RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-09_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 18.0762 0.615953 2 to 25 15.99 22.5003 0.833764 3 to 26 15.74 14.8057 0.390524 4 to 27 16.03 23.6996 0.872170 5 to 28 15.38 22.5582 0.835807 6 to 29 15.76 23.2444 0.858539 7 to 30 15.70 15.9937 0.475720 8 to 31 16.09 20.6356 0.756985 9 to 32 16.16 19.5027 0.699547 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.037640 Tough bday spacings test for dh-ranFile-2015-12-09_14:31: 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 18 36 70 107 79 74 48 43 15 8 2 (O-E)^2/E 8.5 0.0 0.1 0.9 3.6 0.2 0.3 5.9 0.0 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 20.918, p= 0.978 RESULTS OF GCD FOR dh-ranFile-2015-12-09_14:31 Euclid's algorithm: p-value, steps to gcd: 0.016648 p-value, dist. of gcd's: 0.776920 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-09_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.811 0.300 0.917 0.003 0.054 0.584 0.749 0.647 Bits 8 to 15---> 0.633 0.421 0.115 0.129 0.057 0.276 0.684 0.623 Bits 16 to 23---> 0.457 0.216 0.056 0.793 0.500 0.962 0.134 0.074 Bits 24 to 31---> 0.019 0.669 0.344 0.843 0.538 0.531 0.181 0.707 KS test for the above 32 p values: 0.732 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-09_14:31, p-values for 5 runs: 0.6212, 0.1151, 0.4402, 0.2196, 0.8924 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-09_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5211 5134.0 1.155 1.155 r= 30 22984 23103.0 0.613 1.769 r= 31 11594 11551.5 0.156 1.925 chi-square = 1.925 with df = 3; p-value = 0.412 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-09_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5095 5134.0 0.296 0.501 r= 31 23075 23103.0 0.034 0.535 r= 32 11612 11551.5 0.317 0.852 chi-square = 0.852 with df = 3; p-value = 0.163 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-09_14:31 b-rank test for bits 1 to 8, p=0.56313 b-rank test for bits 2 to 9, p=0.62301 b-rank test for bits 3 to 10, p=0.05535 b-rank test for bits 4 to 11, p=0.12118 b-rank test for bits 5 to 12, p=0.63100 b-rank test for bits 6 to 13, p=0.79577 b-rank test for bits 7 to 14, p=0.76734 b-rank test for bits 8 to 15, p=0.99174 b-rank test for bits 9 to 16, p=0.23788 b-rank test for bits 10 to 17, p=0.67255 b-rank test for bits 11 to 18, p=0.72416 b-rank test for bits 12 to 19, p=0.31900 b-rank test for bits 13 to 20, p=0.26608 b-rank test for bits 14 to 21, p=0.54150 b-rank test for bits 15 to 22, p=0.35633 b-rank test for bits 16 to 23, p=0.05733 b-rank test for bits 17 to 24, p=0.69145 b-rank test for bits 18 to 25, p=0.83578 b-rank test for bits 19 to 26, p=0.67615 b-rank test for bits 20 to 27, p=0.35763 b-rank test for bits 21 to 28, p=0.16047 b-rank test for bits 22 to 29, p=0.04229 b-rank test for bits 23 to 30, p=0.77905 b-rank test for bits 24 to 31, p=0.71325 b-rank test for bits 25 to 32, p=0.14450 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 = 0.734512 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-09_14:31 (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 141940 0.07 0.528563 2 142826 2.14 0.983893 3 142545 1.49 0.931256 4 142068 0.37 0.644579 5 141858 -0.12 0.452269 6 141167 -1.73 0.041422 7 141834 -0.18 0.430145 8 141977 0.16 0.562814 9 142211 0.70 0.759544 10 142161 0.59 0.721739 11 142069 0.37 0.645448 12 