RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-04_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 13.1953 0.276982 2 to 25 15.58 21.8233 0.808390 3 to 26 15.99 13.3350 0.286515 4 to 27 15.93 18.3065 0.630243 5 to 28 15.88 14.2034 0.347344 6 to 29 15.69 19.4591 0.697175 7 to 30 15.59 21.2385 0.784196 8 to 31 15.72 22.1783 0.822041 9 to 32 15.58 13.0106 0.264521 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.542741 Tough bday spacings test for dh-ranFile-2015-11-04_22:31: 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 14 42 91 76 104 76 52 25 17 2 1 (O-E)^2/E 2.6 0.8 4.3 4.8 0.4 0.1 0.0 0.8 0.3 3.2 2.3 Birthday Spacings: Sum(O-E)^2/E= 19.519, p= 0.966 RESULTS OF GCD FOR dh-ranFile-2015-11-04_22:31 Euclid's algorithm: p-value, steps to gcd: 0.805080 p-value, dist. of gcd's: 0.222984 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-04_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.878 0.050 0.079 0.836 0.820 0.122 0.331 0.775 Bits 8 to 15---> 0.158 0.670 0.771 0.370 0.160 0.353 0.296 0.901 Bits 16 to 23---> 0.645 0.845 0.891 0.240 0.503 0.020 0.952 0.682 Bits 24 to 31---> 0.534 0.561 0.169 0.215 0.677 0.256 0.495 0.528 KS test for the above 32 p values: 0.010 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-04_22:31, p-values for 5 runs: 0.0944, 0.9501, 0.2515, 0.7725, 0.6149 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-04_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 191 211.4 1.972 1.972 r= 29 5164 5134.0 0.175 2.147 r= 30 23021 23103.0 0.291 2.438 r= 31 11624 11551.5 0.455 2.893 chi-square = 2.893 with df = 3; p-value = 0.592 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-04_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5144 5134.0 0.019 1.168 r= 31 23162 23103.0 0.150 1.318 r= 32 11467 11551.5 0.618 1.937 chi-square = 1.937 with df = 3; p-value = 0.414 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-04_22:31 b-rank test for bits 1 to 8, p=0.14553 b-rank test for bits 2 to 9, p=0.89891 b-rank test for bits 3 to 10, p=0.39385 b-rank test for bits 4 to 11, p=0.12492 b-rank test for bits 5 to 12, p=0.08710 b-rank test for bits 6 to 13, p=0.34934 b-rank test for bits 7 to 14, p=0.98925 b-rank test for bits 8 to 15, p=0.84165 b-rank test for bits 9 to 16, p=0.94315 b-rank test for bits 10 to 17, p=0.03343 b-rank test for bits 11 to 18, p=0.52826 b-rank test for bits 12 to 19, p=0.90915 b-rank test for bits 13 to 20, p=0.29910 b-rank test for bits 14 to 21, p=0.51591 b-rank test for bits 15 to 22, p=0.47483 b-rank test for bits 16 to 23, p=0.67790 b-rank test for bits 17 to 24, p=0.98933 b-rank test for bits 18 to 25, p=0.67869 b-rank test for bits 19 to 26, p=0.74344 b-rank test for bits 20 to 27, p=0.02139 b-rank test for bits 21 to 28, p=0.64138 b-rank test for bits 22 to 29, p=0.08500 b-rank test for bits 23 to 30, p=0.12706 b-rank test for bits 24 to 31, p=0.67338 b-rank test for bits 25 to 32, p=0.19875 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 = 0.621211 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-04_22:31 (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 142496 1.37 0.914770 2 141792 -0.27 0.391990 3 143009 2.57 0.994905 4 142237 0.77 0.778038 5 142861 2.22 0.986910 6 141728 -0.42 0.335904 7 141892 -0.04 0.483851 8 141594 -0.74 0.230637 9 141762 -0.34 0.365337 10 141319 -1.38 0.083905 11 142002 0.22 0.585708 12 