RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-20_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.51 24.0247 0.881236 2 to 25 15.57 18.5789 0.646770 3 to 26 15.55 28.6806 0.962412 4 to 27 15.58 19.9339 0.722378 5 to 28 15.90 20.6138 0.755959 6 to 29 15.52 24.5480 0.894707 7 to 30 15.86 13.2429 0.280217 8 to 31 15.91 15.2067 0.419405 9 to 32 15.61 20.3444 0.743008 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.058997 Tough bday spacings test for dh-ranFile-2015-12-20_12:31: 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 11 34 82 97 92 77 41 35 22 4 5 (O-E)^2/E 0.4 0.2 1.0 0.0 0.3 0.0 2.4 0.9 3.4 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.886, p= 0.549 RESULTS OF GCD FOR dh-ranFile-2015-12-20_12:31 Euclid's algorithm: p-value, steps to gcd: 0.364786 p-value, dist. of gcd's: 0.532270 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-20_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.218 0.407 0.852 0.458 0.231 0.171 0.326 0.439 Bits 8 to 15---> 0.139 0.862 0.468 0.669 0.052 0.268 0.564 0.625 Bits 16 to 23---> 0.536 0.467 0.064 0.131 0.097 0.109 0.234 0.822 Bits 24 to 31---> 0.786 0.542 0.407 0.432 0.330 0.551 0.429 0.431 KS test for the above 32 p values: 0.936 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-20_12:31, p-values for 5 runs: 0.6238, 0.7830, 0.9979, 0.7145, 0.7497 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-20_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5158 5134.0 0.112 0.211 r= 30 23184 23103.0 0.284 0.495 r= 31 11442 11551.5 1.038 1.533 chi-square = 1.533 with df = 3; p-value = 0.325 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-20_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5021 5134.0 2.488 2.635 r= 31 23313 23103.0 1.908 4.543 r= 32 11449 11551.5 0.910 5.453 chi-square = 5.453 with df = 3; p-value = 0.859 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-20_12:31 b-rank test for bits 1 to 8, p=0.95662 b-rank test for bits 2 to 9, p=0.77548 b-rank test for bits 3 to 10, p=0.01184 b-rank test for bits 4 to 11, p=0.17198 b-rank test for bits 5 to 12, p=0.42672 b-rank test for bits 6 to 13, p=0.62642 b-rank test for bits 7 to 14, p=0.26607 b-rank test for bits 8 to 15, p=0.35844 b-rank test for bits 9 to 16, p=0.92089 b-rank test for bits 10 to 17, p=0.43922 b-rank test for bits 11 to 18, p=0.55730 b-rank test for bits 12 to 19, p=0.14401 b-rank test for bits 13 to 20, p=0.98989 b-rank test for bits 14 to 21, p=0.57783 b-rank test for bits 15 to 22, p=0.18833 b-rank test for bits 16 to 23, p=0.85512 b-rank test for bits 17 to 24, p=0.04732 b-rank test for bits 18 to 25, p=0.92121 b-rank test for bits 19 to 26, p=0.43560 b-rank test for bits 20 to 27, p=0.16223 b-rank test for bits 21 to 28, p=0.19330 b-rank test for bits 22 to 29, p=0.52710 b-rank test for bits 23 to 30, p=0.29828 b-rank test for bits 24 to 31, p=0.67348 b-rank test for bits 25 to 32, p=0.94602 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 = 0.855200 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-20_12:31 (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 141359 -1.29 0.099253 2 141897 -0.03 0.488509 3 142163 0.59 0.723305 4 141542 -0.86 0.195378 5 141317 -1.38 0.083187 6 141970 0.14 0.556362 7 142609 1.63 0.948949 8 141939 0.07 0.527634 9 142002 0.22 0.585708 10 141881 -0.07 0.473613 11 141184 -1.69 0.045067 12 142564 1.53 0.936942 