141957 0.11 0.544342 13 141821 -0.21 0.418248 14 142142 0.54 0.706649 15 141684 -0.53 0.299280 16 141815 -0.22 0.412781 17 141157 -1.76 0.039392 18 141951 0.10 0.538780 19 142282 0.87 0.808048 20 142090 0.42 0.663534 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-09_14:31 Bits used No. missing words z-score p-value 23 to 32 141770 -0.4804 0.315454 22 to 31 141743 -0.5736 0.283136 21 to 30 141381 -1.8218 0.034241 20 to 29 141907 -0.0080 0.496795 19 to 28 142297 1.3368 0.909355 18 to 27 142307 1.3713 0.914856 17 to 26 141631 -0.9598 0.168588 16 to 25 141775 -0.4632 0.321608 15 to 24 142065 0.5368 0.704295 14 to 23 142180 0.9333 0.824679 13 to 22 141626 -0.9770 0.164285 12 to 21 141925 0.0540 0.521546 11 to 20 141736 -0.5977 0.275024 10 to 19 142089 0.6196 0.732224 9 to 18 141536 -1.2873 0.098987 8 to 17 141829 -0.2770 0.390890 7 to 16 142208 1.0299 0.848471 6 to 15 142471 1.9368 0.973615 5 to 14 141565 -1.1873 0.117546 4 to 13 142389 1.6540 0.950940 3 to 12 141996 0.2989 0.617477 2 to 11 142090 0.6230 0.733358 1 to 10 142099 0.6540 0.743455 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-09_14:31 Bits used No. missing words z-score p-value 28 to 32 141758 -0.5130 0.303982 27 to 31 141692 -0.7367 0.230649 26 to 30 142130 0.7480 0.772780 25 to 29 142354 1.5074 0.934140 24 to 28 142081 0.5819 0.719694 23 to 27 142130 0.7480 0.772780 22 to 26 142049 0.4735 0.682057 21 to 25 141948 0.1311 0.552146 20 to 24 141833 -0.2587 0.397916 19 to 23 142026 0.3955 0.653760 18 to 22 141709 -0.6791 0.248542 17 to 21 141961 0.1752 0.569520 16 to 20 141923 0.0463 0.518480 15 to 19 142072 0.5514 0.709328 14 to 18 141827 -0.2791 0.390090 13 to 17 141838 -0.2418 0.404469 12 to 16 141928 0.0633 0.525232 11 to 15 142192 0.9582 0.831020 10 to 14 142068 0.5379 0.704665 9 to 13 141572 -1.1435 0.126417 8 to 12 141832 -0.2621 0.396609 7 to 11 141202 -2.3977 0.008249 6 to 10 142040 0.4429 0.671099 5 to 9 141569 -1.1537 0.124320 4 to 8 141880 -0.0994 0.460401 3 to 7 141478 -1.4621 0.071852 2 to 6 141896 -0.0452 0.481979 1 to 5 141694 -0.7299 0.232716 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-09_14:31 Bits used No. missing words z-score p-value 31 to 32 142033 0.3648 0.642373 30 to 31 142069 0.4710 0.681181 29 to 30 141544 -1.0777 0.140591 28 to 29 142616 2.0846 0.981446 27 to 28 142130 0.6509 0.742459 26 to 27 142019 0.3235 0.626846 25 to 26 141913 0.0108 0.504319 24 to 25 141514 -1.1662 0.121774 23 to 24 141744 -0.4877 0.312882 22 to 23 142135 0.6657 0.747196 21 to 22 141751 -0.4671 0.320232 20 to 21 141455 -1.3402 0.090089 19 to 20 141684 -0.6647 0.253124 18 to 19 142102 0.5683 0.715101 17 to 18 142281 1.0964 0.863542 16 to 17 142166 0.7571 0.775517 15 to 16 141064 -2.4936 0.006323 14 to 15 141848 -0.1809 0.428217 13 to 14 141745 -0.4847 0.313927 12 to 13 142653 2.1937 0.985872 11 to 12 142322 1.2173 0.888258 10 to 11 142157 0.7306 0.767485 9 to 10 141977 0.1996 0.579110 8 to 9 142114 0.6037 0.726994 7 to 8 141923 0.0403 0.516083 6 to 7 141695 -0.6322 0.263614 5 to 6 142018 0.3206 0.625728 4 to 5 141960 0.1495 0.559408 3 to 4 142353 1.3088 0.904692 2 to 3 141187 -2.1308 0.016554 1 to 2 141652 -0.7591 0.223901 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-09_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2458.95 -0.581 0.280755 Test results for specific bytes for