RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-26_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 14.1101 0.340706 2 to 25 15.75 20.9051 0.769437 3 to 26 15.74 24.9986 0.905259 4 to 27 15.62 21.6723 0.802346 5 to 28 15.59 21.1273 0.779354 6 to 29 15.82 13.1950 0.276964 7 to 30 16.00 13.0252 0.265504 8 to 31 15.86 9.7116 0.084733 9 to 32 16.16 8.8922 0.056417 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.758437 Tough bday spacings test for dh-ranFile-2017-01-26_19:31: 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 36 72 105 111 66 52 23 17 7 5 (O-E)^2/E 1.1 0.0 0.0 0.5 1.8 1.9 0.0 1.5 0.3 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.450, p= 0.318 RESULTS OF GCD FOR dh-ranFile-2017-01-26_19:31 Euclid's algorithm: p-value, steps to gcd: 0.313959 p-value, dist. of gcd's: 0.765739 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-26_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.694 0.149 0.922 0.721 0.958 0.752 0.389 0.742 Bits 8 to 15---> 0.696 0.413 0.780 0.707 0.937 0.274 0.597 0.611 Bits 16 to 23---> 0.939 0.970 0.660 0.157 0.347 0.375 0.116 0.822 Bits 24 to 31---> 0.176 0.415 0.461 0.348 0.019 0.288 0.075 0.396 KS test for the above 32 p values: 0.151 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-26_19:31, p-values for 5 runs: 0.9999, 0.9088, 0.8318, 0.9011, 0.6115 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-26_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 246 211.4 5.657 5.657 r= 29 5093 5134.0 0.328 5.984 r= 30 23030 23103.0 0.231 6.215 r= 31 11631 11551.5 0.547 6.762 chi-square = 6.762 with df = 3; p-value = 0.920 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-26_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5094 5134.0 0.312 0.584 r= 31 23115 23103.0 0.006 0.590 r= 32 11572 11551.5 0.036 0.626 chi-square = 0.626 with df = 3; p-value = 0.110 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-26_19:31 b-rank test for bits 1 to 8, p=0.78197 b-rank test for bits 2 to 9, p=0.19449 b-rank test for bits 3 to 10, p=0.94591 b-rank test for bits 4 to 11, p=0.79413 b-rank test for bits 5 to 12, p=0.58367 b-rank test for bits 6 to 13, p=0.72296 b-rank test for bits 7 to 14, p=0.12264 b-rank test for bits 8 to 15, p=0.51063 b-rank test for bits 9 to 16, p=0.99844 b-rank test for bits 10 to 17, p=0.60700 b-rank test for bits 11 to 18, p=0.22399 b-rank test for bits 12 to 19, p=0.38811 b-rank test for bits 13 to 20, p=0.01227 b-rank test for bits 14 to 21, p=0.08005 b-rank test for bits 15 to 22, p=0.50764 b-rank test for bits 16 to 23, p=0.91860 b-rank test for bits 17 to 24, p=0.63595 b-rank test for bits 18 to 25, p=0.51542 b-rank test for bits 19 to 26, p=0.57500 b-rank test for bits 20 to 27, p=0.46961 b-rank test for bits 21 to 28, p=0.83282 b-rank test for bits 22 to 29, p=0.84424 b-rank test for bits 23 to 30, p=0.42654 b-rank test for bits 24 to 31, p=0.25583 b-rank test for bits 25 to 32, p=0.74548 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 = 0.685570 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-26_19:31 (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 141645 -0.62 0.268422 2 142556 1.51 0.934594 3 142173 0.62 0.731070 4 142490 1.36 0.912563 5 141182 -1.70 0.044625 6 141186 -1.69 0.045512 7 141609 -0.70 0.241431 8 141873 -0.08 0.466177 9 141836 -0.17 0.431981 10 141264 -1.51 0.065805 11 142409 1.17 0.878486 12 