RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-16_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.54 28.0442 0.955575 2 to 25 15.65 26.4054 0.932616 3 to 26 15.77 20.0364 0.727628 4 to 27 16.05 20.3344 0.742517 5 to 28 15.87 14.9015 0.397424 6 to 29 15.71 31.8485 0.984287 7 to 30 15.82 16.9871 0.544761 8 to 31 15.63 15.4496 0.436872 9 to 32 15.82 19.4907 0.698897 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.036542 Tough bday spacings test for dh-ranFile-2016-11-16_15:31: 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 41 80 91 79 78 65 32 17 9 1 (O-E)^2/E 0.5 0.5 0.6 0.5 3.6 0.0 3.2 0.2 0.3 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 12.514, p= 0.748 RESULTS OF GCD FOR dh-ranFile-2016-11-16_15:31 Euclid's algorithm: p-value, steps to gcd: 0.107309 p-value, dist. of gcd's: 0.434474 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-16_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.214 0.543 0.057 0.287 0.329 0.352 0.138 0.843 Bits 8 to 15---> 0.233 0.372 0.466 0.157 0.384 0.138 0.885 0.503 Bits 16 to 23---> 0.136 0.473 0.458 0.496 0.340 0.292 0.323 0.745 Bits 24 to 31---> 0.183 0.242 0.923 0.852 0.385 0.584 0.930 0.369 KS test for the above 32 p values: 0.915 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-16_15:31, p-values for 5 runs: 0.3816, 0.5752, 0.8195, 0.2619, 0.8810 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-16_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5072 5134.0 0.749 1.262 r= 30 23164 23103.0 0.161 1.423 r= 31 11563 11551.5 0.011 1.435 chi-square = 1.435 with df = 3; p-value = 0.303 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-16_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5093 5134.0 0.328 0.420 r= 31 23170 23103.0 0.194 0.614 r= 32 11530 11551.5 0.040 0.654 chi-square = 0.654 with df = 3; p-value = 0.116 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-16_15:31 b-rank test for bits 1 to 8, p=0.43671 b-rank test for bits 2 to 9, p=0.12750 b-rank test for bits 3 to 10, p=0.38529 b-rank test for bits 4 to 11, p=0.95063 b-rank test for bits 5 to 12, p=0.95302 b-rank test for bits 6 to 13, p=0.76325 b-rank test for bits 7 to 14, p=0.03251 b-rank test for bits 8 to 15, p=0.02294 b-rank test for bits 9 to 16, p=0.25307 b-rank test for bits 10 to 17, p=0.67893 b-rank test for bits 11 to 18, p=0.13101 b-rank test for bits 12 to 19, p=0.95597 b-rank test for bits 13 to 20, p=0.63717 b-rank test for bits 14 to 21, p=0.15994 b-rank test for bits 15 to 22, p=0.07930 b-rank test for bits 16 to 23, p=0.58202 b-rank test for bits 17 to 24, p=0.06372 b-rank test for bits 18 to 25, p=0.85037 b-rank test for bits 19 to 26, p=0.76605 b-rank test for bits 20 to 27, p=0.84600 b-rank test for bits 21 to 28, p=0.97975 b-rank test for bits 22 to 29, p=0.72250 b-rank test for bits 23 to 30, p=0.05476 b-rank test for bits 24 to 31, p=0.93346 b-rank test for bits 25 to 32, p=0.99621 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 = 0.086859 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-16_15:31 (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 142615 1.65 0.950402 2 141732 -0.41 0.339319 3 142489 1.35 0.912191 4 142251 0.80 0.787650 5 141855 -0.13 0.449494 6 141665 -0.57 0.284046 7 142258 0.81 0.792364 8 141716 -0.45 0.325741 9 142384 1.11 0.866294 10 141459 -1.05 0.146360 11 142012 0.24 0.594790 12 141272 -1.49 0.068232 