RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_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 15.96 14.1202 0.341426 2 to 25 15.87 11.4070 0.165359 3 to 26 15.87 13.3205 0.285518 4 to 27 15.94 26.6435 0.936493 5 to 28 15.78 17.5071 0.579446 6 to 29 16.08 24.8812 0.902600 7 to 30 15.40 26.2825 0.930534 8 to 31 15.63 18.2861 0.628987 9 to 32 15.84 19.9712 0.724295 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.392868 Tough bday spacings test for dh-ranFile-2018-06-22_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 33 81 100 85 80 49 41 11 9 5 (O-E)^2/E 1.1 0.4 0.8 0.1 1.6 0.0 0.2 4.2 1.0 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 10.520, p= 0.604 RESULTS OF GCD FOR dh-ranFile-2018-06-22_19:31 Euclid's algorithm: p-value, steps to gcd: 0.380636 p-value, dist. of gcd's: 0.722030 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.245 0.895 0.508 0.513 0.027 0.678 0.679 0.271 Bits 8 to 15---> 0.106 0.899 0.909 0.112 0.537 0.954 0.332 0.212 Bits 16 to 23---> 0.441 0.356 0.294 0.107 0.145 0.050 0.879 0.982 Bits 24 to 31---> 0.442 0.792 0.923 0.315 0.448 0.048 0.394 0.680 KS test for the above 32 p values: 0.248 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_19:31, p-values for 5 runs: 0.4491, 0.7130, 0.1940, 0.3653, 0.5911 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5157 5134.0 0.103 0.131 r= 30 22959 23103.0 0.898 1.029 r= 31 11675 11551.5 1.320 2.349 chi-square = 2.349 with df = 3; p-value = 0.497 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5131 5134.0 0.002 0.062 r= 31 23080 23103.0 0.023 0.085 r= 32 11574 11551.5 0.044 0.129 chi-square = 0.129 with df = 3; p-value = 0.012 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_19:31 b-rank test for bits 1 to 8, p=0.86561 b-rank test for bits 2 to 9, p=0.60632 b-rank test for bits 3 to 10, p=0.21875 b-rank test for bits 4 to 11, p=0.29753 b-rank test for bits 5 to 12, p=0.64992 b-rank test for bits 6 to 13, p=0.88988 b-rank test for bits 7 to 14, p=0.08580 b-rank test for bits 8 to 15, p=0.19930 b-rank test for bits 9 to 16, p=0.95628 b-rank test for bits 10 to 17, p=0.97090 b-rank test for bits 11 to 18, p=0.40876 b-rank test for bits 12 to 19, p=0.43416 b-rank test for bits 13 to 20, p=0.40357 b-rank test for bits 14 to 21, p=0.00161 b-rank test for bits 15 to 22, p=0.03616 b-rank test for bits 16 to 23, p=0.20996 b-rank test for bits 17 to 24, p=0.82370 b-rank test for bits 18 to 25, p=0.66300 b-rank test for bits 19 to 26, p=0.19771 b-rank test for bits 20 to 27, p=0.79964 b-rank test for bits 21 to 28, p=0.95955 b-rank test for bits 22 to 29, p=0.17332 b-rank test for bits 23 to 30, p=0.23403 b-rank test for bits 24 to 31, p=0.51273 b-rank test for bits 25 to 32, p=0.31868 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 = 0.688685 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_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 141778 -0.31 0.379480 2 141842 -0.16 0.437499 3 142272 0.85 0.801603 4 142422 1.20 0.884508 5 142720 1.89 0.970893 6 142400 1.15 0.874190 7 142412 1.17 0.879895 8 142135 0.53 0.700996 9 141737 -0.40 0.343607 10 141946 0.09 0.534139 11 141909 -0.00 0.499692 12 142906 2.33 0.990062 13 141202 -1.65 0.049202 14 141959 0.12 0.546194 15 142403 1.15 0.875634 16 142400 1.15 0.874190 17 141836 -0.17 0.431981 18 141824 -0.20 0.420987 19 141880 -0.07 0.472683 20 141645 -0.62 0.268422 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-22_19:31 Bits used No. missing words z-score p-value 23 to 32 141924 0.0506 0.520172 22 to 31 141797 -0.3873 0.349251 21 to 30 142661 2.5920 0.995229 20 to 29 142113 0.7023 0.758757 19 to 28 142533 2.1506 0.984246 18 to 27 141326 -2.0115 0.022137 17 to 26 141686 -0.7701 0.220619 16 to 25 141403 -1.7460 0.040408 15 to 24 141261 -2.2356 0.012688 14 to 23 141809 -0.3460 0.364684 13 to 22 141795 -0.3942 0.346701 12 to 21 142000 0.3127 0.622729 11 to 20 142257 1.1989 0.884709 10 to 19 141140 -2.6529 0.003991 9 to 18 141760 -0.5149 0.303301 8 to 17 142035 0.4333 0.667618 7 to 16 141364 -1.8804 0.030024 6 to 15 141326 -2.0115 0.022137 5 to 14 141686 -0.7701 0.220619 4 to 13 141813 -0.3322 0.369880 3 to 12 142541 2.1782 0.985303 2 to 11 142502 2.0437 0.979508 1 to 10 142074 0.5678 0.714924 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-22_19:31 Bits used No. missing words z-score p-value 28 to 32 141796 -0.3842 0.350426 27 to 31 142038 0.4362 0.668643 26 to 30 141861 -0.1638 0.434932 25 to 29 141909 -0.0011 0.499554 24 to 28 142020 0.3752 0.646227 23 to 27 141743 -0.5638 0.286435 22 to 26 141678 -0.7842 0.216470 21 to 25 142280 1.2565 0.895534 20 to 24 141998 0.3006 0.618131 19 to 23 142046 0.4633 0.678421 18 to 22 141717 -0.6520 0.257212 17 to 21 142126 0.7345 0.768670 16 to 20 142100 0.6463 0.740970 15 to 19 141835 -0.2520 0.400534 14 to 18 142178 0.9107 0.818785 13 to 17 142411 1.7006 0.955489 12 to 16 141297 -2.0757 0.018961 11 to 15 141732 -0.6011 0.273881 10 to 14 142125 0.7311 0.767636 9 to 13 141828 -0.2757 0.391391 8 to 12 141868 -0.1401 0.444290 7 to 11 141646 -0.8926 0.186024 6 to 10 142284 1.2701 0.897970 5 to 9 142123 0.7243 0.765561 4 to 8 141631 -0.9435 0.172715 3 to 7 141591 -1.0791 0.140275 2 to 6 142245 1.1379 0.872411 1 to 5 141925 0.0531 0.521181 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-22_19:31 Bits used No. missing words z-score p-value 31 to 32 141428 -1.4199 0.077825 30 to 31 142203 0.8663 0.806833 29 to 30 142149 0.7070 0.760214 28 to 29 141842 -0.1986 0.421283 27 to 28 142373 1.3678 0.914306 26 to 27 141558 -1.0364 0.150014 25 to 26 142020 0.3265 0.627962 24 to 25 142093 0.5418 0.706022 23 to 24 141857 -0.1544 0.438661 22 to 23 141892 -0.0511 0.479615 21 to 22 142078 0.4976 0.690600 20 to 21 142197 0.8486 0.801944 19 to 20 142001 0.2704 0.606579 18 to 19 141882 -0.0806 0.467872 17 to 18 141726 -0.5408 0.294324 16 to 17 141067 -2.4847 0.006482 15 to 16 142140 0.6804 0.751888 14 to 15 141633 -0.8151 0.207498 13 to 14 141741 -0.4965 0.309754 12 to 13 142096 0.5506 0.709063 11 to 12 142045 0.4002 0.655498 10 to 11 142539 1.8574 0.968375 9 to 10 141955 0.1347 0.553583 8 to 9 141931 0.0639 0.525484 7 to 8 140985 -2.7266 0.003199 6 to 7 141439 -1.3874 0.082659 5 to 6 142303 1.1613 0.877234 4 to 5 141323 -1.7296 0.041852 3 to 4 142035 0.3707 0.644573 2 to 3 142288 1.1170 0.868007 1 to 2 141322 -1.7325 0.041589 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2564.06 0.906 0.817500 Test results for specific bytes for dh-ranFile-2018-06-22_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2443.31 -0.802 0.211347 2 to 9 2470.31 -0.420 0.337304 3 to 10 2529.75 0.421 