 BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA=  2.0000
           xrb_rand.dat    using bits  1 to 24 p-value=  .885959
           xrb_rand.dat    using bits  2 to 25 p-value=  .496986
           xrb_rand.dat    using bits  3 to 26 p-value=  .008274
           xrb_rand.dat    using bits  4 to 27 p-value=  .962167
           xrb_rand.dat    using bits  5 to 28 p-value=  .622404
           xrb_rand.dat    using bits  6 to 29 p-value=  .962473
           xrb_rand.dat    using bits  7 to 30 p-value=  .606834
           xrb_rand.dat    using bits  8 to 31 p-value=  .965830
           xrb_rand.dat    using bits  9 to 32 p-value=  .593267
   The 9 p-values were
        .885959   .496986   .008274   .962167   .622404
        .962473   .606834   .965830   .593267
  A KSTEST for the 9 p-values yields  .965554
--------------------------------------------------------------------------------
           OPERM5 test for file xrb_rand.dat   
 chisquare for 99 degrees of freedom= 96.009; p-value= .433531
           OPERM5 test for file xrb_rand.dat   
 chisquare for 99 degrees of freedom=145.665; p-value= .998396
--------------------------------------------------------------------------------
    Binary rank test for xrb_rand.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       206     211.4   .138848     .139
        29      5069    5134.0   .823203     .962
        30     23301   23103.0  1.696116    2.658
        31     11424   11551.5  1.407821    4.066
  chisquare= 4.066 for 3 d. of f.; p-value= .767451
    Binary rank test for xrb_rand.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       244     211.4  5.021265    5.021
        30      5194    5134.0   .700967    5.722
        31     23099   23103.0   .000709    5.723
        32     11463   11551.5   .678402    6.401
  chisquare= 6.401 for 3 d. of f.; p-value= .912066
--------------------------------------------------------------------------------
 b-rank test for bits  1 to  8 p=1-exp(-SUM/2)= .41122
 b-rank test for bits  2 to  9 p=1-exp(-SUM/2)= .91061
 b-rank test for bits  3 to 10 p=1-exp(-SUM/2)= .04394
 b-rank test for bits  4 to 11 p=1-exp(-SUM/2)= .32740
 b-rank test for bits  5 to 12 p=1-exp(-SUM/2)= .71056
 b-rank test for bits  6 to 13 p=1-exp(-SUM/2)= .64955
 b-rank test for bits  7 to 14 p=1-exp(-SUM/2)= .58774
 b-rank test for bits  8 to 15 p=1-exp(-SUM/2)= .45722
 b-rank test for bits  9 to 16 p=1-exp(-SUM/2)= .94817
 b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .25410
 b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .10524
 b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .37912
 b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .79734
 b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .73734
 b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .36778
 b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .38921
 b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .11604
 b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .47708
 b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .72945
 b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .22720
 b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .36796
 b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .01904
 b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .37698
 b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .73259
 b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .35187
   TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
 These should be 25 uniform [0,1] random variables:
     .411223     .910613     .043941     .327402     .710559
     .649551     .587739     .457215     .948168     .254101
     .105239     .379116     .797345     .737338     .367784
     .389207     .116040     .477078     .729455     .227202
     .367959     .019036     .376982     .732594     .351874
   brank test summary for xrb_rand.dat   
       The KS test for those 25 supposed UNI's yields
                    KS p-value= .439428
--------------------------------------------------------------------------------
  No. missing words should average  141909. with sigma=428.
