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<div class="subTitle">org.apache.mahout.math.jet.random.engine</div>
<h2 title="Class MersenneTwister" class="title">Class MersenneTwister</h2>
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<pre>public final class <span class="typeNameLabel">MersenneTwister</span>
extends <a href="../../../../../../../org/apache/mahout/math/jet/random/engine/RandomEngine.html" title="class in org.apache.mahout.math.jet.random.engine">RandomEngine</a></pre>
<div class="block">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
<code>double sum = 0.0;
for (int i=0; i&lt;100000; ++i) {
RandomElement twister = new MersenneTwister(new Date());
sum += twister.raw();
}
</code>
will be wildly inefficient. Consider using
<code>double sum = 0.0;
RandomElement twister = new MersenneTwister(new Date());
for (int i=0; i&amp;lt;100000; ++i) {
sum += twister.raw();
}
</code>
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.
<dl>
<dt>More info on <a HREF="http://www.math.keio.ac.jp/~matumoto/eindex.html"> Masumoto's homepage</a>.</dt>
<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>
<dt>Yet <a HREF="http://nhse.npac.syr.edu/random"> some more info</a>.</dt>
<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>.</dt>
</dl>
<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 &lt;= 623</tt> (except for the zero vector, which appears one time less).
If one looks at only the first <tt>n &lt;= 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):
<table width="75%" border="1" cellspacing="0" cellpadding="0" summary="property table">
<tr>
<td width="2%" align="center"> <div>n</div> </td>
<td width="6%" align="center"> <div>1</div> </td>
<td width="5%" align="center"> <div>2</div> </td>
<td width="5%" align="center"> <div>3</div> </td>
<td width="5%" align="center"> <div>4</div> </td>
<td width="5%" align="center"> <div>5</div> </td>
<td width="5%" align="center"> <div>6</div> </td>
<td width="5%" align="center"> <div>7</div> </td>
<td width="5%" align="center"> <div>8</div> </td>
<td width="5%" align="center"> <div>9</div> </td>
<td width="5%" align="center"> <div>10</div> </td>
<td width="5%" align="center"> <div>11</div> </td>
<td width="10%" align="center"> <div>12 .. 16</div> </td>
<td width="10%" align="center"> <div>17 .. 32</div> </td>
</tr>
<tr>
<td width="2%" align="center"> <div>k</div> </td>
<td width="6%" align="center"> <div>19937</div> </td>
<td width="5%" align="center"> <div>9968</div> </td>
<td width="5%" align="center"> <div>6240</div> </td>
<td width="5%" align="center"> <div>4984</div> </td>
<td width="5%" align="center"> <div>3738</div> </td>
<td width="5%" align="center"> <div>3115</div> </td>
<td width="5%" align="center"> <div>2493</div> </td>
<td width="5%" align="center"> <div>2492</div> </td>
<td width="5%" align="center"> <div>1869</div> </td>
<td width="5%" align="center"> <div>1869</div> </td>
<td width="5%" align="center"> <div>1248</div> </td>
<td width="10%" align="center"> <div>1246</div> </td>
<td width="10%" align="center"> <div>623</div> </td>
</tr>
</table>
<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></div>
<dl>
<dt><span class="simpleTagLabel">Version:</span></dt>
<dd>1.0, 09/24/99</dd>
<dt><span class="simpleTagLabel">Author:</span></dt>
<dd>wolfgang.hoschek@cern.ch</dd>
<dt><span class="seeLabel">See Also:</span></dt>
<dd><a href="http://docs.oracle.com/javase/7/docs/api/java/util/Random.html?is-external=true" title="class or interface in java.util"><code>Random</code></a></dd>
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<td class="colOne"><code><span class="memberNameLink"><a href="../../../../../../../org/apache/mahout/math/jet/random/engine/MersenneTwister.html#MersenneTwister--">MersenneTwister</a></span>()</code>
<div class="block">Constructs and returns a random number generator with a default seed, which is a <b>constant</b>.</div>
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<td class="colOne"><code><span class="memberNameLink"><a href="../../../../../../../org/apache/mahout/math/jet/random/engine/MersenneTwister.html#MersenneTwister-java.util.Date-">MersenneTwister</a></span>(<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Date.html?is-external=true" title="class or interface in java.util">Date</a>&nbsp;d)</code>
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<td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../../org/apache/mahout/math/jet/random/engine/MersenneTwister.html#nextInt--">nextInt</a></span>()</code>
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<pre>public&nbsp;MersenneTwister()</pre>
<div class="block">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.</div>
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<pre>public&nbsp;MersenneTwister(int&nbsp;seed)</pre>
<div class="block">Constructs and returns a random number generator with the given seed.</div>
<dl>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>seed</code> - A number that is used to initialize the internal state of the generator.</dd>
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<pre>public&nbsp;MersenneTwister(<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Date.html?is-external=true" title="class or interface in java.util">Date</a>&nbsp;d)</pre>
<div class="block">Constructs and returns a random number generator seeded with the given date.</div>
<dl>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>d</code> - typically <tt>new Date()</tt></dd>
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<pre>public&nbsp;int&nbsp;nextInt()</pre>
<div class="block">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>).</div>
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<dt><span class="returnLabel">Returns:</span></dt>
<dd>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>);</dd>
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