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dl |
1.1 |
/* |
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jsr166 |
1.4 |
* %W% %E% |
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dl |
1.1 |
* |
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dl |
1.3 |
* Copyright 2003 Sun Microsystems, Inc. All rights reserved. |
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dl |
1.1 |
* SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms. |
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*/ |
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package java.util; |
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import java.io.*; |
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dl |
1.3 |
import java.util.concurrent.atomic.AtomicLong; |
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1.1 |
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/** |
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* An instance of this class is used to generate a stream of |
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* pseudorandom numbers. The class uses a 48-bit seed, which is |
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* modified using a linear congruential formula. (See Donald Knuth, |
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* <i>The Art of Computer Programming, Volume 2</i>, Section 3.2.1.) |
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* <p> |
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* If two instances of <code>Random</code> are created with the same |
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* seed, and the same sequence of method calls is made for each, they |
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* will generate and return identical sequences of numbers. In order to |
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* guarantee this property, particular algorithms are specified for the |
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* class <tt>Random</tt>. Java implementations must use all the algorithms |
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* shown here for the class <tt>Random</tt>, for the sake of absolute |
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* portability of Java code. However, subclasses of class <tt>Random</tt> |
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* are permitted to use other algorithms, so long as they adhere to the |
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* general contracts for all the methods. |
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* <p> |
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* The algorithms implemented by class <tt>Random</tt> use a |
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* <tt>protected</tt> utility method that on each invocation can supply |
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* up to 32 pseudorandomly generated bits. |
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* <p> |
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* Many applications will find the <code>random</code> method in |
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* class <code>Math</code> simpler to use. |
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* |
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* @author Frank Yellin |
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jsr166 |
1.4 |
* @version %I%, %G% |
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dl |
1.1 |
* @see java.lang.Math#random() |
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* @since JDK1.0 |
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*/ |
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public |
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class Random implements java.io.Serializable { |
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/** use serialVersionUID from JDK 1.1 for interoperability */ |
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static final long serialVersionUID = 3905348978240129619L; |
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/** |
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* The internal state associated with this pseudorandom number generator. |
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* (The specs for the methods in this class describe the ongoing |
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* computation of this value.) |
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* |
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* @serial |
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*/ |
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dl |
1.3 |
private AtomicLong seed; |
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dl |
1.1 |
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private final static long multiplier = 0x5DEECE66DL; |
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private final static long addend = 0xBL; |
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private final static long mask = (1L << 48) - 1; |
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jsr166 |
1.4 |
/** |
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* Creates a new random number generator. This constructor sets |
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* the seed of the random number generator to a value very likely |
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* to be distinct from any other invocation of this constructor. |
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dl |
1.1 |
*/ |
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jsr166 |
1.4 |
public Random() { this(++seedUniquifier + System.nanoTime()); } |
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private static volatile long seedUniquifier = 8682522807148012L; |
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dl |
1.1 |
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/** |
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* Creates a new random number generator using a single |
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* <code>long</code> seed: |
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* <blockquote><pre> |
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* public Random(long seed) { setSeed(seed); }</pre></blockquote> |
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* Used by method <tt>next</tt> to hold |
