RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-17_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.60 21.5252 0.796327 2 to 25 15.43 30.9773 0.979901 3 to 26 15.84 16.3391 0.500063 4 to 27 15.91 8.8211 0.054292 5 to 28 15.98 9.0257 0.060549 6 to 29 15.74 27.3414 0.946753 7 to 30 15.83 17.8363 0.600765 8 to 31 15.64 21.8819 0.810695 9 to 32 15.85 13.2686 0.281973 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.519245 Tough bday spacings test for dh-ranFile-2016-03-17_13:31: 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 6 39 73 86 105 75 57 30 19 5 5 (O-E)^2/E 1.1 0.2 0.0 1.4 0.5 0.1 0.5 0.0 1.1 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 5.525, p= 0.147 RESULTS OF GCD FOR dh-ranFile-2016-03-17_13:31 Euclid's algorithm: p-value, steps to gcd: 0.339194 p-value, dist. of gcd's: 0.329097 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-17_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.819 0.799 0.499 0.528 0.212 0.979 0.922 0.499 Bits 8 to 15---> 0.473 0.092 0.462 0.570 0.060 0.723 0.309 0.863 Bits 16 to 23---> 0.808 0.063 0.415 0.490 0.878 0.425 0.171 0.636 Bits 24 to 31---> 0.278 0.987 0.732 0.481 0.103 0.766 0.441 0.989 KS test for the above 32 p values: 0.492 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-17_13:31, p-values for 5 runs: 0.4324, 0.6372, 0.0492, 0.0009, 0.9192 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-17_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5191 5134.0 0.633 1.933 r= 30 22998 23103.0 0.478 2.411 r= 31 11583 11551.5 0.086 2.497 chi-square = 2.497 with df = 3; p-value = 0.524 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-17_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5012 5134.0 2.900 2.927 r= 31 23237 23103.0 0.777 3.704 r= 32 11542 11551.5 0.008 3.712 chi-square = 3.712 with df = 3; p-value = 0.706 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-17_13:31 b-rank test for bits 1 to 8, p=0.35789 b-rank test for bits 2 to 9, p=0.51895 b-rank test for bits 3 to 10, p=0.08780 b-rank test for bits 4 to 11, p=0.16684 b-rank test for bits 5 to 12, p=0.21419 b-rank test for bits 6 to 13, p=0.68843 b-rank test for bits 7 to 14, p=0.35289 b-rank test for bits 8 to 15, p=0.33216 b-rank test for bits 9 to 16, p=0.39337 b-rank test for bits 10 to 17, p=0.80918 b-rank test for bits 11 to 18, p=0.02530 b-rank test for bits 12 to 19, p=0.61005 b-rank test for bits 13 to 20, p=0.18628 b-rank test for bits 14 to 21, p=0.32401 b-rank test for bits 15 to 22, p=0.53674 b-rank test for bits 16 to 23, p=0.49756 b-rank test for bits 17 to 24, p=0.67466 b-rank test for bits 18 to 25, p=0.83331 b-rank test for bits 19 to 26, p=0.07379 b-rank test for bits 20 to 27, p=0.50904 b-rank test for bits 21 to 28, p=0.37857 b-rank test for bits 22 to 29, p=0.60119 b-rank test for bits 23 to 30, p=0.80858 b-rank test for bits 24 to 31, p=0.68393 b-rank test for bits 25 to 32, p=0.20049 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 = 0.285399 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-17_13:31 (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 142093 0.43 0.666088 2 141700 -0.49 0.312389 3 141784 -0.29 0.384827 4 141300 -1.42 0.077271 5 141919 0.02 0.509013 6 141409 -1.17 0.121203 7 142057 0.35 0.634962 8 142304 0.92 0.821769 9 141786 -0.29 0.386614 10 142293 0.90 0.814987 11 141651 -0.60 0.273063 12 142392 1.13 