RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-28_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 15.72 16.7079 0.525681 2 to 25 15.77 22.4644 0.832489 3 to 26 15.72 28.2702 0.958121 4 to 27 15.83 7.9709 0.032834 5 to 28 15.76 16.2760 0.495638 6 to 29 15.95 9.6749 0.083315 7 to 30 15.64 20.7699 0.763246 8 to 31 15.85 21.8554 0.809655 9 to 32 15.59 32.1344 0.985520 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.216583 Tough bday spacings test for dh-ranFile-2015-06-28_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 9 46 67 120 80 73 34 34 25 9 3 (O-E)^2/E 0.0 2.4 0.5 5.1 3.2 0.3 6.3 0.6 6.9 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 26.473, p= 0.997 RESULTS OF GCD FOR dh-ranFile-2015-06-28_01:31 Euclid's algorithm: p-value, steps to gcd: 0.023107 p-value, dist. of gcd's: 0.585575 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-28_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.307 0.138 0.158 0.982 0.678 0.750 0.744 0.142 Bits 8 to 15---> 0.821 0.759 0.257 0.002 0.577 0.986 0.880 0.589 Bits 16 to 23---> 0.793 0.430 0.552 0.183 0.536 0.907 0.003 0.651 Bits 24 to 31---> 0.787 0.397 0.061 0.478 0.775 0.770 0.039 0.801 KS test for the above 32 p values: 0.594 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-28_01:31, p-values for 5 runs: 0.4458, 0.5992, 0.6820, 0.7964, 0.7375 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-28_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 192 211.4 1.783 1.783 r= 29 5226 5134.0 1.648 3.432 r= 30 22997 23103.0 0.487 3.918 r= 31 11585 11551.5 0.097 4.016 chi-square = 4.016 with df = 3; p-value = 0.740 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-28_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5194 5134.0 0.701 0.703 r= 31 22952 23103.0 0.988 1.690 r= 32 11642 11551.5 0.709 2.399 chi-square = 2.399 with df = 3; p-value = 0.506 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-28_01:31 b-rank test for bits 1 to 8, p=0.91360 b-rank test for bits 2 to 9, p=0.27502 b-rank test for bits 3 to 10, p=0.48723 b-rank test for bits 4 to 11, p=0.48427 b-rank test for bits 5 to 12, p=0.71128 b-rank test for bits 6 to 13, p=0.51805 b-rank test for bits 7 to 14, p=0.24595 b-rank test for bits 8 to 15, p=0.17292 b-rank test for bits 9 to 16, p=0.64125 b-rank test for bits 10 to 17, p=0.62845 b-rank test for bits 11 to 18, p=0.58458 b-rank test for bits 12 to 19, p=0.79500 b-rank test for bits 13 to 20, p=0.56795 b-rank test for bits 14 to 21, p=0.09280 b-rank test for bits 15 to 22, p=0.91386 b-rank test for bits 16 to 23, p=0.85688 b-rank test for bits 17 to 24, p=0.74627 b-rank test for bits 18 to 25, p=0.84134 b-rank test for bits 19 to 26, p=0.45393 b-rank test for bits 20 to 27, p=0.48179 b-rank test for bits 21 to 28, p=0.63094 b-rank test for bits 22 to 29, p=0.80208 b-rank test for bits 23 to 30, p=0.65713 b-rank test for bits 24 to 31, p=0.18844 b-rank test for bits 25 to 32, p=0.40090 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 = 0.243795 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-28_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 142077 0.39 0.652379 2 141699 -0.49 0.311563 3 141568 -0.80 0.212580 4 141983 0.17 0.568331 5 141252 -1.54 0.062292 6 141255 -1.53 0.063156 7 142693 1.83 0.966450 8 141197 -1.66 0.048024 9 142414 1.18 0.880828 10 141457 -1.06 0.145291 11 141863 -0.11 0.456900 