 tst no  1:  142016 missing words,     .25 sigmas from mean, p-value= .59841
 tst no  2:  142900 missing words,    2.31 sigmas from mean, p-value= .98968
 tst no  3:  141991 missing words,     .19 sigmas from mean, p-value= .57567
 tst no  4:  141735 missing words,    -.41 sigmas from mean, p-value= .34189
 tst no  5:  141813 missing words,    -.23 sigmas from mean, p-value= .41096
 tst no  6:  142009 missing words,     .23 sigmas from mean, p-value= .59207
 tst no  7:  142236 missing words,     .76 sigmas from mean, p-value= .77734
 tst no  8:  141347 missing words,   -1.31 sigmas from mean, p-value= .09445
 tst no  9:  141174 missing words,   -1.72 sigmas from mean, p-value= .04289
 tst no 10:  142380 missing words,    1.10 sigmas from mean, p-value= .86427
 tst no 11:  142225 missing words,     .74 sigmas from mean, p-value= .76961
 tst no 12:  142212 missing words,     .71 sigmas from mean, p-value= .76027
 tst no 13:  140867 missing words,   -2.44 sigmas from mean, p-value= .00744
 tst no 14:  142627 missing words,    1.68 sigmas from mean, p-value= .95321
 tst no 15:  141547 missing words,    -.85 sigmas from mean, p-value= .19862
 tst no 16:  142292 missing words,     .89 sigmas from mean, p-value= .81436
 tst no 17:  141495 missing words,    -.97 sigmas from mean, p-value= .16651
 tst no 18:  142363 missing words,    1.06 sigmas from mean, p-value= .85542
 tst no 19:  142223 missing words,     .73 sigmas from mean, p-value= .76818
 tst no 20:  141795 missing words,    -.27 sigmas from mean, p-value= .39469
--------------------------------------------------------------------------------
    OPSO for xrb_rand.dat    using bits 23 to 32        142065   .537  .7043
    OPSO for xrb_rand.dat    using bits 22 to 31        142207  1.026  .8477
    OPSO for xrb_rand.dat    using bits 21 to 30        142095   .640  .7390
    OPSO for xrb_rand.dat    using bits 20 to 29        142002   .320  .6253
    OPSO for xrb_rand.dat    using bits 19 to 28        141957   .164  .5653
    OPSO for xrb_rand.dat    using bits 18 to 27        142404  1.706  .9560
    OPSO for xrb_rand.dat    using bits 17 to 26        142036   .437  .6689
    OPSO for xrb_rand.dat    using bits 16 to 25        142245  1.157  .8765
    OPSO for xrb_rand.dat    using bits 15 to 24        142049   .482  .6850
    OPSO for xrb_rand.dat    using bits 14 to 23        141585 -1.118  .1317
    OPSO for xrb_rand.dat    using bits 13 to 22        141650  -.894  .1856
    OPSO for xrb_rand.dat    using bits 12 to 21        142299  1.344  .9105
    OPSO for xrb_rand.dat    using bits 11 to 20        141805  -.360  .3595
    OPSO for xrb_rand.dat    using bits 10 to 19        141889  -.070  .4721
    OPSO for xrb_rand.dat    using bits  9 to 18        141757  -.525  .2997
    OPSO for xrb_rand.dat    using bits  8 to 17        142027   .406  .6575
    OPSO for xrb_rand.dat    using bits  7 to 16        141907  -.008  .4968
    OPSO for xrb_rand.dat    using bits  6 to 15        141541 -1.270  .1020
    OPSO for xrb_rand.dat    using bits  5 to 14        141507 -1.387  .0827
    OPSO for xrb_rand.dat    using bits  4 to 13        142145   .813  .7918
    OPSO for xrb_rand.dat    using bits  3 to 12        142552  2.216  .9867
    OPSO for xrb_rand.dat    using bits  2 to 11        142141   .799  .7878
    OPSO for xrb_rand.dat    using bits  1 to 10        141572 -1.163  .1224
    OQSO for xrb_rand.dat    using bits 28 to 32        142191   .955  .8302
    OQSO for xrb_rand.dat    using bits 27 to 31        142203   .995  .8403
    OQSO for xrb_rand.dat    using bits 26 to 30        141784  -.425  .3355
    OQSO for xrb_rand.dat    using bits 25 to 29        141882  -.093  .4631
    OQSO for xrb_rand.dat    using bits 24 to 28        141831  -.266  .3953
    OQSO for xrb_rand.dat    using bits 23 to 27        142089   .609  .7288
    OQSO for xrb_rand.dat    using bits 22 to 26        142326  1.412  .9211
