RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.90 15.9501 0.472623 2 to 25 15.76 21.2728 0.785674 3 to 26 15.86 30.2449 0.975368 4 to 27 15.74 15.3500 0.429716 5 to 28 15.78 14.9776 0.402902 6 to 29 15.74 15.2524 0.422696 7 to 30 15.68 12.2389 0.214541 8 to 31 15.90 14.5665 0.373326 9 to 32 15.83 12.4023 0.224809 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.480565 Tough bday spacings test for dh-ranFile-2018-07-04_20:31: 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 5 43 78 104 92 67 48 28 17 12 6 (O-E)^2/E 1.9 1.1 0.3 0.4 0.3 1.6 0.3 0.1 0.3 4.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.661, p= 0.692 RESULTS OF GCD FOR dh-ranFile-2018-07-04_20:31 Euclid's algorithm: p-value, steps to gcd: 0.132444 p-value, dist. of gcd's: 0.889071 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.804 0.227 0.476 0.739 0.120 0.328 0.564 0.538 Bits 8 to 15---> 0.969 0.181 0.669 0.704 0.436 0.795 0.974 0.165 Bits 16 to 23---> 0.608 0.046 0.793 0.306 0.384 0.525 0.541 0.478 Bits 24 to 31---> 0.124 0.427 0.146 0.080 0.699 0.019 0.323 0.850 KS test for the above 32 p values: 0.110 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_20:31, p-values for 5 runs: 0.6135, 0.5457, 0.0558, 0.6145, 0.4505 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5167 5134.0 0.212 0.267 r= 30 22958 23103.0 0.911 1.178 r= 31 11667 11551.5 1.154 2.332 chi-square = 2.332 with df = 3; p-value = 0.494 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 186 211.4 3.056 3.056 r= 30 5165 5134.0 0.187 3.243 r= 31 22997 23103.0 0.487 3.730 r= 32 11652 11551.5 0.874 4.604 chi-square = 4.604 with df = 3; p-value = 0.797 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_20:31 b-rank test for bits 1 to 8, p=0.97836 b-rank test for bits 2 to 9, p=0.86487 b-rank test for bits 3 to 10, p=0.16450 b-rank test for bits 4 to 11, p=0.73717 b-rank test for bits 5 to 12, p=0.66401 b-rank test for bits 6 to 13, p=0.74693 b-rank test for bits 7 to 14, p=0.00504 b-rank test for bits 8 to 15, p=0.98379 b-rank test for bits 9 to 16, p=0.70786 b-rank test for bits 10 to 17, p=0.90365 b-rank test for bits 11 to 18, p=0.78037 b-rank test for bits 12 to 19, p=0.27293 b-rank test for bits 13 to 20, p=0.48340 b-rank test for bits 14 to 21, p=0.73037 b-rank test for bits 15 to 22, p=0.36441 b-rank test for bits 16 to 23, p=0.51901 b-rank test for bits 17 to 24, p=0.83024 b-rank test for bits 18 to 25, p=0.47984 b-rank test for bits 19 to 26, p=0.22827 b-rank test for bits 20 to 27, p=0.14105 b-rank test for bits 21 to 28, p=0.15470 b-rank test for bits 22 to 29, p=0.34522 b-rank test for bits 23 to 30, p=0.61634 b-rank test for bits 24 to 31, p=0.64630 b-rank test for bits 25 to 32, p=0.00458 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 = 0.640846 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_20:31 (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 142906 2.33 0.990062 2 142336 1.00 0.840592 3 141798 -0.26 0.397387 4 141961 0.12 0.548045 5 142077 0.39 0.652379 6 141932 0.05 0.521121 7 141576 -0.78 0.218046 8 142098 0.44 0.670328 9 141296 -1.43 0.075927 10 141274 -1.48 0.068849 11 141935 0.06 0.523913 12 141961 0.12 0.548045 13 142298 0.91 0.818089 14 141588 -0.75 0.226395 15 142484 1.34 0.910313 16 142692 1.83 0.966275 17 141941 0.07 