RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-30_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 22.1150 0.819665 2 to 25 15.91 23.9816 0.880064 3 to 26 15.73 22.3698 0.829089 4 to 27 15.88 17.0073 0.546127 5 to 28 15.61 24.5493 0.894738 6 to 29 15.53 25.0538 0.906489 7 to 30 15.73 16.1006 0.483282 8 to 31 15.60 17.2543 0.562732 9 to 32 15.91 10.4921 0.118284 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.090087 Tough bday spacings test for dh-ranFile-2018-03-30_10:31: 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 35 74 122 83 67 60 27 17 3 3 (O-E)^2/E 0.0 0.1 0.0 6.1 2.2 1.6 1.2 0.3 0.3 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 13.946, p= 0.825 RESULTS OF GCD FOR dh-ranFile-2018-03-30_10:31 Euclid's algorithm: p-value, steps to gcd: 0.989093 p-value, dist. of gcd's: 0.369917 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-30_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.693 0.069 0.331 0.166 0.444 0.920 0.728 0.617 Bits 8 to 15---> 0.603 0.899 0.579 0.906 0.857 0.499 0.809 0.401 Bits 16 to 23---> 0.449 0.039 0.618 0.096 0.978 0.057 0.002 0.758 Bits 24 to 31---> 0.035 0.813 0.883 0.196 0.128 0.892 0.051 0.863 KS test for the above 32 p values: 0.724 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-30_10:31, p-values for 5 runs: 0.2065, 0.1747, 0.4689, 0.2818, 0.5378 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-30_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 191 211.4 1.972 1.972 r= 29 5034 5134.0 1.948 3.920 r= 30 23236 23103.0 0.765 4.685 r= 31 11539 11551.5 0.014 4.699 chi-square = 4.699 with df = 3; p-value = 0.805 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-30_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 186 211.4 3.056 3.056 r= 30 5192 5134.0 0.655 3.711 r= 31 22871 23103.0 2.331 6.042 r= 32 11751 11551.5 3.445 9.486 chi-square = 9.486 with df = 3; p-value = 0.977 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-30_10:31 b-rank test for bits 1 to 8, p=0.59281 b-rank test for bits 2 to 9, p=0.07566 b-rank test for bits 3 to 10, p=0.82912 b-rank test for bits 4 to 11, p=0.50481 b-rank test for bits 5 to 12, p=0.17693 b-rank test for bits 6 to 13, p=0.91905 b-rank test for bits 7 to 14, p=0.95519 b-rank test for bits 8 to 15, p=0.98834 b-rank test for bits 9 to 16, p=0.94896 b-rank test for bits 10 to 17, p=0.07389 b-rank test for bits 11 to 18, p=0.84676 b-rank test for bits 12 to 19, p=0.88725 b-rank test for bits 13 to 20, p=0.31385 b-rank test for bits 14 to 21, p=0.04183 b-rank test for bits 15 to 22, p=0.93114 b-rank test for bits 16 to 23, p=0.18270 b-rank test for bits 17 to 24, p=0.37608 b-rank test for bits 18 to 25, p=0.12154 b-rank test for bits 19 to 26, p=0.89178 b-rank test for bits 20 to 27, p=0.27398 b-rank test for bits 21 to 28, p=0.72416 b-rank test for bits 22 to 29, p=0.38895 b-rank test for bits 23 to 30, p=0.07535 b-rank test for bits 24 to 31, p=0.54325 b-rank test for bits 25 to 32, p=0.72180 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 = 0.286336 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-30_10:31 (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 142338 1.00 0.841723 2 141616 -0.69 0.246561 3 141757 -0.36 0.360954 4 142368 1.07 0.858063 5 142386 1.11 0.867299 6 142241 0.77 0.780809 7 142327 0.98 0.835434 8 142417 1.19 0.882217 9 142680 1.80 0.964119 10 141521 -0.91 0.182121 11 