improved documentation (javadoc, code comments about optimization and userguide)
JIRA: MATH-419 git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@999577 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe
parent
669cdc6719
commit
62dc5114ec
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@ -26,7 +26,8 @@ import java.io.Serializable;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -36,23 +37,27 @@ import java.io.Serializable;
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public abstract class AbstractWell extends BitsStreamGenerator implements Serializable {
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/** Serializable version identifier. */
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private static final long serialVersionUID = -8068371019303673353L;
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/** Bit mask preserving the first w - p bits in a w bits block. */
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protected final int mp;
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/** Bit mask preserving the last p bits in a w bits block. */
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protected final int mpTilde;
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private static final long serialVersionUID = -817701723016583596L;
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/** Current index in the bytes pool. */
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protected int index;
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/** Bytes pool. */
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protected final int[] v;
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/** Index indirection table giving for each index its predecessor taking table size into account. */
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protected final int[] iRm1;
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/** Index indirection table giving for each index its second predecessor taking table size into account. */
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protected final int[] iRm2;
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/** Index indirection table giving for each index the value index + m1 taking table size into account. */
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protected final int[] i1;
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/** Index indirection table giving for each index the value index + m2 taking table size into account. */
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protected final int[] i2;
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/** Index indirection table giving for each index the value index + m3 taking table size into account. */
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protected final int[] i3;
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/** Creates a new random number generator.
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@ -93,15 +98,11 @@ public abstract class AbstractWell extends BitsStreamGenerator implements Serial
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// and p is the number of unused bits in the last block
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final int w = 32;
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final int r = (k + w - 1) / w;
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final int p = r * w - k;
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this.v = new int[r];
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this.index = 0;
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// set up generator parameters
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this.mp = (-1) << p;
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this.mpTilde = ~mp;
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this.v = new int[r];
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this.index = 0;
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// set up indirection indices
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// precompute indirection index tables. These tables are used for optimizing access
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// they allow saving computations like "(j + r - 2) % r" with costly modulo operations
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iRm1 = new int[r];
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iRm2 = new int[r];
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i1 = new int[r];
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@ -24,7 +24,8 @@ package org.apache.commons.math.random;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -82,7 +83,6 @@ public class Well1024a extends AbstractWell {
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protected int next(final int bits) {
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final int indexRm1 = iRm1[index];
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final int indexRm2 = iRm2[index];
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final int v0 = v[index];
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final int vM1 = v[i1[index]];
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@ -97,7 +97,6 @@ public class Well1024a extends AbstractWell {
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v[index] = z3;
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v[indexRm1] = z4;
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v[indexRm2] &= mp;
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index = indexRm1;
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return z4 >>> (32 - bits);
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@ -24,7 +24,8 @@ package org.apache.commons.math.random;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -97,7 +98,7 @@ public class Well19937a extends AbstractWell {
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v[index] = z3;
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v[indexRm1] = z4;
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v[indexRm2] &= mp;
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v[indexRm2] &= 0x80000000;
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index = indexRm1;
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return z4 >>> (32 - bits);
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@ -24,7 +24,8 @@ package org.apache.commons.math.random;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -97,7 +98,7 @@ public class Well19937c extends AbstractWell {
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v[index] = z3;
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v[indexRm1] = z4;
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v[indexRm2] &= mp;
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v[indexRm2] &= 0x80000000;
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index = indexRm1;
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@ -24,7 +24,8 @@ package org.apache.commons.math.random;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -89,6 +90,7 @@ public class Well44497a extends AbstractWell {
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final int vM2 = v[i2[index]];
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final int vM3 = v[i3[index]];
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// the values below include the errata of the original article
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final int z0 = (0xFFFF8000 & v[indexRm1]) ^ (0x00007FFF & v[indexRm2]);
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final int z1 = (v0 ^ (v0 << 24)) ^ (vM1 ^ (vM1 >>> 30));
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final int z2 = (vM2 ^ (vM2 << 10)) ^ (vM3 << 26);
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@ -99,7 +101,7 @@ public class Well44497a extends AbstractWell {
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v[index] = z3;
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v[indexRm1] = z4;
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v[indexRm2] &= mp;
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v[indexRm2] &= 0xFFFF8000;
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index = indexRm1;
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return z4 >>> (32 - bits);
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@ -24,7 +24,8 @@ package org.apache.commons.math.random;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -91,6 +92,7 @@ public class Well44497b extends AbstractWell {
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final int vM2 = v[i2[index]];
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final int vM3 = v[i3[index]];
