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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 tetris.32      
                   For a sample of size 500:     mean   
           tetris.32       using bits  1 to 24   1.940
  duplicate       number       number 
  spacings       observed     expected
        0          57.       67.668
        1         154.      135.335
        2         142.      135.335
        3          82.       90.224
        4          44.       45.112
        5          16.       18.045
  6 to INF          5.        8.282
 Chisquare with  6 d.o.f. =     6.89 p-value=  .669161
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  2 to 25   2.066
  duplicate       number       number 
  spacings       observed     expected
        0          54.       67.668
        1         124.      135.335
        2         158.      135.335
        3          99.       90.224
        4          40.       45.112
        5          17.       18.045
  6 to INF          8.        8.282
 Chisquare with  6 d.o.f. =     9.01 p-value=  .826913
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  3 to 26   2.048
  duplicate       number       number 
  spacings       observed     expected
        0          58.       67.668
        1         148.      135.335
        2         130.      135.335
        3          82.       90.224
        4          53.       45.112
        5          19.       18.045
  6 to INF         10.        8.282
 Chisquare with  6 d.o.f. =     5.31 p-value=  .495614
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  4 to 27   2.026
  duplicate       number       number 
  spacings       observed     expected
        0          63.       67.668
        1         134.      135.335
        2         141.      135.335
        3          93.       90.224
        4          37.       45.112
        5          23.       18.045
  6 to INF          9.        8.282
 Chisquare with  6 d.o.f. =     3.54 p-value=  .261276
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  5 to 28   2.016
  duplicate       number       number 
  spacings       observed     expected
        0          61.       67.668
        1         140.      135.335
        2         131.      135.335
        3         103.       90.224
        4          39.       45.112
        5          16.       18.045
  6 to INF         10.        8.282
 Chisquare with  6 d.o.f. =     4.18 p-value=  .347952
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  6 to 29   2.036
  duplicate       number       number 
  spacings       observed     expected
        0          60.       67.668
        1         140.      135.335
        2         131.      135.335
        3          94.       90.224
        4          50.       45.112
        5          18.       18.045
  6 to INF          7.        8.282
 Chisquare with  6 d.o.f. =     2.05 p-value=  .085406
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  7 to 30   2.044
  duplicate       number       number 
  spacings       observed     expected
        0          71.       67.668
        1         116.      135.335
        2         148.      135.335
        3          84.       90.224
        4          56.       45.112
        5          18.       18.045
  6 to INF          7.        8.282
 Chisquare with  6 d.o.f. =     7.37 p-value=  .711806
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  8 to 31   2.118
  duplicate       number       number 
  spacings       observed     expected
        0          67.       67.668
        1         124.      135.335
        2         130.      135.335
        3          90.       90.224
        4          54.       45.112
        5          26.       18.045
  6 to INF          9.        8.282
 Chisquare with  6 d.o.f. =     6.49 p-value=  .629163
  :::::::::::::::::::::::::::::::::::::::::
                   For a sample of size 500:     mean   
           tetris.32       using bits  9 to 32   2.098
  duplicate       number       number 
  spacings       observed     expected
        0          68.       67.668
        1         120.      135.335
        2         130.      135.335
        3         102.       90.224
        4          54.       45.112
        5          14.       18.045
  6 to INF         12.        8.282
 Chisquare with  6 d.o.f. =     7.81 p-value=  .747946
  :::::::::::::::::::::::::::::::::::::::::
   The 9 p-values were
        .669161   .826913   .495614   .261276   .347952
        .085406   .711806   .629163   .747946
  A KSTEST for the 9 p-values yields  .219359