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* the state of the pseudorandom number generator. |
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* |
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* @param seed the initial seed. |
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* @see java.util.Random#setSeed(long) |
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*/ |
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public Random(long seed) { |
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dl |
1.3 |
this.seed = new AtomicLong(0L); |
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dl |
1.1 |
setSeed(seed); |
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} |
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/** |
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* Sets the seed of this random number generator using a single |
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* <code>long</code> seed. The general contract of <tt>setSeed</tt> |
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* is that it alters the state of this random number generator |
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* object so as to be in exactly the same state as if it had just |
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* been created with the argument <tt>seed</tt> as a seed. The method |
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* <tt>setSeed</tt> is implemented by class Random as follows: |
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* <blockquote><pre> |
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* synchronized public void setSeed(long seed) { |
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* this.seed = (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1); |
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* haveNextNextGaussian = false; |
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* }</pre></blockquote> |
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* The implementation of <tt>setSeed</tt> by class <tt>Random</tt> |
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* happens to use only 48 bits of the given seed. In general, however, |
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* an overriding method may use all 64 bits of the long argument |
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* as a seed value. |
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* |
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1.3 |
* Note: Although the seed value is an AtomicLong, this method |
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1.1 |
* must still be synchronized to ensure correct semantics |
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* of haveNextNextGaussian. |
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* |
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* @param seed the initial seed. |
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*/ |
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synchronized public void setSeed(long seed) { |
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dl |
1.3 |
seed = (seed ^ multiplier) & mask; |
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this.seed.set(seed); |
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dl |
1.1 |
haveNextNextGaussian = false; |
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} |
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/** |
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* Generates the next pseudorandom number. Subclass should |
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* override this, as this is used by all other methods.<p> |
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* The general contract of <tt>next</tt> is that it returns an |
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* <tt>int</tt> value and if the argument bits is between <tt>1</tt> |
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* and <tt>32</tt> (inclusive), then that many low-order bits of the |
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* returned value will be (approximately) independently chosen bit |
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* values, each of which is (approximately) equally likely to be |
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* <tt>0</tt> or <tt>1</tt>. The method <tt>next</tt> is implemented |
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* by class <tt>Random</tt> as follows: |
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* <blockquote><pre> |
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* synchronized protected int next(int bits) { |
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* seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1); |
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* return (int)(seed >>> (48 - bits)); |
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* }</pre></blockquote> |
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* This is a linear congruential pseudorandom number generator, as |
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* defined by D. H. Lehmer and described by Donald E. Knuth in <i>The |
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* Art of Computer Programming,</i> Volume 2: <i>Seminumerical |
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* Algorithms</i>, section 3.2.1. |
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* |
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* @param bits random bits |
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* @return the next pseudorandom value from this random number generator's sequence. |
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* @since JDK1.1 |
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*/ |
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protected int next(int bits) { |
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long oldseed, nextseed; |
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do { |
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jozart |
1.5 |
oldseed = seed.get(); |
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nextseed = (oldseed * multiplier + addend) & mask; |
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dl |
1.3 |
} while (!seed.compareAndSet(oldseed, nextseed)); |
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dl |
1.1 |
