RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-13_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 22.8910 0.847168 2 to 25 15.55 26.8602 0.939850 3 to 26 16.18 17.8182 0.599601 4 to 27 15.86 19.9947 0.725501 5 to 28 15.70 17.3045 0.566073 6 to 29 15.88 28.5650 0.961245 7 to 30 15.83 9.7926 0.087918 8 to 31 15.81 8.9952 0.059588 9 to 32 15.46 32.5915 0.987308 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.089651 Tough bday spacings test for dh-ranFile-2017-01-13_01:31: 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 39 68 85 99 84 56 36 15 2 4 (O-E)^2/E 0.9 0.2 0.4 1.6 0.0 0.4 0.3 1.3 0.0 3.2 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.334, p= 0.404 RESULTS OF GCD FOR dh-ranFile-2017-01-13_01:31 Euclid's algorithm: p-value, steps to gcd: 0.913837 p-value, dist. of gcd's: 0.662360 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-13_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.883 0.692 0.631 0.393 0.747 0.328 0.347 0.049 Bits 8 to 15---> 0.475 0.169 0.014 0.143 0.181 0.058 0.763 0.764 Bits 16 to 23---> 0.815 0.613 0.351 0.934 0.424 0.937 0.776 0.525 Bits 24 to 31---> 0.996 0.053 0.265 0.428 0.860 0.283 0.167 0.480 KS test for the above 32 p values: 0.015 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-13_01:31, p-values for 5 runs: 0.0064, 0.6371, 0.1166, 0.4489, 0.7278 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-13_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5191 5134.0 0.633 0.664 r= 30 23033 23103.0 0.212 0.877 r= 31 11562 11551.5 0.010 0.886 chi-square = 0.886 with df = 3; p-value = 0.171 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-13_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 233 211.4 2.203 2.203 r= 30 5207 5134.0 1.038 3.241 r= 31 22956 23103.0 0.936 4.177 r= 32 11604 11551.5 0.238 4.415 chi-square = 4.415 with df = 3; p-value = 0.780 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-13_01:31 b-rank test for bits 1 to 8, p=0.34935 b-rank test for bits 2 to 9, p=0.36529 b-rank test for bits 3 to 10, p=0.63537 b-rank test for bits 4 to 11, p=0.76305 b-rank test for bits 5 to 12, p=0.30624 b-rank test for bits 6 to 13, p=0.96639 b-rank test for bits 7 to 14, p=0.75446 b-rank test for bits 8 to 15, p=0.69999 b-rank test for bits 9 to 16, p=0.71112 b-rank test for bits 10 to 17, p=0.79261 b-rank test for bits 11 to 18, p=0.88774 b-rank test for bits 12 to 19, p=0.45603 b-rank test for bits 13 to 20, p=0.21567 b-rank test for bits 14 to 21, p=0.70067 b-rank test for bits 15 to 22, p=0.09300 b-rank test for bits 16 to 23, p=0.98321 b-rank test for bits 17 to 24, p=0.89780 b-rank test for bits 18 to 25, p=0.73557 b-rank test for bits 19 to 26, p=0.60788 b-rank test for bits 20 to 27, p=0.06586 b-rank test for bits 21 to 28, p=0.47779 b-rank test for bits 22 to 29, p=0.23806 b-rank test for bits 23 to 30, p=0.62020 b-rank test for bits 24 to 31, p=0.19696 b-rank test for bits 25 to 32, p=0.42073 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 = 0.546919 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-13_01:31 (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 142352 1.03 0.849496 2 142221 0.73 0.766755 3 141663 -0.58 0.282464 4 142066 0.37 0.642837 5 142236 0.76 0.777342 6 142386 1.11 0.867299 7 141618 -0.68 0.248038 8 141694 -0.50 0.307444 9 141534 -0.88 0.190260 10 141296 -1.43 0.075927 11 141685 -0.52 0.300092 12 