| Random.java |
1 /*
2 * %W% %E%
3 *
4 * Copyright (c) 2006, Oracle and/or its affiliates. All rights reserved.
5 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
6 */
7
8 package java.util;
9 import java.io.*;
10 import java.util.concurrent.atomic.AtomicLong;
11 import sun.misc.Unsafe;
12
13 /**
14 * An instance of this class is used to generate a stream of
15 * pseudorandom numbers. The class uses a 48-bit seed, which is
16 * modified using a linear congruential formula. (See Donald Knuth,
17 * <i>The Art of Computer Programming, Volume 3</i>, Section 3.2.1.)
18 * <p>
19 * If two instances of {@code Random} are created with the same
20 * seed, and the same sequence of method calls is made for each, they
21 * will generate and return identical sequences of numbers. In order to
22 * guarantee this property, particular algorithms are specified for the
23 * class {@code Random}. Java implementations must use all the algorithms
24 * shown here for the class {@code Random}, for the sake of absolute
25 * portability of Java code. However, subclasses of class {@code Random}
26 * are permitted to use other algorithms, so long as they adhere to the
27 * general contracts for all the methods.
28 * <p>
29 * The algorithms implemented by class {@code Random} use a
30 * {@code protected} utility method that on each invocation can supply
31 * up to 32 pseudorandomly generated bits.
32 * <p>
33 * Many applications will find the method {@link Math#random} simpler to use.
34 *
35 * @author Frank Yellin
36 * @version %I%, %G%
37 * @since 1.0
38 */
39 public
40 class Random implements java.io.Serializable {
41 /** use serialVersionUID from JDK 1.1 for interoperability */
42 static final long serialVersionUID = 3905348978240129619L;
43
44 /**
45 * The internal state associated with this pseudorandom number generator.
46 * (The specs for the methods in this class describe the ongoing
47 * computation of this value.)
48 *
49 * @serial
50 */
51 private final AtomicLong seed;
52
53 private final static long multiplier = 0x5DEECE66DL;
54 private final static long addend = 0xBL;
55 private final static long mask = (1L << 48) - 1;
56
57 /**
58 * Creates a new random number generator. This constructor sets
59 * the seed of the random number generator to a value very likely
60 * to be distinct from any other invocation of this constructor.
61 */
62 public Random() { this(++seedUniquifier + System.nanoTime()); }
63 private static volatile long seedUniquifier = 8682522807148012L;
64
65 /**
66 * Creates a new random number generator using a single {@code long} seed.
67 * The seed is the initial value of the internal state of the pseudorandom
68 * number generator which is maintained by method {@link #next}.
69 *
70 * <p>The invocation {@code new Random(seed)} is equivalent to:
71 * <pre> {@code
72 * Random rnd = new Random();
73 * rnd.setSeed(seed);}</pre>
74 *
75 * @param seed the initial seed
76 * @see #setSeed(long)
77 */
78 public Random(long seed) {
79 this.seed = new AtomicLong(0L);
80 setSeed(seed);
81 }
82
83 /**
84 * Sets the seed of this random number generator using a single
85 * {@code long} seed. The general contract of {@code setSeed} is
86 * that it alters the state of this random number generator object
87 * so as to be in exactly the same state as if it had just been
88 * created with the argument {@code seed} as a seed. The method
89 * {@code setSeed} is implemented by class {@code Random} by
90 * atomically updating the seed to
91 * <pre>{@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}</pre>
92 * and clearing the {@code haveNextNextGaussian} flag used by {@link
93 * #nextGaussian}.
94 *
95 * <p>The implementation of {@code setSeed} by class {@code Random}
96 * happens to use only 48 bits of the given seed. In general, however,
97 * an overriding method may use all 64 bits of the {@code long}
98 * argument as a seed value.
99 *
100 * @param seed the initial seed
101 */
102 synchronized public void setSeed(long seed) {
103 seed = (seed ^ multiplier) & mask;
104 this.seed.set(seed);
105 haveNextNextGaussian = false;
106 }
107
108 /**
109 * Generates the next pseudorandom number. Subclasses should
110 * override this, as this is used by all other methods.
111 *
112 * <p>The general contract of {@code next} is that it returns an
113 * {@code int} value and if the argument {@code bits} is between
114 * {@code 1} and {@code 32} (inclusive), then that many low-order
115 * bits of the returned value will be (approximately) independently
116 * chosen bit values, each of which is (approximately) equally
117 * likely to be {@code 0} or {@code 1}. The method {@code next} is
118 * implemented by class {@code Random} by atomically updating the seed to
119 * <pre>{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}</pre>
120 * and returning
121 * <pre>{@code (int)(seed >>> (48 - bits))}.</pre>
122 *
123 * This is a linear congruential pseudorandom number generator, as
124 * defined by D. H. Lehmer and described by Donald E. Knuth in
125 * <i>The Art of Computer Programming,</i> Volume 3:
126 * <i>Seminumerical Algorithms</i>, section 3.2.1.
