RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-30_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.68 21.5897 0.798982 2 to 25 15.84 10.4958 0.118458 3 to 26 15.65 25.2380 0.910492 4 to 27 15.73 20.8137 0.765267 5 to 28 15.74 11.5423 0.172976 6 to 29 15.56 17.2020 0.559239 7 to 30 15.67 18.4151 0.636882 8 to 31 15.88 29.5868 0.970517 9 to 32 15.80 23.3332 0.861286 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.193269 Tough bday spacings test for dh-ranFile-2015-07-30_04:31: 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 41 82 88 99 82 55 23 11 7 6 (O-E)^2/E 1.1 0.5 1.0 1.0 0.0 0.2 0.2 1.5 1.0 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.477, p= 0.320 RESULTS OF GCD FOR dh-ranFile-2015-07-30_04:31 Euclid's algorithm: p-value, steps to gcd: 0.631992 p-value, dist. of gcd's: 0.491797 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-30_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.061 0.598 0.840 0.187 0.652 0.988 0.657 0.206 Bits 8 to 15---> 0.073 0.738 0.904 0.631 0.486 0.075 0.833 0.132 Bits 16 to 23---> 0.850 0.095 0.432 0.663 0.719 0.403 0.489 0.026 Bits 24 to 31---> 0.508 0.051 0.753 0.723 0.838 0.566 0.318 0.973 KS test for the above 32 p values: 0.285 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-30_04:31, p-values for 5 runs: 0.4483, 0.9359, 0.3508, 0.6166, 0.5192 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-30_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5073 5134.0 0.725 1.598 r= 30 22952 23103.0 0.988 2.585 r= 31 11750 11551.5 3.410 5.995 chi-square = 5.995 with df = 3; p-value = 0.888 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-30_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5070 5134.0 0.798 0.826 r= 31 23115 23103.0 0.006 0.832 r= 32 11606 11551.5 0.257 1.089 chi-square = 1.089 with df = 3; p-value = 0.220 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-30_04:31 b-rank test for bits 1 to 8, p=0.58760 b-rank test for bits 2 to 9, p=0.86957 b-rank test for bits 3 to 10, p=0.15621 b-rank test for bits 4 to 11, p=0.17469 b-rank test for bits 5 to 12, p=0.36578 b-rank test for bits 6 to 13, p=0.55547 b-rank test for bits 7 to 14, p=0.72199 b-rank test for bits 8 to 15, p=0.31018 b-rank test for bits 9 to 16, p=0.11681 b-rank test for bits 10 to 17, p=0.54410 b-rank test for bits 11 to 18, p=0.12750 b-rank test for bits 12 to 19, p=0.40689 b-rank test for bits 13 to 20, p=0.34621 b-rank test for bits 14 to 21, p=0.80256 b-rank test for bits 15 to 22, p=0.35891 b-rank test for bits 16 to 23, p=0.85933 b-rank test for bits 17 to 24, p=0.74900 b-rank test for bits 18 to 25, p=0.15357 b-rank test for bits 19 to 26, p=0.11731 b-rank test for bits 20 to 27, p=0.73068 b-rank test for bits 21 to 28, p=0.75333 b-rank test for bits 22 to 29, p=0.95182 b-rank test for bits 23 to 30, p=0.03066 b-rank test for bits 24 to 31, p=0.09381 b-rank test for bits 25 to 32, p=0.01346 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 = 0.381771 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-30_04:31 (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 141900 -0.02 0.491304 2 142121 0.49 0.689543 3 142236 0.76 0.777342 4 141158 -1.76 0.039592 5 141389 -1.22 0.112045 6 143008 2.57 0.994871 7 142020 0.26 0.602018 8 142018 0.25 0.600214 9 142351 1.03 0.848950 10 141966 0.13 0.552669 11 142360 1.05 0.853822 12 141655 -0.59 0.276180 13 