Class MersenneTwister
- All Implemented Interfaces:
DoubleFunction
,IntFunction
,Serializable
,Cloneable
- Direct Known Subclasses:
MersenneTwister64
Quality: MersenneTwister is designed to pass the k-distribution test. It has an astronomically large period of 219937-1 (=106001) and 623-dimensional equidistribution up to 32-bit accuracy. It passes many stringent statistical tests, including the diehard test of G. Marsaglia and the load test of P. Hellekalek and S. Wegenkittl.
Performance: Its speed is comparable to other modern generators (in particular, as fast as java.util.Random.nextFloat()). 2.5 million calls to raw() per second (Pentium Pro 200 Mhz, JDK 1.2, NT). Be aware, however, that there is a non-negligible amount of overhead required to initialize the data structures used by a MersenneTwister. Code like
double sum = 0.0;
for (int i=0; iinvalid input: '<'100000; ++i) {
RandomElement twister = new MersenneTwister(new java.util.Date());
sum += twister.raw();
}
will be wildly inefficient. Consider using
double sum = 0.0;
RandomElement twister = new MersenneTwister(new java.util.Date());
for (int i=0; iinvalid input: '<'100000; ++i) {
sum += twister.raw();
}
instead. This allows the cost of constructing the MersenneTwister object
to be borne only once, rather than once for each iteration in the loop.
Implementation: After M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3--30.
The correctness of this implementation has been verified against the published output sequence mt19937-2.out of the C-implementation mt19937-2.c. (Call test(1000) to print the sequence).
Details: MersenneTwister is designed with consideration of the flaws of various existing generators in mind. It is an improved version of TT800, a very successful generator. MersenneTwister is based on linear recurrences modulo 2. Such generators are very fast, have extremely long periods, and appear quite robust. MersenneTwister produces 32-bit numbers, and every k-dimensional vector of such numbers appears the same number of times as k successive values over the period length, for each k <= 623 (except for the zero vector, which appears one time less). If one looks at only the first n <= 16 bits of each number, then the property holds for even larger k, as shown in the following table (taken from the publication cited above):
n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 .. 16 |
17 .. 32 |
k |
19937 |
9968 |
6240 |
4984 |
3738 |
3115 |
2493 |
2492 |
1869 |
1869 |
1248 |
1246 |
623 |
MersenneTwister generates random numbers in batches of 624 numbers at a time, so the caching and pipelining of modern systems is exploited. The generator is implemented to generate the output by using the fastest arithmetic operations only: 32-bit additions and bit operations (no division, no multiplication, no mod). These operations generate sequences of 32 random bits (int's). long's are formed by concatenating two 32 bit int's. float's are formed by dividing the interval [0.0,1.0] into 232 sub intervals, then randomly choosing one subinterval. double's are formed by dividing the interval [0.0,1.0] into 264 sub intervals, then randomly choosing one subinterval.
- Version:
- 1.0, 09/24/99
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionstatic final int
private static final int
private static final int
private static final int
private static final int
private static final int
private int[]
private int
private static final int
private static final int
private static final int
private static final int
Fields inherited from class cern.colt.PersistentObject
serialVersionUID
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Constructor Summary
ConstructorsConstructorDescriptionConstructs and returns a random number generator with a default seed, which is a constant.MersenneTwister
(int seed) Constructs and returns a random number generator with the given seed.Constructs and returns a random number generator seeded with the given date. -
Method Summary
Modifier and TypeMethodDescriptionclone()
Returns a copy of the receiver; the copy will produce identical sequences.protected void
Generates N words at one time.int
nextInt()
Returns a 32 bit uniformly distributed random number in the closed interval [Integer.MIN_VALUE,Integer.MAX_VALUE] (including Integer.MIN_VALUE and Integer.MAX_VALUE).protected void
setSeed
(int seed) Sets the receiver's seed.Methods inherited from class cern.jet.random.engine.RandomEngine
apply, apply, makeDefault, nextDouble, nextFloat, nextLong, raw
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Field Details
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mti
private int mti -
mt
private int[] mt -
N
private static final int N- See Also:
-
M
private static final int M- See Also:
-
MATRIX_A
private static final int MATRIX_A- See Also:
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UPPER_MASK
private static final int UPPER_MASK- See Also:
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LOWER_MASK
private static final int LOWER_MASK- See Also:
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TEMPERING_MASK_B
private static final int TEMPERING_MASK_B- See Also:
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TEMPERING_MASK_C
private static final int TEMPERING_MASK_C- See Also:
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mag0
private static final int mag0- See Also:
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mag1
private static final int mag1- See Also:
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DEFAULT_SEED
public static final int DEFAULT_SEED- See Also:
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Constructor Details
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MersenneTwister
public MersenneTwister()Constructs and returns a random number generator with a default seed, which is a constant. Thus using this constructor will yield generators that always produce exactly the same sequence. This method is mainly intended to ease testing and debugging. -
MersenneTwister
public MersenneTwister(int seed) Constructs and returns a random number generator with the given seed. -
MersenneTwister
Constructs and returns a random number generator seeded with the given date.- Parameters:
d
- typically new java.util.Date()
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Method Details
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clone
Returns a copy of the receiver; the copy will produce identical sequences. After this call has returned, the copy and the receiver have equal but separate state.- Overrides:
clone
in classPersistentObject
- Returns:
- a copy of the receiver.
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nextBlock
protected void nextBlock()Generates N words at one time. -
nextInt
public int nextInt()Returns a 32 bit uniformly distributed random number in the closed interval [Integer.MIN_VALUE,Integer.MAX_VALUE] (including Integer.MIN_VALUE and Integer.MAX_VALUE).- Specified by:
nextInt
in classRandomEngine
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setSeed
protected void setSeed(int seed) Sets the receiver's seed. This method resets the receiver's entire internal state.
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