141455 -1.06 0.144227 12 142147 0.56 0.710657 13 142115 0.48 0.684577 14 141244 -1.55 0.060031 15 141767 -0.33 0.369738 16 141957 0.11 0.544342 17 141504 -0.95 0.171811 18 142026 0.27 0.607417 19 141916 0.02 0.506217 20 141623 -0.67 0.251749 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-30_10:31 Bits used No. missing words z-score p-value 23 to 32 142005 0.3299 0.629261 22 to 31 141511 -1.3736 0.084790 21 to 30 142024 0.3954 0.653731 20 to 29 142006 0.3333 0.630563 19 to 28 142407 1.7161 0.956928 18 to 27 141998 0.3058 0.620106 17 to 26 142185 0.9506 0.829093 16 to 25 142007 0.3368 0.631864 15 to 24 141565 -1.1873 0.117546 14 to 23 142574 2.2920 0.989046 13 to 22 141780 -0.4460 0.327811 12 to 21 141629 -0.9667 0.166858 11 to 20 142098 0.6506 0.742343 10 to 19 141781 -0.4425 0.329058 9 to 18 141862 -0.1632 0.435178 8 to 17 142129 0.7575 0.775620 7 to 16 141996 0.2989 0.617477 6 to 15 141402 -1.7494 0.040110 5 to 14 142238 1.1333 0.871465 4 to 13 141717 -0.6632 0.253599 3 to 12 141611 -1.0287 0.151805 2 to 11 141392 -1.7839 0.037220 1 to 10 141784 -0.4322 0.332808 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-30_10:31 Bits used No. missing words z-score p-value 28 to 32 141862 -0.1604 0.436267 27 to 31 141786 -0.4181 0.337949 26 to 30 142245 1.1379 0.872411 25 to 29 141900 -0.0316 0.487385 24 to 28 141880 -0.0994 0.460401 23 to 27 141645 -0.8960 0.185117 22 to 26 142006 0.3277 0.628429 21 to 25 141786 -0.4181 0.337949 20 to 24 142308 1.3514 0.911720 19 to 23 141593 -1.0723 0.141792 18 to 22 142065 0.5277 0.701145 17 to 21 141666 -0.8248 0.204729 16 to 20 142197 0.9752 0.835258 15 to 19 142170 0.8836 0.811551 14 to 18 142046 0.4633 0.678421 13 to 17 142450 1.8328 0.966582 12 to 16 141783 -0.4282 0.334239 11 to 15 141744 -0.5604 0.287589 10 to 14 141964 0.1853 0.573512 9 to 13 142275 1.2396 0.892431 8 to 12 142009 0.3379 0.632267 7 to 11 142179 0.9141 0.819677 6 to 10 142024 0.3887 0.651255 5 to 9 142038 0.4362 0.668643 4 to 8 141015 -3.0316 0.001216 3 to 7 142343 1.4701 0.929228 2 to 6 142432 1.7718 0.961783 1 to 5 142046 0.4633 0.678421 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-30_10:31 Bits used No. missing words z-score p-value 31 to 32 141805 -0.3078 0.379133 30 to 31 141586 -0.9538 0.170099 29 to 30 141800 -0.3225 0.373534 28 to 29 142082 0.5094 0.694747 27 to 28 141645 -0.7797 0.217774 26 to 27 141694 -0.6352 0.262652 25 to 26 141890 -0.0570 0.477264 24 to 25 141715 -0.5732 0.283240 23 to 24 141709 -0.5909 0.277279 22 to 23 141464 -1.3137 0.094481 21 to 22 141035 -2.5791 0.004952 20 to 21 141492 -1.2311 0.109150 19 to 20 142051 0.4179 0.661992 18 to 19 142180 0.7984 0.787691 17 to 18 141900 -0.0275 0.489022 16 to 17 142312 1.1878 0.882547 15 to 16 141591 -0.9390 0.173859 14 to 15 141919 0.0285 0.511378 13 to 14 141661 -0.7325 0.231921 12 to 13 142449 1.5919 0.944302 11 to 12 141775 -0.3963 0.345959 10 to 11 141727 -0.5378 0.295342 9 to 10 142132 0.6568 0.744359 8 to 9 142140 0.6804 0.751888 7 to 8 142167 0.7601 0.776399 6 to 7 142504 1.7542 0.960301 5 to 6 142071 0.4769 0.683284 4 to 5 141559 -1.0334 0.150703 3 to 4 142005 0.2822 0.611110 2 to 3 142324 1.2232 0.889376 1 to 2 141646 -0.7768 0.218643 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-30_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2489.96 -0.142 0.443573 Test results for specific bytes for