0.870284 13 142120 0.49 0.688718 14 142485 1.35 0.910691 15 142423 1.20 0.884962 16 141917 0.02 0.507149 17 142272 0.85 0.801603 18 141429 -1.12 0.130875 19 142829 2.15 0.984173 20 142190 0.66 0.744014 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-17_13:31 Bits used No. missing words z-score p-value 23 to 32 141930 0.0713 0.528411 22 to 31 142236 1.1264 0.870012 21 to 30 142070 0.5540 0.710222 20 to 29 141973 0.2196 0.586890 19 to 28 142282 1.2851 0.900616 18 to 27 141833 -0.2632 0.396196 17 to 26 141940 0.1058 0.542113 16 to 25 142206 1.0230 0.846846 15 to 24 142004 0.3264 0.627957 14 to 23 141736 -0.5977 0.275024 13 to 22 141578 -1.1425 0.126620 12 to 21 141893 -0.0563 0.477547 11 to 20 141843 -0.2287 0.409542 10 to 19 141956 0.1609 0.563926 9 to 18 141999 0.3092 0.621418 8 to 17 142258 1.2023 0.885378 7 to 16 142522 2.1127 0.982685 6 to 15 142370 1.5885 0.943915 5 to 14 141686 -0.7701 0.220619 4 to 13 142311 1.3851 0.916984 3 to 12 141677 -0.8011 0.211526 2 to 11 141672 -0.8184 0.206570 1 to 10 142531 2.1437 0.983971 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-17_13:31 Bits used No. missing words z-score p-value 28 to 32 141533 -1.2757 0.101032 27 to 31 141692 -0.7367 0.230649 26 to 30 141908 -0.0045 0.498201 25 to 29 141787 -0.4147 0.339189 24 to 28 142652 2.5175 0.994091 23 to 27 141468 -1.4960 0.067322 22 to 26 142022 0.3819 0.648744 21 to 25 142130 0.7480 0.772780 20 to 24 141303 -2.0554 0.019922 19 to 23 142112 0.6870 0.753964 18 to 22 142135 0.7650 0.777859 17 to 21 141573 -1.1401 0.127122 16 to 20 141496 -1.4011 0.080589 15 to 19 141703 -0.6994 0.242144 14 to 18 141933 0.0802 0.531976 13 to 17 142152 0.8226 0.794635 12 to 16 141551 -1.2147 0.112244 11 to 15 141619 -0.9842 0.162516 10 to 14 141975 0.2226 0.588081 9 to 13 141879 -0.1028 0.459056 8 to 12 141739 -0.5774 0.281838 7 to 11 141865 -0.1503 0.440275 6 to 10 142195 0.9684 0.833571 5 to 9 141832 -0.2621 0.396609 4 to 8 142469 1.8972 0.971098 3 to 7 141674 -0.7977 0.212514 2 to 6 142223 1.0633 0.856174 1 to 5 142049 0.4735 0.682057 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-17_13:31 Bits used No. missing words z-score p-value 31 to 32 141814 -0.2812 0.389275 30 to 31 141745 -0.4847 0.313927 29 to 30 141381 -1.5585 0.059558 28 to 29 142026 0.3442 0.634637 27 to 28 142114 0.6037 0.726994 26 to 27 141667 -0.7148 0.237355 25 to 26 141813 -0.2842 0.388144 24 to 25 141528 -1.1249 0.130323 23 to 24 141366 -1.6027 0.054496 22 to 23 142185 0.8132 0.791944 21 to 22 141955 0.1347 0.553583 20 to 21 142045 0.4002 0.655498 19 to 20 142234 0.9577 0.830900 18 to 19 142210 0.8869 0.812442 17 to 18 142117 0.6126 0.729928 16 to 17 142148 0.7040 0.759297 15 to 16 141595 -0.9272 0.176904 14 to 15 142062 0.4504 0.673772 13 to 14 142495 1.7276 0.957974 12 to 13 142224 0.9282 0.823356 11 to 12 141706 -0.5998 0.274322 10 to 11 141766 -0.4228 0.336220 9 to 10 142059 0.4415 0.670576 8 to 9 141902 -0.0216 0.491375 7 to 8 142100 0.5624 0.713095 6 to 7 142016 0.3147 0.623490 5 to 6 142192 0.8338 0.797813 4 to 5 142236 0.9636 0.832384 3 to 4 141245 -1.9597 0.025017 2 to 3 142300 1.1524 0.875426 1 to 2 141443 -1.3756 0.084472 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-17_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2411.69 -1.249 0.105845 Test results for specific bytes for dh-ranFile-2016-03-17_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2533.23 