0.663030 4 to 11 2544.14 0.624 0.733776 5 to 12 2540.25 0.569 0.715412 6 to 13 2507.54 0.107 0.542478 7 to 14 2597.99 1.386 0.917091 8 to 15 2451.48 -0.686 0.246282 9 to 16 2422.31 -1.099 0.135946 10 to 17 2480.21 -0.280 0.389812 11 to 18 2511.91 0.168 0.566871 12 to 19 2509.93 0.140 0.555829 13 to 20 2623.21 1.742 0.959282 14 to 21 2487.49 -0.177 0.429783 15 to 22 2538.41 0.543 0.706497 16 to 23 2426.70 -1.037 0.149946 17 to 24 2430.88 -0.978 0.164147 18 to 25 2462.00 -0.537 0.295507 19 to 26 2534.31 0.485 0.686253 20 to 27 2460.58 -0.557 0.288594 21 to 28 2511.40 0.161 0.564014 22 to 29 2528.00 0.396 0.653963 23 to 30 2448.64 -0.726 0.233806 24 to 31 2484.43 -0.220 0.412843 25 to 32 2420.41 -1.126 0.130186 CDPARK for dh-ranFile-2018-06-22_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 3559 1.6438 0.949895 3542 0.8676 0.807188 3530 0.3196 0.625377 3529 0.2740 0.607947 3520 -0.1370 0.445521 3492 -1.4155 0.078457 3526 0.1370 0.554479 3525 0.0913 0.536383 3512 -0.5023 0.307734 3485 -1.7352 0.041356 Square side=100, avg. no. parked=3522.00 sample std.=20.69 p-value of the KSTEST for those 10 p-values: 0.930641 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_19:31 0.4182,0.4754,0.0351,0.8480,0.2937,0.8676,0.7913,0.0623,0.7641,0.4521, The KS test for those 10 p-values: 0.866934 The 3DSPHERES test for dh-ranFile-2018-06-22_19:31 sample no r^3 equiv. uni. 1 31.613 0.651377 2 4.484 0.138827 3 9.820 0.279148 4 18.833 0.466222 5 4.531 0.140195 6 98.548 0.962557 7 71.671 0.908282 8 46.534 0.787991 9 20.835 0.500669 10 17.636 0.444488 11 2.489 0.079619 12 28.295 0.610603 13 18.065 0.452378 14 18.090 0.452831 15 2.441 0.078147 16 31.394 0.648828 17 7.834 0.229818 18 37.198 0.710595 19 22.947 0.534625 20 29.939 0.631366 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.806022 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -1.1 -1.9 -1.5 0.2 -1.4 -0.6 -1.0 -2.2 0.3 0.0 -0.9 -1.3 -0.3 -0.5 1.4 -0.7 0.1 2.1 -0.3 1.9 0.6 -1.5 0.6 1.7 -0.0 0.5 0.4 -0.3 -0.5 -0.3 1.8 0.9 -0.6 -0.8 -0.5 -1.3 -1.2 0.4 -1.3 0.0 1.8 Chi-square with 42 degrees of freedom:48.886013 z-score=0.751326, p-value=0.783970 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-22_19:31 Test no p-value 1 0.161264 2 0.123371 3 0.081537 4 0.015259 5 0.813101 6 0.002057 7 0.173738 8 0.000520 9 0.521709 10 0.528814 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000620 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_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 66644 0.01 66679 0.00 3 25000.00 25019 0.01 24974 0.03 4 6666.67 6652 0.03 6626 0.25 5 1388.89 1400 0.09 1425 0.94 6 238.10 245 0.20 249 0.50 7 34.72 34 0.01 37 0.15 8 4.96 5 0.00 9 3.29 p=0.00084 p=0.47604 Number of rngs required: 689364, p-value: 0.868 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_19:31 No. of wins: Observed Expected 98563 98585.9 z-score=-0.102, pvalue=0.45928 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66448 66666.7 0.717 0.717 2 37745 37654.3 0.218 0.936 3 26713 26954.7 2.168 3.103 4 19391 19313.5 0.311 3.415 5 13996 13851.4 1.509 4.924 6 9881 9943.5 0.393 5.317 7 7237 7145.0 1.184 6.501 8 5130 5139.1 0.016 6.517 9 3856 3699.9 6.589 13.106 10 2620 2666.3 0.804 13.910 11 1998 1923.3 2.899 16.809 12 1419 1388.7 0.659 17.468 13 918 1003.7 7.320 24.788 14 767 726.1 