    OQSO for xrb_rand.dat    using bits 21 to 25        141095 -2.760  .0029
    OQSO for xrb_rand.dat    using bits 20 to 24        141619  -.984  .1625
    OQSO for xrb_rand.dat    using bits 19 to 23        141789  -.408  .3417
    OQSO for xrb_rand.dat    using bits 18 to 22        141513 -1.343  .0896
    OQSO for xrb_rand.dat    using bits 17 to 21        142046   .463  .6784
    OQSO for xrb_rand.dat    using bits 16 to 20        142145   .799  .7878
    OQSO for xrb_rand.dat    using bits 15 to 19        141957   .162  .5642
    OQSO for xrb_rand.dat    using bits 14 to 18        141876  -.113  .4550
    OQSO for xrb_rand.dat    using bits 13 to 17        141871  -.130  .4483
    OQSO for xrb_rand.dat    using bits 12 to 16        142031   .412  .6600
    OQSO for xrb_rand.dat    using bits 11 to 15        142201   .989  .8386
    OQSO for xrb_rand.dat    using bits 10 to 14        142208  1.012  .8443
    OQSO for xrb_rand.dat    using bits  9 to 13        141960   .172  .5682
    OQSO for xrb_rand.dat    using bits  8 to 12        142286  1.277  .8992
    OQSO for xrb_rand.dat    using bits  7 to 11        141735  -.591  .2773
    OQSO for xrb_rand.dat    using bits  6 to 10        141953   .148  .5588
    OQSO for xrb_rand.dat    using bits  5 to  9        142562  2.212  .9865
    OQSO for xrb_rand.dat    using bits  4 to  8        141976   .226  .5894
    OQSO for xrb_rand.dat    using bits  3 to  7        141948   .131  .5521
    OQSO for xrb_rand.dat    using bits  2 to  6        142125   .731  .7676
    OQSO for xrb_rand.dat    using bits  1 to  5        142008   .334  .6310
     DNA for xrb_rand.dat    using bits 31 to 32        141613  -.874  .1910
     DNA for xrb_rand.dat    using bits 30 to 31        141368 -1.597  .0552
     DNA for xrb_rand.dat    using bits 29 to 30        141557 -1.039  .1493
     DNA for xrb_rand.dat    using bits 28 to 29        141842  -.199  .4213
     DNA for xrb_rand.dat    using bits 27 to 28        142105   .577  .7181
     DNA for xrb_rand.dat    using bits 26 to 27        141513 -1.169  .1212
     DNA for xrb_rand.dat    using bits 25 to 26        141654  -.753  .2257
     DNA for xrb_rand.dat    using bits 24 to 25        142000   .267  .6054
     DNA for xrb_rand.dat    using bits 23 to 24        141414 -1.461  .0720
     DNA for xrb_rand.dat    using bits 22 to 23        141996   .256  .6009
     DNA for xrb_rand.dat    using bits 21 to 22        141547 -1.069  .1426
     DNA for xrb_rand.dat    using bits 20 to 21        142202   .863  .8060
     DNA for xrb_rand.dat    using bits 19 to 20        141758  -.446  .3277
     DNA for xrb_rand.dat    using bits 18 to 19        141718  -.564  .2862
     DNA for xrb_rand.dat    using bits 17 to 18        142316  1.200  .8849
     DNA for xrb_rand.dat    using bits 16 to 17        141914   .014  .5055
     DNA for xrb_rand.dat    using bits 15 to 16        141718  -.564  .2862
     DNA for xrb_rand.dat    using bits 14 to 15        142013   .306  .6201
     DNA for xrb_rand.dat    using bits 13 to 14        142293  1.132  .8711
     DNA for xrb_rand.dat    using bits 12 to 13        142227   .937  .8256
     DNA for xrb_rand.dat    using bits 11 to 12        141658  -.741  .2292
     DNA for xrb_rand.dat    using bits 10 to 11        142157   .731  .7675
     DNA for xrb_rand.dat    using bits  9 to 10        141953   .129  .5513
     DNA for xrb_rand.dat    using bits  8 to  9        142008   .291  .6145
     DNA for xrb_rand.dat    using bits  7 to  8        142378  1.383  .9166
     DNA for xrb_rand.dat    using bits  6 to  7        141675  -.691  .2447
     DNA for xrb_rand.dat    using bits  5 to  6        141260 -1.915  .0277
     DNA for xrb_rand.dat    using bits  4 to  5        141764  -.429  .3341
     DNA for xrb_rand.dat    using bits  3 to  4        141827  -.243  .4041
     DNA for xrb_rand.dat    using bits  2 to  3        142273  1.073  .8583
     DNA for xrb_rand.dat    using bits  1 to  2        142185   .813  .7919
