高效随机数算法Java实现

jiezi

6 年前

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…
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.
* 
* 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.
* 
* 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.
* 
* 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 {

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.
* 
* 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.
* 
* 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>
* 
* 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