RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-23_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 15.92 13.7026 0.311968 2 to 25 15.65 16.6231 0.519829 3 to 26 15.76 12.2842 0.217369 4 to 27 15.67 14.2881 0.353389 5 to 28 15.94 16.9791 0.544219 6 to 29 15.88 19.0748 0.675745 7 to 30 16.10 17.2286 0.561014 8 to 31 15.77 23.0022 0.850822 9 to 32 15.78 28.2814 0.958245 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.719536 Tough bday spacings test for dh-ranFile-2016-02-23_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 6 29 89 111 87 66 50 34 16 5 7 (O-E)^2/E 1.1 1.6 3.4 1.8 1.2 1.9 0.1 0.6 0.1 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 14.211, p= 0.836 RESULTS OF GCD FOR dh-ranFile-2016-02-23_04:31 Euclid's algorithm: p-value, steps to gcd: 0.600559 p-value, dist. of gcd's: 0.531082 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-23_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.367 0.972 0.416 0.762 0.920 0.471 0.161 0.318 Bits 8 to 15---> 0.169 0.724 0.279 0.771 0.029 0.090 0.619 0.032 Bits 16 to 23---> 0.580 0.006 0.805 0.951 0.699 0.301 0.988 0.669 Bits 24 to 31---> 0.437 0.672 0.135 0.415 0.026 0.675 0.226 0.341 KS test for the above 32 p values: 0.294 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-23_04:31, p-values for 5 runs: 0.8158, 0.6449, 0.1700, 0.3335, 0.7120 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-23_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5045 5134.0 1.543 2.395 r= 30 23119 23103.0 0.011 2.406 r= 31 11638 11551.5 0.647 3.053 chi-square = 3.053 with df = 3; p-value = 0.617 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-23_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5057 5134.0 1.155 1.669 r= 31 23130 23103.0 0.031 1.700 r= 32 11612 11551.5 0.317 2.017 chi-square = 2.017 with df = 3; p-value = 0.431 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-23_04:31 b-rank test for bits 1 to 8, p=0.18246 b-rank test for bits 2 to 9, p=0.25924 b-rank test for bits 3 to 10, p=0.78713 b-rank test for bits 4 to 11, p=0.15579 b-rank test for bits 5 to 12, p=0.30548 b-rank test for bits 6 to 13, p=0.74402 b-rank test for bits 7 to 14, p=0.57423 b-rank test for bits 8 to 15, p=0.74693 b-rank test for bits 9 to 16, p=0.15716 b-rank test for bits 10 to 17, p=0.84743 b-rank test for bits 11 to 18, p=0.30101 b-rank test for bits 12 to 19, p=0.94771 b-rank test for bits 13 to 20, p=0.55725 b-rank test for bits 14 to 21, p=0.05860 b-rank test for bits 15 to 22, p=0.25680 b-rank test for bits 16 to 23, p=0.03156 b-rank test for bits 17 to 24, p=0.05619 b-rank test for bits 18 to 25, p=0.20414 b-rank test for bits 19 to 26, p=0.59739 b-rank test for bits 20 to 27, p=0.52490 b-rank test for bits 21 to 28, p=0.00032 b-rank test for bits 22 to 29, p=0.59969 b-rank test for bits 23 to 30, p=0.56812 b-rank test for bits 24 to 31, p=0.15734 b-rank test for bits 25 to 32, p=0.96497 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 = 0.220887 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-23_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 141884 -0.06 0.476404 2 142001 0.21 0.584798 3 141712 -0.46 0.322381 4 142024 0.27 0.605620 5 141986 0.18 0.571084 6 141400 -1.19 0.117019 7 141701 -0.49 0.313217 8 142379 1.10 0.863758 9 141677 -0.54 0.293624 10 142158 0.58 0.719381 11 142400 1.15 0.874190 12 141975 0.15 0.560972 