RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-09_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 14.9627 0.401834 2 to 25 15.64 27.0209 0.942238 3 to 26 15.65 21.8915 0.811073 4 to 27 15.43 21.1400 0.779910 5 to 28 15.74 25.4283 0.914475 6 to 29 15.85 13.1030 0.270733 7 to 30 15.70 24.2020 0.885950 8 to 31 15.84 20.7349 0.761628 9 to 32 15.77 11.4133 0.165708 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.116897 Tough bday spacings test for dh-ranFile-2015-10-09_04:31: 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 41 83 97 91 84 39 28 14 6 5 (O-E)^2/E 0.9 0.5 1.3 0.0 0.5 0.4 3.3 0.1 0.1 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.320, p= 0.305 RESULTS OF GCD FOR dh-ranFile-2015-10-09_04:31 Euclid's algorithm: p-value, steps to gcd: 0.434784 p-value, dist. of gcd's: 0.126805 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-09_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.422 0.713 0.010 0.171 0.564 0.291 0.219 0.054 Bits 8 to 15---> 0.035 0.756 0.022 0.903 0.986 0.766 0.921 0.434 Bits 16 to 23---> 0.070 0.202 0.869 0.501 0.080 0.690 0.330 0.458 Bits 24 to 31---> 0.936 0.086 0.525 0.499 0.274 0.882 0.273 0.541 KS test for the above 32 p values: 0.554 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-09_04:31, p-values for 5 runs: 0.3765, 0.0231, 0.0554, 0.7457, 0.2073 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-09_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5094 5134.0 0.312 0.367 r= 30 23036 23103.0 0.195 0.562 r= 31 11662 11551.5 1.057 1.618 chi-square = 1.618 with df = 3; p-value = 0.345 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-09_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5217 5134.0 1.341 1.480 r= 31 22921 23103.0 1.435 2.915 r= 32 11656 11551.5 0.945 3.860 chi-square = 3.860 with df = 3; p-value = 0.723 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-09_04:31 b-rank test for bits 1 to 8, p=0.91083 b-rank test for bits 2 to 9, p=0.71890 b-rank test for bits 3 to 10, p=0.38608 b-rank test for bits 4 to 11, p=0.82905 b-rank test for bits 5 to 12, p=0.88219 b-rank test for bits 6 to 13, p=0.88360 b-rank test for bits 7 to 14, p=0.21207 b-rank test for bits 8 to 15, p=0.02390 b-rank test for bits 9 to 16, p=0.66358 b-rank test for bits 10 to 17, p=0.74708 b-rank test for bits 11 to 18, p=0.18249 b-rank test for bits 12 to 19, p=0.32755 b-rank test for bits 13 to 20, p=0.35824 b-rank test for bits 14 to 21, p=0.84013 b-rank test for bits 15 to 22, p=0.93833 b-rank test for bits 16 to 23, p=0.30223 b-rank test for bits 17 to 24, p=0.75744 b-rank test for bits 18 to 25, p=0.93013 b-rank test for bits 19 to 26, p=0.79605 b-rank test for bits 20 to 27, p=0.97004 b-rank test for bits 21 to 28, p=0.58462 b-rank test for bits 22 to 29, p=0.58622 b-rank test for bits 23 to 30, p=0.09355 b-rank test for bits 24 to 31, p=0.43972 b-rank test for bits 25 to 32, p=0.10524 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 = 0.249188 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-09_04:31 (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 141921 0.03 0.510876 2 142617 1.65 0.950879 3 142701 1.85 0.967821 4 142346 1.02 0.846197 5 141673 -0.55 0.290415 6 141300 -1.42 0.077271 7 142122 0.50 0.690368 8 142034 0.29 0.614583 9 142361 1.06 0.854357 10 141518 -0.91 0.180274 11 140970 -2.19 0.014093 12 141942 0.08 0.530422 13 