Java实现高效随机数算法的示例代码

前言

事情起源于一位网友分享了一个有趣的面试题：

生成由六位数字组成的ID，要求随机数字，不排重，不可自增，且数字不重复。ID总数为几十万。

初次解答

我一开始想到的办法是

• 生成一个足够大的ID池（其实就是需要多少就生成多少）
• 对ID池中的数字进行随机排序
• 依次消费ID池中的数字

可惜这个方法十分浪费空间，且性能很差。

初遇梅森旋转算法

后面咨询了网友后得知了一个高效的随机数算法：梅森旋转（Mersenne Twister/MT）。通过搜索资料得知：

梅森旋转算法（Mersenne twister）是一个伪随机数发生算法。由松本真和西村拓士在1997年开发，基于有限二进制字段上的矩阵线性递归。可以快速产生高质量的伪随机数，修正了古典随机数发生算法的很多缺陷。
最为广泛使用Mersenne Twister的一种变体是MT19937，可以产生32位整数序列。

PS：此算法依然无法完美解决面试题，但是也算学到了新知识

MT19937算法实现

后面通过Google，找到了一个高效的MT19937的Java版本代码。原代码链接为http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/JAVA/MTRandom.java

import java.util.Random;

/**
 * MT19937的Java实现
 */
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;
  }
}

测试

测试代码

    // MT19937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));

测试结果

times:1000000
num:999886
proportion:0.999886
time:374

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