* If two instances of {@code Random} are created with the same seed, and the same sequence of * method calls is made for each, they will generate and return identical sequences of numbers. In * order to guarantee this property, particular algorithms are specified for the class * {@code Random}. Java implementations must use all the algorithms shown here for the class * {@code Random}, for the sake of absolute portability of Java code. However, subclasses of class * {@code Random} are permitted to use other algorithms, so long as they adhere to the general * contracts for all the methods. *
* The algorithms implemented by class {@code Random} use a {@code protected} utility method that on * each invocation can supply up to 32 pseudorandomly generated bits. *
* Many applications will find the method {@link Math#random} simpler to use. */ public class Random implements java.io.Serializable { /** * Creates a new random number generator. This constructor sets the seed of the random number * generator to a value very likely to be distinct from any other invocation of this constructor. */ public Random() { throw new RuntimeException(); } /** * Creates a new random number generator using a single {@code long} seed. The seed is the initial * value of the internal state of the pseudorandom number generator which is maintained by method * {@link #next}. * *
* The invocation {@code new Random(seed)} is equivalent to: * *
* {
* @code
* Random rnd = new Random();
* rnd.setSeed(seed);
* }
*
*
* @param seed
* the initial seed
* @see #setSeed(long)
*/
public Random(long seed) {
throw new RuntimeException();
}
/**
* Generates the next pseudorandom number. Subclasses should override this, as this is used by all
* other methods.
*
* * The general contract of {@code next} is that it returns an {@code int} value and if the argument * {@code bits} is between {@code 1} and {@code 32} (inclusive), then that many low-order bits of * the returned value will be (approximately) independently chosen bit values, each of which is * (approximately) equally likely to be {@code 0} or {@code 1}. The method {@code next} is * implemented by class {@code Random} by atomically updating the seed to * *
* {@code (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)}
*
*
* and returning
*
*
* {@code (int)(seed >>> (48 - bits))}.
*
*
* This is a linear congruential pseudorandom number generator, as defined by D. H. Lehmer and
* described by Donald E. Knuth in The Art of Computer Programming, Volume 3:
* Seminumerical Algorithms, section 3.2.1.
*
* @param bits
* random bits
* @return the next pseudorandom value from this random number generator's sequence
*/
protected int next(int bits) {
throw new RuntimeException();
}
/**
* Returns the next pseudorandom, uniformly distributed {@code boolean} value from this random
* number generator's sequence. The general contract of {@code nextBoolean} is that one
* {@code boolean} value is pseudorandomly generated and returned. The values {@code true} and
* {@code false} are produced with (approximately) equal probability.
*
* * The method {@code nextBoolean} is implemented by class {@code Random} as if by: * *
* {@code
* public boolean nextBoolean() {
* return next(1) != 0;
* }}
*
*
* @return the next pseudorandom, uniformly distributed {@code boolean} value from this random
* number generator's sequence
*/
public boolean nextBoolean() {
throw new RuntimeException();
}
/**
* Generates random bytes and places them into a user-supplied byte array. The number of random
* bytes produced is equal to the length of the byte array.
*
* * The method {@code nextBytes} is implemented by class {@code Random} as if by: * *
* {@code
* public void nextBytes(byte[] bytes) {
* for (int i = 0; i < bytes.length; )
* for (int rnd = nextInt(), n = Math.min(bytes.length - i, 4);
* n-- > 0; rnd >>= 8)
* bytes[i++] = (byte)rnd;
* }}
*
*
* @param bytes
* the byte array to fill with random bytes
* @throws NullPointerException
* if the byte array is null
*/
public void nextBytes(byte[] bytes) {
throw new RuntimeException();
}
/**
* Returns the next pseudorandom, uniformly distributed {@code double} value between {@code 0.0} and
* {@code 1.0} from this random number generator's sequence.
