BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA= 2.0000 rnd.bin using bits 1 to 24 p-value= .653601 rnd.bin using bits 2 to 25 p-value= .697736 rnd.bin using bits 3 to 26 p-value= .098666 rnd.bin using bits 4 to 27 p-value= .843126 rnd.bin using bits 5 to 28 p-value= .231664 rnd.bin using bits 6 to 29 p-value= .799270 rnd.bin using bits 7 to 30 p-value= .883073 rnd.bin using bits 8 to 31 p-value= .430172 rnd.bin using bits 9 to 32 p-value= .276591 The 9 p-values were .653601 .697736 .098666 .843126 .231664 .799270 .883073 .430172 .276591 A KSTEST for the 9 p-values yields .105646 -------------------------------------------------------------------------------- OPERM5 test for file rnd.bin chisquare for 99 degrees of freedom= 95.104; p-value= .407799 OPERM5 test for file rnd.bin chisquare for 99 degrees of freedom= 88.306; p-value= .229111 -------------------------------------------------------------------------------- Binary rank test for rnd.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 28 232 211.4 2.003699 2.004 29 5104 5134.0 .175421 2.179 30 22976 23103.0 .698648 2.878 31 11688 11551.5 1.612392 4.490 chisquare= 4.490 for 3 d. of f.; p-value= .803876 Binary rank test for rnd.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 29 215 211.4 .060688 .061 30 5195 5134.0 .724531 .785 31 23189 23103.0 .319782 1.105 32 11401 11551.5 1.961438 3.066 chisquare= 3.066 for 3 d. of f.; p-value= .658468 -------------------------------------------------------------------------------- b-rank test for bits 1 to 8 p=1-exp(-SUM/2)= .44483 b-rank test for bits 2 to 9 p=1-exp(-SUM/2)= .30290 b-rank test for bits 3 to 10 p=1-exp(-SUM/2)= .65441 b-rank test for bits 4 to 11 p=1-exp(-SUM/2)= .60179 b-rank test for bits 5 to 12 p=1-exp(-SUM/2)= .88781 b-rank test for bits 6 to 13 p=1-exp(-SUM/2)= .94791 b-rank test for bits 7 to 14 p=1-exp(-SUM/2)= .61033 b-rank test for bits 8 to 15 p=1-exp(-SUM/2)= .37118 b-rank test for bits 9 to 16 p=1-exp(-SUM/2)= .12323 b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .26139 b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .84535 b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .52570 b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .81149 b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .02827 b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .43236 b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .93563 b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .68722 b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .31011 b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .49116 b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .38881 b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .57102 b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .74574 b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .50045 b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .16018 b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .83130 TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices These should be 25 uniform [0,1] random variables: .444833 .302897 .654411 .601795 .887807 .947911 .610331 .371185 .123234 .261390 .845349 .525699 .811490 .028272 .432364 .935629 .687224 .310110 .491159 .388812 .571015 .745737 .500448 .160184 .831300 brank test summary for rnd.bin The KS test for those 25 supposed UNI's yields KS p-value= .291913 -------------------------------------------------------------------------------- No. missing words should average 141909. with sigma=428. tst no 1: 141749 missing words, -.37 sigmas from mean, p-value= .35398 tst no 2: 142657 missing words, 1.75 sigmas from mean, p-value= .95967 tst no 3: 141559 missing words, -.82 sigmas from mean, p-value= .20653 tst no 4: 142411 missing words, 1.17 sigmas