RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-25_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 8.2253 0.038511 2 to 25 15.43 22.2673 0.825345 3 to 26 15.75 18.7300 0.655751 4 to 27 15.81 11.9051 0.194148 5 to 28 16.06 11.8260 0.189443 6 to 29 15.99 20.0898 0.730336 7 to 30 15.93 7.6109 0.025825 8 to 31 15.93 14.2143 0.348122 9 to 32 15.54 21.6952 0.803275 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.448309 Tough bday spacings test for dh-ranFile-2015-08-25_16:31: 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 42 72 116 94 69 46 26 15 10 1 (O-E)^2/E 0.0 0.8 0.0 3.4 0.1 1.1 0.7 0.5 0.0 1.7 2.3 Birthday Spacings: Sum(O-E)^2/E= 10.691, p= 0.618 RESULTS OF GCD FOR dh-ranFile-2015-08-25_16:31 Euclid's algorithm: p-value, steps to gcd: 0.442900 p-value, dist. of gcd's: 0.252444 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-25_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.491 0.431 0.891 0.416 0.270 0.721 0.964 0.978 Bits 8 to 15---> 0.802 0.433 0.762 0.988 0.781 0.778 0.296 0.122 Bits 16 to 23---> 0.662 0.714 0.628 0.961 0.113 0.116 0.210 0.623 Bits 24 to 31---> 0.764 0.162 0.619 0.078 0.063 0.136 0.979 0.866 KS test for the above 32 p values: 0.767 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-25_16:31, p-values for 5 runs: 0.7352, 0.4547, 0.7408, 0.5496, 0.2971 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-25_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5186 5134.0 0.526 0.721 r= 30 22973 23103.0 0.732 1.453 r= 31 11636 11551.5 0.618 2.071 chi-square = 2.071 with df = 3; p-value = 0.442 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-25_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5173 5134.0 0.296 0.631 r= 31 23090 23103.0 0.007 0.639 r= 32 11534 11551.5 0.027 0.665 chi-square = 0.665 with df = 3; p-value = 0.119 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-25_16:31 b-rank test for bits 1 to 8, p=0.91312 b-rank test for bits 2 to 9, p=0.82181 b-rank test for bits 3 to 10, p=0.29279 b-rank test for bits 4 to 11, p=0.22681 b-rank test for bits 5 to 12, p=0.68869 b-rank test for bits 6 to 13, p=0.29346 b-rank test for bits 7 to 14, p=0.48826 b-rank test for bits 8 to 15, p=0.65501 b-rank test for bits 9 to 16, p=0.84204 b-rank test for bits 10 to 17, p=0.97262 b-rank test for bits 11 to 18, p=0.30098 b-rank test for bits 12 to 19, p=0.99107 b-rank test for bits 13 to 20, p=0.83432 b-rank test for bits 14 to 21, p=0.77127 b-rank test for bits 15 to 22, p=0.24416 b-rank test for bits 16 to 23, p=0.04988 b-rank test for bits 17 to 24, p=0.68294 b-rank test for bits 18 to 25, p=0.93582 b-rank test for bits 19 to 26, p=0.39242 b-rank test for bits 20 to 27, p=0.11177 b-rank test for bits 21 to 28, p=0.13997 b-rank test for bits 22 to 29, p=0.80620 b-rank test for bits 23 to 30, p=0.21987 b-rank test for bits 24 to 31, p=0.48491 b-rank test for bits 25 to 32, p=0.89586 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 = 0.364732 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-25_16:31 (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 141754 -0.36 0.358332 2 142707 1.86 0.968819 3 142607 1.63 0.948457 4 142176 0.62 0.733378 5 141631 -0.65 0.257748 6 142499 1.38 0.915857 7 141790 -0.28 0.390196 8 141942 0.08 0.530422 9 141786 -0.29 0.386614 10 141940 0.07 0.528563 11 141689 -0.51 0.303350 12 141644 -0.62 0.267652 13 142553 1.50 