RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-18_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 21.8303 0.808668 2 to 25 15.69 20.3071 0.741175 3 to 26 16.07 10.5960 0.123219 4 to 27 15.77 14.1404 0.342857 5 to 28 15.91 10.4972 0.118523 6 to 29 15.74 19.7815 0.714440 7 to 30 15.35 34.8168 0.993425 8 to 31 15.60 23.6707 0.871338 9 to 32 16.01 11.4799 0.169443 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.551554 Tough bday spacings test for dh-ranFile-2015-12-18_13:31: 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 34 71 116 109 76 36 24 14 9 2 (O-E)^2/E 0.0 0.2 0.1 3.4 1.3 0.1 5.0 1.1 0.1 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.121, p= 0.783 RESULTS OF GCD FOR dh-ranFile-2015-12-18_13:31 Euclid's algorithm: p-value, steps to gcd: 0.744729 p-value, dist. of gcd's: 0.156884 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-18_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.200 0.208 0.630 0.511 0.623 0.704 0.166 0.193 Bits 8 to 15---> 0.207 0.569 0.745 0.680 0.067 0.607 0.050 0.468 Bits 16 to 23---> 0.301 0.865 0.561 0.640 0.324 0.046 0.145 0.012 Bits 24 to 31---> 0.261 0.619 0.102 0.783 0.678 0.254 0.220 0.880 KS test for the above 32 p values: 0.882 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-18_13:31, p-values for 5 runs: 0.2225, 0.6575, 0.7440, 0.9478, 0.2562 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-18_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5212 5134.0 1.185 1.819 r= 30 23069 23103.0 0.050 1.869 r= 31 11496 11551.5 0.267 2.136 chi-square = 2.136 with df = 3; p-value = 0.455 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-18_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5137 5134.0 0.002 0.003 r= 31 23159 23103.0 0.136 0.139 r= 32 11492 11551.5 0.307 0.446 chi-square = 0.446 with df = 3; p-value = 0.069 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-18_13:31 b-rank test for bits 1 to 8, p=0.62786 b-rank test for bits 2 to 9, p=0.62384 b-rank test for bits 3 to 10, p=0.55354 b-rank test for bits 4 to 11, p=0.14646 b-rank test for bits 5 to 12, p=0.43516 b-rank test for bits 6 to 13, p=0.63658 b-rank test for bits 7 to 14, p=0.06937 b-rank test for bits 8 to 15, p=0.51943 b-rank test for bits 9 to 16, p=0.73594 b-rank test for bits 10 to 17, p=0.93650 b-rank test for bits 11 to 18, p=0.92752 b-rank test for bits 12 to 19, p=0.28764 b-rank test for bits 13 to 20, p=0.23881 b-rank test for bits 14 to 21, p=0.05508 b-rank test for bits 15 to 22, p=0.02802 b-rank test for bits 16 to 23, p=0.35817 b-rank test for bits 17 to 24, p=0.25694 b-rank test for bits 18 to 25, p=0.02465 b-rank test for bits 19 to 26, p=0.45236 b-rank test for bits 20 to 27, p=0.91229 b-rank test for bits 21 to 28, p=0.77931 b-rank test for bits 22 to 29, p=0.32842 b-rank test for bits 23 to 30, p=0.57344 b-rank test for bits 24 to 31, p=0.93912 b-rank test for bits 25 to 32, p=0.81295 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 = 0.953865 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-18_13:31 (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 142372 1.08 0.860153 2 142017 0.25 0.599312 3 142234 0.76 0.775947 4 142442 1.24 0.893353 5 141822 -0.20 0.419160 6 141591 -0.74 0.228510 7 142266 0.83 0.797674 8 141692 -0.51 0.305804 9 141706 -0.48 0.317369 10 142143 0.55 0.707453 11 141704 -0.48 0.315705 12 141888 -0.05 0.480126 