BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA= 2.0000 rnd-aeg.bin using bits 1 to 24 p-value= .282707 rnd-aeg.bin using bits 2 to 25 p-value= .835054 rnd-aeg.bin using bits 3 to 26 p-value= .301694 rnd-aeg.bin using bits 4 to 27 p-value= .721486 rnd-aeg.bin using bits 5 to 28 p-value= .502951 rnd-aeg.bin using bits 6 to 29 p-value= .211412 rnd-aeg.bin using bits 7 to 30 p-value= .110033 rnd-aeg.bin using bits 8 to 31 p-value= .913814 rnd-aeg.bin using bits 9 to 32 p-value= .239704 The 9 p-values were .282707 .835054 .301694 .721486 .502951 .211412 .110033 .913814 .239704 A KSTEST for the 9 p-values yields .175299 -------------------------------------------------------------------------------- OPERM5 test for file rnd-aeg.bin chisquare for 99 degrees of freedom=151.097; p-value= .999406 OPERM5 test for file rnd-aeg.bin chisquare for 99 degrees of freedom= 96.645; p-value= .451720 -------------------------------------------------------------------------------- Binary rank test for rnd-aeg.bin Rank test for 31x31 binary matrices: rows from leftmost 31 bits of each 32-bit integer rank observed expected (o-e)^2/e sum 28 213 211.4 .011838 .012 29 4990 5134.0 4.039523 4.051 30 23322 23103.0 2.075071 6.126 31 11475 11551.5 .506945 6.633 chisquare= 6.633 for 3 d. of f.; p-value= .920456 Binary rank test for rnd-aeg.bin Rank test for 32x32 binary matrices: rows from leftmost 32 bits of each 32-bit integer rank observed expected (o-e)^2/e sum 29 188 211.4 2.593929 2.594 30 5044 5134.0 1.578074 4.172 31 23221 23103.0 .602212 4.774 32 11547 11551.5 .001772 4.776 chisquare= 4.776 for 3 d. of f.; p-value= .825475 -------------------------------------------------------------------------------- b-rank test for bits 1 to 8 p=1-exp(-SUM/2)= .63015 b-rank test for bits 2 to 9 p=1-exp(-SUM/2)= .83806 b-rank test for bits 3 to 10 p=1-exp(-SUM/2)= .78636 b-rank test for bits 4 to 11 p=1-exp(-SUM/2)= .08852 b-rank test for bits 5 to 12 p=1-exp(-SUM/2)= .14937 b-rank test for bits 6 to 13 p=1-exp(-SUM/2)= .62995 b-rank test for bits 7 to 14 p=1-exp(-SUM/2)= .60402 b-rank test for bits 8 to 15 p=1-exp(-SUM/2)= .44290 b-rank test for bits 9 to 16 p=1-exp(-SUM/2)= .76289 b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .39851 b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .83832 b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .26540 b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .87269 b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .14547 b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .46188 b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .68161 b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .72405 b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .79438 b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .33177 b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .57013 b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .90415 b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .38112 b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .58047 b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .19749 b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .75627 TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices These should be 25 uniform [0,1] random variables: .630150 .838059 .786356 .088524 .149368 .629947 .604015 .442902 .762894 .398514 .838319 .265400 .872694 .145469 .461881 .681614 .724054 .794376 .331766 .570128 .904152 .381118 .580471 .197489 .756272 brank test summary for rnd-aeg.bin The KS test for those 25 supposed UNI's yields KS p-value= .639914 -------------------------------------------------------------------------------- No. missing words should average 141909. with sigma=428. tst no 1: 141655 missing words, -.59 sigmas from mean, p-value= .27618 tst no 2: 141504 missing words, -.95 sigmas from mean, p-value= .17181 tst no 3: 142394 missing words, 1.13 sigmas from mean, p-value= .87127 tst no 4: 141724 missing words, -.43 sigmas from mean, p-value= .33250 tst no 5: 140928 missing words, -2.29 sigmas from mean, p-value= .01093 tst no 6: 141748 missing words, -.38 sigmas from mean, p-value= .35311 tst no 7: 142225 missing words, .74 sigmas from mean, p-value= .76961 tst no 8: 142101 missing words, .45 sigmas from mean, p-value= .67286 tst no 9: 142669 missing words, 1.77 sigmas from mean, p-value= .96205 tst no 10: 142293 missing words, .90 sigmas from mean, p-value= .81499 tst no 11: 141752 missing words, -.37 sigmas from mean, p-value= .35659 tst no 12: 142058 missing words, .35 sigmas from mean, p-value= .63584 tst no 13: 141655 missing words, -.59 sigmas from mean, p-value= .27618 tst no 14: 142051 missing words, .33 sigmas from mean, p-value= .62968 tst no 15: 141509 missing words, -.94 sigmas from mean, p-value= .17480 tst no 16: 141621 missing words, -.67 sigmas from mean, p-value= .25026 tst no 17: 141285 missing words, -1.46 sigmas from mean, p-value= .07232 tst no 18: 142230 missing words, .75 sigmas from mean, p-value= .77314 tst no 19: 142672 missing words, 1.78 sigmas from mean, p-value= .96262 tst no 20: 141605 missing words, -.71 sigmas from mean, p-value= .23853 -------------------------------------------------------------------------------- OPSO for rnd-aeg.bin using bits 23 to 32 141841 -.236 .4069 OPSO for rnd-aeg.bin using bits 22 to 31 142102 .664 .7468 OPSO for rnd-aeg.bin using bits 21 to 30 141710 -.687 .2459 OPSO for rnd-aeg.bin using bits 20 to 29 141489 -1.449 .0736 OPSO for rnd-aeg.bin using bits 19 to 28 142098 .651 .7423 OPSO for rnd-aeg.bin using bits 18 to 27 142003 .323 .6267 OPSO for rnd-aeg.bin using bits 17 to 26 141609 -1.036 .1502 OPSO for rnd-aeg.bin using bits 16 to 25 141822 -.301 .3817 OPSO for rnd-aeg.bin using bits 15 to 24 142566 2.264 .9882 OPSO for rnd-aeg.bin using bits 14 to 23 142187 .957 .8308 OPSO for rnd-aeg.bin using bits 13 to 22 142357 1.544 .9387 OPSO for rnd-aeg.bin using bits 12 to 21 142041 .454 .6751 OPSO for rnd-aeg.bin using bits 11 to 20 142291 1.316 .9059 OPSO for rnd-aeg.bin using bits 10 to 19 141718 -.660 .2547 OPSO for rnd-aeg.bin using bits 9 to 18 141710 -.687 .2459 OPSO for rnd-aeg.bin using bits 8 to 17 141604 -1.053 .1462 OPSO for rnd-aeg.bin using bits 7 to 16 141951 .144 .5571 OPSO for rnd-aeg.bin using bits 6 to 15 142271 1.247 .8938 OPSO for rnd-aeg.bin using bits 5 to 14 141313 -2.056 .0199 OPSO for rnd-aeg.bin using bits 4 to 13 142196 .989 .8386 OPSO for rnd-aeg.bin using bits 3 to 12 142256 1.195 .8840 OPSO for rnd-aeg.bin using bits 2 to 11 141871 -.132 .4474 OPSO for rnd-aeg.bin using bits 1 to 10 142089 .620 .7322 OQSO for rnd-aeg.bin using bits 28 to 32 142184 .931 .8241 OQSO for rnd-aeg.bin using bits 27 to 31 142060 .511 .6952 OQSO for rnd-aeg.bin using bits 26 to 30 142419 1.728 .9580 OQSO for rnd-aeg.bin using bits 25 to 29 142161 .853 .8032 OQSO for rnd-aeg.bin using bits 24 to 28 141996 .294 .6155 OQSO for rnd-aeg.bin using bits 23 to 27 141586 -1.096 .1365 OQSO for rnd-aeg.bin using bits 22 to 26 142173 .894 .8143 OQSO for rnd-aeg.bin using bits 21 to 25 142607 2.365 .9910 OQSO for rnd-aeg.bin using bits 20 to 24 141866 -.147 .4416 OQSO for rnd-aeg.bin using bits 19 to 23 141886 -.079 .4685 OQSO for rnd-aeg.bin using bits 18 to 22 142118 .707 .7603 OQSO for rnd-aeg.bin using bits 17 to 21 141832 -.262 .3966 OQSO for rnd-aeg.bin using bits 16 to 20 141562 -1.177 .1195 OQSO for rnd-aeg.bin using bits 15 to 19 142125 .731 .7676 OQSO for rnd-aeg.bin using bits 14 to 18 141645 -.896 .1851 OQSO for rnd-aeg.bin using bits 13 to 17 141812 -.330 .3707 OQSO for rnd-aeg.bin using bits 12 to 16 142321 1.395 .9186 OQSO for rnd-aeg.bin using bits 11 to 15 141882 -.093 .4631 OQSO for rnd-aeg.bin using bits 10 to 14 141988 .267 .6051 OQSO for rnd-aeg.bin using bits 9 to 13 141579 -1.120 .1314 OQSO for rnd-aeg.bin using bits 8 to 12 142152 .823 .7946 OQSO for rnd-aeg.bin using bits 7 to 11 141799 -.374 .3542 OQSO for rnd-aeg.bin using bits 6 to 10 141861 -.164 .4349 OQSO for rnd-aeg.bin using bits 5 to 9 141718 -.649 .2583 OQSO for rnd-aeg.bin using bits 4 to 8 141445 -1.574 .0577 OQSO for rnd-aeg.bin using bits 3 to 7 141400 -1.727 .0421 OQSO for rnd-aeg.bin using bits 2 to 6 142133 .758 .7758 OQSO for rnd-aeg.bin using bits 1 to 5 141789 -.408 .3417 DNA for rnd-aeg.bin using bits 31 to 32 141912 .008 .5031 DNA for rnd-aeg.bin using bits 30 to 31 142131 .654 .7434 DNA for rnd-aeg.bin using bits 29 to 30 141989 .235 .5929 DNA for rnd-aeg.bin using bits 28 to 29 141937 .082 .5325 DNA for rnd-aeg.bin using bits 27 to 28 141550 -1.060 .1446 DNA for rnd-aeg.bin using bits 26 to 27 141341 -1.676 .0468 DNA for rnd-aeg.bin using bits 25 to 26 141606 -.895 .1855 DNA for rnd-aeg.bin using bits 24 to 25 142468 1.648 .9503 DNA for rnd-aeg.bin using bits 23 to 24 142019 .324 .6268 DNA for rnd-aeg.bin using bits 22 to 23 142167 .760 .7764 DNA for rnd-aeg.bin using bits 21 to 22 141084 -2.435 .0075 DNA for rnd-aeg.bin using bits 20 to 21 142159 .736 .7693 DNA for rnd-aeg.bin using bits 19 to 20 142054 .427 .6652 DNA for rnd-aeg.bin using bits 18 to 19 141174 -2.169 .0150 DNA for rnd-aeg.bin using bits 17 to 18 142125 .636 .7377 DNA for rnd-aeg.bin using bits 16 to 17 142048 .409 .6588 DNA for rnd-aeg.bin using bits 15 to 16 141394 -1.520 .0642 DNA for rnd-aeg.bin using bits 14 to 15 142172 .775 .7808 DNA for rnd-aeg.bin using bits 13 to 14 142162 .745 .7720 DNA for rnd-aeg.bin using bits 12 to 13 141904 -.016 .4937 DNA for rnd-aeg.bin using bits 11 to 12 142044 .397 .6544 DNA for rnd-aeg.bin using bits 10 