 BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA=  2.0000
           xrb_bxor.dat    using bits  1 to 24 p-value=  .356943
           xrb_bxor.dat    using bits  2 to 25 p-value=  .028246
           xrb_bxor.dat    using bits  3 to 26 p-value=  .389668
           xrb_bxor.dat    using bits  4 to 27 p-value=  .098073
           xrb_bxor.dat    using bits  5 to 28 p-value=  .692706
           xrb_bxor.dat    using bits  6 to 29 p-value=  .230505
           xrb_bxor.dat    using bits  7 to 30 p-value=  .768981
           xrb_bxor.dat    using bits  8 to 31 p-value=  .413285
           xrb_bxor.dat    using bits  9 to 32 p-value=  .205326
   The 9 p-values were
        .356943   .028246   .389668   .098073   .692706
        .230505   .768981   .413285   .205326
  A KSTEST for the 9 p-values yields  .772249
--------------------------------------------------------------------------------
           OPERM5 test for file xrb_bxor.dat   
 chisquare for 99 degrees of freedom=120.881; p-value= .933203
           OPERM5 test for file xrb_bxor.dat   
 chisquare for 99 degrees of freedom= 87.111; p-value= .202198
--------------------------------------------------------------------------------
    Binary rank test for xrb_bxor.dat   
         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       210     211.4   .009511     .010
        29      5193    5134.0   .677792     .687
        30     23123   23103.0   .017233     .705
        31     11474   11551.5   .520281    1.225
  chisquare= 1.225 for 3 d. of f.; p-value= .387150
    Binary rank test for xrb_bxor.dat   
         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       210     211.4   .009511     .010
        30      5103    5134.0   .187307     .197
        31     23132   23103.0   .036285     .233
        32     11555   11551.5   .001046     .234
  chisquare=  .234 for 3 d. of f.; p-value= .342336
--------------------------------------------------------------------------------
 b-rank test for bits  1 to  8 p=1-exp(-SUM/2)= .80254
 b-rank test for bits  2 to  9 p=1-exp(-SUM/2)= .98891
 b-rank test for bits  3 to 10 p=1-exp(-SUM/2)= .57783
 b-rank test for bits  4 to 11 p=1-exp(-SUM/2)= .93662
 b-rank test for bits  5 to 12 p=1-exp(-SUM/2)= .30541
 b-rank test for bits  6 to 13 p=1-exp(-SUM/2)= .96806
 b-rank test for bits  7 to 14 p=1-exp(-SUM/2)= .40955
 b-rank test for bits  8 to 15 p=1-exp(-SUM/2)= .56065
 b-rank test for bits  9 to 16 p=1-exp(-SUM/2)= .59828
 b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .06670
 b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .77958
 b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .16469
 b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .39747
 b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .23960
 b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .72153
 b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .11723
 b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .16465
 b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .11330
 b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .31543
 b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .48866
 b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .91266
 b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .74440
 b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .52154
 b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .06142
 b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .01293
   TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
 These should be 25 uniform [0,1] random variables:
     .802543     .988912     .577827     .936619     .305413
     .968055     .409553     .560653     .598279     .066702
     .779579     .164689     .397466     .239597     .721532
     .117231     .164653     .113296     .315435     .488662
     .912662     .744404     .521543     .061424     .012933
   brank test summary for xrb_bxor.dat   
       The KS test for those 25 supposed UNI's yields
                    KS p-value= .092047
--------------------------------------------------------------------------------
  No. missing words should average  141909. with sigma=428.
