File import
File name:     E:\DIEHARD\xr_p.dat
Operator:      
Date and time: 11/18/06 15:51:06
Bit count      8388608

Balancing
No balancing has been performed
Ones ratio: 49.97%

Run Test
Runs of 0
Lenght    number
-----------------
   1    1047632
   2     524052
   3     262545
   4     130556
   5      65997
   6      33026
   7      16173
   8       8269
   9       4211
  10       2064
  11       1019
  12        512
  13        277
  14        127
  15         65
>= 16        64

Runs of 1
Lenght    number
-----------------
   1    1048335
   2     524463
   3     261919
   4     130879
   5      65666
   6      32588
   7      16327
   8       8251
   9       4134
  10       2007
  11       1000
  12        538
  13        234
  14        128
  15         44
>= 16        75

Comparaison with the c distribution with 2L degrees of freedom
p-value: 41.06%
The sequence of bits seems to be random.

One level Serial Test
Lenght of Blocks:   4 
Nb of Blocks:       2097152

V value:   18.642
p-value:   23.043% 
The sequence of bits seems to be random because the probability that V is greater than the expected V is not too close from 0 or 1.

One Level Frequency Test
Number of zeros: 4196428 (50.03%)
Number of zeros: 4192180 (49.97%)
Number of s from 50/50 distribution: -1.466694
The sequence of bits is equidistributed because there is only -1.47 s of difference with the expected 50% mean.

One Level Entropy Test
Lenght of Blocks:   4 
Nb of Blocks:       2097152

Entropie H:           11.301 
Expected value:       15.000
Standard deviation s:  5.477

The sequence of bits seems to be random because there is only 0.68 s of difference with the expected mean.

Maurer Universal Test
 L      Q        K      fTU mean    stand. dev. s    fTU    Nb. of s
----------------------------------------------------------------------
 1     100    8388508    0.7326       undefined    0.7326   undefined
 2     200    4194104    1.5378      1.736e-004    1.5374    1.9796
 3     400    2795802    2.4013      4.311e-004    2.4016    0.6962
 4     800    2096352    3.3101      5.852e-004    3.3112    1.9336
 5    1600    1676121    4.2531      7.293e-004    4.2534    0.5055
 6    3200    1394901    5.2184      8.597e-004    5.2177    0.8053
 7    6400    1191972    6.1973      9.759e-004    6.1963    1.0974
 8   12800    1035776    7.1838      1.080e-003    7.1837    0.0842
 9   25600     906467    8.1768      1.179e-003    8.1764    0.2979

The value of the column "Nb. of s" must not be greater than 3 because it give the number of standard deviation from the mean.

Autocorrelation Test
The autocorrelation test calcul the normalized correlation function G(n).

  n    G(n)    p-value
-----------------------
  1   0.4999    0.218
  2   0.5000    0.531
  3   0.4999    0.270
  4   0.5000    0.430
  5   0.5000    0.520
  6   0.5004    0.982
  7   0.5002    0.872
  8   0.5001    0.768
  9   0.5002    0.823
 10   0.5001    0.709

Kolmogorov-Smirnov Test on the 10 values
D value of the K-S test:   0.230 
Probability (D>observed):  66.335%
The sequence of bits seems to be random because the probability that D is greater than the expected D is not too close from 0 or 1.