142201 0.68 0.752214 13 142061 0.35 0.638469 14 141201 -1.65 0.048965 15 142182 0.64 0.737963 16 141637 -0.64 0.262295 17 142055 0.34 0.633204 18 142373 1.08 0.860672 19 142211 0.70 0.759544 20 140793 -2.61 0.004550 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-26_19:31 Bits used No. missing words z-score p-value 23 to 32 141802 -0.3701 0.355653 22 to 31 141999 0.3092 0.621418 21 to 30 142138 0.7885 0.784803 20 to 29 142456 1.8851 0.970290 19 to 28 142334 1.4644 0.928455 18 to 27 141959 0.1713 0.567997 17 to 26 142327 1.4402 0.925100 16 to 25 141809 -0.3460 0.364684 15 to 24 142438 1.8230 0.965848 14 to 23 141976 0.2299 0.590914 13 to 22 141968 0.2023 0.580163 12 to 21 141597 -1.0770 0.140740 11 to 20 142027 0.4058 0.657540 10 to 19 141992 0.2851 0.612204 9 to 18 141954 0.1540 0.561209 8 to 17 141732 -0.6115 0.270440 7 to 16 142363 1.5644 0.941136 6 to 15 141752 -0.5425 0.293731 5 to 14 142156 0.8506 0.802500 4 to 13 141718 -0.6598 0.254704 3 to 12 141976 0.2299 0.590914 2 to 11 142013 0.3575 0.639635 1 to 10 141835 -0.2563 0.398856 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-26_19:31 Bits used No. missing words z-score p-value 28 to 32 141780 -0.4384 0.330546 27 to 31 141747 -0.5503 0.291067 26 to 30 142187 0.9413 0.826713 25 to 29 141620 -0.9808 0.163351 24 to 28 142376 1.5819 0.943167 23 to 27 142006 0.3277 0.628429 22 to 26 142288 1.2836 0.900364 21 to 25 141680 -0.7774 0.218464 20 to 24 141820 -0.3028 0.381016 19 to 23 141528 -1.2926 0.098067 18 to 22 141856 -0.1808 0.428270 17 to 21 142018 0.3684 0.643702 16 to 20 142550 2.1718 0.985063 15 to 19 141919 0.0328 0.513075 14 to 18 142246 1.1413 0.873118 13 to 17 141783 -0.4282 0.334239 12 to 16 142016 0.3616 0.641172 11 to 15 142165 0.8667 0.806941 10 to 14 142331 1.4294 0.923554 9 to 13 141878 -0.1062 0.457711 8 to 12 141638 -0.9198 0.178848 7 to 11 141800 -0.3706 0.355464 6 to 10 141873 -0.1232 0.450993 5 to 9 141859 -0.1706 0.432265 4 to 8 141986 0.2599 0.602529 3 to 7 141473 -1.4791 0.069559 2 to 6 141921 0.0396 0.515778 1 to 5 141988 0.2667 0.605141 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-26_19:31 Bits used No. missing words z-score p-value 31 to 32 141585 -0.9567 0.169353 30 to 31 142137 0.6716 0.749079 29 to 30 141975 0.1937 0.576801 28 to 29 141926 0.0492 0.519610 27 to 28 141484 -1.2547 0.104801 26 to 27 141714 -0.5762 0.282242 25 to 26 141439 -1.3874 0.082659 24 to 25 141824 -0.2517 0.400632 23 to 24 141880 -0.0865 0.465527 22 to 23 141315 -1.7532 0.039785 21 to 22 142223 0.9253 0.822590 20 to 21 141947 0.1111 0.544240 19 to 20 141635 -0.8092 0.209191 18 to 19 142097 0.5536 0.710073 17 to 18 141827 -0.2429 0.404056 16 to 17 142118 0.6155 0.730903 15 to 16 142571 1.9518 0.974521 14 to 15 141860 -0.1455 0.442152 13 to 14 141779 -0.3845 0.350321 12 to 13 141586 -0.9538 0.170099 11 to 12 142582 1.9843 0.976388 10 to 11 141914 0.0138 0.505496 9 to 10 141867 -0.1249 0.450314 8 to 9 142228 0.9400 0.826399 7 to 8 141918 0.0256 0.510202 6 to 7 141752 -0.4641 0.321288 5 to 6 142048 0.4091 0.658751 4 to 5 142369 1.3560 0.912444 3 to 4 141997 0.2586 0.602033 2 to 3 142002 0.2734 0.607713 1 to 2 141872 -0.1101 0.456158 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-26_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2483.57 -0.232 0.408104 Test results for specific bytes for dh-ranFile-2017-01-26_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.34 