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Plain Text, pasted on Feb 4:
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       NOTE: Most of the tests in DIEHARD return a p-value, which               
       should be uniform on [0,1) if the input file contains truly              
       independent random bits.   Those p-values are obtained by                
       p=F(X), where F is the assumed distribution of the sample                
       random variable X---often normal. But that assumed F is just             
       an asymptotic approximation, for which the fit will be worst             
       in the tails. Thus you should not be surprised with                      
       occasional p-values near 0 or 1, such as .0012 or .9983.                 
       When a bit stream really FAILS BIG, you will get p's of 0 or             
       1 to six or more places.  By all means, do not, as a                     
       Statistician might, think that a p < .025 or p> .975 means               
       that the RNG has "failed the test at the .05 level".  Such               
       p's happen among the hundreds that DIEHARD produces, even                
       with good RNG's.  So keep in mind that " p happens".                     
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::            This is the BIRTHDAY SPACINGS TEST                 ::        
     :: Choose m birthdays in a year of n days.  List the spacings    ::        
     :: between the birthdays.  If j is the number of values that     ::        
     :: occur more than once in that list, then j is asymptotically   ::        
     :: Poisson distributed with mean m^3/(4n).  Experience shows n   ::        
     :: must be quite large, say n>=2^18, for comparing the results   ::        
     :: to the Poisson distribution with that mean.  This test uses   ::        
     :: n=2^24 and m=2^9,  so that the underlying distribution for j  ::        
     :: is taken to be Poisson with lambda=2^27/(2^26)=2.  A sample   ::        
     :: of 500 j's is taken, and a chi-square goodness of fit test    ::        
     :: provides a p value.  The first test uses bits 1-24 (counting  ::        
     :: from the left) from integers in the specified file.           ::        
     ::   Then the file is closed and reopened. Next, bits 2-25 are   ::        
     :: used to provide birthdays, then 3-26 and so on to bits 9-32.  ::        
     :: Each set of bits provides a p-value, and the nine p-values    ::        
     :: provide a sample for a KSTEST.                                ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
 BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA=  2.0000
           Results for bbs.32         
                   For a sample of size 500:     mean   
           bbs.32          using bits  1 to 24   1.926
  duplicate       number       number 
  spacings       observed     expected
        0          72.       67.668
        1         143.      135.335
        2         125.      135.335
        3          99.       90.224
        4          41.       45.112
        5          14.       18.045
  6 to INF          6.        8.282
 Chisquare with  6 d.o.f. =     4.26 p-value=  .359077
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  2 to 25   1.960
  duplicate       number       number 
  spacings       observed     expected
        0          71.       67.668
        1         133.      135.335
        2         152.      135.335
        3          73.       90.224
        4          39.       45.112
        5          26.       18.045
  6 to INF          6.        8.282
 Chisquare with  6 d.o.f. =    10.51 p-value=  .895186
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  3 to 26   2.090
  duplicate       number       number 
  spacings       observed     expected
        0          54.       67.668
        1         135.      135.335
        2         133.      135.335
        3         102.       90.224
        4          50.       45.112
        5          18.       18.045
  6 to INF          8.        8.282
 Chisquare with  6 d.o.f. =     4.88 p-value=  .440480
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  4 to 27   1.978
  duplicate       number       number 
  spacings       observed     expected
        0          67.       67.668
        1         144.      135.335
        2         123.      135.335
        3          99.       90.224
        4          42.       45.112
        5          19.       18.045
  6 to INF          6.        8.282
 Chisquare with  6 d.o.f. =     3.43 p-value=  .247177
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  5 to 28   1.932
  duplicate       number       number 
  spacings       observed     expected
        0          64.       67.668
        1         147.      135.335
        2         144.      135.335
        3          86.       90.224
        4          32.       45.112
        5          19.       18.045
  6 to INF          8.        8.282
 Chisquare with  6 d.o.f. =     5.83 p-value=  .557240
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  6 to 29   1.986
  duplicate       number       number 
  spacings       observed     expected
        0          62.       67.668
        1         145.      135.335
        2         137.      135.335
        3          92.       90.224
        4          37.       45.112
        5          16.       18.045
  6 to INF         11.        8.282
 Chisquare with  6 d.o.f. =     3.80 p-value=  .296657
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  7 to 30   1.914
  duplicate       number       number 
  spacings       observed     expected
        0          66.       67.668
        1         147.      135.335
        2         133.      135.335
        3          92.       90.224
        4          46.       45.112
        5          12.       18.045
  6 to INF          4.        8.282
 Chisquare with  6 d.o.f. =     5.38 p-value=  .503665
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  8 to 31   1.874
  duplicate       number       number 
  spacings       observed     expected
        0          66.       67.668
        1         151.      135.335
        2         137.      135.335
        3          93.       90.224
        4          37.       45.112
        5          12.       18.045
  6 to INF          4.        8.282
 Chisquare with  6 d.o.f. =     7.66 p-value=  .735709
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           bbs.32          using bits  9 to 32   2.060
  duplicate       number       number 
  spacings       observed     expected
        0          62.       67.668
        1         140.      135.335
        2         121.      135.335
        3         103.       90.224
        4          46.       45.112
        5          18.       18.045
  6 to INF         10.        8.282
 Chisquare with  6 d.o.f. =     4.34 p-value=  .368865
  :::::::::::::::::::::::::::::::::::::::::
   The 9 p-values were
        .359077   .895186   .440480   .247177   .557240
        .296657   .503665   .735709   .368865
  A KSTEST for the 9 p-values yields  .464784

