 BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA=  2.0000
           xrb_xor.dat     using bits  1 to 24 p-value=  .343618
           xrb_xor.dat     using bits  2 to 25 p-value=  .476062
           xrb_xor.dat     using bits  3 to 26 p-value=  .038661
           xrb_xor.dat     using bits  4 to 27 p-value=  .060470
           xrb_xor.dat     using bits  5 to 28 p-value=  .810481
           xrb_xor.dat     using bits  6 to 29 p-value=  .621855
           xrb_xor.dat     using bits  7 to 30 p-value=  .162238
           xrb_xor.dat     using bits  8 to 31 p-value=  .262262
           xrb_xor.dat     using bits  9 to 32 p-value=  .907785
   The 9 p-values were
        .343618   .476062   .038661   .060470   .810481
        .621855   .162238   .262262   .907785
  A KSTEST for the 9 p-values yields  .381518
--------------------------------------------------------------------------------
           OPERM5 test for file xrb_xor.dat    
 chisquare for 99 degrees of freedom= 88.574; p-value= .235387
           OPERM5 test for file xrb_xor.dat    
 chisquare for 99 degrees of freedom= 47.180; p-value= .000002
--------------------------------------------------------------------------------
    Binary rank test for xrb_xor.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       230     211.4  1.633211    1.633
        29      5174    5134.0   .311487    1.945
        30     22921   23103.0  1.434489    3.379
        31     11675   11551.5  1.319845    4.699
  chisquare= 4.699 for 3 d. of f.; p-value= .819881
    Binary rank test for xrb_xor.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       240     211.4  3.864051    3.864
        30      5073    5134.0   .725018    4.589
        31     23073   23103.0   .039078    4.628
        32     11614   11551.5   .337895    4.966
  chisquare= 4.966 for 3 d. of f.; p-value= .838624
--------------------------------------------------------------------------------
 b-rank test for bits  1 to  8 p=1-exp(-SUM/2)= .82597
 b-rank test for bits  2 to  9 p=1-exp(-SUM/2)= .23124
 b-rank test for bits  3 to 10 p=1-exp(-SUM/2)= .63545
 b-rank test for bits  4 to 11 p=1-exp(-SUM/2)= .17561
 b-rank test for bits  5 to 12 p=1-exp(-SUM/2)= .59136
 b-rank test for bits  6 to 13 p=1-exp(-SUM/2)= .25357
 b-rank test for bits  7 to 14 p=1-exp(-SUM/2)= .71653
 b-rank test for bits  8 to 15 p=1-exp(-SUM/2)= .27899
 b-rank test for bits  9 to 16 p=1-exp(-SUM/2)= .08934
 b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .42856
 b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .19897
 b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .27101
 b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .70673
 b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .42442
 b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .98059
 b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .91091
 b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .60289
 b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .20080
 b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .04662
 b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .19971
 b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .20084
 b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .84321
 b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .50999
 b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .98290
 b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .90416
   TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
 These should be 25 uniform [0,1] random variables:
     .825969     .231244     .635452     .175608     .591358
     .253575     .716533     .278994     .089339     .428555
     .198967     .271006     .706728     .424420     .980589
     .910908     .602888     .200802     .046619     .199714
     .200844     .843215     .509990     .982899     .904159
   brank test summary for xrb_xor.dat    
       The KS test for those 25 supposed UNI's yields
                    KS p-value= .257843
--------------------------------------------------------------------------------
  No. missing words should average  141909. with sigma=428.
