RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-15_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.89 18.8691 0.663901 2 to 25 15.73 14.1792 0.345623 3 to 26 15.80 21.0334 0.775201 4 to 27 15.77 23.3603 0.862115 5 to 28 15.71 18.7093 0.654530 6 to 29 15.89 12.6696 0.241994 7 to 30 15.68 23.5355 0.867383 8 to 31 16.14 19.2155 0.683698 9 to 32 15.79 13.1241 0.272159 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.393976 Tough bday spacings test for dh-ranFile-2016-10-15_16:31: 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 8 41 75 112 99 70 41 32 8 8 6 (O-E)^2/E 0.1 0.5 0.0 2.1 0.0 0.8 2.4 0.2 3.2 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.599, p= 0.610 RESULTS OF GCD FOR dh-ranFile-2016-10-15_16:31 Euclid's algorithm: p-value, steps to gcd: 0.632830 p-value, dist. of gcd's: 0.629542 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-15_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.034 0.039 0.544 0.876 0.780 0.264 0.077 0.093 Bits 8 to 15---> 0.632 0.094 0.186 0.890 0.049 0.599 0.439 0.019 Bits 16 to 23---> 0.825 0.665 0.004 0.161 0.875 0.279 0.093 0.543 Bits 24 to 31---> 0.303 0.413 0.631 0.192 0.474 0.024 0.678 0.283 KS test for the above 32 p values: 0.988 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-15_16:31, p-values for 5 runs: 0.5446, 0.1452, 0.8442, 0.7541, 0.4955 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-15_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5186 5134.0 0.526 2.160 r= 30 23077 23103.0 0.029 2.189 r= 31 11507 11551.5 0.172 2.361 chi-square = 2.361 with df = 3; p-value = 0.499 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-15_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5054 5134.0 1.247 2.099 r= 31 23393 23103.0 3.639 5.738 r= 32 11355 11551.5 3.343 9.081 chi-square = 9.081 with df = 3; p-value = 0.972 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-15_16:31 b-rank test for bits 1 to 8, p=0.13138 b-rank test for bits 2 to 9, p=0.52330 b-rank test for bits 3 to 10, p=0.80091 b-rank test for bits 4 to 11, p=0.90490 b-rank test for bits 5 to 12, p=0.84490 b-rank test for bits 6 to 13, p=0.90452 b-rank test for bits 7 to 14, p=0.83855 b-rank test for bits 8 to 15, p=0.28644 b-rank test for bits 9 to 16, p=0.10399 b-rank test for bits 10 to 17, p=0.01264 b-rank test for bits 11 to 18, p=0.98034 b-rank test for bits 12 to 19, p=0.85037 b-rank test for bits 13 to 20, p=0.21043 b-rank test for bits 14 to 21, p=0.35073 b-rank test for bits 15 to 22, p=0.33871 b-rank test for bits 16 to 23, p=0.07123 b-rank test for bits 17 to 24, p=0.93848 b-rank test for bits 18 to 25, p=0.08923 b-rank test for bits 19 to 26, p=0.52906 b-rank test for bits 20 to 27, p=0.76575 b-rank test for bits 21 to 28, p=0.18684 b-rank test for bits 22 to 29, p=0.48938 b-rank test for bits 23 to 30, p=0.87512 b-rank test for bits 24 to 31, p=0.06184 b-rank test for bits 25 to 32, p=0.70845 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 = 0.429760 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-15_16:31 (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 141602 -0.72 0.236360 2 141429 -1.12 0.130875 3 142168 0.60 0.727201 4 142326 0.97 0.834855 5 141529 -0.89 0.187103 6 141892 -0.04 0.483851 7 141315 -1.39 0.082474 8 141908 -0.00 0.498760 9 141593 -0.74 0.229927 10 141845 -0.15 0.440263 11 141909 -0.00 0.499692 12 142770 2.01 