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

转载自： http://www.cnblogs.com/napoleon_liu/articles/1911571.html

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 [email protected]

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.

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