127 *
128 * @param bits random bits
129 * @return the next pseudorandom value from this random number
130 * generator's sequence
131 * @since 1.1
132 */
133 protected int next(int bits) {
134 long oldseed, nextseed;
135 AtomicLong seed = this.seed;
136 do {
137 oldseed = seed.get();
138 nextseed = (oldseed * multiplier + addend) & mask;
139 } while (!seed.compareAndSet(oldseed, nextseed));
140 return (int)(nextseed >>> (48 - bits));
141 }
142
143 /**
144 * Generates random bytes and places them into a user-supplied
145 * byte array. The number of random bytes produced is equal to
146 * the length of the byte array.
147 *
148 * <p>The method {@code nextBytes} is implemented by class {@code Random}
149 * as if by:
150 * <pre> {@code
151 * public void nextBytes(byte[] bytes) {
152 * for (int i = 0; i < bytes.length; )
153 * for (int rnd = nextInt(), n = Math.min(bytes.length - i, 4);
154 * n-- > 0; rnd >>= 8)
155 * bytes[i++] = (byte)rnd;
156 * }}</pre>
157 *
158 * @param bytes the byte array to fill with random bytes
159 * @throws NullPointerException if the byte array is null
160 * @since 1.1
161 */
162 public void nextBytes(byte[] bytes) {
163 for (int i = 0, len = bytes.length; i < len; )
164 for (int rnd = nextInt(),
165 n = Math.min(len - i, Integer.SIZE/Byte.SIZE);
166 n-- > 0; rnd >>= Byte.SIZE)
167 bytes[i++] = (byte)rnd;
168 }
169
170 /**
171 * Returns the next pseudorandom, uniformly distributed {@code int}
172 * value from this random number generator's sequence. The general
173 * contract of {@code nextInt} is that one {@code int} value is
174 * pseudorandomly generated and returned. All 2<font size="-1"><sup>32
175 * </sup></font> possible {@code int} values are produced with
176 * (approximately) equal probability.
177 *
178 * <p>The method {@code nextInt} is implemented by class {@code Random}
179 * as if by:
180 * <pre> {@code
181 * public int nextInt() {
182 * return next(32);
183 * }}</pre>
184 *
185 * @return the next pseudorandom, uniformly distributed {@code int}
186 * value from this random number generator's sequence
187 */
188 public int nextInt() {
189 return next(32);
190 }
191
192 /**
193 * Returns a pseudorandom, uniformly distributed {@code int} value
194 * between 0 (inclusive) and the specified value (exclusive), drawn from
195 * this random number generator's sequence. The general contract of
196 * {@code nextInt} is that one {@code int} value in the specified range
197 * is pseudorandomly generated and returned. All {@code n} possible
198 * {@code int} values are produced with (approximately) equal
199 * probability. The method {@code nextInt(int n)} is implemented by
200 * class {@code Random} as if by:
201 * <pre> {@code
202 * public int nextInt(int n) {
203 * if (n <= 0)
204 * throw new IllegalArgumentException("n must be positive");
205 *
206 * if ((n & -n) == n) // i.e., n is a power of 2
207 * return (int)((n * (long)next(31)) >> 31);
208 *
209 * int bits, val;
210 * do {
211 * bits = next(31);
212 * val = bits % n;
213 * } while (bits - val + (n-1) < 0);
214 * return val;
215 * }}</pre>
216 *
217 * <p>The hedge "approximately" is used in the foregoing description only
218 * because the next method is only approximately an unbiased source of
219 * independently chosen bits. If it were a perfect source of randomly
220 * chosen bits, then the algorithm shown would choose {@code int}
221 * values from the stated range with perfect uniformity.
222 * <p>
223 * The algorithm is slightly tricky. It rejects values that would result
224 * in an uneven distribution (due to the fact that 2^31 is not divisible
225 * by n). The probability of a value being rejected depends on n. The
226 * worst case is n=2^30+1, for which the probability of a reject is 1/2,
227 * and the expected number of iterations before the loop terminates is 2.
228 * <p>
229 * The algorithm treats the case where n is a power of two specially: it
230 * returns the correct number of high-order bits from the underlying
231 * pseudo-random number generator. In the absence of special treatment,
232 * the correct number of <i>low-order</i> bits would be returned. Linear
233 * congruential pseudo-random number generators such as the one
234 * implemented by this class are known to have short periods in the
235 * sequence of values of their low-order bits. Thus, this special case
236 * greatly increases the length of the sequence of values returned by
237 * successive calls to this method if n is a small power of two.
238 *
239 * @param n the bound on the random number to be returned. Must be
240 * positive.