13 141764 -0.34 0.367095 14 141429 -1.12 0.130875 15 141405 -1.18 0.119330 16 141613 -0.69 0.244356 17 141761 -0.35 0.364459 18 141933 0.06 0.522052 19 142298 0.91 0.818089 20 141693 -0.51 0.306624 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-20_12:31 Bits used No. missing words z-score p-value 23 to 32 142108 0.6851 0.753350 22 to 31 142205 1.0196 0.846029 21 to 30 141817 -0.3184 0.375099 20 to 29 141854 -0.1908 0.424344 19 to 28 141948 0.1333 0.553040 18 to 27 141810 -0.3425 0.365981 17 to 26 141815 -0.3253 0.372486 16 to 25 141749 -0.5529 0.290179 15 to 24 142115 0.7092 0.760902 14 to 23 141877 -0.1115 0.455617 13 to 22 142120 0.7264 0.766218 12 to 21 142057 0.5092 0.694696 11 to 20 141152 -2.6115 0.004508 10 to 19 141894 -0.0529 0.478921 9 to 18 142184 0.9471 0.828216 8 to 17 142060 0.5196 0.698312 7 to 16 141959 0.1713 0.567997 6 to 15 141834 -0.2598 0.397525 5 to 14 142082 0.5954 0.724217 4 to 13 141555 -1.2218 0.110886 3 to 12 141532 -1.3011 0.096606 2 to 11 141907 -0.0080 0.496795 1 to 10 141716 -0.6667 0.252496 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-20_12:31 Bits used No. missing words z-score p-value 28 to 32 142024 0.3887 0.651255 27 to 31 142088 0.6057 0.727630 26 to 30 141752 -0.5333 0.296905 25 to 29 141865 -0.1503 0.440275 24 to 28 141404 -1.7130 0.043358 23 to 27 141712 -0.6689 0.251775 22 to 26 141729 -0.6113 0.270504 21 to 25 141493 -1.4113 0.079080 20 to 24 141637 -0.9232 0.177964 19 to 23 141718 -0.6486 0.258306 18 to 22 141556 -1.1977 0.115511 17 to 21 141292 -2.0926 0.018190 16 to 20 142123 0.7243 0.765561 15 to 19 142502 2.0091 0.977734 14 to 18 141439 -1.5943 0.055430 13 to 17 141717 -0.6520 0.257212 12 to 16 142086 0.5989 0.725374 11 to 15 142432 1.7718 0.961783 10 to 14 142163 0.8599 0.805077 9 to 13 141998 0.3006 0.618131 8 to 12 141661 -0.8418 0.199951 7 to 11 141841 -0.2316 0.408414 6 to 10 141718 -0.6486 0.258306 5 to 9 142026 0.3955 0.653760 4 to 8 141130 -2.6418 0.004123 3 to 7 141645 -0.8960 0.185117 2 to 6 142070 0.5446 0.707001 1 to 5 142226 1.0735 0.858467 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-20_12:31 Bits used No. missing words z-score p-value 31 to 32 141600 -0.9125 0.180759 30 to 31 141937 0.0816 0.532527 29 to 30 141824 -0.2517 0.400632 28 to 29 141569 -1.0039 0.157708 27 to 28 141873 -0.1072 0.457328 26 to 27 141431 -1.4110 0.079122 25 to 26 141534 -1.1072 0.134111 24 to 25 141928 0.0551 0.521960 23 to 24 142513 1.7807 0.962522 22 to 23 141615 -0.8682 0.192634 21 to 22 141753 -0.4612 0.322345 20 to 21 141878 -0.0924 0.463183 19 to 20 142101 0.5654 0.714099 18 to 19 142269 1.0610 0.855649 17 to 18 141410 -1.4729 0.070382 16 to 17 142304 1.1642 0.877832 15 to 16 141835 -0.2193 0.413223 14 to 15 141703 -0.6086 0.271381 13 to 14 141573 -0.9921 0.160569 12 to 13 141438 -1.3904 0.082211 11 to 12 141502 -1.2016 0.114766 10 to 11 141606 -0.8948 0.185453 9 to 10 141567 -1.0098 0.156290 8 to 9 141688 -0.6529 0.256913 7 to 8 141937 0.0816 0.532527 6 to 7 141680 -0.6765 0.249365 5 to 6 142554 1.9017 0.971394 4 to 5 142062 0.4504 0.673772 3 to 4 142282 1.0993 0.864186 2 to 3 141714 -0.5762 0.282242 1 to 2 141944 0.1023 0.540729 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-20_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2605.16 1.487 0.931521 Test results for specific bytes for dh-ranFile-2015-12-20_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2560.74 