字符串Hash函数评估

Hash查找因为其O(1)的查找性能而著称，被对查找性能要求高的应用所广泛采用。它的基本思想是：
(1) 创建一个定长的线性Hash表，一般可以初始化时指定length;

(2) 设计Hash函数，将关键字key散射到Hash表中。其中hash函数设计是最为关键的，均匀分布、冲突概率小全在它；

(3) 通常采用拉链方法来解决hash冲突问题，即散射到同一个hash表项的关键字，以链表形式来表示(也称为桶backet);

(4) 给定关键字key，就可以在O(1) + O(m)的时间复杂度内定位到目标。其中，m为拉链长度，即桶深。

 

Hash应用中，字符串是最为常见的关键字，应用非常普通，现在的程序设计语言中基本上都提供了字符串hash表的支持。字符串hash函数非常多，常见的主要有Simple_hash, RS_hash, JS_hash, PJW_hash, ELF_hash, BKDR_hash, SDBM_hash, DJB_hash, AP_hash, CRC_hash等。它们的C语言实现见后面附录代码: hash.h, hash.c。那么这么些字符串hash函数，谁好熟非呢？评估hash函数优劣的基准主要有以下两个指标：

(1) 散列分布性

即桶的使用率backet_usage = (已使用桶数) / (总的桶数)，这个比例越高，说明分布性良好，是好的hash设计。

(2) 平均桶长

即avg_backet_len，所有已使用桶的平均长度。理想状态下这个值应该=1，越小说明冲突发生地越少，是好的hash设计。

hash函数计算一般都非常简洁，因此在耗费计算时间复杂性方面判别甚微，这里不作对比。

 

评估方案设计是这样的：

(1) 以200M的视频文件作为输入源，以4KB的块为大小计算MD5值，并以此作为hash关键字;

(2) 分别应用上面提到的各种字符串hash函数，进行hash散列模拟；

(3) 统计结果，用散列分布性和平均桶长两个指标进行评估分析。

 

测试程序见附录代码hashtest.c，测试结果如下表所示。从这个结果我们也可以看出，这些字符串hash函数真是不相仲伯，难以决出高低，所以实际应用中可以根据喜好选择。当然，最好实际测试一下，毕竟应用特点不大相同。其他几组测试结果也类似，这里不再给出。

Hash函数桶数Hash调用总数最大桶长平均桶长桶使用率%simple_hash1024047198164.6399.00%RS_hash1024047198164.6398.91%JS_hash1024047198154.6498.87%PJW_hash1024047198164.6399.00%ELF_hash1024047198164.6399.00%BKDR_hash1024047198164.6399.00%SDBM_hash1024047198164.6398.90%DJB_hash1024047198154.6498.85%AP_hash1024047198164.6398.96%CRC_hash1024047198164.6498.77%

 

附录源代码：

hash.h

#ifndef _HASH_H#define _HASH_H#ifdef __cplusplusextern "C" {#endif/* A Simple Hash Function */unsigned int simple_hash(char *str);/* RS Hash Function */unsigned int RS_hash(char *str);/* JS Hash Function */unsigned int JS_hash(char *str);/* P. J. Weinberger Hash Function */unsigned int PJW_hash(char *str);/* ELF Hash Function */unsigned int ELF_hash(char *str);/* BKDR Hash Function */unsigned int BKDR_hash(char *str);/* SDBM Hash Function */unsigned int SDBM_hash(char *str);/* DJB Hash Function */unsigned int DJB_hash(char *str);/* AP Hash Function */unsigned int AP_hash(char *str);/* CRC Hash Function */unsigned int CRC_hash(char *str);#ifdef __cplusplus}#endif#endif