0.933697 14 141916 0.02 0.506217 15 141568 -0.80 0.212580 16 142208 0.70 0.757357 17 142135 0.53 0.700996 18 142342 1.01 0.843971 19 141841 -0.16 0.436579 20 141832 -0.18 0.428310 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-25_16:31 Bits used No. missing words z-score p-value 23 to 32 141978 0.2368 0.593591 22 to 31 141729 -0.6218 0.267028 21 to 30 142110 0.6920 0.755521 20 to 29 141882 -0.0942 0.462459 19 to 28 142122 0.7333 0.768326 18 to 27 141548 -1.2460 0.106389 17 to 26 141757 -0.5253 0.299696 16 to 25 142040 0.4506 0.673856 15 to 24 142102 0.6644 0.746776 14 to 23 141852 -0.1977 0.421644 13 to 22 141827 -0.2839 0.388245 12 to 21 141238 -2.3149 0.010308 11 to 20 141950 0.1402 0.555765 10 to 19 141359 -1.8977 0.028868 9 to 18 141828 -0.2804 0.389567 8 to 17 141485 -1.4632 0.071705 7 to 16 141775 -0.4632 0.321608 6 to 15 141744 -0.5701 0.284304 5 to 14 142110 0.6920 0.755521 4 to 13 141814 -0.3287 0.371182 3 to 12 142172 0.9058 0.817468 2 to 11 141968 0.2023 0.580163 1 to 10 142377 1.6127 0.946590 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-25_16:31 Bits used No. missing words z-score p-value 28 to 32 141772 -0.4655 0.320778 27 to 31 142057 0.5006 0.691665 26 to 30 141636 -0.9265 0.177082 25 to 29 142162 0.8565 0.804142 24 to 28 141507 -1.3638 0.086310 23 to 27 141144 -2.5943 0.004739 22 to 26 141892 -0.0587 0.476577 21 to 25 141996 0.2938 0.615543 20 to 24 141708 -0.6825 0.247470 19 to 23 142755 2.8667 0.997926 18 to 22 142181 0.9209 0.821453 17 to 21 141966 0.1921 0.576169 16 to 20 141864 -0.1537 0.438939 15 to 19 141327 -1.9740 0.024191 14 to 18 142167 0.8735 0.808793 13 to 17 141844 -0.2215 0.412368 12 to 16 141896 -0.0452 0.481979 11 to 15 142180 0.9175 0.820566 10 to 14 141775 -0.4554 0.324427 9 to 13 141440 -1.5909 0.055811 8 to 12 141786 -0.4181 0.337949 7 to 11 141631 -0.9435 0.172715 6 to 10 142008 0.3345 0.630989 5 to 9 142189 0.9480 0.828444 4 to 8 142128 0.7413 0.770730 3 to 7 141809 -0.3401 0.366890 2 to 6 141708 -0.6825 0.247470 1 to 5 141720 -0.6418 0.260503 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-25_16:31 Bits used No. missing words z-score p-value 31 to 32 142055 0.4297 0.666295 30 to 31 141888 -0.0629 0.474915 29 to 30 142508 1.7660 0.961301 28 to 29 141866 -0.1278 0.449147 27 to 28 141512 -1.1721 0.120586 26 to 27 141947 0.1111 0.544240 25 to 26 142018 0.3206 0.625728 24 to 25 141674 -0.6942 0.243782 23 to 24 142019 0.3235 0.626846 22 to 23 141989 0.2350 0.592901 21 to 22 142016 0.3147 0.623490 20 to 21 142632 2.1318 0.983487 19 to 20 141580 -0.9715 0.165656 18 to 19 142011 0.2999 0.617878 17 to 18 141568 -1.0069 0.156998 16 to 17 141715 -0.5732 0.283240 15 to 16 141765 -0.4258 0.335144 14 to 15 142143 0.6893 0.754680 13 to 14 141903 -0.0187 0.492551 12 to 13 142520 1.8014 0.964179 11 to 12 141886 -0.0688 0.472566 10 to 11 142031 0.3589 0.640168 9 to 10 141490 -1.2370 0.108051 8 to 9 142395 1.4327 0.924022 7 to 8 141325 -1.7237 0.042382 6 to 7 141758 -0.4464 0.327654 5 to 6 141711 -0.5850 0.279259 4 to 5 142125 0.6362 0.737675 3 to 4 142154 0.7217 0.764773 2 to 3 141595 -0.9272 0.176904 1 to 2 142182 0.8043 0.789399 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-25_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2455.11 -0.635 0.262748 Test results for specific bytes for dh-ranFile-2015-08-25_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2407.66 -1.306 0.095789 2 to 9 2391.03 -1.541 0.061651 3 to 10 2398.99 -1.429 0.076570 4 to 11 2479.05 -0.296 0.383502 5 to 12 2450.36 -0.702 0.241322 6 to 13 2499.37 -0.009 0.496446 7 to 14 2467.78 -0.456 0.324317 8 to 15 2534.95 0.494 0.689424 9 to 16 2556.23 0.795 0.786747 10 to 17 2570.09 0.991 0.839215 11 to 18 2419.40 -1.140 0.127164 12 to 19 2513.47 0.190 0.575516 13 to 20 2491.71 -0.117 0.453340 14 to 21 2517.68 0.250 0.598720 15 to 22 2510.39 0.147 0.558430 16 to 23 2571.38 1.009 0.843611 17 to 24 2459.29 -0.576 0.282401 18 to 25 2522.11 0.313 0.622764 19 to 26 2491.53 -0.120 0.452325 20 to 27 2412.63 -1.236 0.108311 21 to 28 2415.08 -1.201 0.114895 22 to 29 2381.67 -1.673 0.047124 23 to 30 2380.98 -1.683 0.046171 24 to 31 2582.50 1.167 0.878334 25 to 32 2555.46 0.784 0.783560 CDPARK for dh-ranFile-2015-08-25_16:31: 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 3543 0.9132 0.819442 3499 -1.0959 0.136563 3546 1.0502 0.853193 3488 -1.5982 0.055002 3510 -0.5936 0.276387 3489 -1.5525 0.060270 3519 -0.1826 0.427537 3548 1.1416 0.873180 3518 -0.2283 0.409702 3533 0.4566 0.676028 Square side=100, avg. no. parked=3519.30 sample std.=21.64 p-value of the KSTEST for those 10 p-values: 0.783549 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-25_16:31 0.3249,0.5433,0.9389,0.9958,0.6973,0.9855,0.1020,0.7151,0.3399,0.0731, The KS test for those 10 p-values: 0.245738 The 3DSPHERES test for dh-ranFile-2015-08-25_16:31 sample no r^3 equiv. uni. 1 84.761 0.940712 2 23.874 0.548778 3 96.542 0.959968 4 15.714 0.407743 5 27.392 0.598709 6 2.679 0.085434 7 94.898 0.957712 8 21.847 0.517243 9 101.168 0.965688 10 2.862 0.090990 11 21.953 0.518946 12 72.062 0.909469 13 24.068 0.551696 14 18.533 0.460854 15 20.752 0.499288 16 13.233 0.356666 17 12.893 0.349346 18 26.534 0.587068 19 20.400 0.493391 20 2.827 0.089920 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.272975 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-25_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 1.1 -0.3 0.0 0.3 0.1 0.4 -0.2 1.8 -1.4 0.6 -0.8 0.7 0.5 0.5 0.0 -0.6 1.1 -0.6 -1.5 -0.7 0.2 1.0 0.8 1.6 -1.0 -1.4 -1.4 -1.8 -1.1 0.1 1.5 -0.2 1.0 0.6 1.4 -0.1 -2.0 -0.1 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:42.942023 z-score=0.102783, p-value=0.569347 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-25_16:31 Test no p-value 1 0.488188 2 0.261011 3 0.012550 4 0.355853 5 0.631545 6 0.810574 7 0.204619 8 0.465334 9 0.203753 10 0.397468 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.278904 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-25_16:31: (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 66510 0.37 66676 0.00 3 25000.00 25113 0.51 24892 0.47 4 6666.67 6724 0.49 6754 1.14 5 1388.89 1377 0.10 1420 0.70 6 238.10 233 0.11 222 1.09 7 34.72 38 0.31 28 1.30 8 4.96 4 0.19 7 0.84 p=0.08766 p=0.52293 Number of rngs required: 688051, p-value: 0.343 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-25_16:31 No. of wins: Observed Expected 98302 98585.9 z-score=-1.270, pvalue=0.10212 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66722 66666.7 0.046 0.046 2 37463 37654.3 0.972 1.018 3 27082 26954.7 0.601 1.619 4 19476 19313.5 1.368 2.987 5 13680 13851.4 2.121 5.108 6 10016 9943.5 0.528 5.636 7 7204 7145.0 0.487 6.123 8 5073 5139.1 0.849 6.972 9 3720 3699.9 0.110 7.082 10 2638 2666.3 0.300 7.382 11 2005 1923.3 3.468 