0.529493 18 141793 -0.27 0.392888 19 142052 0.33 0.630562 20 142250 0.80 0.786972 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-04_20:31 Bits used No. missing words z-score p-value 23 to 32 142315 1.3989 0.919073 22 to 31 141757 -0.5253 0.299696 21 to 30 141962 0.1816 0.572060 20 to 29 142580 2.3127 0.989629 19 to 28 141782 -0.4391 0.330306 18 to 27 141406 -1.7356 0.041315 17 to 26 141670 -0.8253 0.204608 16 to 25 141873 -0.1253 0.450153 15 to 24 141848 -0.2115 0.416255 14 to 23 141649 -0.8977 0.184676 13 to 22 141342 -1.9563 0.025214 12 to 21 141522 -1.3356 0.090837 11 to 20 141748 -0.5563 0.288999 10 to 19 142115 0.7092 0.760902 9 to 18 141886 -0.0804 0.467940 8 to 17 141768 -0.4873 0.313007 7 to 16 141836 -0.2529 0.400187 6 to 15 141944 0.1196 0.547581 5 to 14 141966 0.1954 0.577466 4 to 13 141628 -0.9701 0.165998 3 to 12 141702 -0.7149 0.237326 2 to 11 141544 -1.2598 0.103878 1 to 10 142022 0.3885 0.651183 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-04_20:31 Bits used No. missing words z-score p-value 28 to 32 142249 1.1514 0.875221 27 to 31 141759 -0.5096 0.305168 26 to 30 141596 -1.0621 0.144087 25 to 29 141996 0.2938 0.615543 24 to 28 142082 0.5853 0.720834 23 to 27 141663 -0.8350 0.201854 22 to 26 141799 -0.3740 0.354202 21 to 25 141694 -0.7299 0.232716 20 to 24 142179 0.9141 0.819677 19 to 23 141691 -0.7401 0.229619 18 to 22 142042 0.4497 0.673547 17 to 21 141783 -0.4282 0.334239 16 to 20 141885 -0.0825 0.467135 15 to 19 141768 -0.4791 0.315939 14 to 18 141770 -0.4723 0.318355 13 to 17 141997 0.2972 0.616838 12 to 16 142187 0.9413 0.826713 11 to 15 142039 0.4396 0.669872 10 to 14 142408 1.6904 0.954525 9 to 13 141446 -1.5706 0.058137 8 to 12 142029 0.4057 0.657504 7 to 11 141970 0.2057 0.581472 6 to 10 141971 0.2091 0.582796 5 to 9 141656 -0.8587 0.195240 4 to 8 141915 0.0192 0.507667 3 to 7 141538 -1.2587 0.104061 2 to 6 141996 0.2938 0.615543 1 to 5 142673 2.5887 0.995183 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-04_20:31 Bits used No. missing words z-score p-value 31 to 32 142309 1.1790 0.880794 30 to 31 141702 -0.6116 0.270404 29 to 30 142207 0.8781 0.810051 28 to 29 142106 0.5801 0.719092 27 to 28 141655 -0.7502 0.226556 26 to 27 141696 -0.6293 0.264579 25 to 26 141512 -1.1721 0.120586 24 to 25 142116 0.6096 0.728952 23 to 24 141966 0.1672 0.566381 22 to 23 142541 1.8633 0.968792 21 to 22 141848 -0.1809 0.428217 20 to 21 141426 -1.4258 0.076970 19 to 20 142116 0.6096 0.728952 18 to 19 142090 0.5329 0.702966 17 to 18 142329 1.2380 0.892135 16 to 17 142166 0.7571 0.775517 15 to 16 141754 -0.4582 0.323404 14 to 15 141954 0.1318 0.552417 13 to 14 142586 1.9961 0.977037 12 to 13 141843 -0.1957 0.422437 11 to 12 141935 0.0757 0.530180 10 to 11 141802 -0.3166 0.375771 9 to 10 142236 0.9636 0.832384 8 to 9 142083 0.5123 0.695780 7 to 8 141989 0.2350 0.592901 6 to 7 141996 0.2557 0.600895 5 to 6 142220 0.9164 0.820280 4 to 5 141599 -0.9154 0.179984 3 to 4 142052 0.4209 0.663070 2 to 3 141737 -0.5083 0.305605 1 to 2 141981 0.2114 0.583719 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2610.49 1.563 0.940927 Test results for specific bytes for dh-ranFile-2018-07-04_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2481.65 -0.260 0.397608 2 to 9 2484.51 -0.219 0.413308 3 to 10 2560.00 0.849 0.801930 