from mean, p-value= .87943 tst no 5: 142392 missing words, 1.13 sigmas from mean, p-value= .87028 tst no 6: 141920 missing words, .02 sigmas from mean, p-value= .50995 tst no 7: 141831 missing words, -.18 sigmas from mean, p-value= .42740 tst no 8: 142238 missing words, .77 sigmas from mean, p-value= .77873 tst no 9: 141485 missing words, -.99 sigmas from mean, p-value= .16074 tst no 10: 140379 missing words, -3.58 sigmas from mean, p-value= .00017 tst no 11: 142545 missing words, 1.49 sigmas from mean, p-value= .93126 tst no 12: 141367 missing words, -1.27 sigmas from mean, p-value= .10256 tst no 13: 141661 missing words, -.58 sigmas from mean, p-value= .28089 tst no 14: 142771 missing words, 2.01 sigmas from mean, p-value= .97796 tst no 15: 141568 missing words, -.80 sigmas from mean, p-value= .21258 tst no 16: 141488 missing words, -.98 sigmas from mean, p-value= .16246 tst no 17: 143105 missing words, 2.79 sigmas from mean, p-value= .99739 tst no 18: 142456 missing words, 1.28 sigmas from mean, p-value= .89925 tst no 19: 142335 missing words, .99 sigmas from mean, p-value= .84002 tst no 20: 142481 missing words, 1.34 sigmas from mean, p-value= .90917 -------------------------------------------------------------------------------- OPSO for rnd.bin using bits 23 to 32 142297 1.337 .9094 OPSO for rnd.bin using bits 22 to 31 141850 -.205 .4190 OPSO for rnd.bin using bits 21 to 30 142256 1.195 .8840 OPSO for rnd.bin using bits 20 to 29 142182 .940 .8265 OPSO for rnd.bin using bits 19 to 28 141993 .289 .6135 OPSO for rnd.bin using bits 18 to 27 141611 -1.029 .1518 OPSO for rnd.bin using bits 17 to 26 142068 .547 .7079 OPSO for rnd.bin using bits 16 to 25 141450 -1.584 .0566 OPSO for rnd.bin using bits 15 to 24 142219 1.068 .8572 OPSO for rnd.bin using bits 14 to 23 142264 1.223 .8893 OPSO for rnd.bin using bits 13 to 22 142219 1.068 .8572 OPSO for rnd.bin using bits 12 to 21 141897 -.043 .4830 OPSO for rnd.bin using bits 11 to 20 141823 -.298 .3830 OPSO for rnd.bin using bits 10 to 19 141825 -.291 .3856 OPSO for rnd.bin using bits 9 to 18 141977 .233 .5923 OPSO for rnd.bin using bits 8 to 17 141379 -1.829 .0337 OPSO for rnd.bin using bits 7 to 16 141422 -1.680 .0464 OPSO for rnd.bin using bits 6 to 15 142132 .768 .7787 OPSO for rnd.bin using bits 5 to 14 141722 -.646 .2592 OPSO for rnd.bin using bits 4 to 13 141616 -1.011 .1559 OPSO for rnd.bin using bits 3 to 12 142077 .578 .7184 OPSO for rnd.bin using bits 2 to 11 141444 -1.605 .0543 OPSO for rnd.bin using bits 1 to 10 142173 .909 .8184 OQSO for rnd.bin using bits 28 to 32 141921 .040 .5158 OQSO for rnd.bin using bits 27 to 31 141897 -.042 .4833 OQSO for rnd.bin using bits 26 to 30 141853 -.191 .4243 OQSO for rnd.bin using bits 25 to 29 141842 -.228 .4097 OQSO for rnd.bin using bits 24 to 28 142336 1.446 .9260 OQSO for rnd.bin using bits 23 to 27 142041 .446 .6723 OQSO for rnd.bin using bits 22 to 26 141398 -1.733 .0415 OQSO for rnd.bin using bits 21 to 25 141486 -1.435 .0756 OQSO for rnd.bin using bits 20 to 24 141447 -1.567 .0585 OQSO for rnd.bin using bits 19 to 23 141898 -.038 .4847 OQSO for rnd.bin using bits 18 to 22 141714 -.662 .2539 OQSO for rnd.bin using bits 17 to 21 141517 -1.330 .0918 OQSO for rnd.bin using bits 16 to 20 142449 1.829 .9663 OQSO for rnd.bin using bits 15 to 19 141762 -.499 .3087 OQSO for rnd.bin using bits 14 to 18 141851 -.198 .4216 OQSO for rnd.bin using bits 13 to 17 141652 -.872 .1915 OQSO for rnd.bin using bits 12 to 16 141912 .009 .5036 OQSO for rnd.bin using bits 11 to 15 141774 -.459 .3232 OQSO for rnd.bin using bits 10 to 14 141268 -2.174 .0149 OQSO for rnd.bin using bits 9 to 13 141685 -.760 .2235 OQSO for rnd.bin using bits 8 to 12 141879 -.103 .4591 OQSO for rnd.bin using bits 7 to 11 142004 .321 .6259 OQSO for