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::            THE OVERLAPPING 5-PERMUTATION TEST                 ::        
     :: This is the OPERM5 test.  It looks at a sequence of one mill- ::        
     :: ion 32-bit random integers.  Each set of five consecutive     ::        
     :: integers can be in one of 120 states, for the 5! possible or- ::        
     :: derings of five numbers.  Thus the 5th, 6th, 7th,...numbers   ::        
     :: each provide a state. As many thousands of state transitions  ::        
     :: are observed,  cumulative counts are made of the number of    ::        
     :: occurences of each state.  Then the quadratic form in the     ::        
     :: weak inverse of the 120x120 covariance matrix yields a test   ::        
     :: equivalent to the likelihood ratio test that the 120 cell     ::        
     :: counts came from the specified (asymptotically) normal dis-   ::        
     :: tribution with the specified 120x120 covariance matrix (with  ::        
     :: rank 99).  This version uses 1,000,000 integers, twice.       ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
           OPERM5 test for file bbs.32         
     For a sample of 1,000,000 consecutive 5-tuples,
 chisquare for 99 degrees of freedom=108.056; p-value= .749294
           OPERM5 test for file bbs.32         
     For a sample of 1,000,000 consecutive 5-tuples,
 chisquare for 99 degrees of freedom=100.789; p-value= .568978
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: This is the BINARY RANK TEST for 31x31 matrices. The leftmost ::        
     :: 31 bits of 31 random integers from the test sequence are used ::        
     :: to form a 31x31 binary matrix over the field {0,1}. The rank  ::        
     :: is determined. That rank can be from 0 to 31, but ranks< 28   ::        
     :: are rare, and their counts are pooled with those for rank 28. ::        
     :: Ranks are found for 40,000 such random matrices and a chisqua-::        
     :: re test is performed on counts for ranks 31,30,29 and <=28.   ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
    Binary rank test for bbs.32         
         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       224     211.4   .748784     .749
        29      5147    5134.0   .032866     .782
        30     23153   23103.0   .108008     .890
        31     11476   11551.5   .493782    1.383
  chisquare= 1.383 for 3 d. of f.; p-value= .410337
--------------------------------------------------------------
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: This is the BINARY RANK TEST for 32x32 matrices. A random 32x ::        
     :: 32 binary matrix is formed, each row a 32-bit random integer. ::        
     :: The rank is determined. That rank can be from 0 to 32, ranks  ::        
     :: less than 29 are rare, and their counts are pooled with those ::        
     :: for rank 29.  Ranks are found for 40,000 such random matrices ::        
     :: and a chisquare test is performed on counts for ranks  32,31, ::        
     :: 30 and <=29.                                                  ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
    Binary rank test for bbs.32         
         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       206     211.4   .138848     .139
        30      5158    5134.0   .112097     .251
        31     23104   23103.0   .000039     .251
        32     11532   11551.5   .033000     .284
  chisquare=  .284 for 3 d. of f.; p-value= .334039
--------------------------------------------------------------