return (int)(nextseed >>> (48 - bits)); |
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} |
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private static final int BITS_PER_BYTE = 8; |
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private static final int BYTES_PER_INT = 4; |
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/** |
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* Generates random bytes and places them into a user-supplied |
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* byte array. The number of random bytes produced is equal to |
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* the length of the byte array. |
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* |
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* @param bytes the non-null byte array in which to put the |
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* random bytes. |
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* @since JDK1.1 |
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*/ |
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public void nextBytes(byte[] bytes) { |
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int numRequested = bytes.length; |
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int numGot = 0, rnd = 0; |
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while (true) { |
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for (int i = 0; i < BYTES_PER_INT; i++) { |
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if (numGot == numRequested) |
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return; |
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rnd = (i==0 ? next(BITS_PER_BYTE * BYTES_PER_INT) |
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: rnd >> BITS_PER_BYTE); |
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bytes[numGot++] = (byte)rnd; |
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} |
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} |
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} |
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/** |
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* Returns the next pseudorandom, uniformly distributed <code>int</code> |
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* value from this random number generator's sequence. The general |
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* contract of <tt>nextInt</tt> is that one <tt>int</tt> value is |
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* pseudorandomly generated and returned. All 2<font size="-1"><sup>32 |
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* </sup></font> possible <tt>int</tt> values are produced with |
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* (approximately) equal probability. The method <tt>nextInt</tt> is |
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* implemented by class <tt>Random</tt> as follows: |
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* <blockquote><pre> |
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* public int nextInt() { return next(32); }</pre></blockquote> |
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* |
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* @return the next pseudorandom, uniformly distributed <code>int</code> |
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* value from this random number generator's sequence. |
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*/ |
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public int nextInt() { return next(32); } |
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/** |
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* Returns a pseudorandom, uniformly distributed <tt>int</tt> value |
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* between 0 (inclusive) and the specified value (exclusive), drawn from |
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* this random number generator's sequence. The general contract of |
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* <tt>nextInt</tt> is that one <tt>int</tt> value in the specified range |
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* is pseudorandomly generated and returned. All <tt>n</tt> possible |
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* <tt>int</tt> values are produced with (approximately) equal |
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* probability. The method <tt>nextInt(int n)</tt> is implemented by |
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* class <tt>Random</tt> as follows: |
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* <blockquote><pre> |
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* public int nextInt(int n) { |
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* if (n<=0) |
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* throw new IllegalArgumentException("n must be positive"); |
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* |
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* if ((n & -n) == n) // i.e., n is a power of 2 |
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* return (int)((n * (long)next(31)) >> 31); |
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* |
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* int bits, val; |
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* do { |
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* bits = next(31); |
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* val = bits % n; |
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* } while(bits - val + (n-1) < 0); |
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* return val; |
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* } |
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* </pre></blockquote> |
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* <p> |
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* The hedge "approximately" is used in the foregoing description only |
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* because the next method is only approximately an unbiased source of |
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* independently chosen bits. If it were a perfect source of randomly |
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* chosen bits, then the algorithm shown would choose <tt>int</tt> |
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* values from the stated range with perfect uniformity. |