10.850 12 1308 1388.7 4.694 15.545 13 998 1003.7 0.033 15.577 14 733 726.1 0.065 15.642 15 529 525.8 0.019 15.661 16 386 381.2 0.062 15.723 17 263 276.5 0.663 16.386 18 187 200.8 0.952 17.338 19 133 146.0 1.155 18.493 20 117 106.2 1.095 19.588 21 267 287.1 1.409 20.997 Chisq= 21.00 for 20 degrees of freedom, p= 0.60269 SUMMARY of craptest p-value for no. of wins: 0.102117 p-value for throws/game: 0.602688 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-25_16:31 No. of wins: Observed Expected 98575 98585.9 z-score=-0.049, pvalue=0.48063 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66758 66666.7 0.125 0.125 2 37343 37654.3 2.574 2.699 3 26913 26954.7 0.065 2.764 4 19319 19313.5 0.002 2.765 5 13915 13851.4 0.292 3.057 6 10047 9943.5 1.076 4.134 7 7160 7145.0 0.031 4.165 8 5065 5139.1 1.068 5.233 9 3683 3699.9 0.077 5.309 10 2781 2666.3 4.934 10.244 11 1990 1923.3 2.311 12.555 12 1372 1388.7 0.202 12.757 13 972 1003.7 1.002 13.759 14 738 726.1 0.194 13.953 15 527 525.8 0.003 13.955 16 406 381.2 1.620 15.575 17 299 276.5 1.824 17.399 18 187 200.8 0.952 18.352 19 139 146.0 0.334 18.686 20 99 106.2 0.490 19.176 21 287 287.1 0.000 19.176 Chisq= 19.18 for 20 degrees of freedom, p= 0.48960 SUMMARY of craptest p-value for no. of wins: 0.480633 p-value for throws/game: 0.489599 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0047,0.0103,0.0125,0.0242,0.0258,0.0289,0.0385,0.0424,0.0462,0.0471, 0.0499,0.0550,0.0558,0.0603,0.0617,0.0628,0.0717,0.0731,0.0766,0.0783, 0.0854,0.0863,0.0877,0.0899,0.0910,0.0958,0.1020,0.1021,0.1064,0.1081, 0.1083,0.1118,0.1130,0.1149,0.1160,0.1187,0.1206,0.1221,0.1272,0.1357, 0.1366,0.1400,0.1570,0.1622,0.1657,0.1727,0.1769,0.1771,0.1894,0.1941, 0.2038,0.2046,0.2095,0.2126,0.2199,0.2268,0.2413,0.2438,0.2442,0.2457, 0.2475,0.2475,0.2524,0.2577,0.2605,0.2610,0.2627,0.2670,0.2677,0.2696, 0.2730,0.2764,0.2789,0.2793,0.2824,0.2832,0.2843,0.2928,0.2935,0.2960, 0.2971,0.2997,0.3010,0.3034,0.3208,0.3216,0.3243,0.3244,0.3249,0.3277, 0.3351,0.3379,0.3399,0.3426,0.3481,0.3493,0.3559,0.3567,0.3583,0.3647, 0.3669,0.3712,0.3835,0.3866,0.3882,0.3896,0.3902,0.3924,0.3975,0.4077, 0.4097,0.4124,0.4163,0.4216,0.4275,0.4283,0.4308,0.4328,0.4366,0.4389, 0.4422,0.4429,0.4483,0.4491,0.4523,0.4533,0.4547,0.4609,0.4625,0.4653, 0.4726,0.4749,0.4766,0.4806,0.4820,0.4849,0.4882,0.4883,0.4896,0.4913, 0.4926,0.4934,0.4964,0.4993,0.5062,0.5172,0.5189,0.5229,0.5286,0.5304, 0.5433,0.5442,0.5488,0.5496,0.5517,0.5558,0.5584,0.5693,0.5755,0.5762, 0.5802,0.5871,0.5929,0.5936,0.5987,0.5987,0.6027,0.6155,0.6179,0.6179, 0.6186,0.6228,0.6232,0.6235,0.6257,0.6268,0.6277,0.6310,0.6315,0.6402, 0.6550,0.6558,0.6619,0.6663,0.6739,0.6760,0.6829,0.6887,0.6894,0.6917, 0.6973,0.7010,0.7135,0.7151,0.7209,0.7303,0.7334,0.7352,0.7377,0.7408, 0.7468,0.7547,0.7555,0.7555,0.7574,0.7618,0.7639,0.7648,0.7666,0.7683, 0.7707,0.7713,0.7781,0.7812,0.7835,0.7836,0.7867,0.7894,0.8022,0.8033, 0.8041,0.8062,0.8088,0.8106,0.8175,0.8194,0.8206,0.8215,0.8218,0.8253, 0.8284,0.8343,0.8392,0.8420,0.8436,0.8440,0.8532,0.8662,0.8732,0.8783, 0.8914,0.8959,0.9095,0.9131,0.9159,0.9240,0.9337,0.9358,0.9389,0.9407, 0.9466,0.9485,0.9577,0.9600,0.9611,0.9613,0.9642,0.9643,0.9657,0.9688, 0.9726,0.9782,0.9793,0.9835,0.9855,0.9878,0.9911,0.9958,0.9979, Overall p-value after applying KStest on 269 p-values = 0.854114 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.