Mersenne Twister 算法译为马特赛特旋转演算法，是伪随机数发生器之一，其主要作用是生成伪随机数。此算法是 Makoto Matsumoto（松本）和 Takuji Nishimura（西村）于 1997 年开发的，基于有限二进制字段上的矩阵线性再生。可以快速产生高质量的伪随机数，修正了古老随机数产生算法的很多缺陷。
Mersenne Twister 这个名字来自周期长度通常取 Mersenne 质数这样一个事实。常见的有两个变种 Mersenne Twister MT19937 和 Mersenne Twister MT19937-64 。
Mersenne Twister 有以下优点：随机性好，在计算机上容易实现，占用内存较少（mt19937 的 C 程式码执行仅需 624 个字的工作区域），与其它已使用的伪随机数发生器相比，产生随机数的速度快、周期长，可达到 ，且具有 623 维均匀分布的性质，对于一般的应用来说，足够大了，序列关联比较小，能通过很多随机性测试。
import java.util.HashMap;
import java.util.Map;
import java.util.Random;
/**
* MT19937 的 Java 实现。用于高效生成伪随机数。
*/
public class MTRandom extends Random {
// Constants used in the original C implementation
private final static int UPPER_MASK = 0x80000000;
private final static int LOWER_MASK = 0x7fffffff;
private final static int N = 624;
private final static int M = 397;
private final static int MAGIC[] = {0x0, 0x9908b0df};
private final static int MAGIC_FACTOR1 = 1812433253;
private final static int MAGIC_FACTOR2 = 1664525;
private final static int MAGIC_FACTOR3 = 1566083941;
private final static int MAGIC_MASK1 = 0x9d2c5680;
private final static int MAGIC_MASK2 = 0xefc60000;
private final static int MAGIC_SEED = 19650218;
private final static long DEFAULT_SEED = 5489L;
// Internal state
private transient int[] mt;
private transient int mti;
private transient boolean compat = false;
// Temporary buffer used during setSeed(long)
private transient int[] ibuf;
/**
* The default constructor for an instance of MTRandom. This invokes
* the no-argument constructor for java.util.Random which will result
* in the class being initialised with a seed value obtained by calling
* System.currentTimeMillis().
*/
public MTRandom() {
}
/**
* This version of the constructor can be used to implement identical
* behaviour to the original C code version of this algorithm including
* exactly replicating the case where the seed value had not been set
* prior to calling genrand_int32.
* <p>
* If the compatibility flag is set to true, then the algorithm will be
* seeded with the same default value as was used in the original C
* code. Furthermore the setSeed() method, which must take a 64 bit
* long value, will be limited to using only the lower 32 bits of the
* seed to facilitate seamless migration of existing C code into Java
* where identical behaviour is required.
* <p>
* Whilst useful for ensuring backwards compatibility, it is advised
* that this feature not be used unless specifically required, due to
* the reduction in strength of the seed value.
*
* @param compatible Compatibility flag for replicating original
* behaviour.
*/
public MTRandom(boolean compatible) {
super(0L);
compat = compatible;
setSeed(compat ? DEFAULT_SEED : System.currentTimeMillis());
}
/**
* This version of the constructor simply initialises the class with
* the given 64 bit seed value. For a better random number sequence
* this seed value should contain as much entropy as possible.
*
* @param seed The seed value with which to initialise this class.
*/
public MTRandom(long seed) {
super(seed);
}
/**
* This version of the constructor initialises the class with the
* given byte array. All the data will be used to initialise this
* instance.
*
* @param buf The non-empty byte array of seed information.
* @throws NullPointerException if the buffer is null.
* @throws IllegalArgumentException if the buffer has zero length.
*/
public MTRandom(byte[] buf) {
super(0L);
setSeed(buf);
}
/**
* This version of the constructor initialises the class with the
* given integer array. All the data will be used to initialise
* this instance.
*
* @param buf The non-empty integer array of seed information.
* @throws NullPointerException if the buffer is null.
* @throws IllegalArgumentException if the buffer has zero length.
