RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-14_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 19.7352 0.712003 2 to 25 15.63 19.2052 0.683117 3 to 26 15.70 10.0246 0.097426 4 to 27 15.72 15.5140 0.441489 5 to 28 15.44 24.0210 0.881134 6 to 29 15.72 15.3290 0.428206 7 to 30 15.80 32.6053 0.987358 8 to 31 15.70 13.5988 0.304728 9 to 32 15.59 25.8939 0.923585 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.439849 Tough bday spacings test for dh-ranFile-2015-12-14_04:31: 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 37 74 107 100 79 51 31 8 4 1 (O-E)^2/E 0.1 0.0 0.0 0.9 0.1 0.0 0.0 0.1 3.2 1.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 7.715, p= 0.343 RESULTS OF GCD FOR dh-ranFile-2015-12-14_04:31 Euclid's algorithm: p-value, steps to gcd: 0.783504 p-value, dist. of gcd's: 0.788992 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-14_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.002 0.199 0.811 0.865 0.677 0.354 0.327 0.037 Bits 8 to 15---> 0.295 0.841 0.142 0.249 0.962 0.769 0.806 0.182 Bits 16 to 23---> 0.102 0.021 0.889 0.001 0.471 0.970 0.081 0.090 Bits 24 to 31---> 0.970 0.584 0.127 0.964 0.994 0.801 0.529 0.137 KS test for the above 32 p values: 0.942 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-14_04:31, p-values for 5 runs: 0.8170, 0.9411, 0.9808, 0.2394, 0.3027 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-14_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5115 5134.0 0.070 0.687 r= 30 22936 23103.0 1.208 1.895 r= 31 11749 11551.5 3.376 5.271 chi-square = 5.271 with df = 3; p-value = 0.847 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-14_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5138 5134.0 0.003 0.102 r= 31 23246 23103.0 0.885 0.987 r= 32 11400 11551.5 1.988 2.975 chi-square = 2.975 with df = 3; p-value = 0.604 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-14_04:31 b-rank test for bits 1 to 8, p=0.61992 b-rank test for bits 2 to 9, p=0.33340 b-rank test for bits 3 to 10, p=0.61718 b-rank test for bits 4 to 11, p=0.05435 b-rank test for bits 5 to 12, p=0.49197 b-rank test for bits 6 to 13, p=0.83126 b-rank test for bits 7 to 14, p=0.15871 b-rank test for bits 8 to 15, p=0.69962 b-rank test for bits 9 to 16, p=0.14459 b-rank test for bits 10 to 17, p=0.29128 b-rank test for bits 11 to 18, p=0.87486 b-rank test for bits 12 to 19, p=0.63467 b-rank test for bits 13 to 20, p=0.39665 b-rank test for bits 14 to 21, p=0.76237 b-rank test for bits 15 to 22, p=0.30006 b-rank test for bits 16 to 23, p=0.79981 b-rank test for bits 17 to 24, p=0.88624 b-rank test for bits 18 to 25, p=0.14760 b-rank test for bits 19 to 26, p=0.42760 b-rank test for bits 20 to 27, p=0.71063 b-rank test for bits 21 to 28, p=0.74813 b-rank test for bits 22 to 29, p=0.43748 b-rank test for bits 23 to 30, p=0.86180 b-rank test for bits 24 to 31, p=0.17524 b-rank test for bits 25 to 32, p=0.19537 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 = 0.836220 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-14_04:31 (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 142419 1.19 0.883137 2 141383 -1.23 0.109397 3 141878 -0.07 0.470823 4 142590 1.59 0.944122 5 142414 1.18 0.880828 6 141884 -0.06 0.476404 7 141769 -0.33 0.371504 8 141335 -1.34 0.089815 9 141196 -1.67 0.047791 10 141524 -0.90 0.183979 11 141576 -0.78 0.218046 12 142366 1.07 