RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-04_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 14.4356 0.363936 2 to 25 15.78 23.0836 0.853450 3 to 26 15.75 14.6516 0.379443 4 to 27 15.86 16.9497 0.542223 5 to 28 15.91 12.6585 0.241268 6 to 29 15.82 12.9314 0.259235 7 to 30 15.53 12.8516 0.253940 8 to 31 15.76 18.6080 0.648510 9 to 32 15.97 12.8076 0.251034 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.290005 Tough bday spacings test for dh-ranFile-2016-01-04_11:31: 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 14 44 61 91 97 78 52 33 13 10 7 (O-E)^2/E 2.6 1.5 2.1 0.5 0.0 0.0 0.0 0.4 0.2 1.7 2.1 Birthday Spacings: Sum(O-E)^2/E= 10.995, p= 0.642 RESULTS OF GCD FOR dh-ranFile-2016-01-04_11:31 Euclid's algorithm: p-value, steps to gcd: 0.945816 p-value, dist. of gcd's: 0.831047 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-04_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.031 0.628 0.178 0.574 0.218 0.293 0.109 0.220 Bits 8 to 15---> 0.929 0.665 0.488 0.458 0.385 0.248 0.994 0.019 Bits 16 to 23---> 0.272 0.381 0.351 0.839 0.827 0.025 0.750 0.960 Bits 24 to 31---> 0.102 0.323 0.717 0.771 0.066 0.326 0.152 0.935 KS test for the above 32 p values: 0.607 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-04_11:31, p-values for 5 runs: 0.2194, 0.2909, 0.0115, 0.2561, 0.4088 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-04_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5055 5134.0 1.216 1.850 r= 30 23107 23103.0 0.001 1.851 r= 31 11615 11551.5 0.349 2.200 chi-square = 2.200 with df = 3; p-value = 0.468 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-04_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5167 5134.0 0.212 0.407 r= 31 23150 23103.0 0.095 0.502 r= 32 11478 11551.5 0.468 0.970 chi-square = 0.970 with df = 3; p-value = 0.192 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-04_11:31 b-rank test for bits 1 to 8, p=0.64140 b-rank test for bits 2 to 9, p=0.89763 b-rank test for bits 3 to 10, p=0.54225 b-rank test for bits 4 to 11, p=0.19092 b-rank test for bits 5 to 12, p=0.76145 b-rank test for bits 6 to 13, p=0.57188 b-rank test for bits 7 to 14, p=0.16146 b-rank test for bits 8 to 15, p=0.88103 b-rank test for bits 9 to 16, p=0.31848 b-rank test for bits 10 to 17, p=0.16178 b-rank test for bits 11 to 18, p=0.21610 b-rank test for bits 12 to 19, p=0.60329 b-rank test for bits 13 to 20, p=0.65149 b-rank test for bits 14 to 21, p=0.77572 b-rank test for bits 15 to 22, p=0.13862 b-rank test for bits 16 to 23, p=0.57883 b-rank test for bits 17 to 24, p=0.12882 b-rank test for bits 18 to 25, p=0.48590 b-rank test for bits 19 to 26, p=0.65933 b-rank test for bits 20 to 27, p=0.64816 b-rank test for bits 21 to 28, p=0.33470 b-rank test for bits 22 to 29, p=0.20472 b-rank test for bits 23 to 30, p=0.07057 b-rank test for bits 24 to 31, p=0.92884 b-rank test for bits 25 to 32, p=0.16315 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 = 0.582414 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-04_11:31 (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 141796 -0.26 0.395586 2 142108 0.46 0.678741 3 141346 -1.32 0.094055 4 141429 -1.12 0.130875 5 142635 1.70 0.955009 6 141429 -1.12 0.130875 7 142036 0.30 0.616369 8 142291 0.89 0.813737 9 141783 -0.30 0.383935 10 141876 -0.08 0.468964 11 141373 -1.25 0.105083 12 142154 0.57 0.716223 13 