RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-01_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 26.4541 0.933424 2 to 25 15.91 21.2948 0.786619 3 to 26 15.57 24.6122 0.896269 4 to 27 15.79 25.9853 0.925272 5 to 28 15.87 14.6745 0.381086 6 to 29 15.82 10.7285 0.129674 7 to 30 16.11 18.5411 0.644500 8 to 31 16.08 14.5199 0.369978 9 to 32 16.06 20.3415 0.742863 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.197246 Tough bday spacings test for dh-ranFile-2016-03-01_00:31: 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 7 41 75 85 108 78 51 27 19 6 3 (O-E)^2/E 0.5 0.5 0.0 1.6 1.1 0.0 0.0 0.3 1.1 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.563, p= 0.149 RESULTS OF GCD FOR dh-ranFile-2016-03-01_00:31 Euclid's algorithm: p-value, steps to gcd: 0.716843 p-value, dist. of gcd's: 0.361670 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-01_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.956 0.265 0.981 0.588 0.630 0.834 0.252 0.823 Bits 8 to 15---> 0.018 0.320 0.250 0.614 0.937 0.408 0.384 0.161 Bits 16 to 23---> 0.819 0.916 0.091 0.954 0.031 0.331 0.412 0.217 Bits 24 to 31---> 0.296 0.649 0.214 0.242 0.655 0.717 0.576 0.851 KS test for the above 32 p values: 0.135 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-01_00:31, p-values for 5 runs: 0.7689, 0.3167, 0.0724, 0.3730, 0.2379 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-01_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5085 5134.0 0.468 1.903 r= 30 23165 23103.0 0.166 2.069 r= 31 11556 11551.5 0.002 2.071 chi-square = 2.071 with df = 3; p-value = 0.442 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-01_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5152 5134.0 0.063 0.576 r= 31 23096 23103.0 0.002 0.579 r= 32 11551 11551.5 0.000 0.579 chi-square = 0.579 with df = 3; p-value = 0.099 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-01_00:31 b-rank test for bits 1 to 8, p=0.44810 b-rank test for bits 2 to 9, p=0.26124 b-rank test for bits 3 to 10, p=0.36356 b-rank test for bits 4 to 11, p=0.84181 b-rank test for bits 5 to 12, p=0.37504 b-rank test for bits 6 to 13, p=0.58996 b-rank test for bits 7 to 14, p=0.15438 b-rank test for bits 8 to 15, p=0.45514 b-rank test for bits 9 to 16, p=0.57143 b-rank test for bits 10 to 17, p=0.65482 b-rank test for bits 11 to 18, p=0.09005 b-rank test for bits 12 to 19, p=0.77114 b-rank test for bits 13 to 20, p=0.34781 b-rank test for bits 14 to 21, p=0.26064 b-rank test for bits 15 to 22, p=0.27324 b-rank test for bits 16 to 23, p=0.67238 b-rank test for bits 17 to 24, p=0.33947 b-rank test for bits 18 to 25, p=0.73916 b-rank test for bits 19 to 26, p=0.12804 b-rank test for bits 20 to 27, p=0.94304 b-rank test for bits 21 to 28, p=0.48201 b-rank test for bits 22 to 29, p=0.76355 b-rank test for bits 23 to 30, p=0.58061 b-rank test for bits 24 to 31, p=0.62481 b-rank test for bits 25 to 32, p=0.98550 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 = 0.711668 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-01_00:31 (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 141514 -0.92 0.177830 2 142045 0.32 0.624373 3 141800 -0.26 0.399190 4 142152 0.57 0.714638 5 142257 0.81 0.791694 6 141487 -0.99 0.161882 7 142037 0.30 0.617261 8 141750 -0.37 0.354847 9 141477 -1.01 0.156220 10 142459 1.28 0.900477 11 142543 1.48 0.930635 12 142765 2.00 0.977208 