*/
public MTRandom(int[] buf) {
super(0L);
setSeed(buf);
}
// Initializes mt[N] with a simple integer seed. This method is
// required as part of the Mersenne Twister algorithm but need
// not be made public.
private final void setSeed(int seed) {
// Annoying runtime check for initialisation of internal data
// caused by java.util.Random invoking setSeed() during init.
// This is unavoidable because no fields in our instance will
// have been initialised at this point, not even if the code
// were placed at the declaration of the member variable.
if (mt == null) mt = new int[N];
// ---- Begin Mersenne Twister Algorithm ----
mt[0] = seed;
for (mti = 1; mti < N; mti++) {
mt[mti] = (MAGIC_FACTOR1 * (mt[mti - 1] ^ (mt[mti - 1] >>> 30)) + mti);
}
// ---- End Mersenne Twister Algorithm ----
}
/**
* This method resets the state of this instance using the 64
* bits of seed data provided. Note that if the same seed data
* is passed to two different instances of MTRandom (both of
* which share the same compatibility state) then the sequence
* of numbers generated by both instances will be identical.
* <p>
* If this instance was initialised in 'compatibility' mode then
* this method will only use the lower 32 bits of any seed value
* passed in and will match the behaviour of the original C code
* exactly with respect to state initialisation.
*
* @param seed The 64 bit value used to initialise the random
* number generator state.
*/
public final synchronized void setSeed(long seed) {
if (compat) {
setSeed((int) seed);
} else {
// Annoying runtime check for initialisation of internal data
// caused by java.util.Random invoking setSeed() during init.
// This is unavoidable because no fields in our instance will
// have been initialised at this point, not even if the code
// were placed at the declaration of the member variable.
if (ibuf == null) ibuf = new int[2];
ibuf[0] = (int) seed;
ibuf[1] = (int) (seed >>> 32);
setSeed(ibuf);
}
}
/**
* This method resets the state of this instance using the byte
* array of seed data provided. Note that calling this method
* is equivalent to calling "setSeed(pack(buf))" and in particular
* will result in a new integer array being generated during the
* call. If you wish to retain this seed data to allow the pseudo
* random sequence to be restarted then it would be more efficient
* to use the "pack()" method to convert it into an integer array
* first and then use that to re-seed the instance. The behaviour
* of the class will be the same in both cases but it will be more
* efficient.
*
* @param buf The non-empty byte array of seed information.
* @throws NullPointerException if the buffer is null.
* @throws IllegalArgumentException if the buffer has zero length.
*/
public final void setSeed(byte[] buf) {
setSeed(pack(buf));
}
/**
* This method resets the state of this instance using the integer
* array of seed data provided. This is the canonical way of
* resetting the pseudo random number sequence.
*
* @param buf The non-empty integer array of seed information.
* @throws NullPointerException if the buffer is null.
* @throws IllegalArgumentException if the buffer has zero length.
*/
public final synchronized void setSeed(int[] buf) {
int length = buf.length;
if (length == 0) throw new IllegalArgumentException("Seed buffer may not be empty");
// ---- Begin Mersenne Twister Algorithm ----
int i = 1, j = 0, k = (N > length ? N : length);
setSeed(MAGIC_SEED);
for (; k > 0; k--) {
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >>> 30)) * MAGIC_FACTOR2)) + buf[j] + j;
i++;
j++;
if (i >= N) {
mt[0] = mt[N - 1];
i = 1;
}
if (j >= length) j = 0;
}
for (k = N - 1; k > 0; k--) {
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >>> 30)) * MAGIC_FACTOR3)) - i;
i++;
if (i >= N) {
mt[0] = mt[N - 1];
i = 1;
}
}
mt[0] = UPPER_MASK; // MSB is 1; assuring non-zero initial array
// ---- End Mersenne Twister Algorithm ----
}
/**
* This method forms the basis for generating a pseudo random number
* sequence from this class. If given a value of 32, this method
* behaves identically to the genrand_int32 function in the original
* C code and ensures that using the standard nextInt() function
* (inherited from Random) we are able to replicate behaviour exactly.