0.859 0.804844 2 to 9 2499.57 -0.006 0.497577 3 to 10 2555.98 0.792 0.785719 4 to 11 2515.29 0.216 0.585594 5 to 12 2503.96 0.056 0.522354 6 to 13 2411.51 -1.251 0.105384 7 to 14 2506.30 0.089 0.535497 8 to 15 2525.86 0.366 0.642735 9 to 16 2485.55 -0.204 0.419047 10 to 17 2437.27 -0.887 0.187511 11 to 18 2505.33 0.075 0.530065 12 to 19 2553.00 0.750 0.773250 13 to 20 2447.62 -0.741 0.229403 14 to 21 2489.67 -0.146 0.441951 15 to 22 2501.27 0.018 0.507180 16 to 23 2451.10 -0.692 0.244621 17 to 24 2597.43 1.378 0.915882 18 to 25 2588.90 1.257 0.895678 19 to 26 2506.08 0.086 0.534242 20 to 27 2643.39 2.028 0.978713 21 to 28 2575.94 1.074 0.858576 22 to 29 2466.82 -0.469 0.319468 23 to 30 2490.60 -0.133 0.447127 24 to 31 2455.11 -0.635 0.262772 25 to 32 2386.18 -1.610 0.053734 CDPARK for dh-ranFile-2015-12-20_12:31: 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 3508 -0.6849 0.246694 3542 0.8676 0.807188 3519 -0.1826 0.427537 3528 0.2283 0.590298 3501 -1.0046 0.157553 3564 1.8721 0.969407 3520 -0.1370 0.445521 3527 0.1826 0.572463 3505 -0.8219 0.205562 3560 1.6895 0.954438 Square side=100, avg. no. parked=3527.40 sample std.=20.78 p-value of the KSTEST for those 10 p-values: 0.804681 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-20_12:31 0.5708,0.3415,0.2254,0.9117,0.2680,0.1350,0.0655,0.0980,0.0817,0.6269, The KS test for those 10 p-values: 0.090039 The 3DSPHERES test for dh-ranFile-2015-12-20_12:31 sample no r^3 equiv. uni. 1 78.758 0.927579 2 32.961 0.666697 3 41.976 0.753207 4 32.377 0.660145 5 2.000 0.064478 6 5.750 0.174422 7 6.612 0.197789 8 8.549 0.247969 9 17.572 0.443308 10 1.779 0.057587 11 55.154 0.840941 12 1.039 0.034033 13 33.426 0.671824 14 24.504 0.558156 15 21.586 0.513021 16 31.044 0.644699 17 70.877 0.905821 18 50.169 0.812186 19 4.676 0.144320 20 20.197 0.489947 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.908655 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-20_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 -1.1 0.3 -0.1 -1.6 1.8 0.3 -1.5 1.1 0.2 -1.3 -0.8 -2.4 0.4 0.5 -0.5 -0.7 1.6 0.4 1.8 -1.1 0.7 -0.4 1.0 -0.1 1.2 0.5 0.5 -0.8 0.1 -1.1 -0.9 0.3 -0.9 -0.1 -1.9 0.5 0.9 -0.7 0.1 3.0 -1.1 Chi-square with 42 degrees of freedom:52.065134 z-score=1.098196, p-value=0.862688 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-20_12:31 Test no p-value 1 0.027704 2 0.098950 3 0.172286 4 0.318574 5 0.088572 6 0.284436 7 0.118139 8 0.309493 9 0.067202 10 0.604281 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001604 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-20_12:31: (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 66686 0.01 66536 0.26 3 25000.00 24946 0.12 25065 0.17 4 6666.67 6663 0.00 6708 0.26 5 1388.89 1432 1.34 1414 0.45 6 238.10 232 0.16 217 1.87 7 34.72 36 0.05 50 6.72 8 4.96 4 0.19 9 3.29 p=0.06715 p=0.95727 Number of rngs required: 688665, p-value: 0.619 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-20_12:31 No. of wins: Observed Expected 98732 98585.9 z-score= 0.654, pvalue=0.74332 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66803 66666.7 0.279 0.279 2 37558 37654.3 0.246 0.525 3 26991 26954.7 0.049 0.574 4 19310 19313.5 0.001 0.575 5 13705 13851.4 1.548 2.122 6 9843 9943.5 1.017 3.139 7 7026 7145.0 1.983 5.122 8 5191 5139.1 0.525 5.647 9 3629 3699.9 1.357 7.004 10 2776 2666.3 4.514 11.517 11 1982 1923.3 