RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-07_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 23.1393 0.855228 2 to 25 15.40 23.7960 0.874916 3 to 26 15.66 11.6793 0.180845 4 to 27 15.89 14.4826 0.367308 5 to 28 15.89 15.1619 0.416181 6 to 29 15.78 23.1419 0.855312 7 to 30 15.62 28.1759 0.957076 8 to 31 15.88 5.4545 0.003835 9 to 32 15.56 20.0761 0.729642 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.331638 Tough bday spacings test for dh-ranFile-2015-09-07_12:31: 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 7 38 72 99 97 83 54 22 14 11 3 (O-E)^2/E 0.5 0.1 0.0 0.0 0.0 0.3 0.1 2.0 0.1 2.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 6.241, p= 0.205 RESULTS OF GCD FOR dh-ranFile-2015-09-07_12:31 Euclid's algorithm: p-value, steps to gcd: 0.023110 p-value, dist. of gcd's: 0.214638 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-07_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.186 0.979 0.467 0.345 0.275 0.041 0.897 0.381 Bits 8 to 15---> 0.345 0.130 0.045 0.079 0.772 0.606 0.688 0.451 Bits 16 to 23---> 0.917 0.978 0.842 0.850 0.602 0.766 0.266 0.673 Bits 24 to 31---> 0.261 0.814 0.236 0.633 0.769 0.891 0.435 0.035 KS test for the above 32 p values: 0.083 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-07_12:31, p-values for 5 runs: 0.6149, 0.8261, 0.5686, 0.2309, 0.0683 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-07_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5143 5134.0 0.016 0.043 r= 30 23045 23103.0 0.146 0.189 r= 31 11603 11551.5 0.229 0.419 chi-square = 0.419 with df = 3; p-value = 0.064 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-07_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 195 211.4 1.275 1.275 r= 30 5101 5134.0 0.212 1.487 r= 31 23036 23103.0 0.195 1.682 r= 32 11668 11551.5 1.174 2.856 chi-square = 2.856 with df = 3; p-value = 0.586 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-07_12:31 b-rank test for bits 1 to 8, p=0.47292 b-rank test for bits 2 to 9, p=0.18145 b-rank test for bits 3 to 10, p=0.01377 b-rank test for bits 4 to 11, p=0.16291 b-rank test for bits 5 to 12, p=0.82758 b-rank test for bits 6 to 13, p=0.52200 b-rank test for bits 7 to 14, p=0.25711 b-rank test for bits 8 to 15, p=0.63274 b-rank test for bits 9 to 16, p=0.89598 b-rank test for bits 10 to 17, p=0.06999 b-rank test for bits 11 to 18, p=0.49051 b-rank test for bits 12 to 19, p=0.07115 b-rank test for bits 13 to 20, p=0.48510 b-rank test for bits 14 to 21, p=0.18369 b-rank test for bits 15 to 22, p=0.24932 b-rank test for bits 16 to 23, p=0.03838 b-rank test for bits 17 to 24, p=0.32671 b-rank test for bits 18 to 25, p=0.27098 b-rank test for bits 19 to 26, p=0.28019 b-rank test for bits 20 to 27, p=0.65666 b-rank test for bits 21 to 28, p=0.11255 b-rank test for bits 22 to 29, p=0.37957 b-rank test for bits 23 to 30, p=0.73066 b-rank test for bits 24 to 31, p=0.49133 b-rank test for bits 25 to 32, p=0.47175 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 = 0.041137 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-07_12:31 (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 141223 -1.60 0.054404 2 142147 0.56 0.710657 3 142126 0.51 0.693655 4 141869 -0.09 0.462464 5 141180 -1.70 0.044187 6 141209 -1.64 0.050890 7 142298 0.91 0.818089 8 142250 0.80 0.786972 9 142633 1.69 0.954564 10 142117 0.49 0.686236 11 141349 -1.31 0.095236 