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

     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     ::            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 tetris.32      
     For a sample of 1,000,000 consecutive 5-tuples,
 chisquare for 99 degrees of freedom= 93.151; p-value= .353185
           OPERM5 test for file tetris.32      
     For a sample of 1,000,000 consecutive 5-tuples,
 chisquare for 99 degrees of freedom= 87.818; p-value= .217913
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: 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 tetris.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       198     211.4   .851598     .852
        29      5053    5134.0  1.278272    2.130
        30     23260   23103.0  1.066279    3.196
        31     11489   11551.5   .338423    3.535
  chisquare= 3.535 for 3 d. of f.; p-value= .713745
--------------------------------------------------------------
     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: 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 tetris.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       213     211.4   .011838     .012
        30      5038    5134.0  1.795471    1.807
        31     23170   23103.0   .194032    2.001
        32     11579   11551.5   .065351    2.067
  chisquare= 2.067 for 3 d. of f.; p-value= .516594
--------------------------------------------------------------

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

     :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::        
     :: 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 tetris.32      
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  1 to  8
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          892       944.3       2.897       2.897
          r =5        21597     21743.9        .992       3.889
          r =6        77511     77311.8        .513       4.402
                        p=1-exp(-SUM/2)= .88933
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  2 to  9
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          904       944.3       1.720       1.720
          r =5        21648     21743.9        .423       2.143
          r =6        77448     77311.8        .240       2.383
                        p=1-exp(-SUM/2)= .69622
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  3 to 10
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          950       944.3        .034        .034
          r =5        21577     21743.9       1.281       1.315
          r =6        77473     77311.8        .336       1.652
                        p=1-exp(-SUM/2)= .56211
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  4 to 11
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          934       944.3        .112        .112
          r =5        21828     21743.9        .325        .438
          r =6        77238     77311.8        .070        .508
                        p=1-exp(-SUM/2)= .22435
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  5 to 12
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          955       944.3        .121        .121
          r =5        21778     21743.9        .053        .175
          r =6        77267     77311.8        .026        .201
                        p=1-exp(-SUM/2)= .09546
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  6 to 13
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          894       944.3       2.679       2.679
          r =5        21820     21743.9        .266       2.946
          r =6        77286     77311.8        .009       2.954
                        p=1-exp(-SUM/2)= .77172
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  7 to 14
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          954       944.3        .100        .100
          r =5        21675     21743.9        .218        .318
          r =6        77371     77311.8        .045        .363
                        p=1-exp(-SUM/2)= .16609
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  8 to 15
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          957       944.3        .171        .171
          r =5        21759     21743.9        .010        .181
          r =6        77284     77311.8        .010        .191
                        p=1-exp(-SUM/2)= .09120
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits  9 to 16
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          975       944.3        .998        .998
          r =5        21911     21743.9       1.284       2.282
          r =6        77114     77311.8        .506       2.788
                        p=1-exp(-SUM/2)= .75195
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 10 to 17
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          999       944.3       3.168       3.168
          r =5        21765     21743.9        .020       3.189
          r =6        77236     77311.8        .074       3.263
                        p=1-exp(-SUM/2)= .80439
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 11 to 18
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          953       944.3        .080        .080
          r =5        21791     21743.9        .102        .182
          r =6        77256     77311.8        .040        .222
                        p=1-exp(-SUM/2)= .10526
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 12 to 19
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          957       944.3        .171        .171
          r =5        21641     21743.9        .487        .658
          r =6        77402     77311.8        .105        .763
                        p=1-exp(-SUM/2)= .31715
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 13 to 20
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          954       944.3        .100        .100
          r =5        21656     21743.9        .355        .455
          r =6        77390     77311.8        .079        .534
                        p=1-exp(-SUM/2)= .23434
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 14 to 21
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          938       944.3        .042        .042
          r =5        21933     21743.9       1.645       1.687
          r =6        77129     77311.8        .432       2.119
                        p=1-exp(-SUM/2)= .65334
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 15 to 22
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          940       944.3        .020        .020
          r =5        21877     21743.9        .815        .834
          r =6        77183     77311.8        .215       1.049
                        p=1-exp(-SUM/2)= .40813
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 16 to 23
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          939       944.3        .030        .030
          r =5        21819     21743.9        .259        .289
          r =6        77242     77311.8        .063        .352
                        p=1-exp(-SUM/2)= .16145
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 17 to 24
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          936       944.3        .073        .073
          r =5        21759     21743.9        .010        .083
          r =6        77305     77311.8        .001        .084
                        p=1-exp(-SUM/2)= .04116
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 18 to 25
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          977       944.3       1.132       1.132
          r =5        21587     21743.9       1.132       2.264
          r =6        77436     77311.8        .200       2.464
                        p=1-exp(-SUM/2)= .70828
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 19 to 26
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          896       944.3       2.471       2.471
          r =5        21892     21743.9       1.009       3.479
          r =6        77212     77311.8        .129       3.608
                        p=1-exp(-SUM/2)= .83538
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 20 to 27
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          966       944.3        .499        .499
          r =5        21664     21743.9        .294        .792
          r =6        77370     77311.8        .044        .836
                        p=1-exp(-SUM/2)= .34164
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 21 to 28
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          886       944.3       3.600       3.600
          r =5        21746     21743.9        .000       3.600
          r =6        77368     77311.8        .041       3.641
                        p=1-exp(-SUM/2)= .83802
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 22 to 29
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          925       944.3        .395        .395
          r =5        21757     21743.9        .008        .402
          r =6        77318     77311.8        .000        .403
                        p=1-exp(-SUM/2)= .18246
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 23 to 30
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4          934       944.3        .112        .112
          r =5        21652     21743.9        .388        .501
          r =6        77414     77311.8        .135        .636
                        p=1-exp(-SUM/2)= .27235
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 24 to 31
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4         1005       944.3       3.902       3.902
          r =5        21609     21743.9        .837       4.739
          r =6        77386     77311.8        .071       4.810
                        p=1-exp(-SUM/2)= .90972
        Rank of a 6x8 binary matrix,
     rows formed from eight bits of the RNG tetris.32      
     b-rank test for bits 25 to 32
                     OBSERVED   EXPECTED     (O-E)^2/E      SUM
          r<=4         1004       944.3       3.774       3.774
          r =5        21763     21743.9        .017       3.791
          r =6        77233     77311.8        .080       3.871
                        p=1-exp(-SUM/2)= .85567
   TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
 These should be 25 uniform [0,1] random variables:
     .889332     .696217     .562108     .224350     .095459
     .771725     .166092     .091197     .751948     .804387
     .105256     .317150     .234343     .653341     .408125
     .161453     .041159     .708284     .835376     .341643
     .838021     .182456     .272353     .909725     .855666
   brank test summary for tetris.32      
       The KS test for those 25 supposed UNI's yields
                    KS p-value= .390822