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* <p> |
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* The algorithm is slightly tricky. It rejects values that would result |
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* in an uneven distribution (due to the fact that 2^31 is not divisible |
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* by n). The probability of a value being rejected depends on n. The |
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* worst case is n=2^30+1, for which the probability of a reject is 1/2, |
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* and the expected number of iterations before the loop terminates is 2. |
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* <p> |
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* The algorithm treats the case where n is a power of two specially: it |
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* returns the correct number of high-order bits from the underlying |
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* pseudo-random number generator. In the absence of special treatment, |
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* the correct number of <i>low-order</i> bits would be returned. Linear |
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* congruential pseudo-random number generators such as the one |
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* implemented by this class are known to have short periods in the |
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* sequence of values of their low-order bits. Thus, this special case |
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* greatly increases the length of the sequence of values returned by |
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* successive calls to this method if n is a small power of two. |
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* |
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* @param n the bound on the random number to be returned. Must be |
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* positive. |
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* @return a pseudorandom, uniformly distributed <tt>int</tt> |
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* value between 0 (inclusive) and n (exclusive). |
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* @exception IllegalArgumentException n is not positive. |
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* @since 1.2 |
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*/ |
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public int nextInt(int n) { |
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if (n<=0) |
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throw new IllegalArgumentException("n must be positive"); |
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if ((n & -n) == n) // i.e., n is a power of 2 |
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return (int)((n * (long)next(31)) >> 31); |
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int bits, val; |
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do { |
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bits = next(31); |
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val = bits % n; |
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} while(bits - val + (n-1) < 0); |
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return val; |
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} |
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/** |
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* Returns the next pseudorandom, uniformly distributed <code>long</code> |
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* value from this random number generator's sequence. The general |
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* contract of <tt>nextLong</tt> is that one long value is pseudorandomly |
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* generated and returned. All 2<font size="-1"><sup>64</sup></font> |
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* possible <tt>long</tt> values are produced with (approximately) equal |
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* probability. The method <tt>nextLong</tt> is implemented by class |
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* <tt>Random</tt> as follows: |
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* <blockquote><pre> |
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* public long nextLong() { |
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* return ((long)next(32) << 32) + next(32); |
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* }</pre></blockquote> |
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* |
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* @return the next pseudorandom, uniformly distributed <code>long</code> |
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* value from this random number generator's sequence. |
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*/ |
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public long nextLong() { |
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// it's okay that the bottom word remains signed. |
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return ((long)(next(32)) << 32) + next(32); |
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} |
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/** |
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* Returns the next pseudorandom, uniformly distributed |
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* <code>boolean</code> value from this random number generator's |
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* sequence. The general contract of <tt>nextBoolean</tt> is that one |
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* <tt>boolean</tt> value is pseudorandomly generated and returned. The |
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* values <code>true</code> and <code>false</code> are produced with |
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* (approximately) equal probability. The method <tt>nextBoolean</tt> is |
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* implemented by class <tt>Random</tt> as follows: |
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* <blockquote><pre> |