142284 0.88 0.809321 14 141600 -0.72 0.234922 15 141563 -0.81 0.209205 16 141665 -0.57 0.284046 17 142361 1.06 0.854357 18 142552 1.50 0.933395 19 141530 -0.89 0.187732 20 141884 -0.06 0.476404 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-30_04:31 Bits used No. missing words z-score p-value 23 to 32 141958 0.1678 0.566641 22 to 31 141827 -0.2839 0.388245 21 to 30 142198 0.9954 0.840233 20 to 29 142239 1.1368 0.872188 19 to 28 142079 0.5851 0.720749 18 to 27 142023 0.3920 0.652458 17 to 26 141593 -1.0908 0.137682 16 to 25 142277 1.2678 0.897570 15 to 24 142208 1.0299 0.848471 14 to 23 142204 1.0161 0.845210 13 to 22 142138 0.7885 0.784803 12 to 21 141262 -2.2322 0.012802 11 to 20 142301 1.3506 0.911586 10 to 19 141894 -0.0529 0.478921 9 to 18 141445 -1.6011 0.054673 8 to 17 142000 0.3127 0.622729 7 to 16 141774 -0.4667 0.320373 6 to 15 142148 0.8230 0.794746 5 to 14 142311 1.3851 0.916984 4 to 13 141733 -0.6080 0.271582 3 to 12 141863 -0.1598 0.436536 2 to 11 141953 0.1506 0.559849 1 to 10 142041 0.4540 0.675098 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-30_04:31 Bits used No. missing words z-score p-value 28 to 32 141677 -0.7876 0.215477 27 to 31 142390 1.6294 0.948385 26 to 30 141921 0.0396 0.515778 25 to 29 142395 1.6463 0.950153 24 to 28 142603 2.3514 0.990649 23 to 27 141887 -0.0757 0.469831 22 to 26 141610 -1.0147 0.155130 21 to 25 142676 2.5989 0.995324 20 to 24 142286 1.2768 0.899172 19 to 23 141807 -0.3469 0.364340 18 to 22 141931 0.0735 0.529279 17 to 21 142228 1.0802 0.859982 16 to 20 141788 -0.4113 0.340431 15 to 19 142023 0.3853 0.650001 14 to 18 141862 -0.1604 0.436267 13 to 17 141809 -0.3401 0.366890 12 to 16 142120 0.7141 0.762428 11 to 15 141750 -0.5401 0.294564 10 to 14 142080 0.5785 0.718551 9 to 13 141726 -0.6215 0.267149 8 to 12 142362 1.5345 0.937544 7 to 11 141566 -1.1638 0.122246 6 to 10 141620 -0.9808 0.163351 5 to 9 141372 -1.8215 0.034269 4 to 8 142305 1.3413 0.910081 3 to 7 141983 0.2497 0.598602 2 to 6 142120 0.7141 0.762428 1 to 5 141766 -0.4859 0.313532 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-30_04:31 Bits used No. missing words z-score p-value 31 to 32 141735 -0.5142 0.303539 30 to 31 141607 -0.8918 0.186242 29 to 30 141756 -0.4523 0.325526 28 to 29 141624 -0.8417 0.199983 27 to 28 141989 0.2350 0.592901 26 to 27 142141 0.6834 0.752821 25 to 26 142579 1.9754 0.975890 24 to 25 142156 0.7276 0.766583 23 to 24 142188 0.8220 0.794472 22 to 23 142104 0.5742 0.717100 21 to 22 142336 1.2586 0.895915 20 to 21 141314 -1.7561 0.039533 19 to 20 142375 1.3737 0.915226 18 to 19 142022 0.3324 0.630191 17 to 18 141095 -2.4022 0.008149 16 to 17 141583 -0.9626 0.167868 15 to 16 142409 1.4740 0.929753 14 to 15 141813 -0.2842 0.388144 13 to 14 141682 -0.6706 0.251241 12 to 13 141770 -0.4110 0.340535 11 to 12 141953 0.1288 0.551250 10 to 11 141528 -1.1249 0.130323 9 to 10 141805 -0.3078 0.379133 8 to 9 141769 -0.4140 0.339454 7 to 8 141595 -0.9272 0.176904 6 to 7 142159 0.7365 0.769284 5 to 6 141927 0.0521 0.520785 4 to 5 142687 2.2940 0.989105 3 to 4 142074 0.4858 0.686429 2 to 3 141559 -1.0334 0.150703 1 to 2 141247 -1.9538 0.025364 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-30_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2493.07 -0.098 0.460965 Test results for specific bytes for dh-ranFile-2015-07-30_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2421.75 -1.107 0.134230 2 to 9 2510.27 0.145 0.557715 3 to 10 2520.57 0.291 0.614417 4 to 11 2544.22 0.625 0.734139 5 to 12 2541.51 0.587 0.721435 6 to 13 2425.21 -1.058 0.145111 7 to 14 2566.23 0.937 0.825521 8 to 15 2442.14 -0.818 0.206595 9 to 16 2563.93 0.904 0.817023 10 to 17 2388.83 -1.572 0.057954 11 to 18 2403.69 -1.362 0.086588 12 to 19 2542.38 0.599 0.725530 13 to 20 2415.81 -1.191 0.116899 14 to 21 2453.39 -0.659 0.254897 15 to 22 2512.76 0.180 0.571578 16 to 23 2467.10 -0.465 0.320850 17 to 24 2493.74 -0.088 0.464746 18 to 25 2498.96 -0.015 0.494148 19 to 26 2506.28 0.089 0.535378 20 to 27 2623.19 1.742 0.959255 21 to 28 2487.75 -0.173 0.431219 22 to 29 2453.04 -0.664 0.253309 23 to 30 2629.11 1.826 0.966068 24 to 31 2406.59 -1.321 0.093248 25 to 32 2423.09 -1.088 0.138355 CDPARK for dh-ranFile-2015-07-30_04:31: 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 3498 -1.1416 0.126820 3545 1.0046 0.842447 3538 0.6849 0.753306 3523 0.0000 0.500000 3512 -0.5023 0.307734 3521 -0.0913 0.463617 3493 -1.3699 0.085365 3545 1.0046 0.842447 3490 -1.5068 0.065925 3542 0.8676 0.807188 Square side=100, avg. no. parked=3520.70 sample std.=20.59 p-value of the KSTEST for those 10 p-values: 0.805785 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-30_04:31 0.2379,0.2175,0.6238,0.7707,0.1829,0.1292,0.0876,0.6264,0.6115,0.7333, The KS test for those 10 p-values: 0.448463 The 3DSPHERES test for dh-ranFile-2015-07-30_04:31 sample no r^3 equiv. uni. 1 13.448 0.361259 2 107.736 0.972435 3 76.152 0.921007 4 58.184 0.856218 5 54.031 0.834873 6 34.427 0.682587 7 8.326 0.242339 8 53.609 0.832533 9 7.346 0.217197 10 10.456 0.294268 11 51.918 0.822821 12 2.600 0.083003 13 53.784 0.833508 14 9.371 0.268281 15 64.513 0.883567 16 8.579 0.248714 17 20.864 0.501159 18 40.511 0.740859 19 12.835 0.348075 20 44.544 0.773453 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.182838 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-30_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 0.1 -1.0 -0.4 0.5 0.3 0.2 -0.1 -1.0 -1.0 -0.5 0.3 0.1 0.6 0.7 2.0 -1.6 0.5 -0.3 -2.1 -0.6 0.2 -0.8 1.1 -0.7 -0.5 2.1 1.2 1.6 0.6 -1.1 0.8 0.3 0.8 0.8 2.8 -0.4 0.5 -1.3 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:44.982766 z-score=0.325446, p-value=0.651897 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-30_04:31 Test no p-value 1 0.088245 2 0.914766 3 0.680973 4 0.325499 5 0.404870 6 0.855787 7 0.506375 8 0.213810 9 0.042500 10 0.601425 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.991548 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-30_04:31: (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 66577 0.12 66658 0.00 3 25000.00 25009 0.00 25177 1.25 4 6666.67 6714 0.34 6535 2.60 5 1388.89 1412 0.38 1363 0.48 6 238.10 240 0.02 228 0.43 7 34.72 41 1.14 31 0.40 8 4.96 6 0.22 7 0.84 p=0.10096 p=0.57716 Number of rngs required: 688982, p-value: 0.748 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-30_04:31 No. of wins: Observed Expected 98779 98585.9 z-score= 0.864, pvalue=0.80616 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66752 66666.7 0.109 0.109 2 37488 37654.3 0.735 0.844 3 27070 26954.7 0.493 1.337 4 19459 19313.5 1.097 2.434 5 13721 13851.4 1.228 3.661 6 9778 9943.5 2.756 6.418 7 7157 7145.0 0.020 6.438 8 5201 5139.1 0.746 7.184 9 3800 3699.9 2.710 9.894 10 2632 2666.3 0.441 10.335 11 1914 1923.3 0.045 