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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:  141453 missing words,   -1.07 sigmas from mean, p-value= .14317
 tst no  2:  142456 missing words,    1.28 sigmas from mean, p-value= .89925
 tst no  3:  142305 missing words,     .92 sigmas from mean, p-value= .82238
 tst no  4:  141557 missing words,    -.82 sigmas from mean, p-value= .20520
 tst no  5:  141402 missing words,   -1.19 sigmas from mean, p-value= .11794
 tst no  6:  141749 missing words,    -.37 sigmas from mean, p-value= .35398
 tst no  7:  142175 missing words,     .62 sigmas from mean, p-value= .73261
 tst no  8:  141877 missing words,    -.08 sigmas from mean, p-value= .46990
 tst no  9:  141085 missing words,   -1.93 sigmas from mean, p-value= .02705
 tst no 10:  141751 missing words,    -.37 sigmas from mean, p-value= .35572
 tst no 11:  141317 missing words,   -1.38 sigmas from mean, p-value= .08319
 tst no 12:  141780 missing words,    -.30 sigmas from mean, p-value= .38126
 tst no 13:  141915 missing words,     .01 sigmas from mean, p-value= .50529
 tst no 14:  142210 missing words,     .70 sigmas from mean, p-value= .75882
 tst no 15:  141548 missing words,    -.84 sigmas from mean, p-value= .19927
 tst no 16:  142186 missing words,     .65 sigmas from mean, p-value= .74100
 tst no 17:  141181 missing words,   -1.70 sigmas from mean, p-value= .04441
 tst no 18:  140968 missing words,   -2.20 sigmas from mean, p-value= .01393
 tst no 19:  142689 missing words,    1.82 sigmas from mean, p-value= .96575
 tst no 20:  141406 missing words,   -1.18 sigmas from mean, p-value= .11980

