RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-16_13:31 (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 17.6382 0.587999 2 to 25 15.95 21.8570 0.809718 3 to 26 15.94 12.1635 0.209866 4 to 27 15.56 34.6788 0.993146 5 to 28 15.88 13.2564 0.281142 6 to 29 15.77 23.0128 0.851165 7 to 30 15.68 24.0376 0.881582 8 to 31 15.98 9.7600 0.086629 9 to 32 15.54 23.3149 0.860723 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.206936 Tough bday spacings test for dh-ranFile-2016-07-16_13:31: 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 9 39 80 95 95 81 54 24 14 6 3 (O-E)^2/E 0.0 0.2 0.6 0.1 0.1 0.1 0.1 1.1 0.1 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 2.604, p= 0.011 RESULTS OF GCD FOR dh-ranFile-2016-07-16_13:31 Euclid's algorithm: p-value, steps to gcd: 0.953599 p-value, dist. of gcd's: 0.641237 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-16_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.307 0.190 0.598 0.552 0.619 0.658 0.722 0.073 Bits 8 to 15---> 0.809 0.084 0.266 0.768 0.412 0.236 0.962 0.202 Bits 16 to 23---> 0.840 0.699 0.681 0.568 0.820 0.322 0.005 0.345 Bits 24 to 31---> 0.012 0.582 0.036 0.250 0.457 0.973 0.418 0.403 KS test for the above 32 p values: 0.262 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-16_13:31, p-values for 5 runs: 0.8522, 0.6115, 0.1388, 0.6072, 0.2758 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-16_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 185 211.4 3.301 3.301 r= 29 5172 5134.0 0.281 3.582 r= 30 22943 23103.0 1.109 4.691 r= 31 11700 11551.5 1.908 6.599 chi-square = 6.599 with df = 3; p-value = 0.914 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-16_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 234 211.4 2.412 2.412 r= 30 5180 5134.0 0.412 2.824 r= 31 22936 23103.0 1.208 4.032 r= 32 11650 11551.5 0.840 4.871 chi-square = 4.871 with df = 3; p-value = 0.819 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-16_13:31 b-rank test for bits 1 to 8, p=0.66249 b-rank test for bits 2 to 9, p=0.24198 b-rank test for bits 3 to 10, p=0.03293 b-rank test for bits 4 to 11, p=0.74910 b-rank test for bits 5 to 12, p=0.45223 b-rank test for bits 6 to 13, p=0.40284 b-rank test for bits 7 to 14, p=0.85567 b-rank test for bits 8 to 15, p=0.98219 b-rank test for bits 9 to 16, p=0.87023 b-rank test for bits 10 to 17, p=0.63769 b-rank test for bits 11 to 18, p=0.23424 b-rank test for bits 12 to 19, p=0.38147 b-rank test for bits 13 to 20, p=0.24199 b-rank test for bits 14 to 21, p=0.40839 b-rank test for bits 15 to 22, p=0.95454 b-rank test for bits 16 to 23, p=0.98562 b-rank test for bits 17 to 24, p=0.98370 b-rank test for bits 18 to 25, p=0.33638 b-rank test for bits 19 to 26, p=0.08704 b-rank test for bits 20 to 27, p=0.93610 b-rank test for bits 21 to 28, p=0.54089 b-rank test for bits 22 to 29, p=0.67058 b-rank test for bits 23 to 30, p=0.26780 b-rank test for bits 24 to 31, p=0.09277 b-rank test for bits 25 to 32, p=0.28068 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 = 0.415908 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-16_13:31 (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 142449 1.26 0.896330 2 141977 0.16 0.562814 3 142060 0.35 0.637593 4 141913 0.01 0.503421 5 141906 -0.01 0.496896 6 141908 -0.00 0.498760 7 142327 0.98 0.835434 8 142142 0.54 0.706649 9 141620 -0.68 0.249519 10 142017 0.25 0.599312 11 