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: This is the BINARY RANK TEST for 6x8 matrices.  From each of  ::        
     :: six random 32-bit integers from the generator under test, a   ::        
     :: specified byte is chosen, and the resulting six bytes form a  ::        
     :: 6x8 binary matrix whose rank is determined.  That rank can be ::        
     :: from 0 to 6, but ranks 0,1,2,3 are rare; their counts are     ::        
     :: pooled with those for rank 4. Ranks are found for 100,000     ::        
     :: random matrices, and a chi-square test is performed on        ::        
     :: counts for ranks 6,5 and <=4.                                 ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
         Binary Rank Test for bbs.32         
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  1 to  8
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          911       944.3       1.174       1.174
          r =5        21551     21743.9       1.711       2.886
          r =6        77538     77311.8        .662       3.547
                        p=1-exp(-SUM/2)= .83030
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  2 to  9
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          955       944.3        .121        .121
          r =5        21633     21743.9        .566        .687
          r =6        77412     77311.8        .130        .817
                        p=1-exp(-SUM/2)= .33525
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  3 to 10
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          996       944.3       2.830       2.830
          r =5        21838     21743.9        .407       3.238
          r =6        77166     77311.8        .275       3.513
                        p=1-exp(-SUM/2)= .82732
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  4 to 11
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          897       944.3       2.369       2.369
          r =5        21849     21743.9        .508       2.877
          r =6        77254     77311.8        .043       2.921
                        p=1-exp(-SUM/2)= .76783
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  5 to 12
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          880       944.3       4.379       4.379
          r =5        21809     21743.9        .195       4.573
          r =6        77311     77311.8        .000       4.573
                        p=1-exp(-SUM/2)= .89840
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  6 to 13
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          918       944.3        .733        .733
          r =5        21729     21743.9        .010        .743
          r =6        77353     77311.8        .022        .765
                        p=1-exp(-SUM/2)= .31775
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  7 to 14
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          943       944.3        .002        .002
          r =5        21649     21743.9        .414        .416
          r =6        77408     77311.8        .120        .536
                        p=1-exp(-SUM/2)= .23497
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  8 to 15
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          968       944.3        .595        .595
          r =5        21688     21743.9        .144        .738
          r =6        77344     77311.8        .013        .752
                        p=1-exp(-SUM/2)= .31336
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits  9 to 16
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          972       944.3        .812        .812
          r =5        21527     21743.9       2.164       2.976
          r =6        77501     77311.8        .463       3.439
                        p=1-exp(-SUM/2)= .82085
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 10 to 17
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          942       944.3        .006        .006
          r =5        21936     21743.9       1.697       1.703
          r =6        77122     77311.8        .466       2.169
                        p=1-exp(-SUM/2)= .66188
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 11 to 18
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          887       944.3       3.477       3.477
          r =5        21820     21743.9        .266       3.743
          r =6        77293     77311.8        .005       3.748
                        p=1-exp(-SUM/2)= .84649
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 12 to 19
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          918       944.3        .733        .733
          r =5        21623     21743.9        .672       1.405
          r =6        77459     77311.8        .280       1.685
                        p=1-exp(-SUM/2)= .56938
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 13 to 20
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          910       944.3       1.246       1.246
          r =5        21573     21743.9       1.343       2.589
          r =6        77517     77311.8        .545       3.134
                        p=1-exp(-SUM/2)= .79131
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 14 to 21
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          945       944.3        .001        .001
          r =5        21730     21743.9        .009        .009
          r =6        77325     77311.8        .002        .012
                        p=1-exp(-SUM/2)= .00581
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 15 to 22
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          959       944.3        .229        .229
          r =5        21794     21743.9        .115        .344
          r =6        77247     77311.8        .054        .399
                        p=1-exp(-SUM/2)= .18068
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 16 to 23
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          963       944.3        .370        .370
          r =5        21918     21743.9       1.394       1.764
          r =6        77119     77311.8        .481       2.245
                        p=1-exp(-SUM/2)= .67455
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 17 to 24
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          968       944.3        .595        .595
          r =5        21842     21743.9        .443       1.037
          r =6        77190     77311.8        .192       1.229
                        p=1-exp(-SUM/2)= .45916
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 18 to 25
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          911       944.3       1.174       1.174
          r =5        21493     21743.9       2.895       4.069
          r =6        77596     77311.8       1.045       5.114
                        p=1-exp(-SUM/2)= .92247
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 19 to 26
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          880       944.3       4.379       4.379
          r =5        21592     21743.9       1.061       5.440
          r =6        77528     77311.8        .605       6.044
                        p=1-exp(-SUM/2)= .95130
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 20 to 27
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          941       944.3        .012        .012
          r =5        21655     21743.9        .363        .375
          r =6        77404     77311.8        .110        .485
                        p=1-exp(-SUM/2)= .21532
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 21 to 28
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          944       944.3        .000        .000
          r =5        21757     21743.9        .008        .008
          r =6        77299     77311.8        .002        .010
                        p=1-exp(-SUM/2)= .00504
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 22 to 29
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          926       944.3        .355        .355
          r =5        21703     21743.9        .077        .432
          r =6        77371     77311.8        .045        .477
                        p=1-exp(-SUM/2)= .21217
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 23 to 30
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          957       944.3        .171        .171
          r =5        21597     21743.9        .992       1.163
          r =6        77446     77311.8        .233       1.396
                        p=1-exp(-SUM/2)= .50246
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 24 to 31
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          918       944.3        .733        .733
          r =5        21763     21743.9        .017        .749
          r =6        77319     77311.8        .001        .750
                        p=1-exp(-SUM/2)= .31271
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG bbs.32         
     b-rank test for bits 25 to 32
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          978       944.3       1.203       1.203
          r =5        21575     21743.9       1.312       2.515
          r =6        77447     77311.8        .236       2.751
                        p=1-exp(-SUM/2)= .74728
   TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
 These should be 25 uniform [0,1] random variables:
     .830304     .335251     .827319     .767834     .898401
     .317751     .234967     .313355     .820853     .661882
     .846493     .569375     .791310     .005811     .180676
     .674548     .459155     .922470     .951303     .215319
     .005042     .212172     .502458     .312713     .747283
   brank test summary for bbs.32         
       The KS test for those 25 supposed UNI's yields
                    KS p-value= .489480

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::                   THE BITSTREAM TEST                          ::        
     :: The file under test is viewed as a stream of bits. Call them  ::        
     :: b1,b2,... .  Consider an alphabet with two "letters", 0 and 1 ::        
     :: and think of the stream of bits as a succession of 20-letter  ::        
     :: "words", overlapping.  Thus the first word is b1b2...b20, the ::        
     :: second is b2b3...b21, and so on.  The bitstream test counts   ::        
     :: the number of missing 20-letter (20-bit) words in a string of ::        
     :: 2^21 overlapping 20-letter words.  There are 2^20 possible 20 ::        
     :: letter words.  For a truly random string of 2^21+19 bits, the ::        
     :: number of missing words j should be (very close to) normally  ::        
     :: distributed with mean 141,909 and sigma 428.  Thus            ::        
     ::  (j-141909)/428 should be a standard normal variate (z score) ::        
     :: that leads to a uniform [0,1) p value.  The test is repeated  ::        
     :: twenty times.                                                 ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
 THE OVERLAPPING 20-tuples BITSTREAM  TEST, 20 BITS PER WORD, N words
   This test uses N=2^21 and samples the bitstream 20 times.
  No. missing words should average  141909. with sigma=428.
---------------------------------------------------------
 tst no  1:  141941 missing words,     .07 sigmas from mean, p-value= .52949
 tst no  2:  142006 missing words,     .23 sigmas from mean, p-value= .58935
 tst no  3:  142560 missing words,    1.52 sigmas from mean, p-value= .93578
 tst no  4:  141882 missing words,    -.06 sigmas from mean, p-value= .47454
 tst no  5:  141850 missing words,    -.14 sigmas from mean, p-value= .44488
 tst no  6:  141636 missing words,    -.64 sigmas from mean, p-value= .26154
 tst no  7:  141596 missing words,    -.73 sigmas from mean, p-value= .23206
 tst no  8:  141217 missing words,   -1.62 sigmas from mean, p-value= .05288
 tst no  9:  142129 missing words,     .51 sigmas from mean, p-value= .69611
 tst no 10:  141929 missing words,     .05 sigmas from mean, p-value= .51833
 tst no 11:  141610 missing words,    -.70 sigmas from mean, p-value= .24216
 tst no 12:  141338 missing words,   -1.33 sigmas from mean, p-value= .09096
 tst no 13:  142410 missing words,    1.17 sigmas from mean, p-value= .87896
 tst no 14:  141810 missing words,    -.23 sigmas from mean, p-value= .40824
 tst no 15:  140993 missing words,   -2.14 sigmas from mean, p-value= .01614
 tst no 16:  141832 missing words,    -.18 sigmas from mean, p-value= .42831
 tst no 17:  142000 missing words,     .21 sigmas from mean, p-value= .58389
 tst no 18:  141327 missing words,   -1.36 sigmas from mean, p-value= .08682
 tst no 19:  141897 missing words,    -.03 sigmas from mean, p-value= .48851
 tst no 20:  141759 missing words,    -.35 sigmas from mean, p-value= .36271