*
* * The general contract of {@code nextDouble} is that one {@code double} value, chosen * (approximately) uniformly from the range {@code 0.0d} (inclusive) to {@code 1.0d} (exclusive), is * pseudorandomly generated and returned. * *
* The method {@code nextDouble} is implemented by class {@code Random} as if by: * *
* {@code
* public double nextDouble() {
* return (((long)next(26) << 27) + next(27))
* / (double)(1L << 53);
* }}
*
*
* * The hedge "approximately" is used in the foregoing description only because the {@code next} * method is only approximately an unbiased source of independently chosen bits. If it were a * perfect source of randomly chosen bits, then the algorithm shown would choose {@code double} * values from the stated range with perfect uniformity. *
* [In early versions of Java, the result was incorrectly calculated as: * *
* {@code
* return (((long)next(27) << 27) + next(27))
* / (double)(1L << 54);}
*
*
* This might seem to be equivalent, if not better, but in fact it introduced a large nonuniformity
* because of the bias in the rounding of floating-point numbers: it was three times as likely that
* the low-order bit of the significand would be 0 than that it would be 1! This nonuniformity
* probably doesn't matter much in practice, but we strive for perfection.]
*
* @return the next pseudorandom, uniformly distributed {@code double} value between {@code 0.0} and
* {@code 1.0} from this random number generator's sequence
*/
public double nextDouble() {
throw new RuntimeException();
}
/**
* Returns the next pseudorandom, uniformly distributed {@code float} value between {@code 0.0} and
* {@code 1.0} from this random number generator's sequence.
*
* * The general contract of {@code nextFloat} is that one {@code float} value, chosen (approximately) * uniformly from the range {@code 0.0f} (inclusive) to {@code 1.0f} (exclusive), is pseudorandomly * generated and returned. All 224 possible {@code float} values * of the form m x 2-24, where m is a * positive integer less than 224, are produced with * (approximately) equal probability. * *
* The method {@code nextFloat} is implemented by class {@code Random} as if by: * *
* {@code
* public float nextFloat() {
* return next(24) / ((float)(1 << 24));
* }}
*
*
* * The hedge "approximately" is used in the foregoing description only because the next method is * only approximately an unbiased source of independently chosen bits. If it were a perfect source * of randomly chosen bits, then the algorithm shown would choose {@code float} values from the * stated range with perfect uniformity. *
* [In early versions of Java, the result was incorrectly calculated as: * *
* {@code
* return next(30) / ((float)(1 << 30));}
*
*
* This might seem to be equivalent, if not better, but in fact it introduced a slight nonuniformity
* because of the bias in the rounding of floating-point numbers: it was slightly more likely that
* the low-order bit of the significand would be 0 than that it would be 1.]
*
* @return the next pseudorandom, uniformly distributed {@code float} value between {@code 0.0} and
* {@code 1.0} from this random number generator's sequence
*/
public float nextFloat() {
throw new RuntimeException();
}
/**
* Returns the next pseudorandom, Gaussian ("normally") distributed {@code double} value with mean
* {@code 0.0} and standard deviation {@code 1.0} from this random number generator's sequence.
* * The general contract of {@code nextGaussian} is that one {@code double} value, chosen from * (approximately) the usual normal distribution with mean {@code 0.0} and standard deviation * {@code 1.0}, is pseudorandomly generated and returned. * *
* The method {@code nextGaussian} is implemented by class {@code Random} as if by a threadsafe * version of the following: * *
* {@code
* private double nextNextGaussian;
* private boolean haveNextNextGaussian = false;
*
* public double nextGaussian() {
* if (haveNextNextGaussian) {
* haveNextNextGaussian = false;
* return nextNextGaussian;
* } else {
* double v1, v2, s;
* do {
* v1 = 2 * nextDouble() - 1; // between -1.0 and 1.0
* v2 = 2 * nextDouble() - 1; // between -1.0 and 1.0
* s = v1 * v1 + v2 * v2;
* } while (s >= 1 || s == 0);
* double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
* nextNextGaussian = v2 * multiplier;
* haveNextNextGaussian = true;
* return v1 * multiplier;
* }
* }}
*
*
* This uses the polar method of G. E. P. Box, M. E. Muller, and G. Marsaglia, as described
* by Donald E. Knuth in The Art of Computer Programming, Volume 3: Seminumerical
* Algorithms, section 3.4.1, subsection C, algorithm P. Note that it generates two independent
* values at the cost of only one call to {@code StrictMath.log} and one call to
* {@code StrictMath.sqrt}.
