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/* |
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* @(#)Random.java 1.46 05/11/30 |
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* |
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* Copyright 2006 Sun Microsystems, Inc. All rights reserved. |
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* SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms. |
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*/ |
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|
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package java.util; |
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import java.io.*; |
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import java.util.concurrent.atomic.AtomicLong; |
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import sun.misc.Unsafe; |
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|
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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 3</i>, Section 3.2.1.) |
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* <p> |
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* If two instances of {@code Random} 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 {@code Random}. Java implementations must use all the algorithms |
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* shown here for the class {@code Random}, for the sake of absolute |
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* portability of Java code. However, subclasses of class {@code Random} |
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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 {@code Random} use a |
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* {@code protected} 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 method {@link Math#random} simpler to use. |
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* |
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* @author Frank Yellin |
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* @version 1.46, 11/30/05 |
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* @since 1.0 |
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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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/** |
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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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private final AtomicLong seed; |
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|
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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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|
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/** |
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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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*/ |
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public Random() { this(++seedUniquifier + System.nanoTime()); } |
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private static volatile long seedUniquifier = 8682522807148012L; |
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|
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/** |
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* Creates a new random number generator using a single {@code long} seed. |
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* The seed is the initial value of the internal state of the pseudorandom |
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* number generator which is maintained by method {@link #next}. |
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* |
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* <p>The invocation {@code new Random(seed)} is equivalent to: |
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* <pre> {@code |
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* Random rnd = new Random(); |
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* rnd.setSeed(seed);}</pre> |
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* |
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* @param seed the initial seed |
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* @see #setSeed(long) |
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*/ |
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public Random(long seed) { |
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this.seed = new AtomicLong(0L); |
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setSeed(seed); |
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} |
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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} seed. The general contract of {@code setSeed} is |
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* that it alters the state of this random number generator object |
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* so as to be in exactly the same state as if it had just been |
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* created with the argument {@code seed} as a seed. The method |
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* {@code setSeed} is implemented by class {@code Random} by |
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* atomically updating the seed to |
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* <pre>{@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}</pre> |
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* and clearing the {@code haveNextNextGaussian} flag used by {@link |
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* #nextGaussian}. |
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* |
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* <p>The implementation of {@code setSeed} by class {@code Random} |
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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 {@code long} |
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* argument as a seed value. |
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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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seed = (seed ^ multiplier) & mask; |
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this.seed.set(seed); |
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haveNextNextGaussian = false; |
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} |
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|
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/** |
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* Generates the next pseudorandom number. Subclasses should |
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* override this, as this is used by all other methods. |
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* |
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* <p>The general contract of {@code next} is that it returns an |
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* {@code int} value and if the argument {@code bits} is between |
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* {@code 1} and {@code 32} (inclusive), then that many low-order |
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* bits of the returned value will be (approximately) independently |
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* chosen bit values, each of which is (approximately) equally |
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* likely to be {@code 0} or {@code 1}. The method {@code next} is |
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* implemented by class {@code Random} by atomically updating the seed to |