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::             The tests OPSO, OQSO and DNA                      ::        
     ::         OPSO means Overlapping-Pairs-Sparse-Occupancy         ::        
     :: The OPSO test considers 2-letter words from an alphabet of    ::        
     :: 1024 letters.  Each letter is determined by a specified ten   ::        
     :: bits from a 32-bit integer in the sequence to be tested. OPSO ::        
     :: generates  2^21 (overlapping) 2-letter words  (from 2^21+1    ::        
     :: "keystrokes")  and counts the number of missing words---that  ::        
     :: is 2-letter words which do not appear in the entire sequence. ::        
     :: That count should be very close to normally distributed with  ::        
     :: mean 141,909, sigma 290. Thus (missingwrds-141909)/290 should ::        
     :: be a standard normal variable. The OPSO test takes 32 bits at ::        
     :: a time from the test file and uses a designated set of ten    ::        
     :: consecutive bits. It then restarts the file for the next de-  ::        
     :: signated 10 bits, and so on.                                  ::        
     ::                                                               ::        
     ::     OQSO means Overlapping-Quadruples-Sparse-Occupancy        ::        
     ::   The test OQSO is similar, except that it considers 4-letter ::        
     :: words from an alphabet of 32 letters, each letter determined  ::        
     :: by a designated string of 5 consecutive bits from the test    ::        
     :: file, elements of which are assumed 32-bit random integers.   ::        
     :: The mean number of missing words in a sequence of 2^21 four-  ::        
     :: letter words,  (2^21+3 "keystrokes"), is again 141909, with   ::        
     :: sigma = 295.  The mean is based on theory; sigma comes from   ::        
     :: extensive simulation.                                         ::        
     ::                                                               ::        
     ::    The DNA test considers an alphabet of 4 letters::  C,G,A,T,::        
     :: determined by two designated bits in the sequence of random   ::        
     :: integers being tested.  It considers 10-letter words, so that ::        
     :: as in OPSO and OQSO, there are 2^20 possible words, and the   ::        
     :: mean number of missing words from a string of 2^21  (over-    ::        
     :: lapping)  10-letter  words (2^21+9 "keystrokes") is 141909.   ::        
     :: The standard deviation sigma=339 was determined as for OQSO   ::        
     :: by simulation.  (Sigma for OPSO, 290, is the true value (to   ::        
     :: three places), not determined by simulation.                  ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
 OPSO test for generator bbs.32         
  Output: No. missing words (mw), equiv normal variate (z), p-value (p)
                                                           mw     z     p
    OPSO for bbs.32          using bits 23 to 32        786515******* 1.0000
    OPSO for bbs.32          using bits 22 to 31        781523******* 1.0000
    OPSO for bbs.32          using bits 21 to 30        780165******* 1.0000
    OPSO for bbs.32          using bits 20 to 29        780450******* 1.0000
    OPSO for bbs.32          using bits 19 to 28        786514******* 1.0000
    OPSO for bbs.32          using bits 18 to 27        786521******* 1.0000
    OPSO for bbs.32          using bits 17 to 26        786524******* 1.0000
    OPSO for bbs.32          using bits 16 to 25        533946******* 1.0000
    OPSO for bbs.32          using bits 15 to 24        142636  2.506  .9939
    OPSO for bbs.32          using bits 14 to 23        142264  1.223  .8893
    OPSO for bbs.32          using bits 13 to 22        142262  1.216  .8880
    OPSO for bbs.32          using bits 12 to 21        142563  2.254  .9879
    OPSO for bbs.32          using bits 11 to 20        142385  1.640  .9495
    OPSO for bbs.32          using bits 10 to 19        142628  2.478  .9934
    OPSO for bbs.32          using bits  9 to 18        141963   .185  .5734
    OPSO for bbs.32          using bits  8 to 17        141258 -2.246  .0124
    OPSO for bbs.32          using bits  7 to 16        141669  -.829  .2036
    OPSO for bbs.32          using bits  6 to 15        142523  2.116  .9828
    OPSO for bbs.32          using bits  5 to 14        141604 -1.053  .1462
    OPSO for bbs.32          using bits  4 to 13        142241  1.144  .8736
    OPSO for bbs.32          using bits  3 to 12        142272  1.251  .8945
    OPSO for bbs.32          using bits  2 to 11        141756  -.529  .2985
    OPSO for bbs.32          using bits  1 to 10        142041   .454  .6751
 OQSO test for generator bbs.32         
  Output: No. missing words (mw), equiv normal variate (z), p-value (p)
                                                           mw     z     p
    OQSO for bbs.32          using bits 28 to 32        142133   .758  .7758
    OQSO for bbs.32          using bits 27 to 31        141422 -1.652  .0493
    OQSO for bbs.32          using bits 26 to 30        142208  1.012  .8443
    OQSO for bbs.32          using bits 25 to 29        141938   .097  .5387
    OQSO for bbs.32          using bits 24 to 28        142494  1.982  .9763
    OQSO for bbs.32          using bits 23 to 27        142183   .928  .8232
    OQSO for bbs.32          using bits 22 to 26        142333  1.436  .9245
    OQSO for bbs.32          using bits 21 to 25        141604 -1.035  .1503
    OQSO for bbs.32          using bits 20 to 24        142343  1.470  .9292
    OQSO for bbs.32          using bits 19 to 23        142550  2.172  .9851
    OQSO for bbs.32          using bits 18 to 22        143346  4.870 1.0000
    OQSO for bbs.32          using bits 17 to 21        148748 23.182 1.0000
    OQSO for bbs.32          using bits 16 to 20        144574  9.033 1.0000
    OQSO for bbs.32          using bits 15 to 19        142860  3.223  .9994
    OQSO for bbs.32          using bits 14 to 18        142641  2.480  .9934
    OQSO for bbs.32          using bits 13 to 17        142544  2.151  .9843
    OQSO for bbs.32          using bits 12 to 16        142387  1.619  .9473
    OQSO for bbs.32          using bits 11 to 15        142031   .412  .6600
    OQSO for bbs.32          using bits 10 to 14        142235  1.104  .8652
    OQSO for bbs.32          using bits  9 to 13        142663  2.555  .9947
    OQSO for bbs.32          using bits  8 to 12        141960   .172  .5682
    OQSO for bbs.32          using bits  7 to 11        141662  -.838  .2009
    OQSO for bbs.32          using bits  6 to 10        141742  -.567  .2853
    OQSO for bbs.32          using bits  5 to  9        142373  1.572  .9420
    OQSO for bbs.32          using bits  4 to  8        141564 -1.171  .1209
    OQSO for bbs.32          using bits  3 to  7        142394  1.643  .9498
    OQSO for bbs.32          using bits  2 to  6        142159   .846  .8013
    OQSO for bbs.32          using bits  1 to  5        141972   .212  .5841
  DNA test for generator bbs.32         
  Output: No. missing words (mw), equiv normal variate (z), p-value (p)
                                                           mw     z     p
     DNA for bbs.32          using bits 31 to 32        141938   .085  .5337
     DNA for bbs.32          using bits 30 to 31        141977   .200  .5791
     DNA for bbs.32          using bits 29 to 30        142116   .610  .7290
     DNA for bbs.32          using bits 28 to 29        142790  2.598  .9953
     DNA for bbs.32          using bits 27 to 28        144084  6.415 1.0000
     DNA for bbs.32          using bits 26 to 27        145779 11.415 1.0000
     DNA for bbs.32          using bits 25 to 26        158902 50.126 1.0000
     DNA for bbs.32          using bits 24 to 25        143162  3.695  .9999
     DNA for bbs.32          using bits 23 to 24        141512 -1.172  .1206
     DNA for bbs.32          using bits 22 to 23        141325 -1.724  .0424
     DNA for bbs.32          using bits 21 to 22        141716  -.570  .2842
     DNA for bbs.32          using bits 20 to 21        141804  -.311  .3780
     DNA for bbs.32          using bits 19 to 20        142240   .975  .8353
     DNA for bbs.32          using bits 18 to 19        142721  2.394  .9917
     DNA for bbs.32          using bits 17 to 18        145810 11.506 1.0000
     DNA for bbs.32          using bits 16 to 17        143094  3.495  .9998
     DNA for bbs.32          using bits 15 to 16        141864  -.134  .4468
     DNA for bbs.32          using bits 14 to 15        141241 -1.971  .0243
     DNA for bbs.32          using bits 13 to 14        141594  -.930  .1761
     DNA for bbs.32          using bits 12 to 13        142119   .619  .7319
     DNA for bbs.32          using bits 11 to 12        141704  -.606  .2724
     DNA for bbs.32          using bits 10 to 11        141651  -.762  .2230
     DNA for bbs.32          using bits  9 to 10        142047   .406  .6577
     DNA for bbs.32          using bits  8 to  9        142300  1.152  .8754
     DNA for bbs.32          using bits  7 to  8        141887  -.066  .4737
     DNA for bbs.32          using bits  6 to  7        141843  -.196  .4224
     DNA for bbs.32          using bits  5 to  6        142044   .397  .6544
     DNA for bbs.32          using bits  4 to  5        142007   .288  .6134
     DNA for bbs.32          using bits  3 to  4        141490 -1.237  .1081
     DNA for bbs.32          using bits  2 to  3        142088   .527  .7009
     DNA for bbs.32          using bits  1 to  2        141773  -.402  .3438