13 142080 0.40 0.654966 14 141695 -0.50 0.308266 15 142103 0.45 0.674546 16 141612 -0.69 0.243623 17 141592 -0.74 0.229218 18 142530 1.45 0.926494 19 141196 -1.67 0.047791 20 141840 -0.16 0.435658 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-23_04:31 Bits used No. missing words z-score p-value 23 to 32 141656 -0.8736 0.191181 22 to 31 141570 -1.1701 0.120980 21 to 30 142144 0.8092 0.790802 20 to 29 142125 0.7437 0.771468 19 to 28 141608 -1.0391 0.149386 18 to 27 142468 1.9264 0.972976 17 to 26 142560 2.2437 0.987574 16 to 25 141963 0.1851 0.573413 15 to 24 142116 0.7127 0.761970 14 to 23 141955 0.1575 0.562568 13 to 22 142160 0.8644 0.806310 12 to 21 142280 1.2782 0.899406 11 to 20 141919 0.0333 0.513300 10 to 19 142238 1.1333 0.871465 9 to 18 142575 2.2954 0.989145 8 to 17 141994 0.2920 0.614844 7 to 16 141990 0.2782 0.609560 6 to 15 141694 -0.7425 0.228887 5 to 14 141229 -2.3460 0.009489 4 to 13 142104 0.6713 0.748978 3 to 12 141645 -0.9115 0.181021 2 to 11 141891 -0.0632 0.474801 1 to 10 141980 0.2437 0.596264 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-23_04:31 Bits used No. missing words z-score p-value 28 to 32 141801 -0.3672 0.356727 27 to 31 141906 -0.0113 0.495497 26 to 30 141415 -1.6757 0.046899 25 to 29 141989 0.2701 0.606446 24 to 28 142305 1.3413 0.910081 23 to 27 141443 -1.5808 0.056964 22 to 26 142506 2.0226 0.978443 21 to 25 142108 0.6735 0.749672 20 to 24 142293 1.3006 0.903298 19 to 23 141686 -0.7571 0.224510 18 to 22 141802 -0.3638 0.357992 17 to 21 141876 -0.1130 0.455022 16 to 20 141714 -0.6621 0.253942 15 to 19 141716 -0.6554 0.256119 14 to 18 142318 1.3853 0.917023 13 to 17 141691 -0.7401 0.229619 12 to 16 141841 -0.2316 0.408414 11 to 15 141820 -0.3028 0.381016 10 to 14 142385 1.6124 0.946567 9 to 13 141493 -1.4113 0.079080 8 to 12 141814 -0.3232 0.373290 7 to 11 141765 -0.4893 0.312331 6 to 10 142420 1.7311 0.958282 5 to 9 142027 0.3989 0.655010 4 to 8 141512 -1.3469 0.089009 3 to 7 142410 1.6972 0.955169 2 to 6 141998 0.3006 0.618131 1 to 5 141769 -0.4757 0.317146 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-23_04:31 Bits used No. missing words z-score p-value 31 to 32 141947 0.1111 0.544240 30 to 31 141472 -1.2901 0.098515 29 to 30 142046 0.4032 0.656583 28 to 29 142105 0.5772 0.718097 27 to 28 142439 1.5624 0.940909 26 to 27 141411 -1.4700 0.070781 25 to 26 141817 -0.2724 0.392673 24 to 25 141900 -0.0275 0.489022 23 to 24 141267 -1.8948 0.029061 22 to 23 142684 2.2852 0.988848 21 to 22 142417 1.4976 0.932875 20 to 21 141429 -1.4169 0.078256 19 to 20 142026 0.3442 0.634637 18 to 19 141749 -0.4729 0.318125 17 to 18 140847 -3.1337 0.000863 16 to 17 141987 0.2291 0.590610 15 to 16 141810 -0.2930 0.384758 14 to 15 141925 0.0462 0.518434 13 to 14 142062 0.4504 0.673772 12 to 13 141533 -1.1101 0.133474 11 to 12 142023 0.3353 0.631304 10 to 11 142394 1.4297 0.923599 9 to 10 142077 0.4946 0.689559 8 to 9 141515 -1.1632 0.122371 7 to 8 142244 0.9872 0.838234 6 to 7 141952 0.1259 0.550083 5 to 6 141771 -0.4081 0.341617 4 to 5 141874 -0.1042 0.458498 3 to 4 141362 -1.6145 0.053205 2 to 3 142130 0.6509 0.742459 1 to 2 141483 -1.2576 0.104266 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-23_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2635.79 1.920 0.972593 Test results for specific bytes for dh-ranFile-2016-02-23_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2526.18 