 tst no  1:  141469 missing words,   -1.03 sigmas from mean, p-value= .15179
 tst no  2:  141852 missing words,    -.13 sigmas from mean, p-value= .44672
 tst no  3:  141643 missing words,    -.62 sigmas from mean, p-value= .26688
 tst no  4:  141269 missing words,   -1.50 sigmas from mean, p-value= .06731
 tst no  5:  141524 missing words,    -.90 sigmas from mean, p-value= .18398
 tst no  6:  140874 missing words,   -2.42 sigmas from mean, p-value= .00778
 tst no  7:  141830 missing words,    -.19 sigmas from mean, p-value= .42648
 tst no  8:  142617 missing words,    1.65 sigmas from mean, p-value= .95088
 tst no  9:  141825 missing words,    -.20 sigmas from mean, p-value= .42190
 tst no 10:  141797 missing words,    -.26 sigmas from mean, p-value= .39649
 tst no 11:  142524 missing words,    1.44 sigmas from mean, p-value= .92452
 tst no 12:  141962 missing words,     .12 sigmas from mean, p-value= .54897
 tst no 13:  142161 missing words,     .59 sigmas from mean, p-value= .72174
 tst no 14:  141497 missing words,    -.96 sigmas from mean, p-value= .16768
 tst no 15:  141768 missing words,    -.33 sigmas from mean, p-value= .37062
 tst no 16:  141585 missing words,    -.76 sigmas from mean, p-value= .22429
 tst no 17:  141782 missing words,    -.30 sigmas from mean, p-value= .38304
 tst no 18:  142408 missing words,    1.17 sigmas from mean, p-value= .87802
 tst no 19:  141603 missing words,    -.72 sigmas from mean, p-value= .23708
 tst no 20:  141894 missing words,    -.04 sigmas from mean, p-value= .48572
--------------------------------------------------------------------------------
    OPSO for xrb_xor.dat     using bits 23 to 32        142706  2.747  .9970
    OPSO for xrb_xor.dat     using bits 22 to 31        141736  -.598  .2750
    OPSO for xrb_xor.dat     using bits 21 to 30        141891  -.063  .4748
    OPSO for xrb_xor.dat     using bits 20 to 29        141585 -1.118  .1317
    OPSO for xrb_xor.dat     using bits 19 to 28        142462  1.906  .9717
    OPSO for xrb_xor.dat     using bits 18 to 27        141791  -.408  .3416
    OPSO for xrb_xor.dat     using bits 17 to 26        142064   .533  .7031
    OPSO for xrb_xor.dat     using bits 16 to 25        141836  -.253  .4002
    OPSO for xrb_xor.dat     using bits 15 to 24        142037   .440  .6701
    OPSO for xrb_xor.dat     using bits 14 to 23        141519 -1.346  .0892
    OPSO for xrb_xor.dat     using bits 13 to 22        142217  1.061  .8556
    OPSO for xrb_xor.dat     using bits 12 to 21        142243  1.151  .8751
    OPSO for xrb_xor.dat     using bits 11 to 20        142188   .961  .8317
    OPSO for xrb_xor.dat     using bits 10 to 19        141925   .054  .5215
    OPSO for xrb_xor.dat     using bits  9 to 18        141903  -.022  .4913
    OPSO for xrb_xor.dat     using bits  8 to 17        141803  -.367  .3569
    OPSO for xrb_xor.dat     using bits  7 to 16        141392 -1.784  .0372
    OPSO for xrb_xor.dat     using bits  6 to 15        141756  -.529  .2985
    OPSO for xrb_xor.dat     using bits  5 to 14        141708  -.694  .2438
    OPSO for xrb_xor.dat     using bits  4 to 13        142059   .516  .6971
    OPSO for xrb_xor.dat     using bits  3 to 12        142343  1.495  .9326
    OPSO for xrb_xor.dat     using bits  2 to 11        141705  -.705  .2405
    OPSO for xrb_xor.dat     using bits  1 to 10        142265  1.226  .8900
    OQSO for xrb_xor.dat     using bits 28 to 32        142342  1.467  .9288
    OQSO for xrb_xor.dat     using bits 27 to 31        141992   .280  .6104
    OQSO for xrb_xor.dat     using bits 26 to 30        141913   .012  .5050
    OQSO for xrb_xor.dat     using bits 25 to 29        141763  -.496  .3099
    OQSO for xrb_xor.dat     using bits 24 to 28        141968   .199  .5788
    OQSO for xrb_xor.dat     using bits 23 to 27        141570 -1.150  .1250
    OQSO for xrb_xor.dat     using bits 22 to 26        141937   .094  .5374
