1 /*
2 * Copyright 1995-2008 Sun Microsystems, Inc. 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. Sun designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Sun 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
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
22 * CA 95054 USA or visit www.sun.com if you need additional information or
23 * have any questions.
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 * @author Frank Yellin
54 * @since 1.0
55 */
56 public
57 class Random implements java.io.Serializable {
58 /** use serialVersionUID from JDK 1.1 for interoperability */
59 static final long serialVersionUID = 3905348978240129619L;
60
61 /**
62 * The internal state associated with this pseudorandom number generator.
63 * (The specs for the methods in this class describe the ongoing
64 * computation of this value.)
65 */
66 private final AtomicLong seed;
67
68 private final static long multiplier = 0x5DEECE66DL;
69 private final static long addend = 0xBL;
70 private final static long mask = (1L << 48) - 1;
71
72 /**
73 * Creates a new random number generator. This constructor sets
74 * the seed of the random number generator to a value very likely
75 * to be distinct from any other invocation of this constructor.
76 */
77 public Random() { this(++seedUniquifier + System.nanoTime()); }
78 private static volatile long seedUniquifier = 8682522807148012L;
79
80 /**
81 * Creates a new random number generator using a single {@code long} seed.
82 * The seed is the initial value of the internal state of the pseudorandom
83 * number generator which is maintained by method {@link #next}.
84 *
85 * <p>The invocation {@code new Random(seed)} is equivalent to:
86 * <pre> {@code
87 * Random rnd = new Random();
88 * rnd.setSeed(seed);}</pre>
89 *
90 * @param seed the initial seed
91 * @see #setSeed(long)
92 */
93 public Random(long seed) {
94 this.seed = new AtomicLong(0L);
95 setSeed(seed);
96 }
97
98 /**
99 * Sets the seed of this random number generator using a single
100 * {@code long} seed. The general contract of {@code setSeed} is
101 * that it alters the state of this random number generator object
102 * so as to be in exactly the same state as if it had just been
103 * created with the argument {@code seed} as a seed. The method
104 * {@code setSeed} is implemented by class {@code Random} by
105 * atomically updating the seed to
106 * <pre>{@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}</pre>
107 * and clearing the {@code haveNextNextGaussian} flag used by {@link
108 * #nextGaussian}.
109 *
110 * <p>The implementation of {@code setSeed} by class {@code Random}
111 * happens to use only 48 bits of the given seed. In general, however,
112 * an overriding method may use all 64 bits of the {@code long}
113 * argument as a seed value.
114 *
115 * @param seed the initial seed
116 */
117 synchronized public void setSeed(long seed) {
118 seed = (seed ^ multiplier) & mask;
119 this.seed.set(seed);
120 haveNextNextGaussian = false;
121 }
122
123 /**
124 * Generates the next pseudorandom number. Subclasses should
125 * override this, as this is used by all other methods.
126 *
127 * <p>The general contract of {@code next} is that it returns an
128 * {@code int} value and if the argument {@code bits} is between
129 * {@code 1} and {@code 32} (inclusive), then that many low-order
130 * bits of the returned value will be (approximately) independently
131 * chosen bit values, each of which is (approximately) equally
132 * likely to be {@code 0} or {@code 1}. The method {@code next} is
133 * implemented by class {@code Random} by atomically updating the seed to
134 * <pre>{@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}</pre>
135 * and returning
136 * <pre>{@code (int)(seed >>> (48 - bits))}.</pre>
137 *
138 * This is a linear congruential pseudorandom number generator, as
139 * defined by D. H. Lehmer and described by Donald E. Knuth in
140 * <i>The Art of Computer Programming,</i> Volume 3:
141 * <i>Seminumerical Algorithms</i>, section 3.2.1.
