RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-08_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 9.0736 0.062076 2 to 25 15.63 20.5754 0.754141 3 to 26 15.85 15.6036 0.447909 4 to 27 15.94 14.5753 0.373958 5 to 28 15.83 13.3579 0.288083 6 to 29 15.67 19.1651 0.680861 7 to 30 15.96 16.7416 0.527999 8 to 31 15.86 30.9105 0.979521 9 to 32 15.76 19.1352 0.679172 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.913982 Tough bday spacings test for dh-ranFile-2016-06-08_22:31: 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 38 81 99 94 90 45 25 11 7 1 (O-E)^2/E 0.0 0.1 0.8 0.0 0.1 1.8 1.0 0.8 1.0 0.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 7.905, p= 0.362 RESULTS OF GCD FOR dh-ranFile-2016-06-08_22:31 Euclid's algorithm: p-value, steps to gcd: 0.108599 p-value, dist. of gcd's: 0.678066 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-08_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.903 0.780 0.413 0.937 0.472 0.465 0.306 0.810 Bits 8 to 15---> 0.175 0.336 0.679 0.502 0.653 0.324 0.289 0.577 Bits 16 to 23---> 0.057 0.419 0.593 0.487 0.872 0.661 0.771 0.009 Bits 24 to 31---> 0.835 0.086 0.082 0.880 0.199 0.300 0.641 0.333 KS test for the above 32 p values: 0.054 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-08_22:31, p-values for 5 runs: 0.3332, 0.5747, 0.5107, 0.6211, 0.4716 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-08_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5055 5134.0 1.216 1.218 r= 30 23204 23103.0 0.441 1.659 r= 31 11529 11551.5 0.044 1.703 chi-square = 1.703 with df = 3; p-value = 0.364 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-08_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5200 5134.0 0.848 0.849 r= 31 23136 23103.0 0.047 0.896 r= 32 11453 11551.5 0.840 1.736 chi-square = 1.736 with df = 3; p-value = 0.371 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-08_22:31 b-rank test for bits 1 to 8, p=0.50921 b-rank test for bits 2 to 9, p=0.28122 b-rank test for bits 3 to 10, p=0.40769 b-rank test for bits 4 to 11, p=0.68157 b-rank test for bits 5 to 12, p=0.81709 b-rank test for bits 6 to 13, p=0.20608 b-rank test for bits 7 to 14, p=0.36159 b-rank test for bits 8 to 15, p=0.38508 b-rank test for bits 9 to 16, p=0.20557 b-rank test for bits 10 to 17, p=0.35034 b-rank test for bits 11 to 18, p=0.12319 b-rank test for bits 12 to 19, p=0.63794 b-rank test for bits 13 to 20, p=0.65315 b-rank test for bits 14 to 21, p=0.31317 b-rank test for bits 15 to 22, p=0.24229 b-rank test for bits 16 to 23, p=0.01184 b-rank test for bits 17 to 24, p=0.56957 b-rank test for bits 18 to 25, p=0.57212 b-rank test for bits 19 to 26, p=0.78242 b-rank test for bits 20 to 27, p=0.29810 b-rank test for bits 21 to 28, p=0.67808 b-rank test for bits 22 to 29, p=0.68242 b-rank test for bits 23 to 30, p=0.15635 b-rank test for bits 24 to 31, p=0.66407 b-rank test for bits 25 to 32, p=0.16222 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 = 0.172214 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-08_22:31 (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 141644 -0.62 0.267652 2 141429 -1.12 0.130875 3 141598 -0.73 0.233489 4 142269 0.84 0.799644 5 141596 -0.73 0.232060 6 141376 -1.25 0.106364 7 141430 -1.12 0.131372 8 142888 2.29 0.988891 9 141138 -1.80 0.035759 10 142084 0.41 0.658403 11 141075 -1.95 0.025626 12 142755 1.98 0.975915 