RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-27_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 15.90 24.1810 0.885401 2 to 25 15.88 18.2601 0.627389 3 to 26 16.02 25.4338 0.914588 4 to 27 15.97 9.4832 0.076126 5 to 28 15.82 10.7055 0.128545 6 to 29 15.78 30.3261 0.975913 7 to 30 15.95 6.8924 0.015101 8 to 31 16.02 18.6860 0.653151 9 to 32 16.00 9.7292 0.085420 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.216509 Tough bday spacings test for dh-ranFile-2016-03-27_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 11 43 74 102 86 81 58 20 11 12 2 (O-E)^2/E 0.4 1.1 0.0 0.2 1.4 0.1 0.7 3.2 1.0 4.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.499, p= 0.803 RESULTS OF GCD FOR dh-ranFile-2016-03-27_14:31 Euclid's algorithm: p-value, steps to gcd: 0.442763 p-value, dist. of gcd's: 0.512563 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-27_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.677 0.820 0.701 0.296 0.794 0.396 0.323 0.088 Bits 8 to 15---> 0.343 0.032 0.856 0.202 0.393 0.743 0.419 0.120 Bits 16 to 23---> 0.425 0.408 0.990 0.090 0.326 0.074 0.968 0.846 Bits 24 to 31---> 0.197 0.979 0.617 0.226 0.573 0.293 0.325 0.435 KS test for the above 32 p values: 0.382 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-27_14:31, p-values for 5 runs: 0.3109, 0.6206, 0.3193, 0.2922, 0.6540 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-27_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 242 211.4 4.424 4.424 r= 29 5111 5134.0 0.103 4.527 r= 30 23223 23103.0 0.623 5.150 r= 31 11424 11551.5 1.408 6.557 chi-square = 6.557 with df = 3; p-value = 0.913 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-27_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 230 211.4 1.633 1.633 r= 30 5321 5134.0 6.810 8.444 r= 31 23115 23103.0 0.006 8.450 r= 32 11334 11551.5 4.096 12.546 chi-square = 12.546 with df = 3; p-value = 0.994 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-27_14:31 b-rank test for bits 1 to 8, p=0.45512 b-rank test for bits 2 to 9, p=0.72747 b-rank test for bits 3 to 10, p=0.33075 b-rank test for bits 4 to 11, p=0.58913 b-rank test for bits 5 to 12, p=0.99757 b-rank test for bits 6 to 13, p=0.49669 b-rank test for bits 7 to 14, p=0.18422 b-rank test for bits 8 to 15, p=0.95455 b-rank test for bits 9 to 16, p=0.93656 b-rank test for bits 10 to 17, p=0.66678 b-rank test for bits 11 to 18, p=0.24358 b-rank test for bits 12 to 19, p=0.03478 b-rank test for bits 13 to 20, p=0.69556 b-rank test for bits 14 to 21, p=0.10475 b-rank test for bits 15 to 22, p=0.54977 b-rank test for bits 16 to 23, p=0.36804 b-rank test for bits 17 to 24, p=0.00192 b-rank test for bits 18 to 25, p=0.18277 b-rank test for bits 19 to 26, p=0.55081 b-rank test for bits 20 to 27, p=0.07887 b-rank test for bits 21 to 28, p=0.24519 b-rank test for bits 22 to 29, p=0.79616 b-rank test for bits 23 to 30, p=0.66758 b-rank test for bits 24 to 31, p=0.80177 b-rank test for bits 25 to 32, p=0.19868 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 = 0.868823 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-27_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 141642 -0.62 0.266116 2 141414 -1.16 0.123572 3 142486 1.35 0.911068 4 141843 -0.15 0.438420 5 141582 -0.76 0.222198 6 141695 -0.50 0.308266 7 141952 0.10 0.539707 8 141931 0.05 0.520190 9 141953 0.10 0.540635 10 141565 -0.80 0.210551 11 