0.857011 13 142378 1.10 0.863247 14 142396 1.14 0.872247 15 142311 0.94 0.826001 16 142156 0.58 0.717805 17 141825 -0.20 0.421901 18 142119 0.49 0.687892 19 141057 -1.99 0.023217 20 141819 -0.21 0.416424 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-14_04:31 Bits used No. missing words z-score p-value 23 to 32 141601 -1.0632 0.143844 22 to 31 141276 -2.1839 0.014485 21 to 30 141624 -0.9839 0.162583 20 to 29 142039 0.4471 0.672612 19 to 28 141742 -0.5770 0.281970 18 to 27 141854 -0.1908 0.424344 17 to 26 141624 -0.9839 0.162583 16 to 25 141801 -0.3736 0.354369 15 to 24 141444 -1.6046 0.054292 14 to 23 141744 -0.5701 0.284304 13 to 22 141986 0.2644 0.604256 12 to 21 142057 0.5092 0.694696 11 to 20 141933 0.0816 0.532526 10 to 19 142123 0.7368 0.769376 9 to 18 142087 0.6127 0.729948 8 to 17 141733 -0.6080 0.271582 7 to 16 141501 -1.4080 0.079560 6 to 15 141468 -1.5218 0.064026 5 to 14 142215 1.0540 0.854066 4 to 13 141825 -0.2908 0.385605 3 to 12 142494 2.0161 0.978105 2 to 11 142112 0.6989 0.757681 1 to 10 142549 2.2058 0.986300 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-14_04:31 Bits used No. missing words z-score p-value 28 to 32 141994 0.2870 0.612950 27 to 31 142428 1.7582 0.960644 26 to 30 141615 -0.9977 0.159205 25 to 29 141705 -0.6926 0.244267 24 to 28 142300 1.3243 0.907299 23 to 27 141904 -0.0181 0.492792 22 to 26 141716 -0.6554 0.256119 21 to 25 141595 -1.0655 0.143319 20 to 24 141587 -1.0926 0.137275 19 to 23 141913 0.0124 0.504963 18 to 22 142165 0.8667 0.806941 17 to 21 142128 0.7413 0.770730 16 to 20 142136 0.7684 0.778867 15 to 19 142140 0.7819 0.782873 14 to 18 142701 2.6836 0.996359 13 to 17 142147 0.8057 0.789781 12 to 16 142438 1.7921 0.963442 11 to 15 142089 0.6091 0.728755 10 to 14 141733 -0.5977 0.275010 9 to 13 142257 1.1785 0.880710 8 to 12 141824 -0.2893 0.386193 7 to 11 141491 -1.4181 0.078086 6 to 10 141913 0.0124 0.504963 5 to 9 141642 -0.9062 0.182414 4 to 8 141307 -2.0418 0.020586 3 to 7 141567 -1.1604 0.122935 2 to 6 142292 1.2972 0.902717 1 to 5 142036 0.4294 0.666180 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-14_04:31 Bits used No. missing words z-score p-value 31 to 32 141724 -0.5467 0.292294 30 to 31 141852 -0.1691 0.432853 29 to 30 142142 0.6863 0.753751 28 to 29 141090 -2.4169 0.007827 27 to 28 141705 -0.6027 0.273340 26 to 27 141353 -1.6411 0.050389 25 to 26 141771 -0.4081 0.341617 24 to 25 141288 -1.8328 0.033414 23 to 24 141509 -1.1809 0.118818 22 to 23 142347 1.2911 0.901659 21 to 22 141954 0.1318 0.552417 20 to 21 141781 -0.3786 0.352509 19 to 20 142148 0.7040 0.759297 18 to 19 142411 1.4799 0.930544 17 to 18 141480 -1.2665 0.102674 16 to 17 141923 0.0403 0.516083 15 to 16 141464 -1.3137 0.094481 14 to 15 140946 -2.8417 0.002244 13 to 14 141932 0.0669 0.526659 12 to 13 141905 -0.0128 0.494905 11 to 12 141702 -0.6116 0.270404 10 to 11 141443 -1.3756 0.084472 9 to 10 141759 -0.4435 0.328720 8 to 9 142034 0.3678 0.643473 7 to 8 141759 -0.4435 0.328720 6 to 7 141594 -0.9302 0.176140 5 to 6 141901 -0.0246 0.490198 4 to 5 141883 -0.0777 0.469045 3 to 4 141562 -1.0246 0.152783 2 to 3 142217 0.9076 0.817950 1 to 2 142288 1.1170 0.868007 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-14_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2515.48 0.219 0.586627 Test results for specific bytes for dh-ranFile-2015-12-14_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2434.13 -0.932 0.175771 2 to 9 2498.06 -0.027 0.489036 3 to 10 2477.65 -0.316 0.375956 4 to 11 2456.85 -0.610 0.270859 5 to 12 2440.21 -0.846 0.198908 6 to 13 2492.59 -0.105 0.458288 7 to 14 2477.05 -0.325 0.372747 8 to 15 2561.34 0.867 0.807151 9 to 16 2564.84 0.917 0.820412 10 to 17 2579.47 1.124 0.869474 11 to 18 2483.16 -0.238 0.405877 12 to 19 2595.75 1.354 0.912153 13 to 20 2538.44 0.544 0.706664 14 to 21 2431.45 -0.969 0.166160 15 to 22 2501.41 0.020 0.507965 16 to 23 2544.27 0.626 0.734347 17 to 24 2497.48 -0.036 0.485762 18 to 25 2450.40 -0.701 0.241533 19 to 26 2480.57 -0.275 0.391724 20 to 27 2521.10 0.298 0.617306 21 to 28 2529.04 0.411 0.659324 22 to 29 2576.34 1.080 0.859846 23 to 30 2493.81 -0.088 0.465124 24 to 31 2549.81 0.704 0.759434 25 to 32 2425.85 -1.049 0.147181 CDPARK for dh-ranFile-2015-12-14_04:31: 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 3546 1.0502 0.853193 3530 0.3196 0.625377 3556 1.5068 0.934075 3544 0.9589 0.831196 3571 2.1918 0.985802 3528 0.2283 0.590298 3527 0.1826 0.572463 3519 -0.1826 0.427537 3509 -0.6393 0.261324 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3534.20 sample std.=18.79 p-value of the KSTEST for those 10 p-values: 0.211116 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-14_04:31 0.2574,0.1520,0.6658,0.9822,0.6888,0.8229,0.5102,0.3889,0.0389,0.8997, The KS test for those 10 p-values: 0.963278 The 3DSPHERES test for dh-ranFile-2015-12-14_04:31 sample no r^3 equiv. uni. 1 25.269 0.569278 2 32.195 0.658075 3 7.838 0.229913 4 19.447 0.477024 5 51.182 0.818420 6 10.081 0.285392 7 36.040 0.699204 8 13.083 0.353440 9 25.321 0.570031 10 12.174 0.333565 11 19.431 0.476758 12 97.520 0.961252 13 12.061 0.331048 14 4.050 0.126279 15 33.289 0.670318 16 23.493 0.543011 17 92.017 0.953451 18 35.341 0.692112 19 1.817 0.058774 20 0.453 0.014981 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.930039 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-14_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 0.3 1.5 0.4 -1.2 -0.7 -1.4 0.5 1.4 0.7 0.1 0.3 -1.3 -1.5 -1.0 0.9 -1.2 -0.9 1.0 1.0 1.7 0.2 0.6 0.3 0.6 -1.6 0.9 -0.7 -0.2 -0.7 0.4 0.6 0.8 -0.8 -0.5 0.3 2.1 1.3 -0.7 0.9 3.0 -1.1 Chi-square with 42 degrees of freedom:48.913022 z-score=0.754273, p-value=0.784749 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-14_04:31 Test no p-value 1 0.106631 2 0.221261 3 0.863525 4 0.266275 5 0.002536 6 0.171050 7 0.451038 8 0.000931 9 0.419272 10 0.045870 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002794 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-14_04:31: (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 66737 0.07 66719 0.04 3 25000.00 24769 2.13 24965 0.05 4 6666.67 6717 0.38 6724 0.49 5 1388.89 1490 7.36 1327 2.76 6 238.10 248 0.41 234 0.07 7 34.72 33 0.09 27 1.72 8 4.96 5 0.00 3 0.77 p=0.89295 p=0.56579 Number of rngs required: 688183, p-value: 0.400 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-14_04:31 No. of wins: Observed Expected 98526 98585.9 z-score=-0.268, pvalue=0.39446 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66585 66666.7 0.100 0.100 2 37532 37654.3 0.397 0.497 3 27164 26954.7 1.625 2.122 4 19179 19313.5 0.936 3.058 5 13886 13851.4 0.086 3.145 6 9972 9943.5 0.081 3.226 7 7100 7145.0 0.284 3.510 8 5074 5139.1 0.824 4.334 9 3822 3699.9 4.032 8.365 10 2738 2666.3 1.928 10.294 11 1865 