1 /*
2 * Copyright (c) 1995, 2010, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
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19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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24 */
25
26 package java.util;
27 import java.io.*;
28 import java.util.concurrent.atomic.AtomicLong;
29 import sun.misc.Unsafe;
30
31 /**
32 * An instance of this class is used to generate a stream of
33 * pseudorandom numbers. The class uses a 48-bit seed, which is
34 * modified using a linear congruential formula. (See Donald Knuth,
35 * <i>The Art of Computer Programming, Volume 2</i>, Section 3.2.1.)
36 * <p>
37 * If two instances of {@code Random} are created with the same
38 * seed, and the same sequence of method calls is made for each, they
39 * will generate and return identical sequences of numbers. In order to
40 * guarantee this property, particular algorithms are specified for the
41 * class {@code Random}. Java implementations must use all the algorithms
42 * shown here for the class {@code Random}, for the sake of absolute
43 * portability of Java code. However, subclasses of class {@code Random}
44 * are permitted to use other algorithms, so long as they adhere to the
45 * general contracts for all the methods.
46 * <p>
47 * The algorithms implemented by class {@code Random} use a
48 * {@code protected} utility method that on each invocation can supply
49 * up to 32 pseudorandomly generated bits.
50 * <p>
51 * Many applications will find the method {@link Math#random} simpler to use.
52 *
53 * <p>Instances of {@code java.util.Random} are threadsafe.
54 * However, the concurrent use of the same {@code java.util.Random}
55 * instance across threads may encounter contention and consequent
56 * poor performance. Consider instead using
57 * {@link java.util.concurrent.ThreadLocalRandom} in multithreaded
58 * designs.
59 *
60 * <p>Instances of {@code java.util.Random} are not cryptographically
61 * secure. Consider instead using {@link java.security.SecureRandom} to
62 * get a cryptographically secure pseudo-random number generator for use
63 * by security-sensitive applications.
64 *
65 * @author Frank Yellin
66 * @since 1.0
67 */
68 public
69 class Random implements java.io.Serializable {
70 /** use serialVersionUID from JDK 1.1 for interoperability */
71 static final long serialVersionUID = 3905348978240129619L;
72
73 /**
74 * The internal state associated with this pseudorandom number generator.
75 * (The specs for the methods in this class describe the ongoing
76 * computation of this value.)
77 */
78 private final AtomicLong seed;
79
80 private static final long multiplier = 0x5DEECE66DL;
81 private static final long addend = 0xBL;
82 private static final long mask = (1L << 48) - 1;
83
84 /**
85 * Creates a new random number generator. This constructor sets
86 * the seed of the random number generator to a value very likely
87 * to be distinct from any other invocation of this constructor.
88 */
89 public Random() {
90 this(seedUniquifier() ^ System.nanoTime());
91 }
92
93 private static long seedUniquifier() {
94 // L'Ecuyer, "Tables of Linear Congruential Generators of
95 // Different Sizes and Good Lattice Structure", 1999
96 for (;;) {
97 long current = seedUniquifier.get();
98 long next = current * 181783497276652981L;
99 if (seedUniquifier.compareAndSet(current, next))
100 return next;
101 }
102 }
103
104 private static final AtomicLong seedUniquifier
105 = new AtomicLong(8682522807148012L);
106
107 /**
108 * Creates a new random number generator using a single {@code long} seed.
109 * The seed is the initial value of the internal state of the pseudorandom
110 * number generator which is maintained by method {@link #next}.
111 *
112 * <p>The invocation {@code new Random(seed)} is equivalent to:
113 * <pre> {@code
114 * Random rnd = new Random();
115 * rnd.setSeed(seed);}</pre>
116 *
117 * @param seed the initial seed
118 * @see #setSeed(long)
119 */
120 public Random(long seed) {
121 this.seed = new AtomicLong(initialScramble(seed));
122 }
123
124 private static long initialScramble(long seed) {
125 return (seed ^ multiplier) & mask;
126 }
127
128 /**
129 * Sets the seed of this random number generator using a single
130 * {@code long} seed. The general contract of {@code setSeed} is
131 * that it alters the state of this random number generator object
132 * so as to be in exactly the same state as if it had just been
133 * created with the argument {@code seed} as a seed. The method
134 * {@code setSeed} is implemented by class {@code Random} by
135 * atomically updating the seed to
136 * <pre>{@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}</pre>
137 * and clearing the {@code haveNextNextGaussian} flag used by {@link
138 * #nextGaussian}.