10.380 12 1360 1388.7 0.595 10.975 13 1023 1003.7 0.371 11.346 14 685 726.1 2.331 13.677 15 539 525.8 0.330 14.006 16 384 381.2 0.021 14.027 17 282 276.5 0.108 14.135 18 208 200.8 0.256 14.391 19 145 146.0 0.007 14.398 20 98 106.2 0.635 15.033 21 304 287.1 0.993 16.026 Chisq= 16.03 for 20 degrees of freedom, p= 0.28501 SUMMARY of craptest p-value for no. of wins: 0.806162 p-value for throws/game: 0.285015 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-30_04:31 No. of wins: Observed Expected 98696 98585.9 z-score= 0.493, pvalue=0.68886 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66368 66666.7 1.338 1.338 2 37689 37654.3 0.032 1.370 3 27150 26954.7 1.415 2.785 4 19302 19313.5 0.007 2.791 5 13747 13851.4 0.787 3.579 6 9905 9943.5 0.149 3.728 7 7177 7145.0 0.143 3.871 8 5312 5139.1 5.819 9.690 9 3691 3699.9 0.021 9.711 10 2625 2666.3 0.640 10.351 11 1916 1923.3 0.028 10.379 12 1418 1388.7 0.616 10.995 13 981 1003.7 0.514 11.509 14 736 726.1 0.134 11.643 15 551 525.8 1.204 12.847 16 383 381.2 0.009 12.856 17 268 276.5 0.264 13.120 18 195 200.8 0.169 13.289 19 154 146.0 0.440 13.729 20 120 106.2 1.789 15.518 21 312 287.1 2.157 17.675 Chisq= 17.68 for 20 degrees of freedom, p= 0.39122 SUMMARY of craptest p-value for no. of wins: 0.688858 p-value for throws/game: 0.391224 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0081,0.0128,0.0135,0.0254,0.0260,0.0307,0.0343,0.0395,0.0396,0.0425, 0.0514,0.0547,0.0580,0.0607,0.0659,0.0734,0.0746,0.0830,0.0854,0.0866, 0.0876,0.0882,0.0932,0.0938,0.0947,0.1010,0.1120,0.1168,0.1169,0.1173, 0.1185,0.1222,0.1268,0.1275,0.1292,0.1303,0.1319,0.1342,0.1377,0.1384, 0.1451,0.1507,0.1536,0.1551,0.1562,0.1634,0.1679,0.1730,0.1747,0.1769, 0.1828,0.1829,0.1862,0.1873,0.1877,0.1933,0.2000,0.2065,0.2066,0.2092, 0.2138,0.2155,0.2172,0.2175,0.2202,0.2349,0.2379,0.2423,0.2487,0.2512, 0.2533,0.2549,0.2671,0.2683,0.2716,0.2762,0.2840,0.2850,0.2854,0.2943, 0.2946,0.3035,0.3077,0.3102,0.3135,0.3185,0.3202,0.3204,0.3209,0.3255, 0.3255,0.3395,0.3404,0.3405,0.3462,0.3481,0.3508,0.3589,0.3613,0.3643, 0.3658,0.3669,0.3791,0.3818,0.3881,0.3882,0.3912,0.4035,0.4049,0.4069, 0.4312,0.4322,0.4363,0.4365,0.4483,0.4485,0.4610,0.4636,0.4647,0.4698, 0.4764,0.4789,0.4864,0.4885,0.4913,0.4918,0.4941,0.5000,0.5012,0.5064, 0.5084,0.5158,0.5192,0.5208,0.5293,0.5354,0.5441,0.5513,0.5527,0.5555, 0.5577,0.5592,0.5598,0.5664,0.5666,0.5716,0.5772,0.5876,0.5929,0.5979, 0.5986,0.6002,0.6014,0.6020,0.6115,0.6144,0.6166,0.6227,0.6238,0.6264, 0.6302,0.6306,0.6320,0.6369,0.6500,0.6517,0.6519,0.6525,0.6566,0.6632, 0.6751,0.6810,0.6826,0.6864,0.6889,0.6895,0.7171,0.7186,0.7191,0.7207, 0.7214,0.7220,0.7226,0.7255,0.7307,0.7333,0.7341,0.7381,0.7409,0.7480, 0.7490,0.7528,0.7532,0.7533,0.7533,0.7624,0.7624,0.7653,0.7666,0.7693, 0.7707,0.7735,0.7773,0.7848,0.7945,0.7947,0.7990,0.8026,0.8058,0.8062, 0.8072,0.8093,0.8170,0.8228,0.8255,0.8325,0.8334,0.8335,0.8349,0.8379, 0.8400,0.8402,0.8424,0.8424,0.8452,0.8485,0.8489,0.8497,0.8538,0.8544, 0.8558,0.8562,0.8593,0.8600,0.8613,0.8696,0.8722,0.8836,0.8882,0.8959, 0.8976,0.8992,0.9040,0.9101,0.9105,0.9116,0.9148,0.9152,0.9170,0.9210, 0.9298,0.9334,0.9359,0.9375,0.9484,0.9502,0.9518,0.9593,0.9661,0.9705, 0.9724,0.9727,0.9759,0.9883,0.9891,0.9906,0.9915,0.9949,0.9953, Overall p-value after applying KStest on 269 p-values = 0.525540 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.