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// the values below include the errata of the original article
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final int z0 = (0xFFFF8000 & v[indexRm1]) ^ (0x00007FFF & v[indexRm2]);
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final int z1 = (v0 ^ (v0 << 24)) ^ (vM1 ^ (vM1 >>> 30));
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final int z2 = (vM2 ^ (vM2 << 10)) ^ (vM3 << 26);
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@ -101,7 +103,7 @@ public class Well44497b extends AbstractWell {
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v[index] = z3;
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v[indexRm1] = z4;
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v[indexRm2] &= mp;
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v[indexRm2] &= 0xFFFF8000;
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index = indexRm1;
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// add Matsumoto-Kurita tempering
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@ -24,7 +24,8 @@ package org.apache.commons.math.random;
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* Pierre L'Ecuyer and Makoto Matsumoto <a
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* href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved
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* Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM
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* Transactions on Mathematical Software, 32, 1 (2006).</p>
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* Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper
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* are in <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.</p>
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* @see <a href="http://www.iro.umontreal.ca/~panneton/WELLRNG.html">WELL Random number generator</a>
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* @version $Revision$ $Date$
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@ -87,8 +88,8 @@ public class Well512a extends AbstractWell {
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final int vi1 = v[i1[index]];
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final int vi2 = v[i2[index]];
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final int z0 = v[indexRm1];
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// m3: x ^ ((t >= 0) ? (x >>> t) : (x << -t));
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// the values below include the errata of the original article
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final int z1 = (vi ^ (vi << 16)) ^ (vi1 ^ (vi1 << 15));
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final int z2 = vi2 ^ (vi2 >>> 11);
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final int z3 = z1 ^ z2;
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@ -16,5 +16,117 @@
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limitations under the License.
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-->
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<!-- $Revision$ $Date$ -->
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<body>Random number and random data generators.</body>
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<body>
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<p>Random number and random data generators.</p>
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<p>Commons-math provides a few pseudo random number generators. The top level interface is RandomGenerator.
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It is implemented by three classes:
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<ul>
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<li>{@link org.apache.commons.math.random.JDKRandomGenerator JDKRandomGenerator}
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that extends the JDK provided generator</li>
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<li>AbstractRandomGenerator as a helper for users generators</li>
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<li>BitStreamGenerator which is an abstract class for several generators and
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which in turn is extended by:
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<ul>
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<li>{@link org.apache.commons.math.random.MersenneTwister MersenneTwister}</li>
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<li>{@link org.apache.commons.math.random.Well512a Well512a}</li>
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<li>{@link org.apache.commons.math.random.Well1024a Well1024a}</li>
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<li>{@link org.apache.commons.math.random.Well19937a Well19937a}</li>
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<li>{@link org.apache.commons.math.random.Well19937c Well19937c}</li>
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<li>{@link org.apache.commons.math.random.Well44497a Well44497a}</li>
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<li>{@link org.apache.commons.math.random.Well44497b Well44497b}</li>
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</ul>
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</li>
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</ul>
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</p>
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<p>
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The JDK provided generator is a simple one that can be used only for very simple needs.
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The Mersenne Twister is a fast generator with very good properties well suited for
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Monte-Carlo simulation. It is equidistributed for generating vectors up to dimension 623
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and has a huge period: 2<sup>19937</sup> - 1 (which is a Mersenne prime). This generator
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is described in a paper by Makoto Matsumoto and Takuji Nishimura in 1998: <a
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href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf">Mersenne Twister:
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A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator</a>, ACM
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Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3--30.
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The WELL generators are a family of generators with period ranging from 2<sup>512</sup> - 1
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to 2<sup>44497</sup> - 1 (this last one is also a Mersenne prime) with even better properties
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than Mersenne Twister. These generators are described in a paper by François Panneton,
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Pierre L'Ecuyer and Makoto Matsumoto <a
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href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved Long-Period
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Generators Based on Linear Recurrences Modulo 2</a> ACM Transactions on Mathematical Software,
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32, 1 (2006). The errata for the paper are in <a
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href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>.
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</p>
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<p>
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For simple sampling, any of these generators is sufficient. For Monte-Carlo simulations the
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JDK generator does not have any of the good mathematical properties of the other generators,
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so it should be avoided. The Mersenne twister and WELL generators have equidistribution properties
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proven according to their bits pool size which is directly linked to their period (all of them
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have maximal period, i.e. a generator with size n pool has a period 2<sup>n</sup>-1). They also
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have equidistribution properties for 32 bits blocks up to s/32 dimension where s is their pool size.