1.790 13.307 12 1440 1388.7 1.892 15.199 13 1066 1003.7 3.865 19.064 14 764 726.1 1.974 21.038 15 508 525.8 0.605 21.643 16 376 381.2 0.070 21.713 17 282 276.5 0.108 21.821 18 196 200.8 0.116 21.937 19 155 146.0 0.557 22.494 20 115 106.2 0.727 23.220 21 284 287.1 0.034 23.254 Chisq= 23.25 for 20 degrees of freedom, p= 0.72350 SUMMARY of craptest p-value for no. of wins: 0.743325 p-value for throws/game: 0.723498 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-20_12:31 No. of wins: Observed Expected 98520 98585.9 z-score=-0.295, pvalue=0.38417 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66501 66666.7 0.412 0.412 2 38064 37654.3 4.457 4.869 3 26740 26954.7 1.711 6.580 4 19235 19313.5 0.319 6.898 5 13864 13851.4 0.011 6.910 6 10034 9943.5 0.823 7.733 7 7003 7145.0 2.823 10.556 8 5235 5139.1 1.791 12.346 9 3621 3699.9 1.681 14.028 10 2671 2666.3 0.008 14.036 11 2009 1923.3 3.816 17.852 12 1396 1388.7 0.038 17.890 13 988 1003.7 0.246 18.136 14 740 726.1 0.265 18.400 15 527 525.8 0.003 18.403 16 366 381.2 0.602 19.005 17 283 276.5 0.151 19.156 18 191 200.8 0.481 19.637 19 137 146.0 0.553 20.190 20 108 106.2 0.030 20.220 21 287 287.1 0.000 20.220 Chisq= 20.22 for 20 degrees of freedom, p= 0.55577 SUMMARY of craptest p-value for no. of wins: 0.384166 p-value for throws/game: 0.555768 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0041,0.0045,0.0118,0.0182,0.0277,0.0340,0.0434,0.0451,0.0473, 0.0524,0.0537,0.0554,0.0576,0.0590,0.0643,0.0645,0.0655,0.0672,0.0672, 0.0704,0.0791,0.0791,0.0817,0.0822,0.0832,0.0886,0.0900,0.0966,0.0975, 0.0980,0.0989,0.0993,0.1054,0.1094,0.1109,0.1148,0.1155,0.1181,0.1193, 0.1307,0.1309,0.1341,0.1350,0.1393,0.1440,0.1443,0.1563,0.1576,0.1577, 0.1606,0.1622,0.1713,0.1720,0.1723,0.1744,0.1780,0.1808,0.1851,0.1855, 0.1875,0.1883,0.1926,0.1933,0.1954,0.1978,0.2000,0.2056,0.2177,0.2254, 0.2294,0.2305,0.2337,0.2444,0.2446,0.2467,0.2480,0.2494,0.2518,0.2525, 0.2569,0.2572,0.2583,0.2583,0.2628,0.2661,0.2680,0.2685,0.2705,0.2714, 0.2802,0.2822,0.2844,0.2902,0.2969,0.2983,0.3066,0.3095,0.3186,0.3195, 0.3223,0.3254,0.3261,0.3298,0.3415,0.3584,0.3645,0.3648,0.3660,0.3671, 0.3725,0.3751,0.3842,0.3975,0.4006,0.4065,0.4071,0.4084,0.4132,0.4190, 0.4194,0.4243,0.4267,0.4275,0.4288,0.4305,0.4318,0.4356,0.4392,0.4395, 0.4403,0.4420,0.4433,0.4455,0.4471,0.4556,0.4573,0.4582,0.4632,0.4673, 0.4682,0.4736,0.4789,0.4885,0.4899,0.4968,0.4976,0.5072,0.5130,0.5220, 0.5221,0.5224,0.5271,0.5276,0.5301,0.5323,0.5325,0.5325,0.5342,0.5355, 0.5357,0.5407,0.5420,0.5495,0.5509,0.5530,0.5558,0.5564,0.5573,0.5582, 0.5645,0.5680,0.5708,0.5725,0.5778,0.5856,0.5857,0.5903,0.6043,0.6181, 0.6185,0.6238,0.6248,0.6264,0.6269,0.6427,0.6447,0.6468,0.6513,0.6538, 0.6601,0.6667,0.6690,0.6718,0.6735,0.6738,0.6947,0.6983,0.7070,0.7141, 0.7145,0.7224,0.7233,0.7235,0.7242,0.7254,0.7276,0.7430,0.7433,0.7497, 0.7532,0.7533,0.7560,0.7609,0.7656,0.7662,0.7732,0.7755,0.7830,0.7856, 0.7857,0.8047,0.8048,0.8051,0.8072,0.8122,0.8181,0.8223,0.8282,0.8409, 0.8460,0.8525,0.8551,0.8552,0.8556,0.8585,0.8585,0.8586,0.8617,0.8627, 0.8642,0.8778,0.8812,0.8947,0.8957,0.9058,0.9087,0.9117,0.9159,0.9209, 0.9212,0.9276,0.9315,0.9355,0.9369,0.9460,0.9489,0.9544,0.9566,0.9573, 0.9618,0.9624,0.9625,0.9694,0.9714,0.9777,0.9787,0.9899,0.9979, Overall p-value after applying KStest on 269 p-values = 0.103584 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.