141310 -1.40 0.080711 14 142360 1.05 0.853822 15 141159 -1.75 0.039792 16 141149 -1.78 0.037828 17 142645 1.72 0.957180 18 141554 -0.83 0.203210 19 142150 0.56 0.713049 20 141817 -0.22 0.414601 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-09_04:31 Bits used No. missing words z-score p-value 23 to 32 142040 0.4506 0.673856 22 to 31 141899 -0.0356 0.485792 21 to 30 141763 -0.5046 0.306925 20 to 29 142117 0.7161 0.763036 19 to 28 142084 0.6023 0.726516 18 to 27 142290 1.3127 0.905350 17 to 26 142151 0.8333 0.797675 16 to 25 141599 -1.0701 0.142286 15 to 24 141740 -0.5839 0.279645 14 to 23 141790 -0.4115 0.340359 13 to 22 141842 -0.2322 0.408202 12 to 21 141477 -1.4908 0.068008 11 to 20 142071 0.5575 0.711401 10 to 19 142147 0.8196 0.793764 9 to 18 141769 -0.4839 0.314230 8 to 17 141679 -0.7942 0.213528 7 to 16 141686 -0.7701 0.220619 6 to 15 141954 0.1540 0.561209 5 to 14 141653 -0.8839 0.188376 4 to 13 142173 0.9092 0.818380 3 to 12 141709 -0.6908 0.244848 2 to 11 141456 -1.5632 0.059002 1 to 10 141390 -1.7908 0.036663 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-09_04:31 Bits used No. missing words z-score p-value 28 to 32 141895 -0.0486 0.480629 27 to 31 142114 0.6938 0.756095 26 to 30 142063 0.5209 0.698787 25 to 29 142198 0.9785 0.836097 24 to 28 142077 0.5684 0.715109 23 to 27 141961 0.1752 0.569520 22 to 26 141648 -0.8859 0.187845 21 to 25 142142 0.7887 0.784860 20 to 24 142003 0.3175 0.624578 19 to 23 142261 1.1921 0.883389 18 to 22 141727 -0.6181 0.268265 17 to 21 141613 -1.0045 0.157567 16 to 20 143003 3.7074 0.999895 15 to 19 142000 0.3074 0.620714 14 to 18 141890 -0.0655 0.473878 13 to 17 141707 -0.6859 0.246399 12 to 16 141429 -1.6282 0.051737 11 to 15 141982 0.2463 0.597290 10 to 14 141574 -1.1367 0.127829 9 to 13 141778 -0.4452 0.328093 8 to 12 142109 0.6768 0.750749 7 to 11 141756 -0.5198 0.301615 6 to 10 141757 -0.5164 0.302797 5 to 9 141649 -0.8825 0.188760 4 to 8 142156 0.8362 0.798470 3 to 7 142136 0.7684 0.778867 2 to 6 141726 -0.6215 0.267149 1 to 5 141732 -0.6011 0.273881 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-09_04:31 Bits used No. missing words z-score p-value 31 to 32 142024 0.3383 0.632416 30 to 31 141620 -0.8535 0.196696 29 to 30 142049 0.4120 0.659832 28 to 29 142350 1.2999 0.903184 27 to 28 141806 -0.3048 0.380256 26 to 27 141859 -0.1485 0.440988 25 to 26 141649 -0.7679 0.221263 24 to 25 141723 -0.5496 0.291281 23 to 24 141983 0.2173 0.586019 22 to 23 142194 0.8397 0.799471 21 to 22 142247 0.9961 0.840394 20 to 21 142248 0.9990 0.841109 19 to 20 142490 1.7129 0.956634 18 to 19 141616 -0.8653 0.193443 17 to 18 141199 -2.0954 0.018069 16 to 17 141089 -2.4199 0.007763 15 to 16 141923 0.0403 0.516083 14 to 15 142118 0.6155 0.730903 13 to 14 141433 -1.4051 0.079995 12 to 13 142097 0.5536 0.710073 11 to 12 141334 -1.6971 0.044835 10 to 11 141580 -0.9715 0.165656 9 to 10 140994 -2.7001 0.003466 8 to 9 141651 -0.7620 0.223019 7 to 8 141753 -0.4612 0.322345 6 to 7 141749 -0.4729 0.318125 5 to 6 141338 -1.6853 0.045962 4 to 5 141247 -1.9538 0.025364 3 to 4 141890 -0.0570 0.477264 2 to 3 141571 -0.9980 0.159134 1 to 2 142576 1.9666 0.975384 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-09_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2655.40 2.198 0.986014 Test results for specific bytes for dh-ranFile-2015-10-09_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2456.54 -0.615 0.269400 2 to 9 2363.21 -1.935 0.026526 3 to 10 2462.99 -0.523 0.300347 4 to 11 2508.51 0.120 0.547902 5 to 12 2458.33 -0.589 0.277822 6 to 13 2449.62 -0.712 0.238094 7 to 14 2513.22 0.187 0.574160 8 to 15 2560.42 0.854 0.803575 9 to 16 2454.95 -0.637 0.262041 10 to 17 2503.22 0.045 0.518143 11 to 18 2466.54 -0.473 0.318058 12 to 19 2570.52 0.997 0.840702 13 to 20 2539.46 0.558 0.711611 14 to 21 2536.62 0.518 0.697732 15 to 22 2460.26 -0.562 0.287070 16 to 23 2524.50 0.347 0.635533 17 to 24 2496.15 -0.054 0.478310 18 to 25 2464.51 -0.502 0.307858 19 to 26 2550.07 0.708 0.760538 20 to 27 2652.69 2.159 0.984587 21 to 28 2477.30 -0.321 0.374078 22 to 29 2556.17 0.794 0.786525 23 to 30 2658.11 2.236 0.987323 24 to 31 2534.33 0.486 0.686351 25 to 32 2530.46 0.431 0.666667 CDPARK for dh-ranFile-2015-10-09_04:31: 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 3521 -0.0913 0.463617 3487 -1.6438 0.050105 3511 -0.5479 0.291865 3528 0.2283 0.590298 3532 0.4110 0.659449 3542 0.8676 0.807188 3537 0.6393 0.738676 3518 -0.2283 0.409702 3494 -1.3242 0.092718 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3518.80 sample std.=16.80 p-value of the KSTEST for those 10 p-values: 0.777068 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-09_04:31 0.0285,0.5082,0.6843,0.0609,0.4533,0.4314,0.4318,0.6375,0.2414,0.9469, The KS test for those 10 p-values: 0.702965 The 3DSPHERES test for dh-ranFile-2015-10-09_04:31 sample no r^3 equiv. uni. 1 57.797 0.854353 2 2.690 0.085778 3 50.407 0.813667 4 133.197 0.988203 5 5.707 0.173248 6 64.513 0.883567 7 37.400 0.712540 8 9.070 0.260913 9 29.569 0.626803 10 56.597 0.848410 11 7.629 0.224549 12 75.653 0.919683 13 60.919 0.868748 14 26.678 0.589039 15 144.172 0.991817 16 163.126 0.995650 17 9.308 0.266741 18 107.164 0.971904 19 16.343 0.420024 20 4.479 0.138683 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.013227 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-09_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.4 -0.4 -0.1 2.1 -0.0 -0.2 -0.3 -0.7 -0.1 1.8 1.2 -1.7 -0.5 0.8 -0.7 -0.9 0.1 1.1 -0.6 -1.3 0.6 1.1 -1.3 0.9 1.1 0.7 -2.0 -0.3 0.3 -0.2 0.9 0.9 1.0 -0.1 -0.5 -0.7 0.9 0.4 1.6 0.0 0.8 Chi-square with 42 degrees of freedom:36.871444 z-score=-0.559571, p-value=0.304838 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-09_04:31 Test no p-value 1 0.780761 2 0.923032 3 0.734325 4 0.852790 5 0.095757 6 0.935692 7 0.354536 8 0.456789 9 0.262952 10 0.549820 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.560331 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-09_04:31: (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 66444 0.74 66720 0.04 3 25000.00 25196 1.54 24867 0.71 4 6666.67 6648 0.05 6646 0.06 5 1388.89 1428 1.10 1502 9.21 6 238.10 251 0.70 225 0.72 7 34.72 30 0.64 34 0.01 8 4.96 2 1.77 5 0.00 p=0.63467 p=0.90396 Number of rngs required: 687909, p-value: 0.284 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-09_04:31 No. of wins: Observed Expected 98296 98585.9 z-score=-1.296, pvalue=0.09742 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66751 66666.7 0.107 0.107 2 37785 37654.3 0.454 0.560 3 26831 26954.7 0.568 1.128 4 19304 19313.5 0.005 1.133 5 13971 13851.4 1.032 2.165 6 9966 9943.5 0.051 2.216 7 7054 7145.0 1.160 3.376 8 5137 5139.1 0.001 3.376 9 3597 3699.9 2.860 6.236 10 2698 2666.3 0.377 6.613 11 1878 