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* <pre>{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}</pre> |
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* and returning |
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* <pre>{@code (int)(seed >>> (48 - bits))}.</pre> |
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* |
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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 |
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* <i>The Art of Computer Programming,</i> Volume 3: |
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* <i>Seminumerical 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 |
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* generator's sequence |
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* @since 1.1 |
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*/ |
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protected int next(int bits) { |
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long oldseed, nextseed; |
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AtomicLong seed = this.seed; |
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do { |
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oldseed = seed.get(); |
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nextseed = (oldseed * multiplier + addend) & mask; |
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} while (!seed.compareAndSet(oldseed, nextseed)); |
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return (int)(nextseed >>> (48 - bits)); |
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} |
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|
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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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* <p>The method {@code nextBytes} is implemented by class {@code Random} |
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* as if by: |
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* <pre> {@code |
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* public void nextBytes(byte[] bytes) { |
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* for (int i = 0; i < bytes.length; ) |
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* for (int rnd = nextInt(), n = Math.min(bytes.length - i, 4); |
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* n-- > 0; rnd >>= 8) |
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* bytes[i++] = (byte)rnd; |
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* }}</pre> |
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* |
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* @param bytes the byte array to fill with random bytes |
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* @throws NullPointerException if the byte array is null |
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* @since 1.1 |
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*/ |
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public void nextBytes(byte[] bytes) { |
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for (int i = 0, len = bytes.length; i < len; ) |
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for (int rnd = nextInt(), |
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n = Math.min(len - i, Integer.SIZE/Byte.SIZE); |
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n-- > 0; rnd >>= Byte.SIZE) |
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bytes[i++] = (byte)rnd; |
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} |
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|
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/** |
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* Returns the next pseudorandom, uniformly distributed {@code int} |
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* value from this random number generator's sequence. The general |
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* contract of {@code nextInt} is that one {@code int} value is |
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* pseudorandomly generated and returned. All 2<font size="-1"><sup>32 |
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* </sup></font> possible {@code int} values are produced with |
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* (approximately) equal probability. |
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* |
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* <p>The method {@code nextInt} is implemented by class {@code Random} |
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* as if by: |
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* <pre> {@code |
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* public int nextInt() { |
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* return next(32); |
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* }}</pre> |
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* |
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* @return the next pseudorandom, uniformly distributed {@code int} |
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* value from this random number generator's sequence |
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*/ |
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public int nextInt() { |
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return next(32); |
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} |
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|
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/** |
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* Returns a pseudorandom, uniformly distributed {@code int} 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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* {@code nextInt} is that one {@code int} value in the specified range |
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* is pseudorandomly generated and returned. All {@code n} possible |
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* {@code int} values are produced with (approximately) equal |
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* probability. The method {@code nextInt(int n)} is implemented by |
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* class {@code Random} as if by: |
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* <pre> {@code |
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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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* }}</pre> |
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* |
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* <p>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 {@code int} |
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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 the next pseudorandom, uniformly distributed {@code int} |
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* value between {@code 0} (inclusive) and {@code n} (exclusive) |
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* from this random number generator's sequence |
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* @exception IllegalArgumentException if n is not positive |
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* @since 1.2 |
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*/ |
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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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|
