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CONTRIBUTING.md

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+# Contributing to Fourmilab Random Sequence Tester
+
+You're welcome to use this repository as the starting point for your
+own developments.  If you've found and fixed a bug or developed a new
+feature you'd like to share, please submit a pull request to this
+repository so it can be considered for inclusion.

LICENSE.md

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+# Software Licenses
+
+This product (software, documents, and data files) is licensed under a
+Creative Commons
+[Attribution-ShareAlike 4.0 International
+License](https://creativecommons.org/licenses/by-sa/4.0/)
+([legal text](https://creativecommons.org/licenses/by-sa/4.0/legalcode)).
+You are free to copy and redistribute this material in any
+medium or format, and to remix, transform, and build upon the
+material for any purpose, including commercially.  You must give
+credit, provide a link to the license, and indicate if changes
+were made.  If you remix, transform, or build upon this
+material, you must distribute your contributions under the same
+license as the original.
+
+This product is provided with no warranty, either expressed or implied,
+including but not limited to any implied warranties of merchantability
+or fitness for a particular purpose, regarding these materials and is
+made available available solely on an “as-is” basis.
+
+In no event shall John Walker be liable to anyone for special,
+collateral, incidental, or consequential damages in connection with or
+arising out of distribution or use of these materials.  The sole and
+exclusive liability of John Walker, regardless of the form of action,
+shall not exceed the compensation received by the author for the
+product.
+
+John Walker reserves the right to revise and improve this products as
+he sees fit.  This publication describes the state of this product at
+the time of its publication, and may not reflect the product at all
+times in the future.

README.md

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+# ENT — Fourmilab Random Sequence Tester
+
+The [Fourmilab Random Sequence Tester](https://www.fourmilab.ch/random/),
+**ent**, applies various tests to sequences of bytes stored in files
+and reports the results of those tests. The program is useful for
+evaluating pseudorandom number generators for encryption and
+statistical sampling applications, compression algorithms, and other
+applications where the information density of a file is of interest.
+
+## Description
+
+**ent** performs a variety of tests on the stream of bytes in its input
+file (or standard input if no input file is specified) and produces
+output as follows on the standard output stream:
+
+    Entropy = 7.980627 bits per character.
+
+    Optimum compression would reduce the size
+    of this 51768 character file by 0 percent.
+
+    Chi square distribution for 51768 samples is 1542.26, and randomly
+    would exceed this value less than 0.01 percent of the times.
+
+    Arithmetic mean value of data bytes is 125.93 (127.5 = random).
+    Monte Carlo value for Pi is 3.169834647 (error 0.90 percent).
+    Serial correlation coefficient is 0.004249 (totally uncorrelated = 0.0).
+
+The values calculated are as follows:
+
+#### Entropy
+The information density of the contents of the file, expressed as a
+number of bits per character. The results above, which resulted from
+processing an image file compressed with JPEG, indicate that the file
+is extremely dense in information—essentially random. Hence,
+compression of the file is unlikely to reduce its size. By contrast,
+the C source code of the program has entropy of about 4.9 bits per
+character, indicating that optimal compression of the file would reduce
+its size by 38%. \[Hamming, pp. 104–108\]
+
+#### Chi-square Test
+The chi-square test is the most commonly used test for the randomness
+of data, and is extremely sensitive to errors in pseudorandom sequence
+generators. The chi-square distribution is calculated for the stream of
+bytes in the file and expressed as an absolute number and a percentage
+which indicates how frequently a truly random sequence would exceed the
+value calculated. We interpret the percentage as the degree to which
+the sequence tested is suspected of being non-random. If the percentage
+is greater than 99% or less than 1%, the sequence is almost certainly
+not random. If the percentage is between 99% and 95% or between 1% and
+5%, the sequence is suspect. Percentages between 90% and 95% and 5% and
+10% indicate the sequence is “almost suspect”. Note that our JPEG file,
+while very dense in information, is far from random as revealed by the
+chi-square test.
+
+Applying this test to the output of various pseudorandom sequence
+generators is interesting. The low-order 8 bits returned by the
+standard Unix `rand()` function, for example, yields:
+
+    Chi square distribution for 500000 samples is 0.01, and randomly
+    would exceed this value more than 99.99 percent of the times.
+
+While an improved generator \[Park & Miller\] reports:
+
+    Chi square distribution for 500000 samples is 212.53, and randomly
+    would exceed this value 97.53 percent of the times.
+
+Thus, the standard Unix generator (or at least the low-order bytes it
+returns) is unacceptably non-random, while the improved generator is
+much better but still sufficiently non-random to cause concern for
+demanding applications. Contrast both of these software generators with
+the chi-square result of a genuine random sequence created by timing
+radioactive decay events.
+
+    Chi square distribution for 500000 samples is 249.51, and randomly
+    would exceed this value 40.98 percent of the times.
+
+See \[Knuth, pp. 35–40\] for more information on the chi-square test.
+
+#### Arithmetic Mean
+This is simply the result of summing the all the bytes (bits if the 
+`-b` option is specified) in the file and dividing by the file length. 
+If the data are close to random, this should be about 127.5 (0.5 for 
+`-b` option output). If the mean departs from this value, the values 
+are consistently high or low.
+
+#### Monte Carlo Value for Pi
+Each successive sequence of six bytes is used as 24 bit X and Y 
+co-ordinates within a square.  If the distance of the 
+randomly-generated point is less than the radius of a circle inscribed 
+within the square, the six-byte sequence is considered a “hit”.  The 
+percentage of hits can be used to calculate the value of π.  For very 
+large streams (this approximation converges very slowly), the value 
+will approach the correct value of π if the sequence is close to 
+random.  A 500000 byte file created by radioactive decay yielded:
+
+    Monte Carlo value for Pi is 3.143580574 (error 0.06 percent).
+
+#### Serial Correlation Coefficient
+This quantity measures the extent to which each byte in the file 
+depends upon the previous byte. For random sequences, this value (which 
+can be positive or negative) will, of course, be close to zero.  A 
+non-random byte stream such as a C program will yield a serial 
+correlation coefficient on the order of 0.5.  Wildly predictable data 
+such as uncompressed bitmaps will exhibit serial correlation 
+coefficients approaching 1.  See [Knuth, pp. 64–65] for more details.
+
+## License
+
+This software is licensed under the Creative Commons
+Attribution-ShareAlike license.  Please see [LICENSE.md](LICENSE.md) in
+this repository for details.
+
+## References
+
+[Hamming]
+Hamming, Richard W.  *Coding and Information Theory*. Englewood Cliffs 
+NJ: Prentice-Hall, 1980.  ISBN 978-0-13-139139-0.
+
+[Knuth]
+Knuth, Donald E.  *The Art of Computer Programming, Volume 2 / 
+Seminumerical Algorithms*.  Reading MA: Addison-Wesley, 1969. ISBN 
+978-0-201-89684-8.
+
+[Lempel & Ziv]
+Ziv J. and A. Lempel.  “A Universal Algorithm for Sequential Data 
+Compression”. IEEE Transactions on Information Theory 23, 3, pp. 
+337–343.
+
+[Park & Miller]
+Park, Stephen K. and Keith W. Miller.  “Random Number Generators: Good 
+Ones Are Hard to Find”. Communications of the ACM, October 1988, p. 
+1192.
+
+*[Introduction to Probability and
+Statistics](https://www.fourmilab.ch/rpkp/experiments/statistics.html)*
+at Fourmilab