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MersenneTwister (Colt 1.2.0 - API Specification)
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cern.jet.random.engine</FONT>
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Class MersenneTwister</H2>
<PRE>
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">java.lang.Object</A>
<IMG SRC="../../../../resources/inherit.gif" ALT="extended by"><A HREF="../../../../cern/colt/PersistentObject.html" title="class in cern.colt">cern.colt.PersistentObject</A>
<IMG SRC="../../../../resources/inherit.gif" ALT="extended by"><A HREF="../../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">cern.jet.random.engine.RandomEngine</A>
<IMG SRC="../../../../resources/inherit.gif" ALT="extended by"><B>cern.jet.random.engine.MersenneTwister</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Cloneable.html" title="class or interface in java.lang">Cloneable</A>, <A HREF="../../../../cern/colt/function/DoubleFunction.html" title="interface in cern.colt.function">DoubleFunction</A>, <A HREF="../../../../cern/colt/function/IntFunction.html" title="interface in cern.colt.function">IntFunction</A>, <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/io/Serializable.html" title="class or interface in java.io">Serializable</A></DD>
</DL>
<DL>
<DT><B>Direct Known Subclasses:</B> <DD><A HREF="../../../../cern/jet/random/engine/MersenneTwister64.html" title="class in cern.jet.random.engine">MersenneTwister64</A></DD>
</DL>
<HR>
<DL>
<DT>public class <B>MersenneTwister</B><DT>extends <A HREF="../../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A></DL>
<P>
MersenneTwister (MT19937) is one of the strongest uniform pseudo-random number generators known so far; at the same time it is quick.
Produces uniformly distributed <tt>int</tt>'s and <tt>long</tt>'s in the closed intervals <tt>[Integer.MIN_VALUE,Integer.MAX_VALUE]</tt> and <tt>[Long.MIN_VALUE,Long.MAX_VALUE]</tt>, respectively,
as well as <tt>float</tt>'s and <tt>double</tt>'s in the open unit intervals <tt>(0.0f,1.0f)</tt> and <tt>(0.0,1.0)</tt>, respectively.
The seed can be any 32-bit integer except <tt>0</tt>. Shawn J. Cokus commented that perhaps the seed should preferably be odd.
<p>
<b>Quality:</b> MersenneTwister is designed to pass the k-distribution test. It has an astronomically large period of 2<sup>19937</sup>-1 (=10<sup>6001</sup>) and 623-dimensional equidistribution up to 32-bit accuracy.
It passes many stringent statistical tests, including the <A HREF="http://stat.fsu.edu/~geo/diehard.html">diehard</A> test of G. Marsaglia and the load test of P. Hellekalek and S. Wegenkittl.
<p>
<b>Performance:</b> Its speed is comparable to other modern generators (in particular, as fast as <tt>java.util.Random.nextFloat()</tt>).
2.5 million calls to <tt>raw()</tt> per second (Pentium Pro 200 Mhz, JDK 1.2, NT).
Be aware, however, that there is a non-negligible amount of overhead required to initialize the data
structures used by a MersenneTwister. Code like
<pre>
double sum = 0.0;
for (int i=0; i<100000; ++i) {
RandomElement twister = new MersenneTwister(new java.util.Date());
sum += twister.raw();
}
</pre>
will be wildly inefficient. Consider using
<pre>
double sum = 0.0;
RandomElement twister = new MersenneTwister(new java.util.Date());
for (int i=0; i<100000; ++i) {
sum += twister.raw();
}
</pre>
instead. This allows the cost of constructing the MersenneTwister object
to be borne only once, rather than once for each iteration in the loop.
<p>
<b>Implementation:</b> After M. Matsumoto and T. Nishimura,
"Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator",
ACM Transactions on Modeling and Computer Simulation,
Vol. 8, No. 1, January 1998, pp 3--30.
<dt>More info on <A HREF="http://www.math.keio.ac.jp/~matumoto/eindex.html"> Masumoto's homepage</A>.
<dt>More info on <A HREF="http://www.ncsa.uiuc.edu/Apps/CMP/RNG/www-rng.html"> Pseudo-random number generators is on the Web</A>.
<dt>Yet <A HREF="http://nhse.npac.syr.edu/random"> some more info</A>.
<p>
The correctness of this implementation has been verified against the published output sequence
<a href="http://www.math.keio.ac.jp/~nisimura/random/real2/mt19937-2.out">mt19937-2.out</a> of the C-implementation
<a href="http://www.math.keio.ac.jp/~nisimura/random/real2/mt19937-2.c">mt19937-2.c</a>.