13 142069 0.37 0.645448 14 142382 1.10 0.865284 15 141452 -1.07 0.142641 16 141930 0.05 0.519259 17 141823 -0.20 0.420073 18 142246 0.79 0.784246 19 141919 0.02 0.509013 20 142272 0.85 0.801603 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-16_15:31 Bits used No. missing words z-score p-value 23 to 32 141872 -0.1287 0.448788 22 to 31 141847 -0.2149 0.414911 21 to 30 141900 -0.0322 0.487167 20 to 29 141977 0.2333 0.592253 19 to 28 141653 -0.8839 0.188376 18 to 27 141850 -0.2046 0.418948 17 to 26 141881 -0.0977 0.461089 16 to 25 141473 -1.5046 0.066215 15 to 24 141394 -1.7770 0.037784 14 to 23 141873 -0.1253 0.450153 13 to 22 142201 1.0058 0.842734 12 to 21 142030 0.4161 0.661333 11 to 20 141791 -0.4080 0.341624 10 to 19 141364 -1.8804 0.030024 9 to 18 141354 -1.9149 0.027751 8 to 17 141972 0.2161 0.585547 7 to 16 142191 0.9713 0.834295 6 to 15 141581 -1.1322 0.128781 5 to 14 141813 -0.3322 0.369880 4 to 13 141801 -0.3736 0.354369 3 to 12 141658 -0.8667 0.193066 2 to 11 141962 0.1816 0.572060 1 to 10 141669 -0.8287 0.203630 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-16_15:31 Bits used No. missing words z-score p-value 28 to 32 142426 1.7514 0.960064 27 to 31 142050 0.4768 0.683265 26 to 30 141755 -0.5232 0.300434 25 to 29 141767 -0.4825 0.314734 24 to 28 142211 1.0226 0.846754 23 to 27 142243 1.1311 0.870990 22 to 26 141773 -0.4621 0.321992 21 to 25 142271 1.2260 0.889901 20 to 24 141572 -1.1435 0.126417 19 to 23 141692 -0.7367 0.230649 18 to 22 141756 -0.5198 0.301615 17 to 21 141619 -0.9842 0.162516 16 to 20 141806 -0.3503 0.363068 15 to 19 141912 0.0091 0.503611 14 to 18 141647 -0.8893 0.186933 13 to 17 141759 -0.5096 0.305168 12 to 16 141993 0.2836 0.611652 11 to 15 141631 -0.9435 0.172715 10 to 14 141510 -1.3537 0.087922 9 to 13 141714 -0.6621 0.253942 8 to 12 142328 1.4192 0.922083 7 to 11 141888 -0.0723 0.471180 6 to 10 141682 -0.7706 0.220469 5 to 9 142021 0.3785 0.647486 4 to 8 141722 -0.6350 0.262709 3 to 7 141810 -0.3367 0.368167 2 to 6 141496 -1.4011 0.080589 1 to 5 142214 1.0328 0.849147 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-16_15:31 Bits used No. missing words z-score p-value 31 to 32 141812 -0.2871 0.387014 30 to 31 142349 1.2970 0.902678 29 to 30 141578 -0.9774 0.164192 28 to 29 142045 0.4002 0.655498 27 to 28 141363 -1.6116 0.053525 26 to 27 142233 0.9548 0.830155 25 to 26 141866 -0.1278 0.449147 24 to 25 141773 -0.4022 0.343786 23 to 24 141569 -1.0039 0.157708 22 to 23 142107 0.5831 0.720086 21 to 22 141669 -0.7089 0.239182 20 to 21 142422 1.5123 0.934771 19 to 20 141408 -1.4788 0.069590 18 to 19 141938 0.0846 0.533699 17 to 18 141822 -0.2576 0.398354 16 to 17 141682 -0.6706 0.251241 15 to 16 142011 0.2999 0.617878 14 to 15 141571 -0.9980 0.159134 13 to 14 141766 -0.4228 0.336220 12 to 13 142324 1.2232 0.889376 11 to 12 142265 1.0492 0.852951 10 to 11 141549 -1.0629 0.143909 9 to 10 141848 -0.1809 0.428217 8 to 9 141662 -0.7296 0.232821 7 to 8 142062 0.4504 0.673772 6 to 7 142082 0.5094 0.694747 5 to 6 141780 -0.3815 0.351415 4 to 5 142586 1.9961 0.977037 3 to 4 142382 1.3943 0.918388 2 to 3 141557 -1.0393 0.149328 1 to 2 142025 0.3412 0.633527 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-16_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2550.00 0.707 0.760271 Test results for specific bytes for dh-ranFile-2016-11-16_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2563.43 