13 142919 2.36 0.990839 14 141854 -0.13 0.448570 15 141794 -0.27 0.393787 16 141276 -1.48 0.069471 17 142226 0.74 0.770315 18 141431 -1.12 0.131870 19 141804 -0.25 0.402803 20 141961 0.12 0.548045 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-18_13:31 Bits used No. missing words z-score p-value 23 to 32 141900 -0.0322 0.487167 22 to 31 141787 -0.4218 0.336575 21 to 30 142185 0.9506 0.829093 20 to 29 142028 0.4092 0.658806 19 to 28 141929 0.0678 0.527039 18 to 27 142050 0.4851 0.686186 17 to 26 142283 1.2885 0.901217 16 to 25 141951 0.1437 0.557127 15 to 24 142188 0.9609 0.831707 14 to 23 141889 -0.0701 0.472056 13 to 22 141888 -0.0736 0.470684 12 to 21 141843 -0.2287 0.409542 11 to 20 141752 -0.5425 0.293731 10 to 19 141865 -0.1529 0.439254 9 to 18 141865 -0.1529 0.439254 8 to 17 141865 -0.1529 0.439254 7 to 16 141575 -1.1529 0.124484 6 to 15 141439 -1.6218 0.052420 5 to 14 141757 -0.5253 0.299696 4 to 13 142286 1.2989 0.903004 3 to 12 142404 1.7058 0.955973 2 to 11 142091 0.6264 0.734490 1 to 10 142066 0.5402 0.705485 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-18_13:31 Bits used No. missing words z-score p-value 28 to 32 142108 0.6735 0.749672 27 to 31 142081 0.5819 0.719694 26 to 30 141960 0.1718 0.568188 25 to 29 142118 0.7074 0.760327 24 to 28 142160 0.8497 0.802262 23 to 27 141977 0.2294 0.590717 22 to 26 141601 -1.0452 0.147968 21 to 25 141854 -0.1876 0.425611 20 to 24 141958 0.1650 0.565521 19 to 23 141964 0.1853 0.573512 18 to 22 142266 1.2091 0.886678 17 to 21 141714 -0.6621 0.253942 16 to 20 142137 0.7718 0.779873 15 to 19 142293 1.3006 0.903298 14 to 18 141698 -0.7164 0.236881 13 to 17 141550 -1.2181 0.111599 12 to 16 141875 -0.1164 0.453679 11 to 15 142024 0.3887 0.651255 10 to 14 142477 1.9243 0.972842 9 to 13 141972 0.2124 0.584118 8 to 12 142169 0.8802 0.810635 7 to 11 142346 1.4802 0.930595 6 to 10 142267 1.2124 0.887328 5 to 9 142154 0.8294 0.796558 4 to 8 141723 -0.6316 0.263815 3 to 7 142046 0.4633 0.678421 2 to 6 142138 0.7752 0.780875 1 to 5 141333 -1.9537 0.025371 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-18_13:31 Bits used No. missing words z-score p-value 31 to 32 141028 -2.5998 0.004664 30 to 31 142253 1.0138 0.844655 29 to 30 141724 -0.5467 0.292294 28 to 29 141860 -0.1455 0.442152 27 to 28 142086 0.5212 0.698869 26 to 27 142175 0.7837 0.783388 25 to 26 141931 0.0639 0.525484 24 to 25 142057 0.4356 0.668438 23 to 24 141988 0.2321 0.591756 22 to 23 142474 1.6657 0.952113 21 to 22 141845 -0.1898 0.424747 20 to 21 142582 1.9843 0.976388 19 to 20 141644 -0.7827 0.216906 18 to 19 141972 0.1849 0.573333 17 to 18 141663 -0.7266 0.233724 16 to 17 142366 1.3471 0.911027 15 to 16 142065 0.4592 0.676956 14 to 15 142485 1.6981 0.955259 13 to 14 141845 -0.1898 0.424747 12 to 13 141850 -0.1750 0.430534 11 to 12 141908 -0.0039 0.498435 10 to 11 141716 -0.5703 0.284239 9 to 10 141769 -0.4140 0.339454 8 to 9 141745 -0.4847 0.313927 7 to 8 141829 -0.2370 0.406343 6 to 7 141731 -0.5260 0.299428 5 to 6 141829 -0.2370 0.406343 4 to 5 142733 2.4297 0.992444 3 to 4 142030 0.3560 0.639064 2 to 3 141515 -1.1632 0.122371 1 to 2 142854 2.7866 0.997337 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-18_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2430.18 -0.987 0.161729 Test results for specific bytes for dh-ranFile-2015-12-18_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2480.09 -0.282 0.389130 2 to 9 2515.12 0.214 0.584671 3 to 10 2580.02 1.132 0.871109 4 to 11 2580.76 1.142 0.873292 5 to 12 2384.67 -1.631 0.051440 6 to 13 2423.40 -1.083 0.139346 7 to 14 2540.44 0.572 0.716318 8 to 15 2592.90 1.314 0.905535 9 to 16 2537.12 0.525 0.700205 10 to 17 2579.02 1.118 0.868118 11 to 18 2553.04 0.750 0.773407 12 to 19 2400.01 -1.414 0.078665 13 to 20 2431.64 -0.967 0.166846 14 to 21 2447.46 -0.743 0.228729 15 to 22 2364.03 -1.923 0.027248 16 to 23 2415.66 -1.193 0.116486 17 to 24 2630.32 1.843 0.967337 18 to 25 2503.35 0.047 0.518880 19 to 26 2489.16 -0.153 0.439093 20 to 27 2581.52 1.153 0.875504 21 to 28 2577.07 1.090 0.862114 22 to 29 2502.04 0.029 0.511509 23 to 30 2440.46 -0.842 0.199890 24 to 31 2484.47 -0.220 0.413067 25 to 32 2522.56 0.319 0.625161 CDPARK for dh-ranFile-2015-12-18_13:31: 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 3541 0.8219 0.794438 3526 0.1370 0.554479 3498 -1.1416 0.126820 3524 0.0457 0.518210 3541 0.8219 0.794438 3511 -0.5479 0.291865 3482 -1.8721 0.030593 3522 -0.0457 0.481790 3534 0.5023 0.692266 3544 0.9589 0.831196 Square side=100, avg. no. parked=3522.30 sample std.=19.15 p-value of the KSTEST for those 10 p-values: 0.884947 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-18_13:31 0.4613,0.0761,0.2479,0.2705,0.8864,0.9370,0.4358,0.5503,0.0151,0.0144, The KS test for those 10 p-values: 0.193394 The 3DSPHERES test for dh-ranFile-2015-12-18_13:31 sample no r^3 equiv. uni. 1 19.079 0.470578 2 17.135 0.435139 3 52.087 0.823816 4 7.285 0.215595 5 17.292 0.438089 6 7.530 0.221968 7 32.823 0.665156 8 47.810 0.796818 9 0.307 0.010171 10 8.696 0.251625 11 119.036 0.981086 12 11.462 0.317551 13 6.007 0.181463 14 14.520 0.383694 15 36.107 0.699874 16 11.660 0.322043 17 118.104 0.980489 18 15.255 0.398609 19 6.886 0.205104 20 4.108 0.127980 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.428773 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-18_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 2.0 0.8 0.7 0.1 0.5 1.4 0.4 0.8 0.2 0.2 -0.0 -1.1 -0.7 1.1 -0.1 -1.0 -0.1 -0.0 0.4 1.3 -1.0 0.5 0.1 -0.3 0.2 -1.2 -0.5 -0.7 0.4 0.6 -0.1 0.1 -0.9 -0.7 -0.5 -0.7 -0.8 0.4 2.4 -1.0 -0.1 Chi-square with 42 degrees of freedom:28.690355 z-score=-1.452201, p-value=0.058525 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-18_13:31 Test no p-value 1 0.262203 2 0.099713 3 0.645176 4 0.300771 5 0.163903 6 0.098774 7 0.116685 8 0.163991 9 0.012664 10 0.255533 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001649 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-18_13:31: (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 66552 0.20 66656 0.00 3 25000.00 25098 0.38 25305 3.72 4 6666.67 6670 0.00 6458 6.53 5 1388.89 1412 0.38 1336 2.01 6 238.10 229 0.35 212 2.86 7 34.72 34 0.01 28 1.30 8 4.96 4 0.19 4 0.19 p=0.04156 p=0.98919 Number of rngs required: 687833, p-value: 0.255 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-18_13:31 No. of wins: Observed Expected 98470 98585.9 z-score=-0.518, pvalue=0.30216 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67042 66666.7 2.113 2.113 2 37431 37654.3 1.324 3.438 3 26932 26954.7 0.019 3.457 4 19316 19313.5 0.000 3.457 5 13919 13851.4 0.330 3.787 6 10023 9943.5 0.635 4.422 7 7049 7145.0 1.291 5.712 8 5074 5139.1 0.824 6.536 9 3704 3699.9 0.005 6.541 10 2620 2666.3 0.804 7.345 11 1918 