141350 -1.31 0.095633 13 141388 -1.22 0.111600 14 142414 1.18 0.880828 15 141192 -1.68 0.046869 16 142625 1.67 0.952750 17 141895 -0.03 0.486645 18 142025 0.27 0.606519 19 141443 -1.09 0.137954 20 142100 0.45 0.672017 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-13_01:31 Bits used No. missing words z-score p-value 23 to 32 142010 0.3471 0.635756 22 to 31 142183 0.9437 0.827336 21 to 30 141625 -0.9804 0.163432 20 to 29 141827 -0.2839 0.388245 19 to 28 141840 -0.2391 0.405526 18 to 27 141865 -0.1529 0.439254 17 to 26 142198 0.9954 0.840233 16 to 25 141892 -0.0598 0.476174 15 to 24 142049 0.4816 0.684962 14 to 23 141871 -0.1322 0.447424 13 to 22 141831 -0.2701 0.393540 12 to 21 141905 -0.0149 0.494044 11 to 20 141594 -1.0873 0.138442 10 to 19 142076 0.5747 0.717261 9 to 18 141777 -0.4563 0.324083 8 to 17 141544 -1.2598 0.103878 7 to 16 141784 -0.4322 0.332808 6 to 15 141852 -0.1977 0.421644 5 to 14 141891 -0.0632 0.474801 4 to 13 140947 -3.3184 0.000453 3 to 12 141183 -2.5046 0.006130 2 to 11 141670 -0.8253 0.204608 1 to 10 141384 -1.8115 0.035033 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-13_01:31 Bits used No. missing words z-score p-value 28 to 32 141978 0.2328 0.592034 27 to 31 142552 2.1785 0.985317 26 to 30 141738 -0.5808 0.280695 25 to 29 141748 -0.5469 0.292230 24 to 28 142121 0.7175 0.763475 23 to 27 142197 0.9752 0.835258 22 to 26 142097 0.6362 0.737667 21 to 25 141855 -0.1842 0.426940 20 to 24 142252 1.1616 0.877300 19 to 23 141803 -0.3604 0.359259 18 to 22 141934 0.0836 0.533324 17 to 21 142258 1.1819 0.881384 16 to 20 142172 0.8904 0.813376 15 to 19 141594 -1.0689 0.142554 14 to 18 141645 -0.8960 0.185117 13 to 17 142017 0.3650 0.642438 12 to 16 141920 0.0362 0.514426 11 to 15 141571 -1.1469 0.125715 10 to 14 141894 -0.0520 0.479278 9 to 13 141916 0.0226 0.509019 8 to 12 142334 1.4396 0.925004 7 to 11 141814 -0.3232 0.373290 6 to 10 141639 -0.9164 0.179736 5 to 9 141695 -0.7265 0.233753 4 to 8 141980 0.2396 0.594664 3 to 7 142189 0.9480 0.828444 2 to 6 142399 1.6599 0.951533 1 to 5 141855 -0.1842 0.426940 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-13_01:31 Bits used No. missing words z-score p-value 31 to 32 141902 -0.0216 0.491375 30 to 31 142528 1.8250 0.965998 29 to 30 142558 1.9135 0.972157 28 to 29 142237 0.9666 0.833123 27 to 28 141627 -0.8328 0.202470 26 to 27 141278 -1.8623 0.031278 25 to 26 141844 -0.1927 0.423592 24 to 25 141671 -0.7030 0.241016 23 to 24 141956 0.1377 0.554749 22 to 23 141401 -1.4995 0.066872 21 to 22 142015 0.3117 0.622370 20 to 21 141709 -0.5909 0.277279 19 to 20 142388 1.4120 0.921026 18 to 19 141597 -0.9213 0.178440 17 to 18 141851 -0.1721 0.431693 16 to 17 142153 0.7188 0.763865 15 to 16 142477 1.6745 0.952988 14 to 15 142086 0.5212 0.698869 13 to 14 142560 1.9194 0.972532 12 to 13 141748 -0.4759 0.317073 11 to 12 141478 -1.2724 0.101623 10 to 11 142057 0.4356 0.668438 9 to 10 141291 -1.8240 0.034077 8 to 9 142056 0.4327 0.667367 7 to 8 141982 0.2144 0.584869 6 to 7 142037 0.3766 0.646767 5 to 6 141767 -0.4199 0.337297 4 to 5 142296 1.1406 0.872986 3 to 4 141794 -0.3402 0.366851 2 to 3 142205 0.8722 0.808446 1 to 2 141861 -0.1426 0.443316 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-13_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2398.13 -1.441 0.074849 Test results for specific bytes for dh-ranFile-2017-01-13_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2551.76 