hash.c

#include <string.h>#include "hash.h"/* A Simple Hash Function */unsigned int simple_hash(char *str){register unsigned int hash;register unsigned char *p;for(hash = 0, p = (unsigned char *)str; *p ; p++)hash = 31 * hash + *p;return (hash & 0x7FFFFFFF);}/* RS Hash Function */unsigned int RS_hash(char *str){ unsigned int b = 378551; unsigned int a = 63689; unsigned int hash = 0; while (*str) { hash = hash * a + (*str++); a *= b; } return (hash & 0x7FFFFFFF);}/* JS Hash Function */unsigned int JS_hash(char *str){ unsigned int hash = 1315423911; while (*str) { hash ^= ((hash << 5) + (*str++) + (hash >> 2)); } return (hash & 0x7FFFFFFF);}/* P. J. Weinberger Hash Function */unsigned int PJW_hash(char *str){ unsigned int BitsInUnignedInt = (unsigned int)(sizeof(unsigned int) * 8); unsigned int ThreeQuarters = (unsigned int)((BitsInUnignedInt * 3) / 4); unsigned int OneEighth = (unsigned int)(BitsInUnignedInt / 8); unsigned int HighBits = (unsigned int)(0xFFFFFFFF) << (BitsInUnignedInt - OneEighth); unsigned int hash = 0; unsigned int test = 0; while (*str) { hash = (hash << OneEighth) + (*str++); if ((test = hash & HighBits) != 0) { hash = ((hash ^ (test >> ThreeQuarters)) & (~HighBits)); } } return (hash & 0x7FFFFFFF);}/* ELF Hash Function */unsigned int ELF_hash(char *str){ unsigned int hash = 0; unsigned int x = 0; while (*str) { hash = (hash << 4) + (*str++); if ((x = hash & 0xF0000000L) != 0) { hash ^= (x >> 24); hash &= ~x; } } return (hash & 0x7FFFFFFF);}/* BKDR Hash Function */unsigned int BKDR_hash(char *str){ unsigned int seed = 131; // 31 131 1313 13131 131313 etc.. unsigned int hash = 0; while (*str) { hash = hash * seed + (*str++); } return (hash & 0x7FFFFFFF);}/* SDBM Hash Function */unsigned int SDBM_hash(char *str){ unsigned int hash = 0; while (*str) { hash = (*str++) + (hash << 6) + (hash << 16) - hash; } return (hash & 0x7FFFFFFF);}/* DJB Hash Function */unsigned int DJB_hash(char *str){ unsigned int hash = 5381; while (*str) { hash += (hash << 5) + (*str++); } return (hash & 0x7FFFFFFF);}/* AP Hash Function */unsigned int AP_hash(char *str){ unsigned int hash = 0; int i; for (i=0; *str; i++) { if ((i & 1) == 0) { hash ^= ((hash << 7) ^ (*str++) ^ (hash >> 3)); } else { hash ^= (~((hash << 11) ^ (*str++) ^ (hash >> 5))); } } return (hash & 0x7FFFFFFF);}/* CRC Hash Function */unsigned int CRC_hash(char *str){ unsigned int nleft = strlen(str); unsigned long long sum = 0; unsigned short int *w = (unsigned short int *)str; unsigned short int answer = 0; /* * Our algorithm is simple, using a 32 bit accumulator (sum), we add * sequential 16 bit words to it, and at the end, fold back all the * carry bits from the top 16 bits into the lower 16 bits. */ while ( nleft > 1 ) { sum += *w++; nleft -= 2; } /* * mop up an odd byte, if necessary */ if ( 1 == nleft ) { *( unsigned char * )( &answer ) = *( unsigned char * )w ; sum += answer; } /* * add back carry outs from top 16 bits to low 16 bits * add hi 16 to low 16 */ sum = ( sum >> 16 ) + ( sum & 0xFFFF ); /* add carry */ sum += ( sum >> 16 ); /* truncate to 16 bits */ answer = ~sum; return (answer & 0xFFFFFFFF);}