142230 0.75 0.773140 14 141951 0.10 0.538780 15 142566 1.53 0.937519 16 141627 -0.66 0.254739 17 142120 0.49 0.688718 18 141266 -1.50 0.066406 19 141943 0.08 0.531352 20 142990 2.52 0.994214 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-04_11:31 Bits used No. missing words z-score p-value 23 to 32 141586 -1.1149 0.132440 22 to 31 141403 -1.7460 0.040408 21 to 30 141878 -0.1080 0.456984 20 to 29 142009 0.3437 0.634460 19 to 28 142018 0.3747 0.646067 18 to 27 142524 2.1196 0.982978 17 to 26 142354 1.5333 0.937405 16 to 25 141113 -2.7460 0.003017 15 to 24 141580 -1.1356 0.128058 14 to 23 142013 0.3575 0.639635 13 to 22 141938 0.0989 0.539376 12 to 21 142164 0.8782 0.810075 11 to 20 141295 -2.1184 0.017071 10 to 19 141425 -1.6701 0.047449 9 to 18 141681 -0.7873 0.215540 8 to 17 141920 0.0368 0.514675 7 to 16 142120 0.7264 0.766218 6 to 15 142163 0.8747 0.809138 5 to 14 142015 0.3644 0.642213 4 to 13 142544 2.1885 0.985684 3 to 12 142350 1.5196 0.935688 2 to 11 142082 0.5954 0.724217 1 to 10 141810 -0.3425 0.365981 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-04_11:31 Bits used No. missing words z-score p-value 28 to 32 141445 -1.5740 0.057744 27 to 31 141744 -0.5604 0.287589 26 to 30 142274 1.2362 0.891802 25 to 29 141707 -0.6859 0.246399 24 to 28 142082 0.5853 0.720834 23 to 27 142040 0.4429 0.671099 22 to 26 142312 1.3650 0.913871 21 to 25 141618 -0.9876 0.161684 20 to 24 142368 1.5548 0.940005 19 to 23 142276 1.2429 0.893057 18 to 22 142285 1.2735 0.898572 17 to 21 142089 0.6091 0.728755 16 to 20 142239 1.1175 0.868115 15 to 19 141920 0.0362 0.514426 14 to 18 141872 -0.1265 0.449651 13 to 17 142047 0.4667 0.679635 12 to 16 141850 -0.2011 0.420303 11 to 15 141589 -1.0859 0.138770 10 to 14 141286 -2.1130 0.017301 9 to 13 142185 0.9345 0.824970 8 to 12 141527 -1.2960 0.097482 7 to 11 141855 -0.1842 0.426940 6 to 10 141660 -0.8452 0.199003 5 to 9 141939 0.1006 0.540057 4 to 8 141619 -0.9842 0.162516 3 to 7 141849 -0.2045 0.418978 2 to 6 141660 -0.8452 0.199003 1 to 5 141844 -0.2215 0.412368 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-04_11:31 Bits used No. missing words z-score p-value 31 to 32 142169 0.7660 0.778158 30 to 31 141985 0.2232 0.588316 29 to 30 142791 2.6008 0.995350 28 to 29 142122 0.6273 0.734784 27 to 28 141528 -1.1249 0.130323 26 to 27 141991 0.2409 0.595189 25 to 26 142487 1.7040 0.955813 24 to 25 141699 -0.6204 0.267483 23 to 24 142217 0.9076 0.817950 22 to 23 142761 2.5123 0.994003 21 to 22 141472 -1.2901 0.098515 20 to 21 142138 0.6745 0.750017 19 to 20 141809 -0.2960 0.383631 18 to 19 141936 0.0787 0.531354 17 to 18 142043 0.3943 0.653323 16 to 17 142008 0.2911 0.614498 15 to 16 141864 -0.1337 0.446813 14 to 15 141914 0.0138 0.505496 13 to 14 141356 -1.6322 0.051314 12 to 13 141884 -0.0747 0.470219 11 to 12 142245 0.9902 0.838956 10 to 11 141450 -1.3550 0.087716 9 to 10 142146 0.6981 0.757456 8 to 9 142235 0.9607 0.831643 7 to 8 142307 1.1731 0.879616 6 to 7 141643 -0.7856 0.216041 5 to 6 141765 -0.4258 0.335144 4 to 5 142169 0.7660 0.778158 3 to 4 141863 -0.1367 0.445647 2 to 3 141979 0.2055 0.581416 1 to 2 141414 -1.4612 0.071987 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-04_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2389.78 -1.559 0.059536 Test results for specific bytes for dh-ranFile-2016-01-04_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2551.65 