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From l..@apache.org
Subject svn commit: r999577 - in /commons/proper/math/trunk/src: main/java/org/apache/commons/math/random/ site/xdoc/ site/xdoc/userguide/
Date Tue, 21 Sep 2010 19:50:44 GMT
Author: luc
Date: Tue Sep 21 19:50:43 2010
New Revision: 999577

URL: http://svn.apache.org/viewvc?rev=999577&view=rev
Log:
improved documentation (javadoc, code comments about optimization and userguide)
JIRA: MATH-419

Modified:
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/AbstractWell.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well1024a.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937a.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937c.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497a.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497b.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well512a.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/package.html
    commons/proper/math/trunk/src/site/xdoc/changes.xml
    commons/proper/math/trunk/src/site/xdoc/userguide/random.xml

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/AbstractWell.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/AbstractWell.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/AbstractWell.java
(original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/AbstractWell.java
Tue Sep 21 19:50:43 2010
@@ -26,7 +26,8 @@ import java.io.Serializable;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -36,23 +37,27 @@ import java.io.Serializable;
 public abstract class AbstractWell extends BitsStreamGenerator implements Serializable {
 
     /** Serializable version identifier. */
-    private static final long serialVersionUID = -8068371019303673353L;
-
-    /** Bit mask preserving the first w - p bits in a w bits block. */
-    protected final int mp;
-
-    /** Bit mask preserving the last p bits in a w bits block. */
-    protected final int mpTilde;
+    private static final long serialVersionUID = -817701723016583596L;
 
     /** Current index in the bytes pool. */
     protected int index;
 
     /** Bytes pool. */
     protected final int[] v;
+
+    /** Index indirection table giving for each index its predecessor taking table size into
account. */
     protected final int[] iRm1;
+
+    /** Index indirection table giving for each index its second predecessor taking table
size into account. */
     protected final int[] iRm2;
+
+    /** Index indirection table giving for each index the value index + m1 taking table size
into account. */
     protected final int[] i1;
+
+    /** Index indirection table giving for each index the value index + m2 taking table size
into account. */
     protected final int[] i2;
+
+    /** Index indirection table giving for each index the value index + m3 taking table size
into account. */
     protected final int[] i3;
 
     /** Creates a new random number generator.
@@ -93,15 +98,11 @@ public abstract class AbstractWell exten
         // and p is the number of unused bits in the last block
         final int w = 32;
         final int r = (k + w - 1) / w;
-        final int p = r * w - k;
-
-        // set up  generator parameters
-        this.mp      = (-1) << p;
-        this.mpTilde = ~mp;
-        this.v       = new int[r];
-        this.index   = 0;
+        this.v      = new int[r];
+        this.index  = 0;
 
-        // set up indirection indices
+        // precompute indirection index tables. These tables are used for optimizing access
+        // they allow saving computations like "(j + r - 2) % r" with costly modulo operations
         iRm1 = new int[r];
         iRm2 = new int[r];
         i1   = new int[r];

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well1024a.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well1024a.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well1024a.java
(original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well1024a.java
Tue Sep 21 19:50:43 2010
@@ -24,7 +24,8 @@ package org.apache.commons.math.random;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -82,7 +83,6 @@ public class Well1024a extends AbstractW
     protected int next(final int bits) {
 
         final int indexRm1 = iRm1[index];
-        final int indexRm2 = iRm2[index];
 
         final int v0       = v[index];
         final int vM1      = v[i1[index]];
@@ -97,7 +97,6 @@ public class Well1024a extends AbstractW
 
         v[index]     = z3;
         v[indexRm1]  = z4;
-        v[indexRm2] &= mp;
         index        = indexRm1;
 
         return z4 >>> (32 - bits);

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937a.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937a.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937a.java
(original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937a.java
Tue Sep 21 19:50:43 2010
@@ -24,7 +24,8 @@ package org.apache.commons.math.random;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -97,7 +98,7 @@ public class Well19937a extends Abstract
 
         v[index]     = z3;
         v[indexRm1]  = z4;
-        v[indexRm2] &= mp;
+        v[indexRm2] &= 0x80000000;
         index        = indexRm1;
 
         return z4 >>> (32 - bits);

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937c.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937c.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937c.java
(original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well19937c.java
Tue Sep 21 19:50:43 2010
@@ -24,7 +24,8 @@ package org.apache.commons.math.random;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -97,7 +98,7 @@ public class Well19937c extends Abstract
 
         v[index]     = z3;
         v[indexRm1]  = z4;
-        v[indexRm2] &= mp;
+        v[indexRm2] &= 0x80000000;
         index        = indexRm1;
 