* <p>
* Note that where the number of bits requested is not equal to 32
* then bits will simply be masked out from the top of the returned
* integer value. That is to say that:
* <pre>
* mt.setSeed(12345);
* int foo = mt.nextInt(16) + (mt.nextInt(16) << 16);</pre>
* will not give the same result as
* <pre>
* mt.setSeed(12345);
* int foo = mt.nextInt(32);</pre>
*
* @param bits The number of significant bits desired in the output.
* @return The next value in the pseudo random sequence with the
* specified number of bits in the lower part of the integer.
*/
protected final synchronized int next(int bits) {
// ---- Begin Mersenne Twister Algorithm ----
int y, kk;
if (mti >= N) { // generate N words at one time
// In the original C implementation, mti is checked here
// to determine if initialisation has occurred; if not
// it initialises this instance with DEFAULT_SEED (5489).
// This is no longer necessary as initialisation of the
// Java instance must result in initialisation occurring
// Use the constructor MTRandom(true) to enable backwards
// compatible behaviour.
for (kk = 0; kk < N - M; kk++) {
y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
mt[kk] = mt[kk + M] ^ (y >>> 1) ^ MAGIC[y & 0x1];
}
for (; kk < N - 1; kk++) {
y = (mt[kk] & UPPER_MASK) | (mt[kk + 1] & LOWER_MASK);
mt[kk] = mt[kk + (M - N)] ^ (y >>> 1) ^ MAGIC[y & 0x1];
}
y = (mt[N - 1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
mt[N - 1] = mt[M - 1] ^ (y >>> 1) ^ MAGIC[y & 0x1];
mti = 0;
}
y = mt[mti++];
// Tempering
y ^= (y >>> 11);
y ^= (y << 7) & MAGIC_MASK1;
y ^= (y << 15) & MAGIC_MASK2;
y ^= (y >>> 18);
// ---- End Mersenne Twister Algorithm ----
return (y >>> (32 - bits));
}
// This is a fairly obscure little code section to pack a
// byte[] into an int[] in little endian ordering.
/**
* This simply utility method can be used in cases where a byte
* array of seed data is to be used to repeatedly re-seed the
* random number sequence. By packing the byte array into an
* integer array first, using this method, and then invoking
* setSeed() with that; it removes the need to re-pack the byte
* array each time setSeed() is called.
* <p>
* If the length of the byte array is not a multiple of 4 then
* it is implicitly padded with zeros as necessary. For example:
* <pre> byte[] { 0x01, 0x02, 0x03, 0x04, 0x05, 0x06 }</pre>
* becomes
* <pre> int[] { 0x04030201, 0x00000605 }</pre>
* <p>
* Note that this method will not complain if the given byte array
* is empty and will produce an empty integer array, but the
* setSeed() method will throw an exception if the empty integer
* array is passed to it.
*
* @param buf The non-null byte array to be packed.
* @return A non-null integer array of the packed bytes.
* @throws NullPointerException if the given byte array is null.
*/
public static int[] pack(byte[] buf) {
int k, blen = buf.length, ilen = ((buf.length + 3) >>> 2);
int[] ibuf = new int[ilen];
for (int n = 0; n < ilen; n++) {
int m = (n + 1) << 2;
if (m > blen) m = blen;
for (k = buf[--m] & 0xff; (m & 0x3) != 0; k = (k << 8) | buf[--m] & 0xff)
;
ibuf[n] = k;
}
return ibuf;
}
/**
* 使用/验证代码
*/
public static void main(String[] args) {
// MT19937 随机算法的 Java 实现
MTRandom mtRandom = new MTRandom();
Map<Integer, Integer> map = new HashMap<>();
// 循环次数
int times = 1000000;
long startTime = System.currentTimeMillis();
for (int i = 0; i < times; i++) {
// 使用 Map 去重
map.put(mtRandom.next(32), 0);
}
// 打印循环次数
System.out.println("times:" + times);
// 打印 Map 的个数
System.out.println("num:" + map.size());
// 打印非重复比率
System.out.println("proportion:" + map.size() / (double) times);
// 花费的时间(单位为毫秒)
System.out.println("time:" + (System.currentTimeMillis() - startTime));
}
}
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