142 *
143 * @param bits random bits
144 * @return the next pseudorandom value from this random number
145 * generator's sequence
146 * @since 1.1
147 */
148 protected int next(int bits) {
149 long oldseed, nextseed;
150 AtomicLong seed = this.seed;
151 do {
152 oldseed = seed.get();
153 nextseed = (oldseed * multiplier + addend) & mask;
154 } while (!seed.compareAndSet(oldseed, nextseed));
155 return (int)(nextseed >>> (48 - bits));
156 }
157
158 /**
159 * Generates random bytes and places them into a user-supplied
160 * byte array. The number of random bytes produced is equal to
161 * the length of the byte array.
162 *
163 * <p>The method {@code nextBytes} is implemented by class {@code Random}
164 * as if by:
165 * <pre> {@code
166 * public void nextBytes(byte[] bytes) {
167 * for (int i = 0; i < bytes.length; )
168 * for (int rnd = nextInt(), n = Math.min(bytes.length - i, 4);
169 * n-- > 0; rnd >>= 8)
170 * bytes[i++] = (byte)rnd;
171 * }}</pre>
172 *
173 * @param bytes the byte array to fill with random bytes
174 * @throws NullPointerException if the byte array is null
175 * @since 1.1
176 */
177 public void nextBytes(byte[] bytes) {
178 for (int i = 0, len = bytes.length; i < len; )
179 for (int rnd = nextInt(),
180 n = Math.min(len - i, Integer.SIZE/Byte.SIZE);
181 n-- > 0; rnd >>= Byte.SIZE)
182 bytes[i++] = (byte)rnd;
183 }
184
185 /**
186 * Returns the next pseudorandom, uniformly distributed {@code int}
187 * value from this random number generator's sequence. The general
188 * contract of {@code nextInt} is that one {@code int} value is
189 * pseudorandomly generated and returned. All 2<font size="-1"><sup>32
190 * </sup></font> possible {@code int} values are produced with
191 * (approximately) equal probability.
192 *
193 * <p>The method {@code nextInt} is implemented by class {@code Random}
194 * as if by:
195 * <pre> {@code
196 * public int nextInt() {
197 * return next(32);
198 * }}</pre>
199 *
200 * @return the next pseudorandom, uniformly distributed {@code int}
201 * value from this random number generator's sequence
202 */
203 public int nextInt() {
204 return next(32);
205 }
206
207 /**
208 * Returns a pseudorandom, uniformly distributed {@code int} value
209 * between 0 (inclusive) and the specified value (exclusive), drawn from
210 * this random number generator's sequence. The general contract of
211 * {@code nextInt} is that one {@code int} value in the specified range
212 * is pseudorandomly generated and returned. All {@code n} possible
213 * {@code int} values are produced with (approximately) equal
214 * probability. The method {@code nextInt(int n)} is implemented by
215 * class {@code Random} as if by:
216 * <pre> {@code
217 * public int nextInt(int n) {
218 * if (n <= 0)
219 * throw new IllegalArgumentException("n must be positive");
220 *
221 * if ((n & -n) == n) // i.e., n is a power of 2
222 * return (int)((n * (long)next(31)) >> 31);
223 *
224 * int bits, val;
225 * do {
226 * bits = next(31);
227 * val = bits % n;
228 * } while (bits - val + (n-1) < 0);
229 * return val;
230 * }}</pre>
231 *
232 * <p>The hedge "approximately" is used in the foregoing description only
233 * because the next method is only approximately an unbiased source of
234 * independently chosen bits. If it were a perfect source of randomly
235 * chosen bits, then the algorithm shown would choose {@code int}
236 * values from the stated range with perfect uniformity.
237 * <p>
238 * The algorithm is slightly tricky. It rejects values that would result
239 * in an uneven distribution (due to the fact that 2^31 is not divisible
240 * by n). The probability of a value being rejected depends on n. The
241 * worst case is n=2^30+1, for which the probability of a reject is 1/2,
242 * and the expected number of iterations before the loop terminates is 2.
243 * <p>
244 * The algorithm treats the case where n is a power of two specially: it
245 * returns the correct number of high-order bits from the underlying
246 * pseudo-random number generator. In the absence of special treatment,
247 * the correct number of <i>low-order</i> bits would be returned. Linear
248 * congruential pseudo-random number generators such as the one
249 * implemented by this class are known to have short periods in the
250 * sequence of values of their low-order bits. Thus, this special case
251 * greatly increases the length of the sequence of values returned by
252 * successive calls to this method if n is a small power of two.
