time33 哈希函数,又叫 DJBX33A,Bernstein's hash

php, apache, perl, bsddb都使用time33哈希.

最简单的版本

    uint32_t time33(char const *str, int len)
    {
        unsigned long  hash = 0;
        for (int i = 0; i < len; i++) {
            hash = hash *33 + (unsigned long) str[i];
        }
        return hash;
    }

这个版本最可以体现time33的算法思路,够简单。

 

把乘法操作换成位操作

        unsigned long time33(char const *str, int len)
    {
        unsigned long  hash = 0;
        for (int i = 0; i < len; i++) {
            hash = ((hash <<5) + hash) + (unsigned long) str[i];
        }
        return hash;
    }

59个字符1000 0000次运行(gcc没有开启优化,因为开了优化后两个函数的实际代码会一样)

第一个:

real    0m4.389s
user    0m4.388s
sys     0m0.000s

第二个:

real    0m4.137s
user    0m4.120s
sys     0m0.000s

gcc –O2优化后是

real    0m1.367s
user    0m1.360s
sys     0m0.000s

 

php版本

inline unsigned time33(char const*str, int len)
{
     unsigned long hash = 5381;
     /* variant with the hash unrolled eight times */
     for (; len >= 8; len -= 8) {
         hash = ((hash << 5) + hash) + *str++;
         hash = ((hash << 5) + hash) + *str++;
         hash = ((hash << 5) + hash) + *str++;
         hash = ((hash << 5) + hash) + *str++;
        hash = ((hash << 5) + hash) + *str++;
        hash = ((hash << 5) + hash) + *str++;
        hash = ((hash << 5) + hash) + *str++;
        hash = ((hash << 5) + hash) + *str++;
    }
    switch (len) {
        case 7: hash = ((hash << 5) + hash) + *str++; /* fallthrough... */
        case 6: hash = ((hash << 5) + hash) + *str++; /* fallthrough... */
        case 5: hash = ((hash << 5) + hash) + *str++; /* fallthrough... */
        case 4: hash = ((hash << 5) + hash) + *str++; /* fallthrough... */
        case 3: hash = ((hash << 5) + hash) + *str++; /* fallthrough... */
        case 2: hash = ((hash << 5) + hash) + *str++; /* fallthrough... */
        case 1: hash = ((hash << 5) + hash) + *str++; break;
        case 0: break;
    }
    return hash;
}

59个字符,1000 0000次

real    0m1.088s
user    0m1.068s
sys     0m0.000s

速度提升主要在循环展开, 对于短字符,这个是不明显的。

php版本的hash初始值是5381, 这个

Magic Constant 5381:

  1. odd number

  2. prime number

  3. deficient number

  4. 001/010/100/000/101 b

Apache版本

unsigned long time33(char const  *str, int *len)
{
    unsigned long hash = 0;

    const char *p=str;
    if (*len<=0) {
        for(p = str; *p; p++) {
            hash = hash * 33 + *p;
        }
        *len = p - str;
    }
    else {
        int i = *len;
        for (p = str;i; i--, p++) {
            hash = hash * 33 + *p;
        }
    }
    return hash;
}

测试结果

real    0m1.418s
user    0m1.412s
sys     0m0.004s

 

综上,我的改进版本

#define likely(x) __builtin_expect((x),1)
#define unlikely(x) __builtin_expect((x),0)
    //php版本
    unsigned long time33(char const *str, int len=-1)
    {
        unsigned long hash = 5381;
        /* variant with the hash unrolled eight times */
        char const *p = str;
        if (unlikely(len<0)) {
                for(; *p; p++) {
                    hash = hash * 33 + *p;
                }
                return hash;
        }

#define TIME33_HASH_MIXED_CH()  hash = ((hash<<5)+hash) + *p++
        for (; len >= 8; len -= 8) {
            TIME33_HASH_MIXED_CH(); //1
            TIME33_HASH_MIXED_CH(); //2
            TIME33_HASH_MIXED_CH(); //3
            TIME33_HASH_MIXED_CH(); //4
            TIME33_HASH_MIXED_CH(); //5
            TIME33_HASH_MIXED_CH(); //6
            TIME33_HASH_MIXED_CH(); //7
            TIME33_HASH_MIXED_CH(); //8
       }
       switch (len) {
           case 7: TIME33_HASH_MIXED_CH(); /* fallthrough... */
           case 6: TIME33_HASH_MIXED_CH(); /* fallthrough... */
           case 5: TIME33_HASH_MIXED_CH(); /* fallthrough... */
           case 4: TIME33_HASH_MIXED_CH(); /* fallthrough... */
           case 3: TIME33_HASH_MIXED_CH(); /* fallthrough... */
           case 2: TIME33_HASH_MIXED_CH(); /* fallthrough... */
           case 1: TIME33_HASH_MIXED_CH(); break;
           case 0: break;
       }
       return hash;
   }

#undef TIME33_HASH_MIXED_CH

测试结果

real    0m1.072s
user    0m1.064s
sys     0m0.000s

测试过, 重复率在 1/2000。

 

为什么是33的倍数, PHP中注释是

  • DJBX33A (Daniel J. Bernstein, Times 33 with Addition)
  •   This is Daniel J. Bernstein's popular `times 33' hash function as
  •   posted by him years ago on comp.lang.c. It basically uses a function
  •   like ``hash(i) = hash(i-1) * 33 + str[i]''. This is one of the best
  •   known hash functions for strings. Because it is both computed very
  •   fast and distributes very well.
  •   The magic of number 33, i.e. why it works better than many other
  •   constants, prime or not, has never been adequately explained by
  •   anyone. So I try an explanation: if one experimentally tests all
  •   multipliers between 1 and 256 (as RSE did now) one detects that even
  •   numbers are not useable at all. The remaining 128 odd numbers
  •   (except for the number 1) work more or less all equally well. They
  •   all distribute in an acceptable way and this way fill a hash table
  •   with an average percent of approx. 86%.
  •   If one compares the Chi^2 values of the variants, the number 33 not
  •   even has the best value. But the number 33 and a few other equally
  •   good numbers like 17, 31, 63, 127 and 129 have nevertheless a great
  •   advantage to the remaining numbers in the large set of possible
  •   multipliers: their multiply operation can be replaced by a faster
  •   operation based on just one shift plus either a single addition
  •   or subtraction operation. And because a hash function has to both
  •   distribute good _and_ has to be very fast to compute, those few
  •   numbers should be preferred and seems to be the reason why Daniel J.
  •   Bernstein also preferred it.
  •                    -- Ralf S. Engelschall rse@engelschall.com
  • 其它倍数

    Ngix使用的是 time31

    Tokyo Cabinet使用的是 time37

    Bob在他的文章说,小写英文词汇适合33, 大小写混合使用65。time33比较适合的是英文词汇的hash.

    posted @ 2010-12-20 16:35  napoleon_liu  阅读(6619)  评论(0编辑  收藏  举报