13 142010 0.24 0.592977 14 142042 0.31 0.621711 15 141935 0.06 0.523913 16 141806 -0.24 0.404613 17 141814 -0.22 0.411871 18 140869 -2.43 0.007535 19 141913 0.01 0.503421 20 141861 -0.11 0.455047 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-08_22:31 Bits used No. missing words z-score p-value 23 to 32 142256 1.1954 0.884037 22 to 31 141813 -0.3322 0.369880 21 to 30 141665 -0.8425 0.199749 20 to 29 142214 1.0506 0.853276 19 to 28 142101 0.6609 0.745672 18 to 27 141804 -0.3632 0.358225 17 to 26 142306 1.3678 0.914317 16 to 25 142433 1.8058 0.964522 15 to 24 142168 0.8920 0.813794 14 to 23 141608 -1.0391 0.149386 13 to 22 141705 -0.7046 0.240534 12 to 21 142028 0.4092 0.658806 11 to 20 141401 -1.7529 0.039813 10 to 19 142012 0.3540 0.638344 9 to 18 141948 0.1333 0.553040 8 to 17 141768 -0.4873 0.313007 7 to 16 142059 0.5161 0.697109 6 to 15 142279 1.2747 0.898797 5 to 14 142207 1.0264 0.847660 4 to 13 141379 -1.8287 0.033720 3 to 12 141939 0.1023 0.540745 2 to 11 141723 -0.6425 0.260269 1 to 10 141702 -0.7149 0.237326 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-08_22:31 Bits used No. missing words z-score p-value 28 to 32 141884 -0.0859 0.465787 27 to 31 141703 -0.6994 0.242144 26 to 30 141806 -0.3503 0.363068 25 to 29 141309 -2.0350 0.020925 24 to 28 141940 0.1040 0.541402 23 to 27 142170 0.8836 0.811551 22 to 26 141385 -1.7774 0.037752 21 to 25 142366 1.5480 0.939193 20 to 24 141890 -0.0655 0.473878 19 to 23 142381 1.5989 0.945077 18 to 22 141631 -0.9435 0.172715 17 to 21 141406 -1.7062 0.043985 16 to 20 141281 -2.1299 0.016589 15 to 19 141465 -1.5062 0.066008 14 to 18 142036 0.4294 0.666180 13 to 17 142145 0.7989 0.787820 12 to 16 142166 0.8701 0.807868 11 to 15 141868 -0.1401 0.444290 10 to 14 141946 0.1243 0.549463 9 to 13 142562 2.2124 0.986532 8 to 12 142100 0.6463 0.740970 7 to 11 141707 -0.6859 0.246399 6 to 10 142240 1.1209 0.868838 5 to 9 142251 1.1582 0.876610 4 to 8 141923 0.0463 0.518480 3 to 7 142126 0.7345 0.768670 2 to 6 142435 1.7819 0.962620 1 to 5 141856 -0.1808 0.428270 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-08_22:31 Bits used No. missing words z-score p-value 31 to 32 142090 0.5329 0.702966 30 to 31 141712 -0.5821 0.280252 29 to 30 141045 -2.5496 0.005392 28 to 29 142180 0.7984 0.787691 27 to 28 141352 -1.6440 0.050084 26 to 27 141894 -0.0452 0.481966 25 to 26 142168 0.7630 0.777280 24 to 25 141882 -0.0806 0.467872 23 to 24 141715 -0.5732 0.283240 22 to 23 142172 0.7748 0.780782 21 to 22 141811 -0.2901 0.385886 20 to 21 142335 1.2557 0.895381 19 to 20 141981 0.2114 0.583719 18 to 19 141734 -0.5172 0.302509 17 to 18 141845 -0.1898 0.424747 16 to 17 141970 0.1790 0.571018 15 to 16 141604 -0.9007 0.183880 14 to 15 142104 0.5742 0.717100 13 to 14 142235 0.9607 0.831643 12 to 13 141456 -1.3373 0.090569 11 to 12 141883 -0.0777 0.469045 10 to 11 141754 -0.4582 0.323404 9 to 10 141696 -0.6293 0.264579 8 to 9 141457 -1.3343 0.091052 7 to 8 142420 1.5064 0.934018 6 to 7 141822 -0.2576 0.398354 5 to 6 141997 0.2586 0.602033 4 to 5 141805 -0.3078 0.379133 3 to 4 142048 0.4091 0.658751 2 to 3 141767 -0.4199 0.337297 1 to 2 141703 -0.6086 0.271381 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-08_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2459.65 -0.571 0.284121 Test results for specific bytes for dh-ranFile-2016-06-08_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2439.38 -0.857 0.195660 2 to 9 2474.89 -0.355 0.361258 3 to 10 2452.01 -0.679 0.248672 4 to 11 2472.06 -0.395 0.346353 5 to 12 2460.92 -0.553 0.290251 6 to 13 2427.52 -1.025 0.152680 7 to 14 2534.04 0.481 0.684891 8 to 15 2570.74 1.000 0.841434 9 to 16 2560.79 0.860 0.805019 10 to 17 2526.17 0.370 0.644349 11 to 18 2384.31 -1.636 0.050906 12 to 19 2414.56 -1.208 0.113457 13 to 20 2503.81 0.054 0.521510 14 to 21 2435.24 -0.916 0.179891 15 to 22 2596.26 1.361 0.913295 16 to 23 2690.06 2.688 0.996404 17 to 24 2452.98 -0.665 0.253047 18 to 25 2294.62 -2.905 0.001839 19 to 26 2306.04 -2.743 0.003044 20 to 27 2353.70 -2.069 0.019275 21 to 28 2430.05 -0.989 0.161260 22 to 29 2376.81 -1.742 0.040744 23 to 30 2554.82 0.775 0.780911 24 to 31 2424.13 -1.073 0.141632 25 to 32 2477.86 -0.313 0.377122 CDPARK for dh-ranFile-2016-06-08_22:31: 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 3553 1.3699 0.914635 3545 1.0046 0.842447 3514 -0.4110 0.340551 3502 -0.9589 0.168804 3551 1.2785 0.899470 3500 -1.0502 0.146807 3509 -0.6393 0.261324 3517 -0.2740 0.392053 3536 0.5936 0.723613 3555 1.4612 0.928018 Square side=100, avg. no. parked=3528.20 sample std.=20.91 p-value of the KSTEST for those 10 p-values: 0.492202 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-08_22:31 0.5788,0.2277,0.8050,0.7262,0.3712,0.0810,0.6575,0.1471,0.0297,0.2057, The KS test for those 10 p-values: 0.345652 The 3DSPHERES test for dh-ranFile-2016-06-08_22:31 sample no r^3 equiv. uni. 1 70.173 0.903584 2 12.739 0.345994 3 0.841 0.027642 4 42.962 0.761184 5 16.420 0.421509 6 18.519 0.460605 7 37.742 0.715796 8 32.590 0.662551 9 3.429 0.108015 10 6.327 0.190135 11 12.461 0.339901 12 3.510 0.110401 13 45.278 0.778928 14 31.702 0.652413 15 21.473 0.511185 16 105.772 0.970570 17 10.415 0.293301 18 9.799 0.278661 19 2.887 0.091753 20 24.276 0.554782 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.916741 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-08_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 0.1 0.3 0.7 0.7 1.3 0.2 2.2 -1.4 -1.1 1.1 -0.0 -1.4 0.7 0.4 1.5 -0.2 -1.0 -0.4 1.2 -1.4 -0.5 0.8 -0.9 0.1 0.1 -0.6 0.3 -0.2 -0.7 0.6 -0.5 0.4 -0.6 -0.3 -0.7 -1.0 0.5 0.4 0.1 0.0 2.7 Chi-square with 42 degrees of freedom:36.112351 z-score=-0.642395, p-value=0.273777 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-08_22:31 Test no p-value 1 0.750622 2 0.972754 3 0.728051 4 0.085273 5 0.600922 6 0.048004 7 0.225436 8 0.343500 9 0.076509 10 0.023231 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.157402 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-08_22:31: (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 66439 0.78 66645 0.01 3 25000.00 25206 1.70 24913 0.30 4 6666.67 6708 0.26 6759 1.28 5 1388.89 1371 0.23 1380 0.06 6 238.10 235 0.04 257 1.50 7 34.72 38 0.31 40 0.80 8 4.96 2 1.77 5 0.00 p=0.46617 p=0.31652 Number of rngs required: 688262, p-value: 0.436 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-08_22:31 No. of wins: Observed Expected 98708 98585.9 z-score= 0.546, pvalue=0.70757 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66725 66666.7 0.051 0.051 2 37551 37654.3 0.284 0.335 3 26918 26954.7 0.050 0.385 4 19028 19313.5 4.219 4.604 5 14102 13851.4 4.533 9.137 6 9833 9943.5 1.229 10.366 7 7103 7145.0 0.247 10.613 8 5202 5139.1 0.771 11.384 9 3720 3699.9 0.110 11.493 10 2681 2666.3 0.081 11.574 11 1997 