RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-18_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 22.0722 0.818040 2 to 25 15.90 11.5682 0.174452 3 to 26 15.68 11.8003 0.187926 4 to 27 15.65 14.3205 0.355697 5 to 28 15.83 20.3733 0.744418 6 to 29 16.11 20.1324 0.732487 7 to 30 15.57 16.7230 0.526717 8 to 31 15.79 11.5116 0.171232 9 to 32 16.09 8.4080 0.042973 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.582811 Tough bday spacings test for dh-ranFile-2018-03-18_03:31: 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 12 36 68 106 106 81 43 24 18 5 1 (O-E)^2/E 0.9 0.0 0.4 0.7 0.7 0.1 1.6 1.1 0.7 0.4 2.3 Birthday Spacings: Sum(O-E)^2/E= 8.857, p= 0.454 RESULTS OF GCD FOR dh-ranFile-2018-03-18_03:31 Euclid's algorithm: p-value, steps to gcd: 0.844957 p-value, dist. of gcd's: 0.912251 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-18_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.618 0.568 0.899 0.886 0.716 0.077 0.436 0.478 Bits 8 to 15---> 0.714 0.415 0.298 0.543 0.726 0.094 0.605 0.709 Bits 16 to 23---> 0.594 0.232 0.429 0.759 0.907 0.745 0.661 0.792 Bits 24 to 31---> 0.398 0.622 0.471 0.362 0.547 0.294 0.372 0.808 KS test for the above 32 p values: 0.887 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-18_03:31, p-values for 5 runs: 0.6944, 0.8928, 0.6488, 0.7048, 0.4498 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-18_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5146 5134.0 0.028 0.558 r= 30 23076 23103.0 0.032 0.589 r= 31 11556 11551.5 0.002 0.591 chi-square = 0.591 with df = 3; p-value = 0.102 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-18_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5253 5134.0 2.758 4.362 r= 31 23063 23103.0 0.069 4.432 r= 32 11491 11551.5 0.317 4.749 chi-square = 4.749 with df = 3; p-value = 0.809 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-18_03:31 b-rank test for bits 1 to 8, p=0.07007 b-rank test for bits 2 to 9, p=0.14275 b-rank test for bits 3 to 10, p=0.39520 b-rank test for bits 4 to 11, p=0.73469 b-rank test for bits 5 to 12, p=0.52267 b-rank test for bits 6 to 13, p=0.59857 b-rank test for bits 7 to 14, p=0.44204 b-rank test for bits 8 to 15, p=0.21133 b-rank test for bits 9 to 16, p=0.08710 b-rank test for bits 10 to 17, p=0.01814 b-rank test for bits 11 to 18, p=0.05953 b-rank test for bits 12 to 19, p=0.41122 b-rank test for bits 13 to 20, p=0.01303 b-rank test for bits 14 to 21, p=0.69699 b-rank test for bits 15 to 22, p=0.82387 b-rank test for bits 16 to 23, p=0.87566 b-rank test for bits 17 to 24, p=0.53726 b-rank test for bits 18 to 25, p=0.29204 b-rank test for bits 19 to 26, p=0.52986 b-rank test for bits 20 to 27, p=0.39840 b-rank test for bits 21 to 28, p=0.98845 b-rank test for bits 22 to 29, p=0.05106 b-rank test for bits 23 to 30, p=0.54514 b-rank test for bits 24 to 31, p=0.39610 b-rank test for bits 25 to 32, p=0.22513 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 = 0.124031 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-18_03:31 (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 141646 -0.62 0.269193 2 142604 1.62 0.947712 3 142361 1.06 0.854357 4 142249 0.79 0.786292 5 141587 -0.75 0.225693 6 142686 1.81 0.965211 7 141867 -0.10 0.460608 8 141911 0.00 0.501557 9 141928 0.04 0.517397 10 140937 -2.27 0.011549 11 142001 0.21 0.584798 12 142352 1.03 0.849496 13 141988 