253 *
254 * @param n the bound on the random number to be returned. Must be
255 * positive.
256 * @return the next pseudorandom, uniformly distributed {@code int}
257 * value between {@code 0} (inclusive) and {@code n} (exclusive)
258 * from this random number generator's sequence
259 * @exception IllegalArgumentException if n is not positive
260 * @since 1.2
261 */
262
263 public int nextInt(int n) {
264 if (n <= 0)
265 throw new IllegalArgumentException("n must be positive");
266
267 if ((n & -n) == n) // i.e., n is a power of 2
268 return (int)((n * (long)next(31)) >> 31);
269
270 int bits, val;
271 do {
272 bits = next(31);
273 val = bits % n;
274 } while (bits - val + (n-1) < 0);
275 return val;
276 }
277
278 /**
279 * Returns the next pseudorandom, uniformly distributed {@code long}
280 * value from this random number generator's sequence. The general
281 * contract of {@code nextLong} is that one {@code long} value is
282 * pseudorandomly generated and returned.
283 *
284 * <p>The method {@code nextLong} is implemented by class {@code Random}
285 * as if by:
286 * <pre> {@code
287 * public long nextLong() {
288 * return ((long)next(32) << 32) + next(32);
289 * }}</pre>
290 *
291 * Because class {@code Random} uses a seed with only 48 bits,
292 * this algorithm will not return all possible {@code long} values.
293 *
294 * @return the next pseudorandom, uniformly distributed {@code long}
295 * value from this random number generator's sequence
296 */
297 public long nextLong() {
298 // it's okay that the bottom word remains signed.
299 return ((long)(next(32)) << 32) + next(32);
300 }
301
302 /**
303 * Returns the next pseudorandom, uniformly distributed
304 * {@code boolean} value from this random number generator's
305 * sequence. The general contract of {@code nextBoolean} is that one
306 * {@code boolean} value is pseudorandomly generated and returned. The
307 * values {@code true} and {@code false} are produced with
308 * (approximately) equal probability.
309 *
310 * <p>The method {@code nextBoolean} is implemented by class {@code Random}
311 * as if by:
312 * <pre> {@code
313 * public boolean nextBoolean() {
314 * return next(1) != 0;
315 * }}</pre>
316 *
317 * @return the next pseudorandom, uniformly distributed
318 * {@code boolean} value from this random number generator's
319 * sequence
320 * @since 1.2
321 */
322 public boolean nextBoolean() {
323 return next(1) != 0;
324 }
325
326 /**
327 * Returns the next pseudorandom, uniformly distributed {@code float}
328 * value between {@code 0.0} and {@code 1.0} from this random
329 * number generator's sequence.
330 *
331 * <p>The general contract of {@code nextFloat} is that one
332 * {@code float} value, chosen (approximately) uniformly from the
333 * range {@code 0.0f} (inclusive) to {@code 1.0f} (exclusive), is
334 * pseudorandomly generated and returned. All 2<font
335 * size="-1"><sup>24</sup></font> possible {@code float} values
336 * of the form <i>m x </i>2<font
337 * size="-1"><sup>-24</sup></font>, where <i>m</i> is a positive
338 * integer less than 2<font size="-1"><sup>24</sup> </font>, are
339 * produced with (approximately) equal probability.
340 *
341 * <p>The method {@code nextFloat} is implemented by class {@code Random}
342 * as if by:
343 * <pre> {@code
344 * public float nextFloat() {
345 * return next(24) / ((float)(1 << 24));
346 * }}</pre>
347 *
348 * <p>The hedge "approximately" is used in the foregoing description only
349 * because the next method is only approximately an unbiased source of
350 * independently chosen bits. If it were a perfect source of randomly
351 * chosen bits, then the algorithm shown would choose {@code float}
352 * values from the stated range with perfect uniformity.<p>
353 * [In early versions of Java, the result was incorrectly calculated as:
354 * <pre> {@code
355 * return next(30) / ((float)(1 << 30));}</pre>
356 * This might seem to be equivalent, if not better, but in fact it
357 * introduced a slight nonuniformity because of the bias in the rounding
358 * of floating-point numbers: it was slightly more likely that the
359 * low-order bit of the significand would be 0 than that it would be 1.]