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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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|
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/** |
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* Returns the next pseudorandom, uniformly distributed {@code long} |
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* value from this random number generator's sequence. The general |
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* contract of {@code nextLong} is that one {@code long} value is |
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* pseudorandomly generated and returned. |
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* |
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* <p>The method {@code nextLong} is implemented by class {@code Random} |
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* as if by: |
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* <pre> {@code |
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* public long nextLong() { |
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* return ((long)next(32) << 32) + next(32); |
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* }}</pre> |
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* |
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* Because class {@code Random} uses a seed with only 48 bits, |
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* this algorithm will not return all possible {@code long} values. |
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* |
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* @return the next pseudorandom, uniformly distributed {@code long} |
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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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/** |
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* Returns the next pseudorandom, uniformly distributed |
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* {@code boolean} value from this random number generator's |
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* sequence. The general contract of {@code nextBoolean} is that one |
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* {@code boolean} value is pseudorandomly generated and returned. The |
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* values {@code true} and {@code false} are produced with |
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* (approximately) equal probability. |
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* |
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* <p>The method {@code nextBoolean} is implemented by class {@code Random} |
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* as if by: |
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* <pre> {@code |
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* public boolean nextBoolean() { |
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* return next(1) != 0; |
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* }}</pre> |
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* |
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* @return the next pseudorandom, uniformly distributed |
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* {@code boolean} 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() { |
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return next(1) != 0; |
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} |
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|
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/** |
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* Returns the next pseudorandom, uniformly distributed {@code float} |
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* value between {@code 0.0} and {@code 1.0} from this random |
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* number generator's sequence. |
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* |
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* <p>The general contract of {@code nextFloat} is that one |
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* {@code float} value, chosen (approximately) uniformly from the |
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* range {@code 0.0f} (inclusive) to {@code 1.0f} (exclusive), is |
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* pseudorandomly generated and returned. All 2<font |
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* size="-1"><sup>24</sup></font> possible {@code float} values |
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* of the form <i>m x </i>2<font |
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* size="-1"><sup>-24</sup></font>, where <i>m</i> is a positive |
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* integer less than 2<font size="-1"><sup>24</sup> </font>, are |
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* produced with (approximately) equal probability. |
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* |
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* <p>The method {@code nextFloat} is implemented by class {@code Random} |
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* as if by: |
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* <pre> {@code |
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* public float nextFloat() { |
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* return next(24) / ((float)(1 << 24)); |
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* }}</pre> |
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* |
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* <p>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 {@code float} |
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* values from the stated range with perfect uniformity.<p> |
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* [In early versions of Java, the result was incorrectly calculated as: |
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* <pre> {@code |
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* return next(30) / ((float)(1 << 30));}</pre> |
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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} |
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* value between {@code 0.0} and {@code 1.0} from this |
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* random number generator's sequence |
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*/ |
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public float nextFloat() { |
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return next(24) / ((float)(1 << 24)); |
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} |
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|
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/** |
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* Returns the next pseudorandom, uniformly distributed |
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* {@code double} value between {@code 0.0} and |
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* {@code 1.0} from this random number generator's sequence. |
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* |
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* <p>The general contract of {@code nextDouble} is that one |
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* {@code double} value, chosen (approximately) uniformly from the |
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* range {@code 0.0d} (inclusive) to {@code 1.0d} (exclusive), is |
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* pseudorandomly generated and returned. |
