RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-30_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 15.7843 0.460825 2 to 25 15.61 15.0511 0.408199 3 to 26 15.88 13.7035 0.312031 4 to 27 15.80 12.0433 0.202495 5 to 28 15.72 19.5318 0.701127 6 to 29 15.58 14.3430 0.357307 7 to 30 15.81 13.8689 0.323644 8 to 31 15.54 23.4128 0.863712 9 to 32 15.57 22.6105 0.837636 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.667070 Tough bday spacings test for dh-ranFile-2017-01-30_08:31: 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 32 79 95 81 83 56 32 20 8 6 (O-E)^2/E 0.1 0.6 0.4 0.1 2.8 0.3 0.3 0.2 1.8 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.832, p= 0.355 RESULTS OF GCD FOR dh-ranFile-2017-01-30_08:31 Euclid's algorithm: p-value, steps to gcd: 0.815473 p-value, dist. of gcd's: 0.103846 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-30_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.157 0.114 0.140 0.502 0.758 0.528 0.670 0.700 Bits 8 to 15---> 0.160 0.454 0.915 0.348 0.467 0.736 0.504 0.692 Bits 16 to 23---> 0.115 0.665 0.735 0.773 0.049 0.548 0.860 0.923 Bits 24 to 31---> 0.850 0.750 0.459 0.142 0.858 0.775 0.634 0.072 KS test for the above 32 p values: 0.593 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-30_08:31, p-values for 5 runs: 0.9805, 0.2013, 0.5606, 0.8102, 0.9573 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-30_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5168 5134.0 0.225 1.349 r= 30 23044 23103.0 0.151 1.500 r= 31 11592 11551.5 0.142 1.642 chi-square = 1.642 with df = 3; p-value = 0.350 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-30_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5090 5134.0 0.377 0.378 r= 31 23045 23103.0 0.146 0.524 r= 32 11654 11551.5 0.909 1.433 chi-square = 1.433 with df = 3; p-value = 0.302 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-30_08:31 b-rank test for bits 1 to 8, p=0.51705 b-rank test for bits 2 to 9, p=0.71498 b-rank test for bits 3 to 10, p=0.32661 b-rank test for bits 4 to 11, p=0.36673 b-rank test for bits 5 to 12, p=0.38698 b-rank test for bits 6 to 13, p=0.46359 b-rank test for bits 7 to 14, p=0.38821 b-rank test for bits 8 to 15, p=0.66638 b-rank test for bits 9 to 16, p=0.16419 b-rank test for bits 10 to 17, p=0.62677 b-rank test for bits 11 to 18, p=0.93715 b-rank test for bits 12 to 19, p=0.41809 b-rank test for bits 13 to 20, p=0.46227 b-rank test for bits 14 to 21, p=0.06244 b-rank test for bits 15 to 22, p=0.24595 b-rank test for bits 16 to 23, p=0.60625 b-rank test for bits 17 to 24, p=0.22837 b-rank test for bits 18 to 25, p=0.51618 b-rank test for bits 19 to 26, p=0.75002 b-rank test for bits 20 to 27, p=0.07474 b-rank test for bits 21 to 28, p=0.04135 b-rank test for bits 22 to 29, p=0.58783 b-rank test for bits 23 to 30, p=0.86616 b-rank test for bits 24 to 31, p=0.95901 b-rank test for bits 25 to 32, p=0.97106 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 = 0.935920 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-30_08:31 (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 141290 -1.45 0.073944 2 142129 0.51 0.696111 3 141361 -1.28 0.100071 4 141848 -0.14 0.443029 5 141731 -0.42 0.338464 6 142319 0.96 0.830760 7 140953 -2.23 0.012728 8 141836 -0.17 0.431981 9 141507 -0.94 0.173603 10 142386 1.11 0.867299 11 142042 0.31 0.621711 12 141616 -0.69 