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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 tetris.32      
  Output: No. missing words (mw), equiv normal variate (z), p-value (p)
                                                           mw     z     p
    OPSO for tetris.32       using bits 23 to 32        141929   .068  .5270
    OPSO for tetris.32       using bits 22 to 31        142293  1.323  .9071
    OPSO for tetris.32       using bits 21 to 30        141848  -.211  .4163
    OPSO for tetris.32       using bits 20 to 29        141673  -.815  .2076
    OPSO for tetris.32       using bits 19 to 28        142164   .878  .8101
    OPSO for tetris.32       using bits 18 to 27        142254  1.189  .8827
    OPSO for tetris.32       using bits 17 to 26        141776  -.460  .3228
    OPSO for tetris.32       using bits 16 to 25        141881  -.098  .4611
    OPSO for tetris.32       using bits 15 to 24        141586 -1.115  .1324
    OPSO for tetris.32       using bits 14 to 23        141698  -.729  .2331
    OPSO for tetris.32       using bits 13 to 22        142394  1.671  .9527
    OPSO for tetris.32       using bits 12 to 21        142304  1.361  .9132
    OPSO for tetris.32       using bits 11 to 20        141809  -.346  .3647
    OPSO for tetris.32       using bits 10 to 19        142056   .506  .6935
    OPSO for tetris.32       using bits  9 to 18        141867  -.146  .4420
    OPSO for tetris.32       using bits  8 to 17        141912   .009  .5037
    OPSO for tetris.32       using bits  7 to 16        141996   .299  .6175
    OPSO for tetris.32       using bits  6 to 15        141547 -1.249  .1058
    OPSO for tetris.32       using bits  5 to 14        142064   .533  .7031
    OPSO for tetris.32       using bits  4 to 13        142449  1.861  .9686
    OPSO for tetris.32       using bits  3 to 12        141902  -.025  .4899
    OPSO for tetris.32       using bits  2 to 11        142609  2.413  .9921
    OPSO for tetris.32       using bits  1 to 10        141764  -.501  .3081
 OQSO test for generator tetris.32      
  Output: No. missing words (mw), equiv normal variate (z), p-value (p)
                                                           mw     z     p
    OQSO for tetris.32       using bits 28 to 32        141546 -1.232  .1090
    OQSO for tetris.32       using bits 27 to 31        141918   .029  .5117
    OQSO for tetris.32       using bits 26 to 30        141854  -.188  .4256
    OQSO for tetris.32       using bits 25 to 29        142195   .968  .8336
    OQSO for tetris.32       using bits 24 to 28        141793  -.394  .3467
    OQSO for tetris.32       using bits 23 to 27        141237 -2.279  .0113
    OQSO for tetris.32       using bits 22 to 26        141785  -.421  .3367
    OQSO for tetris.32       using bits 21 to 25        142162   .857  .8041
    OQSO for tetris.32       using bits 20 to 24        141453 -1.547  .0609
    OQSO for tetris.32       using bits 19 to 23        141791  -.401  .3442
    OQSO for tetris.32       using bits 18 to 22        141594 -1.069  .1426
    OQSO for tetris.32       using bits 17 to 21        142029   .406  .6575
    OQSO for tetris.32       using bits 16 to 20        141671  -.808  .2096
    OQSO for tetris.32       using bits 15 to 19        141736  -.588  .2784
    OQSO for tetris.32       using bits 14 to 18        141960   .172  .5682
    OQSO for tetris.32       using bits 13 to 17        142092   .619  .7321