(Call <tt>test(1000)</tt> to print the sequence).
<dt>
Note that this implementation is <b>not synchronized</b>.
<p>
<b>Details:</b> MersenneTwister is designed with consideration of the flaws of various existing generators in mind.
It is an improved version of TT800, a very successful generator.
MersenneTwister is based on linear recurrences modulo 2.
Such generators are very fast, have extremely long periods, and appear quite robust.
MersenneTwister produces 32-bit numbers, and every <tt>k</tt>-dimensional vector of such numbers appears the same number of times as <tt>k</tt> successive values over the
period length, for each <tt>k <= 623</tt> (except for the zero vector, which appears one time less).
If one looks at only the first <tt>n <= 16</tt> bits of each number, then the property holds for even larger <tt>k</tt>, as shown in the following table (taken from the publication cited above):
<div align="center">
<table width="75%" border="1" cellspacing="0" cellpadding="0">
<tr>
<td width="2%"> <div align="center">n</div> </td>
<td width="6%"> <div align="center">1</div> </td>
<td width="5%"> <div align="center">2</div> </td>
<td width="5%"> <div align="center">3</div> </td>
<td width="5%"> <div align="center">4</div> </td>
<td width="5%"> <div align="center">5</div> </td>
<td width="5%"> <div align="center">6</div> </td>
<td width="5%"> <div align="center">7</div> </td>
<td width="5%"> <div align="center">8</div> </td>
<td width="5%"> <div align="center">9</div> </td>
<td width="5%"> <div align="center">10</div> </td>
<td width="5%"> <div align="center">11</div> </td>
<td width="10%"> <div align="center">12 .. 16</div> </td>
<td width="10%"> <div align="center">17 .. 32</div> </td>
</tr>
<tr>
<td width="2%"> <div align="center">k</div> </td>
<td width="6%"> <div align="center">19937</div> </td>
<td width="5%"> <div align="center">9968</div> </td>
<td width="5%"> <div align="center">6240</div> </td>
<td width="5%"> <div align="center">4984</div> </td>
<td width="5%"> <div align="center">3738</div> </td>
<td width="5%"> <div align="center">3115</div> </td>
<td width="5%"> <div align="center">2493</div> </td>
<td width="5%"> <div align="center">2492</div> </td>
<td width="5%"> <div align="center">1869</div> </td>
<td width="5%"> <div align="center">1869</div> </td>
<td width="5%"> <div align="center">1248</div> </td>
<td width="10%"> <div align="center">1246</div> </td>
<td width="10%"> <div align="center">623</div> </td>
</tr>
</table>
</div>
<p>
MersenneTwister generates random numbers in batches of 624 numbers at a time, so the caching and pipelining of modern systems is exploited.
The generator is implemented to generate the output by using the fastest arithmetic operations only: 32-bit additions and bit operations (no division, no multiplication, no mod).
These operations generate sequences of 32 random bits (<tt>int</tt>'s).
<tt>long</tt>'s are formed by concatenating two 32 bit <tt>int</tt>'s.
<tt>float</tt>'s are formed by dividing the interval <tt>[0.0,1.0]</tt> into 2<sup>32</sup> sub intervals, then randomly choosing one subinterval.
<tt>double</tt>'s are formed by dividing the interval <tt>[0.0,1.0]</tt> into 2<sup>64</sup> sub intervals, then randomly choosing one subinterval.