 

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497a.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497a.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497a.java
(original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497a.java
Tue Sep 21 19:50:43 2010
@@ -24,7 +24,8 @@ package org.apache.commons.math.random;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -89,6 +90,7 @@ public class Well44497a extends Abstract
         final int vM2      = v[i2[index]];
         final int vM3      = v[i3[index]];
 
+        // the values below include the errata of the original article
         final int z0       = (0xFFFF8000 & v[indexRm1]) ^ (0x00007FFF & v[indexRm2]);
         final int z1       = (v0 ^ (v0 << 24))  ^ (vM1 ^ (vM1 >>> 30));
         final int z2       = (vM2 ^ (vM2 << 10)) ^ (vM3 << 26);
@@ -99,7 +101,7 @@ public class Well44497a extends Abstract
 
         v[index]     = z3;
         v[indexRm1]  = z4;
-        v[indexRm2] &= mp;
+        v[indexRm2] &= 0xFFFF8000;
         index        = indexRm1;
 
         return z4 >>> (32 - bits);

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497b.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497b.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497b.java
(original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well44497b.java
Tue Sep 21 19:50:43 2010
@@ -24,7 +24,8 @@ package org.apache.commons.math.random;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -91,6 +92,7 @@ public class Well44497b extends Abstract
         final int vM2      = v[i2[index]];
         final int vM3      = v[i3[index]];
 
+        // the values below include the errata of the original article
         final int z0       = (0xFFFF8000 & v[indexRm1]) ^ (0x00007FFF & v[indexRm2]);
         final int z1       = (v0 ^ (v0 << 24))  ^ (vM1 ^ (vM1 >>> 30));
         final int z2       = (vM2 ^ (vM2 << 10)) ^ (vM3 << 26);
@@ -101,7 +103,7 @@ public class Well44497b extends Abstract
 
         v[index]     = z3;
         v[indexRm1]  = z4;
-        v[indexRm2] &= mp;
+        v[indexRm2] &= 0xFFFF8000;
         index        = indexRm1;
 
         // add Matsumoto-Kurita tempering

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well512a.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well512a.java?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well512a.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/Well512a.java Tue
Sep 21 19:50:43 2010
@@ -24,7 +24,8 @@ package org.apache.commons.math.random;
  * Pierre L'Ecuyer and Makoto Matsumoto <a
  * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
  * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
- * Transactions on Mathematical Software, 32, 1 (2006).</p>
+ * Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
+ * are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
 
  * @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number
generator</a>
  * @version $Revision$ $Date$
@@ -87,8 +88,8 @@ public class Well512a extends AbstractWe
         final int vi1 = v[i1[index]];
         final int vi2 = v[i2[index]];
         final int z0 = v[indexRm1];
-        // m3: x ^ ((t >= 0) ? (x >>> t) : (x << -t));
 
+        // the values below include the errata of the original article
         final int z1 = (vi ^ (vi << 16))   ^ (vi1 ^ (vi1 << 15));
         final int z2 = vi2 ^ (vi2 >>> 11);
         final int z3 = z1 ^ z2;