142177 0.63 0.734145 12 142315 0.95 0.828391 13 141722 -0.44 0.330807 14 141911 0.00 0.501557 15 140864 -2.44 0.007296 16 142468 1.31 0.904105 17 141897 -0.03 0.488509 18 141959 0.12 0.546194 19 141961 0.12 0.548045 20 142119 0.49 0.687892 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-16_13:31 Bits used No. missing words z-score p-value 23 to 32 141897 -0.0425 0.483043 22 to 31 142031 0.4196 0.662594 21 to 30 142356 1.5402 0.938249 20 to 29 142205 1.0196 0.846029 19 to 28 142356 1.5402 0.938249 18 to 27 141859 -0.1736 0.431109 17 to 26 142289 1.3092 0.904768 16 to 25 141810 -0.3425 0.365981 15 to 24 141739 -0.5873 0.278486 14 to 23 142228 1.0989 0.864086 13 to 22 141700 -0.7218 0.235200 12 to 21 141744 -0.5701 0.284304 11 to 20 142162 0.8713 0.808198 10 to 19 142083 0.5989 0.725368 9 to 18 141838 -0.2460 0.402855 8 to 17 141882 -0.0942 0.462459 7 to 16 141792 -0.4046 0.342891 6 to 15 142145 0.8127 0.791792 5 to 14 142242 1.1471 0.874338 4 to 13 141701 -0.7184 0.236262 3 to 12 141245 -2.2908 0.010988 2 to 11 141727 -0.6287 0.264765 1 to 10 142484 1.9816 0.976239 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-16_13:31 Bits used No. missing words z-score p-value 28 to 32 141536 -1.2655 0.102842 27 to 31 141900 -0.0316 0.487385 26 to 30 142045 0.4599 0.677205 25 to 29 141942 0.1107 0.544091 24 to 28 141928 0.0633 0.525232 23 to 27 141972 0.2124 0.584118 22 to 26 141910 0.0023 0.500906 21 to 25 141771 -0.4689 0.319565 20 to 24 141773 -0.4621 0.321992 19 to 23 142198 0.9785 0.836097 18 to 22 141902 -0.0248 0.490088 17 to 21 141872 -0.1265 0.449651 16 to 20 141956 0.1582 0.562852 15 to 19 142366 1.5480 0.939193 14 to 18 142125 0.7311 0.767636 13 to 17 142220 1.0531 0.853857 12 to 16 141635 -0.9299 0.176203 11 to 15 142097 0.6362 0.737667 10 to 14 141478 -1.4621 0.071852 9 to 13 142147 0.8057 0.789781 8 to 12 141806 -0.3503 0.363068 7 to 11 141761 -0.5028 0.307548 6 to 10 141585 -1.0994 0.135792 5 to 9 141609 -1.0181 0.154323 4 to 8 141245 -2.2520 0.012162 3 to 7 142145 0.7989 0.787820 2 to 6 141691 -0.7401 0.229619 1 to 5 141301 -2.0621 0.019597 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-16_13:31 Bits used No. missing words z-score p-value 31 to 32 141996 0.2557 0.600895 30 to 31 142086 0.5212 0.698869 29 to 30 142090 0.5329 0.702966 28 to 29 141715 -0.5732 0.283240 27 to 28 141658 -0.7414 0.229230 26 to 27 141192 -2.1160 0.017172 25 to 26 141815 -0.2783 0.390407 24 to 25 141332 -1.7030 0.044280 23 to 24 142115 0.6067 0.727974 22 to 23 142136 0.6686 0.748138 21 to 22 142252 1.0108 0.843950 20 to 21 142401 1.4504 0.926520 19 to 20 141838 -0.2104 0.416673 18 to 19 141192 -2.1160 0.017172 17 to 18 141603 -0.9036 0.183096 16 to 17 141867 -0.1249 0.450314 15 to 16 141457 -1.3343 0.091052 14 to 15 141790 -0.3520 0.362417 13 to 14 141914 0.0138 0.505496 12 to 13 141480 -1.2665 0.102674 11 to 12 141931 0.0639 0.525484 10 to 11 142126 0.6391 0.738636 9 to 10 141720 -0.5585 0.288253 8 to 9 142153 0.7188 0.763865 7 to 8 141993 0.2468 0.597474 6 to 7 141640 -0.7945 0.213457 5 to 6 142082 0.5094 0.694747 4 to 5 142385 1.4032 0.919715 3 to 4 141254 -1.9331 0.026610 2 to 3 142254 1.0167 0.845358 1 to 2 141610 -0.8830 0.188624 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-16_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2485.91 -0.199 0.421025 Test results for specific bytes for dh-ranFile-2016-07-16_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2451.15 -0.691 0.244835 2 to 9 2496.03 -0.056 0.477628 3 to 10 2544.46 0.629 0.735224 4 to 11 2553.54 0.757 0.775509 5 to 12 2394.63 -1.490 0.068088 6 to 13 2444.21 -0.789 0.215040 7 to 14 2629.68 1.834 0.966667 8 to 15 2562.60 0.885 0.811989 9 to 16 2474.63 -0.359 0.359862 10 to 17 2492.45 -0.107 0.457467 11 to 18 2531.88 0.451 0.673974 12 to 19 2591.21 1.290 0.901447 13 to 20 2500.85 0.012 0.504769 14 to 21 2540.75 0.576 0.717769 15 to 22 2537.45 0.530 0.701822 16 to 23 2509.43 0.133 0.553038 17 to 24 2517.46 0.247 0.597491 18 to 25 2405.84 -1.332 0.091481 19 to 26 2423.47 -1.082 0.139557 20 to 27 2456.40 -0.617 0.268759 21 to 28 2443.17 -0.804 0.210790 22 to 29 2459.33 -0.575 0.282572 23 to 30 2443.78 -0.795 0.213275 24 to 31 2605.78 1.496 0.932673 25 to 32 2498.38 -0.023 0.490836 CDPARK for dh-ranFile-2016-07-16_13:31: 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 3510 -0.5936 0.276387 3490 -1.5068 0.065925 3542 0.8676 0.807188 3525 0.0913 0.536383 3503 -0.9132 0.180558 3517 -0.2740 0.392053 3555 1.4612 0.928018 3550 1.2329 0.891189 3525 0.0913 0.536383 3476 -2.1461 0.015932 Square side=100, avg. no. parked=3519.30 sample std.=24.27 p-value of the KSTEST for those 10 p-values: 0.871046 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-16_13:31 0.8156,0.6132,0.7715,0.4734,0.7467,0.0356,0.2344,0.9756,0.7555,0.6083, The KS test for those 10 p-values: 0.364725 The 3DSPHERES test for dh-ranFile-2016-07-16_13:31 sample no r^3 equiv. uni. 1 73.036 0.912361 2 7.375 0.217945 3 43.237 0.763364 4 121.054 0.982317 5 35.893 0.697735 6 43.577 0.766034 7 0.338 0.011217 8 14.364 0.380481 9 37.527 0.713753 10 4.818 0.148374 11 34.432 0.682647 12 7.972 0.233360 13 1.250 0.040823 14 15.946 0.412300 15 13.037 0.352449 16 45.455 0.780231 17 55.202 0.841194 18 0.388 0.012840 19 30.457 0.637686 20 18.512 0.460481 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.736548 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-16_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.3 -0.4 1.2 1.2 -0.3 -0.2 -0.3 -0.5 -0.4 2.2 -1.5 1.0 0.2 0.3 0.7 0.0 0.1 -0.2 -0.0 -0.9 -0.9 -0.9 1.3 1.8 -2.0 -0.6 0.8 0.4 -0.9 1.7 -1.3 -0.4 -0.8 -2.0 -1.9 0.5 0.2 0.1 1.0 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:50.579787 z-score=0.936132, p-value=0.829124 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-16_13:31 Test no p-value 1 0.010495 2 0.875062 3 0.068512 4 0.009611 5 0.777820 6 0.382349 7 0.772116 8 0.194134 9 0.575955 10 0.182078 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.125221 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-16_13:31: (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 66831 0.41 66852 0.52 3 25000.00 24825 1.23 24775 2.02 4 6666.67 6755 1.17 6705 0.22 5 1388.89 1313 4.15 1368 0.31 6 238.10 240 0.02 262 2.40 7 34.72 30 0.64 33 0.09 8 4.96 5 0.00 4 0.19 p=0.73145 p=0.54775 Number of rngs required: 688387, p-value: 0.493 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-16_13:31 No. of wins: Observed Expected 98626 98585.9 z-score= 0.180, pvalue=0.57124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66686 66666.7 0.006 0.006 2 37420 37654.3 1.458 1.464 3 26885 26954.7 0.180 1.644 4 19345 19313.5 0.051 1.696 5 13928 13851.4 0.423 2.119 6 9981 9943.5 0.141 2.260 7 7046 7145.0 1.372 3.633 8 5228 5139.1 1.539 5.171 9 3742 3699.9 0.480 5.651 10 2625 2666.3 0.640 6.291 