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* |
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* <p>The method {@code nextDouble} is implemented by class {@code Random} |
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* as if by: |
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* <pre> {@code |
| 367 |
* public double nextDouble() { |
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* return (((long)next(26) << 27) + next(27)) |
| 369 |
* / (double)(1L << 53); |
| 370 |
* }}</pre> |
| 371 |
* |
| 372 |
* <p>The hedge "approximately" is used in the foregoing description only |
| 373 |
* because the {@code next} method is only approximately an unbiased |
| 374 |
* source of independently chosen bits. If it were a perfect source of |
| 375 |
* randomly chosen bits, then the algorithm shown would choose |
| 376 |
* {@code double} values from the stated range with perfect uniformity. |
| 377 |
* <p>[In early versions of Java, the result was incorrectly calculated as: |
| 378 |
* <pre> {@code |
| 379 |
* return (((long)next(27) << 27) + next(27)) |
| 380 |
* / (double)(1L << 54);}</pre> |
| 381 |
* This might seem to be equivalent, if not better, but in fact it |
| 382 |
* introduced a large nonuniformity because of the bias in the rounding |
| 383 |
* of floating-point numbers: it was three times as likely that the |
| 384 |
* low-order bit of the significand would be 0 than that it would be 1! |
| 385 |
* This nonuniformity probably doesn't matter much in practice, but we |
| 386 |
* strive for perfection.] |
| 387 |
* |
| 388 |
* @return the next pseudorandom, uniformly distributed {@code double} |
| 389 |
* value between {@code 0.0} and {@code 1.0} from this |
| 390 |
* random number generator's sequence |
| 391 |
* @see Math#random |
| 392 |
*/ |
| 393 |
public double nextDouble() { |
| 394 |
return (((long)(next(26)) << 27) + next(27)) |
| 395 |
/ (double)(1L << 53); |
| 396 |
} |
| 397 |
|
| 398 |
private double nextNextGaussian; |
| 399 |
private boolean haveNextNextGaussian = false; |
| 400 |
|
| 401 |
/** |
| 402 |
* Returns the next pseudorandom, Gaussian ("normally") distributed |
| 403 |
* {@code double} value with mean {@code 0.0} and standard |
| 404 |
* deviation {@code 1.0} from this random number generator's sequence. |
| 405 |
* <p> |
| 406 |
* The general contract of {@code nextGaussian} is that one |
| 407 |
* {@code double} value, chosen from (approximately) the usual |
| 408 |
* normal distribution with mean {@code 0.0} and standard deviation |
| 409 |
* {@code 1.0}, is pseudorandomly generated and returned. |
| 410 |
* |
| 411 |
* <p>The method {@code nextGaussian} is implemented by class |
| 412 |
* {@code Random} as if by a threadsafe version of the following: |
| 413 |
* <pre> {@code |
| 414 |
* private double nextNextGaussian; |
| 415 |
* private boolean haveNextNextGaussian = false; |
| 416 |
* |
| 417 |
* public double nextGaussian() { |
| 418 |
* if (haveNextNextGaussian) { |
| 419 |
* haveNextNextGaussian = false; |
| 420 |
* return nextNextGaussian; |
| 421 |
* } else { |
| 422 |
* double v1, v2, s; |
| 423 |
* do { |
| 424 |
* v1 = 2 * nextDouble() - 1; // between -1.0 and 1.0 |
| 425 |
* v2 = 2 * nextDouble() - 1; // between -1.0 and 1.0 |
| 426 |
* s = v1 * v1 + v2 * v2; |
| 427 |
* } while (s >= 1 || s == 0); |
| 428 |
* double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s); |
| 429 |
* nextNextGaussian = v2 * multiplier; |
| 430 |
* haveNextNextGaussian = true; |
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* return v1 * multiplier; |
| 432 |
* } |
| 433 |
* }}</pre> |
| 434 |
* This uses the <i>polar method</i> of G. E. P. Box, M. E. Muller, and |
| 435 |
* G. Marsaglia, as described by Donald E. Knuth in <i>The Art of |
| 436 |
* Computer Programming</i>, Volume 3: <i>Seminumerical Algorithms</i>, |
| 437 |
* section 3.4.1, subsection C, algorithm P. Note that it generates two |
| 438 |
* independent values at the cost of only one call to {@code StrictMath.log} |
| 439 |
* and one call to {@code StrictMath.sqrt}. |
| 440 |
* |
| 441 |
* @return the next pseudorandom, Gaussian ("normally") distributed |
| 442 |
* {@code double} value with mean {@code 0.0} and |
| 443 |
* standard deviation {@code 1.0} from this random number |
| 444 |
* generator's sequence |
| 445 |
*/ |
| 446 |
synchronized public double nextGaussian() { |
| 447 |
// See Knuth, ACP, Section 3.4.1 Algorithm C. |
| 448 |
if (haveNextNextGaussian) { |
| 449 |
haveNextNextGaussian = false; |
| 450 |
return nextNextGaussian; |
| 451 |
} else { |
| 452 |
double v1, v2, s; |
| 453 |
do { |
| 454 |
v1 = 2 * nextDouble() - 1; // between -1 and 1 |
| 455 |
v2 = 2 * nextDouble() - 1; // between -1 and 1 |
| 456 |
s = v1 * v1 + v2 * v2; |
| 457 |
} while (s >= 1 || s == 0); |
| 458 |
double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s); |
| 459 |
nextNextGaussian = v2 * multiplier; |
| 460 |
haveNextNextGaussian = true; |
| 461 |
return v1 * multiplier; |
| 462 |
} |
| 463 |
} |
| 464 |
|
| 465 |
/** |
| 466 |
* Serializable fields for Random. |
| 467 |
* |
| 468 |
* @serialField seed long; |
| 469 |
* seed for random computations |
| 470 |
* @serialField nextNextGaussian double; |
| 471 |
* next Gaussian to be returned |
| 472 |
* @serialField haveNextNextGaussian boolean |
| 473 |
* nextNextGaussian is valid |
| 474 |
*/ |
| 475 |
private static final ObjectStreamField[] serialPersistentFields = { |
| 476 |
new ObjectStreamField("seed", Long.TYPE), |
| 477 |
new ObjectStreamField("nextNextGaussian", Double.TYPE), |
| 478 |
new ObjectStreamField("haveNextNextGaussian", Boolean.TYPE) |
| 479 |
}; |
| 480 |
|
| 481 |
/** |
| 482 |
* Reconstitute the {@code Random} instance from a stream (that is, |
| 483 |
* deserialize it). |
| 484 |
*/ |
| 485 |
private void readObject(java.io.ObjectInputStream s) |
| 486 |
throws java.io.IOException, ClassNotFoundException { |
| 487 |
|
| 488 |
ObjectInputStream.GetField fields = s.readFields(); |
| 489 |
|
| 490 |
// The seed is read in as {@code long} for |
| 491 |
// historical reasons, but it is converted to an AtomicLong. |
| 492 |
long seedVal = (long) fields.get("seed", -1L); |
| 493 |
if (seedVal < 0) |
| 494 |
throw new java.io.StreamCorruptedException( |
| 495 |
"Random: invalid seed"); |
| 496 |
resetSeed(seedVal); |
| 497 |
nextNextGaussian = fields.get("nextNextGaussian", 0.0); |
| 498 |
haveNextNextGaussian = fields.get("haveNextNextGaussian", false); |
| 499 |
} |
| 500 |
|
| 501 |
/** |
| 502 |
* Save the {@code Random} instance to a stream. |
| 503 |
*/ |
| 504 |
synchronized private void writeObject(ObjectOutputStream s) |
| 505 |
throws IOException { |
| 506 |
|
| 507 |
// set the values of the Serializable fields |
| 508 |
ObjectOutputStream.PutField fields = s.putFields(); |
| 509 |
|
| 510 |
// The seed is serialized as a long for historical reasons. |
| 511 |
fields.put("seed", seed.get()); |
| 512 |
fields.put("nextNextGaussian", nextNextGaussian); |
| 513 |
fields.put("haveNextNextGaussian", haveNextNextGaussian); |
| 514 |
|
| 515 |
// save them |
| 516 |
s.writeFields(); |
| 517 |
} |
| 518 |
|
| 519 |
// Support for resetting seed while deserializing |
| 520 |
private static final Unsafe unsafe = Unsafe.getUnsafe(); |
| 521 |
private static final long seedOffset; |
| 522 |
static { |
| 523 |
try { |
| 524 |
seedOffset = unsafe.objectFieldOffset |
| 525 |
(Random.class.getDeclaredField("seed")); |
| 526 |
} catch (Exception ex) { throw new Error(ex); } |
| 527 |
} |
| 528 |
private void resetSeed(long seedVal) { |
| 529 |
unsafe.putObjectVolatile(this, seedOffset, new AtomicLong(seedVal)); |
| 530 |
} |
| 531 |
|
| 532 |
} |