--------------------------------------------------------------------------------
   Test results for xrb_rand.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_rand.dat     2528.45       .402      .656299
 byte stream for xrb_rand.dat     2423.85     -1.077      .140773
--------------------------------------------------------------------------------
 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  2491.93      -.114      .454593
           bits  2 to  9  2398.04     -1.442      .074653
           bits  3 to 10  2545.33       .641      .739277
           bits  4 to 11  2521.93       .310      .621785
           bits  5 to 12  2507.28       .103      .540981
           bits  6 to 13  2421.24     -1.114      .132689
           bits  7 to 14  2497.39      -.037      .485280
           bits  8 to 15  2396.66     -1.462      .071938
           bits  9 to 16  2595.27      1.347      .911069
           bits 10 to 17  2305.73     -2.747      .003004
           bits 11 to 18  2480.96      -.269      .393835
           bits 12 to 19  2456.34      -.618      .268449
           bits 13 to 20  2483.68      -.231      .408761
           bits 14 to 21  2448.70      -.726      .234054
           bits 15 to 22  2436.95      -.892      .186273
           bits 16 to 23  2465.04      -.494      .310493
           bits 17 to 24  2533.53       .474      .682303
           bits 18 to 25  2559.96       .848      .801767
           bits 19 to 26  2627.09      1.797      .963860
           bits 20 to 27  2569.72       .986      .837924
           bits 21 to 28  2393.05     -1.513      .065200
           bits 22 to 29  2418.35     -1.155      .124120
           bits 23 to 30  2583.31      1.178      .880646
           bits 24 to 31  2437.42      -.885      .188079
           bits 25 to 32  2631.98      1.866      .969008
--------------------------------------------------------------------------------
           CDPARK: result of ten tests on file xrb_rand.dat   
            Of 12,000 tries, the average no. of successes
                 should be 3523 with sigma=21.9
            Successes: 3530    z-score:   .320 p-value: .625377
            Successes: 3516    z-score:  -.320 p-value: .374623
            Successes: 3513    z-score:  -.457 p-value: .323972
            Successes: 3513    z-score:  -.457 p-value: .323972
            Successes: 3547    z-score:  1.096 p-value: .863437
            Successes: 3537    z-score:   .639 p-value: .738676
            Successes: 3543    z-score:   .913 p-value: .819442
            Successes: 3544    z-score:   .959 p-value: .831196
            Successes: 3540    z-score:   .776 p-value: .781201
            Successes: 3549    z-score:  1.187 p-value: .882429
 
           square size   avg. no.  parked   sample sigma
             100.            3533.200       13.541
            KSTEST for the above 10: p=  .904977
--------------------------------------------------------------------------------
               This is the MINIMUM DISTANCE test
              for random integers in the file xrb_rand.dat   
     Sample no.    d^2     avg     equiv uni            
           5     .0978    .4966     .093655
          10     .0310    .4534     .030711
          15     .8279    .5059     .564830
          20    1.8384    .6053     .842396
          25     .7626    .6305     .535327
          30     .8900    .6915     .591175
          35     .2614    .6575     .231033
          40    1.5632    .7580     .792172
          45    2.0697    .7847     .875080
          50     .1340    .9049     .126036
          55     .2765    .8842     .242642
          60     .4474    .8709     .362116
          65    1.5482    .8438     .789011
          70     .2595    .8304     .229531
          75     .7432    .8080     .526195
          80    1.7443    .8739     .826751
          85    1.0850    .8983     .663942
          90    1.3323    .9475     .737900
          95    3.5685    .9661     .972302