rnd.bin using bits 6 to 10 142068 .538 .7047 OQSO for rnd.bin using bits 5 to 9 142094 .626 .7343 OQSO for rnd.bin using bits 4 to 8 142486 1.955 .9747 OQSO for rnd.bin using bits 3 to 7 141657 -.855 .1962 OQSO for rnd.bin using bits 2 to 6 141319 -2.001 .0227 OQSO for rnd.bin using bits 1 to 5 141736 -.588 .2784 DNA for rnd.bin using bits 31 to 32 142538 1.854 .9682 DNA for rnd.bin using bits 30 to 31 142218 .911 .8187 DNA for rnd.bin using bits 29 to 30 142613 2.076 .9810 DNA for rnd.bin using bits 28 to 29 142263 1.043 .8516 DNA for rnd.bin using bits 27 to 28 142195 .843 .8003 DNA for rnd.bin using bits 26 to 27 141775 -.396 .3460 DNA for rnd.bin using bits 25 to 26 142043 .394 .6533 DNA for rnd.bin using bits 24 to 25 141641 -.792 .2143 DNA for rnd.bin using bits 23 to 24 141527 -1.128 .1297 DNA for rnd.bin using bits 22 to 23 142179 .795 .7868 DNA for rnd.bin using bits 21 to 22 142036 .374 .6457 DNA for rnd.bin using bits 20 to 21 142463 1.633 .9488 DNA for rnd.bin using bits 19 to 20 141369 -1.594 .0555 DNA for rnd.bin using bits 18 to 19 141844 -.193 .4236 DNA for rnd.bin using bits 17 to 18 142197 .849 .8019 DNA for rnd.bin using bits 16 to 17 141389 -1.535 .0624 DNA for rnd.bin using bits 15 to 16 141544 -1.078 .1406 DNA for rnd.bin using bits 14 to 15 141360 -1.620 .0526 DNA for rnd.bin using bits 13 to 14 142070 .474 .6822 DNA for rnd.bin using bits 12 to 13 142064 .456 .6759 DNA for rnd.bin using bits 11 to 12 142584 1.990 .9767 DNA for rnd.bin using bits 10 to 11 142029 .353 .6380 DNA for rnd.bin using bits 9 to 10 141605 -.898 .1847 DNA for rnd.bin using bits 8 to 9 141823 -.255 .3995 DNA for rnd.bin using bits 7 to 8 141416 -1.455 .0728 DNA for rnd.bin using bits 6 to 7 141874 -.104 .4585 DNA for rnd.bin using bits 5 to 6 141700 -.617 .2685 DNA for rnd.bin using bits 4 to 5 141804 -.311 .3780 DNA for rnd.bin using bits 3 to 4 141940 .090 .5360 DNA for rnd.bin using bits 2 to 3 141953 .129 .5513 DNA for rnd.bin using bits 1 to 2 141735 -.514 .3035 -------------------------------------------------------------------------------- Test results for rnd.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.bin 2517.94 .254 .600133 byte stream for rnd.bin 2473.14 -.380 .352014 -------------------------------------------------------------------------------- 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 2594.96 1.343 .910355 bits 2 to 9 2476.10 -.338 .367672 bits 3 to 10 2556.26 .796 .786892 bits 4 to 11 2469.28 -.434 .331983 bits 5 to 12 2557.02 .806 .790003 bits 6 to 13 2598.83 1.398 .918900 bits 7 to 14 2566.03 .934 .824799 bits 8 to 15 2498.86 -.016 .493570 bits 9 to 16 2481.43 -.263 .396410 bits 10 to 17 2529.83 .422 .663448 bits 11 to 18 2451.66 -.684 .247097 bits 12 to 19 2526.24 .371 .644696 bits 13 to 20 2506.35 .090 .535797 bits 14 to 21 2627.96 1.810 .964823 bits 15 to 22 2601.48 1.435 .924372 bits 16 to 23 2593.94 1.328 .907993 bits 17 to 24 2472.44 -.390 .348342 bits 18 to 25 2482.07 -.254 .399938 bits 19 to 26 2376.47 -1.747 .040323 bits 20 to 27 2496.80 -.045 .481950 bits 21 to 28 2550.60 .716 .762863 bits 22 to 29 2470.94 -.411 .340538 bits 23 to 30 2602.51 1.450 .926434 bits 24 to 31 2406.24 -1.326 .092434 bits 25 to 32 2528.82 .408 .658188 -------------------------------------------------------------------------------- CDPARK: result of ten tests on file rnd.bin Of 12,000 tries, the average no. of successes should be 3523 with sigma=21.9 Successes: 3482 z-score: -1.872 p-value: .030593 Successes: 3488 z-score: -1.598 p-value: .055002 Successes: 3545 z-score: 1.005 p-value: .842447 Successes: 3518 z-score: -.228 p-value: .409702 Successes: 3506 z-score: -.776 p-value: .218799 Successes: 3535 z-score: .548 p-value: .708135 Successes: 3542 z-score: .868 p-value: .807188 Successes: 3508 z-score: -.685 p-value: .246694 Successes: 3533 z-score: .457 p-value: .676028 Successes: 3477 z-score: -2.100 p-value: .017844 square size avg. no. parked sample sigma 100. 