0.977833 13 141908 -0.00 0.498760 14 141191 -1.68 0.046640 15 141480 -1.00 0.157905 16 141327 -1.36 0.086823 17 141995 0.20 0.579324 18 141604 -0.71 0.237803 19 141916 0.02 0.506217 20 141694 -0.50 0.307444 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-15_16:31 Bits used No. missing words z-score p-value 23 to 32 141089 -2.8287 0.002337 22 to 31 142324 1.4299 0.923627 21 to 30 141907 -0.0080 0.496795 20 to 29 142393 1.6678 0.952325 19 to 28 141863 -0.1598 0.436536 18 to 27 142237 1.1299 0.870740 17 to 26 142287 1.3023 0.903595 16 to 25 141729 -0.6218 0.267028 15 to 24 141990 0.2782 0.609560 14 to 23 142097 0.6471 0.741229 13 to 22 142136 0.7816 0.782781 12 to 21 141781 -0.4425 0.329058 11 to 20 141689 -0.7598 0.223699 10 to 19 141847 -0.2149 0.414911 9 to 18 141538 -1.2804 0.100194 8 to 17 141850 -0.2046 0.418948 7 to 16 141535 -1.2908 0.098388 6 to 15 141436 -1.6322 0.051322 5 to 14 141444 -1.6046 0.054292 4 to 13 141625 -0.9804 0.163432 3 to 12 142211 1.0402 0.850886 2 to 11 142090 0.6230 0.733358 1 to 10 141802 -0.3701 0.355653 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-15_16:31 Bits used No. missing words z-score p-value 28 to 32 141469 -1.4926 0.067765 27 to 31 141951 0.1413 0.556166 26 to 30 141559 -1.1876 0.117504 25 to 29 142293 1.3006 0.903298 24 to 28 141863 -0.1571 0.437602 23 to 27 141956 0.1582 0.562852 22 to 26 142532 2.1107 0.982603 21 to 25 142586 2.2938 0.989099 20 to 24 142041 0.4463 0.672324 19 to 23 142036 0.4294 0.666180 18 to 22 142193 0.9616 0.831873 17 to 21 141710 -0.6757 0.249617 16 to 20 141635 -0.9299 0.176203 15 to 19 141597 -1.0587 0.144858 14 to 18 142077 0.5684 0.715109 13 to 17 142429 1.7616 0.960931 12 to 16 141516 -1.3333 0.091213 11 to 15 142151 0.8192 0.793670 10 to 14 141658 -0.8520 0.197116 9 to 13 141363 -1.8520 0.032015 8 to 12 142306 1.3446 0.910630 7 to 11 141825 -0.2859 0.387491 6 to 10 141663 -0.8350 0.201854 5 to 9 142319 1.3887 0.917540 4 to 8 141692 -0.7367 0.230649 3 to 7 141998 0.3006 0.618131 2 to 6 141823 -0.2926 0.384897 1 to 5 141784 -0.4248 0.335474 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-15_16:31 Bits used No. missing words z-score p-value 31 to 32 141615 -0.8682 0.192634 30 to 31 141239 -1.9774 0.024000 29 to 30 141831 -0.2311 0.408633 28 to 29 141674 -0.6942 0.243782 27 to 28 141644 -0.7827 0.216906 26 to 27 141514 -1.1662 0.121774 25 to 26 142011 0.2999 0.617878 24 to 25 141630 -0.8240 0.204975 23 to 24 142095 0.5477 0.708051 22 to 23 142001 0.2704 0.606579 21 to 22 141718 -0.5644 0.286243 20 to 21 142151 0.7129 0.762043 19 to 20 142291 1.1259 0.869890 18 to 19 141804 -0.3107 0.378011 17 to 18 142389 1.4150 0.921459 16 to 17 141949 0.1170 0.546578 15 to 16 141846 -0.1868 0.425903 14 to 15 142137 0.6716 0.749079 13 to 14 142141 0.6834 0.752821 12 to 13 141604 -0.9007 0.183880 11 to 12 141720 -0.5585 0.288253 10 to 11 142287 1.1141 0.867376 9 to 10 141923 0.0403 0.516083 8 to 9 141869 -0.1190 0.452651 7 to 8 141550 -1.0600 0.144579 6 to 7 141609 -0.8859 0.187828 5 to 6 141947 0.1111 0.544240 4 to 5 141597 -0.9213 0.178440 3 to 4 141931 0.0639 0.525484 2 to 3 141745 -0.4847 0.313927 1 to 2 141778 -0.3874 0.349229 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-15_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2428.17 -1.016 0.154861 Test results for specific bytes for dh-ranFile-2016-10-15_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2568.24 