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/package.html
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/package.html?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/package.html (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/random/package.html Tue
Sep 21 19:50:43 2010
@@ -16,5 +16,117 @@
    limitations under the License.
   -->
     <!-- $Revision$ $Date$ -->
-    <body>Random number and random data generators.</body>
+    <body>
+      <p>Random number and random data generators.</p>
+      <p>Commons-math provides a few pseudo random number generators. The top level
interface is RandomGenerator.
+      It is implemented by three classes:
+      <ul>
+        <li>{@link org.apache.commons.math.random.JDKRandomGenerator JDKRandomGenerator}
+            that extends the JDK provided generator</li>
+        <li>AbstractRandomGenerator as a helper for users generators</li>
+        <li>BitStreamGenerator which is an abstract class for several generators and
+            which in turn is extended by:
+            <ul>
+              <li>{@link org.apache.commons.math.random.MersenneTwister MersenneTwister}</li>
+              <li>{@link org.apache.commons.math.random.Well512a Well512a}</li>
+              <li>{@link org.apache.commons.math.random.Well1024a Well1024a}</li>
+              <li>{@link org.apache.commons.math.random.Well19937a Well19937a}</li>
+              <li>{@link org.apache.commons.math.random.Well19937c Well19937c}</li>
+              <li>{@link org.apache.commons.math.random.Well44497a Well44497a}</li>
+              <li>{@link org.apache.commons.math.random.Well44497b Well44497b}</li>
+            </ul>
+          </li>
+        </ul>
+      </p>
+
+      <p>
+      The JDK provided generator is a simple one that can be used only for very simple needs.
+      The Mersenne Twister is a fast generator with very good properties well suited for
+      Monte-Carlo simulation. It is equidistributed for generating vectors up to dimension
623
+      and has a huge period: 2<sup>19937</sup> - 1 (which is a Mersenne prime).
This generator
+      is described in a paper by Makoto Matsumoto and Takuji Nishimura in 1998: <a
+      href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf">Mersenne
Twister:
+      A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator</a>,
ACM
+      Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3--30.
+      The WELL generators are a family of generators with period ranging from 2<sup>512</sup>
- 1
+      to 2<sup>44497</sup> - 1 (this last one is also a Mersenne prime) with
even better properties
+      than Mersenne Twister. These generators are described in a paper by Fran&ccedil;ois
Panneton,
+      Pierre L'Ecuyer and Makoto Matsumoto <a
+      href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved Long-Period
+      Generators Based on Linear Recurrences Modulo 2</a> ACM Transactions on Mathematical
Software,
+      32, 1 (2006). The errata for the paper are in <a
+      href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.
+      </p>
+
+      <p>
+      For simple sampling, any of these generators is sufficient. For Monte-Carlo simulations
the
+      JDK generator does not have any of the good mathematical properties of the other generators,
+      so it should be avoided. The Mersenne twister and WELL generators have equidistribution
properties
+      proven according to their bits pool size which is directly linked to their period (all
of them
+      have maximal period, i.e. a generator with size n pool has a period 2<sup>n</sup>-1).
They also
+      have equidistribution properties for 32 bits blocks up to s/32 dimension where s is
their pool size.
+      So WELL19937c for exemple is equidistributed up to dimension 623 (19937/32). This means
a Monte-Carlo
+      simulation generating a vector of n variables at each iteration has some guarantees
on the properties
+      of the vector as long as its dimension does not exceed the limit. However, since we
use bits from two
+      successive 32 bits generated integers to create one double, this limit is smaller when
the variables are
+      of type double. so for Monte-Carlo simulation where less the 16 doubles are generated
at each round,
+      WELL1024 may be sufficient. If a larger number of doubles are needed a generator with
a larger pool
+      would be useful.
+      </p>
+
+      <p>
+      The WELL generators are more modern then MersenneTwister (the paper describing than
has been published
+      in 2006 instead of 1998) and fix some of its (few) drawbacks. If initialization array
contains many
+      zero bits, MersenneTwister may take a very long time (several hundreds of thousands
of iterations to
+      reach a steady state with a balanced number of zero and one in its bits pool). So the
WELL generators
+      are better to <i>escape zeroland</i> as explained by the WELL generators
creators. The Well19937a and
+      Well44497a generator are not maximally equidistributed (i.e. there are some dimensions
or bits blocks
+      size for which they are not equidistributed). The Well512a, Well1024a, Well19937c and
Well44497b are
+      maximally equidistributed for blocks size up to 32 bits (they should behave correctly
also for double
+      based on more than 32 bits blocks, but equidistribution is not proven at these blocks
sizes).
+      </p>
+
+      <p>
+      The MersenneTwister generator uses a 624 elements integer array, so it consumes less
than 2.5 kilobytes.
+      The WELL generators use 6 integer arrays with a size equal to the pool size, so for
example the
+      WELL44497b generator uses about 33 kilobytes. This may be important if a very large
number of
+      generator instances were used at the same time.
+      </p> 
+
+      <p>
+      All generators are quite fast. As an example, here are some comparisons, obtained on
a 64 bits JVM on a
+      linux computer with a 2008 processor (AMD phenom Quad 9550 at 2.2 GHz). The generation
rate for
+      MersenneTwister was about 27 millions doubles per second (remember we generate two
32 bits integers for
+      each double). Generation rates for other PRNG, relative to MersenneTwister:
+      </p>
+
+      <p>
+        <table border="1" align="center">
+          <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example
of performances</font></td></tr>
+          <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation
rate (relative to MersenneTwister)</td></font></tr>
+          <tr><td>{@link org.apache.commons.math.random.MersenneTwister MersenneTwister}</td><td>1</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.JDKRandomGenerator JDKRandomGenerator}</td><td>between
0.96 and 1.16</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.Well512a Well512a}</td><td>between
0.85 and 0.88</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.Well1024a Well1024a}</td><td>between
0.63 and 0.73</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.Well19937a Well19937a}</td><td>between
0.70 and 0.71</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.Well19937c Well19937c}</td><td>between
0.57 and 0.71</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.Well44497a Well44497a}</td><td>between
0.69 and 0.71</td></tr>
+          <tr><td>{@link org.apache.commons.math.random.Well44497b Well44497b}</td><td>between
0.65 and 0.71</td></tr>
+        </table>
+      </p>
+
+      <p>
+      So for most simulation problems, the better generators like {@link
+      org.apache.commons.math.random.Well19937c Well19937c} and {@link
+      org.apache.commons.math.random.Well44497b Well44497b} are probably very good choices.
+      </p>
+
+      <p>
+      Note that <em>none</em> of these generators are suitable for cryptography.
They are devoted
+      to simulation, and to generate very long series with strong properties on the series
as a whole
+      (equidistribution, no correlation ...). They do not attempt to create small series
but with
+      very strong properties of unpredictability as needed in cryptography.
+      </p>
+
+    </body>
 </html>