    OQSO for tetris.32       using bits 12 to 16        141527 -1.296  .0975
    OQSO for tetris.32       using bits 11 to 15        142387  1.619  .9473
    OQSO for tetris.32       using bits 10 to 14        142139   .779  .7819
    OQSO for tetris.32       using bits  9 to 13        141752  -.533  .2969
    OQSO for tetris.32       using bits  8 to 12        141679  -.781  .2175
    OQSO for tetris.32       using bits  7 to 11        142105   .663  .7464
    OQSO for tetris.32       using bits  6 to 10        142029   .406  .6575
    OQSO for tetris.32       using bits  5 to  9        142297  1.314  .9056
    OQSO for tetris.32       using bits  4 to  8        142099   .643  .7399
    OQSO for tetris.32       using bits  3 to  7        141764  -.493  .3111
    OQSO for tetris.32       using bits  2 to  6        141554 -1.205  .1142
    OQSO for tetris.32       using bits  1 to  5        141633  -.937  .1745
  DNA test for generator tetris.32      
  Output: No. missing words (mw), equiv normal variate (z), p-value (p)
                                                           mw     z     p
     DNA for tetris.32       using bits 31 to 32        141817  -.272  .3927
     DNA for tetris.32       using bits 30 to 31        141921   .034  .5137
     DNA for tetris.32       using bits 29 to 30        141888  -.063  .4749
     DNA for tetris.32       using bits 28 to 29        141903  -.019  .4926
     DNA for tetris.32       using bits 27 to 28        142037   .377  .6468
     DNA for tetris.32       using bits 26 to 27        141602  -.907  .1823
     DNA for tetris.32       using bits 25 to 26        142184   .810  .7911
     DNA for tetris.32       using bits 24 to 25        142929  3.008  .9987
     DNA for tetris.32       using bits 23 to 24        141644  -.783  .2169
     DNA for tetris.32       using bits 22 to 23        142072   .480  .6843
     DNA for tetris.32       using bits 21 to 22        142154   .722  .7648
     DNA for tetris.32       using bits 20 to 21        141989   .235  .5929
     DNA for tetris.32       using bits 19 to 20        142013   .306  .6201
     DNA for tetris.32       using bits 18 to 19        141590  -.942  .1731
     DNA for tetris.32       using bits 17 to 18        141869  -.119  .4527
     DNA for tetris.32       using bits 16 to 17        142849  2.772  .9972
     DNA for tetris.32       using bits 15 to 16        141596  -.924  .1777
     DNA for tetris.32       using bits 14 to 15        142818  2.680  .9963
     DNA for tetris.32       using bits 13 to 14        142247   .996  .8404
     DNA for tetris.32       using bits 12 to 13        141909  -.001  .4996
     DNA for tetris.32       using bits 11 to 12        142250  1.005  .8425
     DNA for tetris.32       using bits 10 to 11        142179   .795  .7868
     DNA for tetris.32       using bits  9 to 10        141622  -.848  .1983
     DNA for tetris.32       using bits  8 to  9        142379  1.385  .9170
     DNA for tetris.32       using bits  7 to  8        141956   .138  .5548
     DNA for tetris.32       using bits  6 to  7        141452 -1.349  .0887
     DNA for tetris.32       using bits  5 to  6        141683  -.668  .2522
     DNA for tetris.32       using bits  4 to  5        141364 -1.609  .0538
     DNA for tetris.32       using bits  3 to  4        142118   .616  .7309
     DNA for tetris.32       using bits  2 to  3        141326 -1.721  .0426
     DNA for tetris.32       using bits  1 to  2        141801  -.320  .3747