12 141959 0.12 0.546194 13 142032 0.29 0.612795 14 141547 -0.85 0.198619 15 142464 1.30 0.902505 16 142080 0.40 0.654966 17 141914 0.01 0.504353 18 141877 -0.08 0.469894 19 142339 1.00 0.842287 20 141785 -0.29 0.385720 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-07_12:31 Bits used No. missing words z-score p-value 23 to 32 141953 0.1506 0.559849 22 to 31 141768 -0.4873 0.313007 21 to 30 142085 0.6058 0.727663 20 to 29 142359 1.5506 0.939500 19 to 28 141850 -0.2046 0.418948 18 to 27 141709 -0.6908 0.244848 17 to 26 141989 0.2747 0.608236 16 to 25 142354 1.5333 0.937405 15 to 24 141713 -0.6770 0.249203 14 to 23 142440 1.8299 0.966367 13 to 22 141840 -0.2391 0.405526 12 to 21 142347 1.5092 0.934377 11 to 20 141980 0.2437 0.596264 10 to 19 141953 0.1506 0.559849 9 to 18 141797 -0.3873 0.349251 8 to 17 142256 1.1954 0.884037 7 to 16 141748 -0.5563 0.288999 6 to 15 142315 1.3989 0.919073 5 to 14 141943 0.1161 0.546215 4 to 13 141695 -0.7391 0.229933 3 to 12 141647 -0.9046 0.182842 2 to 11 141510 -1.3770 0.084256 1 to 10 141570 -1.1701 0.120980 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-07_12:31 Bits used No. missing words z-score p-value 28 to 32 141802 -0.3638 0.357992 27 to 31 141618 -0.9876 0.161684 26 to 30 141778 -0.4452 0.328093 25 to 29 141837 -0.2452 0.403156 24 to 28 142016 0.3616 0.641172 23 to 27 142415 1.7141 0.956748 22 to 26 141705 -0.6926 0.244267 21 to 25 141887 -0.0757 0.469831 20 to 24 142244 1.1345 0.871702 19 to 23 142302 1.3311 0.908419 18 to 22 141598 -1.0554 0.145631 17 to 21 141531 -1.2825 0.099838 16 to 20 141622 -0.9740 0.165028 15 to 19 142146 0.8023 0.788802 14 to 18 141492 -1.4147 0.078581 13 to 17 141222 -2.3299 0.009905 12 to 16 141331 -1.9604 0.024972 11 to 15 142043 0.4531 0.674768 10 to 14 141915 0.0192 0.507667 9 to 13 141636 -0.9265 0.177082 8 to 12 141814 -0.3232 0.373290 7 to 11 142302 1.3311 0.908419 6 to 10 142038 0.4362 0.668643 5 to 9 141896 -0.0452 0.481979 4 to 8 141999 0.3040 0.619423 3 to 7 142043 0.4531 0.674768 2 to 6 141876 -0.1130 0.455022 1 to 5 142174 0.8972 0.815190 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-07_12:31 Bits used No. missing words z-score p-value 31 to 32 141561 -1.0275 0.152087 30 to 31 141742 -0.4936 0.310795 29 to 30 141745 -0.4847 0.313927 28 to 29 142562 1.9253 0.972903 27 to 28 141935 0.0757 0.530180 26 to 27 141722 -0.5526 0.290270 25 to 26 142244 0.9872 0.838234 24 to 25 142568 1.9430 0.973991 23 to 24 142199 0.8545 0.803582 22 to 23 141642 -0.7886 0.215178 21 to 22 141491 -1.2340 0.108599 20 to 21 141728 -0.5349 0.296361 19 to 20 141888 -0.0629 0.474915 18 to 19 141554 -1.0482 0.147280 17 to 18 141699 -0.6204 0.267483 16 to 17 141875 -0.1013 0.459669 15 to 16 141702 -0.6116 0.270404 14 to 15 141778 -0.3874 0.349229 13 to 14 142266 1.0521 0.853629 12 to 13 141303 -1.7886 0.036841 11 to 12 141827 -0.2429 0.404056 10 to 11 142041 0.3884 0.651143 9 to 10 141718 -0.5644 0.286243 8 to 9 142022 0.3324 0.630191 7 to 8 141784 -0.3697 0.355801 6 to 7 142338 1.2645 0.896977 5 to 6 142043 0.3943 0.653323 4 to 5 141906 -0.0098 0.496081 3 to 4 142055 0.4297 0.666295 2 to 3 142038 0.3796 0.647863 1 to 2 141767 -0.4199 0.337297 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-07_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2460.39 -0.560 0.287681 Test results for specific bytes for dh-ranFile-2015-09-07_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2516.47 