RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-22_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 15.0749 0.409916 2 to 25 15.45 21.9001 0.811409 3 to 26 15.89 29.1985 0.967261 4 to 27 16.10 10.8792 0.137228 5 to 28 15.50 18.9782 0.670215 6 to 29 15.55 12.8566 0.254270 7 to 30 15.86 13.0485 0.267070 8 to 31 15.92 18.0019 0.611282 9 to 32 15.56 17.9356 0.607088 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.954551 Tough bday spacings test for dh-ranFile-2016-09-22_10:31: 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 16 30 76 91 110 76 50 26 16 4 5 (O-E)^2/E 5.1 1.2 0.1 0.5 1.6 0.1 0.1 0.5 0.1 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 10.378, p= 0.592 RESULTS OF GCD FOR dh-ranFile-2016-09-22_10:31 Euclid's algorithm: p-value, steps to gcd: 0.329801 p-value, dist. of gcd's: 0.025924 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-22_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.692 0.523 0.428 0.422 0.856 0.372 0.470 0.562 Bits 8 to 15---> 0.437 0.355 0.740 0.184 0.074 0.714 0.861 0.174 Bits 16 to 23---> 0.349 0.317 0.995 0.278 0.872 0.139 0.200 0.085 Bits 24 to 31---> 0.784 0.571 0.351 0.046 0.083 0.856 0.849 0.686 KS test for the above 32 p values: 0.115 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-22_10:31, p-values for 5 runs: 0.2339, 0.8250, 0.2611, 0.2397, 0.8728 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-22_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5095 5134.0 0.296 0.444 r= 30 23164 23103.0 0.161 0.605 r= 31 11524 11551.5 0.066 0.670 chi-square = 0.670 with df = 3; p-value = 0.120 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-22_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5013 5134.0 2.852 3.382 r= 31 23103 23103.0 0.000 3.382 r= 32 11662 11551.5 1.057 4.438 chi-square = 4.438 with df = 3; p-value = 0.782 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-22_10:31 b-rank test for bits 1 to 8, p=0.88368 b-rank test for bits 2 to 9, p=0.34801 b-rank test for bits 3 to 10, p=0.69287 b-rank test for bits 4 to 11, p=0.99531 b-rank test for bits 5 to 12, p=0.79126 b-rank test for bits 6 to 13, p=0.44770 b-rank test for bits 7 to 14, p=0.84282 b-rank test for bits 8 to 15, p=0.97962 b-rank test for bits 9 to 16, p=0.23047 b-rank test for bits 10 to 17, p=0.03022 b-rank test for bits 11 to 18, p=0.30768 b-rank test for bits 12 to 19, p=0.33721 b-rank test for bits 13 to 20, p=0.20942 b-rank test for bits 14 to 21, p=0.80803 b-rank test for bits 15 to 22, p=0.12431 b-rank test for bits 16 to 23, p=0.16398 b-rank test for bits 17 to 24, p=0.31794 b-rank test for bits 18 to 25, p=0.11315 b-rank test for bits 19 to 26, p=0.50625 b-rank test for bits 20 to 27, p=0.24066 b-rank test for bits 21 to 28, p=0.71483 b-rank test for bits 22 to 29, p=0.19327 b-rank test for bits 23 to 30, p=0.87828 b-rank test for bits 24 to 31, p=0.03186 b-rank test for bits 25 to 32, p=0.46343 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 = 0.603217 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-22_10:31 (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 142008 0.23 0.591163 2 141974 0.15 0.560051 3 141920 0.02 0.509945 4 142001 0.21 0.584798 5 142155 0.57 0.717015 6 141990 0.19 0.574750 7 142263 0.83 0.795692 8 142208 0.70 0.757357 9 142057 0.35 0.634962 10 141901 -0.02 0.492236 11 142079 0.40 0.654104 12 142195 0.67 0.747759 