141743 -0.39 0.348778 13 141300 -1.42 0.077271 14 142364 1.06 0.855953 15 141484 -0.99 0.160169 16 141828 -0.19 0.424645 17 141819 -0.21 0.416424 18 141832 -0.18 0.428310 19 141565 -0.80 0.210551 20 141934 0.06 0.522982 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-04_22:31 Bits used No. missing words z-score p-value 23 to 32 141809 -0.3460 0.364684 22 to 31 141775 -0.4632 0.321608 21 to 30 141878 -0.1080 0.456984 20 to 29 142232 1.1127 0.867072 19 to 28 141745 -0.5667 0.285474 18 to 27 142173 0.9092 0.818380 17 to 26 142035 0.4333 0.667618 16 to 25 142247 1.1644 0.877865 15 to 24 142021 0.3851 0.649907 14 to 23 141541 -1.2701 0.102024 13 to 22 141791 -0.4080 0.341624 12 to 21 141740 -0.5839 0.279645 11 to 20 141708 -0.6942 0.243765 10 to 19 141539 -1.2770 0.100801 9 to 18 141916 0.0230 0.509175 8 to 17 141836 -0.2529 0.400187 7 to 16 142150 0.8299 0.796701 6 to 15 141561 -1.2011 0.114849 5 to 14 141892 -0.0598 0.476174 4 to 13 142044 0.4644 0.678812 3 to 12 142252 1.1816 0.881322 2 to 11 141889 -0.0701 0.472056 1 to 10 141608 -1.0391 0.149386 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-04_22:31 Bits used No. missing words z-score p-value 28 to 32 141366 -1.8418 0.032752 27 to 31 142116 0.7006 0.758216 26 to 30 141966 0.1921 0.576169 25 to 29 141785 -0.4215 0.336711 24 to 28 142381 1.5989 0.945077 23 to 27 142319 1.3887 0.917540 22 to 26 142039 0.4396 0.669872 21 to 25 142107 0.6701 0.748593 20 to 24 142448 1.8260 0.966075 19 to 23 141972 0.2124 0.584118 18 to 22 141619 -0.9842 0.162516 17 to 21 141989 0.2701 0.606446 16 to 20 141701 -0.7062 0.240031 15 to 19 141884 -0.0859 0.465787 14 to 18 142183 0.9277 0.823217 13 to 17 141963 0.1819 0.572182 12 to 16 141849 -0.2045 0.418978 11 to 15 141728 -0.6147 0.269384 10 to 14 142088 0.6057 0.727630 9 to 13 142388 1.6226 0.947664 8 to 12 142373 1.5718 0.941997 7 to 11 141905 -0.0147 0.494145 6 to 10 141604 -1.0350 0.150331 5 to 9 142319 1.3887 0.917540 4 to 8 141760 -0.5062 0.306357 3 to 7 141759 -0.5096 0.305168 2 to 6 141455 -1.5401 0.061768 1 to 5 141695 -0.7265 0.233753 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-04_22:31 Bits used No. missing words z-score p-value 31 to 32 141851 -0.1721 0.431693 30 to 31 142279 1.0905 0.862247 29 to 30 141552 -1.0541 0.145925 28 to 29 142270 1.0639 0.856318 27 to 28 141314 -1.7561 0.039533 26 to 27 141314 -1.7561 0.039533 25 to 26 142133 0.6598 0.745307 24 to 25 141561 -1.0275 0.152087 23 to 24 142305 1.1672 0.878429 22 to 23 142014 0.3088 0.621248 21 to 22 142347 1.2911 0.901659 20 to 21 142008 0.2911 0.614498 19 to 20 142618 2.0905 0.981712 18 to 19 142247 0.9961 0.840394 17 to 18 141804 -0.3107 0.378011 16 to 17 141576 -0.9833 0.162736 15 to 16 142649 2.1819 0.985442 14 to 15 141385 -1.5467 0.060968 13 to 14 141528 -1.1249 0.130323 12 to 13 142266 1.0521 0.853629 11 to 12 142228 0.9400 0.826399 10 to 11 142135 0.6657 0.747196 9 to 10 141823 -0.2547 0.399493 8 to 9 141699 -0.6204 0.267483 7 to 8 142460 1.6244 0.947854 6 to 7 141334 -1.6971 0.044835 5 to 6 142303 1.1613 0.877234 4 to 5 142138 0.6745 0.750017 3 to 4 141767 -0.4199 0.337297 2 to 3 141877 -0.0954 0.462011 1 to 2 141515 -1.1632 0.122371 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-04_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2507.00 0.099 0.539412 Test results for specific bytes for dh-ranFile-2015-11-04_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2526.26 