dh-ranFile-2015-12-09_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2511.21 0.159 0.562972 2 to 9 2468.46 -0.446 0.327808 3 to 10 2598.92 1.399 0.919093 4 to 11 2353.78 -2.068 0.019328 5 to 12 2540.45 0.572 0.716358 6 to 13 2598.20 1.389 0.917552 7 to 14 2513.17 0.186 0.573892 8 to 15 2384.37 -1.635 0.050996 9 to 16 2534.40 0.487 0.686695 10 to 17 2427.42 -1.026 0.152353 11 to 18 2554.29 0.768 0.778670 12 to 19 2401.16 -1.398 0.081088 13 to 20 2623.99 1.753 0.960238 14 to 21 2537.45 0.530 0.701833 15 to 22 2523.72 0.335 0.631364 16 to 23 2555.96 0.791 0.785627 17 to 24 2479.84 -0.285 0.387761 18 to 25 2549.02 0.693 0.755920 19 to 26 2533.33 0.471 0.681318 20 to 27 2473.97 -0.368 0.356409 21 to 28 2481.94 -0.255 0.399220 22 to 29 2538.44 0.544 0.706674 23 to 30 2619.64 1.692 0.954671 24 to 31 2462.12 -0.536 0.296061 25 to 32 2578.73 1.113 0.867234 CDPARK for dh-ranFile-2015-12-09_14:31: 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 3583 2.7397 0.996925 3524 0.0457 0.518210 3498 -1.1416 0.126820 3512 -0.5023 0.307734 3488 -1.5982 0.055002 3505 -0.8219 0.205562 3522 -0.0457 0.481790 3512 -0.5023 0.307734 3492 -1.4155 0.078457 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3514.60 sample std.=25.38 p-value of the KSTEST for those 10 p-values: 0.069978 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-09_14:31 0.1813,0.2430,0.4395,0.9106,0.5811,0.0755,0.5931,0.0283,0.2391,0.9548, The KS test for those 10 p-values: 0.589424 The 3DSPHERES test for dh-ranFile-2015-12-09_14:31 sample no r^3 equiv. uni. 1 1.033 0.033840 2 9.761 0.277726 3 63.581 0.879891 4 71.812 0.908712 5 14.302 0.379194 6 112.660 0.976607 7 12.916 0.349837 8 23.852 0.548449 9 2.412 0.077237 10 3.053 0.096755 11 4.913 0.151061 12 2.525 0.080718 13 3.900 0.121910 14 36.281 0.701609 15 65.663 0.887945 16 49.255 0.806378 17 88.815 0.948207 18 17.676 0.445236 19 8.384 0.243812 20 21.268 0.507839 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.556334 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-09_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 0.3 -0.4 -0.5 0.3 -0.2 0.8 -0.7 0.8 -1.2 -0.2 -1.4 0.1 -0.9 2.5 -0.7 -0.2 0.8 1.1 -1.5 -1.0 -0.2 0.7 0.4 -0.9 1.9 0.8 0.3 0.0 0.1 0.0 0.0 -0.6 -0.1 -0.8 0.0 -0.4 0.1 -0.7 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:30.243710 z-score=-1.282716, p-value=0.088169 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-09_14:31 Test no p-value 1 0.742103 2 0.344808 3 0.079745 4 0.652784 5 0.091291 6 0.050656 7 0.083874 8 0.017767 9 0.960664 10 0.828659 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.077234 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-09_14:31: (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 66589 0.09 66635 0.02 3 25000.00 25094 0.35 24962 0.06 4 6666.67 6720 0.43 6659 0.01 5 1388.89 1324 3.03 1443 2.11 6 238.10 228 0.43 257 1.50 7 34.72 40 0.80 38 0.31 8 4.96 4 0.19 5 0.00 p=0.49641 p=0.32345 Number of rngs required: 688114, p-value: 0.370 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-09_14:31 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 66692 66666.7 0.010 0.010 2 37297 37654.3 3.391 3.400 3 27263 26954.7 3.525 6.926 4 19177 19313.5 0.964 7.890 5 13737 13851.4 0.945 8.835 6 10108 9943.5 2.720 11.555 7 7105 7145.0 0.224 11.779 8 5183 5139.1 0.375 12.155 9 3705 3699.9 0.007 12.162 10 2699 2666.3 0.401 12.563 11 1987 1923.3 2.108 14.671 12 