    OQSO for xrb_xor.dat     using bits 21 to 25        141982   .246  .5973
    OQSO for xrb_xor.dat     using bits 20 to 24        141614 -1.001  .1584
    OQSO for xrb_xor.dat     using bits 19 to 23        141893  -.055  .4779
    OQSO for xrb_xor.dat     using bits 18 to 22        142227  1.077  .8592
    OQSO for xrb_xor.dat     using bits 17 to 21        142045   .460  .6772
    OQSO for xrb_xor.dat     using bits 16 to 20        142001   .311  .6220
    OQSO for xrb_xor.dat     using bits 15 to 19        141752  -.533  .2969
    OQSO for xrb_xor.dat     using bits 14 to 18        141931   .073  .5293
    OQSO for xrb_xor.dat     using bits 13 to 17        142360  1.528  .9367
    OQSO for xrb_xor.dat     using bits 12 to 16        141434 -1.611  .0536
    OQSO for xrb_xor.dat     using bits 11 to 15        141895  -.049  .4806
    OQSO for xrb_xor.dat     using bits 10 to 14        142435  1.782  .9626
    OQSO for xrb_xor.dat     using bits  9 to 13        141733  -.598  .2750
    OQSO for xrb_xor.dat     using bits  8 to 12        141969   .202  .5802
    OQSO for xrb_xor.dat     using bits  7 to 11        141939   .101  .5401
    OQSO for xrb_xor.dat     using bits  6 to 10        141752  -.533  .2969
    OQSO for xrb_xor.dat     using bits  5 to  9        141820  -.303  .3810
    OQSO for xrb_xor.dat     using bits  4 to  8        142193   .962  .8319
    OQSO for xrb_xor.dat     using bits  3 to  7        142508  2.029  .9788
    OQSO for xrb_xor.dat     using bits  2 to  6        141722  -.635  .2627
    OQSO for xrb_xor.dat     using bits  1 to  5        141985   .257  .6012
     DNA for xrb_xor.dat     using bits 31 to 32        142223   .925  .8226
     DNA for xrb_xor.dat     using bits 30 to 31        141890  -.057  .4773
     DNA for xrb_xor.dat     using bits 29 to 30        141788  -.358  .3602
     DNA for xrb_xor.dat     using bits 28 to 29        141362 -1.615  .0532
     DNA for xrb_xor.dat     using bits 27 to 28        142529  1.828  .9662
     DNA for xrb_xor.dat     using bits 26 to 27        141561 -1.028  .1521
     DNA for xrb_xor.dat     using bits 25 to 26        142062   .450  .6738
     DNA for xrb_xor.dat     using bits 24 to 25        141769  -.414  .3395
     DNA for xrb_xor.dat     using bits 23 to 24        142152   .716  .7630
     DNA for xrb_xor.dat     using bits 22 to 23        142013   .306  .6201
     DNA for xrb_xor.dat     using bits 21 to 22        141781  -.379  .3525
     DNA for xrb_xor.dat     using bits 20 to 21        142563  1.928  .9731
     DNA for xrb_xor.dat     using bits 19 to 20        141433 -1.405  .0800
     DNA for xrb_xor.dat     using bits 18 to 19        141845  -.190  .4247
     DNA for xrb_xor.dat     using bits 17 to 18        141901  -.025  .4902
     DNA for xrb_xor.dat     using bits 16 to 17        141540 -1.089  .1380
     DNA for xrb_xor.dat     using bits 15 to 16        141868  -.122  .4515
     DNA for xrb_xor.dat     using bits 14 to 15        141530 -1.119  .1316
     DNA for xrb_xor.dat     using bits 13 to 14        141995   .253  .5998
     DNA for xrb_xor.dat     using bits 12 to 13        142220   .916  .8203
     DNA for xrb_xor.dat     using bits 11 to 12        142119   .619  .7319
     DNA for xrb_xor.dat     using bits 10 to 11        141692  -.641  .2607
     DNA for xrb_xor.dat     using bits  9 to 10        141930   .061  .5243
     DNA for xrb_xor.dat     using bits  8 to  9        141958   .144  .5571
     DNA for xrb_xor.dat     using bits  7 to  8        141931   .064  .5255
     DNA for xrb_xor.dat     using bits  6 to  7        141775  -.396  .3460
     DNA for xrb_xor.dat     using bits  5 to  6        141686  -.659  .2550
     DNA for xrb_xor.dat     using bits  4 to  5        141141 -2.266  .0117
     DNA for xrb_xor.dat     using bits  3 to  4        141748  -.476  .3171
     DNA for xrb_xor.dat     using bits  2 to  3        141630  -.824  .2050