0.246561 13 141856 -0.12 0.450419 14 142818 2.12 0.983126 15 142553 1.50 0.933697 16 142417 1.19 0.882217 17 142390 1.12 0.869294 18 141679 -0.54 0.295235 19 141769 -0.33 0.371504 20 141577 -0.78 0.218735 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-30_08:31 Bits used No. missing words z-score p-value 23 to 32 141688 -0.7632 0.222670 22 to 31 142442 1.8368 0.966880 21 to 30 141498 -1.4184 0.078040 20 to 29 141829 -0.2770 0.390890 19 to 28 142431 1.7989 0.963980 18 to 27 142020 0.3816 0.648629 17 to 26 142556 2.2299 0.987123 16 to 25 142480 1.9678 0.975456 15 to 24 142128 0.7540 0.774586 14 to 23 141848 -0.2115 0.416255 13 to 22 142362 1.5609 0.940730 12 to 21 142100 0.6575 0.744565 11 to 20 142305 1.3644 0.913776 10 to 19 141383 -1.8149 0.034767 9 to 18 142032 0.4230 0.663852 8 to 17 142059 0.5161 0.697109 7 to 16 141752 -0.5425 0.293731 6 to 15 141986 0.2644 0.604256 5 to 14 141830 -0.2736 0.392215 4 to 13 141588 -1.1080 0.133923 3 to 12 141868 -0.1425 0.443336 2 to 11 141817 -0.3184 0.375099 1 to 10 141834 -0.2598 0.397525 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-30_08:31 Bits used No. missing words z-score p-value 28 to 32 142087 0.6023 0.726503 27 to 31 141691 -0.7401 0.229619 26 to 30 142135 0.7650 0.777859 25 to 29 141795 -0.3876 0.349171 24 to 28 141912 0.0091 0.503611 23 to 27 142026 0.3955 0.653760 22 to 26 141831 -0.2655 0.395302 21 to 25 141715 -0.6587 0.255030 20 to 24 141982 0.2463 0.597290 19 to 23 142312 1.3650 0.913871 18 to 22 142354 1.5074 0.934140 17 to 21 141517 -1.3299 0.091770 16 to 20 141712 -0.6689 0.251775 15 to 19 141423 -1.6486 0.049617 14 to 18 141342 -1.9232 0.027230 13 to 17 141906 -0.0113 0.495497 12 to 16 142159 0.8463 0.801318 11 to 15 142117 0.7040 0.759273 10 to 14 141421 -1.6554 0.048926 9 to 13 141877 -0.1096 0.456366 8 to 12 141810 -0.3367 0.368167 7 to 11 142010 0.3413 0.633544 6 to 10 141968 0.1989 0.578822 5 to 9 142113 0.6904 0.755031 4 to 8 142527 2.0938 0.981861 3 to 7 141640 -0.9130 0.180626 2 to 6 142249 1.1514 0.875221 1 to 5 142216 1.0396 0.850728 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-30_08:31 Bits used No. missing words z-score p-value 31 to 32 141748 -0.4759 0.317073 30 to 31 142033 0.3648 0.642373 29 to 30 142159 0.7365 0.769284 28 to 29 141667 -0.7148 0.237355 27 to 28 141208 -2.0688 0.019281 26 to 27 141651 -0.7620 0.223019 25 to 26 142066 0.4622 0.678014 24 to 25 142315 1.1967 0.884282 23 to 24 141671 -0.7030 0.241016 22 to 23 141598 -0.9184 0.179211 21 to 22 141671 -0.7030 0.241016 20 to 21 141310 -1.7679 0.038536 19 to 20 141405 -1.4877 0.068415 18 to 19 141727 -0.5378 0.295342 17 to 18 141793 -0.3432 0.365740 16 to 17 142113 0.6008 0.726012 15 to 16 142237 0.9666 0.833123 14 to 15 141700 -0.6175 0.268455 13 to 14 142016 0.3147 0.623490 12 to 13 141833 -0.2252 0.410927 11 to 12 141594 -0.9302 0.176140 10 to 11 142011 0.2999 0.617878 9 to 10 142066 0.4622 0.678014 8 to 9 141602 -0.9066 0.182315 7 to 8 142146 0.6981 0.757456 6 to 7 142411 1.4799 0.930544 5 to 6 141891 -0.0541 0.478439 4 to 5 142136 0.6686 0.748138 3 to 4 141678 -0.6824 0.247496 2 to 3 142573 1.9577 0.974869 1 to 2 141748 -0.4759 0.317073 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-30_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2493.47 -0.092 0.463214 Test results for specific bytes for dh-ranFile-2017-01-30_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2618.00 