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guava之BloomFilter

作者:互联网

Guava中的布隆过滤器

采用Guava 27.0.1版本的源码,BF的具体逻辑位于com.google.common.hash.BloomFilter类中。开始读代码吧。

BloomFilter类的成员属性

不多,只有4个。

  /** The bit set of the BloomFilter (not necessarily power of 2!) */
  private final LockFreeBitArray bits;

  /** Number of hashes per element */
  private final int numHashFunctions;

  /** The funnel to translate Ts to bytes */
  private final Funnel<? super T> funnel;

  /** The strategy we employ to map an element T to {@code numHashFunctions} bit indexes. */
  private final Strategy strategy;

BloomFilter的构造

这个类的构造方法是私有的。要创建它的实例,应该通过公有的create()方法。它一共有5种重载方法,但最终都是调用了如下的逻辑。

  @VisibleForTesting
  static <T> BloomFilter<T> create(
      Funnel<? super T> funnel, long expectedInsertions, double fpp, Strategy strategy) {
    checkNotNull(funnel);
    checkArgument(
        expectedInsertions >= 0, "Expected insertions (%s) must be >= 0", expectedInsertions);
    checkArgument(fpp > 0.0, "False positive probability (%s) must be > 0.0", fpp);
    checkArgument(fpp < 1.0, "False positive probability (%s) must be < 1.0", fpp);
    checkNotNull(strategy);

    if (expectedInsertions == 0) {
      expectedInsertions = 1;
    }
    /*
     * TODO(user): Put a warning in the javadoc about tiny fpp values, since the resulting size
     * is proportional to -log(p), but there is not much of a point after all, e.g.
     * optimalM(1000, 0.0000000000000001) = 76680 which is less than 10kb. Who cares!
     */
    long numBits = optimalNumOfBits(expectedInsertions, fpp);
    int numHashFunctions = optimalNumOfHashFunctions(expectedInsertions, numBits);
    try {
      return new BloomFilter<T>(new LockFreeBitArray(numBits), numHashFunctions, funnel, strategy);
    } catch (IllegalArgumentException e) {
      throw new IllegalArgumentException("Could not create BloomFilter of " + numBits + " bits", e);
    }
  }

该方法接受4个参数:funnel是插入数据的Funnel,expectedInsertions是期望插入的元素总个数n,fpp即期望假阳性率p,strategy即哈希策略。

由上可知,位数组的长度m和哈希函数的个数k分别通过optimalNumOfBits()方法和optimalNumOfHashFunctions()方法来估计。

估计最优m值和k值

  @VisibleForTesting
  static long optimalNumOfBits(long n, double p) {
    if (p == 0) {
      p = Double.MIN_VALUE;
    }
    return (long) (-n * Math.log(p) / (Math.log(2) * Math.log(2)));
  }

  @VisibleForTesting
  static int optimalNumOfHashFunctions(long n, long m) {
    // (m / n) * log(2), but avoid truncation due to division!
    return Math.max(1, (int) Math.round((double) m / n * Math.log(2)));
  }

要看懂这两个方法,我们得接着上一节的推导继续做下去。

 

 

由假阳性率的近似计算方法可知,如果要使假阳性率尽量小,在m和n给定的情况下,k值应为:

   

这就是optimalNumOfHashFunctions()方法的逻辑。那么m该如何估计呢?

将k代入上一节的式子并化简,我们可以整理出期望假阳性率p与m、n的关系:

   

 

 

亦即:

   

这就是optimalNumOfBits()方法的逻辑。

从上也可以得出:

所以,在创建BloomFilter时,确定合适的p和n值很重要。

哈希策略

在BloomFilterStrategies枚举中定义了两种哈希策略,都基于著名的MurmurHash算法,分别是MURMUR128_MITZ_32和MURMUR128_MITZ_64。前者是一个简化版,所以我们来看看后者的实现方法。

  MURMUR128_MITZ_64() {
    @Override
    public <T> boolean put(
        T object, Funnel<? super T> funnel, int numHashFunctions, LockFreeBitArray bits) {
      long bitSize = bits.bitSize();
      byte[] bytes = Hashing.murmur3_128().hashObject(object, funnel).getBytesInternal();
      long hash1 = lowerEight(bytes);
      long hash2 = upperEight(bytes);

      boolean bitsChanged = false;
      long combinedHash = hash1;
      for (int i = 0; i < numHashFunctions; i++) {
        // Make the combined hash positive and indexable
        bitsChanged |= bits.set((combinedHash & Long.MAX_VALUE) % bitSize);
        combinedHash += hash2;
      }
      return bitsChanged;
    }