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* public boolean nextBoolean() {return next(1) != 0;} |
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* </pre></blockquote> |
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* @return the next pseudorandom, uniformly distributed |
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* <code>boolean</code> value from this random number generator's |
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* sequence. |
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* @since 1.2 |
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*/ |
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public boolean nextBoolean() {return next(1) != 0;} |
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/** |
| 300 |
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* Returns the next pseudorandom, uniformly distributed <code>float</code> |
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* value between <code>0.0</code> and <code>1.0</code> from this random |
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* number generator's sequence. <p> |
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* The general contract of <tt>nextFloat</tt> is that one <tt>float</tt> |
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* value, chosen (approximately) uniformly from the range <tt>0.0f</tt> |
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* (inclusive) to <tt>1.0f</tt> (exclusive), is pseudorandomly |
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* generated and returned. All 2<font size="-1"><sup>24</sup></font> |
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* possible <tt>float</tt> values of the form |
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* <i>m x </i>2<font size="-1"><sup>-24</sup></font>, where |
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* <i>m</i> is a positive integer less than 2<font size="-1"><sup>24</sup> |
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* </font>, are produced with (approximately) equal probability. The |
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* method <tt>nextFloat</tt> is implemented by class <tt>Random</tt> as |
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* follows: |
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* <blockquote><pre> |
| 314 |
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* public float nextFloat() { |
| 315 |
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* return next(24) / ((float)(1 << 24)); |
| 316 |
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* }</pre></blockquote> |
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* The hedge "approximately" is used in the foregoing description only |
| 318 |
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* because the next method is only approximately an unbiased source of |
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* independently chosen bits. If it were a perfect source or randomly |
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* chosen bits, then the algorithm shown would choose <tt>float</tt> |
| 321 |
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* values from the stated range with perfect uniformity.<p> |
| 322 |
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* [In early versions of Java, the result was incorrectly calculated as: |
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* <blockquote><pre> |
| 324 |
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* return next(30) / ((float)(1 << 30));</pre></blockquote> |
| 325 |
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* This might seem to be equivalent, if not better, but in fact it |
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* introduced a slight nonuniformity because of the bias in the rounding |
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* of floating-point numbers: it was slightly more likely that the |
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* low-order bit of the significand would be 0 than that it would be 1.] |
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* |
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* @return the next pseudorandom, uniformly distributed <code>float</code> |
| 331 |
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* value between <code>0.0</code> and <code>1.0</code> from this |
| 332 |
|
|
* random number generator's sequence. |
| 333 |
|
|
*/ |
| 334 |
|
|
public float nextFloat() { |
| 335 |
|
|
int i = next(24); |
| 336 |
|
|
return i / ((float)(1 << 24)); |
| 337 |
|
|
} |
| 338 |
|
|
|
| 339 |
|
|
/** |
| 340 |
|
|
* Returns the next pseudorandom, uniformly distributed |
| 341 |
|
|
* <code>double</code> value between <code>0.0</code> and |
| 342 |
|
|
* <code>1.0</code> from this random number generator's sequence. <p> |
| 343 |
|
|
* The general contract of <tt>nextDouble</tt> is that one |
| 344 |
|
|
* <tt>double</tt> value, chosen (approximately) uniformly from the |
| 345 |
|
|
* range <tt>0.0d</tt> (inclusive) to <tt>1.0d</tt> (exclusive), is |
| 346 |
|
|
* pseudorandomly generated and returned. All |
| 347 |
|
|
* 2<font size="-1"><sup>53</sup></font> possible <tt>float</tt> |
| 348 |
|
|
* values of the form <i>m x </i>2<font size="-1"><sup>-53</sup> |
| 349 |
|
|
* </font>, where <i>m</i> is a positive integer less than |
| 350 |
|
|
* 2<font size="-1"><sup>53</sup></font>, are produced with |
| 351 |
|
|
* (approximately) equal probability. The method <tt>nextDouble</tt> is |
| 352 |
|
|
* implemented by class <tt>Random</tt> as follows: |
| 353 |
|
|
* <blockquote><pre> |
| 354 |
|
|
* public double nextDouble() { |
| 355 |
|
|
* return (((long)next(26) << 27) + next(27)) |
| 356 |
|
|
* / (double)(1L << 53); |
| 357 |
|
|
* }</pre></blockquote><p> |
| 358 |
|
|
* The hedge "approximately" is used in the foregoing description only |
| 359 |
|
|
* because the <tt>next</tt> method is only approximately an unbiased |
| 360 |
|
|
* source of independently chosen bits. If it were a perfect source or |
| 361 |
|
|
* randomly chosen bits, then the algorithm shown would choose |
| 362 |
|
|
* <tt>double</tt> values from the stated range with perfect uniformity. |
| 363 |
|
|
* <p>[In early versions of Java, the result was incorrectly calculated as: |
| 364 |
|
|
* <blockquote><pre> |
| 365 |
|
|
* return (((long)next(27) << 27) + next(27)) |
| 366 |
|
|