0.897 0.815135 2 to 9 2574.92 1.060 0.855320 3 to 10 2596.06 1.358 0.912836 4 to 11 2360.79 -1.969 0.024491 5 to 12 2514.76 0.209 0.582672 6 to 13 2570.21 0.993 0.839626 7 to 14 2484.57 -0.218 0.413653 8 to 15 2560.85 0.861 0.805272 9 to 16 2489.51 -0.148 0.441032 10 to 17 2527.40 0.388 0.650821 11 to 18 2524.69 0.349 0.636500 12 to 19 2633.67 1.890 0.970647 13 to 20 2526.45 0.374 0.645845 14 to 21 2461.62 -0.543 0.293665 15 to 22 2591.78 1.298 0.902852 16 to 23 2515.58 0.220 0.587217 17 to 24 2496.06 -0.056 0.477779 18 to 25 2481.28 -0.265 0.395594 19 to 26 2615.88 1.639 0.949374 20 to 27 2509.41 0.133 0.552916 21 to 28 2371.14 -1.822 0.034196 22 to 29 2464.69 -0.499 0.308767 23 to 30 2504.53 0.064 0.525558 24 to 31 2436.90 -0.892 0.186081 25 to 32 2488.36 -0.165 0.434625 CDPARK for dh-ranFile-2016-11-16_15:31: 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 3513 -0.4566 0.323972 3528 0.2283 0.590298 3484 -1.7808 0.037471 3526 0.1370 0.554479 3505 -0.8219 0.205562 3467 -2.5571 0.005278 3522 -0.0457 0.481790 3497 -1.1872 0.117571 3541 0.8219 0.794438 3525 0.0913 0.536383 Square side=100, avg. no. parked=3510.80 sample std.=21.52 p-value of the KSTEST for those 10 p-values: 0.179955 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-16_15:31 0.8251,0.4413,0.5312,0.7547,0.0449,0.0687,0.8775,0.3290,0.3165,0.7070, The KS test for those 10 p-values: 0.963610 The 3DSPHERES test for dh-ranFile-2016-11-16_15:31 sample no r^3 equiv. uni. 1 3.550 0.111611 2 17.203 0.436421 3 0.021 0.000702 4 22.426 0.526464 5 2.096 0.067477 6 5.718 0.173528 7 7.204 0.213471 8 36.358 0.702377 9 81.625 0.934180 10 17.939 0.450070 11 128.436 0.986174 12 33.822 0.676129 13 36.269 0.701493 14 2.033 0.065509 15 4.572 0.141364 16 0.526 0.017392 17 42.231 0.755291 18 8.497 0.246658 19 4.003 0.124920 20 11.488 0.318147 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.061034 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-16_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 -0.4 -0.3 2.6 -0.2 -0.8 1.1 -0.9 -0.4 0.9 -2.8 -1.1 -0.3 0.2 -0.3 2.6 -0.2 0.2 0.9 0.8 -2.2 0.2 0.2 -0.1 -0.3 0.0 1.3 -0.0 -0.4 0.5 0.9 -1.6 0.5 0.5 -0.8 -0.5 -0.4 -0.4 -1.3 1.6 0.0 -0.1 Chi-square with 42 degrees of freedom:47.362008 z-score=0.585043, p-value=0.736937 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-16_15:31 Test no p-value 1 0.822803 2 0.225940 3 0.474892 4 0.012103 5 0.713971 6 0.588063 7 0.113849 8 0.006073 9 0.411454 10 0.846754 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.314733 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-16_15:31: (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 66508 0.38 66584 0.10 3 25000.00 25067 0.18 24991 0.00 4 6666.67 6714 0.34 6710 0.28 5 1388.89 1427 1.05 1419 0.65 6 238.10 238 0.00 250 0.60 7 34.72 42 1.53 39 0.53 8 4.96 3 0.77 6 0.22 p=0.35576 p=0.11846 Number of rngs required: 688975, p-value: 0.745 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-16_15:31 No. of wins: Observed Expected 98574 98585.9 z-score=-0.053, pvalue=0.47885 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67057 66666.7 2.285 2.285 2 37492 37654.3 0.700 2.985 3 26888 26954.7 0.165 3.150 4 19317 19313.5 0.001 3.151 5 13812 13851.4 0.112 3.263 6 9832 9943.5 1.251 4.514 7 7120 7145.0 0.088 4.602 8 5250 5139.1 2.394 6.996 9 3678 3699.9 0.129 7.126 10 2670 2666.3 0.005 7.131 11 1885 