0.730 0.767449 2 to 9 2454.50 -0.643 0.259957 3 to 10 2514.07 0.199 0.578862 4 to 11 2470.26 -0.421 0.337005 5 to 12 2706.96 2.927 0.998288 6 to 13 2464.74 -0.499 0.308997 7 to 14 2550.34 0.712 0.761731 8 to 15 2551.30 0.726 0.765935 9 to 16 2467.91 -0.454 0.324979 10 to 17 2436.34 -0.900 0.183992 11 to 18 2512.63 0.179 0.570853 12 to 19 2474.25 -0.364 0.357895 13 to 20 2430.65 -0.981 0.163361 14 to 21 2695.03 2.758 0.997094 15 to 22 2577.89 1.102 0.864675 16 to 23 2532.10 0.454 0.675054 17 to 24 2360.13 -1.978 0.023959 18 to 25 2542.62 0.603 0.726642 19 to 26 2663.71 2.315 0.989698 20 to 27 2571.37 1.009 0.843592 21 to 28 2545.07 0.637 0.738078 22 to 29 2590.49 1.280 0.899685 23 to 30 2614.71 1.622 0.947630 24 to 31 2503.82 0.054 0.521546 25 to 32 2425.58 -1.053 0.146280 CDPARK for dh-ranFile-2016-01-04_11:31: 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 3501 -1.0046 0.157553 3532 0.4110 0.659449 3507 -0.7306 0.232514 3473 -2.2831 0.011212 3541 0.8219 0.794438 3513 -0.4566 0.323972 3546 1.0502 0.853193 3536 0.5936 0.723613 3529 0.2740 0.607947 3529 0.2740 0.607947 Square side=100, avg. no. parked=3520.70 sample std.=21.12 p-value of the KSTEST for those 10 p-values: 0.857053 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-04_11:31 0.0164,0.0306,0.0893,0.3310,0.2197,0.5386,0.9109,0.3015,0.1226,0.3106, The KS test for those 10 p-values: 0.022978 The 3DSPHERES test for dh-ranFile-2016-01-04_11:31 sample no r^3 equiv. uni. 1 7.074 0.210059 2 65.060 0.885669 3 40.931 0.744457 4 144.155 0.991813 5 15.970 0.412771 6 18.295 0.456552 7 16.123 0.415748 8 115.495 0.978717 9 14.034 0.373621 10 0.397 0.013143 11 16.466 0.422401 12 7.610 0.224038 13 19.689 0.481236 14 102.324 0.966985 15 28.779 0.616840 16 20.851 0.500941 17 65.328 0.886687 18 18.380 0.458094 19 15.126 0.396011 20 17.579 0.443427 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.255411 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-04_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.3 0.3 0.0 0.4 -0.4 -0.7 -1.6 -0.6 -0.5 -0.6 0.5 -0.8 -1.0 -0.3 -0.9 -0.6 0.7 0.9 1.7 2.3 0.1 -1.0 1.7 -1.0 1.4 -0.6 -1.9 -0.2 -1.4 -1.3 0.4 1.9 0.2 -0.8 1.7 0.0 0.8 -0.4 1.0 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:45.273696 z-score=0.357189, p-value=0.663002 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-04_11:31 Test no p-value 1 0.125164 2 0.036507 3 0.668205 4 0.011946 5 0.053304 6 0.443111 7 0.753954 8 0.523156 9 0.509068 10 0.461642 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.104941 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-04_11:31: (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 66649 0.00 66677 0.00 3 25000.00 25007 0.00 24967 0.04 4 6666.67 6673 0.01 6692 0.10 5 1388.89 1400 0.09 1388 0.00 6 238.10 235 0.04 247 0.33 7 34.72 31 0.40 25 2.72 8 4.96 4 0.19 3 0.77 p=0.00609 p=0.31936 Number of rngs required: 688604, p-value: 0.591 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-04_11:31 No. of wins: Observed Expected 98419 98585.9 z-score=-0.746, pvalue=0.22775 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66600 66666.7 0.067 0.067 2 37515 37654.3 0.515 0.582 3 26955 26954.7 0.000 0.582 4 19485 19313.5 1.524 2.106 5 13975 13851.4 1.103 3.208 6 9924 9943.5 0.038 3.247 7 7074 7145.0 0.706 3.953 8 5220 5139.1 1.274 5.227 9 3699 3699.9 0.000 5.227 10 2587 2666.3 2.358 7.586 11 1873 