1417 1388.7 0.575 15.246 13 1006 1003.7 0.005 15.251 14 729 726.1 0.011 15.263 15 515 525.8 0.223 15.486 16 352 381.2 2.229 17.715 17 272 276.5 0.075 17.790 18 186 200.8 1.095 18.885 19 169 146.0 3.629 22.513 20 110 106.2 0.135 22.648 21 291 287.1 0.053 22.701 Chisq= 22.70 for 20 degrees of freedom, p= 0.69628 SUMMARY of craptest p-value for no. of wins: 0.802455 p-value for throws/game: 0.696282 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-09_14:31 No. of wins: Observed Expected 98943 98585.9 z-score= 1.597, pvalue=0.94491 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66642 66666.7 0.009 0.009 2 37529 37654.3 0.417 0.426 3 27100 26954.7 0.783 1.209 4 19341 19313.5 0.039 1.248 5 13819 13851.4 0.076 1.324 6 9937 9943.5 0.004 1.329 7 7042 7145.0 1.486 2.814 8 5180 5139.1 0.326 3.140 9 3683 3699.9 0.077 3.217 10 2671 2666.3 0.008 3.225 11 1964 1923.3 0.860 4.085 12 1449 1388.7 2.615 6.700 13 990 1003.7 0.187 6.887 14 685 726.1 2.331 9.218 15 510 525.8 0.477 9.695 16 399 381.2 0.836 10.531 17 309 276.5 3.810 14.341 18 202 200.8 0.007 14.348 19 145 146.0 0.007 14.355 20 103 106.2 0.097 14.452 21 300 287.1 0.578 15.030 Chisq= 15.03 for 20 degrees of freedom, p= 0.22534 SUMMARY of craptest p-value for no. of wins: 0.944906 p-value for throws/game: 0.225340 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0026,0.0063,0.0082,0.0166,0.0166,0.0178,0.0190,0.0193,0.0283,0.0338, 0.0342,0.0376,0.0394,0.0414,0.0423,0.0507,0.0510,0.0539,0.0550,0.0553, 0.0555,0.0570,0.0573,0.0700,0.0719,0.0744,0.0755,0.0772,0.0772,0.0785, 0.0797,0.0807,0.0811,0.0839,0.0882,0.0901,0.0913,0.0968,0.0990,0.1150, 0.1151,0.1175,0.1212,0.1218,0.1219,0.1243,0.1264,0.1268,0.1288,0.1340, 0.1406,0.1445,0.1511,0.1524,0.1605,0.1630,0.1643,0.1686,0.1810,0.1813, 0.2056,0.2158,0.2196,0.2239,0.2253,0.2306,0.2327,0.2379,0.2391,0.2430, 0.2438,0.2485,0.2531,0.2636,0.2661,0.2750,0.2761,0.2764,0.2777,0.2808, 0.2831,0.2961,0.2993,0.2999,0.3040,0.3077,0.3077,0.3129,0.3139,0.3155, 0.3190,0.3202,0.3216,0.3235,0.3278,0.3445,0.3448,0.3498,0.3563,0.3564, 0.3576,0.3697,0.3792,0.3878,0.3901,0.3905,0.3909,0.3966,0.3979,0.3992, 0.4045,0.4119,0.4128,0.4182,0.4205,0.4282,0.4301,0.4395,0.4402,0.4452, 0.4523,0.4568,0.4604,0.4757,0.4818,0.4820,0.4964,0.4968,0.5004,0.5043, 0.5078,0.5161,0.5182,0.5185,0.5215,0.5252,0.5286,0.5314,0.5377,0.5388, 0.5415,0.5443,0.5484,0.5521,0.5563,0.5594,0.5628,0.5630,0.5631,0.5695, 0.5739,0.5791,0.5811,0.5837,0.5894,0.5931,0.6160,0.6175,0.6212,0.6228, 0.6230,0.6257,0.6268,0.6310,0.6314,0.6325,0.6424,0.6446,0.6454,0.6471, 0.6528,0.6538,0.6635,0.6688,0.6711,0.6726,0.6762,0.6812,0.6813,0.6821, 0.6842,0.6867,0.6915,0.6963,0.6995,0.7016,0.7018,0.7043,0.7047,0.7066, 0.7067,0.7074,0.7093,0.7133,0.7151,0.7164,0.7197,0.7217,0.7242,0.7270, 0.7320,0.7322,0.7334,0.7345,0.7421,0.7425,0.7435,0.7472,0.7495,0.7559, 0.7570,0.7595,0.7673,0.7675,0.7728,0.7728,0.7755,0.7769,0.7787,0.7790, 0.7856,0.7935,0.7958,0.8025,0.8064,0.8080,0.8109,0.8247,0.8287,0.8310, 0.8338,0.8358,0.8358,0.8431,0.8485,0.8585,0.8635,0.8672,0.8722,0.8799, 0.8879,0.8883,0.8924,0.9047,0.9087,0.9094,0.9106,0.9149,0.9171,0.9176, 0.9191,0.9313,0.9341,0.9449,0.9482,0.9509,0.9547,0.9548,0.9602,0.9607, 0.9620,0.9736,0.9766,0.9783,0.9814,0.9839,0.9859,0.9917,0.9969, Overall p-value after applying KStest on 269 p-values = 0.404985 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.