hash function for string

Question

I'm working on hash table in C language and I'm testing hash function for string.

The first function I've tried is to add ascii code and use modulo (% 100) but i've got poor results with the first test of data: 40 collisions for 130 words.

The final input data will contain 8000 words (it's a dictionary stores in a file). The hash table is declared as int table[10000] and contains the position of the word in a .txt file.

• Which is the best algorithm for hashing string?
• And how to determinate the size of hash table?

Answer 1

I've had nice results with djb2 by Dan Bernstein.

unsigned long
hash(unsigned char *str)
{
    unsigned long hash = 5381;
    int c;

    while (c = *str++)
        hash = ((hash << 5) + hash) + c; /* hash * 33 + c */

    return hash;
}

Answer 2

First, you generally do not want to use a cryptographic hash for a hash table. An algorithm that's very fast by cryptographic standards is still excruciatingly slow by hash table standards.

Second, you want to ensure that every bit of the input can/will affect the result. One easy way to do that is to rotate the current result by some number of bits, then XOR the current hash code with the current byte. Repeat until you reach the end of the string. Note that you generally do not want the rotation to be an even multiple of the byte size either.

For example, assuming the common case of 8 bit bytes, you might rotate by 5 bits:

int hash(char const *input) { 
    int result = 0x55555555;

    while (*input) { 
        result ^= *input++;
        result = rol(result, 5);
    }
}

Edit: Also note that 10000 slots is rarely a good choice for a hash table size. You usually want one of two things: you either want a prime number as the size (required to ensure correctness with some types of hash resolution) or else a power of 2 (so reducing the value to the correct range can be done with a simple bit-mask).

Answer 3

I wanted to verify Xiaoning Bian's answer, but unfortunately he didn't post his code. So I implemented a little test suite and ran different little hashing functions on the list of 466K English words to see number of collisions for each:

Hash function      |     Collisions | Time (words) | Time (file)
=================================================================
CRC32              |    23 (0.005%) |      112 ms  |      38 ms
MurmurOAAT         |    26 (0.006%) |       86 ms  |      10 ms
FNV hash           |    32 (0.007%) |       87 ms  |       7 ms
Jenkins OAAT       |    36 (0.008%) |       90 ms  |       8 ms
DJB2 hash          |   344 (0.074%) |       87 ms  |       5 ms
K&R V2             |   356 (0.076%) |       86 ms  |       5 ms
Coffin             |   763 (0.164%) |       86 ms  |       4 ms
x17 hash           |  2242 (0.481%) |       87 ms  |       7 ms
-----------------------------------------------------------------
MurmurHash3_x86_32 |    19 (0.004%) |       90 ms  |       3 ms

I included time for both: hashing all words individually and hashing the entire file of all English words once. I also included a more complex MurmurHash3_x86_32 into my test for reference.

Conclusion:

• there is almost no point of using the popular DJB2 hash function for strings on Intel x86-64 (or AArch64 for that matter) architecture. Because it has much more collisions than similar functions (MurmurOAAT, FNV and Jenkins OAAT) while having very similar throughput. Bernstein's DJB2 performs especially bad on short strings. Example collisions: Liz/MHz, Bon/COM, Rey/SEX.

Test code:

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>

#define MAXLINE 2048
#define SEED    0x12345678

uint32_t DJB2_hash(const uint8_t *str)
{
    uint32_t hash = 5381;
    uint8_t c;
    while ((c = *str++))
        hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
    return hash;
}

uint32_t FNV(const void* key, int len, uint32_t h)
{
    // Source: https://github.com/aappleby/smhasher/blob/master/src/Hashes.cpp
    h ^= 2166136261UL;
    const uint8_t* data = (const uint8_t*)key;
    for(int i = 0; i < len; i++)
    {
        h ^= data[i];
        h *= 16777619;
    }
    return h;
}

uint32_t MurmurOAAT_32(const char* str, uint32_t h)
{
    // One-byte-at-a-time hash based on Murmur's mix
    // Source: https://github.com/aappleby/smhasher/blob/master/src/Hashes.cpp
    for (; *str; ++str) {
        h ^= *str;
        h *= 0x5bd1e995;
        h ^= h >> 15;
    }
    return h;
}

uint32_t KR_v2_hash(const char *s)
{
    // Source: https://stackoverflow.com/a/45641002/5407270
    // a.k.a. Java String hashCode()
    uint32_t hashval = 0;
    for (hashval = 0; *s != '\0'; s++)
        hashval = *s + 31*hashval;
    return hashval;
}

uint32_t Jenkins_one_at_a_time_hash(const char *str, size_t len)
{
    uint32_t hash, i;
    for(hash = i = 0; i < len; ++i)
    {
        hash += str[i];
        hash += (hash << 10);
        hash ^= (hash >> 6);
    }
    hash += (hash << 3);
    hash ^= (hash >> 11);
    hash += (hash << 15);
    return hash;
}