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So WELL19937c for exemple is equidistributed up to dimension 623 (19937/32). This means a Monte-Carlo
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simulation generating a vector of n variables at each iteration has some guarantees on the properties
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of the vector as long as its dimension does not exceed the limit. However, since we use bits from two
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successive 32 bits generated integers to create one double, this limit is smaller when the variables are
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of type double. so for Monte-Carlo simulation where less the 16 doubles are generated at each round,
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WELL1024 may be sufficient. If a larger number of doubles are needed a generator with a larger pool
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would be useful.
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</p>
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<p>
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The WELL generators are more modern then MersenneTwister (the paper describing than has been published
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in 2006 instead of 1998) and fix some of its (few) drawbacks. If initialization array contains many
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zero bits, MersenneTwister may take a very long time (several hundreds of thousands of iterations to
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reach a steady state with a balanced number of zero and one in its bits pool). So the WELL generators
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are better to <i>escape zeroland</i> as explained by the WELL generators creators. The Well19937a and
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Well44497a generator are not maximally equidistributed (i.e. there are some dimensions or bits blocks
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size for which they are not equidistributed). The Well512a, Well1024a, Well19937c and Well44497b are
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maximally equidistributed for blocks size up to 32 bits (they should behave correctly also for double
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based on more than 32 bits blocks, but equidistribution is not proven at these blocks sizes).
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</p>
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<p>
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The MersenneTwister generator uses a 624 elements integer array, so it consumes less than 2.5 kilobytes.
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The WELL generators use 6 integer arrays with a size equal to the pool size, so for example the
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WELL44497b generator uses about 33 kilobytes. This may be important if a very large number of
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generator instances were used at the same time.
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</p>
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<p>
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All generators are quite fast. As an example, here are some comparisons, obtained on a 64 bits JVM on a
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linux computer with a 2008 processor (AMD phenom Quad 9550 at 2.2 GHz). The generation rate for
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MersenneTwister was about 27 millions doubles per second (remember we generate two 32 bits integers for
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each double). Generation rates for other PRNG, relative to MersenneTwister:
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</p>
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<p>
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<table border="1" align="center">
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<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example of performances</font></td></tr>
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<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation rate (relative to MersenneTwister)</td></font></tr>
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<tr><td>{@link org.apache.commons.math.random.MersenneTwister MersenneTwister}</td><td>1</td></tr>
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<tr><td>{@link org.apache.commons.math.random.JDKRandomGenerator JDKRandomGenerator}</td><td>between 0.96 and 1.16</td></tr>
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<tr><td>{@link org.apache.commons.math.random.Well512a Well512a}</td><td>between 0.85 and 0.88</td></tr>
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<tr><td>{@link org.apache.commons.math.random.Well1024a Well1024a}</td><td>between 0.63 and 0.73</td></tr>
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<tr><td>{@link org.apache.commons.math.random.Well19937a Well19937a}</td><td>between 0.70 and 0.71</td></tr>
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<tr><td>{@link org.apache.commons.math.random.Well19937c Well19937c}</td><td>between 0.57 and 0.71</td></tr>
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<tr><td>{@link org.apache.commons.math.random.Well44497a Well44497a}</td><td>between 0.69 and 0.71</td></tr>
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<tr><td>{@link org.apache.commons.math.random.Well44497b Well44497b}</td><td>between 0.65 and 0.71</td></tr>
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</table>
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</p>
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<p>
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So for most simulation problems, the better generators like {@link
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org.apache.commons.math.random.Well19937c Well19937c} and {@link
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org.apache.commons.math.random.Well44497b Well44497b} are probably very good choices.
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</p>
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<p>
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Note that <em>none</em> of these generators are suitable for cryptography. They are devoted
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to simulation, and to generate very long series with strong properties on the series as a whole
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(equidistribution, no correlation ...). They do not attempt to create small series but with
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very strong properties of unpredictability as needed in cryptography.
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</p>
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</body>
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</html>
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@ -71,7 +71,7 @@ The <action> type attribute can be add,update,fix,remove.
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</action>
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</release>
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<release version="2.2" date="TBD" description="TBD">
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<action dev="luc" type="add" >
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<action dev="luc" type="add" issue="MATH-419">
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Added new random number generators from the Well Equidistributed Long-period Linear (WELL).
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</action>
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<action dev="psteitz" type="update" issue="MATH-409">
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@ -317,6 +317,120 @@ for (int i = 0; i < 1000; i++) {
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<code>java.util.Random</code> and wraps and delegates calls to
|
||||
a <code>RandomGenerator</code> instance.
|
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</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 François 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>
|
||||
|
|
|
|||
Loading…
Reference in New Issue