*
* @return the next pseudorandom, Gaussian ("normally") distributed {@code double} value with mean
* {@code 0.0} and standard deviation {@code 1.0} from this random number generator's
* sequence
*/
public double nextGaussian() {
throw new RuntimeException();
}
/**
* Returns the next pseudorandom, uniformly distributed {@code int} value from this random number
* generator's sequence. The general contract of {@code nextInt} is that one {@code int} value is
* pseudorandomly generated and returned. All 232 possible
* {@code int} values are produced with (approximately) equal probability.
*
* * The method {@code nextInt} is implemented by class {@code Random} as if by: * *
* {@code
* public int nextInt() {
* return next(32);
* }}
*
*
* @return the next pseudorandom, uniformly distributed {@code int} value from this random number
* generator's sequence
*/
public int nextInt() {
throw new RuntimeException();
}
public int nextInt(int n) {
throw new RuntimeException();
}
/**
* Returns the next pseudorandom, uniformly distributed {@code long} value from this random number
* generator's sequence. The general contract of {@code nextLong} is that one {@code long} value is
* pseudorandomly generated and returned.
*
* * The method {@code nextLong} is implemented by class {@code Random} as if by: * *
* {@code
* public long nextLong() {
* return ((long)next(32) << 32) + next(32);
* }}
*
*
* Because class {@code Random} uses a seed with only 48 bits, this algorithm will not return all
* possible {@code long} values.
*
* @return the next pseudorandom, uniformly distributed {@code long} value from this random number
* generator's sequence
*/
public long nextLong() {
throw new RuntimeException();
}
/**
* Sets the seed of this random number generator using a single {@code long} seed. The general
* contract of {@code setSeed} is that it alters the state of this random number generator object so
* as to be in exactly the same state as if it had just been created with the argument {@code seed}
* as a seed. The method {@code setSeed} is implemented by class {@code Random} by atomically
* updating the seed to
*
*
* {@code (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1)}
*
*
* and clearing the {@code haveNextNextGaussian} flag used by {@link #nextGaussian}.
*
* * The implementation of {@code setSeed} by class {@code Random} happens to use only 48 bits of the * given seed. In general, however, an overriding method may use all 64 bits of the {@code long} * argument as a seed value. * * @param seed * the initial seed */ public void setSeed(long seed) { throw new RuntimeException(); } /** * Returns a pseudorandom, uniformly distributed {@code int} value between 0 (inclusive) and the * specified value (exclusive), drawn from this random number generator's sequence. The general * contract of {@code nextInt} is that one {@code int} value in the specified range is * pseudorandomly generated and returned. All {@code n} possible {@code int} values are produced * with (approximately) equal probability. The method {@code nextInt(int n)} is implemented by class * {@code Random} as if by: * *
* {@code
* public int nextInt(int n) {
* if (n <= 0)
* throw new IllegalArgumentException("n must be positive");
*
* if ((n & -n) == n) // i.e., n is a power of 2
* return (int)((n * (long)next(31)) >> 31);
*
* int bits, val;
* do {
* bits = next(31);
* val = bits % n;
* } while (bits - val + (n-1) < 0);
* return val;
* }}
*
*
* * The hedge "approximately" is used in the foregoing description only because the next method is * only approximately an unbiased source of independently chosen bits. If it were a perfect source * of randomly chosen bits, then the algorithm shown would choose {@code int} values from the stated * range with perfect uniformity. *
* The algorithm is slightly tricky. It rejects values that would result in an uneven distribution * (due to the fact that 2^31 is not divisible by n). The probability of a value being rejected * depends on n. The worst case is n=2^30+1, for which the probability of a reject is 1/2, and the * expected number of iterations before the loop terminates is 2. *
* The algorithm treats the case where n is a power of two specially: it returns the correct number * of high-order bits from the underlying pseudo-random number generator. In the absence of special * treatment, the correct number of low-order bits would be returned. Linear congruential * pseudo-random number generators such as the one implemented by this class are known to have short * periods in the sequence of values of their low-order bits. Thus, this special case greatly * increases the length of the sequence of values returned by successive calls to this method if n * is a small power of two. * * @param n * the bound on the random number to be returned. Must be positive. * @return the next pseudorandom, uniformly distributed {@code int} value between {@code 0} * (inclusive) and {@code n} (exclusive) from this random number generator's sequence * @throws IllegalArgumentException * if n is not positive */ }