1923.3 1.769 12.063 12 1368 1388.7 0.310 12.372 13 1045 1003.7 1.698 14.071 14 705 726.1 0.615 14.686 15 546 525.8 0.773 15.459 16 373 381.2 0.174 15.634 17 271 276.5 0.111 15.745 18 233 200.8 5.153 20.898 19 147 146.0 0.007 20.905 20 109 106.2 0.073 20.978 21 286 287.1 0.004 20.982 Chisq= 20.98 for 20 degrees of freedom, p= 0.60181 SUMMARY of craptest p-value for no. of wins: 0.394456 p-value for throws/game: 0.601813 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-14_04:31 No. of wins: Observed Expected 98607 98585.9 z-score= 0.095, pvalue=0.53767 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66709 66666.7 0.027 0.027 2 37495 37654.3 0.674 0.701 3 26999 26954.7 0.073 0.774 4 19340 19313.5 0.036 0.810 5 13776 13851.4 0.411 1.221 6 9896 9943.5 0.227 1.448 7 7212 7145.0 0.628 2.076 8 5247 5139.1 2.267 4.343 9 3761 3699.9 1.010 5.353 10 2591 2666.3 2.126 7.479 11 1924 1923.3 0.000 7.479 12 1431 1388.7 1.286 8.765 13 970 1003.7 1.132 9.898 14 742 726.1 0.346 10.244 15 510 525.8 0.477 10.721 16 389 381.2 0.162 10.883 17 271 276.5 0.111 10.994 18 202 200.8 0.007 11.001 19 148 146.0 0.028 11.028 20 114 106.2 0.571 11.599 21 273 287.1 0.694 12.293 Chisq= 12.29 for 20 degrees of freedom, p= 0.09437 SUMMARY of craptest p-value for no. of wins: 0.537667 p-value for throws/game: 0.094370 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0011,0.0018,0.0022,0.0025,0.0028,0.0078,0.0145,0.0150,0.0206, 0.0215,0.0232,0.0334,0.0369,0.0389,0.0459,0.0478,0.0504,0.0543,0.0543, 0.0588,0.0640,0.0781,0.0796,0.0810,0.0845,0.0898,0.0903,0.0944,0.0945, 0.0974,0.1015,0.1027,0.1066,0.1094,0.1188,0.1229,0.1263,0.1268,0.1373, 0.1374,0.1416,0.1433,0.1438,0.1446,0.1472,0.1476,0.1520,0.1528,0.1587, 0.1592,0.1626,0.1626,0.1662,0.1710,0.1752,0.1758,0.1761,0.1823,0.1824, 0.1840,0.1954,0.1988,0.1989,0.2111,0.2180,0.2213,0.2299,0.2394,0.2415, 0.2443,0.2489,0.2561,0.2574,0.2613,0.2663,0.2704,0.2709,0.2716,0.2733, 0.2750,0.2820,0.2843,0.2854,0.2913,0.2923,0.2953,0.3001,0.3027,0.3047, 0.3077,0.3271,0.3287,0.3287,0.3310,0.3334,0.3336,0.3416,0.3434,0.3525, 0.3534,0.3544,0.3544,0.3715,0.3727,0.3760,0.3856,0.3862,0.3889,0.3917, 0.3945,0.3967,0.4001,0.4059,0.4164,0.4193,0.4219,0.4243,0.4275,0.4276, 0.4282,0.4329,0.4375,0.4398,0.4415,0.4510,0.4583,0.4651,0.4690,0.4708, 0.4710,0.4764,0.4768,0.4770,0.4858,0.4890,0.4902,0.4920,0.4928,0.4949, 0.5050,0.5050,0.5080,0.5102,0.5161,0.5267,0.5290,0.5325,0.5377,0.5430, 0.5524,0.5658,0.5693,0.5700,0.5725,0.5839,0.5866,0.5903,0.6018,0.6043, 0.6044,0.6130,0.6172,0.6173,0.6199,0.6254,0.6347,0.6435,0.6581,0.6593, 0.6658,0.6662,0.6703,0.6726,0.6767,0.6831,0.6879,0.6888,0.6921,0.6947, 0.6992,0.6996,0.7067,0.7106,0.7120,0.7178,0.7288,0.7299,0.7343,0.7481, 0.7538,0.7577,0.7593,0.7594,0.7624,0.7686,0.7694,0.7707,0.7789,0.7829, 0.7835,0.7847,0.7890,0.7898,0.7998,0.8010,0.8056,0.8069,0.8072,0.8111, 0.8170,0.8180,0.8184,0.8204,0.8229,0.8260,0.8312,0.8313,0.8362,0.8414, 0.8470,0.8532,0.8541,0.8570,0.8598,0.8618,0.8632,0.8635,0.8650,0.8680, 0.8695,0.8722,0.8749,0.8807,0.8808,0.8811,0.8831,0.8862,0.8891,0.8929, 0.8997,0.9017,0.9027,0.9073,0.9122,0.9236,0.9300,0.9305,0.9341,0.9411, 0.9419,0.9441,0.9535,0.9606,0.9613,0.9618,0.9633,0.9634,0.9637,0.9699, 0.9700,0.9781,0.9808,0.9822,0.9858,0.9863,0.9874,0.9942,0.9964, Overall p-value after applying KStest on 269 p-values = 0.362926 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.