139 *
140 * <p>The implementation of {@code setSeed} by class {@code Random}
141 * happens to use only 48 bits of the given seed. In general, however,
142 * an overriding method may use all 64 bits of the {@code long}
143 * argument as a seed value.
144 *
145 * @param seed the initial seed
146 */
147 synchronized public void setSeed(long seed) {
148 this.seed.set(initialScramble(seed));
149 haveNextNextGaussian = false;
150 }
151
152 /**
153 * Generates the next pseudorandom number. Subclasses should
154 * override this, as this is used by all other methods.
155 *
156 * <p>The general contract of {@code next} is that it returns an
157 * {@code int} value and if the argument {@code bits} is between
158 * {@code 1} and {@code 32} (inclusive), then that many low-order
159 * bits of the returned value will be (approximately) independently
160 * chosen bit values, each of which is (approximately) equally
161 * likely to be {@code 0} or {@code 1}. The method {@code next} is
162 * implemented by class {@code Random} by atomically updating the seed to
163 * <pre>{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}</pre>
164 * and returning
165 * <pre>{@code (int)(seed >>> (48 - bits))}.</pre>
166 *
167 * This is a linear congruential pseudorandom number generator, as
168 * defined by D. H. Lehmer and described by Donald E. Knuth in
169 * <i>The Art of Computer Programming,</i> Volume 3:
170 * <i>Seminumerical Algorithms</i>, section 3.2.1.
171 *
172 * @param bits random bits
173 * @return the next pseudorandom value from this random number
174 * generator's sequence
175 * @since 1.1
176 */
177 protected int next(int bits) {
178 long oldseed, nextseed;
179 AtomicLong seed = this.seed;
180 do {
181 oldseed = seed.get();
182 nextseed = (oldseed * multiplier + addend) & mask;
183 } while (!seed.compareAndSet(oldseed, nextseed));
184 return (int)(nextseed >>> (48 - bits));
185 }
186
187 /**
188 * Generates random bytes and places them into a user-supplied
189 * byte array. The number of random bytes produced is equal to
190 * the length of the byte array.
191 *
192 * <p>The method {@code nextBytes} is implemented by class {@code Random}
193 * as if by:
194 * <pre> {@code
195 * public void nextBytes(byte[] bytes) {
196 * for (int i = 0; i < bytes.length; )
197 * for (int rnd = nextInt(), n = Math.min(bytes.length - i, 4);
198 * n-- > 0; rnd >>= 8)
199 * bytes[i++] = (byte)rnd;
200 * }}</pre>
201 *
202 * @param bytes the byte array to fill with random bytes
203 * @throws NullPointerException if the byte array is null
204 * @since 1.1
205 */
206 public void nextBytes(byte[] bytes) {
207 for (int i = 0, len = bytes.length; i < len; )
208 for (int rnd = nextInt(),
209 n = Math.min(len - i, Integer.SIZE/Byte.SIZE);
210 n-- > 0; rnd >>= Byte.SIZE)
211 bytes[i++] = (byte)rnd;
212 }
213
214 /**
215 * Returns the next pseudorandom, uniformly distributed {@code int}
216 * value from this random number generator's sequence. The general
217 * contract of {@code nextInt} is that one {@code int} value is
218 * pseudorandomly generated and returned. All 2<font size="-1"><sup>32
219 * </sup></font> possible {@code int} values are produced with
220 * (approximately) equal probability.
221 *
222 * <p>The method {@code nextInt} is implemented by class {@code Random}
223 * as if by:
224 * <pre> {@code
225 * public int nextInt() {
226 * return next(32);
227 * }}</pre>
228 *
229 * @return the next pseudorandom, uniformly distributed {@code int}
230 * value from this random number generator's sequence
231 */
232 public int nextInt() {
233 return next(32);
234 }
235
236 /**
237 * Returns a pseudorandom, uniformly distributed {@code int} value
238 * between 0 (inclusive) and the specified value (exclusive), drawn from
239 * this random number generator's sequence. The general contract of
240 * {@code nextInt} is that one {@code int} value in the specified range
241 * is pseudorandomly generated and returned. All {@code n} possible
242 * {@code int} values are produced with (approximately) equal
243 * probability. The method {@code nextInt(int n)} is implemented by
244 * class {@code Random} as if by:
245 * <pre> {@code
246 * public int nextInt(int n) {
247 * if (n <= 0)
248 * throw new IllegalArgumentException("n must be positive");
249 *
250 * if ((n & -n) == n) // i.e., n is a power of 2
251 * return (int)((n * (long)next(31)) >> 31);
252 *
253 * int bits, val;
254 * do {
255 * bits = next(31);
256 * val = bits % n;
257 * } while (bits - val + (n-1) < 0);
258 * return val;
259 * }}</pre>
260 *
261 * <p>The hedge "approximately" is used in the foregoing description only
262 * because the next method is only approximately an unbiased source of
263 * independently chosen bits. If it were a perfect source of randomly
264 * chosen bits, then the algorithm shown would choose {@code int}
265 * values from the stated range with perfect uniformity.