13 141723 -0.44 0.331654 14 141701 -0.49 0.313217 15 141663 -0.58 0.282464 16 141883 -0.06 0.475473 17 141982 0.17 0.567412 18 141782 -0.30 0.383042 19 142201 0.68 0.752214 20 141656 -0.59 0.276961 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-22_10:31 Bits used No. missing words z-score p-value 23 to 32 142220 1.0713 0.857977 22 to 31 142803 3.0816 0.998971 21 to 30 141443 -1.6080 0.053914 20 to 29 141518 -1.3494 0.088602 19 to 28 141748 -0.5563 0.288999 18 to 27 142103 0.6678 0.747878 17 to 26 142001 0.3161 0.624038 16 to 25 141820 -0.3080 0.379028 15 to 24 142146 0.8161 0.792780 14 to 23 141748 -0.5563 0.288999 13 to 22 141952 0.1471 0.558488 12 to 21 141983 0.2540 0.600266 11 to 20 141443 -1.6080 0.053914 10 to 19 141749 -0.5529 0.290179 9 to 18 141645 -0.9115 0.181021 8 to 17 142155 0.8471 0.801541 7 to 16 141819 -0.3115 0.377717 6 to 15 141176 -2.5287 0.005724 5 to 14 141488 -1.4529 0.073131 4 to 13 141736 -0.5977 0.275024 3 to 12 141846 -0.2184 0.413567 2 to 11 141971 0.2127 0.584202 1 to 10 142423 1.7713 0.961743 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-22_10:31 Bits used No. missing words z-score p-value 28 to 32 141598 -1.0554 0.145631 27 to 31 141253 -2.2248 0.013046 26 to 30 141911 0.0057 0.502258 25 to 29 141958 0.1650 0.565521 24 to 28 141649 -0.8825 0.188760 23 to 27 142380 1.5955 0.944699 22 to 26 141967 0.1955 0.577496 21 to 25 141994 0.2870 0.612950 20 to 24 142214 1.0328 0.849147 19 to 23 141828 -0.2757 0.391391 18 to 22 141358 -1.8689 0.030817 17 to 21 142134 0.7616 0.776849 16 to 20 141950 0.1379 0.554826 15 to 19 141561 -1.1808 0.118845 14 to 18 141911 0.0057 0.502258 13 to 17 141834 -0.2554 0.399224 12 to 16 141796 -0.3842 0.350426 11 to 15 141806 -0.3503 0.363068 10 to 14 141601 -1.0452 0.147968 9 to 13 141797 -0.3808 0.351683 8 to 12 141883 -0.0893 0.464440 7 to 11 141549 -1.2215 0.110956 6 to 10 142256 1.1752 0.880033 5 to 9 142247 1.1446 0.873822 4 to 8 142359 1.5243 0.936284 3 to 7 141608 -1.0215 0.153519 2 to 6 142127 0.7379 0.769702 1 to 5 141901 -0.0282 0.488737 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-22_10:31 Bits used No. missing words z-score p-value 31 to 32 142524 1.8132 0.965098 30 to 31 142191 0.8309 0.796981 29 to 30 141734 -0.5172 0.302509 28 to 29 141952 0.1259 0.550083 27 to 28 141685 -0.6617 0.254069 26 to 27 141865 -0.1308 0.447980 25 to 26 142130 0.6509 0.742459 24 to 25 140983 -2.7325 0.003142 23 to 24 141456 -1.3373 0.090569 22 to 23 142609 2.0639 0.980488 21 to 22 142000 0.2675 0.605444 20 to 21 141979 0.2055 0.581416 19 to 20 141934 0.0728 0.529007 18 to 19 141478 -1.2724 0.101623 17 to 18 141895 -0.0423 0.483141 16 to 17 142039 0.3825 0.648958 15 to 16 141805 -0.3078 0.379133 14 to 15 141195 -2.1072 0.017552 13 to 14 142104 0.5742 0.717100 12 to 13 142022 0.3324 0.630191 11 to 12 141940 0.0905 0.536044 10 to 11 142507 1.7630 0.961053 9 to 10 141530 -1.1190 0.131577 8 to 9 142607 2.0580 0.980206 7 to 8 142134 0.6627 0.746253 6 to 7 142213 0.8958 0.814815 5 to 6 142513 1.7807 0.962522 4 to 5 141296 -1.8092 0.035207 3 to 4 142513 1.7807 0.962522 2 to 3 141665 -0.7207 0.235536 1 to 2 141510 -1.1780 0.119405 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-22_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2487.80 -0.173 0.431515 Test results for specific bytes for dh-ranFile-2016-09-22_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2499.55 -0.006 0.497484 2 to 9 2360.86 -1.968 0.024552 3 to 10 2473.88 -0.369 0.355898 4 to 11 2432.42 -0.956 0.169593 5 to 12 2512.08 0.171 0.567852 6 to 13 2528.56 0.404 0.656874 7 to 14 2450.25 -0.704 0.240845 8 to 15 2517.81 0.252 0.599422 9 to 16 2655.36 2.197 0.985994 10 to 17 2433.56 -0.940 0.173724 11 to 18 2440.42 -0.843 0.199719 12 to 19 2463.70 -0.513 0.303831 13 to 20 2563.61 0.900 0.815827 14 to 21 2583.32 1.178 0.880669 15 to 22 2519.57 0.277 0.609008 16 to 23 2359.70 -1.984 0.023622 17 to 24 2666.92 2.361 0.990876 18 to 25 2416.73 -1.178 0.119477 19 to 26 2631.88 1.865 0.968917 20 to 27 2581.24 1.149 0.874701 21 to 28 2583.40 1.179 0.880879 22 to 29 2538.43 0.543 0.706586 23 to 30 2384.95 -1.627 0.051858 24 to 31 2367.42 -1.875 0.030403 25 to 32 2641.83 2.006 0.977560 CDPARK for dh-ranFile-2016-09-22_10:31: 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 3503 -0.9132 0.180558 3546 1.0502 0.853193 3502 -0.9589 0.168804 3544 0.9589 0.831196 3520 -0.1370 0.445521 3504 -0.8676 0.192812 3547 1.0959 0.863437 3522 -0.0457 0.481790 3534 0.5023 0.692266 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3524.00 sample std.=17.01 p-value of the KSTEST for those 10 p-values: 0.848497 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-22_10:31 0.6819,0.0262,0.6690,0.6940,0.5798,0.8281,0.5751,0.6855,0.7500,0.7186, The KS test for those 10 p-values: 0.066295 The 3DSPHERES test for dh-ranFile-2016-09-22_10:31 sample no r^3 equiv. uni. 1 20.225 0.490416 2 4.453 0.137955 3 53.342 0.831036 4 5.500 0.167513 5 61.764 0.872393 6 34.485 0.683209 7 28.667 0.615408 8 42.279 0.755683 9 52.095 0.823863 10 12.843 0.348246 11 17.975 0.450723 12 24.014 0.550883 13 13.599 0.364475 14 13.380 0.359812 15 41.055 0.745511 16 7.371 0.217851 17 18.415 0.458721 18 10.018 0.283895 19 55.327 0.841852 20 44.322 0.771773 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.479298 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-22_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.6 0.9 -1.2 0.9 -0.6 -0.1 1.5 1.9 -1.2 1.0 -1.6 0.7 -1.1 2.1 -1.2 -0.5 -2.5 -0.6 0.2 2.1 0.5 -0.3 0.4 -0.4 0.0 1.6 0.1 1.5 1.3 -1.4 -0.0 -0.3 -0.8 0.1 1.2 -0.1 -0.4 -0.7 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:51.519144 z-score=1.038624, p-value=0.850987 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-22_10:31 Test no p-value 1 0.714048 2 0.015908 3 0.034623 4 0.316272 5 0.143904 6 0.643820 7 0.000502 8 0.085578 9 0.186498 10 0.026615 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000354 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-22_10:31: (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 66883 0.70 66668 0.00 3 25000.00 24842 1.00 24766 2.19 4 6666.67 6593 0.81 6832 4.10 5 1388.89 1418 0.61 1454 3.05 6 238.10 218 1.70 230 0.28 7 34.72 42 1.53 46 3.66 8 4.96 3 0.77 3 0.77 p=0.69027 p=0.97100 Number of rngs required: 687627, p-value: 0.185 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-22_10:31 No. of wins: Observed Expected 98993 98585.9 z-score= 1.821, pvalue=0.96569 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67215 66666.7 4.510 4.510 2 37447 37654.3 1.141 5.652 3 26987 26954.7 0.039 5.690 4 19358 19313.5 0.103 5.793 5 13718 13851.4 1.285 7.078 6 9832 9943.5 1.251 8.329 7 7035 7145.0 1.694 10.024 8 5069 5139.1 0.955 10.979 9 3702 3699.9 0.001 10.980 10 2674 2666.3 0.022 11.002 11 