2.299 27.087 15 493 525.8 2.050 29.138 16 367 381.2 0.525 29.663 17 264 276.5 0.569 30.232 18 191 200.8 0.481 30.713 19 165 146.0 2.477 33.190 20 105 106.2 0.014 33.204 21 296 287.1 0.275 33.479 Chisq= 33.48 for 20 degrees of freedom, p= 0.97013 SUMMARY of craptest p-value for no. of wins: 0.459284 p-value for throws/game: 0.970126 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_19:31 No. of wins: Observed Expected 99089 98585.9 z-score= 2.250, pvalue=0.98779 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66841 66666.7 0.456 0.456 2 37460 37654.3 1.003 1.459 3 26864 26954.7 0.305 1.764 4 19147 19313.5 1.435 3.199 5 13805 13851.4 0.156 3.354 6 9969 9943.5 0.065 3.420 7 7266 7145.0 2.048 5.468 8 5083 5139.1 0.612 6.080 9 3846 3699.9 5.772 11.852 10 2706 2666.3 0.591 12.443 11 1932 1923.3 0.039 12.482 12 1411 1388.7 0.357 12.839 13 1061 1003.7 3.269 16.108 14 755 726.1 1.147 17.255 15 531 525.8 0.051 17.306 16 347 381.2 3.060 20.366 17 259 276.5 1.112 21.478 18 194 200.8 0.232 21.710 19 143 146.0 0.061 21.771 20 99 106.2 0.490 22.261 21 281 287.1 0.130 22.392 Chisq= 22.39 for 20 degrees of freedom, p= 0.68036 SUMMARY of craptest p-value for no. of wins: 0.987786 p-value for throws/game: 0.680360 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0006,0.0008,0.0016,0.0021,0.0032,0.0040,0.0065,0.0119,0.0127, 0.0153,0.0190,0.0221,0.0221,0.0271,0.0300,0.0351,0.0362,0.0404,0.0414, 0.0416,0.0419,0.0485,0.0492,0.0500,0.0623,0.0778,0.0781,0.0785,0.0796, 0.0815,0.0827,0.0858,0.1059,0.1071,0.1117,0.1234,0.1302,0.1359,0.1388, 0.1402,0.1403,0.1448,0.1499,0.1500,0.1613,0.1641,0.1654,0.1727,0.1733, 0.1737,0.1860,0.1940,0.1977,0.1993,0.2075,0.2100,0.2113,0.2115,0.2165, 0.2188,0.2206,0.2206,0.2298,0.2338,0.2340,0.2447,0.2463,0.2479,0.2572, 0.2684,0.2715,0.2739,0.2791,0.2855,0.2864,0.2886,0.2937,0.2943,0.2944, 0.2955,0.2975,0.3033,0.3077,0.3098,0.3150,0.3187,0.3319,0.3373,0.3414, 0.3436,0.3467,0.3493,0.3504,0.3556,0.3647,0.3653,0.3699,0.3795,0.3806, 0.3898,0.3914,0.3929,0.3938,0.4005,0.4036,0.4088,0.4128,0.4182,0.4210, 0.4213,0.4298,0.4320,0.4342,0.4349,0.4375,0.4387,0.4411,0.4423,0.4443, 0.4445,0.4455,0.4482,0.4491,0.4521,0.4524,0.4528,0.4593,0.4662,0.4679, 0.4727,0.4754,0.4760,0.4796,0.4967,0.4996,0.4997,0.5007,0.5084,0.5127, 0.5127,0.5202,0.5212,0.5217,0.5255,0.5288,0.5341,0.5346,0.5364,0.5373, 0.5425,0.5462,0.5536,0.5545,0.5558,0.5640,0.5669,0.5794,0.5911,0.6039, 0.6063,0.6066,0.6079,0.6106,0.6181,0.6227,0.6254,0.6280,0.6290,0.6314, 0.6446,0.6462,0.6488,0.6499,0.6514,0.6540,0.6555,0.6630,0.6630,0.6676, 0.6686,0.6782,0.6784,0.6786,0.6800,0.6804,0.6863,0.6887,0.6906,0.7010, 0.7060,0.7065,0.7091,0.7106,0.7130,0.7149,0.7154,0.7220,0.7243,0.7338, 0.7410,0.7519,0.7588,0.7602,0.7641,0.7656,0.7676,0.7687,0.7840,0.7880, 0.7913,0.7924,0.7996,0.8016,0.8019,0.8060,0.8068,0.8072,0.8131,0.8175, 0.8188,0.8237,0.8480,0.8656,0.8669,0.8676,0.8676,0.8680,0.8724,0.8742, 0.8742,0.8756,0.8772,0.8788,0.8799,0.8845,0.8847,0.8899,0.8947,0.8955, 0.8980,0.8988,0.9026,0.9083,0.9090,0.9143,0.9171,0.9231,0.9305,0.9306, 0.9365,0.9499,0.9539,0.9555,0.9563,0.9593,0.9595,0.9626,0.9684,0.9701, 0.9709,0.9709,0.9795,0.9822,0.9842,0.9853,0.9878,0.9901,0.9952, Overall p-value after applying KStest on 269 p-values = 0.413250 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.