266 * <p>
267 * The algorithm is slightly tricky. It rejects values that would result
268 * in an uneven distribution (due to the fact that 2^31 is not divisible
269 * by n). The probability of a value being rejected depends on n. The
270 * worst case is n=2^30+1, for which the probability of a reject is 1/2,
271 * and the expected number of iterations before the loop terminates is 2.
272 * <p>
273 * The algorithm treats the case where n is a power of two specially: it
274 * returns the correct number of high-order bits from the underlying
275 * pseudo-random number generator. In the absence of special treatment,
276 * the correct number of <i>low-order</i> bits would be returned. Linear
277 * congruential pseudo-random number generators such as the one
278 * implemented by this class are known to have short periods in the
279 * sequence of values of their low-order bits. Thus, this special case
280 * greatly increases the length of the sequence of values returned by
281 * successive calls to this method if n is a small power of two.
282 *
283 * @param n the bound on the random number to be returned. Must be
284 * positive.
285 * @return the next pseudorandom, uniformly distributed {@code int}
286 * value between {@code 0} (inclusive) and {@code n} (exclusive)
287 * from this random number generator's sequence
288 * @throws IllegalArgumentException if n is not positive
289 * @since 1.2
290 */
291
292 public int nextInt(int n) {
293 if (n <= 0)
294 throw new IllegalArgumentException("n must be positive");
295
296 if ((n & -n) == n) // i.e., n is a power of 2
297 return (int)((n * (long)next(31)) >> 31);
298
299 int bits, val;
300 do {
301 bits = next(31);
302 val = bits % n;
303 } while (bits - val + (n-1) < 0);
304 return val;
305 }
306
307 /**
308 * Returns the next pseudorandom, uniformly distributed {@code long}
309 * value from this random number generator's sequence. The general
310 * contract of {@code nextLong} is that one {@code long} value is
311 * pseudorandomly generated and returned.
312 *
313 * <p>The method {@code nextLong} is implemented by class {@code Random}
314 * as if by:
315 * <pre> {@code
316 * public long nextLong() {
317 * return ((long)next(32) << 32) + next(32);
318 * }}</pre>
319 *
320 * Because class {@code Random} uses a seed with only 48 bits,
321 * this algorithm will not return all possible {@code long} values.
322 *
323 * @return the next pseudorandom, uniformly distributed {@code long}
324 * value from this random number generator's sequence
325 */
326 public long nextLong() {
327 // it's okay that the bottom word remains signed.
328 return ((long)(next(32)) << 32) + next(32);
329 }
330
331 /**
332 * Returns the next pseudorandom, uniformly distributed
333 * {@code boolean} value from this random number generator's
334 * sequence. The general contract of {@code nextBoolean} is that one
335 * {@code boolean} value is pseudorandomly generated and returned. The
336 * values {@code true} and {@code false} are produced with
337 * (approximately) equal probability.
338 *
339 * <p>The method {@code nextBoolean} is implemented by class {@code Random}
340 * as if by:
341 * <pre> {@code
342 * public boolean nextBoolean() {
343 * return next(1) != 0;
344 * }}</pre>
345 *
346 * @return the next pseudorandom, uniformly distributed
347 * {@code boolean} value from this random number generator's
348 * sequence
349 * @since 1.2
350 */
351 public boolean nextBoolean() {
352 return next(1) != 0;
353 }
354
355 /**
356 * Returns the next pseudorandom, uniformly distributed {@code float}
357 * value between {@code 0.0} and {@code 1.0} from this random
358 * number generator's sequence.
