巧用redis的hyper loglog进行uv数据的统计

在面试的时候我们经常会被问道redis的数据结构,我们经常只会回答5种常见的数据结构,分别是字符串,链表,集合,有序集合,hash。其实在这之外,还有三种数据结构非常的又用,它们分别是bitmap,geo,hyper loglog,这里我们主要讲解下hyper loglog这个数据结构。

存储结构

struct hllhdr {
    char magic[4];      /* "HYLL" */
    uint8_t encoding;   /* HLL_DENSE or HLL_SPARSE. */
    uint8_t notused[3]; /* Reserved for future use, must be zero. */
    uint8_t card[8];    /* Cached cardinality, little endian. */
    uint8_t registers[]; /* Data bytes. */
};

算法

hyper loglog是采用基数统计来计算的,也就是需要分桶,redis默认分为16384个桶,每个桶占用6bit。

当新添加一个数据的时候,会先计算它的hash值,hash函数如下:

uint64_t MurmurHash64A (const void * key, int len, unsigned int seed) {
    const uint64_t m = 0xc6a4a7935bd1e995;
    const int r = 47;
    uint64_t h = seed ^ (len * m);
    const uint8_t *data = (const uint8_t *)key;
    const uint8_t *end = data + (len-(len&7));

    while(data != end) {
        uint64_t k;

#if (BYTE_ORDER == LITTLE_ENDIAN)
    #ifdef USE_ALIGNED_ACCESS
        memcpy(&k,data,sizeof(uint64_t));
    #else
        k = *((uint64_t*)data);
    #endif
#else
        k = (uint64_t) data[0];
        k |= (uint64_t) data[1] << 8;
        k |= (uint64_t) data[2] << 16;
        k |= (uint64_t) data[3] << 24;
        k |= (uint64_t) data[4] << 32;
        k |= (uint64_t) data[5] << 40;
        k |= (uint64_t) data[6] << 48;
        k |= (uint64_t) data[7] << 56;
#endif

        k *= m;
        k ^= k >> r;
        k *= m;
        h ^= k;
        h *= m;
        data += 8;
    }

    switch(len & 7) {
    case 7: h ^= (uint64_t)data[6] << 48; /* fall-thru */
    case 6: h ^= (uint64_t)data[5] << 40; /* fall-thru */
    case 5: h ^= (uint64_t)data[4] << 32; /* fall-thru */
    case 4: h ^= (uint64_t)data[3] << 24; /* fall-thru */
    case 3: h ^= (uint64_t)data[2] << 16; /* fall-thru */
    case 2: h ^= (uint64_t)data[1] << 8; /* fall-thru */
    case 1: h ^= (uint64_t)data[0];
            h *= m; /* fall-thru */
    };

    h ^= h >> r;
    h *= m;
    h ^= h >> r;
    return h;
}

然后我们会计算它的寄存器的索引

int hllPatLen(unsigned char *ele, size_t elesize, long *regp) {
    uint64_t hash, bit, index;
    int count;

    /* Count the number of zeroes starting from bit HLL_REGISTERS
     * (that is a power of two corresponding to the first bit we don't use
     * as index). The max run can be 64-P+1 = Q+1 bits.
     *
     * Note that the final "1" ending the sequence of zeroes must be
     * included in the count, so if we find "001" the count is 3, and
     * the smallest count possible is no zeroes at all, just a 1 bit
     * at the first position, that is a count of 1.
     *
     * This may sound like inefficient, but actually in the average case
     * there are high probabilities to find a 1 after a few iterations. */
    hash = MurmurHash64A(ele,elesize,0xadc83b19ULL);
    index = hash & HLL_P_MASK; /* Register index. */
    hash >>= HLL_P; /* Remove bits used to address the register. */
    hash |= ((uint64_t)1<<HLL_Q); /* Make sure the loop terminates
                                     and count will be <= Q+1. */
    bit = 1;
    count = 1; /* Initialized to 1 since we count the "00000...1" pattern. */
    while((hash & bit) == 0) {
        count++;
        bit <<= 1;
    }
    *regp = (int) index;
    return count;
}

最后如果当前索引大于原来的索引就更新。

/* Low level function to set the dense HLL register at 'index' to the
 * specified value if the current value is smaller than 'count'.
 *
 * 'registers' is expected to have room for HLL_REGISTERS plus an
 * additional byte on the right. This requirement is met by sds strings
 * automatically since they are implicitly null terminated.
 *
 * The function always succeed, however if as a result of the operation
 * the approximated cardinality changed, 1 is returned. Otherwise 0
 * is returned. */
int hllDenseSet(uint8_t *registers, long index, uint8_t count) {
    uint8_t oldcount;

    HLL_DENSE_GET_REGISTER(oldcount,registers,index);
    if (count > oldcount) {
        HLL_DENSE_SET_REGISTER(registers,index,count);
        return 1;
    } else {
        return 0;
    }
}

使用场景

设置键值表示一个小时的用户登录,然后添加用户A

pfadd USER:LOGIN:2020121608 A

添加其它用户

pfadd USER:LOGIN:2020121608 B C D A

统计数量

pfcount USER:LOGIN:2020121608

添加其它时间的用户

pfadd USER:LOGIN:2020121609 B C D A

统计2个小时的用户数量

pfcount USER:LOGIN:2020121608 USER:LOGIN:2020121609