0.18 0.572918 14 141248 -1.55 0.061153 15 142223 0.73 0.768182 16 141473 -1.02 0.153992 17 142311 0.94 0.826001 18 142415 1.18 0.881292 19 141725 -0.43 0.333351 20 142440 1.24 0.892491 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-18_03:31 Bits used No. missing words z-score p-value 23 to 32 141760 -0.5149 0.303301 22 to 31 141914 0.0161 0.506424 21 to 30 142124 0.7402 0.770423 20 to 29 141738 -0.5908 0.277330 19 to 28 142033 0.4264 0.665109 18 to 27 142141 0.7989 0.787815 17 to 26 142253 1.1851 0.882005 16 to 25 141547 -1.2494 0.105757 15 to 24 141695 -0.7391 0.229933 14 to 23 141768 -0.4873 0.313007 13 to 22 141818 -0.3149 0.376407 12 to 21 141945 0.1230 0.548947 11 to 20 141985 0.2609 0.602927 10 to 19 142147 0.8196 0.793764 9 to 18 142034 0.4299 0.666365 8 to 17 141760 -0.5149 0.303301 7 to 16 142028 0.4092 0.658806 6 to 15 142404 1.7058 0.955973 5 to 14 141884 -0.0873 0.465199 4 to 13 142082 0.5954 0.724217 3 to 12 141799 -0.3804 0.351806 2 to 11 142034 0.4299 0.666365 1 to 10 142071 0.5575 0.711401 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-18_03:31 Bits used No. missing words z-score p-value 28 to 32 142028 0.4023 0.656258 27 to 31 141820 -0.3028 0.381016 26 to 30 142162 0.8565 0.804142 25 to 29 141560 -1.1842 0.118173 24 to 28 142115 0.6972 0.757157 23 to 27 141381 -1.7909 0.036651 22 to 26 141899 -0.0350 0.486033 21 to 25 142020 0.3752 0.646227 20 to 24 142087 0.6023 0.726503 19 to 23 141824 -0.2893 0.386193 18 to 22 141493 -1.4113 0.079080 17 to 21 141462 -1.5164 0.064713 16 to 20 141750 -0.5401 0.294564 15 to 19 141430 -1.6248 0.052098 14 to 18 141663 -0.8350 0.201854 13 to 17 141933 0.0802 0.531976 12 to 16 142025 0.3921 0.652509 11 to 15 142356 1.5141 0.935004 10 to 14 142284 1.2701 0.897970 9 to 13 141538 -1.2587 0.104061 8 to 12 142314 1.3718 0.914931 7 to 11 141869 -0.1367 0.445629 6 to 10 141891 -0.0621 0.475227 5 to 9 141975 0.2226 0.588081 4 to 8 141898 -0.0384 0.484682 3 to 7 141888 -0.0723 0.471180 2 to 6 141652 -0.8723 0.191521 1 to 5 142187 0.9413 0.826713 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-18_03:31 Bits used No. missing words z-score p-value 31 to 32 141837 -0.2134 0.415522 30 to 31 141855 -0.1603 0.436336 29 to 30 142489 1.7099 0.956362 28 to 29 142289 1.1200 0.868637 27 to 28 142058 0.4386 0.669508 26 to 27 141697 -0.6263 0.265545 25 to 26 142046 0.4032 0.656583 24 to 25 141958 0.1436 0.557080 23 to 24 142227 0.9371 0.825641 22 to 23 141738 -0.5054 0.306640 21 to 22 141582 -0.9656 0.167128 20 to 21 141259 -1.9184 0.027532 19 to 20 142079 0.5005 0.691639 18 to 19 142036 0.3737 0.645671 17 to 18 141846 -0.1868 0.425903 16 to 17 141965 0.1642 0.565220 15 to 16 142450 1.5949 0.944632 14 to 15 142219 0.9135 0.819505 13 to 14 141831 -0.2311 0.408633 12 to 13 141830 -0.2340 0.407488 11 to 12 141615 -0.8682 0.192634 10 to 11 141796 -0.3343 0.369074 9 to 10 142160 0.7394 0.770180 8 to 9 141731 -0.5260 0.299428 7 to 8 142031 0.3589 0.640168 6 to 7 141695 -0.6322 0.263614 5 to 6 141315 -1.7532 0.039785 4 to 5 141856 -0.1573 0.437498 3 to 4 142049 0.4120 0.659832 2 to 3 142167 0.7601 0.776399 1 to 2 142106 0.5801 0.719092 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-18_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2501.54 0.022 0.508711 Test results for specific bytes for dh-ranFile-2018-03-18_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2394.48 -1.492 0.067822 2 to 9 2533.29 0.471 0.681104 3 to 10 2433.21 -0.945 0.172450 4 to 11 2576.95 1.088 0.861743 5 to 12 2561.76 0.873 0.808763 6 to 13 2501.80 0.025 0.510161 7 to 14 2549.91 0.706 0.759860 8 to 15 2455.66 -0.627 0.265296 9 to 16 2530.87 0.437 0.668781 10 to 17 2564.89 0.918 0.820608 11 to 18 2492.79 -0.102 0.459414 12 to 19 2428.94 -1.005 0.157453 13 to 20 2588.93 1.258 0.895735 14 to 21 2388.64 -1.575 0.057646 15 to 22 2488.44 -0.164 0.435051 16 to 23 2497.46 -0.036 0.485676 17 to 24 2538.19 0.540 0.705442 18 to 25 2529.83 0.422 0.663458 19 to 26 2443.29 -0.802 0.211268 20 to 27 2500.34 0.005 0.501929 21 to 28 2505.72 0.081 0.532245 22 to 29 2542.85 0.606 0.727720 23 to 30 2528.20 0.399 0.654966 24 to 31 2483.43 -0.234 0.407340 25 to 32 2624.61 1.762 0.960986 CDPARK for dh-ranFile-2018-03-18_03:31: 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 3530 0.3196 0.625377 3511 -0.5479 0.291865 3524 0.0457 0.518210 3509 -0.6393 0.261324 3528 0.2283 0.590298 3541 0.8219 0.794438 3504 -0.8676 0.192812 3480 -1.9635 0.024796 3519 -0.1826 0.427537 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3515.50 sample std.=16.12 p-value of the KSTEST for those 10 p-values: 0.385037 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-18_03:31 0.7850,0.6106,0.8027,0.3663,0.1865,0.0677,0.3479,0.5574,0.4582,0.1763, The KS test for those 10 p-values: 0.739412 The 3DSPHERES test for dh-ranFile-2018-03-18_03:31 sample no r^3 equiv. uni. 1 7.715 0.226749 2 23.970 0.550215 3 9.816 0.279071 4 33.934 0.677330 5 119.588 0.981431 6 3.547 0.111517 7 7.079 0.210203 8 6.139 0.185053 9 21.653 0.514103 10 15.733 0.408118 11 35.562 0.694373 12 4.441 0.137605 13 0.407 0.013480 14 11.366 0.315355 15 13.475 0.361848 16 39.247 0.729704 17 51.195 0.818499 18 82.167 0.935359 19 19.026 0.469642 20 40.606 0.741671 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.954652 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-18_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 1.3 -0.5 -0.3 0.2 0.3 0.1 0.4 0.6 1.3 -0.5 -0.7 -1.2 0.5 0.6 0.6 2.0 1.1 -0.6 -0.2 -1.5 -0.2 -0.9 -0.6 -0.5 0.2 -1.3 1.0 -1.9 -0.7 -2.0 0.9 0.1 2.0 0.1 -0.2 -0.4 1.3 1.5 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:38.590818 z-score=-0.371972, p-value=0.378577 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-18_03:31 Test no p-value 1 0.698392 2 0.241646 3 0.753646 4 0.042874 5 0.473890 6 0.005713 7 0.797160 8 0.000047 9 0.013197 10 0.638473 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009672 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-18_03:31: (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 66648 0.01 66527 0.29 3 25000.00 25057 0.13 24882 0.56 4 6666.67 6666 0.00 6864 5.84 5 1388.89 1335 2.09 1456 3.24 6 238.10 255 1.20 222 1.09 7 34.72 33 0.09 40 0.80 8 4.96 5 0.00 8 1.86 p=0.25763 p=0.96667 Number of rngs required: 691597, p-value: 1.000 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-18_03:31 No. of wins: Observed Expected 98913 98585.9 z-score= 1.463, pvalue=0.92829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66767 66666.7 0.151 0.151 2 37456 37654.3 1.045 1.196 3 26748 26954.7 1.586 2.781 4 19572 19313.5 3.461 6.242 5 13798 13851.4 0.206 6.448 6 9981 9943.5 0.141 6.589 7 7143 7145.0 0.001 6.590 8 5190 5139.1 0.505 7.094 9 3701 3699.9 0.000 7.095 10 2583 2666.3 2.602 9.697 11 1981 1923.3 1.729 