1923.3 2.822 14.396 12 1456 1388.7 3.258 17.654 13 1045 1003.7 1.698 19.352 14 738 726.1 0.194 19.546 15 485 525.8 3.171 22.717 16 413 381.2 2.661 25.378 17 283 276.5 0.151 25.529 18 208 200.8 0.256 25.785 19 144 146.0 0.027 25.812 20 93 106.2 1.644 27.456 21 275 287.1 0.511 27.967 Chisq= 27.97 for 20 degrees of freedom, p= 0.88983 SUMMARY of craptest p-value for no. of wins: 0.707566 p-value for throws/game: 0.889827 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-08_22:31 No. of wins: Observed Expected 98230 98585.9 z-score=-1.592, pvalue=0.05574 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66528 66666.7 0.288 0.288 2 37654 37654.3 0.000 0.288 3 26717 26954.7 2.097 2.385 4 19415 19313.5 0.534 2.919 5 13884 13851.4 0.077 2.996 6 10093 9943.5 2.246 5.242 7 7264 7145.0 1.981 7.223 8 5231 5139.1 1.644 8.868 9 3758 3699.9 0.913 9.781 10 2640 2666.3 0.259 10.040 11 1910 1923.3 0.092 10.133 12 1337 1388.7 1.928 12.060 13 993 1003.7 0.114 12.175 14 707 726.1 0.505 12.679 15 483 525.8 3.490 16.169 16 373 381.2 0.174 16.343 17 293 276.5 0.980 17.323 18 173 200.8 3.857 21.179 19 148 146.0 0.028 21.207 20 109 106.2 0.073 21.280 21 290 287.1 0.029 21.309 Chisq= 21.31 for 20 degrees of freedom, p= 0.62087 SUMMARY of craptest p-value for no. of wins: 0.055737 p-value for throws/game: 0.620867 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0030,0.0054,0.0075,0.0086,0.0118,0.0166,0.0193,0.0209,0.0232, 0.0256,0.0276,0.0297,0.0337,0.0358,0.0378,0.0398,0.0407,0.0440,0.0480, 0.0501,0.0509,0.0540,0.0557,0.0566,0.0621,0.0660,0.0765,0.0810,0.0820, 0.0853,0.0857,0.0906,0.0911,0.0918,0.1064,0.1080,0.1086,0.1104,0.1135, 0.1232,0.1309,0.1314,0.1416,0.1468,0.1471,0.1494,0.1527,0.1563,0.1574, 0.1613,0.1622,0.1688,0.1722,0.1727,0.1746,0.1799,0.1839,0.1901,0.1957, 0.1987,0.1997,0.2056,0.2057,0.2061,0.2254,0.2277,0.2321,0.2335,0.2373, 0.2405,0.2421,0.2423,0.2464,0.2487,0.2530,0.2603,0.2613,0.2646,0.2677, 0.2714,0.2738,0.2787,0.2803,0.2812,0.2832,0.2841,0.2881,0.2887,0.2903, 0.2933,0.2981,0.3004,0.3025,0.3059,0.3130,0.3132,0.3165,0.3234,0.3238, 0.3331,0.3332,0.3364,0.3373,0.3399,0.3406,0.3435,0.3457,0.3460,0.3464, 0.3503,0.3582,0.3613,0.3616,0.3619,0.3631,0.3636,0.3699,0.3711,0.3712, 0.3740,0.3771,0.3791,0.3851,0.3859,0.3921,0.3984,0.4046,0.4077,0.4119, 0.4132,0.4189,0.4215,0.4247,0.4283,0.4356,0.4443,0.4479,0.4550,0.4606, 0.4647,0.4658,0.4662,0.4679,0.4690,0.4716,0.4719,0.4739,0.4820,0.4866, 0.4922,0.5021,0.5034,0.5092,0.5107,0.5112,0.5185,0.5215,0.5239,0.5280, 0.5407,0.5414,0.5495,0.5530,0.5548,0.5696,0.5710,0.5721,0.5747,0.5767, 0.5788,0.5837,0.5930,0.5933,0.6009,0.6020,0.6209,0.6211,0.6217,0.6379, 0.6383,0.6407,0.6443,0.6524,0.6527,0.6532,0.6575,0.6584,0.6588,0.6588, 0.6611,0.6626,0.6641,0.6662,0.6781,0.6781,0.6790,0.6792,0.6809,0.6816, 0.6824,0.6849,0.6971,0.7030,0.7076,0.7158,0.7171,0.7236,0.7262,0.7281, 0.7410,0.7457,0.7506,0.7541,0.7612,0.7687,0.7710,0.7773,0.7789,0.7803, 0.7808,0.7809,0.7824,0.7877,0.7878,0.7996,0.8050,0.8050,0.8079,0.8101, 0.8116,0.8138,0.8171,0.8316,0.8354,0.8414,0.8424,0.8477,0.8533,0.8688, 0.8719,0.8766,0.8795,0.8840,0.8898,0.8954,0.8988,0.8995,0.9034,0.9036, 0.9133,0.9140,0.9143,0.9146,0.9167,0.9280,0.9340,0.9369,0.9392,0.9451, 0.9626,0.9645,0.9706,0.9728,0.9759,0.9795,0.9865,0.9889,0.9964, Overall p-value after applying KStest on 269 p-values = 0.038709 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.