0.371 0.644807 2 to 9 2496.54 -0.049 0.480467 3 to 10 2499.00 -0.014 0.494385 4 to 11 2490.06 -0.141 0.444105 5 to 12 2640.50 1.987 0.976533 6 to 13 2618.84 1.681 0.953579 7 to 14 2515.58 0.220 0.587205 8 to 15 2593.51 1.322 0.906987 9 to 16 2478.27 -0.307 0.379301 10 to 17 2440.64 -0.840 0.200593 11 to 18 2479.53 -0.289 0.386104 12 to 19 2481.89 -0.256 0.398930 13 to 20 2415.70 -1.192 0.116593 14 to 21 2566.42 0.939 0.826232 15 to 22 2390.69 -1.546 0.061064 16 to 23 2363.54 -1.930 0.026814 17 to 24 2643.13 2.024 0.978527 18 to 25 2529.11 0.412 0.659701 19 to 26 2388.80 -1.573 0.057907 20 to 27 2523.82 0.337 0.631910 21 to 28 2513.18 0.186 0.573948 22 to 29 2515.77 0.223 0.588225 23 to 30 2516.53 0.234 0.592413 24 to 31 2410.50 -1.266 0.102816 25 to 32 2419.34 -1.141 0.126990 CDPARK for dh-ranFile-2015-11-04_22:31: 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 3507 -0.7306 0.232514 3530 0.3196 0.625377 3532 0.4110 0.659449 3530 0.3196 0.625377 3562 1.7808 0.962529 3531 0.3653 0.642555 3502 -0.9589 0.168804 3510 -0.5936 0.276387 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3525.00 sample std.=16.10 p-value of the KSTEST for those 10 p-values: 0.635841 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-04_22:31 0.7936,0.6862,0.7682,0.6017,0.1937,0.2542,0.5919,0.5772,0.1121,0.2719, The KS test for those 10 p-values: 0.736474 The 3DSPHERES test for dh-ranFile-2015-11-04_22:31 sample no r^3 equiv. uni. 1 30.163 0.634109 2 71.350 0.907296 3 39.873 0.735285 4 63.765 0.880626 5 55.984 0.845280 6 95.949 0.959169 7 68.632 0.898505 8 1.590 0.051630 9 3.655 0.114717 10 15.486 0.403218 11 43.265 0.763582 12 29.283 0.623217 13 3.495 0.109984 14 19.984 0.486304 15 7.617 0.224221 16 18.219 0.455185 17 58.213 0.856356 18 70.239 0.903799 19 10.565 0.296832 20 16.432 0.421743 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.319136 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-04_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 2.3 0.8 -1.6 -0.1 -1.5 -0.8 -3.1 0.3 -0.8 0.0 -0.6 -0.8 0.7 2.0 0.7 -1.4 0.9 -0.2 0.5 -0.5 0.5 -0.2 2.2 -0.6 -0.2 0.5 -0.5 -1.5 -0.9 -0.5 1.5 0.2 -0.8 1.7 -1.2 0.2 0.1 -0.7 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:50.217348 z-score=0.896586, p-value=0.820089 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-04_22:31 Test no p-value 1 0.130716 2 0.700455 3 0.125352 4 0.000152 5 0.419688 6 0.112179 7 0.550499 8 0.435930 9 0.044863 10 0.346250 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.016906 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-04_22:31: (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 66786 0.21 66870 0.62 3 25000.00 24857 0.82 24765 2.21 4 6666.67 6663 0.00 6693 0.10 5 1388.89 1422 0.79 1365 0.41 6 238.10 236 0.02 273 5.12 7 34.72 32 0.21 30 0.64 8 4.96 3 0.77 3 0.77 p=0.17001 p=0.87008 Number of rngs required: 689337, p-value: 0.861 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-04_22:31 No. of wins: Observed Expected 98307 98585.9 z-score=-1.247, pvalue=0.10616 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66761 66666.7 0.133 0.133 2 37428 37654.3 1.360 1.494 3 26884 26954.7 0.186 1.679 4 19353 19313.5 0.081 1.760 5 14019 13851.4 2.027 3.788 6 10057 9943.5 1.295 5.082 7 7121 7145.0 0.081 5.163 8 5128 5139.1 0.024 5.187 9 3649 3699.9 0.699 5.886 10 2735 2666.3 1.770 7.657 11 1895 