0.732 0.767898 2 to 9 2664.46 2.326 0.989986 3 to 10 2530.31 0.429 0.665915 4 to 11 2494.66 -0.076 0.469889 5 to 12 2401.66 -1.391 0.082156 6 to 13 2401.62 -1.391 0.082064 7 to 14 2651.49 2.142 0.983919 8 to 15 2477.40 -0.320 0.374606 9 to 16 2544.21 0.625 0.734082 10 to 17 2650.95 2.135 0.983612 11 to 18 2569.44 0.982 0.836955 12 to 19 2502.52 0.036 0.514221 13 to 20 2559.40 0.840 0.799558 14 to 21 2464.43 -0.503 0.307471 15 to 22 2501.60 0.023 0.509046 16 to 23 2490.55 -0.134 0.446824 17 to 24 2316.65 -2.593 0.004759 18 to 25 2403.14 -1.370 0.085384 19 to 26 2446.16 -0.761 0.223202 20 to 27 2483.53 -0.233 0.407927 21 to 28 2485.67 -0.203 0.419704 22 to 29 2496.84 -0.045 0.482206 23 to 30 2461.82 -0.540 0.294624 24 to 31 2482.63 -0.246 0.402960 25 to 32 2470.77 -0.413 0.339688 CDPARK for dh-ranFile-2017-01-13_01:31: 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 3556 1.5068 0.934075 3510 -0.5936 0.276387 3507 -0.7306 0.232514 3551 1.2785 0.899470 3536 0.5936 0.723613 3461 -2.8311 0.002320 3505 -0.8219 0.205562 3515 -0.3653 0.357445 3539 0.7306 0.767486 3481 -1.9178 0.027568 Square side=100, avg. no. parked=3516.10 sample std.=28.71 p-value of the KSTEST for those 10 p-values: 0.358202 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-13_01:31 0.4254,0.9082,0.0739,0.2025,0.7224,0.2614,0.5277,0.4704,0.8131,0.9130, The KS test for those 10 p-values: 0.977123 The 3DSPHERES test for dh-ranFile-2017-01-13_01:31 sample no r^3 equiv. uni. 1 5.094 0.156158 2 8.020 0.234569 3 52.686 0.827303 4 105.476 0.970278 5 21.648 0.514027 6 16.860 0.429941 7 0.114 0.003790 8 38.524 0.723113 9 2.972 0.094306 10 43.707 0.767046 11 15.887 0.411139 12 42.082 0.754077 13 7.522 0.221774 14 30.809 0.641904 15 72.646 0.911214 16 8.735 0.252617 17 5.322 0.162559 18 2.178 0.070042 19 12.429 0.339201 20 1.203 0.039314 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.387196 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-13_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.8 0.2 1.4 1.2 -0.3 -1.3 -0.7 -1.0 1.4 0.4 0.6 -1.2 -0.5 -0.8 -0.6 0.9 1.3 -1.2 0.7 -0.0 1.3 -0.1 -0.3 0.5 -0.7 -0.1 0.1 -0.7 0.9 -0.9 -0.1 -0.1 1.9 -0.7 0.5 -0.1 -1.6 -0.7 0.1 3.0 -0.1 Chi-square with 42 degrees of freedom:38.844514 z-score=-0.344292, p-value=0.389728 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-13_01:31 Test no p-value 1 0.884928 2 0.787352 3 0.161723 4 0.092846 5 0.513463 6 0.009179 7 0.106482 8 0.210261 9 0.070447 10 0.400381 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.053001 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-13_01:31: (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 67051 2.22 66631 0.02 3 25000.00 24659 4.65 24966 0.05 4 6666.67 6629 0.21 6811 3.12 5 1388.89 1402 0.12 1311 4.37 6 238.10 223 0.96 244 0.15 7 34.72 30 0.64 35 0.00 8 4.96 5 0.00 1 3.16 p=0.81501 p=0.90747 Number of rngs required: 688286, p-value: 0.446 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-13_01:31 No. of wins: Observed Expected 98813 98585.9 z-score= 1.016, pvalue=0.84516 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66950 66666.7 1.204 1.204 2 37750 37654.3 0.243 1.447 3 26637 26954.7 3.745 5.193 4 19380 19313.5 0.229 5.422 5 13871 13851.4 0.028 5.450 6 9891 9943.5 0.278 5.727 7 7035 7145.0 1.694 7.421 8 5038 5139.1 1.988 9.409 9 3743 3699.9 0.503 9.912 10 2703 2666.3 0.505 10.417 