0.370 0.644416 2 to 9 2483.82 -0.229 0.409487 3 to 10 2459.93 -0.567 0.285463 4 to 11 2514.83 0.210 0.583063 5 to 12 2459.82 -0.568 0.284926 6 to 13 2608.81 1.539 0.938072 7 to 14 2467.76 -0.456 0.324205 8 to 15 2616.68 1.650 0.950536 9 to 16 2560.08 0.850 0.802258 10 to 17 2490.75 -0.131 0.447950 11 to 18 2523.23 0.328 0.628726 12 to 19 2562.45 0.883 0.811415 13 to 20 2552.94 0.749 0.772971 14 to 21 2421.06 -1.116 0.132132 15 to 22 2444.01 -0.792 0.214239 16 to 23 2460.76 -0.555 0.289490 17 to 24 2385.20 -1.624 0.052233 18 to 25 2513.25 0.187 0.574307 19 to 26 2516.59 0.235 0.592756 20 to 27 2518.66 0.264 0.604054 21 to 28 2538.53 0.545 0.707086 22 to 29 2492.87 -0.101 0.459854 23 to 30 2590.89 1.285 0.900681 24 to 31 2653.40 2.169 0.984974 25 to 32 2517.76 0.251 0.599167 CDPARK for dh-ranFile-2016-02-23_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 3524 0.0457 0.518210 3532 0.4110 0.659449 3496 -1.2329 0.108811 3483 -1.8265 0.033889 3489 -1.5525 0.060270 3522 -0.0457 0.481790 3504 -0.8676 0.192812 3546 1.0502 0.853193 3563 1.8265 0.966111 3536 0.5936 0.723613 Square side=100, avg. no. parked=3519.50 sample std.=24.71 p-value of the KSTEST for those 10 p-values: 0.748269 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-23_04:31 0.7367,0.0076,0.9582,0.2335,0.6184,0.9856,0.2059,0.4967,0.7132,0.0297, The KS test for those 10 p-values: 0.477510 The 3DSPHERES test for dh-ranFile-2016-02-23_04:31 sample no r^3 equiv. uni. 1 4.721 0.145597 2 25.719 0.575689 3 32.258 0.658795 4 3.753 0.117606 5 68.425 0.897800 6 71.078 0.906451 7 25.592 0.573888 8 5.508 0.167739 9 46.231 0.785841 10 37.103 0.709681 11 14.897 0.391386 12 5.528 0.168274 13 10.441 0.293917 14 28.632 0.614954 15 48.046 0.798413 16 21.403 0.510034 17 0.430 0.014243 18 26.235 0.582925 19 81.398 0.933681 20 1.324 0.043180 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.931221 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-23_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.8 0.2 0.7 -0.4 1.3 -0.9 0.8 0.5 1.8 1.7 -1.1 -0.5 -0.2 -0.5 -1.7 -1.4 1.6 -1.2 1.3 0.6 -0.2 -0.7 0.7 0.2 1.9 -1.3 -1.6 -0.2 1.8 -0.5 0.3 -0.4 -1.0 1.3 0.7 1.1 -0.4 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:43.915530 z-score=0.209001, p-value=0.609669 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-23_04:31 Test no p-value 1 0.087822 2 0.582917 3 0.233326 4 0.041456 5 0.616579 6 0.034421 7 0.148737 8 0.066802 9 0.132286 10 0.230308 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001612 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-23_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 66521 0.32 66642 0.01 3 25000.00 25166 1.10 24949 0.10 4 6666.67 6634 0.16 6712 0.31 5 1388.89 1386 0.01 1426 0.99 6 238.10 243 0.10 237 0.01 7 34.72 43 1.97 31 0.40 8 4.96 6 0.22 2 1.77 p=0.30714 p=0.26710 Number of rngs required: 688880, p-value: 0.709 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-23_04:31 No. of wins: Observed Expected 98508 98585.9 z-score=-0.348, pvalue=0.36383 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66576 66666.7 0.123 0.123 2 37680 37654.3 0.018 0.141 3 27011 26954.7 0.117 0.258 4 19444 19313.5 0.882 1.141 5 13679 13851.4 2.146 3.287 6 10032 9943.5 0.787 4.074 7 7157 7145.0 0.020 4.094 8 5153 5139.1 0.038 4.132 9 3685 3699.9 0.060 4.191 10 2736 2666.3 1.822 6.013 11 1857 1923.3 2.287 