Modified: commons/proper/math/trunk/src/site/xdoc/changes.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/xdoc/changes.xml?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/xdoc/changes.xml (original)
+++ commons/proper/math/trunk/src/site/xdoc/changes.xml Tue Sep 21 19:50:43 2010
@@ -71,7 +71,7 @@ The <action> type attribute can be add,u
       </action>
     </release>
     <release version="2.2" date="TBD" description="TBD">
-      <action dev="luc" type="add" >
+      <action dev="luc" type="add" issue="MATH-419">
         Added new random number generators from the Well Equidistributed Long-period Linear
(WELL).
       </action>
       <action dev="psteitz" type="update" issue="MATH-409">

Modified: commons/proper/math/trunk/src/site/xdoc/userguide/random.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/xdoc/userguide/random.xml?rev=999577&r1=999576&r2=999577&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/xdoc/userguide/random.xml (original)
+++ commons/proper/math/trunk/src/site/xdoc/userguide/random.xml Tue Sep 21 19:50:43 2010
@@ -317,6 +317,120 @@ for (int i = 0; i &lt; 1000; i++) {
       <code>java.util.Random</code> and wraps and delegates calls to
       a <code>RandomGenerator</code> instance.   
   </p>
+
+      <p>Commons-math provides by itself several implementations of the <a
+      href="../apidocs/org/apache/commons/math/random/RandomGenerator.html">
+      RandomGenerator</a> interface:
+      <ul>
+        <li><a href="../apidocs/org/apache/commons/math/random/JDKRandomGenerator.html">JDKRandomGenerator</a>
+            that extends the JDK provided generator</li>
+        <li><a href="../apidocs/org/apache/commons/math/random/AbstractRandomGenerator.html">
+            AbstractRandomGenerator</a> as a helper for users generators</li>
+        <li><a href="../apidocs/org/apache/commons/math/random/BitStreamGenerator.html">
+            BitStreamGenerator</a> which is an abstract class for several generators
and
+            which in turn is extended by:
+            <ul>
+              <li><a href="../apidocs/org/apache/commons/math/random/MersenneTwister.html">MersenneTwister</a></li>
+              <li><a href="../apidocs/org/apache/commons/math/random/Well512a.html">Well512a</a></li>
+              <li><a href="../apidocs/org/apache/commons/math/random/Well1024a.html">Well1024a</a></li>
+              <li><a href="../apidocs/org/apache/commons/math/random/Well19937a.html">Well19937a</a></li>
+              <li><a href="../apidocs/org/apache/commons/math/random/Well19937c.html">Well19937c</a></li>
+              <li><a href="../apidocs/org/apache/commons/math/random/Well44497a.html">Well44497a</a></li>
+              <li><a href="../apidocs/org/apache/commons/math/random/Well44497b.html">Well44497b</a></li>
+            </ul>
+          </li>
+        </ul>
+      </p>
+
+      <p>
+      The JDK provided generator is a simple one that can be used only for very simple needs.
+      The Mersenne Twister is a fast generator with very good properties well suited for
+      Monte-Carlo simulation. It is equidistributed for generating vectors up to dimension
623
+      and has a huge period: 2<sup>19937</sup> - 1 (which is a Mersenne prime).
This generator
+      is described in a paper by Makoto Matsumoto and Takuji Nishimura in 1998: <a
+      href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf">Mersenne
Twister:
+      A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator</a>,
ACM
+      Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3--30.
+      The WELL generators are a family of generators with period ranging from 2<sup>512</sup>
- 1
+      to 2<sup>44497</sup> - 1 (this last one is also a Mersenne prime) with
even better properties
+      than Mersenne Twister. These generators are described in a paper by Fran&#231;ois
Panneton,
+      Pierre L'Ecuyer and Makoto Matsumoto <a
+      href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved Long-Period
+      Generators Based on Linear Recurrences Modulo 2</a> ACM Transactions on Mathematical
Software,
+      32, 1 (2006). The errata for the paper are in <a
+      href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.
+      </p>
+
+      <p>
+      For simple sampling, any of these generators is sufficient. For Monte-Carlo simulations
the
+      JDK generator does not have any of the good mathematical properties of the other generators,
+      so it should be avoided. The Mersenne twister and WELL generators have equidistribution
properties
+      proven according to their bits pool size which is directly linked to their period (all
of them
+      have maximal period, i.e. a generator with size n pool has a period 2<sup>n</sup>-1).