360 *
361 * @return the next pseudorandom, uniformly distributed {@code float}
362 * value between {@code 0.0} and {@code 1.0} from this
363 * random number generator's sequence
364 */
365 public float nextFloat() {
366 return next(24) / ((float)(1 << 24));
367 }
368
369 /**
370 * Returns the next pseudorandom, uniformly distributed
371 * {@code double} value between {@code 0.0} and
372 * {@code 1.0} from this random number generator's sequence.
373 *
374 * <p>The general contract of {@code nextDouble} is that one
375 * {@code double} value, chosen (approximately) uniformly from the
376 * range {@code 0.0d} (inclusive) to {@code 1.0d} (exclusive), is
377 * pseudorandomly generated and returned.
378 *
379 * <p>The method {@code nextDouble} is implemented by class {@code Random}
380 * as if by:
381 * <pre> {@code
382 * public double nextDouble() {
383 * return (((long)next(26) << 27) + next(27))
384 * / (double)(1L << 53);
385 * }}</pre>
386 *
387 * <p>The hedge "approximately" is used in the foregoing description only
388 * because the {@code next} method is only approximately an unbiased
389 * source of independently chosen bits. If it were a perfect source of
390 * randomly chosen bits, then the algorithm shown would choose
391 * {@code double} values from the stated range with perfect uniformity.
392 * <p>[In early versions of Java, the result was incorrectly calculated as:
393 * <pre> {@code
394 * return (((long)next(27) << 27) + next(27))
395 * / (double)(1L << 54);}</pre>
396 * This might seem to be equivalent, if not better, but in fact it
397 * introduced a large nonuniformity because of the bias in the rounding
398 * of floating-point numbers: it was three times as likely that the
399 * low-order bit of the significand would be 0 than that it would be 1!
400 * This nonuniformity probably doesn't matter much in practice, but we
401 * strive for perfection.]
402 *
403 * @return the next pseudorandom, uniformly distributed {@code double}
404 * value between {@code 0.0} and {@code 1.0} from this
405 * random number generator's sequence
406 * @see Math#random
407 */
408 public double nextDouble() {
409 return (((long)(next(26)) << 27) + next(27))
410 / (double)(1L << 53);
411 }
412
413 private double nextNextGaussian;
414 private boolean haveNextNextGaussian = false;
415
416 /**
417 * Returns the next pseudorandom, Gaussian ("normally") distributed
418 * {@code double} value with mean {@code 0.0} and standard
419 * deviation {@code 1.0} from this random number generator's sequence.
420 * <p>
421 * The general contract of {@code nextGaussian} is that one
422 * {@code double} value, chosen from (approximately) the usual
423 * normal distribution with mean {@code 0.0} and standard deviation
424 * {@code 1.0}, is pseudorandomly generated and returned.
425 *
426 * <p>The method {@code nextGaussian} is implemented by class
427 * {@code Random} as if by a threadsafe version of the following:
428 * <pre> {@code
429 * private double nextNextGaussian;
430 * private boolean haveNextNextGaussian = false;
431 *
432 * public double nextGaussian() {
433 * if (haveNextNextGaussian) {
434 * haveNextNextGaussian = false;
435 * return nextNextGaussian;
436 * } else {
437 * double v1, v2, s;
438 * do {
439 * v1 = 2 * nextDouble() - 1; // between -1.0 and 1.0
440 * v2 = 2 * nextDouble() - 1; // between -1.0 and 1.0
441 * s = v1 * v1 + v2 * v2;
442 * } while (s >= 1 || s == 0);
443 * double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
444 * nextNextGaussian = v2 * multiplier;
445 * haveNextNextGaussian = true;
446 * return v1 * multiplier;
447 * }
448 * }}</pre>
449 * This uses the <i>polar method</i> of G. E. P. Box, M. E. Muller, and
450 * G. Marsaglia, as described by Donald E. Knuth in <i>The Art of
451 * Computer Programming</i>, Volume 3: <i>Seminumerical Algorithms</i>,
452 * section 3.4.1, subsection C, algorithm P. Note that it generates two
453 * independent values at the cost of only one call to {@code StrictMath.log}
454 * and one call to {@code StrictMath.sqrt}.
