RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-05_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 14.3271 0.356170 2 to 25 15.33 33.5367 0.990370 3 to 26 15.83 14.9209 0.398823 4 to 27 15.68 12.9212 0.258558 5 to 28 15.56 19.2507 0.685664 6 to 29 15.57 22.3904 0.829833 7 to 30 15.84 26.2623 0.930188 8 to 31 15.70 19.5821 0.703839 9 to 32 16.02 19.9932 0.725422 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.174430 Tough bday spacings test for dh-ranFile-2015-08-05_07:31: 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 8 41 69 78 100 91 50 31 23 4 5 (O-E)^2/E 0.1 0.5 0.2 4.0 0.1 2.1 0.1 0.1 4.4 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.859, p= 0.768 RESULTS OF GCD FOR dh-ranFile-2015-08-05_07:31 Euclid's algorithm: p-value, steps to gcd: 0.606054 p-value, dist. of gcd's: 0.373808 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-05_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.605 0.484 0.108 0.738 0.438 0.146 0.111 0.282 Bits 8 to 15---> 0.482 0.680 0.745 0.212 0.231 0.551 0.028 0.257 Bits 16 to 23---> 0.686 0.617 0.926 0.323 0.474 0.599 0.276 0.762 Bits 24 to 31---> 0.272 0.189 0.434 0.784 0.399 0.298 0.844 0.920 KS test for the above 32 p values: 0.460 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-05_07:31, p-values for 5 runs: 0.7662, 0.2293, 0.0829, 0.4843, 0.7575 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-05_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5150 5134.0 0.050 0.322 r= 30 23158 23103.0 0.131 0.452 r= 31 11473 11551.5 0.534 0.986 chi-square = 0.986 with df = 3; p-value = 0.195 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-05_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5159 5134.0 0.122 1.127 r= 31 23179 23103.0 0.250 1.377 r= 32 11436 11551.5 1.155 2.532 chi-square = 2.532 with df = 3; p-value = 0.531 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-05_07:31 b-rank test for bits 1 to 8, p=0.05526 b-rank test for bits 2 to 9, p=0.54337 b-rank test for bits 3 to 10, p=0.06558 b-rank test for bits 4 to 11, p=0.61671 b-rank test for bits 5 to 12, p=0.01178 b-rank test for bits 6 to 13, p=0.73653 b-rank test for bits 7 to 14, p=0.24274 b-rank test for bits 8 to 15, p=0.28253 b-rank test for bits 9 to 16, p=0.43542 b-rank test for bits 10 to 17, p=0.15866 b-rank test for bits 11 to 18, p=0.01838 b-rank test for bits 12 to 19, p=0.25893 b-rank test for bits 13 to 20, p=0.33511 b-rank test for bits 14 to 21, p=0.72229 b-rank test for bits 15 to 22, p=0.04927 b-rank test for bits 16 to 23, p=0.44461 b-rank test for bits 17 to 24, p=0.49150 b-rank test for bits 18 to 25, p=0.64567 b-rank test for bits 19 to 26, p=0.01561 b-rank test for bits 20 to 27, p=0.37722 b-rank test for bits 21 to 28, p=0.23656 b-rank test for bits 22 to 29, p=0.39277 b-rank test for bits 23 to 30, p=0.76579 b-rank test for bits 24 to 31, p=0.39686 b-rank test for bits 25 to 32, p=0.56353 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 = 0.012692 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-05_07:31 (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 141228 -1.59 0.055704 2 140780 -2.64 0.004162 3 142019 0.26 0.601117 4 141727 -0.43 0.335052 5 141548 -0.84 0.199271 6 141896 -0.03 0.487577 7 141596 -0.73 0.232060 8 141968 0.14 0.554516 9 142318 0.95 0.830170 10 141894 -0.04 0.485714 11 141867 -0.10 0.460608 12 141884 -0.06 0.476404 