359 *
360 * <p>The general contract of {@code nextFloat} is that one
361 * {@code float} value, chosen (approximately) uniformly from the
362 * range {@code 0.0f} (inclusive) to {@code 1.0f} (exclusive), is
363 * pseudorandomly generated and returned. All 2<font
364 * size="-1"><sup>24</sup></font> possible {@code float} values
365 * of the form <i>m x </i>2<font
366 * size="-1"><sup>-24</sup></font>, where <i>m</i> is a positive
367 * integer less than 2<font size="-1"><sup>24</sup> </font>, are
368 * produced with (approximately) equal probability.
369 *
370 * <p>The method {@code nextFloat} is implemented by class {@code Random}
371 * as if by:
372 * <pre> {@code
373 * public float nextFloat() {
374 * return next(24) / ((float)(1 << 24));
375 * }}</pre>
376 *
377 * <p>The hedge "approximately" is used in the foregoing description only
378 * because the next method is only approximately an unbiased source of
379 * independently chosen bits. If it were a perfect source of randomly
380 * chosen bits, then the algorithm shown would choose {@code float}
381 * values from the stated range with perfect uniformity.<p>
382 * [In early versions of Java, the result was incorrectly calculated as:
383 * <pre> {@code
384 * return next(30) / ((float)(1 << 30));}</pre>
385 * This might seem to be equivalent, if not better, but in fact it
386 * introduced a slight nonuniformity because of the bias in the rounding
387 * of floating-point numbers: it was slightly more likely that the
388 * low-order bit of the significand would be 0 than that it would be 1.]
389 *
390 * @return the next pseudorandom, uniformly distributed {@code float}
391 * value between {@code 0.0} and {@code 1.0} from this
392 * random number generator's sequence
393 */
394 public float nextFloat() {
395 return next(24) / ((float)(1 << 24));
396 }
397
398 /**
399 * Returns the next pseudorandom, uniformly distributed
400 * {@code double} value between {@code 0.0} and
401 * {@code 1.0} from this random number generator's sequence.
402 *
403 * <p>The general contract of {@code nextDouble} is that one
404 * {@code double} value, chosen (approximately) uniformly from the
405 * range {@code 0.0d} (inclusive) to {@code 1.0d} (exclusive), is
406 * pseudorandomly generated and returned.
407 *
408 * <p>The method {@code nextDouble} is implemented by class {@code Random}
409 * as if by:
410 * <pre> {@code
411 * public double nextDouble() {
412 * return (((long)next(26) << 27) + next(27))
413 * / (double)(1L << 53);
414 * }}</pre>
415 *
416 * <p>The hedge "approximately" is used in the foregoing description only
417 * because the {@code next} method is only approximately an unbiased
418 * source of independently chosen bits. If it were a perfect source of
419 * randomly chosen bits, then the algorithm shown would choose
420 * {@code double} values from the stated range with perfect uniformity.
421 * <p>[In early versions of Java, the result was incorrectly calculated as:
422 * <pre> {@code
423 * return (((long)next(27) << 27) + next(27))
424 * / (double)(1L << 54);}</pre>
425 * This might seem to be equivalent, if not better, but in fact it
426 * introduced a large nonuniformity because of the bias in the rounding
427 * of floating-point numbers: it was three times as likely that the
428 * low-order bit of the significand would be 0 than that it would be 1!
429 * This nonuniformity probably doesn't matter much in practice, but we
430 * strive for perfection.]
431 *
432 * @return the next pseudorandom, uniformly distributed {@code double}
433 * value between {@code 0.0} and {@code 1.0} from this
434 * random number generator's sequence
435 * @see Math#random
436 */
437 public double nextDouble() {
438 return (((long)(next(26)) << 27) + next(27))
439 / (double)(1L << 53);
440 }
441
442 private double nextNextGaussian;
443 private boolean haveNextNextGaussian = false;
444
445 /**
446 * Returns the next pseudorandom, Gaussian ("normally") distributed
447 * {@code double} value with mean {@code 0.0} and standard
448 * deviation {@code 1.0} from this random number generator's sequence.
449 * <p>
450 * The general contract of {@code nextGaussian} is that one
451 * {@code double} value, chosen from (approximately) the usual
452 * normal distribution with mean {@code 0.0} and standard deviation
453 * {@code 1.0}, is pseudorandomly generated and returned.