* / (double)(1L << 54);</pre></blockquote> |
| 367 |
|
|
* This might seem to be equivalent, if not better, but in fact it |
| 368 |
|
|
* introduced a large nonuniformity because of the bias in the rounding |
| 369 |
|
|
* of floating-point numbers: it was three times as likely that the |
| 370 |
|
|
* low-order bit of the significand would be 0 than that it would be |
| 371 |
|
|
* 1! This nonuniformity probably doesn't matter much in practice, but |
| 372 |
|
|
* we strive for perfection.] |
| 373 |
|
|
* |
| 374 |
|
|
* @return the next pseudorandom, uniformly distributed |
| 375 |
|
|
* <code>double</code> value between <code>0.0</code> and |
| 376 |
|
|
* <code>1.0</code> from this random number generator's sequence. |
| 377 |
|
|
*/ |
| 378 |
|
|
public double nextDouble() { |
| 379 |
|
|
long l = ((long)(next(26)) << 27) + next(27); |
| 380 |
|
|
return l / (double)(1L << 53); |
| 381 |
|
|
} |
| 382 |
|
|
|
| 383 |
|
|
private double nextNextGaussian; |
| 384 |
|
|
private boolean haveNextNextGaussian = false; |
| 385 |
|
|
|
| 386 |
|
|
/** |
| 387 |
|
|
* Returns the next pseudorandom, Gaussian ("normally") distributed |
| 388 |
|
|
* <code>double</code> value with mean <code>0.0</code> and standard |
| 389 |
|
|
* deviation <code>1.0</code> from this random number generator's sequence. |
| 390 |
|
|
* <p> |
| 391 |
|
|
* The general contract of <tt>nextGaussian</tt> is that one |
| 392 |
|
|
* <tt>double</tt> value, chosen from (approximately) the usual |
| 393 |
|
|
* normal distribution with mean <tt>0.0</tt> and standard deviation |
| 394 |
|
|
* <tt>1.0</tt>, is pseudorandomly generated and returned. The method |
| 395 |
|
|
* <tt>nextGaussian</tt> is implemented by class <tt>Random</tt> as follows: |
| 396 |
|
|
* <blockquote><pre> |
| 397 |
|
|
* synchronized public double nextGaussian() { |
| 398 |
|
|
* if (haveNextNextGaussian) { |
| 399 |
|
|
* haveNextNextGaussian = false; |
| 400 |
|
|
* return nextNextGaussian; |
| 401 |
|
|
* } else { |
| 402 |
|
|
* double v1, v2, s; |
| 403 |
|
|
* do { |
| 404 |
|
|
* v1 = 2 * nextDouble() - 1; // between -1.0 and 1.0 |
| 405 |
|
|
* v2 = 2 * nextDouble() - 1; // between -1.0 and 1.0 |
| 406 |
|
|
* s = v1 * v1 + v2 * v2; |
| 407 |
|
|
* } while (s >= 1 || s == 0); |
| 408 |
|
|
* double multiplier = Math.sqrt(-2 * Math.log(s)/s); |
| 409 |
|
|
* nextNextGaussian = v2 * multiplier; |
| 410 |
|
|
* haveNextNextGaussian = true; |
| 411 |
|
|
* return v1 * multiplier; |
| 412 |
|
|
* } |
| 413 |
|
|
* }</pre></blockquote> |
| 414 |
|
|
* This uses the <i>polar method</i> of G. E. P. Box, M. E. Muller, and |
| 415 |
|
|
* G. Marsaglia, as described by Donald E. Knuth in <i>The Art of |
| 416 |
|
|
* Computer Programming</i>, Volume 2: <i>Seminumerical Algorithms</i>, |
| 417 |
|
|
* section 3.4.1, subsection C, algorithm P. Note that it generates two |
| 418 |
|
|
* independent values at the cost of only one call to <tt>Math.log</tt> |
| 419 |
|
|
* and one call to <tt>Math.sqrt</tt>. |
| 420 |
|
|
* |
| 421 |
|
|
* @return the next pseudorandom, Gaussian ("normally") distributed |
| 422 |
|
|
* <code>double</code> value with mean <code>0.0</code> and |
| 423 |
|
|
* standard deviation <code>1.0</code> from this random number |
| 424 |
|
|
* generator's sequence. |
| 425 |
|
|
*/ |
| 426 |
|
|
synchronized public double nextGaussian() { |
| 427 |
|
|
// See Knuth, ACP, Section 3.4.1 Algorithm C. |
| 428 |
|
|
if (haveNextNextGaussian) { |
| 429 |
|
|
haveNextNextGaussian = false; |
| 430 |
|
|
return nextNextGaussian; |
| 431 |
|
|
} else { |
| 432 |
|
|
double v1, v2, s; |
| 433 |
|
|
do { |
| 434 |
|
|
v1 = 2 * nextDouble() - 1; // between -1 and 1 |
| 435 |
|
|
v2 = 2 * nextDouble() - 1; // between -1 and 1 |
| 436 |
|
|
s = v1 * v1 + v2 * v2; |
| 437 |
|
|
} while (s >= 1 || s == 0); |
| 438 |
|
|
double multiplier = Math.sqrt(-2 * Math.log(s)/s); |
| 439 |
|
|
nextNextGaussian = v2 * multiplier; |
| 440 |
|
|
haveNextNextGaussian = true; |
| 441 |
|
|
return v1 * multiplier; |
| 442 |
|
|
} |
| 443 |
|
|
} |
| 444 |
|
|
|
| 445 |
|
|
/** |
| 446 |
|
|
* Serializable fields for Random. |
| 447 |
|
|
* |
| 448 |
|
|
* @serialField seed long; |
| 449 |
|
|
* seed for random computations |
| 450 |
|
|
* @serialField nextNextGaussian double; |
| 451 |
|
|
* next Gaussian to be returned |
| 452 |
|
|
* @serialField haveNextNextGaussian boolean |
| 453 |
|
|
* nextNextGaussian is valid |
| 454 |
|
|
*/ |
| 455 |
|
|
private static final ObjectStreamField[] serialPersistentFields = { |
| 456 |
|
|
new ObjectStreamField("seed", Long.TYPE), |
| 457 |
|
|
new ObjectStreamField("nextNextGaussian", Double.TYPE), |
| 458 |
|
|
new ObjectStreamField("haveNextNextGaussian", Boolean.TYPE) |
| 459 |
|
|
}; |
| 460 |
|
|
|
| 461 |
|
|
/** |
| 462 |
|
|
* Reconstitute the <tt>Random</tt> instance from a stream (that is, |
| 463 |
|
|
* deserialize it). The seed is read in as long for |
| 464 |
|
|
* historical reasons, but it is converted to an AtomicLong. |
| 465 |
|
|
*/ |
| 466 |
|
|
private void readObject(java.io.ObjectInputStream s) |
| 467 |
|
|
throws java.io.IOException, ClassNotFoundException { |
| 468 |
|
|
|
| 469 |
|
|
ObjectInputStream.GetField fields = s.readFields(); |
| 470 |
|
|
long seedVal; |
| 471 |
|
|
|
| 472 |
|
|
seedVal = (long) fields.get("seed", -1L); |
| 473 |
|
|
if (seedVal < 0) |
| 474 |
|
|
throw new java.io.StreamCorruptedException( |
| 475 |
|
|
"Random: invalid seed"); |
| 476 |
dl |
1.3 |
seed = new AtomicLong(seedVal); |
| 477 |
dl |
1.1 |
nextNextGaussian = fields.get("nextNextGaussian", 0.0); |
| 478 |
|
|
haveNextNextGaussian = fields.get("haveNextNextGaussian", false); |
| 479 |
|
|
} |
| 480 |
|
|
|
| 481 |
|
|
|
| 482 |
|
|
/** |
| 483 |
|
|
* Save the <tt>Random</tt> instance to a stream. |
| 484 |
|
|
* The seed of a Random is serialized as a long for |
| 485 |
|
|
* historical reasons. |
| 486 |
|
|
* |
| 487 |
|
|
*/ |
| 488 |
|
|
synchronized private void writeObject(ObjectOutputStream s) throws IOException { |
| 489 |
|
|
// set the values of the Serializable fields |
| 490 |
|
|
ObjectOutputStream.PutField fields = s.putFields(); |
| 491 |
dl |
1.3 |
fields.put("seed", seed.get()); |
| 492 |
dl |
1.1 |
fields.put("nextNextGaussian", nextNextGaussian); |
| 493 |
|
|
fields.put("haveNextNextGaussian", haveNextNextGaussian); |
| 494 |
|
|
|
| 495 |
|
|
// save them |
| 496 |
|
|
s.writeFields(); |
| 497 |
|
|
|
| 498 |
|
|
} |
| 499 |
|
|
|
| 500 |
|
|
} |