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::     This is the COUNT-THE-1's TEST on a stream of bytes.      ::        
     :: Consider the file under test as a stream of bytes (four per   ::        
     :: 32 bit integer).  Each byte can contain from 0 to 8 1's,      ::        
     :: with probabilities 1,8,28,56,70,56,28,8,1 over 256.  Now let  ::        
     :: the stream of bytes provide a string of overlapping  5-letter ::        
     :: words, each "letter" taking values A,B,C,D,E. The letters are ::        
     :: determined by the number of 1's in a byte::  0,1,or 2 yield A,::        
     :: 3 yields B, 4 yields C, 5 yields D and 6,7 or 8 yield E. Thus ::        
     :: we have a monkey at a typewriter hitting five keys with vari- ::        
     :: ous probabilities (37,56,70,56,37 over 256).  There are 5^5   ::        
     :: possible 5-letter words, and from a string of 256,000 (over-  ::        
     :: lapping) 5-letter words, counts are made on the frequencies   ::        
     :: for each word.   The quadratic form in the weak inverse of    ::        
     :: the covariance matrix of the cell counts provides a chisquare ::        
     :: test::  Q5-Q4, the difference of the naive Pearson sums of    ::        
     :: (OBS-EXP)^2/EXP on counts for 5- and 4-letter cell counts.    ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
   Test results for bbs.32         
 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 bbs.32          11721.07    130.406     1.000000
 byte stream for bbs.32          11562.52    128.163     1.000000