0.965 0.832757 2 to 9 2504.23 0.060 0.523836 3 to 10 2545.33 0.641 0.739262 4 to 11 2480.77 -0.272 0.392831 5 to 12 2579.48 1.124 0.869495 6 to 13 2540.49 0.573 0.716544 7 to 14 2427.48 -1.026 0.152550 8 to 15 2613.09 1.599 0.945134 9 to 16 2587.81 1.242 0.892857 10 to 17 2523.79 0.336 0.631730 11 to 18 2500.00 -0.000 0.499972 12 to 19 2468.75 -0.442 0.329282 13 to 20 2589.64 1.268 0.897543 14 to 21 2468.46 -0.446 0.327775 15 to 22 2452.73 -0.668 0.251918 16 to 23 2476.53 -0.332 0.369967 17 to 24 2505.21 0.074 0.529341 18 to 25 2483.53 -0.233 0.407906 19 to 26 2514.01 0.198 0.578548 20 to 27 2381.71 -1.673 0.047180 21 to 28 2596.92 1.371 0.914754 22 to 29 2475.25 -0.350 0.363148 23 to 30 2457.67 -0.599 0.274702 24 to 31 2520.55 0.291 0.614342 25 to 32 2669.83 2.402 0.991842 CDPARK for dh-ranFile-2016-10-15_16:31: 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 3555 1.4612 0.928018 3521 -0.0913 0.463617 3537 0.6393 0.738676 3509 -0.6393 0.261324 3537 0.6393 0.738676 3481 -1.9178 0.027568 3513 -0.4566 0.323972 3521 -0.0913 0.463617 3566 1.9635 0.975204 Square side=100, avg. no. parked=3525.30 sample std.=23.20 p-value of the KSTEST for those 10 p-values: 0.892744 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-15_16:31 0.8834,0.9621,0.8010,0.4821,0.3754,0.2253,0.7779,0.4069,0.6861,0.8920, The KS test for those 10 p-values: 0.173277 The 3DSPHERES test for dh-ranFile-2016-10-15_16:31 sample no r^3 equiv. uni. 1 20.626 0.497181 2 30.138 0.633808 3 16.332 0.419809 4 65.004 0.885455 5 53.107 0.829708 6 2.605 0.083170 7 27.866 0.605002 8 21.419 0.510304 9 5.115 0.156748 10 33.568 0.673368 11 2.959 0.093936 12 8.074 0.235951 13 8.515 0.247099 14 7.754 0.227774 15 24.663 0.560492 16 19.129 0.471466 17 6.475 0.194141 18 29.377 0.624400 19 19.283 0.474160 20 1.163 0.038019 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.310021 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-15_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 0.3 -0.7 0.0 0.6 1.6 0.7 0.4 0.4 -2.3 0.8 1.0 0.1 0.0 -0.7 0.1 -0.7 -0.1 1.1 -0.9 1.1 0.2 -0.7 -0.2 -0.5 0.1 0.2 -0.9 -1.2 -0.1 0.8 0.2 0.0 -0.2 1.5 1.4 1.5 1.3 -0.1 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:30.872269 z-score=-1.214135, p-value=0.102542 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-15_16:31 Test no p-value 1 0.595981 2 0.002769 3 0.246886 4 0.043140 5 0.895223 6 0.269827 7 0.241155 8 0.311683 9 0.002376 10 0.917237 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.028948 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-15_16:31: (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 66724 0.05 66770 0.16 3 25000.00 24852 0.88 24878 0.60 4 6666.67 6697 0.14 6682 0.04 5 1388.89 1418 0.61 1399 0.07 6 238.10 269 4.01 221 1.23 7 34.72 34 0.01 41 1.14 8 4.96 5 0.00 8 1.86 p=0.54241 p=0.46779 Number of rngs required: 687515, p-value: 0.152 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-15_16:31 No. of wins: Observed Expected 98577 98585.9 z-score=-0.040, pvalue=0.48420 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66820 66666.7 0.353 0.353 2 37348 37654.3 2.492 2.845 3 26918 26954.7 0.050 2.895 4 19311 19313.5 0.000 2.895 5 13555 13851.4 6.343 9.238 6 10005 9943.5 0.380 9.618 7 7332 7145.0 4.893 14.511 8 5180 5139.1 0.326 14.837 9 3828 3699.9 4.438 19.275 10 2670 2666.3 0.005 19.280 11 1896 1923.3 