<p>
<P>
<P>
<DL>
<DT><B>Version:</B></DT>
<DD>1.0, 09/24/99</DD>
<DT><B>See Also:</B><DD><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/util/Random.html" title="class or interface in java.util"><CODE>Random</CODE></A>,
<A HREF="../../../../serialized-form.html#cern.jet.random.engine.MersenneTwister">Serialized Form</A></DL>
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<CODE>static int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/jet/random/engine/MersenneTwister.html#DEFAULT_SEED">DEFAULT_SEED</A></B></CODE>
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<TD><CODE><B><A HREF="../../../../cern/jet/random/engine/MersenneTwister.html#MersenneTwister()">MersenneTwister</A></B>()</CODE>
<BR>
Constructs and returns a random number generator with a default seed, which is a <b>constant</b>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../cern/jet/random/engine/MersenneTwister.html#MersenneTwister(java.util.Date)">MersenneTwister</A></B>(<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/util/Date.html" title="class or interface in java.util">Date</A> d)</CODE>
<BR>
Constructs and returns a random number generator seeded with the given date.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../cern/jet/random/engine/MersenneTwister.html#MersenneTwister(int)">MersenneTwister</A></B>(int seed)</CODE>
<BR>
Constructs and returns a random number generator with the given seed.</TD>
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<CODE> <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">Object</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/jet/random/engine/MersenneTwister.html#clone()">clone</A></B>()</CODE>
<BR>
Returns a copy of the receiver; the copy will produce identical sequences.</TD>
</TR>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/jet/random/engine/MersenneTwister.html#nextInt()">nextInt</A></B>()</CODE>
<BR>
Returns a 32 bit uniformly distributed random number in the closed interval <tt>[Integer.MIN_VALUE,Integer.MAX_VALUE]</tt> (including <tt>Integer.MIN_VALUE</tt> and <tt>Integer.MAX_VALUE</tt>).</TD>
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<TD><CODE><A HREF="../../../../cern/jet/random/engine/RandomEngine.html#apply(double)">apply</A>, <A HREF="../../../../cern/jet/random/engine/RandomEngine.html#apply(int)">apply</A>, <A HREF="../../../../cern/jet/random/engine/RandomEngine.html#makeDefault()">makeDefault</A>, <A HREF="../../../../cern/jet/random/engine/RandomEngine.html#nextDouble()">nextDouble</A>, <A HREF="../../../../cern/jet/random/engine/RandomEngine.html#nextFloat()">nextFloat</A>, <A HREF="../../../../cern/jet/random/engine/RandomEngine.html#nextLong()">nextLong</A>, <A HREF="../../../../cern/jet/random/engine/RandomEngine.html#raw()">raw</A></CODE></TD>
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<A NAME="DEFAULT_SEED"><!-- --></A><H3>
DEFAULT_SEED</H3>
<PRE>
public static final int <B>DEFAULT_SEED</B></PRE>
<DL>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../constant-values.html#cern.jet.random.engine.MersenneTwister.DEFAULT_SEED">Constant Field Values</A></DL>
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<A NAME="MersenneTwister()"><!-- --></A><H3>
MersenneTwister</H3>
<PRE>
public <B>MersenneTwister</B>()</PRE>
<DL>
<DD>Constructs and returns a random number generator with a default seed, which is a <b>constant</b>.
Thus using this constructor will yield generators that always produce exactly the same sequence.
This method is mainly intended to ease testing and debugging.
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<A NAME="MersenneTwister(int)"><!-- --></A><H3>
MersenneTwister</H3>
<PRE>
public <B>MersenneTwister</B>(int seed)</PRE>
<DL>
<DD>Constructs and returns a random number generator with the given seed.
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<A NAME="MersenneTwister(java.util.Date)"><!-- --></A><H3>
MersenneTwister</H3>
<PRE>
public <B>MersenneTwister</B>(<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/util/Date.html" title="class or interface in java.util">Date</A> d)</PRE>
<DL>
<DD>Constructs and returns a random number generator seeded with the given date.
<P>
<DT><B>Parameters:</B><DD><CODE>d</CODE> - typically <tt>new java.util.Date()</tt></DL>
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<A NAME="clone()"><!-- --></A><H3>
clone</H3>
<PRE>
public <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">Object</A> <B>clone</B>()</PRE>
<DL>
<DD>Returns a copy of the receiver; the copy will produce identical sequences.
After this call has returned, the copy and the receiver have equal but separate state.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../cern/colt/PersistentObject.html#clone()">clone</A></CODE> in class <CODE><A HREF="../../../../cern/colt/PersistentObject.html" title="class in cern.colt">PersistentObject</A></CODE></DL>
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<DT><B>Returns:</B><DD>a copy of the receiver.</DL>
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<A NAME="nextInt()"><!-- --></A><H3>
nextInt</H3>
<PRE>
public int <B>nextInt</B>()</PRE>
<DL>
<DD>Returns a 32 bit uniformly distributed random number in the closed interval <tt>[Integer.MIN_VALUE,Integer.MAX_VALUE]</tt> (including <tt>Integer.MIN_VALUE</tt> and <tt>Integer.MAX_VALUE</tt>).
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../cern/jet/random/engine/RandomEngine.html#nextInt()">nextInt</A></CODE> in class <CODE><A HREF="../../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A></CODE></DL>
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