4 to 11 2413.14 -1.228 0.109650 5 to 12 2424.86 -1.063 0.143961 6 to 13 2601.64 1.437 0.924704 7 to 14 2452.63 -0.670 0.251454 8 to 15 2703.00 2.871 0.997953 9 to 16 2675.37 2.480 0.993432 10 to 17 2587.93 1.244 0.893170 11 to 18 2408.32 -1.297 0.097381 12 to 19 2510.84 0.153 0.560930 13 to 20 2503.98 0.056 0.522417 14 to 21 2505.08 0.072 0.528648 15 to 22 2525.12 0.355 0.638825 16 to 23 2422.52 -1.096 0.136601 17 to 24 2377.33 -1.735 0.041388 18 to 25 2537.31 0.528 0.701116 19 to 26 2637.52 1.945 0.974103 20 to 27 2512.93 0.183 0.572549 21 to 28 2558.86 0.832 0.797395 22 to 29 2294.88 -2.901 0.001861 23 to 30 2408.99 -1.287 0.099035 24 to 31 2600.24 1.418 0.921851 25 to 32 2455.95 -0.623 0.266666 CDPARK for dh-ranFile-2018-07-04_20:31: 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 3539 0.7306 0.767486 3535 0.5479 0.708135 3518 -0.2283 0.409702 3542 0.8676 0.807188 3534 0.5023 0.692266 3544 0.9589 0.831196 3530 0.3196 0.625377 3569 2.1005 0.982156 3503 -0.9132 0.180558 3543 0.9132 0.819442 Square side=100, avg. no. parked=3535.70 sample std.=16.43 p-value of the KSTEST for those 10 p-values: 0.059486 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_20:31 0.5642,0.9108,0.1918,0.9867,0.3388,0.0816,0.9453,0.9586,0.0502,0.1330, The KS test for those 10 p-values: 0.156131 The 3DSPHERES test for dh-ranFile-2018-07-04_20:31 sample no r^3 equiv. uni. 1 48.787 0.803331 2 23.900 0.549169 3 14.638 0.386097 4 51.293 0.819091 5 44.546 0.773466 6 35.252 0.691206 7 66.704 0.891766 8 82.272 0.935584 9 6.978 0.207524 10 23.866 0.548663 11 26.503 0.586637 12 22.540 0.528263 13 64.206 0.882369 14 48.321 0.800252 15 124.155 0.984053 16 1.796 0.058118 17 28.812 0.617259 18 7.311 0.216276 19 40.449 0.740321 20 97.632 0.961396 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.033593 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -0.4 0.8 -0.4 2.2 0.1 0.9 -0.7 -1.7 -0.6 -1.8 1.1 0.0 1.3 -0.3 -0.9 -1.7 -0.1 -0.6 0.9 -0.7 1.5 0.2 -1.7 2.4 2.3 0.1 0.2 0.9 0.8 0.1 -0.0 1.8 2.7 0.6 0.3 -0.7 -0.8 1.0 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:56.325813 z-score=1.563074, p-value=0.931227 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-04_20:31 Test no p-value 1 0.004556 2 0.167508 3 0.194120 4 0.180503 5 0.390151 6 0.074570 7 0.098449 8 0.693639 9 0.816917 10 0.284673 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.025015 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_20:31: (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 66788 0.22 66777 0.18 3 25000.00 24934 0.17 25001 0.00 4 6666.67 6584 1.03 6562 1.64 5 1388.89 1425 0.94 1370 0.26 6 238.10 225 0.72 250 0.60 7 34.72 37 0.15 36 0.05 8 4.96 6 0.22 3 0.77 p=0.24900 p=0.25601 Number of rngs required: 687893, p-value: 0.278 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_20:31 No. of wins: Observed Expected 98941 98585.9 z-score= 1.588, pvalue=0.94390 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66410 66666.7 0.988 0.988 2 37832 37654.3 0.838 1.827 3 26886 26954.7 0.175 2.002 4 19284 19313.5 0.045 2.047 5 13812 13851.4 0.112 2.159 6 10033 9943.5 0.805 2.964 7 7259 7145.0 1.818 4.782 8 5133 5139.1 0.007 4.789 9 3691 3699.9 0.021 4.810 10 2649 2666.3 0.112 4.922 11 1897 1923.3 0.360 5.283 12 1339 1388.7 1.782 7.064 13 993 1003.7 0.114 7.179 14 