     DNA for xrb_xor.dat     using bits  1 to  2        142036   .374  .6457
--------------------------------------------------------------------------------
   Test results for xrb_xor.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_xor.dat      2523.86       .337      .632126
 byte stream for xrb_xor.dat      2519.00       .269      .605919
--------------------------------------------------------------------------------
 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  2469.14      -.436      .331278
           bits  2 to  9  2416.30     -1.184      .118270
           bits  3 to 10  2546.27       .654      .743543
           bits  4 to 11  2569.24       .979      .836266
           bits  5 to 12  2554.20       .766      .778295
           bits  6 to 13  2450.26      -.703      .240898
           bits  7 to 14  2547.69       .674      .749978
           bits  8 to 15  2441.79      -.823      .205181
           bits  9 to 16  2542.22       .597      .724776
           bits 10 to 17  2448.94      -.722      .235103
           bits 11 to 18  2483.53      -.233      .407916
           bits 12 to 19  2476.85      -.327      .371711
           bits 13 to 20  2459.68      -.570      .284260
           bits 14 to 21  2433.36      -.942      .172987
           bits 15 to 22  2514.24       .201      .579776
           bits 16 to 23  2443.30      -.802      .211338
           bits 17 to 24  2616.60      1.649      .950421
           bits 18 to 25  2407.70     -1.305      .095891
           bits 19 to 26  2586.40      1.222      .889133
           bits 20 to 27  2511.60       .164      .565139
           bits 21 to 28  2621.69      1.721      .957372
           bits 22 to 29  2680.77      2.557      .994714
           bits 23 to 30  2436.58      -.897      .184901
           bits 24 to 31  2484.83      -.215      .415074
           bits 25 to 32  2465.21      -.492      .311350
--------------------------------------------------------------------------------
           CDPARK: result of ten tests on file xrb_xor.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: 3508    z-score:  -.685 p-value: .246694
            Successes: 3488    z-score: -1.598 p-value: .055002
            Successes: 3508    z-score:  -.685 p-value: .246694
            Successes: 3524    z-score:   .046 p-value: .518210
            Successes: 3534    z-score:   .502 p-value: .692266
            Successes: 3521    z-score:  -.091 p-value: .463618
            Successes: 3551    z-score:  1.279 p-value: .899470
            Successes: 3534    z-score:   .502 p-value: .692266
            Successes: 3519    z-score:  -.183 p-value: .427537
 
           square size   avg. no.  parked   sample sigma
             100.            3519.800       16.588
            KSTEST for the above 10: p=  .187030
--------------------------------------------------------------------------------
               This is the MINIMUM DISTANCE test
              for random integers in the file xrb_xor.dat    
     Sample no.    d^2     avg     equiv uni            
           5     .7088    .7325     .509522
          10     .8836   1.3817     .588525
          15     .9771   1.1183     .625424
          20     .0598   1.1305     .058371
          25    1.4099   1.1885     .757562
          30    1.0435   1.2699     .649619
          35    1.0499   1.1899     .651884
          40     .0098   1.0751     .009757
          45     .5008   1.0476     .395467
          50     .5181    .9993     .405908
          55    1.3081    .9753     .731436
          60    1.4067    .9312     .756779
          65     .0870    .9347     .083705
          70     .2648    .9206     .233692
          75     .3289   1.0118     .281477
          80     .1418    .9874     .132839
          85    1.6049   1.0037     .800709
          90    1.6937    .9952     .817727
          95    2.2375   1.0362     .894464
         100    1.1195   1.0644     .675386