13 141259 -1.52 0.064323 14 142309 0.93 0.824799 15 141951 0.10 0.538780 16 142035 0.29 0.615476 17 142226 0.74 0.770315 18 142051 0.33 0.629680 19 141803 -0.25 0.401899 20 142163 0.59 0.723305 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-01_00:31 Bits used No. missing words z-score p-value 23 to 32 141739 -0.5873 0.278486 22 to 31 141603 -1.0563 0.145413 21 to 30 142141 0.7989 0.787815 20 to 29 142144 0.8092 0.790802 19 to 28 141980 0.2437 0.596264 18 to 27 141408 -1.7287 0.041929 17 to 26 141698 -0.7287 0.233085 16 to 25 142134 0.7747 0.780749 15 to 24 142183 0.9437 0.827336 14 to 23 142201 1.0058 0.842734 13 to 22 141816 -0.3218 0.373792 12 to 21 142081 0.5920 0.723063 11 to 20 141660 -0.8598 0.194961 10 to 19 141628 -0.9701 0.165998 9 to 18 142312 1.3885 0.917510 8 to 17 141656 -0.8736 0.191181 7 to 16 141572 -1.1632 0.122373 6 to 15 141834 -0.2598 0.397525 5 to 14 141762 -0.5080 0.305715 4 to 13 142034 0.4299 0.666365 3 to 12 141912 0.0092 0.503673 2 to 11 141527 -1.3184 0.093688 1 to 10 141557 -1.2149 0.112196 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-01_00:31 Bits used No. missing words z-score p-value 28 to 32 141452 -1.5503 0.060538 27 to 31 141949 0.1345 0.553486 26 to 30 141606 -1.0282 0.151919 25 to 29 142119 0.7107 0.761379 24 to 28 141984 0.2531 0.599912 23 to 27 141797 -0.3808 0.351683 22 to 26 142220 1.0531 0.853857 21 to 25 141532 -1.2791 0.100434 20 to 24 141453 -1.5469 0.060946 19 to 23 142540 2.1379 0.983736 18 to 22 141887 -0.0757 0.469831 17 to 21 142196 0.9718 0.834416 16 to 20 142016 0.3616 0.641172 15 to 19 142117 0.7040 0.759273 14 to 18 142087 0.6023 0.726503 13 to 17 141736 -0.5876 0.278414 12 to 16 141359 -1.8655 0.031054 11 to 15 142109 0.6768 0.750749 10 to 14 141427 -1.6350 0.051023 9 to 13 141964 0.1853 0.573512 8 to 12 141532 -1.2791 0.100434 7 to 11 142096 0.6328 0.736561 6 to 10 142296 1.3107 0.905028 5 to 9 142045 0.4599 0.677205 4 to 8 141700 -0.7096 0.238978 3 to 7 142248 1.1480 0.874523 2 to 6 141698 -0.7164 0.236881 1 to 5 141169 -2.5096 0.006044 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-01_00:31 Bits used No. missing words z-score p-value 31 to 32 142127 0.6421 0.739594 30 to 31 141818 -0.2694 0.393807 29 to 30 142037 0.3766 0.646767 28 to 29 142141 0.6834 0.752821 27 to 28 142530 1.8309 0.966441 26 to 27 142269 1.0610 0.855649 25 to 26 141612 -0.8771 0.190222 24 to 25 142227 0.9371 0.825641 23 to 24 142258 1.0285 0.848149 22 to 23 141562 -1.0246 0.152783 21 to 22 142148 0.7040 0.759297 20 to 21 142291 1.1259 0.869890 19 to 20 142084 0.5153 0.696811 18 to 19 142097 0.5536 0.710073 17 to 18 141788 -0.3579 0.360207 16 to 17 141884 -0.0747 0.470219 15 to 16 141790 -0.3520 0.362417 14 to 15 141547 -1.0688 0.142575 13 to 14 142353 1.3088 0.904692 12 to 13 141604 -0.9007 0.183880 11 to 12 141953 0.1288 0.551250 10 to 11 142120 0.6214 0.732847 9 to 10 142082 0.5094 0.694747 8 to 9 142006 0.2852 0.612240 7 to 8 141913 0.0108 0.504319 6 to 7 141747 -0.4788 0.316023 5 to 6 140856 -3.1072 0.000944 4 to 5 141458 -1.3314 0.091536 3 to 4 141844 -0.1927 0.423592 2 to 3 141758 -0.4464 0.327654 1 to 2 142043 0.3943 0.653323 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-01_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2451.01 -0.693 0.244218 Test results for specific bytes for dh-ranFile-2016-03-01_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2391.17 -1.539 0.061892 2 to 9 2473.77 -0.371 0.355322 3 to 10 2626.42 1.788 0.963102 4 to 11 2550.82 0.719 0.763826 5 to 12 2421.50 -1.110 0.133480 6 to 13 2523.03 0.326 0.627679 7 to 14 2470.39 -0.419 0.337692 8 to 15 2487.91 -0.171 0.432130 9 to 16 2500.71 0.010 0.504003 10 to 17 2457.93 -0.595 0.275945 11 to 18 2567.28 0.952 0.829338 12 to 19 2434.20 -0.931 0.176029 13 to 20 2493.55 -0.091 0.463678 14 to 21 2510.52 0.149 0.559118 15 to 22 2505.55 0.078 0.531256 16 to 23 2568.21 0.965 0.832640 17 to 24 2586.64 1.225 0.889771 18 to 25 2573.35 1.037 0.850214 19 to 26 2477.37 -0.320 0.374470 20 to 27 2358.02 -2.008 0.022330 21 to 28 2478.03 -0.311 0.378030 22 to 29 2585.25 1.206 0.886019 23 to 30 2562.19 0.879 0.810429 24 to 31 2413.80 -1.219 0.111410 25 to 32 2649.09 2.108 0.982505 CDPARK for dh-ranFile-2016-03-01_00:31: 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 3476 -2.1461 0.015932 3518 -0.2283 0.409702 3515 -0.3653 0.357445 3540 0.7763 0.781201 3550 1.2329 0.891189 3523 0.0000 0.500000 3531 0.3653 0.642555 3536 0.5936 0.723613 3503 -0.9132 0.180558 3556 1.5068 0.934075 Square side=100, avg. no. parked=3524.80 sample std.=22.37 p-value of the KSTEST for those 10 p-values: 0.940657 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-01_00:31 0.4146,0.7595,0.1358,0.9873,0.2032,0.5416,0.8090,0.3315,0.8256,0.3179, The KS test for those 10 p-values: 0.892707 The 3DSPHERES test for dh-ranFile-2016-03-01_00:31 sample no r^3 equiv. uni. 1 12.903 0.349548 2 19.420 0.476554 3 34.862 0.687161 4 4.493 0.139082 5 1.306 0.042610 6 58.992 0.860040 7 62.232 0.874368 8 31.966 0.655460 9 42.673 0.758876 10 53.635 0.832677 11 76.963 0.923114 12 40.245 0.738543 13 11.359 0.315213 14 113.505 0.977257 15 40.735 0.742786 16 97.665 0.961438 17 44.461 0.772822 18 22.856 0.533204 19 50.692 0.815429 20 19.292 0.474321 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.035102 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-01_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.9 1.1 -0.3 1.7 0.7 0.1 1.5 0.8 -1.4 -2.1 -0.5 -1.7 -0.4 -1.0 0.2 2.1 -0.2 0.9 0.0 -0.3 0.9 -1.4 0.8 -0.2 0.9 -1.1 0.4 0.3 -0.2 0.6 2.2 1.2 0.2 0.3 -1.2 -0.7 1.8 0.1 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:46.015442 z-score=0.438121, p-value=0.690458 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-01_00:31 Test no p-value 1 0.894870 2 0.002546 3 0.454276 4 0.218590 5 0.191926 6 0.081566 7 0.622417 8 0.882738 9 0.412280 10 0.000874 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.059634 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-01_00:31: (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 67034 2.02 66729 0.06 3 25000.00 24674 4.25 24868 0.70 4 6666.67 6644 0.08 6775 1.76 5 1388.89 1377 0.10 1369 0.28 6 238.10 241 0.04 222 1.09 7 34.72 28 1.30 34 0.01 8 4.96 1 3.16 2 1.77 p=0.91012 p=0.53882 Number of rngs required: 687690, p-value: 0.205 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-01_00:31 No. of wins: Observed Expected 98442 98585.9 z-score=-0.643, pvalue=0.25998 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66816 66666.7 0.335 0.335 2 37574 37654.3 0.171 0.506 3 27119 26954.7 1.001 1.507 4 19306 19313.5 0.003 1.510 5 13744 13851.4 0.833 2.343 6 9909 9943.5 0.120 2.463 7 7188 7145.0 0.258 2.721 8 5148 5139.1 0.016 2.737 9 3643 3699.9 0.874 3.611 10 2608 2666.3 1.275 4.885 11 1851 