 tst no  1:  142160 missing words,     .59 sigmas from mean, p-value= .72096
 tst no  2:  141486 missing words,    -.99 sigmas from mean, p-value= .16131
 tst no  3:  141131 missing words,   -1.82 sigmas from mean, p-value= .03449
 tst no  4:  142027 missing words,     .27 sigmas from mean, p-value= .60832
 tst no  5:  142337 missing words,    1.00 sigmas from mean, p-value= .84116
 tst no  6:  141988 missing words,     .18 sigmas from mean, p-value= .57292
 tst no  7:  142069 missing words,     .37 sigmas from mean, p-value= .64545
 tst no  8:  141792 missing words,    -.27 sigmas from mean, p-value= .39199
 tst no  9:  141824 missing words,    -.20 sigmas from mean, p-value= .42099
 tst no 10:  141856 missing words,    -.12 sigmas from mean, p-value= .45042
 tst no 11:  141819 missing words,    -.21 sigmas from mean, p-value= .41643
 tst no 12:  141966 missing words,     .13 sigmas from mean, p-value= .55267
 tst no 13:  141746 missing words,    -.38 sigmas from mean, p-value= .35138
 tst no 14:  142421 missing words,    1.20 sigmas from mean, p-value= .88405
 tst no 15:  142243 missing words,     .78 sigmas from mean, p-value= .78219
 tst no 16:  141927 missing words,     .04 sigmas from mean, p-value= .51647
 tst no 17:  141741 missing words,    -.39 sigmas from mean, p-value= .34705
 tst no 18:  142023 missing words,     .27 sigmas from mean, p-value= .60472
 tst no 19:  142184 missing words,     .64 sigmas from mean, p-value= .73948
 tst no 20:  141403 missing words,   -1.18 sigmas from mean, p-value= .11840
--------------------------------------------------------------------------------
    OPSO for xrb_bxor.dat    using bits 23 to 32        142288  1.306  .9042
    OPSO for xrb_bxor.dat    using bits 22 to 31        141415 -1.705  .0441
    OPSO for xrb_bxor.dat    using bits 21 to 30        141558 -1.211  .1129
    OPSO for xrb_bxor.dat    using bits 20 to 29        142074   .568  .7149
    OPSO for xrb_bxor.dat    using bits 19 to 28        142414  1.740  .9591
    OPSO for xrb_bxor.dat    using bits 18 to 27        142112   .699  .7577
    OPSO for xrb_bxor.dat    using bits 17 to 26        141868  -.143  .4433
    OPSO for xrb_bxor.dat    using bits 16 to 25        141406 -1.736  .0413
    OPSO for xrb_bxor.dat    using bits 15 to 24        141760  -.515  .3033
    OPSO for xrb_bxor.dat    using bits 14 to 23        141617 -1.008  .1567
    OPSO for xrb_bxor.dat    using bits 13 to 22        141940   .106  .5421
    OPSO for xrb_bxor.dat    using bits 12 to 21        141824  -.294  .3843
    OPSO for xrb_bxor.dat    using bits 11 to 20        141706  -.701  .2416
    OPSO for xrb_bxor.dat    using bits 10 to 19        141259 -2.243  .0125
    OPSO for xrb_bxor.dat    using bits  9 to 18        141803  -.367  .3569
    OPSO for xrb_bxor.dat    using bits  8 to 17        141697  -.732  .2320
    OPSO for xrb_bxor.dat    using bits  7 to 16        141902  -.025  .4899
    OPSO for xrb_bxor.dat    using bits  6 to 15        141300 -2.101  .0178
    OPSO for xrb_bxor.dat    using bits  5 to 14        141671  -.822  .2056
    OPSO for xrb_bxor.dat    using bits  4 to 13        142178   .926  .8229
    OPSO for xrb_bxor.dat    using bits  3 to 12        141925   .054  .5215
    OPSO for xrb_bxor.dat    using bits  2 to 11        142049   .482  .6850
    OPSO for xrb_bxor.dat    using bits  1 to 10        141307 -2.077  .0189
    OQSO for xrb_bxor.dat    using bits 28 to 32        142598  2.334  .9902
    OQSO for xrb_bxor.dat    using bits 27 to 31        141500 -1.388  .0826
    OQSO for xrb_bxor.dat    using bits 26 to 30        141795  -.388  .3492
    OQSO for xrb_bxor.dat    using bits 25 to 29        141573 -1.140  .1271
    OQSO for xrb_bxor.dat    using bits 24 to 28        142014   .355  .6386
    OQSO for xrb_bxor.dat    using bits 23 to 27        142078   .572  .7163
    OQSO for xrb_bxor.dat    using bits 22 to 26        142035   .426  .6649
    OQSO for xrb_bxor.dat    using bits 21 to 25        142236  1.107  .8659