1.669 0.952423 2 to 9 2723.34 3.158 0.999207 3 to 10 2435.84 -0.907 0.182090 4 to 11 2511.59 0.164 0.565100 5 to 12 2485.74 -0.202 0.420114 6 to 13 2438.76 -0.866 0.193214 7 to 14 2453.08 -0.664 0.253473 8 to 15 2436.29 -0.901 0.183800 9 to 16 2461.01 -0.551 0.290669 10 to 17 2415.40 -1.196 0.115778 11 to 18 2629.71 1.834 0.966705 12 to 19 2467.59 -0.458 0.323351 13 to 20 2324.68 -2.479 0.006581 14 to 21 2506.76 0.096 0.538098 15 to 22 2559.15 0.836 0.798557 16 to 23 2564.58 0.913 0.819454 17 to 24 2602.25 1.446 0.925908 18 to 25 2641.10 1.995 0.977006 19 to 26 2489.44 -0.149 0.440636 20 to 27 2493.63 -0.090 0.464108 21 to 28 2583.96 1.187 0.882467 22 to 29 2523.33 0.330 0.629300 23 to 30 2509.92 0.140 0.555812 24 to 31 2493.37 -0.094 0.462652 25 to 32 2479.02 -0.297 0.383347 CDPARK for dh-ranFile-2017-01-30_08:31: 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 3546 1.0502 0.853193 3521 -0.0913 0.463617 3516 -0.3196 0.374623 3535 0.5479 0.708135 3535 0.5479 0.708135 3518 -0.2283 0.409702 3544 0.9589 0.831196 3494 -1.3242 0.092718 3500 -1.0502 0.146807 Square side=100, avg. no. parked=3526.50 sample std.=19.16 p-value of the KSTEST for those 10 p-values: 0.884829 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-30_08:31 0.5138,0.1724,0.0824,0.4582,0.8436,0.5415,0.7069,0.2699,0.5817,0.3583, The KS test for those 10 p-values: 0.746436 The 3DSPHERES test for dh-ranFile-2017-01-30_08:31 sample no r^3 equiv. uni. 1 14.787 0.389143 2 13.540 0.363220 3 4.097 0.127663 4 33.342 0.670900 5 14.915 0.391755 6 31.455 0.649542 7 47.616 0.795501 8 117.320 0.979973 9 17.882 0.449030 10 36.175 0.700559 11 40.551 0.741201 12 16.647 0.425861 13 8.208 0.239352 14 4.303 0.133608 15 3.834 0.119981 16 18.470 0.459719 17 27.824 0.604447 18 207.803 0.999019 19 0.773 0.025429 20 43.573 0.765996 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.808386 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-30_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.1 0.8 1.0 -0.2 1.4 0.4 -1.2 -0.4 0.4 0.5 0.9 -1.0 0.3 -1.5 1.3 0.6 -0.9 -0.7 0.1 -2.0 0.9 1.7 0.9 -0.4 -0.3 0.7 1.6 -2.3 1.3 -1.5 -0.2 1.6 0.3 -1.4 0.3 -0.1 -1.2 0.4 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:42.081224 z-score=0.008862, p-value=0.532544 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-30_08:31 Test no p-value 1 0.159500 2 0.007978 3 0.236442 4 0.338943 5 0.989808 6 0.183227 7 0.194677 8 0.019018 9 0.007470 10 0.004310 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000095 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-30_08:31: (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 66532 0.27 66737 0.07 3 25000.00 25146 0.85 24946 0.12 4 6666.67 6604 0.59 6641 0.10 5 1388.89 1434 1.47 1377 0.10 6 238.10 245 0.20 258 1.66 7 34.72 33 0.09 37 0.15 8 4.96 5 0.00 3 0.77 p=0.25134 p=0.18862 Number of rngs required: 687520, p-value: 0.153 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-30_08:31 No. of wins: Observed Expected 98402 98585.9 z-score=-0.822, pvalue=0.20545 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66670 66666.7 0.000 0.000 2 37611 37654.3 0.050 0.050 3 26776 26954.7 1.185 1.235 4 19271 19313.5 0.093 1.329 5 13931 13851.4 0.457 1.786 6 9944 9943.5 0.000 1.786 7 7207 7145.0 0.538 2.323 8 5240 5139.1 1.982 4.305 9 3639 3699.9 1.001 5.307 10 2677 2666.3 0.043 5.350 11 1899 1923.3 