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::     This is the COUNT-THE-1's TEST for specific bytes.        ::        
     :: Consider the file under test as a stream of 32-bit integers.  ::        
     :: From each integer, a specific byte is chosen , say the left-  ::        
     :: most::  bits 1 to 8. Each byte can contain from 0 to 8 1's,   ::        
     :: with probabilitie 1,8,28,56,70,56,28,8,1 over 256.  Now let   ::        
     :: the specified bytes from successive integers provide a string ::        
     :: of (overlapping) 5-letter words, each "letter" taking values  ::        
     :: A,B,C,D,E. The letters are determined  by the number of 1's,  ::        
     :: in that byte::  0,1,or 2 ---> A, 3 ---> B, 4 ---> C, 5 ---> D,::        
     :: and  6,7 or 8 ---> E.  Thus we have a monkey at a typewriter  ::        
     :: hitting five keys with with various probabilities::  37,56,70,::        
     :: 56,37 over 256. There are 5^5 possible 5-letter words, and    ::        
     :: from a string of 256,000 (overlapping) 5-letter words, counts ::        
     :: are made on the frequencies for each word. The quadratic form ::        
     :: in the weak inverse of the covariance matrix of the cell      ::        
     :: counts provides a chisquare test::  Q5-Q4, the difference of  ::        
     :: the naive Pearson  sums of (OBS-EXP)^2/EXP on counts for 5-   ::        
     :: and 4-letter cell counts.                                     ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
 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  2480.08      -.282      .389061
           bits  2 to  9  2494.39      -.079      .468357
           bits  3 to 10  2493.67      -.090      .464323
           bits  4 to 11  2510.60       .150      .559576
           bits  5 to 12  2582.21      1.163      .877509
           bits  6 to 13  2628.93      1.823      .965874
           bits  7 to 14  2438.90      -.864      .193760
           bits  8 to 15  2505.20       .074      .529303
           bits  9 to 16  2513.73       .194      .576967
           bits 10 to 17  2472.09      -.395      .346517
           bits 11 to 18  2644.86      2.049      .979754
           bits 12 to 19  2350.12     -2.120      .017019
           bits 13 to 20  2513.53       .191      .575846
           bits 14 to 21  2416.99     -1.174      .120222
           bits 15 to 22  2571.57      1.012      .844268
           bits 16 to 23  2593.63      1.324      .907267
           bits 17 to 24  2592.24      1.304      .903961
           bits 18 to 25  2540.56       .574      .716871
           bits 19 to 26  2428.61     -1.010      .156333
           bits 20 to 27  2560.91       .861      .805497
           bits 21 to 28  2609.51      1.549      .939270
           bits 22 to 29  2613.39      1.604      .945592
           bits 23 to 30  2708.00      2.942      .998367
           bits 24 to 31  2611.07      1.571      .941875
           bits 25 to 32  2578.18      1.106      .865556

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::               THIS IS A PARKING LOT TEST                      ::        
     :: In a square of side 100, randomly "park" a car---a circle of  ::        
     :: radius 1.   Then try to park a 2nd, a 3rd, and so on, each    ::        
     :: time parking "by ear".  That is, if an attempt to park a car  ::        
     :: causes a crash with one already parked, try again at a new    ::        
     :: random location. (To avoid path problems, consider parking    ::        
     :: helicopters rather than cars.)   Each attempt leads to either ::        
     :: a crash or a success, the latter followed by an increment to  ::        
     :: the list of cars already parked. If we plot n:  the number of ::        
     :: attempts, versus k::  the number successfully parked, we get a::        
     :: curve that should be similar to those provided by a perfect   ::        
     :: random number generator.  Theory for the behavior of such a   ::        
     :: random curve seems beyond reach, and as graphics displays are ::        
     :: not available for this battery of tests, a simple characteriz ::        
     :: ation of the random experiment is used: k, the number of cars ::        
     :: successfully parked after n=12,000 attempts. Simulation shows ::        
     :: that k should average 3523 with sigma 21.9 and is very close  ::        
     :: to normally distributed.  Thus (k-3523)/21.9 should be a st-  ::        
     :: andard normal variable, which, converted to a uniform varia-  ::        
     :: ble, provides input to a KSTEST based on a sample of 10.      ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
           CDPARK: result of ten tests on file bbs.32         
            Of 12,000 tries, the average no. of successes
                 should be 3523 with sigma=21.9
            Successes: 3520    z-score:  -.137 p-value: .445521
            Successes: 3494    z-score: -1.324 p-value: .092718
            Successes: 3511    z-score:  -.548 p-value: .291865
            Successes: 3528    z-score:   .228 p-value: .590298
            Successes: 3509    z-score:  -.639 p-value: .261324
            Successes: 3508    z-score:  -.685 p-value: .246694
            Successes: 3574    z-score:  2.329 p-value: .990064
            Successes: 3499    z-score: -1.096 p-value: .136563
            Successes: 3516    z-score:  -.320 p-value: .374623
            Successes: 3544    z-score:   .959 p-value: .831196
 