13 141912 0.01 0.502489 14 141824 -0.20 0.420987 15 141501 -0.95 0.170031 16 142197 0.67 0.749248 17 141576 -0.78 0.218046 18 141352 -1.30 0.096429 19 141929 0.05 0.518328 20 141614 -0.69 0.245090 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-05_07:31 Bits used No. missing words z-score p-value 23 to 32 141584 -1.1218 0.130968 22 to 31 142123 0.7368 0.769376 21 to 30 142123 0.7368 0.769376 20 to 29 142085 0.6058 0.727663 19 to 28 142308 1.3747 0.915392 18 to 27 141833 -0.2632 0.396196 17 to 26 141808 -0.3494 0.363389 16 to 25 141315 -2.0494 0.020211 15 to 24 141642 -0.9218 0.178309 14 to 23 141820 -0.3080 0.379028 13 to 22 141696 -0.7356 0.230981 12 to 21 141841 -0.2356 0.406864 11 to 20 141766 -0.4942 0.310568 10 to 19 141833 -0.2632 0.396196 9 to 18 141353 -1.9184 0.027531 8 to 17 141880 -0.1011 0.459721 7 to 16 141864 -0.1563 0.437894 6 to 15 142127 0.7506 0.773549 5 to 14 141589 -1.1046 0.134669 4 to 13 142063 0.5299 0.701908 3 to 12 141438 -1.6253 0.052052 2 to 11 142593 2.3575 0.990800 1 to 10 141851 -0.2011 0.420295 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-05_07:31 Bits used No. missing words z-score p-value 28 to 32 142110 0.6802 0.751823 27 to 31 141968 0.1989 0.578822 26 to 30 141786 -0.4181 0.337949 25 to 29 142451 1.8362 0.966834 24 to 28 142344 1.4735 0.929686 23 to 27 142196 0.9718 0.834416 22 to 26 141790 -0.4045 0.342919 21 to 25 141998 0.3006 0.618131 20 to 24 141744 -0.5604 0.287589 19 to 23 141947 0.1277 0.550805 18 to 22 141730 -0.6079 0.271628 17 to 21 142105 0.6633 0.746427 16 to 20 142126 0.7345 0.768670 15 to 19 141925 0.0531 0.521181 14 to 18 142304 1.3379 0.909530 13 to 17 141663 -0.8350 0.201854 12 to 16 141912 0.0091 0.503611 11 to 15 141938 0.0972 0.538711 10 to 14 141727 -0.6181 0.268265 9 to 13 141991 0.2768 0.609051 8 to 12 142377 1.5853 0.943553 7 to 11 142330 1.4260 0.923066 6 to 10 142313 1.3684 0.914402 5 to 9 141764 -0.4926 0.311132 4 to 8 142289 1.2870 0.900956 3 to 7 142121 0.7175 0.763475 2 to 6 142169 0.8802 0.810635 1 to 5 142481 1.9379 0.973680 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-05_07:31 Bits used No. missing words z-score p-value 31 to 32 141306 -1.7797 0.037560 30 to 31 141781 -0.3786 0.352509 29 to 30 141550 -1.0600 0.144579 28 to 29 141331 -1.7060 0.044005 27 to 28 142007 0.2881 0.613370 26 to 27 141098 -2.3933 0.008349 25 to 26 141918 0.0256 0.510202 24 to 25 142180 0.7984 0.787691 23 to 24 141728 -0.5349 0.296361 22 to 23 142015 0.3117 0.622370 21 to 22 141949 0.1170 0.546578 20 to 21 142276 1.0816 0.860290 19 to 20 141617 -0.8623 0.194253 18 to 19 142428 1.5300 0.936992 17 to 18 141954 0.1318 0.552417 16 to 17 141700 -0.6175 0.268455 15 to 16 141789 -0.3550 0.361311 14 to 15 142137 0.6716 0.749079 13 to 14 141832 -0.2281 0.409780 12 to 13 142426 1.5241 0.936258 11 to 12 142294 1.1347 0.871754 10 to 11 141970 0.1790 0.571018 9 to 10 141219 -2.0364 0.020857 8 to 9 142457 1.6155 0.946904 7 to 8 142046 0.4032 0.656583 6 to 7 141249 -1.9479 0.025715 5 to 6 141686 -0.6588 0.255015 4 to 5 141362 -1.6145 0.053205 3 to 4 141897 -0.0364 0.485493 2 to 3 142274 1.0757 0.858974 1 to 2 142054 0.4268 0.665221 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-05_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2554.30 0.768 0.778724 Test results for specific bytes for dh-ranFile-2015-08-05_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2450.10 -0.706 0.240194 2 to 9 2480.67 -0.273 0.392300 3 to 10 2546.84 0.662 0.746126 4 to 11 2520.46 0.289 0.613869 5 to 12 2531.69 0.448 0.673004 6 to 13 2573.45 1.039 0.850535 7 to 14 2520.19 0.286 0.612392 8 to 15 2510.96 0.155 0.561587 9 to 16 2549.50 0.700 0.758032 10 to 17 2392.80 -1.516 0.064750 11 to 18 2496.89 -0.044 0.482461 12 to 19 2613.83 1.610 0.946276 13 to 20 2421.40 -1.112 0.133159 14 to 21 2562.29 0.881 0.810812 15 to 22 2380.41 -1.691 0.045400 16 to 23 2428.80 -1.007 0.156982 17 to 24 2447.07 -0.749 0.227061 18 to 25 2613.86 1.610 0.946327 19 to 26 2407.56 -1.307 0.095565 20 to 27 2450.21 -0.704 0.240694 21 to 28 2398.00 -1.442 0.074585 22 to 29 2424.38 -1.069 0.142447 23 to 30 2505.98 0.085 0.533697 24 to 31 2553.17 0.752 0.773956 25 to 32 2528.15 0.398 0.654717 CDPARK for dh-ranFile-2015-08-05_07:31: 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 3496 -1.2329 0.108811 3531 0.3653 0.642555 3560 1.6895 0.954438 3529 0.2740 0.607947 3524 0.0457 0.518210 3515 -0.3653 0.357445 3519 -0.1826 0.427537 3516 -0.3196 0.374623 3522 -0.0457 0.481790 3540 0.7763 0.781201 Square side=100, avg. no. parked=3525.20 sample std.=16.03 p-value of the KSTEST for those 10 p-values: 0.716110 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-05_07:31 0.4040,0.3958,0.9497,0.8589,0.1248,0.9451,0.5327,0.5284,0.2671,0.1230, The KS test for those 10 p-values: 0.823379 The 3DSPHERES test for dh-ranFile-2015-08-05_07:31 sample no r^3 equiv. uni. 1 29.851 0.630290 2 3.045 0.096513 3 1.659 0.053811 4 5.038 0.154580 5 25.955 0.579016 6 42.388 0.756573 7 28.150 0.608727 8 86.151 0.943398 9 0.198 0.006583 10 6.532 0.195669 11 4.690 0.144722 12 39.688 0.733648 13 20.109 0.488447 14 34.165 0.679807 15 34.951 0.688088 16 7.465 0.220296 17 41.046 0.745433 18 49.263 0.806428 19 21.142 0.505756 20 19.113 0.471173 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.671303 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-05_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 1.8 -0.3 -0.3 0.4 0.8 -1.2 0.7 -0.4 -0.8 -0.2 0.2 2.3 1.4 -0.6 0.8 -0.2 -0.9 -0.7 0.6 -1.1 0.1 -1.6 1.0 -0.9 -0.4 0.5 -0.2 -0.5 -0.0 0.6 0.9 -0.5 1.2 -0.5 0.3 -0.7 0.1 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:30.808176 z-score=-1.221128, p-value=0.101012 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-05_07:31 Test no p-value 1 0.478286 2 0.498050 3 0.533971 4 0.067973 5 0.427785 6 0.665063 7 0.037791 8 0.014081 9 0.695689 10 0.115886 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.099277 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-05_07:31: (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 66771 0.16 66686 0.01 3 25000.00 24794 1.70 24991 0.00 4 6666.67 6684 0.05 6627 0.24 5 1388.89 1468 4.51 1427 1.05 6 238.10 254 1.06 232 0.16 7 34.72 26 2.19 32 0.21 8 4.96 2 1.77 4 0.19 p=0.92406 p=0.06666 Number of rngs required: 688025, p-value: 0.332 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-05_07:31 No. of wins: Observed Expected 98518 98585.9 z-score=-0.304, pvalue=0.38075 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66558 66666.7 0.177 0.177 2 37514 37654.3 0.523 0.700 3 26971 26954.7 0.010 0.710 4 19245 19313.5 0.243 0.953 5 13665 13851.4 2.509 3.461 6 9997 9943.5 0.287 3.749 7 7226 7145.0 0.918 4.667 8 5194 5139.1 0.587 5.254 9 3760 3699.9 0.977 6.231 10 2774 2666.3 4.351 10.582 11 1975 1923.3 