0.470 0.680794 2 to 9 2462.35 -0.532 0.297201 3 to 10 2635.92 1.922 0.972713 4 to 11 2565.68 0.929 0.823503 5 to 12 2490.75 -0.131 0.447946 6 to 13 2417.54 -1.166 0.121783 7 to 14 2412.80 -1.233 0.108750 8 to 15 2597.85 1.384 0.916794 9 to 16 2440.36 -0.843 0.199501 10 to 17 2624.28 1.758 0.960595 11 to 18 2430.80 -0.979 0.163875 12 to 19 2596.25 1.361 0.913261 13 to 20 2403.65 -1.363 0.086504 14 to 21 2405.19 -1.341 0.089982 15 to 22 2523.69 0.335 0.631205 16 to 23 2420.29 -1.127 0.129812 17 to 24 2476.86 -0.327 0.371759 18 to 25 2355.44 -2.044 0.020456 19 to 26 2531.57 0.447 0.672386 20 to 27 2507.22 0.102 0.540659 21 to 28 2457.00 -0.608 0.271555 22 to 29 2581.57 1.154 0.875651 23 to 30 2493.49 -0.092 0.463306 24 to 31 2485.80 -0.201 0.420433 25 to 32 2406.73 -1.319 0.093567 CDPARK for dh-ranFile-2016-03-17_13:31: 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 3539 0.7306 0.767486 3539 0.7306 0.767486 3498 -1.1416 0.126820 3478 -2.0548 0.019949 3559 1.6438 0.949895 3497 -1.1872 0.117571 3533 0.4566 0.676028 3557 1.5525 0.939730 3549 1.1872 0.882429 3525 0.0913 0.536383 Square side=100, avg. no. parked=3527.40 sample std.=26.22 p-value of the KSTEST for those 10 p-values: 0.299676 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-17_13:31 0.7936,0.8404,0.3176,0.7057,0.1311,0.0375,0.8365,0.9404,0.4185,1.0000, The KS test for those 10 p-values: 0.135734 The 3DSPHERES test for dh-ranFile-2016-03-17_13:31 sample no r^3 equiv. uni. 1 19.225 0.473143 2 8.070 0.235849 3 44.885 0.776014 4 0.317 0.010495 5 49.186 0.805928 6 64.107 0.881979 7 19.004 0.469256 8 2.402 0.076956 9 7.363 0.217639 10 0.313 0.010380 11 7.494 0.221037 12 24.366 0.556127 13 27.428 0.599194 14 66.280 0.890228 15 110.931 0.975219 16 12.660 0.344275 17 95.985 0.959217 18 40.278 0.738832 19 17.859 0.448597 20 1.498 0.048721 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.653558 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-17_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 0.8 0.0 -1.3 2.0 0.9 -0.6 1.2 -2.0 -2.3 -1.3 -0.0 1.4 0.7 0.7 0.7 -0.3 -0.2 0.4 -0.8 1.2 1.1 -0.0 -1.0 -2.2 -1.4 0.5 -1.4 1.9 1.4 1.3 -0.5 0.4 -1.2 -1.0 -0.2 0.8 -0.4 0.4 0.1 0.0 2.7 Chi-square with 42 degrees of freedom:56.373923 z-score=1.568324, p-value=0.931798 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-17_13:31 Test no p-value 1 0.996515 2 0.944889 3 0.859662 4 0.138398 5 0.027685 6 0.476710 7 0.784436 8 0.267964 9 0.217631 10 0.004355 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.220419 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-17_13:31: (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 66628 0.02 66781 0.20 3 25000.00 24982 0.01 24913 0.30 4 6666.67 6750 1.04 6558 1.77 5 1388.89 1396 0.04 1455 3.15 6 238.10 213 2.65 252 0.81 7 34.72 25 2.72 35 0.00 8 4.96 5 0.00 5 0.00 p=0.62837 p=0.60225 Number of rngs required: 688299, p-value: 0.452 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-17_13:31 No. of wins: Observed Expected 98298 98585.9 z-score=-1.287, pvalue=0.09897 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66451 66666.7 0.698 0.698 2 37890 37654.3 1.475 2.173 3 27083 26954.7 0.610 2.783 4 19442 19313.5 0.855 3.639 5 13784 13851.4 0.328 3.967 6 9901 9943.5 0.182 4.149 7 7141 7145.0 0.002 4.151 8 5106 5139.1 0.213 4.364 9 3580 3699.9 3.883 8.247 10 2620 2666.3 0.804 9.051 11 1938 