0.344 0.634672 2 to 9 2412.21 -1.241 0.107212 3 to 10 2362.47 -1.945 0.025887 4 to 11 2531.21 0.441 0.670516 5 to 12 2529.37 0.415 0.661052 6 to 13 2506.81 0.096 0.538388 7 to 14 2660.30 2.267 0.988303 8 to 15 2687.68 2.654 0.996025 9 to 16 2411.51 -1.251 0.105393 10 to 17 2529.89 0.423 0.663771 11 to 18 2609.31 1.546 0.938936 12 to 19 2427.75 -1.022 0.153435 13 to 20 2520.27 0.287 0.612811 14 to 21 2579.93 1.130 0.870857 15 to 22 2426.10 -1.045 0.147998 16 to 23 2474.04 -0.367 0.356762 17 to 24 2489.84 -0.144 0.442857 18 to 25 2434.89 -0.921 0.178570 19 to 26 2497.82 -0.031 0.487680 20 to 27 2505.98 0.085 0.533721 21 to 28 2449.53 -0.714 0.237692 22 to 29 2516.66 0.236 0.593104 23 to 30 2522.77 0.322 0.626292 24 to 31 2462.64 -0.528 0.298619 25 to 32 2449.89 -0.709 0.239287 CDPARK for dh-ranFile-2017-01-26_19:31: 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 3536 0.5936 0.723613 3481 -1.9178 0.027568 3552 1.3242 0.907282 3514 -0.4110 0.340551 3520 -0.1370 0.445521 3477 -2.1005 0.017844 3534 0.5023 0.692266 3512 -0.5023 0.307734 3537 0.6393 0.738676 3526 0.1370 0.554479 Square side=100, avg. no. parked=3518.90 sample std.=22.93 p-value of the KSTEST for those 10 p-values: 0.724284 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-26_19:31 0.7660,0.8647,0.2445,0.4380,0.3908,0.2952,0.8237,0.4513,0.4560,0.6066, The KS test for those 10 p-values: 0.543741 The 3DSPHERES test for dh-ranFile-2017-01-26_19:31 sample no r^3 equiv. uni. 1 28.594 0.614471 2 4.480 0.138724 3 29.658 0.627900 4 8.943 0.257779 5 14.504 0.383360 6 12.622 0.343427 7 2.276 0.073056 8 22.388 0.525873 9 139.012 0.990282 10 3.664 0.114976 11 50.555 0.814589 12 5.158 0.157956 13 40.961 0.744714 14 16.391 0.420948 15 14.692 0.387201 16 22.151 0.522106 17 8.420 0.244731 18 40.275 0.738812 19 46.180 0.785474 20 49.890 0.810433 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.925948 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-26_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 0.1 -0.5 -0.2 -1.4 0.7 0.8 1.0 -0.6 -1.2 -0.0 -0.1 0.7 -0.4 -0.5 -1.3 1.4 0.9 0.1 0.5 -1.6 1.0 -0.3 0.7 -0.6 -0.5 0.3 -0.1 1.7 -1.2 -1.4 0.4 1.2 1.0 0.8 -1.2 -0.4 -0.4 -0.1 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:35.314422 z-score=-0.729456, p-value=0.242471 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-26_19:31 Test no p-value 1 0.493406 2 0.345551 3 0.986956 4 0.143537 5 0.266785 6 0.285714 7 0.067314 8 0.092899 9 0.711246 10 0.772674 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.535378 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-26_19:31: (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 66855 0.53 66738 0.08 3 25000.00 24802 1.57 24878 0.60 4 6666.67 6671 0.00 6681 0.03 5 1388.89 1404 0.16 1416 0.53 6 238.10 237 0.01 241 0.04 7 34.72 27 1.72 44 2.48 8 4.96 3 0.77 1 3.16 p=0.42551 p=0.67066 Number of rngs required: 687909, p-value: 0.284 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-26_19:31 No. of wins: Observed Expected 98566 98585.9 z-score=-0.089, pvalue=0.46461 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66686 66666.7 0.006 0.006 2 37490 37654.3 0.717 0.723 3 27091 26954.7 0.689 1.412 4 19473 19313.5 1.318 2.729 5 13842 13851.4 0.006 2.736 6 9888 9943.5 0.310 3.046 7 7053 7145.0 1.185 4.231 8 5130 5139.1 0.016 4.247 9 3613 3699.9 2.039 6.287 10 2671 2666.3 0.008 6.295 11 1878 