They also
+      have equidistribution properties for 32 bits blocks up to s/32 dimension where s is
their pool size.
+      So WELL19937c for exemple is equidistributed up to dimension 623 (19937/32). This means
a Monte-Carlo
+      simulation generating a vector of n variables at each iteration has some guarantees
on the properties
+      of the vector as long as its dimension does not exceed the limit. However, since we
use bits from two
+      successive 32 bits generated integers to create one double, this limit is smaller when
the variables are
+      of type double. so for Monte-Carlo simulation where less the 16 doubles are generated
at each round,
+      WELL1024 may be sufficient. If a larger number of doubles are needed a generator with
a larger pool
+      would be useful.
+      </p>
+
+      <p>
+      The WELL generators are more modern then MersenneTwister (the paper describing than
has been published
+      in 2006 instead of 1998) and fix some of its (few) drawbacks. If initialization array
contains many
+      zero bits, MersenneTwister may take a very long time (several hundreds of thousands
of iterations to
+      reach a steady state with a balanced number of zero and one in its bits pool). So the
WELL generators
+      are better to <i>escape zeroland</i> as explained by the WELL generators
creators. The Well19937a and
+      Well44497a generator are not maximally equidistributed (i.e. there are some dimensions
or bits blocks
+      size for which they are not equidistributed). The Well512a, Well1024a, Well19937c and
Well44497b are
+      maximally equidistributed for blocks size up to 32 bits (they should behave correctly
also for double
+      based on more than 32 bits blocks, but equidistribution is not proven at these blocks
sizes).
+      </p>
+
+      <p>
+      The MersenneTwister generator uses a 624 elements integer array, so it consumes less
than 2.5 kilobytes.
+      The WELL generators use 6 integer arrays with a size equal to the pool size, so for
example the
+      WELL44497b generator uses about 33 kilobytes. This may be important if a very large
number of
+      generator instances were used at the same time.
+      </p> 
+
+      <p>
+      All generators are quite fast. As an example, here are some comparisons, obtained on
a 64 bits JVM on a
+      linux computer with a 2008 processor (AMD phenom Quad 9550 at 2.2 GHz). The generation
rate for
+      MersenneTwister was between 25 and 27 millions doubles per second (remember we generate
two 32 bits integers for
+      each double). Generation rates for other PRNG, relative to MersenneTwister:
+      </p>
+
+      <p>
+        <table border="1" align="center">
+          <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example
of performances</font></td></tr>
+          <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation
rate (relative to MersenneTwister)</td></font></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/MersenneTwister.html">MersenneTwister</a></td><td>1</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/JDKRandomGenerator.html">JDKRandomGenerator</a></td><td>between
0.96 and 1.16</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/Well512a.html">Well512a</a></td><td>between
0.85 and 0.88</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/Well1024a.html">Well1024a</a></td><td>between
0.63 and 0.73</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/Well19937a.html">Well19937a</a></td><td>between
0.70 and 0.71</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/Well19937c.html">Well19937c</a></td><td>between
0.57 and 0.71</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/Well44497a.html">Well44497a</a></td><td>between
0.69 and 0.71</td></tr>
+          <tr><td><a href="../apidocs/org/apache/commons/math/random/Well44497b.html">Well44497b</a></td><td>between
0.65 and 0.71</td></tr>
+        </table>
+      </p>
+
+      <p>
+      So for most simulation problems, the better generators like <a
+      href="../apidocs/org/apache/commons/math/random/Well19937c.html">Well19937c</a>
and <a
+      href="../apidocs/org/apache/commons/math/random/Well44497b.html">Well44497b</a>
are probably very good choices.
+      </p>
+
+      <p>
+      Note that <em>none</em> of these generators are suitable for cryptography.
They are devoted
+      to simulation, and to generate very long series with strong properties on the series
as a whole
+      (equidistribution, no correlation ...). They do not attempt to create small series
but with
+      very strong properties of unpredictability as needed in cryptography.
+      </p>
+
   <p>
      Examples:
      <dl>



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