    OQSO for xrb_bxor.dat    using bits 20 to 24        142231  1.090  .8622
    OQSO for xrb_bxor.dat    using bits 19 to 23        141943   .114  .5454
    OQSO for xrb_bxor.dat    using bits 18 to 22        141728  -.615  .2694
    OQSO for xrb_bxor.dat    using bits 17 to 21        141508 -1.360  .0868
    OQSO for xrb_bxor.dat    using bits 16 to 20        142199   .982  .8369
    OQSO for xrb_bxor.dat    using bits 15 to 19        141893  -.055  .4779
    OQSO for xrb_bxor.dat    using bits 14 to 18        141573 -1.140  .1271
    OQSO for xrb_bxor.dat    using bits 13 to 17        141402 -1.720  .0427
    OQSO for xrb_bxor.dat    using bits 12 to 16        142214  1.033  .8491
    OQSO for xrb_bxor.dat    using bits 11 to 15        142101   .650  .7421
    OQSO for xrb_bxor.dat    using bits 10 to 14        141817  -.313  .3771
    OQSO for xrb_bxor.dat    using bits  9 to 13        141642  -.906  .1824
    OQSO for xrb_bxor.dat    using bits  8 to 12        141607 -1.025  .1527
    OQSO for xrb_bxor.dat    using bits  7 to 11        141998   .301  .6181
    OQSO for xrb_bxor.dat    using bits  6 to 10        142047   .467  .6796
    OQSO for xrb_bxor.dat    using bits  5 to  9        142117   .704  .7593
    OQSO for xrb_bxor.dat    using bits  4 to  8        141984   .253  .5999
    OQSO for xrb_bxor.dat    using bits  3 to  7        141694  -.730  .2327
    OQSO for xrb_bxor.dat    using bits  2 to  6        141951   .141  .5562
    OQSO for xrb_bxor.dat    using bits  1 to  5        142125   .731  .7676
     DNA for xrb_bxor.dat    using bits 31 to 32        141907  -.007  .4973
     DNA for xrb_bxor.dat    using bits 30 to 31        142000   .267  .6054
     DNA for xrb_bxor.dat    using bits 29 to 30        141631  -.821  .2058
     DNA for xrb_bxor.dat    using bits 28 to 29        141819  -.266  .3949
     DNA for xrb_bxor.dat    using bits 27 to 28        141713  -.579  .2812
     DNA for xrb_bxor.dat    using bits 26 to 27        141515 -1.163  .1224
     DNA for xrb_bxor.dat    using bits 25 to 26        141640  -.794  .2135
     DNA for xrb_bxor.dat    using bits 24 to 25        141354 -1.638  .0507
     DNA for xrb_bxor.dat    using bits 23 to 24        141854  -.163  .4352
     DNA for xrb_bxor.dat    using bits 22 to 23        141898  -.033  .4867
     DNA for xrb_bxor.dat    using bits 21 to 22        141803  -.314  .3769
     DNA for xrb_bxor.dat    using bits 20 to 21        141761  -.438  .3309
     DNA for xrb_bxor.dat    using bits 19 to 20        142036   .374  .6457
     DNA for xrb_bxor.dat    using bits 18 to 19        141980   .208  .5826
     DNA for xrb_bxor.dat    using bits 17 to 18        141778  -.387  .3492
     DNA for xrb_bxor.dat    using bits 16 to 17        141824  -.252  .4006
     DNA for xrb_bxor.dat    using bits 15 to 16        141567 -1.010  .1563
     DNA for xrb_bxor.dat    using bits 14 to 15        142011   .300  .6179
     DNA for xrb_bxor.dat    using bits 13 to 14        141861  -.143  .4433
     DNA for xrb_bxor.dat    using bits 12 to 13        142112   .598  .7250
     DNA for xrb_bxor.dat    using bits 11 to 12        141548 -1.066  .1432
     DNA for xrb_bxor.dat    using bits 10 to 11        142090   .533  .7030
     DNA for xrb_bxor.dat    using bits  9 to 10        142345  1.285  .9006
     DNA for xrb_bxor.dat    using bits  8 to  9        141734  -.517  .3025
     DNA for xrb_bxor.dat    using bits  7 to  8        142373  1.368  .9143
     DNA for xrb_bxor.dat    using bits  6 to  7        141746  -.482  .3150
     DNA for xrb_bxor.dat    using bits  5 to  6        142239   .972  .8346
     DNA for xrb_bxor.dat    using bits  4 to  5        141481 -1.264  .1032
     DNA for xrb_bxor.dat    using bits  3 to  4        141911   .005  .5020
     DNA for xrb_bxor.dat    using bits  2 to  3        141713  -.579  .2812
     DNA for xrb_bxor.dat    using bits  1 to  2        141929   .058  .5231