1923.3 1.317 8.903 12 1377 1388.7 0.099 9.002 13 1023 1003.7 0.371 9.372 14 729 726.1 0.011 9.384 15 539 525.8 0.330 9.713 16 381 381.2 0.000 9.713 17 299 276.5 1.824 11.538 18 207 200.8 0.190 11.727 19 162 146.0 1.757 13.484 20 104 106.2 0.046 13.530 21 272 287.1 0.796 14.326 Chisq= 14.33 for 20 degrees of freedom, p= 0.18641 SUMMARY of craptest p-value for no. of wins: 0.227746 p-value for throws/game: 0.186411 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-04_11:31 No. of wins: Observed Expected 97967 98585.9 z-score=-2.768, pvalue=0.00282 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66500 66666.7 0.417 0.417 2 37750 37654.3 0.243 0.660 3 27016 26954.7 0.139 0.799 4 19320 19313.5 0.002 0.801 5 13940 13851.4 0.566 1.368 6 9827 9943.5 1.366 2.734 7 7215 7145.0 0.685 3.419 8 5196 5139.1 0.631 4.050 9 3653 3699.9 0.594 4.643 10 2602 2666.3 1.551 6.194 11 1983 1923.3 1.851 8.045 12 1378 1388.7 0.083 8.128 13 1024 1003.7 0.410 8.538 14 738 726.1 0.194 8.732 15 509 525.8 0.539 9.271 16 369 381.2 0.387 9.658 17 282 276.5 0.108 9.766 18 201 200.8 0.000 9.766 19 129 146.0 1.976 11.742 20 93 106.2 1.644 13.386 21 275 287.1 0.511 13.897 Chisq= 13.90 for 20 degrees of freedom, p= 0.16434 SUMMARY of craptest p-value for no. of wins: 0.002821 p-value for throws/game: 0.164342 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0028,0.0030,0.0061,0.0112,0.0115,0.0119,0.0131,0.0164,0.0171,0.0173, 0.0193,0.0230,0.0240,0.0245,0.0306,0.0313,0.0365,0.0404,0.0474,0.0513, 0.0533,0.0577,0.0595,0.0661,0.0664,0.0706,0.0720,0.0877,0.0893,0.0941, 0.0975,0.0985,0.1016,0.1049,0.1051,0.1094,0.1226,0.1252,0.1281,0.1288, 0.1303,0.1309,0.1309,0.1324,0.1386,0.1388,0.1463,0.1519,0.1576,0.1615, 0.1617,0.1618,0.1625,0.1632,0.1634,0.1643,0.1784,0.1840,0.1864,0.1909, 0.1915,0.1990,0.1990,0.2047,0.2101,0.2155,0.2160,0.2161,0.2180,0.2194, 0.2196,0.2197,0.2240,0.2277,0.2325,0.2413,0.2464,0.2480,0.2510,0.2539, 0.2547,0.2554,0.2561,0.2592,0.2600,0.2675,0.2716,0.2876,0.2900,0.2909, 0.2934,0.3015,0.3090,0.3106,0.3185,0.3194,0.3230,0.3240,0.3250,0.3263, 0.3310,0.3347,0.3351,0.3370,0.3508,0.3579,0.3639,0.3660,0.3736,0.3794, 0.3812,0.3836,0.3839,0.3846,0.3956,0.3960,0.4088,0.4124,0.4128,0.4157, 0.4190,0.4203,0.4224,0.4269,0.4431,0.4434,0.4456,0.4468,0.4497,0.4566, 0.4570,0.4581,0.4584,0.4616,0.4680,0.4690,0.4702,0.4812,0.4859,0.4878, 0.5009,0.5055,0.5091,0.5144,0.5147,0.5215,0.5232,0.5314,0.5314,0.5386, 0.5388,0.5394,0.5401,0.5422,0.5422,0.5709,0.5719,0.5740,0.5788,0.5789, 0.5814,0.5824,0.5883,0.5915,0.5952,0.6033,0.6071,0.6079,0.6079,0.6145, 0.6164,0.6168,0.6285,0.6345,0.6396,0.6414,0.6421,0.6422,0.6461,0.6482, 0.6485,0.6515,0.6533,0.6593,0.6594,0.6630,0.6647,0.6682,0.6711,0.6751, 0.6787,0.6796,0.6887,0.7162,0.7173,0.7208,0.7236,0.7242,0.7266,0.7288, 0.7348,0.7381,0.7445,0.7500,0.7503,0.7540,0.7575,0.7615,0.7617,0.7659, 0.7662,0.7674,0.7712,0.7731,0.7757,0.7782,0.7782,0.7944,0.8091,0.8101, 0.8137,0.8180,0.8250,0.8272,0.8310,0.8316,0.8390,0.8395,0.8436,0.8532, 0.8534,0.8571,0.8647,0.8681,0.8796,0.8810,0.8857,0.8867,0.8918,0.8931, 0.8976,0.8986,0.8997,0.9109,0.9139,0.9288,0.9293,0.9351,0.9357,0.9374, 0.9375,0.9400,0.9458,0.9476,0.9550,0.9558,0.9597,0.9670,0.9787,0.9830, 0.9857,0.9897,0.9918,0.9940,0.9941,0.9942,0.9953,0.9971,0.9983, Overall p-value after applying KStest on 269 p-values = 0.259782 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.