dh-ranFile-2018-03-30_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2416.22 -1.185 0.118054 2 to 9 2428.69 -1.008 0.156611 3 to 10 2418.54 -1.152 0.124670 4 to 11 2562.41 0.883 0.811274 5 to 12 2553.21 0.753 0.774138 6 to 13 2451.92 -0.680 0.248267 7 to 14 2455.49 -0.629 0.264519 8 to 15 2576.75 1.085 0.861131 9 to 16 2429.40 -0.998 0.159022 10 to 17 2413.61 -1.222 0.110898 11 to 18 2525.85 0.366 0.642675 12 to 19 2464.58 -0.501 0.308239 13 to 20 2600.76 1.425 0.922919 14 to 21 2636.84 1.935 0.973514 15 to 22 2468.72 -0.442 0.329110 16 to 23 2580.24 1.135 0.871772 17 to 24 2407.89 -1.303 0.096356 18 to 25 2518.31 0.259 0.602161 19 to 26 2508.07 0.114 0.545442 20 to 27 2585.25 1.206 0.886029 21 to 28 2566.07 0.934 0.824948 22 to 29 2394.35 -1.494 0.067579 23 to 30 2479.13 -0.295 0.383953 24 to 31 2543.01 0.608 0.728501 25 to 32 2428.26 -1.015 0.155167 CDPARK for dh-ranFile-2018-03-30_10:31: 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 3512 -0.5023 0.307734 3519 -0.1826 0.427537 3543 0.9132 0.819442 3526 0.1370 0.554479 3566 1.9635 0.975204 3506 -0.7763 0.218799 3481 -1.9178 0.027568 3543 0.9132 0.819442 3547 1.0959 0.863437 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3525.10 sample std.=23.67 p-value of the KSTEST for those 10 p-values: 0.899747 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-30_10:31 0.7822,0.0458,0.3668,0.9016,0.4242,0.9555,0.7724,0.7841,0.0894,0.1832, The KS test for those 10 p-values: 0.734978 The 3DSPHERES test for dh-ranFile-2018-03-30_10:31 sample no r^3 equiv. uni. 1 7.949 0.232781 2 61.200 0.869971 3 13.063 0.353025 4 2.847 0.090545 5 22.097 0.521249 6 49.899 0.810489 7 5.777 0.175166 8 1.130 0.036968 9 11.169 0.310846 10 4.570 0.141301 11 3.004 0.095292 12 12.964 0.350880 13 34.144 0.679582 14 48.664 0.802524 15 21.993 0.519589 16 12.931 0.350168 17 23.299 0.540056 18 12.674 0.344573 19 3.177 0.100487 20 103.781 0.968550 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.305645 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-30_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 1.1 -0.5 -0.9 -0.8 2.0 1.0 2.8 0.5 -0.1 0.3 -0.0 -0.2 -2.0 -0.2 -0.2 2.4 -1.6 0.2 -0.6 0.2 -0.4 0.9 -0.6 -0.2 0.7 -0.0 -0.1 -0.9 0.3 -0.9 0.0 -1.1 -0.6 0.1 -0.9 -0.4 1.3 2.1 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:45.520863 z-score=0.384158, p-value=0.672291 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-30_10:31 Test no p-value 1 0.048085 2 0.037951 3 0.011135 4 0.345587 5 0.215548 6 0.900850 7 0.385298 8 0.242617 9 0.562319 10 0.716038 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.109257 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-30_10:31: (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 66593 0.08 66682 0.00 3 25000.00 25066 0.17 24948 0.11 4 6666.67 6704 0.21 6641 0.10 5 1388.89 1348 1.20 1457 3.34 6 238.10 249 0.50 234 0.07 7 34.72 32 0.21 31 0.40 8 4.96 7 0.84 6 0.22 p=0.21924 p=0.35545 Number of rngs required: 688016, p-value: 0.328 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-30_10:31 No. of wins: Observed Expected 98792 98585.9 z-score= 0.922, pvalue=0.82173 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66542 66666.7 0.233 0.233 2 37703 37654.3 0.063 0.296 3 27162 26954.7 1.594 1.890 4 19344 19313.5 0.048 1.938 5 13823 13851.4 0.058 1.996 6 9964 9943.5 0.042 2.039 7 7029 7145.0 1.884 3.923 8 5111 5139.1 0.153 4.076 9 3728 3699.9 0.214 4.290 10 2707 2666.3 0.621 