8.301 12 1373 1388.7 0.178 8.479 13 987 1003.7 0.278 8.758 14 740 726.1 0.265 9.022 15 551 525.8 1.204 10.226 16 343 381.2 3.819 14.045 17 259 276.5 1.112 15.157 18 203 200.8 0.023 15.181 19 152 146.0 0.248 15.429 20 111 106.2 0.216 15.644 21 271 287.1 0.904 16.549 Chisq= 16.55 for 20 degrees of freedom, p= 0.31795 SUMMARY of craptest p-value for no. of wins: 0.363834 p-value for throws/game: 0.317950 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-23_04:31 No. of wins: Observed Expected 98495 98585.9 z-score=-0.406, pvalue=0.34223 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66457 66666.7 0.659 0.659 2 37903 37654.3 1.642 2.302 3 27024 26954.7 0.178 2.480 4 19358 19313.5 0.103 2.582 5 13890 13851.4 0.107 2.690 6 9824 9943.5 1.437 4.127 7 7250 7145.0 1.542 5.669 8 5003 5139.1 3.603 9.272 9 3625 3699.9 1.515 10.787 10 2694 2666.3 0.288 11.075 11 1937 1923.3 0.097 11.172 12 1399 1388.7 0.076 11.248 13 1003 1003.7 0.001 11.248 14 740 726.1 0.265 11.513 15 527 525.8 0.003 11.516 16 347 381.2 3.060 14.575 17 272 276.5 0.075 14.650 18 205 200.8 0.087 14.736 19 153 146.0 0.337 15.074 20 106 106.2 0.000 15.074 21 283 287.1 0.059 15.133 Chisq= 15.13 for 20 degrees of freedom, p= 0.23125 SUMMARY of craptest p-value for no. of wins: 0.342234 p-value for throws/game: 0.231254 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0009,0.0016,0.0065,0.0076,0.0095,0.0142,0.0259,0.0291,0.0294, 0.0297,0.0315,0.0316,0.0339,0.0344,0.0415,0.0432,0.0469,0.0478,0.0522, 0.0532,0.0562,0.0570,0.0586,0.0603,0.0668,0.0708,0.0783,0.0791,0.0878, 0.0890,0.0902,0.0985,0.1043,0.1088,0.1170,0.1176,0.1210,0.1224,0.1321, 0.1323,0.1335,0.1351,0.1456,0.1487,0.1494,0.1558,0.1572,0.1573,0.1605, 0.1677,0.1683,0.1691,0.1700,0.1810,0.1825,0.1912,0.1928,0.2041,0.2059, 0.2142,0.2174,0.2209,0.2245,0.2264,0.2289,0.2292,0.2296,0.2303,0.2313, 0.2333,0.2335,0.2436,0.2539,0.2561,0.2568,0.2592,0.2671,0.2793,0.2849, 0.2855,0.2895,0.2936,0.2939,0.2941,0.3009,0.3010,0.3055,0.3071,0.3083, 0.3120,0.3123,0.3132,0.3171,0.3179,0.3180,0.3181,0.3224,0.3242,0.3335, 0.3407,0.3416,0.3422,0.3534,0.3567,0.3580,0.3638,0.3669,0.3733,0.3810, 0.3848,0.3914,0.3927,0.4084,0.4095,0.4151,0.4158,0.4310,0.4357,0.4370, 0.4479,0.4550,0.4585,0.4599,0.4706,0.4748,0.4764,0.4775,0.4818,0.4890, 0.4955,0.4967,0.5100,0.5133,0.5182,0.5184,0.5198,0.5249,0.5311,0.5442, 0.5442,0.5501,0.5573,0.5610,0.5610,0.5626,0.5681,0.5711,0.5734,0.5739, 0.5742,0.5743,0.5757,0.5797,0.5829,0.5829,0.5831,0.5848,0.5906,0.5928, 0.5963,0.5974,0.5992,0.5997,0.6006,0.6041,0.6056,0.6064,0.6096,0.6097, 0.6148,0.6150,0.6165,0.6166,0.6181,0.6184,0.6189,0.6287,0.6313,0.6346, 0.6444,0.6449,0.6550,0.6550,0.6566,0.6588,0.6594,0.6687,0.6720,0.6738, 0.6745,0.6747,0.6757,0.6896,0.6988,0.7071,0.7088,0.7097,0.7120,0.7132, 0.7181,0.7194,0.7195,0.7236,0.7236,0.7367,0.7425,0.7440,0.7469,0.7483, 0.7490,0.7497,0.7616,0.7620,0.7709,0.7715,0.7730,0.7858,0.7871,0.7908, 0.7984,0.8023,0.8054,0.8063,0.8114,0.8158,0.8364,0.8382,0.8474,0.8508, 0.8532,0.8638,0.8715,0.8742,0.8978,0.8994,0.9007,0.9033,0.9065,0.9101, 0.9170,0.9202,0.9236,0.9265,0.9312,0.9329,0.9337,0.9381,0.9409,0.9466, 0.9477,0.9505,0.9514,0.9552,0.9582,0.9582,0.9583,0.9650,0.9661,0.9720, 0.9726,0.9730,0.9784,0.9850,0.9856,0.9876,0.9884,0.9888,0.9891, Overall p-value after applying KStest on 269 p-values = 0.399626 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.