455 *
456 * @return the next pseudorandom, Gaussian ("normally") distributed
457 * {@code double} value with mean {@code 0.0} and
458 * standard deviation {@code 1.0} from this random number
459 * generator's sequence
460 */
461 synchronized public double nextGaussian() {
462 // See Knuth, ACP, Section 3.4.1 Algorithm C.
463 if (haveNextNextGaussian) {
464 haveNextNextGaussian = false;
465 return nextNextGaussian;
466 } else {
467 double v1, v2, s;
468 do {
469 v1 = 2 * nextDouble() - 1; // between -1 and 1
470 v2 = 2 * nextDouble() - 1; // between -1 and 1
471 s = v1 * v1 + v2 * v2;
472 } while (s >= 1 || s == 0);
473 double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
474 nextNextGaussian = v2 * multiplier;
475 haveNextNextGaussian = true;
476 return v1 * multiplier;
477 }
478 }
479
480 /**
481 * Serializable fields for Random.
482 *
483 * @serialField seed long
484 * seed for random computations
485 * @serialField nextNextGaussian double
486 * next Gaussian to be returned
487 * @serialField haveNextNextGaussian boolean
488 * nextNextGaussian is valid
489 */
490 private static final ObjectStreamField[] serialPersistentFields = {
491 new ObjectStreamField("seed", Long.TYPE),
492 new ObjectStreamField("nextNextGaussian", Double.TYPE),
493 new ObjectStreamField("haveNextNextGaussian", Boolean.TYPE)
494 };
495
496 /**
497 * Reconstitute the {@code Random} instance from a stream (that is,
498 * deserialize it).
499 */
500 private void readObject(java.io.ObjectInputStream s)
501 throws java.io.IOException, ClassNotFoundException {
502
503 ObjectInputStream.GetField fields = s.readFields();
504
505 // The seed is read in as {@code long} for
506 // historical reasons, but it is converted to an AtomicLong.
507 long seedVal = fields.get("seed", -1L);
508 if (seedVal < 0)
509 throw new java.io.StreamCorruptedException(
510 "Random: invalid seed");
511 resetSeed(seedVal);
512 nextNextGaussian = fields.get("nextNextGaussian", 0.0);
513 haveNextNextGaussian = fields.get("haveNextNextGaussian", false);
514 }
515
516 /**
517 * Save the {@code Random} instance to a stream.
518 */
519 synchronized private void writeObject(ObjectOutputStream s)
520 throws IOException {
521
522 // set the values of the Serializable fields
523 ObjectOutputStream.PutField fields = s.putFields();
524
525 // The seed is serialized as a long for historical reasons.
526 fields.put("seed", seed.get());
527 fields.put("nextNextGaussian", nextNextGaussian);
528 fields.put("haveNextNextGaussian", haveNextNextGaussian);
529
530 // save them
531 s.writeFields();
532 }
533
534 // Support for resetting seed while deserializing
535 private static final Unsafe unsafe = Unsafe.getUnsafe();
536 private static final long seedOffset;
537 static {
538 try {
539 seedOffset = unsafe.objectFieldOffset
540 (Random.class.getDeclaredField("seed"));
541 } catch (Exception ex) { throw new Error(ex); }
542 }
543 private void resetSeed(long seedVal) {
544 unsafe.putObjectVolatile(this, seedOffset, new AtomicLong(seedVal));
545 }
546 }