--------------------------------------------------------------------------------
   Test results for xrb_bxor.dat   
 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 xrb_bxor.dat     2522.65       .320      .625658
 byte stream for xrb_bxor.dat     2492.78      -.102      .459316
--------------------------------------------------------------------------------
 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  2566.30       .938      .825781
           bits  2 to  9  2589.83      1.270      .898026
           bits  3 to 10  2586.04      1.217      .888165
           bits  4 to 11  2407.63     -1.306      .095718
           bits  5 to 12  2496.44      -.050      .479934
           bits  6 to 13  2566.96       .947      .828172
           bits  7 to 14  2529.27       .414      .660557
           bits  8 to 15  2530.25       .428      .665621
           bits  9 to 16  2569.81       .987      .838227
           bits 10 to 17  2539.86       .564      .713518
           bits 11 to 18  2543.78       .619      .732105
           bits 12 to 19  2427.28     -1.028      .151884
           bits 13 to 20  2546.57       .659      .744904
           bits 14 to 21  2584.51      1.195      .883987
           bits 15 to 22  2623.59      1.748      .959751
           bits 16 to 23  2400.81     -1.403      .080341
           bits 17 to 24  2493.57      -.091      .463799
           bits 18 to 25  2549.95       .706      .760012
           bits 19 to 26  2411.65     -1.250      .105741
           bits 20 to 27  2429.96      -.990      .160968
           bits 21 to 28  2557.92       .819      .793626
           bits 22 to 29  2415.70     -1.192      .116594
           bits 23 to 30  2562.60       .885      .812009
           bits 24 to 31  2568.74       .972      .834503
           bits 25 to 32  2504.28       .061      .524125
--------------------------------------------------------------------------------
           CDPARK: result of ten tests on file xrb_bxor.dat   
            Of 12,000 tries, the average no. of successes
                 should be 3523 with sigma=21.9
            Successes: 3511    z-score:  -.548 p-value: .291865
            Successes: 3507    z-score:  -.731 p-value: .232514
            Successes: 3523    z-score:   .000 p-value: .500000
            Successes: 3506    z-score:  -.776 p-value: .218799
            Successes: 3519    z-score:  -.183 p-value: .427537
            Successes: 3531    z-score:   .365 p-value: .642555
            Successes: 3528    z-score:   .228 p-value: .590298
            Successes: 3517    z-score:  -.274 p-value: .392053
            Successes: 3511    z-score:  -.548 p-value: .291865
            Successes: 3493    z-score: -1.370 p-value: .085365
 
           square size   avg. no.  parked   sample sigma
             100.            3514.600       10.791
            KSTEST for the above 10: p=  .861856
--------------------------------------------------------------------------------
               This is the MINIMUM DISTANCE test
              for random integers in the file xrb_bxor.dat   
     Sample no.    d^2     avg     equiv uni            
           5     .0308   1.0176     .030496
          10    1.6268    .8976     .805052
          15     .4528    .8148     .365615
          20    3.2307    .8483     .961107
          25     .0402    .8271     .039597
          30     .1929    .8980     .176258
          35     .4276    .8346     .349352
          40    1.9528    .8664     .859510
          45     .4995    .9132     .394675
          50    1.6477    .9110     .809086
          55    1.2007    .9673     .700814
          60     .0413    .9618     .040694
          65    1.1419    .9803     .682628
          70     .8169    .9567     .560013
          75    2.3371    .9819     .904520
          80    1.7004   1.0104     .818939
          85     .7121    .9791     .511134
          90     .3588    .9775     .302719
          95     .6504    .9664     .479876