141164 -1.74 0.040805 12 141507 -0.94 0.173603 13 141774 -0.32 0.375929 14 142411 1.17 0.879427 15 141684 -0.53 0.299280 16 142383 1.11 0.865789 17 141733 -0.41 0.340175 18 141879 -0.07 0.471753 19 141779 -0.30 0.380370 20 141999 0.21 0.582975 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-27_14:31 Bits used No. missing words z-score p-value 23 to 32 141757 -0.5253 0.299696 22 to 31 141844 -0.2253 0.410882 21 to 30 142433 1.8058 0.964522 20 to 29 141664 -0.8460 0.198786 19 to 28 141552 -1.2322 0.108942 18 to 27 141917 0.0264 0.510550 17 to 26 141753 -0.5391 0.294920 16 to 25 141477 -1.4908 0.068008 15 to 24 141408 -1.7287 0.041929 14 to 23 141949 0.1368 0.554403 13 to 22 141865 -0.1529 0.439254 12 to 21 142087 0.6127 0.729948 11 to 20 141208 -2.4184 0.007795 10 to 19 141785 -0.4287 0.334062 9 to 18 141881 -0.0977 0.461089 8 to 17 141878 -0.1080 0.456984 7 to 16 142340 1.4851 0.931237 6 to 15 142359 1.5506 0.939500 5 to 14 141978 0.2368 0.593591 4 to 13 141466 -1.5287 0.063166 3 to 12 142073 0.5644 0.713752 2 to 11 141673 -0.8149 0.207556 1 to 10 141537 -1.2839 0.099589 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-27_14:31 Bits used No. missing words z-score p-value 28 to 32 141505 -1.3706 0.085248 27 to 31 141694 -0.7299 0.232716 26 to 30 141784 -0.4248 0.335474 25 to 29 142008 0.3345 0.630989 24 to 28 141866 -0.1469 0.441613 23 to 27 141639 -0.9164 0.179736 22 to 26 141849 -0.2045 0.418978 21 to 25 141461 -1.5198 0.064285 20 to 24 141847 -0.2113 0.416331 19 to 23 142613 2.3853 0.991468 18 to 22 141859 -0.1706 0.432265 17 to 21 142162 0.8565 0.804142 16 to 20 142216 1.0396 0.850728 15 to 19 141265 -2.1842 0.014475 14 to 18 141998 0.3006 0.618131 13 to 17 141654 -0.8655 0.193375 12 to 16 142250 1.1548 0.875917 11 to 15 142461 1.8701 0.969263 10 to 14 142192 0.9582 0.831020 9 to 13 141366 -1.8418 0.032752 8 to 12 141975 0.2226 0.588081 7 to 11 141609 -1.0181 0.154323 6 to 10 141989 0.2701 0.606446 5 to 9 142110 0.6802 0.751823 4 to 8 141553 -1.2079 0.113543 3 to 7 141297 -2.0757 0.018961 2 to 6 141596 -1.0621 0.144087 1 to 5 142615 2.3921 0.991624 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-27_14:31 Bits used No. missing words z-score p-value 31 to 32 142000 0.2675 0.605444 30 to 31 141523 -1.1396 0.127223 29 to 30 141653 -0.7561 0.224784 28 to 29 141868 -0.1219 0.451482 27 to 28 142307 1.1731 0.879616 26 to 27 141862 -0.1396 0.444482 25 to 26 142284 1.1052 0.865468 24 to 25 142173 0.7778 0.781653 23 to 24 142140 0.6804 0.751888 22 to 23 141375 -1.5762 0.057490 21 to 22 141602 -0.9066 0.182315 20 to 21 142189 0.8250 0.795310 19 to 20 142140 0.6804 0.751888 18 to 19 142150 0.7099 0.761130 17 to 18 141178 -2.1573 0.015491 16 to 17 142086 0.5212 0.698869 15 to 16 142472 1.6598 0.951522 14 to 15 141795 -0.3373 0.367962 13 to 14 141885 -0.0718 0.471393 12 to 13 141909 -0.0010 0.499612 11 to 12 142289 1.1200 0.868637 10 to 11 141754 -0.4582 0.323404 9 to 10 142152 0.7158 0.762955 8 to 9 141979 0.2055 0.581416 7 to 8 141300 -1.7974 0.036133 6 to 7 141404 -1.4906 0.068027 5 to 6 141483 -1.2576 0.104266 4 to 5 141601 -0.9095 0.181536 3 to 4 141732 -0.5231 0.300453 2 to 3 141683 -0.6676 0.252182 1 to 2 142089 0.5300 0.701944 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-27_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2377.13 -1.738 0.041142 Test results for specific bytes for