1923.3 0.764 7.895 12 1392 1388.7 0.008 7.902 13 1037 1003.7 1.104 9.006 14 646 726.1 8.845 17.851 15 538 525.8 0.281 18.132 16 366 381.2 0.602 18.734 17 286 276.5 0.324 19.058 18 200 200.8 0.003 19.062 19 166 146.0 2.744 21.806 20 95 106.2 1.184 22.990 21 273 287.1 0.694 23.684 Chisq= 23.68 for 20 degrees of freedom, p= 0.74353 SUMMARY of craptest p-value for no. of wins: 0.478851 p-value for throws/game: 0.743526 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-16_15:31 No. of wins: Observed Expected 98537 98585.9 z-score=-0.219, pvalue=0.41351 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67031 66666.7 1.991 1.991 2 37697 37654.3 0.048 2.039 3 26864 26954.7 0.305 2.345 4 19163 19313.5 1.172 3.517 5 14027 13851.4 2.226 5.743 6 9812 9943.5 1.740 7.483 7 7149 7145.0 0.002 7.485 8 5037 5139.1 2.027 9.512 9 3670 3699.9 0.241 9.754 10 2627 2666.3 0.579 10.333 11 1918 1923.3 0.015 10.347 12 1405 1388.7 0.190 10.538 13 998 1003.7 0.033 10.570 14 727 726.1 0.001 10.571 15 514 525.8 0.266 10.838 16 390 381.2 0.205 11.043 17 278 276.5 0.008 11.051 18 173 200.8 3.857 14.907 19 172 146.0 4.636 19.544 20 100 106.2 0.364 19.907 21 248 287.1 5.329 25.236 Chisq= 25.24 for 20 degrees of freedom, p= 0.80745 SUMMARY of craptest p-value for no. of wins: 0.413510 p-value for throws/game: 0.807447 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0053,0.0061,0.0121,0.0174,0.0229,0.0245,0.0278,0.0300,0.0325, 0.0342,0.0365,0.0375,0.0378,0.0449,0.0535,0.0548,0.0573,0.0610,0.0637, 0.0655,0.0662,0.0675,0.0682,0.0687,0.0696,0.0793,0.0806,0.0869,0.0879, 0.1073,0.1116,0.1138,0.1160,0.1176,0.1185,0.1249,0.1264,0.1275,0.1288, 0.1310,0.1357,0.1379,0.1382,0.1414,0.1426,0.1439,0.1464,0.1493,0.1566, 0.1577,0.1591,0.1599,0.1625,0.1642,0.1727,0.1735,0.1800,0.1830,0.1861, 0.1869,0.1884,0.1931,0.2036,0.2056,0.2135,0.2141,0.2205,0.2259,0.2306, 0.2328,0.2329,0.2392,0.2423,0.2467,0.2512,0.2531,0.2539,0.2619,0.2627, 0.2840,0.2872,0.2924,0.2937,0.3004,0.3016,0.3025,0.3052,0.3088,0.3147, 0.3147,0.3165,0.3181,0.3220,0.3233,0.3240,0.3257,0.3286,0.3290,0.3362, 0.3393,0.3402,0.3416,0.3438,0.3514,0.3521,0.3544,0.3558,0.3631,0.3682, 0.3692,0.3699,0.3722,0.3816,0.3844,0.3850,0.3853,0.3870,0.3956,0.3974, 0.3984,0.4115,0.4135,0.4137,0.4149,0.4189,0.4201,0.4282,0.4345,0.4346, 0.4364,0.4367,0.4369,0.4410,0.4413,0.4488,0.4491,0.4495,0.4501,0.4502, 0.4581,0.4611,0.4664,0.4712,0.4732,0.4749,0.4778,0.4789,0.4818,0.4872, 0.4961,0.5034,0.5036,0.5090,0.5193,0.5256,0.5265,0.5312,0.5337,0.5364, 0.5427,0.5448,0.5529,0.5545,0.5721,0.5752,0.5820,0.5827,0.5839,0.5855, 0.5872,0.5881,0.5903,0.5923,0.5948,0.6117,0.6179,0.6335,0.6365,0.6372, 0.6454,0.6458,0.6475,0.6508,0.6555,0.6613,0.6738,0.6761,0.6789,0.6833, 0.6947,0.6989,0.7015,0.7024,0.7070,0.7140,0.7201,0.7225,0.7276,0.7369, 0.7425,0.7435,0.7453,0.7454,0.7479,0.7547,0.7553,0.7603,0.7632,0.7661, 0.7842,0.7877,0.7924,0.7944,0.8016,0.8053,0.8074,0.8151,0.8195,0.8228, 0.8251,0.8302,0.8343,0.8396,0.8427,0.8435,0.8460,0.8468,0.8468,0.8491, 0.8504,0.8525,0.8530,0.8553,0.8653,0.8663,0.8710,0.8775,0.8810,0.8854, 0.8894,0.8899,0.9027,0.9029,0.9122,0.9128,0.9147,0.9184,0.9221,0.9226, 0.9298,0.9326,0.9335,0.9342,0.9348,0.9494,0.9504,0.9506,0.9530,0.9556, 0.9560,0.9601,0.9636,0.9706,0.9770,0.9798,0.9843,0.9862,0.9962, Overall p-value after applying KStest on 269 p-values = 0.222171 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.