1923.3 1.068 7.363 12 1430 1388.7 1.226 8.589 13 1017 1003.7 0.176 8.765 14 730 726.1 0.021 8.786 15 546 525.8 0.773 9.559 16 412 381.2 2.497 12.056 17 284 276.5 0.201 12.257 18 209 200.8 0.332 12.589 19 141 146.0 0.170 12.759 20 132 106.2 6.260 19.019 21 284 287.1 0.034 19.053 Chisq= 19.05 for 20 degrees of freedom, p= 0.48160 SUMMARY of craptest p-value for no. of wins: 0.464613 p-value for throws/game: 0.481602 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-26_19:31 No. of wins: Observed Expected 98541 98585.9 z-score=-0.201, pvalue=0.42049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66671 66666.7 0.000 0.000 2 37945 37654.3 2.244 2.244 3 26895 26954.7 0.132 2.377 4 19278 19313.5 0.065 2.442 5 13792 13851.4 0.255 2.697 6 9893 9943.5 0.257 2.954 7 7166 7145.0 0.062 3.015 8 5049 5139.1 1.579 4.594 9 3729 3699.9 0.229 4.823 10 2646 2666.3 0.155 4.978 11 1947 1923.3 0.291 5.269 12 1340 1388.7 1.711 6.980 13 1058 1003.7 2.936 9.916 14 731 726.1 0.033 9.948 15 498 525.8 1.474 11.422 16 373 381.2 0.174 11.596 17 258 276.5 1.243 12.839 18 201 200.8 0.000 12.839 19 149 146.0 0.062 12.901 20 103 106.2 0.097 12.999 21 278 287.1 0.289 13.288 Chisq= 13.29 for 20 degrees of freedom, p= 0.13531 SUMMARY of craptest p-value for no. of wins: 0.420492 p-value for throws/game: 0.135310 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0046,0.0123,0.0178,0.0189,0.0259,0.0276,0.0398,0.0446,0.0455,0.0490, 0.0564,0.0658,0.0673,0.0696,0.0731,0.0749,0.0801,0.0827,0.0847,0.0929, 0.0981,0.1048,0.1054,0.1072,0.1096,0.1150,0.1156,0.1226,0.1353,0.1387, 0.1407,0.1435,0.1480,0.1487,0.1509,0.1534,0.1565,0.1580,0.1634,0.1694, 0.1701,0.1758,0.1786,0.1788,0.1945,0.2092,0.2185,0.2240,0.2377,0.2393, 0.2414,0.2425,0.2445,0.2447,0.2547,0.2558,0.2578,0.2623,0.2655,0.2668, 0.2684,0.2704,0.2740,0.2770,0.2822,0.2845,0.2857,0.2883,0.2911,0.2937, 0.2952,0.2986,0.3077,0.3140,0.3176,0.3213,0.3305,0.3342,0.3406,0.3407, 0.3434,0.3456,0.3474,0.3477,0.3503,0.3555,0.3557,0.3568,0.3647,0.3749, 0.3810,0.3834,0.3872,0.3881,0.3894,0.3908,0.3960,0.3989,0.4006,0.4041, 0.4081,0.4132,0.4149,0.4205,0.4209,0.4255,0.4265,0.4283,0.4320,0.4323, 0.4380,0.4422,0.4429,0.4455,0.4503,0.4510,0.4513,0.4560,0.4562,0.4577, 0.4614,0.4646,0.4655,0.4662,0.4696,0.4816,0.4877,0.4934,0.5055,0.5076, 0.5102,0.5106,0.5131,0.5154,0.5158,0.5196,0.5221,0.5259,0.5337,0.5354, 0.5384,0.5437,0.5442,0.5545,0.5612,0.5680,0.5750,0.5768,0.5802,0.5837, 0.5909,0.5909,0.5931,0.5968,0.6020,0.6025,0.6051,0.6066,0.6070,0.6077, 0.6107,0.6115,0.6122,0.6128,0.6145,0.6214,0.6263,0.6279,0.6284,0.6332, 0.6347,0.6360,0.6385,0.6396,0.6412,0.6437,0.6575,0.6588,0.6600,0.6611, 0.6638,0.6705,0.6707,0.6856,0.6923,0.6936,0.6962,0.7071,0.7101,0.7112, 0.7212,0.7230,0.7236,0.7243,0.7309,0.7311,0.7380,0.7387,0.7388,0.7422, 0.7447,0.7455,0.7491,0.7522,0.7525,0.7584,0.7595,0.7657,0.7660,0.7694, 0.7727,0.7794,0.7801,0.7820,0.7848,0.7855,0.7941,0.8023,0.8025,0.8069, 0.8104,0.8146,0.8216,0.8226,0.8237,0.8264,0.8267,0.8318,0.8328,0.8442, 0.8607,0.8647,0.8709,0.8731,0.8785,0.9004,0.9011,0.9053,0.9073,0.9088, 0.9124,0.9126,0.9186,0.9201,0.9218,0.9236,0.9251,0.9259,0.9285,0.9346, 0.9375,0.9388,0.9389,0.9411,0.9432,0.9459,0.9578,0.9658,0.9702,0.9703, 0.9745,0.9764,0.9851,0.9870,0.9883,0.9903,0.9960,0.9984,0.9999, Overall p-value after applying KStest on 269 p-values = 0.371634 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.