1923.3 0.015 7.360 12 1343 1388.7 1.507 8.866 13 987 1003.7 0.278 9.144 14 693 726.1 1.513 10.657 15 560 525.8 2.220 12.877 16 376 381.2 0.070 12.946 17 275 276.5 0.009 12.955 18 190 200.8 0.584 13.539 19 151 146.0 0.172 13.711 20 107 106.2 0.006 13.717 21 290 287.1 0.029 13.746 Chisq= 13.75 for 20 degrees of freedom, p= 0.15686 SUMMARY of craptest p-value for no. of wins: 0.302164 p-value for throws/game: 0.156860 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-18_13:31 No. of wins: Observed Expected 98426 98585.9 z-score=-0.715, pvalue=0.23731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66427 66666.7 0.862 0.862 2 37912 37654.3 1.763 2.625 3 26832 26954.7 0.559 3.184 4 19312 19313.5 0.000 3.184 5 13987 13851.4 1.327 4.511 6 9912 9943.5 0.100 4.611 7 7185 7145.0 0.224 4.835 8 5180 5139.1 0.326 5.161 9 3677 3699.9 0.141 5.302 10 2727 2666.3 1.382 6.684 11 1906 1923.3 0.156 6.840 12 1351 1388.7 1.026 7.866 13 990 1003.7 0.187 8.053 14 705 726.1 0.615 8.669 15 524 525.8 0.006 8.675 16 363 381.2 0.864 9.539 17 258 276.5 1.243 10.782 18 201 200.8 0.000 10.782 19 142 146.0 0.109 10.891 20 106 106.2 0.000 10.892 21 303 287.1 0.879 11.771 Chisq= 11.77 for 20 degrees of freedom, p= 0.07625 SUMMARY of craptest p-value for no. of wins: 0.237310 p-value for throws/game: 0.076253 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0047,0.0102,0.0115,0.0127,0.0144,0.0151,0.0246,0.0254,0.0272, 0.0280,0.0306,0.0416,0.0463,0.0502,0.0514,0.0524,0.0551,0.0585,0.0667, 0.0693,0.0694,0.0695,0.0761,0.0763,0.0787,0.0988,0.0997,0.1025,0.1116, 0.1165,0.1167,0.1185,0.1224,0.1232,0.1245,0.1268,0.1280,0.1319,0.1393, 0.1450,0.1465,0.1480,0.1569,0.1569,0.1617,0.1639,0.1640,0.1660,0.1668, 0.1694,0.1815,0.1933,0.1934,0.1999,0.1999,0.2051,0.2073,0.2079,0.2156, 0.2169,0.2197,0.2220,0.2225,0.2285,0.2287,0.2337,0.2369,0.2373,0.2388, 0.2479,0.2516,0.2539,0.2540,0.2553,0.2555,0.2562,0.2569,0.2608,0.2622, 0.2638,0.2705,0.2842,0.2876,0.2919,0.2923,0.2937,0.2994,0.2997,0.3008, 0.3011,0.3022,0.3058,0.3139,0.3157,0.3174,0.3176,0.3220,0.3243,0.3284, 0.3366,0.3395,0.3429,0.3582,0.3837,0.3891,0.3938,0.3986,0.4028,0.4063, 0.4063,0.4095,0.4131,0.4192,0.4247,0.4247,0.4256,0.4288,0.4305,0.4351, 0.4352,0.4358,0.4381,0.4391,0.4393,0.4393,0.4393,0.4422,0.4486,0.4524, 0.4537,0.4554,0.4613,0.4676,0.4706,0.4707,0.4721,0.4801,0.4818,0.4872, 0.4984,0.5106,0.5115,0.5182,0.5189,0.5194,0.5255,0.5270,0.5480,0.5503, 0.5516,0.5535,0.5545,0.5571,0.5607,0.5655,0.5682,0.5685,0.5733,0.5734, 0.5735,0.5841,0.5847,0.5907,0.5918,0.5993,0.6071,0.6194,0.6227,0.6238, 0.6252,0.6279,0.6303,0.6366,0.6391,0.6400,0.6452,0.6513,0.6575,0.6588, 0.6652,0.6684,0.6770,0.6784,0.6784,0.6805,0.6862,0.6923,0.6989,0.6999, 0.7002,0.7036,0.7055,0.7075,0.7144,0.7163,0.7197,0.7345,0.7359,0.7412, 0.7440,0.7447,0.7447,0.7497,0.7603,0.7703,0.7734,0.7759,0.7793,0.7799, 0.7809,0.7825,0.7830,0.7834,0.7944,0.7944,0.7966,0.7968,0.7977,0.8023, 0.8087,0.8106,0.8130,0.8238,0.8291,0.8312,0.8317,0.8447,0.8602,0.8621, 0.8649,0.8681,0.8711,0.8713,0.8733,0.8755,0.8798,0.8820,0.8849,0.8864, 0.8867,0.8873,0.8934,0.9012,0.9030,0.9033,0.9055,0.9110,0.9123,0.9275, 0.9306,0.9365,0.9370,0.9391,0.9478,0.9521,0.9539,0.9553,0.9560,0.9673, 0.9728,0.9764,0.9805,0.9811,0.9892,0.9908,0.9924,0.9934,0.9973, Overall p-value after applying KStest on 269 p-values = 0.879149 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.