 276.5 1.678 25.817 18 200 200.8 0.003 25.820 19 143 146.0 0.061 25.881 20 94 106.2 1.405 27.286 21 301 287.1 0.672 27.957 Chisq= 27.96 for 20 degrees of freedom, p= 0.88959 SUMMARY of craptest p-value for no. of wins: 0.802455 p-value for throws/game: 0.889589 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-22_05:31 No. of wins: Observed Expected 98422 98585.9 z-score=-0.733, pvalue=0.23182 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66473 66666.7 0.563 0.563 2 37814 37654.3 0.677 1.240 3 26838 26954.7 0.506 1.745 4 19437 19313.5 0.790 2.535 5 13857 13851.4 0.002 2.538 6 9938 9943.5 0.003 2.541 7 7133 7145.0 0.020 2.561 8 5236 5139.1 1.828 4.389 9 3656 3699.9 0.520 4.909 10 2659 2666.3 0.020 4.929 11 1874 1923.3 1.265 6.194 12 1397 1388.7 0.049 6.244 13 980 1003.7 0.560 6.804 14 706 726.1 0.559 7.362 15 579 525.8 5.375 12.738 16 416 381.2 3.186 15.924 17 310 276.5 4.049 19.973 18 196 200.8 0.116 20.089 19 133 146.0 1.155 21.244 20 94 106.2 1.405 22.648 21 274 287.1 0.599 23.247 Chisq= 23.25 for 20 degrees of freedom, p= 0.72319 SUMMARY of craptest p-value for no. of wins: 0.231819 p-value for throws/game: 0.723190 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0040,0.0066,0.0099,0.0110,0.0137,0.0153,0.0166,0.0229,0.0234,0.0304, 0.0307,0.0326,0.0330,0.0341,0.0402,0.0449,0.0454,0.0493,0.0574,0.0593, 0.0703,0.0720,0.0722,0.0735,0.0751,0.0764,0.0778,0.0829,0.0868,0.0887, 0.0951,0.1194,0.1250,0.1271,0.1273,0.1369,0.1393,0.1428,0.1491,0.1516, 0.1528,0.1574,0.1598,0.1607,0.1642,0.1648,0.1659,0.1681,0.1712,0.1738, 0.1742,0.1749,0.1771,0.1795,0.1808,0.1862,0.2000,0.2027,0.2038,0.2050, 0.2051,0.2086,0.2114,0.2199,0.2241,0.2264,0.2280,0.2318,0.2341,0.2346, 0.2352,0.2403,0.2437,0.2447,0.2494,0.2500,0.2515,0.2554,0.2613,0.2638, 0.2670,0.2685,0.2724,0.2750,0.2818,0.2893,0.2931,0.2952,0.2969,0.2988, 0.3056,0.3064,0.3071,0.3175,0.3184,0.3241,0.3266,0.3325,0.3359,0.3368, 0.3373,0.3456,0.3491,0.3518,0.3595,0.3616,0.3627,0.3665,0.3667,0.3746, 0.3784,0.3804,0.3851,0.3870,0.3881,0.4058,0.4091,0.4194,0.4282,0.4344, 0.4359,0.4394,0.4430,0.4430,0.4462,0.4483,0.4493,0.4529,0.4545,0.4597, 0.4698,0.4698,0.4721,0.4775,0.4801,0.4818,0.4882,0.4894,0.4913,0.4917, 0.4921,0.4923,0.4924,0.4926,0.4937,0.5000,0.5000,0.5008,0.5081,0.5100, 0.5116,0.5165,0.5319,0.5326,0.5337,0.5396,0.5441,0.5617,0.5632,0.5637, 0.5691,0.5726,0.5757,0.5889,0.5999,0.6034,0.6054,0.6111,0.6172,0.6242, 0.6254,0.6301,0.6368,0.6374,0.6486,0.6501,0.6528,0.6601,0.6726,0.6779, 0.6794,0.6822,0.6846,0.6867,0.6873,0.6895,0.6992,0.7004,0.7085,0.7092, 0.7098,0.7161,0.7220,0.7232,0.7293,0.7377,0.7424,0.7491,0.7494,0.7507, 0.7532,0.7568,0.7701,0.7760,0.7768,0.7896,0.7936,0.8025,0.8061,0.8071, 0.8102,0.8170,0.8200,0.8248,0.8293,0.8301,0.8323,0.8407,0.8427,0.8468, 0.8523,0.8532,0.8587,0.8655,0.8707,0.8732,0.8754,0.8766,0.8813,0.8848, 0.8896,0.9001,0.9015,0.9032,0.9044,0.9078,0.9121,0.9170,0.9206,0.9251, 0.9254,0.9280,0.9294,0.9315,0.9339,0.9355,0.9412,0.9441,0.9565,0.9588, 0.9626,0.9632,0.9635,0.9663,0.9715,0.9725,0.9749,0.9761,0.9768,0.9781, 0.9808,0.9828,0.9842,0.9864,0.9881,0.9911,0.9968,0.9970,0.9976, Overall p-value after applying KStest on 269 p-values = 0.288084 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.