21 December 2011

ENT 2^{17 }Results, Random Inputs from

http://randomnumber.org/randdata/10MB_200409232110.dat

http://randomnumber.org/randdata/10MB_200409232112.dat

List of Input files to the ENT:

· eMT

· MixBits

· A

· B

· C

· D

· IDS

· K2

· K3

**eMT:**

Byte |
Bit |

Entropy = 7.999714 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 623.33, and randomly would exceed this value less than 0.01 percent of the times.
Arithmetic mean value of data bytes is 128.5542 (127.5 = random). Monte Carlo value for Pi is 3.141967773 (error 0.01 percent). Serial correlation coefficient is -0.000361 (totally uncorrelated = 0.0). |
Entropy = 0.999997 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 58.28, and randomly would exceed this value less than 0.01 percent of the times.
Arithmetic mean value of data bits is 0.5011 (0.5 = random). Monte Carlo value for Pi is 3.141967773 (error 0.01 percent). Serial correlation coefficient is -0.000430 (totally uncorrelated = 0.0). |

**eMT(Z _{i} & Z_{i+1}):**

Byte |
Bit |

Entropy = 7.999896 bits per byte.
Optimum compression would reduce the size of this 1572852 byte file by 0 percent.
Chi square distribution for 1572852 samples is 227.94, and randomly would exceed this value 88.76 percent of the times.
Arithmetic mean value of data bytes is 127.2756 (127.5 = random). Monte Carlo value for Pi is 3.139504543 (error 0.07 percent). Serial correlation coefficient is -0.000644 (totally uncorrelated = 0.0). |
Entropy = 0.999999 bits per bit.
Optimum compression would reduce the size of this 12582816 bit file by 0 percent.
Chi square distribution for 12582816 samples is 10.91, and randomly would exceed this value 0.10 percent of the times.
Arithmetic mean value of data bits is 0.4995 (0.5 = random). Monte Carlo value for Pi is 3.139504543 (error 0.07 percent). Serial correlation coefficient is 0.000069 (totally uncorrelated = 0.0). |

**MixBits:**

Byte |
Bit |

Entropy = 7.999910 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 196.23, and randomly would exceed this value 99.75 percent of the times.
Arithmetic mean value of data bytes is 127.3920 (127.5 = random). Monte Carlo value for Pi is 3.142623901 (error 0.03 percent). Serial correlation coefficient is -0.000152 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 3.56, and randomly would exceed this value 5.91 percent of the times.
Arithmetic mean value of data bits is 0.4997 (0.5 = random). Monte Carlo value for Pi is 3.142623901 (error 0.03 percent). Serial correlation coefficient is -0.000043 (totally uncorrelated = 0.0). |

**MixBits (Z _{i} & Z_{i+1}):**

Byte |
Bit |

Entropy = 7.999885 bits per byte.
Optimum compression would reduce the size of this 1572852 byte file by 0 percent.
Chi square distribution for 1572852 samples is 250.50, and randomly would exceed this value 56.78 percent of the times.
Arithmetic mean value of data bytes is 127.6035 (127.5 = random). Monte Carlo value for Pi is 3.138634786 (error 0.09 percent). Serial correlation coefficient is -0.000331 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582816 bit file by 0 percent.
Chi square distribution for 12582816 samples is 2.60, and randomly would exceed this value 10.68 percent of the times.
Arithmetic mean value of data bits is 0.5002 (0.5 = random). Monte Carlo value for Pi is 3.138634786 (error 0.09 percent). Serial correlation coefficient is 0.000522 (totally uncorrelated = 0.0). |

**A:**

Byte |
Bit |

Entropy = 7.999891 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 237.08, and randomly would exceed this value 78.32 percent of the times.
Arithmetic mean value of data bytes is 127.4997 (127.5 = random). Monte Carlo value for Pi is 3.141204834 (error 0.01 percent). Serial correlation coefficient is -0.000654 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 0.13, and randomly would exceed this value 72.20 percent of the times.
Arithmetic mean value of data bits is 0.5001 (0.5 = random). Monte Carlo value for Pi is 3.141204834 (error 0.01 percent). Serial correlation coefficient is -0.000056 (totally uncorrelated = 0.0). |