    @Override
    public <T> boolean mightContain(
        T object, Funnel<? super T> funnel, int numHashFunctions, LockFreeBitArray bits) {
      long bitSize = bits.bitSize();
      byte[] bytes = Hashing.murmur3_128().hashObject(object, funnel).getBytesInternal();
      long hash1 = lowerEight(bytes);
      long hash2 = upperEight(bytes);

      long combinedHash = hash1;
      for (int i = 0; i < numHashFunctions; i++) {
        // Make the combined hash positive and indexable
        if (!bits.get((combinedHash & Long.MAX_VALUE) % bitSize)) {
          return false;
        }
        combinedHash += hash2;
      }
      return true;
    }

    private /* static */ long lowerEight(byte[] bytes) {
      return Longs.fromBytes(
          bytes[7], bytes[6], bytes[5], bytes[4], bytes[3], bytes[2], bytes[1], bytes[0]);
    }

    private /* static */ long upperEight(byte[] bytes) {
      return Longs.fromBytes(
          bytes[15], bytes[14], bytes[13], bytes[12], bytes[11], bytes[10], bytes[9], bytes[8]);
    }
  };

其中put()方法负责向布隆过滤器中插入元素,mightContain()方法负责判断元素是否存在。以put()方法为例讲解一下流程吧。

  1. 使用MurmurHash算法对funnel的输入数据进行散列,得到128bit(16B)的字节数组。
  2. 取低8字节作为第一个哈希值hash1,取高8字节作为第二个哈希值hash2。
  3. 进行k次循环,每次循环都用hash1与hash2的复合哈希做散列,然后对m取模,将位数组中的对应比特设为1。

这里需要注意两点:

位数组具体实现

来看LockFreeBitArray类的部分代码。

  static final class LockFreeBitArray {
    private static final int LONG_ADDRESSABLE_BITS = 6;
    final AtomicLongArray data;
    private final LongAddable bitCount;

    LockFreeBitArray(long bits) {
      this(new long[Ints.checkedCast(LongMath.divide(bits, 64, RoundingMode.CEILING))]);
    }

    // Used by serialization
    LockFreeBitArray(long[] data) {
      checkArgument(data.length > 0, "data length is zero!");
      this.data = new AtomicLongArray(data);
      this.bitCount = LongAddables.create();
      long bitCount = 0;
      for (long value : data) {
        bitCount += Long.bitCount(value);
      }
      this.bitCount.add(bitCount);
    }

    /** Returns true if the bit changed value. */
    boolean set(long bitIndex) {
      if (get(bitIndex)) {
        return false;
      }

      int longIndex = (int) (bitIndex >>> LONG_ADDRESSABLE_BITS);
      long mask = 1L << bitIndex; // only cares about low 6 bits of bitIndex

      long oldValue;
      long newValue;
      do {
        oldValue = data.get(longIndex);
        newValue = oldValue | mask;
        if (oldValue == newValue) {
          return false;
        }
      } while (!data.compareAndSet(longIndex, oldValue, newValue));

      // We turned the bit on, so increment bitCount.
      bitCount.increment();
      return true;
    }

    boolean get(long bitIndex) {
      return (data.get((int) (bitIndex >>> 6)) & (1L << bitIndex)) != 0;
    }
    // ....
}

看官应该能明白为什么它要叫做“LockFree”BitArray了,因为它是采用原子类型AtomicLongArray作为位数组的存储的,确实不需要加锁。另外还有一个Guava中特有的LongAddable类型的计数器,用来统计置为1的比特数。

采用AtomicLongArray除了有并发上的优势之外,更主要的是它可以表示非常长的位数组。一个长整型数占用64bit,因此data[0]可以代表第0~63bit,data[1]代表64~127bit,data[2]代表128~191bit……依次类推。这样设计的话,将下标i无符号右移6位就可以获得data数组中对应的位置,再在其基础上左移i位就可以取得对应的比特了。

最后多嘴一句,上面的代码中用到了Long.bitCount()方法计算long型二进制表示中1的数量,堪称Java语言中最强的骚操作之一:

 public static int bitCount(long i) {
    // HD, Figure 5-14
    i = i - ((i >>> 1) & 0x5555555555555555L);
    i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
    i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
    i = i + (i >>> 8);
    i = i + (i >>> 16);
    i = i + (i >>> 32);
    return (int)i & 0x7f;
 }

标签:funnel,int,bits,bytes,long,哈希,guava,BloomFilter
来源: https://www.cnblogs.com/duanxz/p/14699028.html