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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 tetris.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 tetris.32        2789.84      4.099      .999979
 byte stream for tetris.32        2826.95      4.624      .999998

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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  2546.39       .656      .744102
           bits  2 to  9  2510.22       .145      .557485
           bits  3 to 10  2566.53       .941      .826618
           bits  4 to 11  2532.80       .464      .678635
           bits  5 to 12  2540.27       .569      .715486
           bits  6 to 13  2488.06      -.169      .432953
           bits  7 to 14  2647.54      2.087      .981537
           bits  8 to 15  2457.42      -.602      .273520
           bits  9 to 16  2435.13      -.917      .179466
           bits 10 to 17  2536.21       .512      .695702
           bits 11 to 18  2452.74      -.668      .251933
           bits 12 to 19  2466.81      -.469      .319376
           bits 13 to 20  2500.65       .009      .503661
           bits 14 to 21  2584.77      1.199      .884708
           bits 15 to 22  2613.60      1.607      .945920
           bits 16 to 23  2573.47      1.039      .850600
           bits 17 to 24  2403.09     -1.371      .085259
           bits 18 to 25  2524.95       .353      .637914
           bits 19 to 26  2481.29      -.265      .395649
           bits 20 to 27  2447.00      -.750      .226756
           bits 21 to 28  2432.18      -.959      .168746
           bits 22 to 29  2340.23     -2.260      .011925
           bits 23 to 30  2548.68       .688      .754396
           bits 24 to 31  2504.91       .069      .527655
           bits 25 to 32  2469.72      -.428      .334262

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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 tetris.32      
            Of 12,000 tries, the average no. of successes
                 should be 3523 with sigma=21.9
            Successes: 3529    z-score:   .274 p-value: .607947
            Successes: 3499    z-score: -1.096 p-value: .136563
            Successes: 3542    z-score:   .868 p-value: .807188
            Successes: 3512    z-score:  -.502 p-value: .307734
            Successes: 3525    z-score:   .091 p-value: .536382
            Successes: 3546    z-score:  1.050 p-value: .853193
            Successes: 3510    z-score:  -.594 p-value: .276387
            Successes: 3568    z-score:  2.055 p-value: .980051
            Successes: 3545    z-score:  1.005 p-value: .842447
            Successes: 3505    z-score:  -.822 p-value: .205562
 
           square size   avg. no.  parked   sample sigma
             100.            3528.100       20.900
            KSTEST for the above 10: p=  .210793

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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 tetris.32      
     Sample no.    d^2     avg     equiv uni            
           5    1.5640   1.7972     .792341
          10    1.1610   1.4524     .688644
          15     .1279   1.2154     .120652
          20     .1622   1.1682     .150392
          25    1.2287   1.1472     .709119
          30     .0844   1.0661     .081289
          35    1.8159   1.0043     .838783
          40     .6441    .9800     .476552
          45     .4647    .9759     .373148
          50     .4496    .9742     .363572
          55     .6022   1.0472     .454072
          60    2.9051   1.0503     .946051
          65     .1139   1.0801     .108153
          70     .0338   1.0505     .033368
          75     .2317   1.0197     .207750
          80     .6231    .9913     .465372
          85    1.0093    .9920     .637362
          90     .9378    .9589     .610351
          95    5.5466    .9980     .996206
         100    1.1842    .9908     .695829
     MINIMUM DISTANCE TEST for tetris.32      
          Result of KS test on 20 transformed mindist^2's:
                                  p-value= .387938