         100     .1879    .9528     .172108
     MINIMUM DISTANCE TEST for xrb_bxor.dat   
          Result of KS test on 20 transformed mindist^2's:
                                  p-value= .061873
--------------------------------------------------------------------------------
               The 3DSPHERES test for file xrb_bxor.dat   
 sample no:  1     r^3=   6.181     p-value= .18619
 sample no:  2     r^3=   9.800     p-value= .27868
 sample no:  3     r^3=  12.894     p-value= .34936
 sample no:  4     r^3=  36.538     p-value= .70416
 sample no:  5     r^3=  19.387     p-value= .47598
 sample no:  6     r^3=   6.207     p-value= .18691
 sample no:  7     r^3=   3.432     p-value= .10811
 sample no:  8     r^3=   1.449     p-value= .04716
 sample no:  9     r^3=  26.971     p-value= .59303
 sample no: 10     r^3=  23.218     p-value= .53880
 sample no: 11     r^3=  29.321     p-value= .62370
 sample no: 12     r^3=   2.500     p-value= .07997
 sample no: 13     r^3=   4.966     p-value= .15256
 sample no: 14     r^3=  32.992     p-value= .66704
 sample no: 15     r^3=   3.250     p-value= .10267
 sample no: 16     r^3=  17.985     p-value= .45092
 sample no: 17     r^3=   9.849     p-value= .27986
 sample no: 18     r^3=  31.277     p-value= .64745
 sample no: 19     r^3=   3.036     p-value= .09624
 sample no: 20     r^3=  42.393     p-value= .75662
       3DSPHERES test for file xrb_bxor.dat         p-value= .950325
--------------------------------------------------------------------------------
            RESULTS OF SQUEEZE TEST FOR xrb_bxor.dat   
         Table of standardized frequency counts
     ( (obs-exp)/sqrt(exp) )^2
        for j taking values <=6,7,8,...,47,>=48:
     -.8    -1.2     -.1     -.8     1.6     -.2
     -.1     1.4      .1      .3     -.2     -.3
     1.5      .1    -1.1     -.1      .1      .2
      .8     -.9    -1.0     -.6     -.4      .9
      .6     -.6     -.3     -.4     1.0      .5
    -1.3      .8      .1     1.6      .2     -.5
     1.9     2.1    -1.2     -.7     1.6    -1.0
    -1.1
           Chi-square with 42 degrees of freedom: 36.981
              z-score=  -.548  p-value= .309135
______________________________________________________________
--------------------------------------------------------------------------------
                Test no.  1      p-value  .551703
                Test no.  2      p-value  .425001
                Test no.  3      p-value  .576077
                Test no.  4      p-value  .034658
                Test no.  5      p-value  .844422
                Test no.  6      p-value  .719263
                Test no.  7      p-value  .917093
                Test no.  8      p-value  .294986
                Test no.  9      p-value  .353782
                Test no. 10      p-value  .819417
   Results of the OSUM test for xrb_bxor.dat   
        KSTEST on the above 10 p-values:  .136183
--------------------------------------------------------------------------------
           The RUNS test for file xrb_bxor.dat   
     Up and down runs in a sample of 10000
_________________________________________________ 
                 Run test for xrb_bxor.dat   :
       runs up; ks test for 10 p's: .113944
     runs down; ks test for 10 p's: .247217
                 Run test for xrb_bxor.dat   :
       runs up; ks test for 10 p's: .926595
     runs down; ks test for 10 p's: .924833
--------------------------------------------------------------------------------
                Results of craps test for xrb_bxor.dat   
  No. of wins:  Observed Expected
                                98399    98585.86
 Chisq=  16.91 for 20 degrees of freedom, p=  .34093
               Throws Observed Expected  Chisq     Sum
            SUMMARY  FOR xrb_bxor.dat   
                p-value for no. of wins: .201649
                p-value for throws/game: .340933
  Test completed.  File xrb_bxor.dat   
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