0.388 19.668 12 1401 1388.7 0.108 19.776 13 1012 1003.7 0.068 19.845 14 773 726.1 3.024 22.869 15 543 525.8 0.560 23.429 16 373 381.2 0.174 23.603 17 287 276.5 0.396 23.999 18 204 200.8 0.050 24.049 19 141 146.0 0.170 24.219 20 114 106.2 0.571 24.790 21 289 287.1 0.012 24.802 Chisq= 24.80 for 20 degrees of freedom, p= 0.79089 SUMMARY of craptest p-value for no. of wins: 0.484198 p-value for throws/game: 0.790891 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-15_16:31 No. of wins: Observed Expected 98545 98585.9 z-score=-0.183, pvalue=0.42750 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66542 66666.7 0.233 0.233 2 37797 37654.3 0.541 0.774 3 26942 26954.7 0.006 0.780 4 19429 19313.5 0.691 1.471 5 13949 13851.4 0.687 2.158 6 10005 9943.5 0.380 2.538 7 7120 7145.0 0.088 2.626 8 5078 5139.1 0.726 3.352 9 3665 3699.9 0.329 3.680 10 2580 2666.3 2.793 6.473 11 1931 1923.3 0.031 6.504 12 1434 1388.7 1.475 7.979 13 963 1003.7 1.652 9.631 14 717 726.1 0.115 9.746 15 500 525.8 1.269 11.015 16 386 381.2 0.062 11.077 17 269 276.5 0.206 11.282 18 207 200.8 0.190 11.472 19 110 146.0 8.870 20.342 20 92 106.2 1.902 22.244 21 284 287.1 0.034 22.278 Chisq= 22.28 for 20 degrees of freedom, p= 0.67438 SUMMARY of craptest p-value for no. of wins: 0.427500 p-value for throws/game: 0.674381 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0024,0.0028,0.0042,0.0126,0.0194,0.0236,0.0240,0.0276,0.0289, 0.0320,0.0338,0.0380,0.0389,0.0431,0.0466,0.0472,0.0494,0.0513,0.0543, 0.0618,0.0678,0.0712,0.0772,0.0825,0.0832,0.0868,0.0892,0.0912,0.0927, 0.0927,0.0939,0.0945,0.0984,0.1002,0.1025,0.1040,0.1175,0.1218,0.1309, 0.1314,0.1446,0.1449,0.1452,0.1517,0.1526,0.1549,0.1567,0.1579,0.1613, 0.1634,0.1733,0.1762,0.1784,0.1839,0.1857,0.1868,0.1871,0.1878,0.1923, 0.1926,0.1941,0.1971,0.2019,0.2050,0.2104,0.2169,0.2237,0.2253,0.2278, 0.2299,0.2306,0.2360,0.2364,0.2378,0.2412,0.2420,0.2438,0.2469,0.2471, 0.2496,0.2519,0.2613,0.2643,0.2670,0.2698,0.2722,0.2747,0.2787,0.2829, 0.2862,0.2864,0.2883,0.3030,0.3074,0.3100,0.3117,0.3139,0.3240,0.3240, 0.3278,0.3291,0.3293,0.3355,0.3387,0.3456,0.3492,0.3507,0.3557,0.3631, 0.3700,0.3754,0.3780,0.3849,0.3875,0.3928,0.3940,0.4069,0.4079,0.4086, 0.4127,0.4149,0.4189,0.4198,0.4259,0.4275,0.4298,0.4365,0.4376,0.4394, 0.4403,0.4527,0.4636,0.4636,0.4678,0.4715,0.4742,0.4742,0.4821,0.4839, 0.4842,0.4894,0.4955,0.4968,0.4972,0.4988,0.4988,0.4990,0.4997,0.5000, 0.5062,0.5103,0.5161,0.5233,0.5238,0.5255,0.5291,0.5293,0.5424,0.5425, 0.5440,0.5442,0.5446,0.5466,0.5562,0.5605,0.5629,0.5785,0.5793,0.5960, 0.5995,0.6050,0.6066,0.6096,0.6104,0.6143,0.6179,0.6181,0.6244,0.6295, 0.6310,0.6317,0.6323,0.6328,0.6338,0.6545,0.6639,0.6654,0.6662,0.6723, 0.6734,0.6744,0.6782,0.6837,0.6861,0.7081,0.7084,0.7151,0.7165,0.7272, 0.7334,0.7387,0.7387,0.7393,0.7412,0.7491,0.7528,0.7541,0.7620,0.7657, 0.7752,0.7779,0.7796,0.7828,0.7909,0.7937,0.8009,0.8010,0.8246,0.8297, 0.8319,0.8328,0.8349,0.8386,0.8442,0.8449,0.8504,0.8509,0.8621,0.8674, 0.8674,0.8695,0.8699,0.8707,0.8748,0.8751,0.8762,0.8834,0.8855,0.8904, 0.8920,0.8927,0.8929,0.8952,0.8975,0.9033,0.9036,0.9045,0.9049,0.9106, 0.9148,0.9172,0.9175,0.9215,0.9236,0.9280,0.9385,0.9451,0.9523,0.9609, 0.9621,0.9718,0.9752,0.9778,0.9803,0.9826,0.9880,0.9891,0.9918, Overall p-value after applying KStest on 269 p-values = 0.197584 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.