3513.400 23.926 KSTEST for the above 10: p= .762003 -------------------------------------------------------------------------------- This is the MINIMUM DISTANCE test for random integers in the file rnd.bin Sample no. d^2 avg equiv uni 5 .3036 .5248 .262945 10 .3360 .6851 .286572 15 1.1599 1.1940 .688294 20 1.0645 1.0072 .656936 25 1.0231 1.1155 .642347 30 .6705 1.0129 .490247 35 .4715 1.0929 .377398 40 1.3242 1.0338 .735756 45 .7723 1.0118 .539819 50 .8890 .9913 .590785 55 .7292 .9775 .519452 60 1.8175 .9686 .839052 65 .0219 .9342 .021765 70 1.0091 .9742 .637312 75 1.6032 .9702 .800373 80 .2622 .9408 .231675 85 .2680 1.0020 .236115 90 .4299 1.0018 .350839 95 2.0348 .9931 .870627 100 .1012 1.0023 .096712 MINIMUM DISTANCE TEST for rnd.bin Result of KS test on 20 transformed mindist^2's: p-value= .424047 -------------------------------------------------------------------------------- The 3DSPHERES test for file rnd.bin sample no: 1 r^3= 9.023 p-value= .25976 sample no: 2 r^3= 3.117 p-value= .09868 sample no: 3 r^3= 15.484 p-value= .40318 sample no: 4 r^3= 49.540 p-value= .80821 sample no: 5 r^3= 76.056 p-value= .92075 sample no: 6 r^3= 1.165 p-value= .03810 sample no: 7 r^3= 8.186 p-value= .23880 sample no: 8 r^3= 26.115 p-value= .58126 sample no: 9 r^3= 46.261 p-value= .78605 sample no: 10 r^3= 10.427 p-value= .29360 sample no: 11 r^3= 22.881 p-value= .53360 sample no: 12 r^3= 2.355 p-value= .07550 sample no: 13 r^3= 20.492 p-value= .49493 sample no: 14 r^3= 13.343 p-value= .35902 sample no: 15 r^3= 57.565 p-value= .85322 sample no: 16 r^3= 64.459 p-value= .88336 sample no: 17 r^3= 8.300 p-value= .24168 sample no: 18 r^3= 13.843 p-value= .36962 sample no: 19 r^3= 83.285 p-value= .93772 sample no: 20 r^3= 5.665 p-value= .17207 3DSPHERES test for file rnd.bin p-value= .153440 -------------------------------------------------------------------------------- RESULTS OF SQUEEZE TEST FOR rnd.bin Table of standardized frequency counts ( (obs-exp)/sqrt(exp) )^2 for j taking values <=6,7,8,...,47,>=48: .6 1.3 1.5 .0 -.5 .4 -.8 1.1 -1.4 -1.6 -1.0 -.3 -.4 -1.7 -.2 2.4 -1.4 .7 1.2 -.3 -.2 -1.6 .7 1.4 1.9 -.6 -.7 1.2 .9 -.2 -1.6 2.8 -.2 .9 2.0 -1.2 -.5 -.1 -.4 1.0 .1 -1.0 .8 Chi-square with 42 degrees of freedom: 56.696 z-score= 1.603 p-value= .935584 ______________________________________________________________ -------------------------------------------------------------------------------- Test no. 1 p-value .518233 Test no. 2 p-value .662380 Test no. 3 p-value .668964 Test no. 4 p-value .433712 Test no. 5 p-value .223061 Test no. 6 p-value .509217 Test no. 7 p-value .869531 Test no. 8 p-value .060233 Test no. 9 p-value .800185 Test no. 10 p-value .899759 Results of the OSUM test for rnd.bin KSTEST on the above 10 p-values: .240137 -------------------------------------------------------------------------------- The RUNS test for file rnd.bin Up and down runs in a sample of 10000 _________________________________________________ Run test for rnd.bin : runs up; ks test for 10 p's: .740732 runs down; ks test for 10 p's: .303067 Run test for rnd.bin : runs up; ks test for 10 p's: .260217 runs down; ks test for 10 p's: .308698 -------------------------------------------------------------------------------- Results of craps test for rnd.bin No. of wins: Observed Expected 98998 98585.86 Chisq= 18.36 for 20 degrees of freedom, p= .43655 Throws Observed Expected Chisq Sum SUMMARY FOR rnd.bin p-value for no. of wins: .967360 p-value for throws/game: .436551 Test completed. File rnd.bin :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::