2022 1923.3 5.062 16.064 12 1386 1388.7 0.005 16.070 13 1021 1003.7 0.298 16.368 14 704 726.1 0.675 17.043 15 522 525.8 0.028 17.071 16 363 381.2 0.864 17.935 17 257 276.5 1.381 19.316 18 179 200.8 2.373 21.688 19 127 146.0 2.469 24.157 20 96 106.2 0.982 25.140 21 286 287.1 0.004 25.144 Chisq= 25.14 for 20 degrees of freedom, p= 0.80402 SUMMARY of craptest p-value for no. of wins: 0.965695 p-value for throws/game: 0.804023 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-22_10:31 No. of wins: Observed Expected 98636 98585.9 z-score= 0.224, pvalue=0.58872 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66588 66666.7 0.093 0.093 2 37586 37654.3 0.124 0.217 3 27048 26954.7 0.323 0.540 4 19197 19313.5 0.702 1.242 5 13911 13851.4 0.256 1.498 6 9980 9943.5 0.134 1.632 7 7212 7145.0 0.628 2.260 8 5183 5139.1 0.375 2.635 9 3760 3699.9 0.977 3.612 10 2645 2666.3 0.170 3.783 11 1940 1923.3 0.144 3.927 12 1347 1388.7 1.255 5.182 13 998 1003.7 0.033 5.214 14 705 726.1 0.615 5.830 15 511 525.8 0.419 6.248 16 401 381.2 1.034 7.282 17 280 276.5 0.043 7.325 18 187 200.8 0.952 8.278 19 150 146.0 0.110 8.388 20 84 106.2 4.646 13.034 21 287 287.1 0.000 13.034 Chisq= 13.03 for 20 degrees of freedom, p= 0.12410 SUMMARY of craptest p-value for no. of wins: 0.588723 p-value for throws/game: 0.124099 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0005,0.0031,0.0057,0.0130,0.0159,0.0176,0.0236,0.0246,0.0259, 0.0262,0.0266,0.0302,0.0304,0.0308,0.0319,0.0346,0.0352,0.0461,0.0519, 0.0539,0.0539,0.0663,0.0731,0.0741,0.0826,0.0852,0.0856,0.0886,0.0906, 0.1016,0.1110,0.1131,0.1148,0.1188,0.1194,0.1195,0.1198,0.1241,0.1243, 0.1316,0.1372,0.1380,0.1393,0.1439,0.1456,0.1480,0.1535,0.1640,0.1675, 0.1688,0.1696,0.1737,0.1740,0.1806,0.1810,0.1835,0.1846,0.1865,0.1888, 0.1928,0.1933,0.1997,0.2001,0.2094,0.2179,0.2305,0.2339,0.2355,0.2397, 0.2407,0.2408,0.2541,0.2543,0.2611,0.2671,0.2750,0.2770,0.2779,0.2825, 0.2839,0.2890,0.2890,0.2902,0.3025,0.3038,0.3077,0.3132,0.3163,0.3169, 0.3179,0.3298,0.3317,0.3372,0.3480,0.3482,0.3492,0.3504,0.3505,0.3517, 0.3548,0.3559,0.3598,0.3631,0.3645,0.3723,0.3777,0.3790,0.3791,0.3830, 0.3914,0.3992,0.4097,0.4099,0.4136,0.4219,0.4276,0.4315,0.4369,0.4455, 0.4477,0.4480,0.4507,0.4587,0.4634,0.4644,0.4700,0.4755,0.4793,0.4818, 0.4831,0.4887,0.4904,0.4922,0.4975,0.5023,0.5023,0.5062,0.5099,0.5230, 0.5290,0.5360,0.5501,0.5509,0.5548,0.5585,0.5601,0.5621,0.5655,0.5674, 0.5679,0.5712,0.5748,0.5751,0.5775,0.5798,0.5814,0.5842,0.5848,0.5887, 0.5912,0.5920,0.5994,0.6003,0.6032,0.6054,0.6071,0.6090,0.6113,0.6130, 0.6154,0.6240,0.6302,0.6350,0.6438,0.6490,0.6541,0.6569,0.6690,0.6702, 0.6819,0.6832,0.6855,0.6862,0.6903,0.6921,0.6923,0.6929,0.6940,0.7066, 0.7138,0.7140,0.7148,0.7170,0.7171,0.7186,0.7404,0.7425,0.7455,0.7463, 0.7478,0.7479,0.7500,0.7522,0.7557,0.7574,0.7697,0.7718,0.7768,0.7822, 0.7839,0.7913,0.7928,0.7957,0.7970,0.8015,0.8040,0.8080,0.8114,0.8148, 0.8158,0.8239,0.8250,0.8281,0.8310,0.8312,0.8419,0.8428,0.8485,0.8487, 0.8491,0.8510,0.8532,0.8555,0.8560,0.8580,0.8610,0.8634,0.8724,0.8725, 0.8728,0.8738,0.8747,0.8783,0.8800,0.8807,0.8809,0.8837,0.9363,0.9447, 0.9546,0.9611,0.9617,0.9625,0.9625,0.9651,0.9657,0.9673,0.9689,0.9710, 0.9776,0.9796,0.9802,0.9805,0.9860,0.9909,0.9948,0.9953,0.9990, Overall p-value after applying KStest on 269 p-values = 0.630000 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.