733 726.1 0.065 7.244 15 568 525.8 3.381 10.625 16 394 381.2 0.433 11.058 17 297 276.5 1.514 12.572 18 203 200.8 0.023 12.595 19 164 146.0 2.223 14.818 20 102 106.2 0.167 14.986 21 321 287.1 3.999 18.985 Chisq= 18.98 for 20 degrees of freedom, p= 0.47719 SUMMARY of craptest p-value for no. of wins: 0.943902 p-value for throws/game: 0.477191 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_20:31 No. of wins: Observed Expected 98414 98585.9 z-score=-0.769, pvalue=0.22105 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66478 66666.7 0.534 0.534 2 37596 37654.3 0.090 0.624 3 27079 26954.7 0.573 1.197 4 19380 19313.5 0.229 1.426 5 13777 13851.4 0.400 1.826 6 9962 9943.5 0.034 1.860 7 7166 7145.0 0.062 1.922 8 5138 5139.1 0.000 1.922 9 3717 3699.9 0.079 2.002 10 2664 2666.3 0.002 2.004 11 1963 1923.3 0.818 2.822 12 1387 1388.7 0.002 2.824 13 1009 1003.7 0.028 2.852 14 717 726.1 0.115 2.967 15 538 525.8 0.281 3.248 16 425 381.2 5.045 8.293 17 291 276.5 0.756 9.049 18 203 200.8 0.023 9.073 19 142 146.0 0.109 9.181 20 119 106.2 1.539 10.720 21 249 287.1 5.060 15.780 Chisq= 15.78 for 20 degrees of freedom, p= 0.26981 SUMMARY of craptest p-value for no. of wins: 0.221050 p-value for throws/game: 0.269811 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0046,0.0046,0.0050,0.0191,0.0250,0.0252,0.0336,0.0413,0.0414, 0.0462,0.0502,0.0558,0.0581,0.0581,0.0595,0.0688,0.0746,0.0759,0.0770, 0.0799,0.0816,0.0908,0.0974,0.0984,0.0990,0.1039,0.1041,0.1097,0.1104, 0.1203,0.1206,0.1244,0.1324,0.1330,0.1366,0.1411,0.1440,0.1441,0.1457, 0.1547,0.1561,0.1645,0.1654,0.1660,0.1675,0.1800,0.1805,0.1806,0.1806, 0.1847,0.1918,0.1941,0.1952,0.2019,0.2046,0.2075,0.2145,0.2163,0.2180, 0.2211,0.2248,0.2264,0.2266,0.2267,0.2283,0.2296,0.2327,0.2373,0.2490, 0.2515,0.2560,0.2646,0.2667,0.2698,0.2704,0.2729,0.2782,0.2847,0.2890, 0.2997,0.3052,0.3055,0.3056,0.3130,0.3159,0.3184,0.3227,0.3234,0.3278, 0.3303,0.3342,0.3388,0.3452,0.3542,0.3644,0.3733,0.3758,0.3840,0.3861, 0.3902,0.3929,0.3974,0.3976,0.4002,0.4029,0.4097,0.4133,0.4163,0.4224, 0.4227,0.4274,0.4282,0.4297,0.4362,0.4502,0.4505,0.4671,0.4679,0.4726, 0.4759,0.4772,0.4784,0.4798,0.4806,0.4834,0.4936,0.5077,0.5190,0.5211, 0.5224,0.5239,0.5252,0.5283,0.5286,0.5295,0.5302,0.5376,0.5409,0.5457, 0.5476,0.5480,0.5480,0.5487,0.5492,0.5524,0.5609,0.5642,0.5644,0.5664, 0.5721,0.5725,0.5775,0.5815,0.5828,0.5837,0.5866,0.5929,0.6009,0.6081, 0.6135,0.6145,0.6155,0.6155,0.6163,0.6168,0.6173,0.6254,0.6306,0.6388, 0.6408,0.6463,0.6512,0.6524,0.6575,0.6631,0.6640,0.6688,0.6699,0.6703, 0.6735,0.6912,0.6916,0.6923,0.6936,0.6958,0.6993,0.7011,0.7030,0.7041, 0.7079,0.7081,0.7191,0.7208,0.7290,0.7290,0.7304,0.7372,0.7389,0.7403, 0.7469,0.7609,0.7675,0.7735,0.7755,0.7804,0.7857,0.7870,0.7930,0.7950, 0.7968,0.7974,0.8003,0.8019,0.8033,0.8039,0.8072,0.8101,0.8169,0.8181, 0.8191,0.8194,0.8197,0.8203,0.8267,0.8302,0.8312,0.8324,0.8406,0.8501, 0.8649,0.8752,0.8808,0.8824,0.8891,0.8918,0.8921,0.8932,0.9036,0.9103, 0.9108,0.9191,0.9219,0.9247,0.9312,0.9356,0.9409,0.9439,0.9453,0.9545, 0.9586,0.9614,0.9663,0.9688,0.9689,0.9735,0.9741,0.9754,0.9770,0.9784, 0.9822,0.9838,0.9841,0.9867,0.9896,0.9901,0.9934,0.9952,0.9980, Overall p-value after applying KStest on 269 p-values = 0.782388 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.