241 * @return the next pseudorandom, uniformly distributed {@code int}
242 * value between {@code 0} (inclusive) and {@code n} (exclusive)
243 * from this random number generator's sequence
244 * @exception IllegalArgumentException if n is not positive
245 * @since 1.2
246 */
247
248 public int nextInt(int n) {
249 if (n <= 0)
250 throw new IllegalArgumentException("n must be positive");
251
252 if ((n & -n) == n) // i.e., n is a power of 2
253 return (int)((n * (long)next(31)) >> 31);
254
255 int bits, val;
256 do {
257 bits = next(31);
258 val = bits % n;
259 } while (bits - val + (n-1) < 0);
260 return val;
261 }
262
263 /**
264 * Returns the next pseudorandom, uniformly distributed {@code long}
265 * value from this random number generator's sequence. The general
266 * contract of {@code nextLong} is that one {@code long} value is
267 * pseudorandomly generated and returned.
268 *
269 * <p>The method {@code nextLong} is implemented by class {@code Random}
270 * as if by:
271 * <pre> {@code
272 * public long nextLong() {
273 * return ((long)next(32) << 32) + next(32);
274 * }}</pre>
275 *
276 * Because class {@code Random} uses a seed with only 48 bits,
277 * this algorithm will not return all possible {@code long} values.
278 *
279 * @return the next pseudorandom, uniformly distributed {@code long}
280 * value from this random number generator's sequence
281 */
282 public long nextLong() {
283 // it's okay that the bottom word remains signed.
284 return ((long)(next(32)) << 32) + next(32);
285 }
286
287 /**
288 * Returns the next pseudorandom, uniformly distributed
289 * {@code boolean} value from this random number generator's
290 * sequence. The general contract of {@code nextBoolean} is that one
291 * {@code boolean} value is pseudorandomly generated and returned. The
292 * values {@code true} and {@code false} are produced with
293 * (approximately) equal probability.
294 *
295 * <p>The method {@code nextBoolean} is implemented by class {@code Random}
296 * as if by:
297 * <pre> {@code
298 * public boolean nextBoolean() {
299 * return next(1) != 0;
300 * }}</pre>
301 *
302 * @return the next pseudorandom, uniformly distributed
303 * {@code boolean} value from this random number generator's
304 * sequence
305 * @since 1.2
306 */
307 public boolean nextBoolean() {
308 return next(1) != 0;
309 }
310
311 /**
312 * Returns the next pseudorandom, uniformly distributed {@code float}
313 * value between {@code 0.0} and {@code 1.0} from this random
314 * number generator's sequence.
315 *
316 * <p>The general contract of {@code nextFloat} is that one
317 * {@code float} value, chosen (approximately) uniformly from the
318 * range {@code 0.0f} (inclusive) to {@code 1.0f} (exclusive), is
319 * pseudorandomly generated and returned. All 2<font
320 * size="-1"><sup>24</sup></font> possible {@code float} values
321 * of the form <i>m x </i>2<font
322 * size="-1"><sup>-24</sup></font>, where <i>m</i> is a positive
323 * integer less than 2<font size="-1"><sup>24</sup> </font>, are
324 * produced with (approximately) equal probability.
325 *
326 * <p>The method {@code nextFloat} is implemented by class {@code Random}
327 * as if by:
328 * <pre> {@code
329 * public float nextFloat() {
330 * return next(24) / ((float)(1 << 24));
331 * }}</pre>
332 *
333 * <p>The hedge "approximately" is used in the foregoing description only
334 * because the next method is only approximately an unbiased source of
335 * independently chosen bits. If it were a perfect source of randomly
336 * chosen bits, then the algorithm shown would choose {@code float}
337 * values from the stated range with perfect uniformity.<p>
338 * [In early versions of Java, the result was incorrectly calculated as:
339 * <pre> {@code
340 * return next(30) / ((float)(1 << 30));}</pre>
341 * This might seem to be equivalent, if not better, but in fact it
342 * introduced a slight nonuniformity because of the bias in the rounding
343 * of floating-point numbers: it was slightly more likely that the
344 * low-order bit of the significand would be 0 than that it would be 1.]
345 *
346 * @return the next pseudorandom, uniformly distributed {@code float}
347 * value between {@code 0.0} and {@code 1.0} from this
348 * random number generator's sequence
349 */
350 public float nextFloat() {
351 return next(24) / ((float)(1 << 24));
352 }
353
354 /**
355 * Returns the next pseudorandom, uniformly distributed
356 * {@code double} value between {@code 0.0} and
357 * {@code 1.0} from this random number generator's sequence.
358 *
359 * <p>The general contract of {@code nextDouble} is that one
360 * {@code double} value, chosen (approximately) uniformly from the
361 * range {@code 0.0d} (inclusive) to {@code 1.0d} (exclusive), is
362 * pseudorandomly generated and returned.
363 *
364 * <p>The method {@code nextDouble} is implemented by class {@code Random}
365 * as if by:
366 * <pre> {@code
367 * public double nextDouble() {
368 * 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;
431 * 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