1923.3 2.720 7.605 12 1378 1388.7 0.083 7.689 13 1099 1003.7 9.046 16.734 14 683 726.1 2.563 19.297 15 531 525.8 0.051 19.348 16 381 381.2 0.000 19.348 17 283 276.5 0.151 19.499 18 195 200.8 0.169 19.668 19 149 146.0 0.062 19.730 20 108 106.2 0.030 19.760 21 287 287.1 0.000 19.760 Chisq= 19.76 for 20 degrees of freedom, p= 0.52700 SUMMARY of craptest p-value for no. of wins: 0.259976 p-value for throws/game: 0.526999 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-01_00:31 No. of wins: Observed Expected 98585 98585.9 z-score=-0.004, pvalue=0.49847 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66861 66666.7 0.566 0.566 2 37696 37654.3 0.046 0.613 3 27051 26954.7 0.344 0.956 4 19221 19313.5 0.443 1.399 5 13928 13851.4 0.423 1.822 6 9817 9943.5 1.610 3.433 7 7077 7145.0 0.648 4.081 8 5034 5139.1 2.148 6.229 9 3631 3699.9 1.282 7.511 10 2641 2666.3 0.240 7.751 11 1935 1923.3 0.071 7.821 12 1437 1388.7 1.677 9.498 13 1000 1003.7 0.014 9.512 14 718 726.1 0.091 9.603 15 551 525.8 1.204 10.808 16 407 381.2 1.753 12.561 17 277 276.5 0.001 12.562 18 185 200.8 1.248 13.809 19 140 146.0 0.245 14.055 20 106 106.2 0.000 14.055 21 287 287.1 0.000 14.055 Chisq= 14.06 for 20 degrees of freedom, p= 0.17231 SUMMARY of craptest p-value for no. of wins: 0.498468 p-value for throws/game: 0.172311 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0009,0.0025,0.0060,0.0159,0.0181,0.0223,0.0311,0.0312,0.0351, 0.0419,0.0426,0.0510,0.0596,0.0605,0.0609,0.0619,0.0643,0.0724,0.0816, 0.0900,0.0907,0.0915,0.0937,0.0987,0.1004,0.1004,0.1114,0.1122,0.1224, 0.1280,0.1297,0.1335,0.1351,0.1358,0.1391,0.1426,0.1454,0.1494,0.1519, 0.1528,0.1544,0.1562,0.1612,0.1619,0.1660,0.1723,0.1760,0.1778,0.1806, 0.1839,0.1902,0.1912,0.1919,0.1950,0.1972,0.2032,0.2049,0.2139,0.2167, 0.2186,0.2331,0.2369,0.2379,0.2390,0.2420,0.2442,0.2504,0.2517,0.2600, 0.2606,0.2612,0.2646,0.2732,0.2759,0.2784,0.2785,0.2956,0.3057,0.3152, 0.3160,0.3167,0.3179,0.3195,0.3277,0.3309,0.3315,0.3377,0.3395,0.3478, 0.3495,0.3517,0.3548,0.3553,0.3574,0.3602,0.3617,0.3624,0.3636,0.3700, 0.3730,0.3738,0.3745,0.3750,0.3780,0.3811,0.3839,0.3938,0.3975,0.3992, 0.4019,0.4079,0.4097,0.4118,0.4123,0.4146,0.4236,0.4321,0.4421,0.4481, 0.4543,0.4551,0.4637,0.4698,0.4702,0.4743,0.4766,0.4820,0.4985,0.5000, 0.5037,0.5040,0.5043,0.5270,0.5313,0.5332,0.5388,0.5388,0.5416,0.5513, 0.5535,0.5591,0.5714,0.5735,0.5755,0.5806,0.5880,0.5900,0.5963,0.5999, 0.6122,0.6137,0.6155,0.6173,0.6224,0.6244,0.6248,0.6277,0.6297,0.6303, 0.6412,0.6426,0.6445,0.6468,0.6485,0.6533,0.6548,0.6548,0.6555,0.6664, 0.6724,0.6772,0.6872,0.6905,0.6947,0.6968,0.7101,0.7117,0.7146,0.7167, 0.7168,0.7231,0.7233,0.7236,0.7265,0.7328,0.7366,0.7385,0.7392,0.7396, 0.7428,0.7429,0.7507,0.7528,0.7589,0.7593,0.7593,0.7595,0.7614,0.7636, 0.7638,0.7689,0.7703,0.7711,0.7728,0.7807,0.7812,0.7866,0.7878,0.7908, 0.7917,0.8090,0.8104,0.8154,0.8189,0.8231,0.8248,0.8256,0.8256,0.8273, 0.8293,0.8326,0.8327,0.8338,0.8344,0.8418,0.8427,0.8481,0.8502,0.8507, 0.8539,0.8556,0.8600,0.8699,0.8744,0.8745,0.8827,0.8860,0.8898,0.8912, 0.8927,0.8949,0.8963,0.9005,0.9047,0.9050,0.9101,0.9161,0.9175,0.9231, 0.9253,0.9306,0.9334,0.9341,0.9366,0.9407,0.9430,0.9539,0.9555,0.9614, 0.9631,0.9664,0.9772,0.9773,0.9815,0.9825,0.9837,0.9855,0.9873, Overall p-value after applying KStest on 269 p-values = 0.606071 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.