     MINIMUM DISTANCE TEST for xrb_xor.dat    
          Result of KS test on 20 transformed mindist^2's:
                                  p-value= .028762
--------------------------------------------------------------------------------
               The 3DSPHERES test for file xrb_xor.dat    
 sample no:  1     r^3=   2.073     p-value= .06678
 sample no:  2     r^3=  34.567     p-value= .68407
 sample no:  3     r^3=   5.021     p-value= .15412
 sample no:  4     r^3=  10.544     p-value= .29634
 sample no:  5     r^3=  53.154     p-value= .82997
 sample no:  6     r^3=   2.478     p-value= .07928
 sample no:  7     r^3=  15.732     p-value= .40809
 sample no:  8     r^3=  12.643     p-value= .34389
 sample no:  9     r^3=  50.706     p-value= .81552
 sample no: 10     r^3=  57.424     p-value= .85253
 sample no: 11     r^3=  48.260     p-value= .79985
 sample no: 12     r^3=  38.872     p-value= .72630
 sample no: 13     r^3=   1.199     p-value= .03916
 sample no: 14     r^3=  57.564     p-value= .85322
 sample no: 15     r^3=  62.786     p-value= .87667
 sample no: 16     r^3=  15.284     p-value= .39919
 sample no: 17     r^3=  26.220     p-value= .58272
 sample no: 18     r^3=  37.991     p-value= .71814
 sample no: 19     r^3=  37.015     p-value= .70883
 sample no: 20     r^3=  52.171     p-value= .82431
       3DSPHERES test for file xrb_xor.dat          p-value= .675122
--------------------------------------------------------------------------------
            RESULTS OF SQUEEZE TEST FOR xrb_xor.dat    
         Table of standardized frequency counts
     ( (obs-exp)/sqrt(exp) )^2
        for j taking values <=6,7,8,...,47,>=48:
     -.8     -.7      .3     -.4      .9     -.3
      .2     -.9     -.4     -.6      .6      .3
     -.7      .2      .3     -.7     2.1      .5
      .4    -1.6    -1.0      .4     -.8      .0
      .5     -.8     1.6     -.3      .8      .5
    -1.5      .7      .7     -.2     -.8      .1
     -.2     -.4     1.7     -.1     -.6    -1.0
    -1.1
           Chi-square with 42 degrees of freedom: 28.110
              z-score= -1.516  p-value= .049520
______________________________________________________________
--------------------------------------------------------------------------------
                Test no.  1      p-value  .626817
                Test no.  2      p-value  .050337
                Test no.  3      p-value  .767406
                Test no.  4      p-value  .116475
                Test no.  5      p-value  .714158
                Test no.  6      p-value  .668256
                Test no.  7      p-value  .540213
                Test no.  8      p-value  .257690
                Test no.  9      p-value  .987758
                Test no. 10      p-value  .668501
   Results of the OSUM test for xrb_xor.dat    
        KSTEST on the above 10 p-values:  .292292
--------------------------------------------------------------------------------
           The RUNS test for file xrb_xor.dat    
     Up and down runs in a sample of 10000
_________________________________________________ 
                 Run test for xrb_xor.dat    :
       runs up; ks test for 10 p's: .592290
     runs down; ks test for 10 p's: .195849
                 Run test for xrb_xor.dat    :
       runs up; ks test for 10 p's: .247791
     runs down; ks test for 10 p's: .466782
--------------------------------------------------------------------------------
                Results of craps test for xrb_xor.dat    
  No. of wins:  Observed Expected
                                98854    98585.86
 Chisq=   9.91 for 20 degrees of freedom, p=  .03030
               Throws Observed Expected  Chisq     Sum
            SUMMARY  FOR xrb_xor.dat    
                p-value for no. of wins: .884791
                p-value for throws/game: .030299
  Test completed.  File xrb_xor.dat    
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