11.426 12 1397 1388.7 0.049 11.475 13 997 1003.7 0.045 11.520 14 747 726.1 0.599 12.120 15 545 525.8 0.698 12.818 16 391 381.2 0.255 13.072 17 275 276.5 0.009 13.081 18 214 200.8 0.864 13.945 19 122 146.0 3.940 17.885 20 102 106.2 0.167 18.053 21 290 287.1 0.029 18.082 Chisq= 18.08 for 20 degrees of freedom, p= 0.41796 SUMMARY of craptest p-value for no. of wins: 0.928289 p-value for throws/game: 0.417962 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-18_03:31 No. of wins: Observed Expected 98610 98585.9 z-score= 0.108, pvalue=0.54299 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66895 66666.7 0.782 0.782 2 37969 37654.3 2.630 3.412 3 26653 26954.7 3.378 6.789 4 19309 19313.5 0.001 6.790 5 13749 13851.4 0.757 7.548 6 9842 9943.5 1.037 8.585 7 7080 7145.0 0.592 9.177 8 5130 5139.1 0.016 9.193 9 3771 3699.9 1.368 10.560 10 2556 2666.3 4.563 15.123 11 1906 1923.3 0.156 15.279 12 1430 1388.7 1.226 16.505 13 1028 1003.7 0.588 17.092 14 714 726.1 0.203 17.295 15 571 525.8 3.879 21.175 16 350 381.2 2.546 23.720 17 294 276.5 1.102 24.823 18 216 200.8 1.146 25.969 19 134 146.0 0.984 26.953 20 112 106.2 0.315 27.268 21 291 287.1 0.053 27.320 Chisq= 27.32 for 20 degrees of freedom, p= 0.87351 SUMMARY of craptest p-value for no. of wins: 0.542992 p-value for throws/game: 0.873509 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0057,0.0097,0.0115,0.0130,0.0132,0.0135,0.0181,0.0248,0.0275, 0.0367,0.0398,0.0429,0.0430,0.0511,0.0521,0.0576,0.0595,0.0612,0.0647, 0.0677,0.0678,0.0701,0.0773,0.0791,0.0871,0.0939,0.1015,0.1041,0.1058, 0.1115,0.1182,0.1240,0.1376,0.1428,0.1540,0.1575,0.1671,0.1712,0.1725, 0.1745,0.1763,0.1851,0.1865,0.1879,0.1915,0.1926,0.1928,0.2019,0.2102, 0.2113,0.2113,0.2251,0.2257,0.2267,0.2299,0.2325,0.2416,0.2576,0.2613, 0.2613,0.2636,0.2653,0.2655,0.2692,0.2773,0.2791,0.2919,0.2920,0.2944, 0.2946,0.2977,0.2994,0.3033,0.3033,0.3066,0.3130,0.3154,0.3334,0.3479, 0.3518,0.3557,0.3616,0.3618,0.3663,0.3691,0.3722,0.3764,0.3786,0.3810, 0.3850,0.3862,0.3952,0.3961,0.3984,0.3985,0.4073,0.4075,0.4081,0.4086, 0.4112,0.4149,0.4155,0.4180,0.4259,0.4275,0.4295,0.4351,0.4362,0.4363, 0.4375,0.4420,0.4456,0.4498,0.4543,0.4582,0.4594,0.4606,0.4652,0.4696, 0.4709,0.4712,0.4739,0.4752,0.4781,0.4847,0.4857,0.4860,0.5016,0.5019, 0.5064,0.5087,0.5102,0.5141,0.5174,0.5182,0.5227,0.5267,0.5299,0.5320, 0.5322,0.5373,0.5430,0.5433,0.5451,0.5470,0.5489,0.5502,0.5571,0.5574, 0.5652,0.5678,0.5729,0.5828,0.5848,0.5881,0.5903,0.5944,0.5986,0.6029, 0.6048,0.6106,0.6184,0.6224,0.6254,0.6385,0.6402,0.6457,0.6462,0.6488, 0.6525,0.6550,0.6563,0.6566,0.6588,0.6598,0.6615,0.6635,0.6651,0.6664, 0.6664,0.6688,0.6695,0.6773,0.6811,0.6916,0.6944,0.6944,0.6970,0.6984, 0.7048,0.7054,0.7087,0.7114,0.7141,0.7162,0.7191,0.7242,0.7257,0.7265, 0.7277,0.7297,0.7325,0.7347,0.7394,0.7417,0.7444,0.7454,0.7536,0.7572, 0.7586,0.7599,0.7682,0.7702,0.7704,0.7764,0.7850,0.7863,0.7878,0.7920, 0.7938,0.7944,0.7972,0.8027,0.8041,0.8079,0.8088,0.8089,0.8180,0.8185, 0.8195,0.8206,0.8239,0.8256,0.8260,0.8267,0.8450,0.8495,0.8544,0.8617, 0.8686,0.8735,0.8757,0.8813,0.8820,0.8861,0.8874,0.8925,0.8928,0.8957, 0.8980,0.8990,0.9070,0.9123,0.9149,0.9283,0.9350,0.9354,0.9446,0.9477, 0.9547,0.9560,0.9564,0.9610,0.9652,0.9667,0.9814,0.9885,1.0000, Overall p-value after applying KStest on 269 p-values = 0.299265 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.