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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 tetris.32      
 sample no:  1     r^3=   2.015     p-value= .06497
 sample no:  2     r^3=   6.126     p-value= .18470
 sample no:  3     r^3= 130.148     p-value= .98694
 sample no:  4     r^3=   5.304     p-value= .16205
 sample no:  5     r^3=  58.352     p-value= .85702
 sample no:  6     r^3=   7.614     p-value= .22416
 sample no:  7     r^3=  17.339     p-value= .43896
 sample no:  8     r^3=  22.463     p-value= .52705
 sample no:  9     r^3=  47.913     p-value= .79752
 sample no: 10     r^3=   9.438     p-value= .26993
 sample no: 11     r^3=  46.228     p-value= .78582
 sample no: 12     r^3=    .428     p-value= .01417
 sample no: 13     r^3=  11.128     p-value= .30992
 sample no: 14     r^3=  24.397     p-value= .55658
 sample no: 15     r^3=  13.163     p-value= .35517
 sample no: 16     r^3=  83.661     p-value= .93850
 sample no: 17     r^3=   5.756     p-value= .17458
 sample no: 18     r^3=  75.235     p-value= .91855
 sample no: 19     r^3=  47.893     p-value= .79738
 sample no: 20     r^3=  44.970     p-value= .77664
  A KS test is applied to those 20 p-values.
---------------------------------------------------------
       3DSPHERES test for file tetris.32            p-value= .157974
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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 tetris.32      
         Table of standardized frequency counts
     ( (obs-exp)/sqrt(exp) )^2
        for j taking values <=6,7,8,...,47,>=48:
     -.8      .1    -1.1     -.5      .5     -.9
    -1.3      .4     1.3     -.4     -.7     1.6
    -1.4     -.8     1.6     -.9    -1.2      .1
     -.7      .0      .4     1.2      .5      .4
     -.2      .4      .0    -1.0     1.8      .0
      .8     1.0    -1.1      .5      .9     -.3
     1.0     -.7      .1    -1.3      .9    -1.0
     1.8
           Chi-square with 42 degrees of freedom: 35.683
              z-score=  -.689  p-value= .256451
______________________________________________________________

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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  .308546
                Test no.  2      p-value  .390783
                Test no.  3      p-value  .425511
                Test no.  4      p-value  .529761
                Test no.  5      p-value  .793372
                Test no.  6      p-value  .453160
                Test no.  7      p-value  .363355
                Test no.  8      p-value  .353380
                Test no.  9      p-value  .557032
                Test no. 10      p-value  .951610
   Results of the OSUM test for tetris.32      
        KSTEST on the above 10 p-values:  .669235

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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 tetris.32      
     Up and down runs in a sample of 10000
_________________________________________________ 
                 Run test for tetris.32      :
       runs up; ks test for 10 p's: .277231
     runs down; ks test for 10 p's: .089944
                 Run test for tetris.32      :
       runs up; ks test for 10 p's: .125164
     runs down; ks test for 10 p's: .807542

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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 tetris.32      
  No. of wins:  Observed Expected
                                98877    98585.86
                  98877= No. of wins, z-score= 1.302 pvalue= .90357
   Analysis of Throws-per-Game:
 Chisq=  24.03 for 20 degrees of freedom, p=  .75881
               Throws Observed Expected  Chisq     Sum
                  1    67111    66666.7   2.961    2.961
                  2    37636    37654.3    .009    2.970
                  3    26766    26954.7   1.321    4.292
                  4    19125    19313.5   1.839    6.131
                  5    13751    13851.4    .728    6.859
                  6     9986     9943.5    .181    7.040
                  7     7093     7145.0    .379    7.419
                  8     5050     5139.1   1.544    8.963
                  9     3671     3699.9    .225    9.188
                 10     2776     2666.3   4.514   13.702
                 11     1951     1923.3    .398   14.100
                 12     1369     1388.7    .281   14.380
                 13     1071     1003.7   4.511   18.891
                 14      726      726.1    .000   18.891
                 15      546      525.8    .773   19.664
                 16      388      381.2    .123   19.787
                 17      276      276.5    .001   19.788
                 18      179      200.8   2.373   22.161
                 19      140      146.0    .245   22.406
                 20       94      106.2   1.405   23.811
                 21      295      287.1    .217   24.028
            SUMMARY  FOR tetris.32      
                p-value for no. of wins: .903568
                p-value for throws/game: .758815

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 Results of DIEHARD battery of tests sent to file tetris.out     



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