1923.3 1.068 7.682 12 1400 1388.7 0.091 7.773 13 972 1003.7 1.002 8.775 14 715 726.1 0.171 8.946 15 518 525.8 0.117 9.063 16 377 381.2 0.045 9.108 17 291 276.5 0.756 9.864 18 206 200.8 0.133 9.997 19 148 146.0 0.028 10.025 20 127 106.2 4.067 14.092 21 274 287.1 0.599 14.691 Chisq= 14.69 for 20 degrees of freedom, p= 0.20620 SUMMARY of craptest p-value for no. of wins: 0.097416 p-value for throws/game: 0.206201 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-09_04:31 No. of wins: Observed Expected 98841 98585.9 z-score= 1.141, pvalue=0.87309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66828 66666.7 0.390 0.390 2 37341 37654.3 2.607 2.998 3 26560 26954.7 5.781 8.778 4 19419 19313.5 0.577 9.355 5 13974 13851.4 1.085 10.440 6 10185 9943.5 5.863 16.303 7 7054 7145.0 1.160 17.463 8 5153 5139.1 0.038 17.500 9 3758 3699.9 0.913 18.414 10 2754 2666.3 2.885 21.299 11 1931 1923.3 0.031 21.329 12 1391 1388.7 0.004 21.333 13 971 1003.7 1.066 22.399 14 742 726.1 0.346 22.746 15 560 525.8 2.220 24.965 16 365 381.2 0.684 25.650 17 288 276.5 0.475 26.124 18 208 200.8 0.256 26.380 19 145 146.0 0.007 26.387 20 114 106.2 0.571 26.958 21 259 287.1 2.753 29.711 Chisq= 29.71 for 20 degrees of freedom, p= 0.92532 SUMMARY of craptest p-value for no. of wins: 0.873094 p-value for throws/game: 0.925319 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0078,0.0101,0.0132,0.0141,0.0181,0.0225,0.0231,0.0239,0.0254, 0.0265,0.0285,0.0349,0.0367,0.0378,0.0398,0.0448,0.0460,0.0501,0.0517, 0.0543,0.0554,0.0590,0.0609,0.0680,0.0701,0.0773,0.0800,0.0800,0.0807, 0.0858,0.0859,0.0927,0.0936,0.0958,0.0974,0.1052,0.1169,0.1268,0.1278, 0.1387,0.1423,0.1576,0.1591,0.1657,0.1657,0.1710,0.1732,0.1803,0.1825, 0.1878,0.1884,0.1888,0.1934,0.1967,0.2021,0.2032,0.2062,0.2073,0.2121, 0.2135,0.2189,0.2206,0.2213,0.2230,0.2245,0.2381,0.2414,0.2448,0.2464, 0.2492,0.2609,0.2620,0.2630,0.2667,0.2671,0.2683,0.2694,0.2707,0.2731, 0.2735,0.2739,0.2778,0.2796,0.2845,0.2871,0.2904,0.2913,0.2915,0.2919, 0.3003,0.3016,0.3022,0.3028,0.3048,0.3051,0.3069,0.3079,0.3142,0.3181, 0.3181,0.3223,0.3276,0.3281,0.3300,0.3404,0.3447,0.3545,0.3582,0.3741, 0.3765,0.3803,0.3861,0.4018,0.4082,0.4097,0.4097,0.4146,0.4200,0.4216, 0.4314,0.4318,0.4338,0.4348,0.4397,0.4410,0.4533,0.4568,0.4581,0.4636, 0.4739,0.4773,0.4783,0.4806,0.4858,0.4986,0.5014,0.5082,0.5109,0.5161, 0.5181,0.5249,0.5304,0.5411,0.5479,0.5498,0.5540,0.5603,0.5612,0.5635, 0.5695,0.5742,0.5846,0.5860,0.5862,0.5890,0.5903,0.5973,0.6146,0.6207, 0.6246,0.6268,0.6324,0.6347,0.6355,0.6375,0.6594,0.6598,0.6636,0.6667, 0.6739,0.6843,0.6864,0.6901,0.6904,0.6977,0.6988,0.7030,0.7101,0.7114, 0.7116,0.7125,0.7130,0.7135,0.7151,0.7189,0.7230,0.7265,0.7309,0.7343, 0.7387,0.7457,0.7471,0.7507,0.7556,0.7561,0.7574,0.7605,0.7616,0.7630, 0.7659,0.7771,0.7789,0.7799,0.7808,0.7849,0.7865,0.7938,0.7960,0.7977, 0.7985,0.7995,0.8036,0.8072,0.8111,0.8137,0.8184,0.8290,0.8361,0.8401, 0.8404,0.8407,0.8411,0.8462,0.8484,0.8528,0.8538,0.8544,0.8544,0.8687, 0.8688,0.8731,0.8822,0.8824,0.8834,0.8836,0.8836,0.8860,0.9030,0.9032, 0.9040,0.9054,0.9108,0.9145,0.9197,0.9215,0.9230,0.9253,0.9301,0.9356, 0.9357,0.9383,0.9422,0.9469,0.9509,0.9566,0.9572,0.9678,0.9700,0.9719, 0.9754,0.9846,0.9857,0.9860,0.9873,0.9882,0.9918,0.9956,0.9999, Overall p-value after applying KStest on 269 p-values = 0.385945 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.