1923.3 0.417 8.074 12 1336 1388.7 2.003 10.077 13 1014 1003.7 0.105 10.182 14 705 726.1 0.615 10.798 15 501 525.8 1.173 11.971 16 384 381.2 0.021 11.992 17 299 276.5 1.824 13.816 18 193 200.8 0.305 14.121 19 141 146.0 0.170 14.292 20 105 106.2 0.014 14.306 21 292 287.1 0.083 14.389 Chisq= 14.39 for 20 degrees of freedom, p= 0.18974 SUMMARY of craptest p-value for no. of wins: 0.106159 p-value for throws/game: 0.189744 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-04_22:31 No. of wins: Observed Expected 98502 98585.9 z-score=-0.375, pvalue=0.35381 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66787 66666.7 0.217 0.217 2 37623 37654.3 0.026 0.243 3 26852 26954.7 0.392 0.635 4 19234 19313.5 0.327 0.962 5 13727 13851.4 1.118 2.079 6 9970 9943.5 0.070 2.150 7 7210 7145.0 0.591 2.741 8 5178 5139.1 0.295 3.035 9 3709 3699.9 0.023 3.058 10 2663 2666.3 0.004 3.062 11 1878 1923.3 1.068 4.130 12 1393 1388.7 0.013 4.143 13 1030 1003.7 0.688 4.832 14 771 726.1 2.771 7.603 15 537 525.8 0.237 7.840 16 392 381.2 0.309 8.149 17 280 276.5 0.043 8.192 18 197 200.8 0.073 8.265 19 167 146.0 3.025 11.291 20 121 106.2 2.058 13.349 21 281 287.1 0.130 13.479 Chisq= 13.48 for 20 degrees of freedom, p= 0.14409 SUMMARY of craptest p-value for no. of wins: 0.353806 p-value for throws/game: 0.144094 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0095,0.0169,0.0201,0.0214,0.0268,0.0328,0.0334,0.0395,0.0395, 0.0448,0.0449,0.0497,0.0516,0.0579,0.0610,0.0611,0.0618,0.0773,0.0786, 0.0839,0.0850,0.0871,0.0944,0.1008,0.1020,0.1028,0.1062,0.1100,0.1121, 0.1122,0.1147,0.1148,0.1166,0.1219,0.1224,0.1249,0.1254,0.1270,0.1271, 0.1303,0.1307,0.1441,0.1455,0.1459,0.1494,0.1503,0.1521,0.1578,0.1600, 0.1602,0.1625,0.1627,0.1688,0.1689,0.1700,0.1897,0.1937,0.1987,0.2006, 0.2106,0.2151,0.2230,0.2242,0.2306,0.2325,0.2338,0.2397,0.2400,0.2438, 0.2515,0.2542,0.2564,0.2645,0.2675,0.2694,0.2719,0.2764,0.2770,0.2796, 0.2855,0.2865,0.2957,0.2968,0.2991,0.3052,0.3064,0.3191,0.3216,0.3307, 0.3359,0.3367,0.3373,0.3416,0.3462,0.3473,0.3488,0.3493,0.3534,0.3538, 0.3647,0.3653,0.3696,0.3780,0.3793,0.3861,0.3920,0.3938,0.3989,0.3995, 0.4002,0.4032,0.4144,0.4164,0.4190,0.4197,0.4217,0.4246,0.4283,0.4317, 0.4359,0.4441,0.4552,0.4570,0.4620,0.4658,0.4721,0.4748,0.4762,0.4805, 0.4818,0.4839,0.4863,0.4941,0.4944,0.4949,0.5030,0.5092,0.5159,0.5182, 0.5230,0.5282,0.5283,0.5340,0.5394,0.5427,0.5505,0.5610,0.5722,0.5739, 0.5762,0.5772,0.5841,0.5857,0.5872,0.5882,0.5916,0.5919,0.5924,0.6017, 0.6064,0.6145,0.6149,0.6212,0.6212,0.6232,0.6254,0.6254,0.6302,0.6319, 0.6341,0.6358,0.6414,0.6426,0.6448,0.6448,0.6499,0.6594,0.6597,0.6676, 0.6699,0.6705,0.6734,0.6766,0.6779,0.6787,0.6788,0.6816,0.6862,0.6972, 0.7005,0.7276,0.7353,0.7365,0.7434,0.7453,0.7472,0.7486,0.7500,0.7582, 0.7636,0.7682,0.7713,0.7725,0.7746,0.7780,0.7842,0.7936,0.7967,0.8051, 0.8084,0.8184,0.8199,0.8201,0.8220,0.8232,0.8262,0.8264,0.8362,0.8404, 0.8416,0.8446,0.8453,0.8536,0.8560,0.8563,0.8564,0.8607,0.8622,0.8671, 0.8701,0.8772,0.8775,0.8779,0.8784,0.8806,0.8813,0.8914,0.8985,0.8989, 0.9009,0.9017,0.9038,0.9070,0.9073,0.9091,0.9148,0.9175,0.9175,0.9420, 0.9432,0.9451,0.9477,0.9479,0.9501,0.9523,0.9536,0.9592,0.9625,0.9659, 0.9661,0.9765,0.9785,0.9817,0.9854,0.9869,0.9893,0.9893,0.9949, Overall p-value after applying KStest on 269 p-values = 0.923596 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.