to 11 141654 -.753 .2257 DNA for rnd-aeg.bin using bits 9 to 10 142101 .565 .7141 DNA for rnd-aeg.bin using bits 8 to 9 141533 -1.110 .1335 DNA for rnd-aeg.bin using bits 7 to 8 141454 -1.343 .0896 DNA for rnd-aeg.bin using bits 6 to 7 141311 -1.765 .0388 DNA for rnd-aeg.bin using bits 5 to 6 142165 .754 .7746 DNA for rnd-aeg.bin using bits 4 to 5 141701 -.615 .2694 DNA for rnd-aeg.bin using bits 3 to 4 141954 .132 .5524 DNA for rnd-aeg.bin using bits 2 to 3 141697 -.626 .2655 DNA for rnd-aeg.bin using bits 1 to 2 141611 -.880 .1894 -------------------------------------------------------------------------------- Test results for rnd-aeg.bin Chi-square with 5^5-5^4=2500 d.of f. for sample size:2560000 chisquare equiv normal p-value Results fo COUNT-THE-1's in successive bytes: byte stream for rnd-aeg.bin 2545.80 .648 .741405 byte stream for rnd-aeg.bin 2500.05 .001 .500278 -------------------------------------------------------------------------------- Chi-square with 5^5-5^4=2500 d.of f. for sample size: 256000 chisquare equiv normal p value Results for COUNT-THE-1's in specified bytes: bits 1 to 8 2612.58 1.592 .944314 bits 2 to 9 2598.13 1.388 .917398 bits 3 to 10 2590.12 1.274 .898755 bits 4 to 11 2572.02 1.019 .845790 bits 5 to 12 2518.21 .258 .601615 bits 6 to 13 2315.54 -2.609 .004545 bits 7 to 14 2566.42 .939 .826208 bits 8 to 15 2464.92 -.496 .309920 bits 9 to 16 2494.85 -.073 .470988 bits 10 to 17 2666.94 2.361 .990886 bits 11 to 18 2561.82 .874 .809022 bits 12 to 19 2480.60 -.274 .391897 bits 13 to 20 2480.82 -.271 .393121 bits 14 to 21 2365.31 -1.905 .028403 bits 15 to 22 2575.16 1.063 .856104 bits 16 to 23 2376.47 -1.747 .040322 bits 17 to 24 2495.28 -.067 .473413 bits 18 to 25 2460.57 -.558 .288543 bits 19 to 26 2524.25 .343 .634175 bits 20 to 27 2378.03 -1.725 .042275 bits 21 to 28 2571.99 1.018 .845667 bits 22 to 29 2453.04 -.664 .253326 bits 23 to 30 2400.51 -1.407 .079714 bits 24 to 31 2535.89 .508 .694099 bits 25 to 32 2468.70 -.443 .329010 -------------------------------------------------------------------------------- CDPARK: result of ten tests on file rnd-aeg.bin Of 12,000 tries, the average no. of successes should be 3523 with sigma=21.9 Successes: 3488 z-score: -1.598 p-value: .055002 Successes: 3482 z-score: -1.872 p-value: .030593 Successes: 3495 z-score: -1.279 p-value: .100530 Successes: 3522 z-score: -.046 p-value: .481790 Successes: 3506 z-score: -.776 p-value: .218799 Successes: 3543 z-score: .913 p-value: .819442 Successes: 3540 z-score: .776 p-value: .781201 Successes: 3528 z-score: .228 p-value: .590298 Successes: 3501 z-score: -1.005 p-value: .157553 Successes: 3530 z-score: .320 p-value: .625377 square size avg. no. parked sample sigma 100. 