hashtest.c

#include <stdio.h>#include <stdlib.h>#include <sys/types.h>#include <sys/stat.h>#include <fcntl.h>#include <errno.h>#include <string.h>#include "hash.h"#include "md5.h"struct hash_key {unsigned char *key;struct hash_key *next; };struct hash_counter_entry {unsigned int hit_count;unsigned int entry_count;struct hash_key *keys;};#define BLOCK_LEN4096static int backet_len = 10240;static int hash_call_count = 0;static struct hash_counter_entry *hlist = NULL;unsigned int (*hash_func)(char *str);void choose_hash_func(char *hash_func_name){if (0 == strcmp(hash_func_name, "simple_hash"))hash_func = simple_hash;else if (0 == strcmp(hash_func_name, "RS_hash"))hash_func = RS_hash;else if (0 == strcmp(hash_func_name, "JS_hash"))hash_func = JS_hash;else if (0 == strcmp(hash_func_name, "PJW_hash"))hash_func = PJW_hash;else if (0 == strcmp(hash_func_name, "ELF_hash"))hash_func = ELF_hash;else if (0 == strcmp(hash_func_name, "BKDR_hash"))hash_func = BKDR_hash;else if (0 == strcmp(hash_func_name, "SDBM_hash"))hash_func = SDBM_hash;else if (0 == strcmp(hash_func_name, "DJB_hash"))hash_func = DJB_hash;else if (0 == strcmp(hash_func_name, "AP_hash"))hash_func = AP_hash;else if (0 == strcmp(hash_func_name, "CRC_hash"))hash_func = CRC_hash;elsehash_func = NULL;}void insert_hash_entry(unsigned char *key, struct hash_counter_entry *hlist){unsigned int hash_value = hash_func(key) % backet_len;struct hash_key *p;p = hlist[hash_value].keys;while(p) {if (0 == strcmp(key, p->key))break;p = p->next;}if (p == NULL){p = (struct hash_key *)malloc(sizeof(struct hash_key));if (p == NULL) {perror("malloc in insert_hash_entry");return;}p->key = strdup(key);p->next = hlist[hash_value].keys;hlist[hash_value].keys = p;hlist[hash_value].entry_count++;}hlist[hash_value].hit_count++;}void hashtest_init(){int i;hash_call_count = 0;hlist = (struct hash_counter_entry *) malloc (sizeof(struct hash_counter_entry) * backet_len);if (NULL == hlist){perror("malloc in hashtest_init");return;}for (i = 0; i < backet_len; i++){hlist[i].hit_count = 0;hlist[i].entry_count = 0;hlist[i].keys = NULL;}}void hashtest_clean(){int i;struct hash_key *pentry, *p;if (NULL == hlist)return;for (i = 0; i < backet_len; ++i){pentry = hlist[i].keys;while(pentry){p = pentry->next;if (pentry->key) free(pentry->key);free(pentry);pentry = p;}}free(hlist);}void show_hashtest_result(){int i, backet = 0, max_link = 0, sum = 0;int conflict_count = 0, hit_count = 0;float avg_link, backet_usage;for(i = 0; i < backet_len; i++){if (hlist[i].hit_count > 0) {backet++;sum += hlist[i].entry_count;if (hlist[i].entry_count > max_link){max_link = hlist[i].entry_count;}if (hlist[i].entry_count > 1){conflict_count++;}hit_count += hlist[i].hit_count;}}backet_usage = backet/1.0/backet_len * 100;;avg_link = sum/1.0/backet;printf("backet_len = %d/n", backet_len);printf("hash_call_count = %d/n", hash_call_count);printf("hit_count = %d/n", hit_count);printf("conflict count = %d/n", conflict_count);printf("longest hash entry = %d/n", max_link);printf("average hash entry length = %.2f/n", avg_link);printf("backet usage = %.2f%/n", backet_usage);}void usage(){printf("Usage: hashtest filename hash_func_name [backet_len]/n");printf("hash_func_name:/n");printf("/tsimple_hash/n");printf("/tRS_hash/n");printf("/tJS_hash/n");printf("/tPJW_hash/n");printf("/tELF_hash/n");printf("/tBKDR_hash/n");printf("/tSDBM_hash/n");printf("/tDJB_hash/n");printf("/tAP_hash/n");printf("/tCRC_hash/n");}void md5_to_32(unsigned char *md5_16, unsigned char *md5_32){int i;for (i = 0; i < 16; ++i){sprintf(md5_32 + i * 2, "%02x", md5_16[i]);}}int main(int argc, char *argv[]){int fd = -1, rwsize = 0;unsigned char md5_checksum[16 + 1] = {0};unsigned char buf[BLOCK_LEN] = {0};if (argc < 3) {usage();return -1;}if (-1 == (fd = open(argv[1], O_RDONLY))){perror("open source file");return errno;}if (argc == 4){backet_len = atoi(argv[3]);}hashtest_init();choose_hash_func(argv[2]);while (rwsize = read(fd, buf, BLOCK_LEN)){md5(buf, rwsize, md5_checksum);insert_hash_entry(md5_checksum, hlist);hash_call_count++;memset(buf, 0, BLOCK_LEN);memset(md5_checksum, 0, 16 + 1);}close(fd);show_hashtest_result();hashtest_clean();return 0;}