         100    1.1894    .9811     .697414
     MINIMUM DISTANCE TEST for xrb_rand.dat   
          Result of KS test on 20 transformed mindist^2's:
                                  p-value= .286322
--------------------------------------------------------------------------------
               The 3DSPHERES test for file xrb_rand.dat   
 sample no:  1     r^3= 103.748     p-value= .96852
 sample no:  2     r^3=  63.047     p-value= .87773
 sample no:  3     r^3=  36.425     p-value= .70304
 sample no:  4     r^3=   9.318     p-value= .26699
 sample no:  5     r^3=   8.566     p-value= .24840
 sample no:  6     r^3=   1.498     p-value= .04871
 sample no:  7     r^3=  46.303     p-value= .78635
 sample no:  8     r^3=  12.208     p-value= .33432
 sample no:  9     r^3=   3.427     p-value= .10795
 sample no: 10     r^3=  18.901     p-value= .46743
 sample no: 11     r^3=   2.809     p-value= .08938
 sample no: 12     r^3=  45.371     p-value= .77961
 sample no: 13     r^3=   2.134     p-value= .06868
 sample no: 14     r^3=  24.212     p-value= .55384
 sample no: 15     r^3=   9.564     p-value= .27298
 sample no: 16     r^3=   6.912     p-value= .20578
 sample no: 17     r^3=   5.376     p-value= .16407
 sample no: 18     r^3=   4.116     p-value= .12821
 sample no: 19     r^3=  92.380     p-value= .95401
 sample no: 20     r^3=  14.148     p-value= .37600
       3DSPHERES test for file xrb_rand.dat         p-value= .741505
--------------------------------------------------------------------------------
            RESULTS OF SQUEEZE TEST FOR xrb_rand.dat   
         Table of standardized frequency counts
     ( (obs-exp)/sqrt(exp) )^2
        for j taking values <=6,7,8,...,47,>=48:
     -.8    -1.6     -.8      .9      .3     -.7
     1.9      .2      .0    -2.1    -1.6      .9
      .2     1.4     -.9     -.3      .8      .6
     -.6     -.8     1.7      .5      .9    -2.2
     -.9      .9     -.6    -1.0     -.3     1.4
     1.5    -1.0     -.9     -.9     1.3     1.0
     -.7     1.1      .5     1.5    -1.3    -1.0
    -1.1
           Chi-square with 42 degrees of freedom: 50.594
              z-score=   .938  p-value= .829665
______________________________________________________________
--------------------------------------------------------------------------------
                Test no.  1      p-value  .488119
                Test no.  2      p-value  .808754
                Test no.  3      p-value  .693690
                Test no.  4      p-value  .996647
                Test no.  5      p-value  .013993
                Test no.  6      p-value  .661341
                Test no.  7      p-value  .766261
                Test no.  8      p-value  .084529
                Test no.  9      p-value  .597676
                Test no. 10      p-value  .094382
   Results of the OSUM test for xrb_rand.dat   
        KSTEST on the above 10 p-values:  .521713
--------------------------------------------------------------------------------
           The RUNS test for file xrb_rand.dat   
     Up and down runs in a sample of 10000
_________________________________________________ 
                 Run test for xrb_rand.dat   :
       runs up; ks test for 10 p's: .177020
     runs down; ks test for 10 p's: .458105
                 Run test for xrb_rand.dat   :
       runs up; ks test for 10 p's: .122590
     runs down; ks test for 10 p's: .233959
--------------------------------------------------------------------------------
                Results of craps test for xrb_rand.dat   
  No. of wins:  Observed Expected
                                98680    98585.86
 Chisq=   7.69 for 20 degrees of freedom, p=  .00625
               Throws Observed Expected  Chisq     Sum
            SUMMARY  FOR xrb_rand.dat   
                p-value for no. of wins: .663141
                p-value for throws/game: .006253
  Test completed.  File xrb_rand.dat   
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