11 1977 1923.3 1.498 7.789 12 1406 1388.7 0.215 8.003 13 1011 1003.7 0.053 8.056 14 767 726.1 2.299 10.355 15 529 525.8 0.019 10.374 16 392 381.2 0.309 10.683 17 277 276.5 0.001 10.684 18 225 200.8 2.909 13.593 19 141 146.0 0.170 13.763 20 115 106.2 0.727 14.489 21 274 287.1 0.599 15.088 Chisq= 15.09 for 20 degrees of freedom, p= 0.22867 SUMMARY of craptest p-value for no. of wins: 0.571242 p-value for throws/game: 0.228672 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-16_13:31 No. of wins: Observed Expected 98583 98585.9 z-score=-0.013, pvalue=0.49490 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66666 66666.7 0.000 0.000 2 37725 37654.3 0.133 0.133 3 26914 26954.7 0.062 0.194 4 19247 19313.5 0.229 0.423 5 13940 13851.4 0.566 0.989 6 10047 9943.5 1.076 2.066 7 7034 7145.0 1.725 3.791 8 5038 5139.1 1.988 5.779 9 3823 3699.9 4.098 9.877 10 2543 2666.3 5.702 15.579 11 1944 1923.3 0.222 15.801 12 1446 1388.7 2.361 18.162 13 990 1003.7 0.187 18.349 14 763 726.1 1.871 20.220 15 511 525.8 0.419 20.639 16 371 381.2 0.270 20.909 17 290 276.5 0.655 21.564 18 170 200.8 4.733 26.297 19 153 146.0 0.337 26.634 20 104 106.2 0.046 26.680 21 281 287.1 0.130 26.810 Chisq= 26.81 for 20 degrees of freedom, p= 0.85932 SUMMARY of craptest p-value for no. of wins: 0.494900 p-value for throws/game: 0.859318 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0045,0.0073,0.0096,0.0105,0.0107,0.0110,0.0112,0.0116,0.0122,0.0128, 0.0159,0.0172,0.0172,0.0196,0.0266,0.0329,0.0356,0.0361,0.0408,0.0443, 0.0659,0.0681,0.0685,0.0719,0.0732,0.0839,0.0866,0.0870,0.0911,0.0915, 0.0928,0.1027,0.1028,0.1252,0.1358,0.1388,0.1396,0.1484,0.1543,0.1762, 0.1806,0.1821,0.1831,0.1886,0.1896,0.1941,0.2021,0.2069,0.2099,0.2108, 0.2133,0.2135,0.2150,0.2179,0.2287,0.2292,0.2296,0.2334,0.2342,0.2344, 0.2352,0.2357,0.2363,0.2420,0.2420,0.2448,0.2495,0.2498,0.2621,0.2648, 0.2663,0.2678,0.2688,0.2758,0.2764,0.2785,0.2807,0.2811,0.2826,0.2832, 0.2843,0.2883,0.3072,0.3075,0.3196,0.3220,0.3221,0.3308,0.3364,0.3429, 0.3449,0.3524,0.3599,0.3624,0.3631,0.3647,0.3660,0.3805,0.3815,0.3823, 0.3904,0.3921,0.4028,0.4029,0.4031,0.4084,0.4118,0.4123,0.4159,0.4167, 0.4175,0.4210,0.4311,0.4497,0.4503,0.4522,0.4570,0.4575,0.4605,0.4625, 0.4734,0.4776,0.4830,0.4874,0.4885,0.4901,0.4908,0.4927,0.4949,0.4969, 0.4988,0.5009,0.5016,0.5034,0.5048,0.5055,0.5252,0.5255,0.5364,0.5364, 0.5409,0.5441,0.5462,0.5477,0.5480,0.5523,0.5530,0.5628,0.5629,0.5682, 0.5712,0.5760,0.5823,0.5841,0.5880,0.5975,0.5975,0.5980,0.5993,0.6009, 0.6072,0.6083,0.6115,0.6132,0.6194,0.6376,0.6377,0.6377,0.6412,0.6579, 0.6625,0.6626,0.6706,0.6740,0.6772,0.6813,0.6826,0.6879,0.6947,0.6977, 0.6985,0.6989,0.7018,0.7030,0.7066,0.7138,0.7178,0.7224,0.7254,0.7280, 0.7315,0.7341,0.7352,0.7365,0.7377,0.7386,0.7467,0.7481,0.7491,0.7555, 0.7634,0.7639,0.7660,0.7676,0.7680,0.7715,0.7721,0.7755,0.7778,0.7802, 0.7878,0.7898,0.7918,0.8072,0.8082,0.8088,0.8097,0.8120,0.8156,0.8185, 0.8200,0.8284,0.8291,0.8354,0.8361,0.8401,0.8412,0.8440,0.8454,0.8460, 0.8512,0.8522,0.8539,0.8557,0.8593,0.8607,0.8641,0.8702,0.8710,0.8743, 0.8751,0.8816,0.8912,0.8963,0.9014,0.9041,0.9048,0.9124,0.9142,0.9197, 0.9265,0.9280,0.9327,0.9361,0.9382,0.9382,0.9392,0.9536,0.9545,0.9616, 0.9667,0.9731,0.9756,0.9762,0.9822,0.9823,0.9837,0.9856,0.9931, Overall p-value after applying KStest on 269 p-values = 0.572124 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.