4.911 11 1843 1923.3 3.355 8.266 12 1367 1388.7 0.340 8.607 13 1037 1003.7 1.104 9.710 14 745 726.1 0.490 10.200 15 512 525.8 0.364 10.564 16 376 381.2 0.070 10.634 17 262 276.5 0.764 11.398 18 197 200.8 0.073 11.471 19 141 146.0 0.170 11.642 20 109 106.2 0.073 11.715 21 298 287.1 0.413 12.127 Chisq= 12.13 for 20 degrees of freedom, p= 0.08837 SUMMARY of craptest p-value for no. of wins: 0.821732 p-value for throws/game: 0.088374 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-30_10:31 No. of wins: Observed Expected 98402 98585.9 z-score=-0.822, pvalue=0.20545 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66670 66666.7 0.000 0.000 2 37645 37654.3 0.002 0.002 3 26784 26954.7 1.081 1.084 4 19335 19313.5 0.024 1.108 5 13886 13851.4 0.086 1.194 6 9973 9943.5 0.087 1.282 7 7237 7145.0 1.184 2.465 8 5248 5139.1 2.309 4.774 9 3685 3699.9 0.060 4.834 10 2587 2666.3 2.358 7.192 11 1903 1923.3 0.215 7.407 12 1391 1388.7 0.004 7.411 13 997 1003.7 0.045 7.456 14 748 726.1 0.658 8.114 15 489 525.8 2.580 10.694 16 374 381.2 0.134 10.828 17 285 276.5 0.259 11.087 18 195 200.8 0.169 11.257 19 134 146.0 0.984 12.240 20 116 106.2 0.901 13.142 21 318 287.1 3.323 16.464 Chisq= 16.46 for 20 degrees of freedom, p= 0.31257 SUMMARY of craptest p-value for no. of wins: 0.205447 p-value for throws/game: 0.312566 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0017,0.0050,0.0111,0.0276,0.0352,0.0370,0.0372,0.0380,0.0390, 0.0401,0.0418,0.0458,0.0481,0.0510,0.0565,0.0600,0.0676,0.0688,0.0739, 0.0753,0.0757,0.0848,0.0884,0.0894,0.0901,0.0905,0.0945,0.0953,0.0956, 0.0964,0.1005,0.1091,0.1093,0.1109,0.1175,0.1181,0.1183,0.1215,0.1247, 0.1277,0.1413,0.1418,0.1442,0.1507,0.1518,0.1552,0.1566,0.1590,0.1661, 0.1669,0.1701,0.1718,0.1739,0.1747,0.1752,0.1769,0.1821,0.1827,0.1832, 0.1851,0.1965,0.2047,0.2054,0.2065,0.2155,0.2178,0.2186,0.2188,0.2192, 0.2319,0.2328,0.2426,0.2466,0.2467,0.2483,0.2517,0.2536,0.2627,0.2645, 0.2740,0.2773,0.2818,0.2832,0.2863,0.2876,0.2953,0.3056,0.3077,0.3082, 0.3108,0.3126,0.3138,0.3278,0.3279,0.3291,0.3291,0.3309,0.3328,0.3342, 0.3379,0.3379,0.3446,0.3456,0.3460,0.3502,0.3509,0.3530,0.3555,0.3610, 0.3668,0.3697,0.3699,0.3735,0.3761,0.3791,0.3840,0.3853,0.3890,0.4011, 0.4242,0.4275,0.4352,0.4363,0.4435,0.4436,0.4487,0.4604,0.4689,0.4773, 0.4833,0.4874,0.4890,0.4994,0.5048,0.5062,0.5114,0.5196,0.5212,0.5378, 0.5401,0.5433,0.5443,0.5454,0.5461,0.5545,0.5623,0.5627,0.5735,0.5788, 0.5928,0.6022,0.6030,0.6074,0.6111,0.6174,0.6175,0.6185,0.6201,0.6284, 0.6293,0.6306,0.6319,0.6323,0.6427,0.6513,0.6537,0.6620,0.6686,0.6723, 0.6784,0.6784,0.6796,0.6833,0.6846,0.6931,0.6947,0.7011,0.7107,0.7160, 0.7218,0.7237,0.7242,0.7281,0.7285,0.7350,0.7423,0.7444,0.7519,0.7579, 0.7724,0.7741,0.7756,0.7764,0.7808,0.7822,0.7841,0.7877,0.8025,0.8048, 0.8086,0.8105,0.8113,0.8116,0.8132,0.8194,0.8194,0.8197,0.8197,0.8217, 0.8245,0.8249,0.8291,0.8291,0.8291,0.8353,0.8354,0.8417,0.8468,0.8571, 0.8581,0.8611,0.8629,0.8634,0.8673,0.8700,0.8715,0.8718,0.8724,0.8801, 0.8822,0.8825,0.8829,0.8860,0.8873,0.8894,0.8918,0.8924,0.8925,0.8947, 0.8990,0.8997,0.9008,0.9016,0.9059,0.9065,0.9117,0.9191,0.9203,0.9229, 0.9292,0.9311,0.9443,0.9490,0.9552,0.9555,0.9569,0.9603,0.9618,0.9641, 0.9666,0.9685,0.9735,0.9752,0.9765,0.9782,0.9883,0.9890,0.9891, Overall p-value after applying KStest on 269 p-values = 0.191529 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.