           square size   avg. no.  parked   sample sigma
             100.            3520.300       22.430
            KSTEST for the above 10: p=  .479080

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::               THE MINIMUM DISTANCE TEST                       ::        
     :: It does this 100 times::   choose n=8000 random points in a   ::        
     :: square of side 10000.  Find d, the minimum distance between   ::        
     :: the (n^2-n)/2 pairs of points.  If the points are truly inde- ::        
     :: pendent uniform, then d^2, the square of the minimum distance ::        
     :: should be (very close to) exponentially distributed with mean ::        
     :: .995 .  Thus 1-exp(-d^2/.995) should be uniform on [0,1) and  ::        
     :: a KSTEST on the resulting 100 values serves as a test of uni- ::        
     :: formity for random points in the square. Test numbers=0 mod 5 ::        
     :: are printed but the KSTEST is based on the full set of 100    ::        
     :: random choices of 8000 points in the 10000x10000 square.      ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
               This is the MINIMUM DISTANCE test
              for random integers in the file bbs.32         
     Sample no.    d^2     avg     equiv uni            
           5     .2334    .9758     .209086
          10    1.0235   1.2516     .642522
          15    4.4559   1.3912     .988647
          20     .2653   1.1487     .234079
          25     .4216   1.0246     .345417
          30     .4678    .9292     .375078
          35    1.2789    .9846     .723448
          40     .1031    .9471     .098441
          45     .0478    .9194     .046890
          50     .7415    .8702     .525368
          55    1.0779    .8616     .661533
          60     .5693    .8257     .435712
          65    1.2151    .8584     .705121
          70    1.3542    .8357     .743603
          75     .5366    .8365     .416854
          80     .1842    .8451     .168992
          85     .1923    .8838     .175777
          90    2.9142    .9198     .946541
          95     .6723    .9009     .491204
         100     .0786    .8861     .075969
     MINIMUM DISTANCE TEST for bbs.32         
          Result of KS test on 20 transformed mindist^2's:
                                  p-value= .800097

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::              THE 3DSPHERES TEST                               ::        
     :: Choose  4000 random points in a cube of edge 1000.  At each   ::        
     :: point, center a sphere large enough to reach the next closest ::        
     :: point. Then the volume of the smallest such sphere is (very   ::        
     :: close to) exponentially distributed with mean 120pi/3.  Thus  ::        
     :: the radius cubed is exponential with mean 30. (The mean is    ::        
     :: obtained by extensive simulation).  The 3DSPHERES test gener- ::        
     :: ates 4000 such spheres 20 times.  Each min radius cubed leads ::        
     :: to a uniform variable by means of 1-exp(-r^3/30.), then a     ::        
     ::  KSTEST is done on the 20 p-values.                           ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
               The 3DSPHERES test for file bbs.32         
 sample no:  1     r^3=  15.442     p-value= .40235
 sample no:  2     r^3=  32.790     p-value= .66479
 sample no:  3     r^3=  35.031     p-value= .68892
 sample no:  4     r^3=  62.943     p-value= .87731
 sample no:  5     r^3=  22.871     p-value= .53344
 sample no:  6     r^3=  19.776     p-value= .48273
 sample no:  7     r^3=  28.503     p-value= .61329
 sample no:  8     r^3=  10.241     p-value= .28920
 sample no:  9     r^3=  17.346     p-value= .43910
 sample no: 10     r^3=  39.290     p-value= .73009
 sample no: 11     r^3=  21.135     p-value= .50564
 sample no: 12     r^3=   1.263     p-value= .04123
 sample no: 13     r^3=    .095     p-value= .00316
 sample no: 14     r^3=  33.559     p-value= .67328
 sample no: 15     r^3=  38.901     p-value= .72656
 sample no: 16     r^3=  76.679     p-value= .92238
 sample no: 17     r^3=  29.361     p-value= .62420
 sample no: 18     r^3=   5.619     p-value= .17082
 sample no: 19     r^3=  36.511     p-value= .70390
 sample no: 20     r^3=  12.862     p-value= .34866
  A KS test is applied to those 20 p-values.
---------------------------------------------------------
       3DSPHERES test for file bbs.32               p-value= .542105
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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::      This is the SQEEZE test                                  ::        
     ::  Random integers are floated to get uniforms on [0,1). Start- ::        
     ::  ing with k=2^31=2147483647, the test finds j, the number of  ::        
     ::  iterations necessary to reduce k to 1, using the reduction   ::        
     ::  k=ceiling(k*U), with U provided by floating integers from    ::        
     ::  the file being tested.  Such j's are found 100,000 times,    ::        
     ::  then counts for the number of times j was <=6,7,...,47,>=48  ::        
     ::  are used to provide a chi-square test for cell frequencies.  ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
            RESULTS OF SQUEEZE TEST FOR bbs.32         
         Table of standardized frequency counts
     ( (obs-exp)/sqrt(exp) )^2
        for j taking values <=6,7,8,...,47,>=48:
     -.1      .5    -1.3     -.3     -.5    -1.4
      .4    -1.0    -1.1     2.8     -.1      .1
      .8      .8      .8    -1.6     -.1     -.3
      .7     -.7      .5     1.4    -1.1     -.4
     -.3    -2.1     -.4      .2    -1.7     1.9
      .5      .6      .9      .8      .8      .4
    -1.6    -1.3    -1.2    -1.3     -.6      .0
     -.1
           Chi-square with 42 degrees of freedom: 45.192
              z-score=   .348  p-value= .660027
______________________________________________________________