dh-ranFile-2016-03-27_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2473.46 -0.375 0.353701 2 to 9 2578.15 1.105 0.865463 3 to 10 2522.16 0.313 0.622990 4 to 11 2524.70 0.349 0.636588 5 to 12 2353.76 -2.068 0.019310 6 to 13 2470.35 -0.419 0.337512 7 to 14 2452.26 -0.675 0.249803 8 to 15 2531.74 0.449 0.673224 9 to 16 2368.67 -1.857 0.031640 10 to 17 2396.13 -1.469 0.070921 11 to 18 2449.85 -0.709 0.239107 12 to 19 2437.57 -0.883 0.188636 13 to 20 2450.56 -0.699 0.242234 14 to 21 2411.51 -1.251 0.105393 15 to 22 2508.14 0.115 0.545831 16 to 23 2456.48 -0.615 0.269132 17 to 24 2484.32 -0.222 0.412241 18 to 25 2359.90 -1.981 0.023778 19 to 26 2371.22 -1.821 0.034283 20 to 27 2514.58 0.206 0.581703 21 to 28 2574.65 1.056 0.854452 22 to 29 2514.04 0.199 0.578673 23 to 30 2582.22 1.163 0.877551 24 to 31 2477.54 -0.318 0.375387 25 to 32 2596.38 1.363 0.913558 CDPARK for dh-ranFile-2016-03-27_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 3530 0.3196 0.625377 3512 -0.5023 0.307734 3528 0.2283 0.590298 3542 0.8676 0.807188 3537 0.6393 0.738676 3527 0.1826 0.572463 3574 2.3288 0.990064 3527 0.1826 0.572463 3563 1.8265 0.966111 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3535.60 sample std.=18.56 p-value of the KSTEST for those 10 p-values: 0.111672 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-27_14:31 0.1434,0.8753,0.5854,0.4465,0.4624,0.2626,0.5650,0.9573,0.7672,0.5971, The KS test for those 10 p-values: 0.708684 The 3DSPHERES test for dh-ranFile-2016-03-27_14:31 sample no r^3 equiv. uni. 1 31.201 0.646562 2 11.950 0.328567 3 28.973 0.619309 4 2.660 0.084851 5 60.488 0.866850 6 35.959 0.698391 7 36.222 0.701028 8 75.738 0.919911 9 9.902 0.281134 10 60.850 0.868445 11 42.931 0.760939 12 13.077 0.353314 13 0.885 0.029081 14 65.111 0.885863 15 43.608 0.766270 16 16.324 0.419655 17 9.281 0.266077 18 9.114 0.261999 19 13.467 0.361675 20 15.372 0.400944 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.813947 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-27_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 -1.3 -1.4 -0.4 -1.2 1.0 -1.9 -0.2 -0.2 -0.0 0.2 -1.7 1.6 -1.2 0.1 0.7 1.0 0.5 0.1 -0.3 -0.8 -1.5 1.2 0.1 -0.7 -1.8 2.1 1.3 0.8 -0.4 1.0 0.3 1.7 2.3 0.4 -1.4 0.5 0.1 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:49.546949 z-score=0.823440, p-value=0.802480 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-27_14:31 Test no p-value 1 0.184235 2 0.125397 3 0.522582 4 0.243796 5 0.446684 6 0.759874 7 0.131027 8 0.542182 9 0.043048 10 0.064675 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.051215 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-27_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 66823 0.37 66628 0.02 3 25000.00 24746 2.58 25024 0.02 4 6666.67 6778 1.86 6659 0.01 5 1388.89 1382 0.03 1423 0.84 6 238.10 231 0.21 233 0.11 7 34.72 34 0.01 31 0.40 8 4.96 5 0.00 1 3.16 p=0.46478 p=0.39881 Number of rngs required: 687795, p-value: 0.241 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-27_14:31 No. of wins: Observed Expected 98741 98585.9 z-score= 0.694, pvalue=0.75612 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66615 66666.7 0.040 0.040 2 38089 37654.3 5.018 5.058 3 26899 26954.7 0.115 5.173 4 19413 19313.5 0.513 5.686 5 13707 13851.4 1.506 7.192 6 9947 9943.5 0.001 7.193 7 7028 7145.0 1.917 9.110 8 5128 5139.1 0.024 9.134 9 3622 3699.9 1.639 10.772 10 2649 2666.3 0.112 10.885 11 