1.388 11.970 12 1418 1388.7 0.616 12.586 13 967 1003.7 1.343 13.929 14 746 726.1 0.543 14.472 15 533 525.8 0.098 14.570 16 404 381.2 1.370 15.940 17 296 276.5 1.369 17.309 18 182 200.8 1.765 19.075 19 150 146.0 0.110 19.185 20 120 106.2 1.789 20.974 21 305 287.1 1.114 22.088 Chisq= 22.09 for 20 degrees of freedom, p= 0.66427 SUMMARY of craptest p-value for no. of wins: 0.380753 p-value for throws/game: 0.664267 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-05_07:31 No. of wins: Observed Expected 98650 98585.9 z-score= 0.287, pvalue=0.61290 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66369 66666.7 1.329 1.329 2 37652 37654.3 0.000 1.329 3 27130 26954.7 1.140 2.469 4 19158 19313.5 1.251 3.720 5 13996 13851.4 1.509 5.229 6 9929 9943.5 0.021 5.251 7 7259 7145.0 1.818 7.069 8 5202 5139.1 0.771 7.839 9 3791 3699.9 2.245 10.084 10 2614 2666.3 1.026 11.110 11 1879 1923.3 1.022 12.132 12 1414 1388.7 0.459 12.591 13 1019 1003.7 0.233 12.824 14 696 726.1 1.251 14.075 15 534 525.8 0.127 14.202 16 352 381.2 2.229 16.431 17 269 276.5 0.206 16.637 18 194 200.8 0.232 16.869 19 158 146.0 0.989 17.858 20 103 106.2 0.097 17.955 21 282 287.1 0.091 18.046 Chisq= 18.05 for 20 degrees of freedom, p= 0.41564 SUMMARY of craptest p-value for no. of wins: 0.612897 p-value for throws/game: 0.415640 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0066,0.0083,0.0118,0.0127,0.0141,0.0156,0.0184,0.0202,0.0209, 0.0257,0.0275,0.0282,0.0376,0.0378,0.0440,0.0454,0.0493,0.0521,0.0532, 0.0538,0.0553,0.0557,0.0648,0.0656,0.0667,0.0680,0.0746,0.0829,0.0956, 0.0964,0.0965,0.0993,0.1010,0.1082,0.1088,0.1106,0.1159,0.1230,0.1248, 0.1310,0.1332,0.1347,0.1424,0.1446,0.1447,0.1463,0.1546,0.1570,0.1587, 0.1700,0.1744,0.1783,0.1886,0.1943,0.1954,0.1957,0.1993,0.2019,0.2116, 0.2180,0.2203,0.2271,0.2293,0.2310,0.2315,0.2321,0.2366,0.2402,0.2407, 0.2427,0.2451,0.2550,0.2571,0.2586,0.2589,0.2671,0.2683,0.2685,0.2716, 0.2723,0.2757,0.2818,0.2825,0.2876,0.2964,0.2982,0.3106,0.3111,0.3235, 0.3316,0.3351,0.3351,0.3379,0.3429,0.3525,0.3562,0.3574,0.3613,0.3634, 0.3738,0.3746,0.3772,0.3790,0.3808,0.3923,0.3928,0.3958,0.3962,0.3962, 0.3969,0.3988,0.3993,0.4040,0.4069,0.4098,0.4156,0.4203,0.4210,0.4275, 0.4278,0.4337,0.4354,0.4376,0.4379,0.4446,0.4597,0.4603,0.4606,0.4712, 0.4735,0.4764,0.4783,0.4816,0.4818,0.4825,0.4836,0.4843,0.4855,0.4857, 0.4876,0.4884,0.4915,0.4981,0.5025,0.5036,0.5058,0.5102,0.5182,0.5183, 0.5212,0.5284,0.5305,0.5327,0.5337,0.5340,0.5387,0.5434,0.5466,0.5507, 0.5508,0.5524,0.5545,0.5616,0.5635,0.5710,0.5788,0.5790,0.5994,0.6011, 0.6046,0.6061,0.6079,0.6087,0.6091,0.6124,0.6129,0.6134,0.6139,0.6167, 0.6172,0.6181,0.6224,0.6303,0.6426,0.6457,0.6547,0.6566,0.6643,0.6651, 0.6652,0.6713,0.6730,0.6798,0.6800,0.6857,0.6858,0.6881,0.6957,0.7019, 0.7038,0.7161,0.7223,0.7254,0.7277,0.7336,0.7365,0.7379,0.7447,0.7454, 0.7461,0.7464,0.7491,0.7492,0.7518,0.7566,0.7575,0.7580,0.7621,0.7635, 0.7658,0.7662,0.7683,0.7687,0.7694,0.7694,0.7735,0.7740,0.7787,0.7812, 0.7841,0.7877,0.8064,0.8106,0.8108,0.8234,0.8298,0.8302,0.8344,0.8443, 0.8505,0.8589,0.8590,0.8603,0.8718,0.9010,0.9095,0.9144,0.9154,0.9199, 0.9231,0.9241,0.9261,0.9297,0.9302,0.9363,0.9370,0.9434,0.9436,0.9451, 0.9463,0.9463,0.9469,0.9497,0.9544,0.9668,0.9737,0.9904,0.9908, Overall p-value after applying KStest on 269 p-values = 0.123017 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.