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::             The  OVERLAPPING SUMS test                        ::        
     :: Integers are floated to get a sequence U(1),U(2),... of uni-  ::        
     :: form [0,1) variables.  Then overlapping sums,                 ::        
     ::   S(1)=U(1)+...+U(100), S2=U(2)+...+U(101),... are formed.    ::        
     :: The S's are virtually normal with a certain covariance mat-   ::        
     :: rix.  A linear transformation of the S's converts them to a   ::        
     :: sequence of independent standard normals, which are converted ::        
     :: to uniform variables for a KSTEST. The  p-values from ten     ::        
     :: KSTESTs are given still another KSTEST.                       ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
                Test no.  1      p-value  .072524
                Test no.  2      p-value  .471695
                Test no.  3      p-value  .070680
                Test no.  4      p-value  .418355
                Test no.  5      p-value  .512679
                Test no.  6      p-value  .030221
                Test no.  7      p-value  .357225
                Test no.  8      p-value  .948149
                Test no.  9      p-value  .934337
                Test no. 10      p-value  .081823
   Results of the OSUM test for bbs.32         
        KSTEST on the above 10 p-values:  .843613

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::     This is the RUNS test.  It counts runs up, and runs down, ::        
     :: in a sequence of uniform [0,1) variables, obtained by float-  ::        
     :: ing the 32-bit integers in the specified file. This example   ::        
     :: shows how runs are counted:  .123,.357,.789,.425,.224,.416,.95::        
     :: contains an up-run of length 3, a down-run of length 2 and an ::        
     :: up-run of (at least) 2, depending on the next values.  The    ::        
     :: covariance matrices for the runs-up and runs-down are well    ::        
     :: known, leading to chisquare tests for quadratic forms in the  ::        
     :: weak inverses of the covariance matrices.  Runs are counted   ::        
     :: for sequences of length 10,000.  This is done ten times. Then ::        
     :: repeated.                                                     ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
           The RUNS test for file bbs.32         
     Up and down runs in a sample of 10000
_________________________________________________ 
                 Run test for bbs.32         :
       runs up; ks test for 10 p's: .114778
     runs down; ks test for 10 p's: .573391
                 Run test for bbs.32         :
       runs up; ks test for 10 p's: .210312
     runs down; ks test for 10 p's: .944975

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     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: This is the CRAPS TEST. It plays 200,000 games of craps, finds::        
     :: the number of wins and the number of throws necessary to end  ::        
     :: each game.  The number of wins should be (very close to) a    ::        
     :: normal with mean 200000p and variance 200000p(1-p), with      ::        
     :: p=244/495.  Throws necessary to complete the game can vary    ::        
     :: from 1 to infinity, but counts for all>21 are lumped with 21. ::        
     :: A chi-square test is made on the no.-of-throws cell counts.   ::        
     :: Each 32-bit integer from the test file provides the value for ::        
     :: the throw of a die, by floating to [0,1), multiplying by 6    ::        
     :: and taking 1 plus the integer part of the result.             ::        
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
                Results of craps test for bbs.32         
  No. of wins:  Observed Expected
                                98687    98585.86
                  98687= No. of wins, z-score=  .452 pvalue= .67450
   Analysis of Throws-per-Game:
 Chisq=  17.55 for 20 degrees of freedom, p=  .38328
               Throws Observed Expected  Chisq     Sum
                  1    66879    66666.7    .676     .676
                  2    37450    37654.3   1.109    1.785
                  3    26928    26954.7    .027    1.811
                  4    19281    19313.5    .055    1.866
                  5    13886    13851.4    .086    1.952
                  6     9924     9943.5    .038    1.991
                  7     7137     7145.0    .009    2.000
                  8     5170     5139.1    .186    2.186
                  9     3690     3699.9    .026    2.212
                 10     2731     2666.3   1.570    3.782
                 11     1896     1923.3    .388    4.171
                 12     1379     1388.7    .068    4.239
                 13      951     1003.7   2.769    7.008
                 14      718      726.1    .091    7.099
                 15      553      525.8   1.403    8.502
                 16      416      381.2   3.186   11.689
                 17      244      276.5   3.829   15.517
                 18      204      200.8    .050   15.567
                 19      146      146.0    .000   15.567
                 20      106      106.2    .000   15.568
                 21      311      287.1   1.987   17.555
            SUMMARY  FOR bbs.32         
                p-value for no. of wins: .674495
                p-value for throws/game: .383281

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 Results of DIEHARD battery of tests sent to file bbs.out4       



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