1972 1923.3 1.232 12.116 12 1322 1388.7 3.207 15.324 13 997 1003.7 0.045 15.369 14 710 726.1 0.359 15.727 15 493 525.8 2.050 17.778 16 354 381.2 1.934 19.712 17 281 276.5 0.072 19.784 18 209 200.8 0.332 20.116 19 148 146.0 0.028 20.144 20 112 106.2 0.315 20.459 21 305 287.1 1.114 21.573 Chisq= 21.57 for 20 degrees of freedom, p= 0.63589 SUMMARY of craptest p-value for no. of wins: 0.756122 p-value for throws/game: 0.635894 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-27_14:31 No. of wins: Observed Expected 98595 98585.9 z-score= 0.041, pvalue=0.51631 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66793 66666.7 0.239 0.239 2 37515 37654.3 0.515 0.755 3 26675 26954.7 2.903 3.658 4 19367 19313.5 0.148 3.806 5 13945 13851.4 0.632 4.439 6 9896 9943.5 0.227 4.666 7 7255 7145.0 1.693 6.359 8 5251 5139.1 2.438 8.796 9 3642 3699.9 0.905 9.701 10 2695 2666.3 0.309 10.010 11 1882 1923.3 0.888 10.898 12 1414 1388.7 0.459 11.358 13 1008 1003.7 0.018 11.376 14 756 726.1 1.228 12.604 15 481 525.8 3.823 16.427 16 379 381.2 0.012 16.439 17 287 276.5 0.396 16.835 18 197 200.8 0.073 16.908 19 159 146.0 1.160 18.068 20 116 106.2 0.901 18.970 21 287 287.1 0.000 18.970 Chisq= 18.97 for 20 degrees of freedom, p= 0.47620 SUMMARY of craptest p-value for no. of wins: 0.516307 p-value for throws/game: 0.476202 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0078,0.0145,0.0151,0.0155,0.0190,0.0193,0.0238,0.0291,0.0316, 0.0320,0.0328,0.0343,0.0348,0.0361,0.0408,0.0411,0.0419,0.0430,0.0512, 0.0575,0.0632,0.0643,0.0647,0.0680,0.0680,0.0709,0.0736,0.0761,0.0789, 0.0849,0.0852,0.0854,0.0881,0.0899,0.0996,0.1043,0.1048,0.1054,0.1089, 0.1117,0.1135,0.1204,0.1236,0.1254,0.1272,0.1285,0.1310,0.1434,0.1441, 0.1543,0.1736,0.1797,0.1815,0.1823,0.1828,0.1842,0.1842,0.1886,0.1934, 0.1973,0.1987,0.1988,0.2020,0.2076,0.2106,0.2165,0.2222,0.2248,0.2263, 0.2327,0.2391,0.2414,0.2422,0.2436,0.2438,0.2452,0.2498,0.2522,0.2620, 0.2626,0.2661,0.2661,0.2691,0.2811,0.2922,0.2934,0.2949,0.2963,0.2993, 0.2997,0.3005,0.3077,0.3083,0.3109,0.3193,0.3229,0.3234,0.3255,0.3265, 0.3286,0.3308,0.3341,0.3355,0.3375,0.3402,0.3426,0.3533,0.3537,0.3617, 0.3680,0.3680,0.3746,0.3754,0.3759,0.3804,0.3822,0.3928,0.3964,0.3988, 0.4009,0.4085,0.4109,0.4122,0.4163,0.4188,0.4190,0.4197,0.4253,0.4323, 0.4349,0.4384,0.4393,0.4416,0.4428,0.4445,0.4465,0.4467,0.4515,0.4551, 0.4570,0.4611,0.4624,0.4648,0.4714,0.4718,0.4762,0.4967,0.4996,0.5106, 0.5126,0.5163,0.5202,0.5226,0.5397,0.5406,0.5422,0.5458,0.5498,0.5508, 0.5544,0.5650,0.5725,0.5725,0.5734,0.5787,0.5814,0.5817,0.5830,0.5854, 0.5881,0.5891,0.5903,0.5936,0.5971,0.6054,0.6064,0.6175,0.6181,0.6193, 0.6206,0.6230,0.6254,0.6274,0.6310,0.6359,0.6366,0.6466,0.6532,0.6540, 0.6668,0.6676,0.6732,0.6767,0.6956,0.6984,0.6989,0.7005,0.7010,0.7019, 0.7087,0.7138,0.7275,0.7299,0.7387,0.7434,0.7518,0.7519,0.7519,0.7561, 0.7599,0.7609,0.7611,0.7630,0.7663,0.7672,0.7817,0.7938,0.7953,0.7962, 0.8018,0.8025,0.8029,0.8041,0.8072,0.8139,0.8203,0.8310,0.8462,0.8507, 0.8545,0.8559,0.8655,0.8655,0.8658,0.8669,0.8684,0.8686,0.8688,0.8753, 0.8759,0.8776,0.8794,0.8796,0.8854,0.8859,0.9111,0.9126,0.9136,0.9146, 0.9199,0.9312,0.9366,0.9395,0.9515,0.9545,0.9573,0.9645,0.9661,0.9684, 0.9693,0.9759,0.9794,0.9899,0.9901,0.9915,0.9916,0.9943,0.9976, Overall p-value after applying KStest on 269 p-values = 0.106673 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.