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.