**B:**

Byte |
Bit |

Entropy = 7.999884 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 253.72, and randomly would exceed this value 51.08 percent of the times.
Arithmetic mean value of data bytes is 127.4679 (127.5 = random). Monte Carlo value for Pi is 3.140136719 (error 0.05 percent). Serial correlation coefficient is -0.001590 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 0.02, and randomly would exceed this value 87.46 percent of the times.
Arithmetic mean value of data bits is 0.5000 (0.5 = random). Monte Carlo value for Pi is 3.140136719 (error 0.05 percent). Serial correlation coefficient is 0.000094 (totally uncorrelated = 0.0). |

**C:**

Byte |
Bit |

Entropy = 7.999873 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 277.64, and randomly would exceed this value 15.78 percent of the times.
Arithmetic mean value of data bytes is 127.4878 (127.5 = random). Monte Carlo value for Pi is 3.143325806 (error 0.06 percent). Serial correlation coefficient is -0.000193 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 0.78, and randomly would exceed this value 37.61 percent of the times.
Arithmetic mean value of data bits is 0.4999 (0.5 = random). Monte Carlo value for Pi is 3.143325806 (error 0.06 percent). Serial correlation coefficient is -0.000199 (totally uncorrelated = 0.0). |

**D:**

Byte |
Bit |

Entropy = 7.999884 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 253.50, and randomly would exceed this value 51.47 percent of the times.
Arithmetic mean value of data bytes is 127.5003 (127.5 = random). Monte Carlo value for Pi is 3.136947632 (error 0.15 percent). Serial correlation coefficient is -0.000680 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 1.03, and randomly would exceed this value 31.07 percent of the times.
Arithmetic mean value of data bits is 0.4999 (0.5 = random). Monte Carlo value for Pi is 3.136947632 (error 0.15 percent). Serial correlation coefficient is 0.000263 (totally uncorrelated = 0.0). |

**IDS:**

Byte |
Bit |

Entropy = 7.999887 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 246.61, and randomly would exceed this value 63.53 percent of the times.
Arithmetic mean value of data bytes is 127.5023 (127.5 = random). Monte Carlo value for Pi is 3.141555786 (error 0.00 percent). Serial correlation coefficient is 0.000921 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 0.73, and randomly would exceed this value 39.27 percent of the times.
Arithmetic mean value of data bits is 0.4999 (0.5 = random). Monte Carlo value for Pi is 3.141555786 (error 0.00 percent). Serial correlation coefficient is -0.000118 (totally uncorrelated = 0.0). |

**K2:**

Byte |
Bit |

Entropy = 7.999875 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 272.13, and randomly would exceed this value 22.02 percent of the times.
Arithmetic mean value of data bytes is 127.4529 (127.5 = random). Monte Carlo value for Pi is 3.141372681 (error 0.01 percent). Serial correlation coefficient is -0.000770 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 2.71, and randomly would exceed this value 9.96 percent of the times.
Arithmetic mean value of data bits is 0.4998 (0.5 = random). Monte Carlo value for Pi is 3.141372681 (error 0.01 percent). Serial correlation coefficient is -0.000001 (totally uncorrelated = 0.0). |

**K3:**

Byte |
Bit |

Entropy = 7.999879 bits per byte.
Optimum compression would reduce the size of this 1572864 byte file by 0 percent.
Chi square distribution for 1572864 samples is 263.61, and randomly would exceed this value 34.22 percent of the times.
Arithmetic mean value of data bytes is 127.5444 (127.5 = random). Monte Carlo value for Pi is 3.135681152 (error 0.19 percent). Serial correlation coefficient is 0.001035 (totally uncorrelated = 0.0). |
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size of this 12582912 bit file by 0 percent.
Chi square distribution for 12582912 samples is 1.84, and randomly would exceed this value 17.55 percent of the times.
Arithmetic mean value of data bits is 0.5002 (0.5 = random). Monte Carlo value for Pi is 3.135681152 (error 0.19 percent). Serial correlation coefficient is 0.000535 (totally uncorrelated = 0.0). |