0.233 0.592115 2 to 9 2442.91 -0.807 0.209709 3 to 10 2401.14 -1.398 0.081043 4 to 11 2502.64 0.037 0.514888 5 to 12 2509.43 0.133 0.553072 6 to 13 2604.64 1.480 0.930533 7 to 14 2549.37 0.698 0.757474 8 to 15 2497.27 -0.039 0.484618 9 to 16 2478.54 -0.303 0.380767 10 to 17 2413.36 -1.225 0.110244 11 to 18 2572.79 1.029 0.848362 12 to 19 2555.99 0.792 0.785757 13 to 20 2429.86 -0.992 0.160631 14 to 21 2385.34 -1.621 0.052457 15 to 22 2506.92 0.098 0.538954 16 to 23 2539.88 0.564 0.713638 17 to 24 2380.64 -1.688 0.045700 18 to 25 2518.16 0.257 0.601346 19 to 26 2440.82 -0.837 0.201334 20 to 27 2502.79 0.039 0.515740 21 to 28 2556.53 0.799 0.787974 22 to 29 2519.15 0.271 0.606731 23 to 30 2557.70 0.816 0.792761 24 to 31 2332.89 -2.363 0.009056 25 to 32 2499.46 -0.008 0.496957 CDPARK for dh-ranFile-2015-09-07_12:31: 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 3538 0.6849 0.753306 3526 0.1370 0.554479 3540 0.7763 0.781201 3476 -2.1461 0.015932 3550 1.2329 0.891189 3527 0.1826 0.572463 3517 -0.2740 0.392053 3540 0.7763 0.781201 3520 -0.1370 0.445521 3524 0.0457 0.518210 Square side=100, avg. no. parked=3525.80 sample std.=19.32 p-value of the KSTEST for those 10 p-values: 0.437853 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-07_12:31 0.3231,0.5161,0.7155,0.9767,0.9696,0.5141,0.1405,0.0781,0.1063,0.8005, The KS test for those 10 p-values: 0.716812 The 3DSPHERES test for dh-ranFile-2015-09-07_12:31 sample no r^3 equiv. uni. 1 26.389 0.585070 2 52.937 0.828737 3 27.342 0.598033 4 9.983 0.283066 5 32.660 0.663337 6 53.663 0.832833 7 48.211 0.799520 8 6.362 0.191076 9 117.983 0.980411 10 15.515 0.403787 11 22.243 0.523563 12 17.700 0.445664 13 18.557 0.461282 14 9.866 0.280268 15 63.663 0.880219 16 38.183 0.719941 17 70.426 0.904396 18 21.798 0.516444 19 64.855 0.884888 20 77.120 0.923514 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.055858 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-07_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 2.3 0.3 -1.3 -1.5 1.3 0.7 0.8 -0.4 -1.1 -1.1 1.2 1.4 -1.2 1.0 -1.0 -0.1 -1.7 -0.7 -0.1 1.9 1.1 0.9 0.1 -0.2 -2.3 0.4 1.6 1.5 0.2 -2.2 -0.5 0.2 -0.1 -0.7 -0.5 -0.4 0.5 1.0 0.1 -1.0 1.8 Chi-square with 42 degrees of freedom:52.157323 z-score=1.108255, p-value=0.864592 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-07_12:31 Test no p-value 1 0.347377 2 0.025706 3 0.181277 4 0.022416 5 0.945777 6 0.104953 7 0.179516 8 0.004403 9 0.021810 10 0.569112 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000738 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-07_12:31: (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 66294 2.08 66765 0.15 3 25000.00 25185 1.37 25066 0.17 4 6666.67 6822 3.62 6540 2.41 5 1388.89 1399 0.07 1358 0.69 6 238.10 241 0.04 238 0.00 7 34.72 52 8.60 30 0.64 8 4.96 6 0.22 2 1.77 p=0.98624 p=0.55649 Number of rngs required: 687695, p-value: 0.207 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-07_12:31 No. of wins: Observed Expected 98986 98585.9 z-score= 1.790, pvalue=0.96325 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66812 66666.7 0.317 0.317 2 37718 37654.3 0.108 0.425 3 27141 26954.7 1.287 1.712 4 19056 19313.5 3.432 5.144 5 13702 13851.4 1.612 6.756 6 9808 9943.5 1.848 8.603 7 7287 7145.0 2.821 11.424 8 5169 5139.1 0.174 11.599 9 3668 3699.9 0.274 11.873 10 2611 2666.3 1.147 13.020 