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.