11 1999 1923.3 2.977 13.395 12 1436 1388.7 1.608 15.003 13 980 1003.7 0.560 15.563 14 729 726.1 0.011 15.574 15 508 525.8 0.605 16.179 16 385 381.2 0.039 16.218 17 239 276.5 5.096 21.314 18 196 200.8 0.116 21.430 19 139 146.0 0.334 21.764 20 108 106.2 0.030 21.794 21 283 287.1 0.059 21.853 Chisq= 21.85 for 20 degrees of freedom, p= 0.65148 SUMMARY of craptest p-value for no. of wins: 0.845164 p-value for throws/game: 0.651482 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-13_01:31 No. of wins: Observed Expected 98820 98585.9 z-score= 1.047, pvalue=0.85250 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66721 66666.7 0.044 0.044 2 37547 37654.3 0.306 0.350 3 27127 26954.7 1.101 1.451 4 19191 19313.5 0.777 2.228 5 13844 13851.4 0.004 2.232 6 9938 9943.5 0.003 2.235 7 7123 7145.0 0.068 2.303 8 5118 5139.1 0.086 2.389 9 3756 3699.9 0.852 3.241 10 2609 2666.3 1.231 4.472 11 1868 1923.3 1.592 6.064 12 1428 1388.7 1.110 7.174 13 1007 1003.7 0.011 7.184 14 758 726.1 1.398 8.582 15 554 525.8 1.508 10.091 16 384 381.2 0.021 10.112 17 277 276.5 0.001 10.113 18 202 200.8 0.007 10.119 19 147 146.0 0.007 10.127 20 98 106.2 0.635 10.762 21 303 287.1 0.879 11.641 Chisq= 11.64 for 20 degrees of freedom, p= 0.07212 SUMMARY of craptest p-value for no. of wins: 0.852500 p-value for throws/game: 0.072119 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0023,0.0038,0.0048,0.0061,0.0064,0.0092,0.0144,0.0149,0.0276, 0.0313,0.0341,0.0350,0.0393,0.0469,0.0486,0.0527,0.0530,0.0576,0.0596, 0.0659,0.0669,0.0700,0.0704,0.0721,0.0739,0.0748,0.0759,0.0821,0.0822, 0.0854,0.0879,0.0897,0.0928,0.0930,0.0943,0.0956,0.1016,0.1039,0.1065, 0.1116,0.1166,0.1257,0.1380,0.1384,0.1426,0.1429,0.1562,0.1617,0.1626, 0.1634,0.1671,0.1694,0.1712,0.1784,0.1797,0.1812,0.1851,0.1903,0.1970, 0.2025,0.2025,0.2046,0.2056,0.2103,0.2157,0.2218,0.2232,0.2325,0.2338, 0.2346,0.2381,0.2410,0.2480,0.2526,0.2614,0.2646,0.2764,0.2773,0.2807, 0.2825,0.2826,0.2922,0.2946,0.3001,0.3062,0.3074,0.3075,0.3171,0.3241, 0.3285,0.3328,0.3373,0.3392,0.3397,0.3467,0.3494,0.3508,0.3574,0.3582, 0.3593,0.3653,0.3669,0.3733,0.3746,0.3872,0.3882,0.3897,0.3928,0.3935, 0.4004,0.4030,0.4038,0.4055,0.4079,0.4111,0.4197,0.4207,0.4216,0.4236, 0.4243,0.4254,0.4269,0.4269,0.4278,0.4299,0.4317,0.4393,0.4433,0.4465, 0.4468,0.4474,0.4489,0.4560,0.4699,0.4704,0.4748,0.4752,0.4762,0.4778, 0.4793,0.4795,0.4822,0.4866,0.4914,0.4940,0.5090,0.5090,0.5135,0.5140, 0.5142,0.5144,0.5253,0.5277,0.5333,0.5469,0.5547,0.5661,0.5849,0.5920, 0.5947,0.5996,0.6065,0.6079,0.6127,0.6202,0.6224,0.6306,0.6354,0.6358, 0.6371,0.6419,0.6424,0.6428,0.6468,0.6515,0.6624,0.6659,0.6674,0.6684, 0.6720,0.6850,0.6925,0.6989,0.7000,0.7007,0.7111,0.7173,0.7224,0.7231, 0.7236,0.7255,0.7278,0.7341,0.7356,0.7377,0.7473,0.7541,0.7545,0.7630, 0.7632,0.7635,0.7637,0.7639,0.7668,0.7670,0.7675,0.7679,0.7758,0.7773, 0.7800,0.7874,0.7926,0.7996,0.8084,0.8131,0.8134,0.8150,0.8150,0.8273, 0.8273,0.8284,0.8331,0.8353,0.8370,0.8402,0.8452,0.8472,0.8495,0.8525, 0.8603,0.8673,0.8730,0.8773,0.8808,0.8814,0.8833,0.8849,0.8877,0.8978, 0.8995,0.9075,0.9082,0.9112,0.9130,0.9138,0.9210,0.9250,0.9341,0.9343, 0.9373,0.9398,0.9515,0.9528,0.9530,0.9612,0.9660,0.9664,0.9703,0.9722, 0.9725,0.9771,0.9832,0.9836,0.9839,0.9853,0.9873,0.9900,0.9956, Overall p-value after applying KStest on 269 p-values = 0.467152 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.