11 1906 1923.3 0.156 13.176 12 1413 1388.7 0.424 13.600 13 991 1003.7 0.161 13.761 14 775 726.1 3.288 17.049 15 525 525.8 0.001 17.050 16 387 381.2 0.090 17.140 17 299 276.5 1.824 18.964 18 201 200.8 0.000 18.964 19 146 146.0 0.000 18.964 20 112 106.2 0.315 19.279 21 273 287.1 0.694 19.973 Chisq= 19.97 for 20 degrees of freedom, p= 0.54037 SUMMARY of craptest p-value for no. of wins: 0.963246 p-value for throws/game: 0.540373 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-07_12:31 No. of wins: Observed Expected 98526 98585.9 z-score=-0.268, pvalue=0.39446 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66538 66666.7 0.248 0.248 2 37959 37654.3 2.465 2.714 3 27140 26954.7 1.273 3.987 4 19211 19313.5 0.544 4.531 5 13675 13851.4 2.247 6.778 6 10017 9943.5 0.543 7.320 7 7099 7145.0 0.296 7.617 8 5124 5139.1 0.044 7.661 9 3669 3699.9 0.257 7.918 10 2698 2666.3 0.377 8.295 11 1901 1923.3 0.259 8.555 12 1405 1388.7 0.190 8.745 13 972 1003.7 1.002 9.747 14 700 726.1 0.941 10.688 15 483 525.8 3.490 14.178 16 380 381.2 0.003 14.181 17 270 276.5 0.155 14.336 18 205 200.8 0.087 14.422 19 148 146.0 0.028 14.450 20 97 106.2 0.800 15.250 21 309 287.1 1.668 16.918 Chisq= 16.92 for 20 degrees of freedom, p= 0.34171 SUMMARY of craptest p-value for no. of wins: 0.394456 p-value for throws/game: 0.341710 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0038,0.0044,0.0091,0.0099,0.0138,0.0159,0.0218,0.0224,0.0231, 0.0250,0.0257,0.0354,0.0368,0.0384,0.0406,0.0411,0.0442,0.0449,0.0457, 0.0509,0.0525,0.0544,0.0559,0.0636,0.0683,0.0700,0.0712,0.0781,0.0786, 0.0791,0.0810,0.0829,0.0843,0.0952,0.0998,0.1050,0.1063,0.1086,0.1102, 0.1126,0.1210,0.1301,0.1405,0.1456,0.1473,0.1521,0.1606,0.1617,0.1629, 0.1650,0.1771,0.1795,0.1808,0.1813,0.1814,0.1828,0.1837,0.1861,0.1911, 0.1986,0.2013,0.2053,0.2066,0.2097,0.2146,0.2152,0.2299,0.2309,0.2364, 0.2443,0.2448,0.2492,0.2493,0.2571,0.2606,0.2660,0.2675,0.2704,0.2710, 0.2747,0.2802,0.2803,0.2831,0.2862,0.2877,0.2890,0.2903,0.2964,0.3108, 0.3130,0.3139,0.3231,0.3267,0.3281,0.3316,0.3373,0.3417,0.3446,0.3449, 0.3474,0.3492,0.3493,0.3558,0.3580,0.3673,0.3733,0.3796,0.3806,0.3808, 0.3857,0.3921,0.3945,0.4032,0.4038,0.4041,0.4055,0.4162,0.4189,0.4353, 0.4379,0.4455,0.4457,0.4506,0.4550,0.4597,0.4613,0.4625,0.4673,0.4698, 0.4699,0.4718,0.4729,0.4749,0.4820,0.4846,0.4851,0.4905,0.4913,0.4961, 0.4970,0.5044,0.5077,0.5141,0.5149,0.5157,0.5161,0.5164,0.5182,0.5220, 0.5236,0.5302,0.5390,0.5404,0.5462,0.5462,0.5531,0.5545,0.5565,0.5598, 0.5598,0.5686,0.5691,0.5725,0.5851,0.5857,0.5921,0.5963,0.5980,0.6013, 0.6015,0.6060,0.6067,0.6082,0.6128,0.6149,0.6194,0.6302,0.6327,0.6328, 0.6412,0.6479,0.6511,0.6533,0.6550,0.6567,0.6633,0.6663,0.6686,0.6729, 0.6748,0.6748,0.6862,0.6882,0.6937,0.7107,0.7136,0.7155,0.7168,0.7199, 0.7277,0.7296,0.7307,0.7533,0.7575,0.7657,0.7692,0.7718,0.7812,0.7812, 0.7858,0.7870,0.7880,0.7888,0.7928,0.7995,0.8005,0.8036,0.8143,0.8152, 0.8181,0.8261,0.8276,0.8287,0.8328,0.8382,0.8422,0.8423,0.8484,0.8499, 0.8536,0.8552,0.8553,0.8646,0.8717,0.8749,0.8802,0.8840,0.8849,0.8912, 0.8912,0.8960,0.8969,0.8970,0.9025,0.9044,0.9084,0.9084,0.9174,0.9191, 0.9235,0.9305,0.9344,0.9374,0.9395,0.9458,0.9546,0.9567,0.9571,0.9632, 0.9664,0.9696,0.9729,0.9740,0.9767,0.9781,0.9786,0.9804,0.9862, Overall p-value after applying KStest on 269 p-values = 0.383626 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.