0.308 5.657 12 1411 1388.7 0.357 6.014 13 1025 1003.7 0.451 6.466 14 778 726.1 3.704 10.169 15 509 525.8 0.539 10.708 16 381 381.2 0.000 10.708 17 280 276.5 0.043 10.752 18 212 200.8 0.621 11.373 19 161 146.0 1.544 12.917 20 119 106.2 1.539 14.456 21 259 287.1 2.753 17.209 Chisq= 17.21 for 20 degrees of freedom, p= 0.36065 SUMMARY of craptest p-value for no. of wins: 0.205447 p-value for throws/game: 0.360648 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-30_08:31 No. of wins: Observed Expected 98442 98585.9 z-score=-0.643, pvalue=0.25998 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66547 66666.7 0.215 0.215 2 37611 37654.3 0.050 0.265 3 27073 26954.7 0.519 0.784 4 19321 19313.5 0.003 0.786 5 13918 13851.4 0.320 1.107 6 9899 9943.5 0.200 1.306 7 7202 7145.0 0.454 1.760 8 5052 5139.1 1.475 3.236 9 3714 3699.9 0.054 3.290 10 2715 2666.3 0.890 4.179 11 1998 1923.3 2.899 7.078 12 1343 1388.7 1.507 8.585 13 929 1003.7 5.562 14.146 14 703 726.1 0.737 14.884 15 561 525.8 2.352 17.235 16 371 381.2 0.270 17.506 17 300 276.5 1.990 19.496 18 175 200.8 3.322 22.818 19 141 146.0 0.170 22.988 20 109 106.2 0.073 23.061 21 318 287.1 3.323 26.384 Chisq= 26.38 for 20 degrees of freedom, p= 0.84650 SUMMARY of craptest p-value for no. of wins: 0.259976 p-value for throws/game: 0.846497 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0043,0.0066,0.0075,0.0080,0.0127,0.0190,0.0193,0.0254,0.0272, 0.0348,0.0385,0.0413,0.0489,0.0491,0.0496,0.0624,0.0684,0.0724,0.0739, 0.0747,0.0780,0.0824,0.0918,0.0927,0.1001,0.1038,0.1139,0.1150,0.1158, 0.1200,0.1277,0.1336,0.1339,0.1399,0.1423,0.1468,0.1531,0.1573,0.1595, 0.1600,0.1642,0.1724,0.1736,0.1761,0.1792,0.1806,0.1821,0.1823,0.1832, 0.1838,0.1886,0.1932,0.1947,0.2013,0.2025,0.2054,0.2187,0.2227,0.2230, 0.2284,0.2296,0.2364,0.2374,0.2394,0.2410,0.2410,0.2459,0.2466,0.2475, 0.2513,0.2518,0.2535,0.2550,0.2600,0.2685,0.2699,0.2907,0.2937,0.2952, 0.2953,0.3022,0.3120,0.3171,0.3171,0.3234,0.3236,0.3266,0.3385,0.3389, 0.3479,0.3492,0.3501,0.3548,0.3573,0.3583,0.3606,0.3632,0.3657,0.3667, 0.3682,0.3715,0.3746,0.3751,0.3833,0.3870,0.3882,0.3891,0.3909,0.3918, 0.3922,0.3953,0.3975,0.4082,0.4097,0.4109,0.4163,0.4181,0.4201,0.4259, 0.4320,0.4406,0.4430,0.4433,0.4490,0.4504,0.4539,0.4564,0.4582,0.4588, 0.4597,0.4608,0.4623,0.4627,0.4632,0.4636,0.4636,0.4641,0.4675,0.4784, 0.4955,0.5020,0.5036,0.5044,0.5138,0.5162,0.5171,0.5281,0.5325,0.5381, 0.5415,0.5480,0.5558,0.5606,0.5651,0.5788,0.5817,0.5878,0.5926,0.5973, 0.6043,0.6044,0.6062,0.6179,0.6217,0.6235,0.6268,0.6293,0.6335,0.6339, 0.6424,0.6486,0.6495,0.6538,0.6639,0.6652,0.6664,0.6671,0.6700,0.6709, 0.6780,0.6780,0.6925,0.6961,0.6971,0.7000,0.7006,0.7011,0.7069,0.7081, 0.7081,0.7150,0.7260,0.7265,0.7346,0.7365,0.7412,0.7446,0.7464,0.7481, 0.7497,0.7500,0.7550,0.7575,0.7580,0.7593,0.7660,0.7693,0.7732,0.7746, 0.7748,0.7779,0.7955,0.7986,0.8013,0.8084,0.8102,0.8155,0.8195,0.8308, 0.8312,0.8331,0.8376,0.8436,0.8465,0.8496,0.8507,0.8532,0.8581,0.8597, 0.8637,0.8662,0.8673,0.8693,0.8752,0.8822,0.8825,0.8843,0.8848,0.9138, 0.9139,0.9154,0.9234,0.9259,0.9305,0.9337,0.9341,0.9341,0.9359,0.9371, 0.9407,0.9524,0.9573,0.9590,0.9640,0.9667,0.9669,0.9711,0.9749,0.9755, 0.9770,0.9800,0.9805,0.9819,0.9831,0.9871,0.9898,0.9990,0.9992, Overall p-value after applying KStest on 269 p-values = 0.901745 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.