1923.3 0.112 9.163 12 1356 1388.7 0.772 9.935 13 995 1003.7 0.076 10.011 14 774 726.1 3.154 13.165 15 549 525.8 1.020 14.185 16 384 381.2 0.021 14.207 17 260 276.5 0.989 15.196 18 186 200.8 1.095 16.291 19 139 146.0 0.334 16.625 20 115 106.2 0.727 17.352 21 306 287.1 1.242 18.594 Chisq= 18.59 for 20 degrees of freedom, p= 0.45166 SUMMARY of craptest p-value for no. of wins: 0.098965 p-value for throws/game: 0.451658 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-17_13:31 No. of wins: Observed Expected 98265 98585.9 z-score=-1.435, pvalue=0.07563 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66298 66666.7 2.039 2.039 2 37604 37654.3 0.067 2.106 3 27173 26954.7 1.767 3.873 4 19337 19313.5 0.029 3.902 5 13928 13851.4 0.423 4.325 6 9893 9943.5 0.257 4.582 7 7226 7145.0 0.918 5.500 8 5117 5139.1 0.095 5.595 9 3675 3699.9 0.167 5.762 10 2636 2666.3 0.344 6.106 11 2006 1923.3 3.553 9.660 12 1378 1388.7 0.083 9.743 13 999 1003.7 0.022 9.765 14 774 726.1 3.154 12.919 15 521 525.8 0.044 12.964 16 386 381.2 0.062 13.025 17 291 276.5 0.756 13.782 18 198 200.8 0.040 13.822 19 158 146.0 0.989 14.810 20 109 106.2 0.073 14.883 21 293 287.1 0.121 15.004 Chisq= 15.00 for 20 degrees of freedom, p= 0.22383 SUMMARY of craptest p-value for no. of wins: 0.075634 p-value for throws/game: 0.223830 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0044,0.0104,0.0105,0.0199,0.0199,0.0205,0.0250,0.0253,0.0277, 0.0375,0.0487,0.0492,0.0543,0.0545,0.0596,0.0598,0.0605,0.0630,0.0673, 0.0738,0.0756,0.0770,0.0773,0.0806,0.0845,0.0865,0.0878,0.0900,0.0923, 0.0936,0.0990,0.1010,0.1028,0.1058,0.1088,0.1122,0.1176,0.1212,0.1218, 0.1266,0.1268,0.1271,0.1298,0.1303,0.1309,0.1311,0.1357,0.1384,0.1465, 0.1625,0.1639,0.1668,0.1709,0.1769,0.1863,0.1995,0.2005,0.2066,0.2115, 0.2118,0.2125,0.2142,0.2176,0.2176,0.2204,0.2206,0.2210,0.2238,0.2306, 0.2358,0.2374,0.2421,0.2680,0.2716,0.2731,0.2743,0.2750,0.2784,0.2818, 0.2820,0.2854,0.2972,0.2997,0.3091,0.3124,0.3139,0.3176,0.3240,0.3291, 0.3322,0.3362,0.3392,0.3392,0.3443,0.3529,0.3579,0.3718,0.3786,0.3848, 0.3866,0.3881,0.3893,0.3934,0.3962,0.3966,0.4095,0.4147,0.4185,0.4204, 0.4251,0.4324,0.4403,0.4406,0.4479,0.4486,0.4517,0.4524,0.4591,0.4623, 0.4633,0.4693,0.4728,0.4731,0.4767,0.4775,0.4810,0.4899,0.4914,0.4917, 0.4976,0.4982,0.4990,0.4992,0.5001,0.5071,0.5090,0.5090,0.5189,0.5192, 0.5241,0.5276,0.5284,0.5320,0.5364,0.5367,0.5407,0.5421,0.5536,0.5561, 0.5639,0.5702,0.5869,0.5881,0.5992,0.6008,0.6012,0.6022,0.6100,0.6214, 0.6235,0.6280,0.6284,0.6312,0.6346,0.6350,0.6360,0.6372,0.6487,0.6536, 0.6555,0.6661,0.6706,0.6724,0.6738,0.6747,0.6760,0.6808,0.6821,0.6839, 0.6884,0.6887,0.7057,0.7057,0.7102,0.7131,0.7230,0.7270,0.7299,0.7324, 0.7388,0.7440,0.7540,0.7593,0.7663,0.7675,0.7675,0.7728,0.7760,0.7779, 0.7844,0.7919,0.7936,0.7946,0.7963,0.7978,0.7992,0.8016,0.8059,0.8079, 0.8086,0.8092,0.8107,0.8124,0.8150,0.8189,0.8218,0.8234,0.8235,0.8309, 0.8324,0.8333,0.8336,0.8365,0.8404,0.8468,0.8562,0.8597,0.8629,0.8700, 0.8703,0.8754,0.8757,0.8778,0.8820,0.8824,0.8850,0.8854,0.8902,0.9006, 0.9107,0.9133,0.9168,0.9170,0.9192,0.9219,0.9318,0.9397,0.9404,0.9439, 0.9449,0.9468,0.9499,0.9580,0.9592,0.9606,0.9711,0.9727,0.9752,0.9787, 0.9799,0.9827,0.9840,0.9842,0.9873,0.9895,0.9941,0.9965,1.0000, Overall p-value after applying KStest on 269 p-values = 0.563708 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.