| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| /** |
| * |
| * <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.math3.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.math3.random.MersenneTwister MersenneTwister}</li> |
| * <li>{@link org.apache.commons.math3.random.Well512a Well512a}</li> |
| * <li>{@link org.apache.commons.math3.random.Well1024a Well1024a}</li> |
| * <li>{@link org.apache.commons.math3.random.Well19937a Well19937a}</li> |
| * <li>{@link org.apache.commons.math3.random.Well19937c Well19937c}</li> |
| * <li>{@link org.apache.commons.math3.random.Well44497a Well44497a}</li> |
| * <li>{@link org.apache.commons.math3.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 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 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.math3.random.MersenneTwister MersenneTwister}</td><td>1</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.random.JDKRandomGenerator JDKRandomGenerator}</td><td>between 0.96 and 1.16</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.random.Well512a Well512a}</td><td>between 0.85 and 0.88</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.random.Well1024a Well1024a}</td><td>between 0.63 and 0.73</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.random.Well19937a Well19937a}</td><td>between 0.70 and 0.71</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.random.Well19937c Well19937c}</td><td>between 0.57 and 0.71</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.random.Well44497a Well44497a}</td><td>between 0.69 and 0.71</td></tr> |
| * <tr><td>{@link org.apache.commons.math3.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.math3.random.Well19937c Well19937c} and {@link |
| * org.apache.commons.math3.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> |
| * |
| * |
| */ |
| package org.apache.commons.math3.random; |