12 140981 -2.17 0.015042 13 142340 1.01 0.842850 14 141855 -0.13 0.449494 15 141947 0.09 0.535067 16 142601 1.62 0.946958 17 141233 -1.58 0.057029 18 142042 0.31 0.621711 19 142105 0.46 0.676227 20 141852 -0.13 0.446722 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-28_01:31 Bits used No. missing words z-score p-value 23 to 32 141353 -1.9184 0.027531 22 to 31 141474 -1.5011 0.066660 21 to 30 141888 -0.0736 0.470684 20 to 29 142181 0.9368 0.825568 19 to 28 141881 -0.0977 0.461089 18 to 27 141680 -0.7908 0.214532 17 to 26 142006 0.3333 0.630563 16 to 25 142357 1.5437 0.938668 15 to 24 141844 -0.2253 0.410882 14 to 23 141752 -0.5425 0.293731 13 to 22 141549 -1.2425 0.107023 12 to 21 142017 0.3713 0.644784 11 to 20 141956 0.1609 0.563926 10 to 19 141454 -1.5701 0.058196 9 to 18 142350 1.5196 0.935688 8 to 17 142031 0.4196 0.662594 7 to 16 141728 -0.6253 0.265895 6 to 15 142325 1.4333 0.924120 5 to 14 141799 -0.3804 0.351806 4 to 13 141807 -0.3529 0.362096 3 to 12 141706 -0.7011 0.241609 2 to 11 141635 -0.9460 0.172083 1 to 10 142155 0.8471 0.801541 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-28_01:31 Bits used No. missing words z-score p-value 28 to 32 141954 0.1514 0.560179 27 to 31 141839 -0.2384 0.405783 26 to 30 141962 0.1785 0.570852 25 to 29 142177 0.9074 0.817891 24 to 28 141901 -0.0282 0.488737 23 to 27 142436 1.7853 0.962895 22 to 26 142027 0.3989 0.655010 21 to 25 141896 -0.0452 0.481979 20 to 24 141836 -0.2486 0.401844 19 to 23 141604 -1.0350 0.150331 18 to 22 141998 0.3006 0.618131 17 to 21 141953 0.1480 0.558842 16 to 20 142445 1.8158 0.965302 15 to 19 141951 0.1413 0.556166 14 to 18 142006 0.3277 0.628429 13 to 17 141993 0.2836 0.611652 12 to 16 142033 0.4192 0.662473 11 to 15 141319 -2.0011 0.022690 10 to 14 142160 0.8497 0.802262 9 to 13 142026 0.3955 0.653760 8 to 12 142265 1.2057 0.886026 7 to 11 141514 -1.3401 0.090106 6 to 10 142257 1.1785 0.880710 5 to 9 142080 0.5785 0.718551 4 to 8 141851 -0.1977 0.421629 3 to 7 141450 -1.5571 0.059729 2 to 6 142324 1.4057 0.920088 1 to 5 142264 1.2023 0.885371 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-28_01:31 Bits used No. missing words z-score p-value 31 to 32 141989 0.2350 0.592901 30 to 31 141985 0.2232 0.588316 29 to 30 142055 0.4297 0.666295 28 to 29 141557 -1.0393 0.149328 27 to 28 142075 0.4887 0.687474 26 to 27 142264 1.0462 0.852271 25 to 26 142802 2.6332 0.995771 24 to 25 141513 -1.1691 0.121179 23 to 24 141713 -0.5791 0.281246 22 to 23 141977 0.1996 0.579110 21 to 22 142340 1.2704 0.898031 20 to 21 141783 -0.3727 0.354703 19 to 20 141646 -0.7768 0.218643 18 to 19 141400 -1.5024 0.066491 17 to 18 142287 1.1141 0.867376 16 to 17 142140 0.6804 0.751888 15 to 16 141725 -0.5437 0.293308 14 to 15 142209 0.8840 0.811647 13 to 14 142077 0.4946 0.689559 12 to 13 141515 -1.1632 0.122371 11 to 12 142219 0.9135 0.819505 10 to 11 142012 0.3029 0.619002 9 to 10 142001 0.2704 0.606579 8 to 9 142367 1.3501 0.911501 7 to 8 142222 0.9223 0.821822 6 to 7 141971 0.1819 0.572176 5 to 6 142207 0.8781 0.810051 4 to 5 141821 -0.2606 0.397216 3 to 4 141589 -0.9449 0.172348 2 to 3 141597 -0.9213 0.178440 1 to 2 142002 0.2734 0.607713 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-28_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2602.74 1.453 0.926888 Test results for specific bytes for dh-ranFile-2015-06-28_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2319.52 -2.552 0.005349 2 to 9 2478.64 -0.302 0.381297 3 to 10 2458.37 -0.589 0.278035 4 to 11 2454.04 -0.650 0.257854 5 to 12 2579.57 1.125 0.869781 6 to 13 2410.79 -1.262 0.103548 7 to 14 2411.41 -1.253 0.105136 8 to 15 2483.21 -0.237 0.406171 9 to 16 2516.85 0.238 0.594198 10 to 17 2441.09 -0.833 0.202389 11 to 18 2544.18 0.625 0.733949 12 to 19 2572.30 1.022 0.846721 13 to 20 2513.25 0.187 0.574345 14 to 21 2506.60 0.093 0.537196 15 to 22 2441.63 -0.825 0.204570 16 to 23 2522.78 0.322 0.626328 17 to 24 2479.80 -0.286 0.387577 18 to 25 2491.43 -0.121 0.451759 19 to 26 2360.45 -1.974 0.024214 20 to 27 2313.78 -2.634 0.004224 21 to 28 2432.82 -0.950 0.171026 22 to 29 2523.79 0.336 0.631735 23 to 30 2498.52 -0.021 0.491673 24 to 31 2479.17 -0.295 0.384154 25 to 32 2493.53 -0.091 0.463563 CDPARK for dh-ranFile-2015-06-28_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 3527 0.1826 0.572463 3504 -0.8676 0.192812 3547 1.0959 0.863437 3558 1.5982 0.944998 3539 0.7306 0.767486 3510 -0.5936 0.276387 3515 -0.3653 0.357445 3546 1.0502 0.853193 3495 -1.2785 0.100530 3544 0.9589 0.831196 Square side=100, avg. no. parked=3528.50 sample std.=20.29 p-value of the KSTEST for those 10 p-values: 0.575130 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-28_01:31 0.0949,0.3322,0.9356,0.7630,0.6453,0.8629,0.6051,0.7143,0.4857,0.8160, The KS test for those 10 p-values: 0.287115 The 3DSPHERES test for dh-ranFile-2015-06-28_01:31 sample no r^3 equiv. uni. 1 68.040 0.896481 2 99.675 0.963938 3 25.658 0.574830 4 5.380 0.164166 5 20.153 0.489198 6 19.438 0.476874 7 24.746 0.561705 8 8.391 0.243985 9 35.116 0.689796 10 43.563 0.765924 11 14.507 0.383411 12 0.842 0.027669 13 21.872 0.517635 14 46.024 0.784357 15 50.605 0.814894 16 0.338 0.011206 17 59.371 0.861796 18 12.089 0.331661 19 33.041 0.667583 20 28.352 0.611341 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.723427 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-28_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 2.0 0.0 -0.8 -0.4 -0.0 1.0 -2.1 -1.7 -1.4 -1.2 0.5 -0.5 -0.6 -1.1 0.7 0.7 1.0 -0.7 1.1 1.1 -0.1 -0.8 0.5 1.3 0.0 0.5 -0.1 0.3 1.0 1.1 1.3 0.1 1.3 1.5 -1.6 -0.1 -0.4 0.4 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:40.550842 z-score=-0.158116, p-value=0.465359 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-28_01:31 Test no p-value 1 0.611570 2 0.519438 3 0.546927 4 0.010304 5 0.842681 6 0.803357 7 0.507876 8 0.664089 9 0.167319 10 0.026028 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.492607 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-28_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 66510 0.37 66632 0.02 3 25000.00 25107 0.46 25164 1.08 4 6666.67 6717 0.38 6607 0.53 5 1388.89 1374 0.16 1343 1.52 6 238.10 253 0.93 217 1.87 7 34.72 33 0.09 32 0.21 8 4.96 5 0.00 4 0.19 p=0.11882 p=0.50786 Number of rngs required: 687390, p-value: 0.120 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-28_01:31 No. of wins: Observed Expected 98585 98585.9 z-score=-0.004, pvalue=0.49847 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66596 66666.7 0.075 0.075 2 37667 37654.3 0.004 0.079 3 26771 26954.7 1.252 1.332 4 19393 19313.5 0.328 1.659 5 13816 13851.4 0.091 1.750 6 9962 9943.5 0.034 1.784 7 7161 7145.0 0.036 1.820 8 5170 5139.1 0.186 2.006 9 3762 3699.9 1.043 3.049 10 2673 2666.3 0.017 3.066 11 