454 *
455 * <p>The method {@code nextGaussian} is implemented by class
456 * {@code Random} as if by a threadsafe version of the following:
457 * <pre> {@code
458 * private double nextNextGaussian;
459 * private boolean haveNextNextGaussian = false;
460 *
461 * public double nextGaussian() {
462 * if (haveNextNextGaussian) {
463 * haveNextNextGaussian = false;
464 * return nextNextGaussian;
465 * } else {
466 * double v1, v2, s;
467 * do {
468 * v1 = 2 * nextDouble() - 1; // between -1.0 and 1.0
469 * v2 = 2 * nextDouble() - 1; // between -1.0 and 1.0
470 * s = v1 * v1 + v2 * v2;
471 * } while (s >= 1 || s == 0);
472 * double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
473 * nextNextGaussian = v2 * multiplier;
474 * haveNextNextGaussian = true;
475 * return v1 * multiplier;
476 * }
477 * }}</pre>
478 * This uses the <i>polar method</i> of G. E. P. Box, M. E. Muller, and
479 * G. Marsaglia, as described by Donald E. Knuth in <i>The Art of
480 * Computer Programming</i>, Volume 3: <i>Seminumerical Algorithms</i>,
481 * section 3.4.1, subsection C, algorithm P. Note that it generates two
482 * independent values at the cost of only one call to {@code StrictMath.log}
483 * and one call to {@code StrictMath.sqrt}.
484 *
485 * @return the next pseudorandom, Gaussian ("normally") distributed
486 * {@code double} value with mean {@code 0.0} and
487 * standard deviation {@code 1.0} from this random number
488 * generator's sequence
489 */
490 synchronized public double nextGaussian() {
491 // See Knuth, ACP, Section 3.4.1 Algorithm C.
492 if (haveNextNextGaussian) {
493 haveNextNextGaussian = false;
494 return nextNextGaussian;
495 } else {
496 double v1, v2, s;
497 do {
498 v1 = 2 * nextDouble() - 1; // between -1 and 1
499 v2 = 2 * nextDouble() - 1; // between -1 and 1
500 s = v1 * v1 + v2 * v2;
501 } while (s >= 1 || s == 0);
502 double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
503 nextNextGaussian = v2 * multiplier;
504 haveNextNextGaussian = true;
505 return v1 * multiplier;
506 }
507 }
508
509 /**
510 * Serializable fields for Random.
511 *
512 * @serialField seed long
513 * seed for random computations
514 * @serialField nextNextGaussian double
515 * next Gaussian to be returned
516 * @serialField haveNextNextGaussian boolean
517 * nextNextGaussian is valid
518 */
519 private static final ObjectStreamField[] serialPersistentFields = {
520 new ObjectStreamField("seed", Long.TYPE),
521 new ObjectStreamField("nextNextGaussian", Double.TYPE),
522 new ObjectStreamField("haveNextNextGaussian", Boolean.TYPE)
523 };
524
525 /**
526 * Reconstitute the {@code Random} instance from a stream (that is,
527 * deserialize it).
528 */
529 private void readObject(java.io.ObjectInputStream s)
530 throws java.io.IOException, ClassNotFoundException {
531
532 ObjectInputStream.GetField fields = s.readFields();
533
534 // The seed is read in as {@code long} for
535 // historical reasons, but it is converted to an AtomicLong.
536 long seedVal = fields.get("seed", -1L);
537 if (seedVal < 0)
538 throw new java.io.StreamCorruptedException(
539 "Random: invalid seed");
540 resetSeed(seedVal);
541 nextNextGaussian = fields.get("nextNextGaussian", 0.0);
542 haveNextNextGaussian = fields.get("haveNextNextGaussian", false);
543 }
544
545 /**
546 * Save the {@code Random} instance to a stream.
547 */
548 synchronized private void writeObject(ObjectOutputStream s)
549 throws IOException {
550
551 // set the values of the Serializable fields
552 ObjectOutputStream.PutField fields = s.putFields();
553
554 // The seed is serialized as a long for historical reasons.
555 fields.put("seed", seed.get());
556 fields.put("nextNextGaussian", nextNextGaussian);
557 fields.put("haveNextNextGaussian", haveNextNextGaussian);
558
559 // save them
560 s.writeFields();
561 }
562
563 // Support for resetting seed while deserializing
564 private static final Unsafe unsafe = Unsafe.getUnsafe();
565 private static final long seedOffset;
566 static {
567 try {
568 seedOffset = unsafe.objectFieldOffset
569 (Random.class.getDeclaredField("seed"));
570 } catch (Exception ex) { throw new Error(ex); }
571 }
572 private void resetSeed(long seedVal) {
573 unsafe.putObjectVolatile(this, seedOffset, new AtomicLong(seedVal));
574 }
575 }