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<h1>Uniform random number generators</h1>
<p align="center">by Agner Fog, 2001 - 2007</p>
<p><a href="randomc.zip">randomc.zip</a> contains a C++ class library of uniform random number generators of good
quality.</p>
<p>The random number generators found in standard libraries are often of a poor
quality, insufficient for large Monte Carlo calculations. This C++
implementation provides
random number generators of a much better quality: Better randomness, higher
resolution, and longer cycle lengths.</p>
<p>The same random number generators are available as libraries coded in assembly language
for higher speed. These libraries can be linked into projects coded in other
programming languages under Windows, Linux, BSD, etc. The library files are
available in the
archive <a href="asmlib.zip">asmlib.zip</a>.</p>
<p>Non-uniform random number generators are provided in <a href="stocc.zip">stocc.zip</a>.</p>
<h2>File list</h2>
<p>The archive <a href="randomc.zip">randomc.zip</a> contains the following
files:</p>
<dl>
<dt>randomc.htm</dt>
<dd>This file. Instructions.</dd>
<dt>licence.htm</dt>
<dd>Licence conditions.</dd>
<dt>randomc.h</dt>
<dd>C++ header file containing class definitions.<br>
You must <code>#include</code> this in all C++ files that use this library.</dd>
<dt>mersenne.cpp</dt>
<dd>Random number generator of type Mersenne twister.</dd>
<dt>mother.cpp</dt>
<dd>Random number generator of type Mother-of-all (multiply with carry).</dd>
<dt>rancombi.cpp</dt>
<dd>Template class for combining any two of these random number generators.</dd>
<dt>userintf.cpp</dt>
<dd>System-dependent user interface functions, used by test programs.</dd>
<dt>ex-ran.cpp</dt>
<dd>Example showing how to use these random number generators.</dd>
</dl>
<h2>Quality of randomness</h2>
<p>All these random number generators provide excellent randomness and extremely
long cycle lengths.</p>
<p>For all but the most demanding applications it doesn't matter
which of the random number generators you use. The Mersenne twister is the one
that is best understood theoretically. For this reason it is recommended by
leading experts. The Mother-of-all generator has the highest
bifurcation of these generators.</p>
<p>For the most demanding scientific applications you may combine these two
generators, using rancombi.cpp.</p>
<h2>Instructions</h2>
<p>Choose which one of the random number generators mentioned above you want to
use.</p>
<p>Write <code>#include "randomc.h"</code> in any C++ file
that uses one of these random number generators.</p>
<p>Add the appropriate cpp file to your project, either as an <code>#include</code>
or as a separate module.</p>
<p>Make an instance (object) of the appropriate class. It needs an integer seed
as initializer.</p>
<p>The seed can be any integer, positive, negative or zero. Repeating the
calculations with the same seed will produce the same sequence of random
numbers. A different seed will give different random numbers. You may use the
time in seconds or milliseconds as seed.</p>
<p>The random number generators that are implemented as C++ classes (CRandomMersenne,
CRandomMother, CRandomMersenneA, CRandomMotherA) are thread-safe if you have one
instance of the class for each thread that needs random numbers. Make sure each
instance has a different seed. You may, for example, add 1 to the seed for each new instance.
The versions that are not wrapped in classes are not thread-safe and should not
be used in multithreaded programs.</p>
<p>The file ex-ran.cpp contains an example of how to use the random number
generators. Try it!</p>
<h2>Portability</h2>
<p>The C++ class library is supposed to work with all C++ compilers and all
operating systems. It has been tested on several different systems.</p>
<p>There are, however, a few system differences that you need to be aware of:</p>
<ol>
<li>Floating point representation. Most systems store floating point
numbers according to the IEEE-754 standard with 64 bits for double precision. The fast conversion to floating point relies on this standard
format. A slightly less efficient method is used when floating point numbers
are not stored in a recognized format.</li>
<li>Integer word size. The C++ language syntax does not define a portable way
of defining integers with a specific number of bits. Therefore it is
necessary to use #if directives in randomc.h for platform-specific type
definitions. You may have to make additional type definitions for any
platform not covered by this file.</li>
</ol>
<h2>Theory</h2>
<p>The theory of the Mersenne twister is given in the article:<br>
M. Matsumoto & T. Nishimura: <i>"Mersenne Twister: A 623-Dimensionally
Equidistributed Uniform Pseudo-Random Number Generator".</i> ACM
Transactions on Modeling and Computer Simulation, vol. 8, no. 1, 1998, pp. 3-30.
See also <A href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/eindex.html">http://www.math.sci.hiroshima-u.ac.jp/~m-mat/eindex.html</A>.</p>
<p>The theory of Mother-of-All generators is given in George Marsaglia's DIEHARD
package, see <a href="http://stat.fsu.edu/~geo/diehard.html">stat.fsu.edu/~geo/diehard.html</a>
or <a href="http://www.cs.hku.hk/internet/randomCD.html">www.cs.hku.hk/internet/randomCD.html</a>.</p>
<h2>Copyright and licence</h2>
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