1973 1923.3 1.283 4.349 12 1415 1388.7 0.497 4.845 13 1025 1003.7 0.451 5.297 14 719 726.1 0.070 5.367 15 526 525.8 0.000 5.367 16 375 381.2 0.099 5.466 17 290 276.5 0.655 6.122 18 190 200.8 0.584 6.706 19 146 146.0 0.000 6.706 20 99 106.2 0.490 7.196 21 271 287.1 0.904 8.100 Chisq= 8.10 for 20 degrees of freedom, p= 0.00882 SUMMARY of craptest p-value for no. of wins: 0.498468 p-value for throws/game: 0.008815 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-28_01:31 No. of wins: Observed Expected 98719 98585.9 z-score= 0.595, pvalue=0.72424 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66585 66666.7 0.100 0.100 2 38044 37654.3 4.033 4.133 3 27064 26954.7 0.443 4.576 4 19245 19313.5 0.243 4.818 5 13839 13851.4 0.011 4.830 6 9798 9943.5 2.130 6.960 7 7066 7145.0 0.874 7.834 8 5056 5139.1 1.343 9.177 9 3644 3699.9 0.844 10.020 10 2609 2666.3 1.231 11.252 11 1965 1923.3 0.903 12.154 12 1323 1388.7 3.112 15.266 13 1058 1003.7 2.936 18.202 14 760 726.1 1.579 19.781 15 512 525.8 0.364 20.145 16 405 381.2 1.492 21.638 17 292 276.5 0.864 22.502 18 190 200.8 0.584 23.086 19 147 146.0 0.007 23.093 20 116 106.2 0.901 23.994 21 282 287.1 0.091 24.085 Chisq= 24.09 for 20 degrees of freedom, p= 0.76132 SUMMARY of craptest p-value for no. of wins: 0.724241 p-value for throws/game: 0.761321 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0032,0.0042,0.0053,0.0088,0.0103,0.0112,0.0150,0.0227,0.0231, 0.0242,0.0260,0.0275,0.0277,0.0328,0.0391,0.0480,0.0570,0.0582,0.0597, 0.0606,0.0623,0.0632,0.0665,0.0667,0.0833,0.0901,0.0928,0.0949,0.1005, 0.1035,0.1051,0.1070,0.1188,0.1196,0.1212,0.1224,0.1378,0.1420,0.1453, 0.1493,0.1503,0.1580,0.1642,0.1673,0.1710,0.1721,0.1723,0.1729,0.1784, 0.1835,0.1884,0.1928,0.2024,0.2046,0.2126,0.2145,0.2166,0.2186,0.2416, 0.2438,0.2440,0.2460,0.2567,0.2579,0.2659,0.2750,0.2764,0.2780,0.2812, 0.2871,0.2933,0.2937,0.3069,0.3116,0.3317,0.3322,0.3518,0.3547,0.3574, 0.3621,0.3813,0.3834,0.3842,0.3876,0.3969,0.3972,0.4009,0.4018,0.4058, 0.4062,0.4109,0.4216,0.4296,0.4458,0.4467,0.4495,0.4518,0.4539,0.4569, 0.4611,0.4636,0.4654,0.4707,0.4769,0.4776,0.4818,0.4820,0.4843,0.4857, 0.4872,0.4887,0.4892,0.4917,0.4926,0.4956,0.4985,0.5061,0.5079,0.5079, 0.5176,0.5180,0.5194,0.5257,0.5351,0.5363,0.5372,0.5469,0.5518,0.5562, 0.5588,0.5602,0.5617,0.5639,0.5679,0.5683,0.5709,0.5722,0.5725,0.5743, 0.5748,0.5751,0.5767,0.5791,0.5846,0.5856,0.5883,0.5893,0.5929,0.5942, 0.5944,0.5992,0.6051,0.6066,0.6077,0.6113,0.6116,0.6117,0.6181,0.6190, 0.6217,0.6263,0.6284,0.6284,0.6306,0.6309,0.6317,0.6413,0.6448,0.6453, 0.6513,0.6524,0.6538,0.6550,0.6571,0.6625,0.6626,0.6641,0.6663,0.6676, 0.6762,0.6777,0.6820,0.6875,0.6896,0.6898,0.7113,0.7143,0.7186,0.7234, 0.7242,0.7339,0.7375,0.7402,0.7436,0.7463,0.7496,0.7519,0.7586,0.7613, 0.7630,0.7632,0.7659,0.7675,0.7701,0.7746,0.7844,0.7868,0.7930,0.7950, 0.7964,0.8013,0.8015,0.8021,0.8023,0.8034,0.8097,0.8101,0.8116,0.8149, 0.8160,0.8179,0.8195,0.8206,0.8218,0.8256,0.8312,0.8325,0.8413,0.8427, 0.8428,0.8467,0.8523,0.8532,0.8569,0.8618,0.8629,0.8634,0.8674,0.8698, 0.8795,0.8807,0.8808,0.8854,0.8860,0.8965,0.8980,0.9075,0.9115,0.9136, 0.9139,0.9201,0.9241,0.9269,0.9356,0.9357,0.9387,0.9450,0.9470,0.9581, 0.9629,0.9639,0.9653,0.9665,0.9818,0.9855,0.9863,0.9958,0.9968, Overall p-value after applying KStest on 269 p-values = 0.092677 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.