3513.500 20.807 KSTEST for the above 10: p= .717766 -------------------------------------------------------------------------------- This is the MINIMUM DISTANCE test for random integers in the file rnd-aeg.bin Sample no. d^2 avg equiv uni 5 1.7530 1.5190 .828263 10 3.6655 1.4083 .974875 15 .5771 1.2664 .440116 20 .0826 1.1531 .079626 25 .3184 1.1354 .273860 30 .5630 1.0329 .432120 35 .4518 .9945 .364954 40 1.2246 .9399 .707927 45 2.8340 .9860 .942054 50 .1654 .9506 .153116 55 .6723 .9380 .491166 60 2.0782 .9174 .876145 65 .1035 .9087 .098818 70 1.6367 .8811 .806974 75 .4167 .8671 .342163 80 1.9917 .9054 .864892 85 1.0229 .9014 .642292 90 .4263 .8765 .348497 95 .0243 .8955 .024130 100 .4846 .9101 .385584 MINIMUM DISTANCE TEST for rnd-aeg.bin Result of KS test on 20 transformed mindist^2's: p-value= .469581 -------------------------------------------------------------------------------- The 3DSPHERES test for file rnd-aeg.bin sample no: 1 r^3= 6.776 p-value= .20218 sample no: 2 r^3= 46.508 p-value= .78781 sample no: 3 r^3= 4.908 p-value= .15092 sample no: 4 r^3= 20.656 p-value= .49769 sample no: 5 r^3= 2.527 p-value= .08080 sample no: 6 r^3= 22.395 p-value= .52598 sample no: 7 r^3= 27.445 p-value= .59941 sample no: 8 r^3= 49.173 p-value= .80585 sample no: 9 r^3= 15.958 p-value= .41254 sample no: 10 r^3= 5.712 p-value= .17338 sample no: 11 r^3= 40.960 p-value= .74471 sample no: 12 r^3= 6.706 p-value= .20031 sample no: 13 r^3= 45.559 p-value= .78099 sample no: 14 r^3= 32.787 p-value= .66476 sample no: 15 r^3= 21.901 p-value= .51811 sample no: 16 r^3= 17.863 p-value= .44867 sample no: 17 r^3= 65.772 p-value= .88835 sample no: 18 r^3= 23.890 p-value= .54901 sample no: 19 r^3= 24.578 p-value= .55925 sample no: 20 r^3= 71.492 p-value= .90773 3DSPHERES test for file rnd-aeg.bin p-value= .324385 -------------------------------------------------------------------------------- RESULTS OF SQUEEZE TEST FOR rnd-aeg.bin Table of standardized frequency counts ( (obs-exp)/sqrt(exp) )^2 for j taking values <=6,7,8,...,47,>=48: .6 .5 -.8 .0 -.1 .6 1.4 -.1 -.6 -.9 1.6 .7 -1.8 -.8 -.5 -.2 1.4 -.7 -.1 -1.0 -.6 .2 2.0 .4 .2 .8 -.9 1.3 -.4 -.5 .8 .1 1.1 -1.0 .6 .6 -.5 -.4 -1.2 -.1 -.6 -1.0 .8 Chi-square with 42 degrees of freedom: 31.099 z-score= -1.189 p-value= .107942 ______________________________________________________________ -------------------------------------------------------------------------------- Test no. 1 p-value .444148 Test no. 2 p-value .851626 Test no. 3 p-value .227098 Test no. 4 p-value .920869 Test no. 5 p-value .626638 Test no. 6 p-value .250095 Test no. 7 p-value .845372 Test no. 8 p-value .391863 Test no. 9 p-value .006843 Test no. 10 p-value .267635 Results of the OSUM test for rnd-aeg.bin KSTEST on the above 10 p-values: .147590 -------------------------------------------------------------------------------- The RUNS test for file rnd-aeg.bin Up and down runs in a sample of 10000 _________________________________________________ Run test for rnd-aeg.bin : runs up; ks test for 10 p's: .511886 runs down; ks test for 10 p's: .673061 Run test for rnd-aeg.bin : runs up; ks test for 10 p's: .316014 runs down; ks test for 10 p's: .211421 -------------------------------------------------------------------------------- Results of craps test for rnd-aeg.bin No. of wins: Observed Expected 98748 98585.86 Chisq= 17.56 for 20 degrees of freedom, p= .38349 Throws Observed Expected Chisq Sum SUMMARY FOR rnd-aeg.bin p-value for no. of wins: .765831 p-value for throws/game: .383494 Test completed. File rnd-aeg.bin :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::