uint32_t crc32b(const uint8_t *str) {
    // Source: https://stackoverflow.com/a/21001712
    unsigned int byte, crc, mask;
    int i = 0, j;
    crc = 0xFFFFFFFF;
    while (str[i] != 0) {
        byte = str[i];
        crc = crc ^ byte;
        for (j = 7; j >= 0; j--) {
            mask = -(crc & 1);
            crc = (crc >> 1) ^ (0xEDB88320 & mask);
        }
        i = i + 1;
    }
    return ~crc;
}

inline uint32_t _rotl32(uint32_t x, int32_t bits)
{
    return x<<bits | x>>(32-bits);      // C idiom: will be optimized to a single operation
}

uint32_t Coffin_hash(char const *input) { 
    // Source: https://stackoverflow.com/a/7666668/5407270
    uint32_t result = 0x55555555;
    while (*input) { 
        result ^= *input++;
        result = _rotl32(result, 5);
    }
    return result;
}

uint32_t x17(const void * key, int len, uint32_t h)
{
    // Source: https://github.com/aappleby/smhasher/blob/master/src/Hashes.cpp
    const uint8_t * data = (const uint8_t*)key;
    for (int i = 0; i < len; ++i)
    {
        h = 17 * h + (data[i] - ' ');
    }
    return h ^ (h >> 16);
}

uint32_t apply_hash(int hash, const char* line)
{
    switch (hash) {
    case 1: return crc32b((const uint8_t*)line);
    case 2: return MurmurOAAT_32(line, SEED);
    case 3: return FNV(line, strlen(line), SEED);
    case 4: return Jenkins_one_at_a_time_hash(line, strlen(line));
    case 5: return DJB2_hash((const uint8_t*)line);
    case 6: return KR_v2_hash(line);
    case 7: return Coffin_hash(line);
    case 8: return x17(line, strlen(line), SEED);
    default: break;
    }
    return 0;
}

int main(int argc, char* argv[])
{
    // Read arguments
    const int hash_choice = atoi(argv[1]);
    char const* const fn = argv[2];

    // Read file
    FILE* f = fopen(fn, "r");

    // Read file line by line, calculate hash
    char line[MAXLINE];
    while (fgets(line, sizeof(line), f)) {
        line[strcspn(line, "\n")] = '\0';   // strip newline
        uint32_t hash = apply_hash(hash_choice, line);
        printf("%08x\n", hash);
    }
    fclose(f);

    return 0;
}

P.S. A more comprehensive review of speed and quality of modern hash functions can be found in SMHasher repository of Reini Urban (rurban). Notice the "Quality problems" column in the table.

Answer 4

Wikipedia shows a nice string hash function called Jenkins One At A Time Hash. It also quotes improved versions of this hash.

uint32_t jenkins_one_at_a_time_hash(char *key, size_t len)
{
    uint32_t hash, i;
    for(hash = i = 0; i < len; ++i)
    {
        hash += key[i];
        hash += (hash << 10);
        hash ^= (hash >> 6);
    }
    hash += (hash << 3);
    hash ^= (hash >> 11);
    hash += (hash << 15);
    return hash;
}

Answer 5

djb2 is good

Though djb2, as presented on stackoverflow by cnicutar, is almost certainly better, I think it's worth showing the K&R hashes too:

One of the K&R hashes is terrible, one is probably pretty good:

1. Apparently a terrible hash algorithm, as presented in K&R 1st edition. This is simply a summation of all bytes in the string (source):

   unsigned long hash(unsigned char *str)
   {
       unsigned int hash = 0;
       int c;
   
       while (c = *str++)
           hash += c;
   
       return hash;
   }
   

2. Probably a pretty decent hash algorithm, as presented in K&R version 2 (verified by me on pg. 144 of the book); NB: be sure to remove % HASHSIZE from the return statement if you plan on doing the modulus sizing-to-your-array-length outside the hash algorithm. Also, I recommend you make the return and "hashval" type unsigned long, or even better: uint32_t or uint64_t, instead of the simple unsigned (int). This is a simple algorithm which takes into account byte order of each byte in the string by doing this style of algorithm: hashvalue = new_byte + 31*hashvalue, for all bytes in the string:

   unsigned hash(char *s)
   {
       unsigned hashval;
   
       for (hashval = 0; *s != '\0'; s++)
           hashval = *s + 31*hashval;
       return hashval % HASHSIZE;
   }
   

Note that it's clear from the two algorithms that one reason the 1st edition hash is so terrible is because it does NOT take into consideration string character order, so hash("ab") would therefore return the same value as hash("ba"). This is not so with the 2nd edition hash, however, which would (much better!) return two different values for those strings.

The GCC C++11 hashing function used by the std::unordered_map<> template container hash table is excellent.

The GCC C++11 hashing functions used for unordered_map (a hash table template) and unordered_set (a hash set template) appear to be as follows.

• This is a partial answer to the question of what are the GCC C++11 hash functions used, stating that GCC uses an implementation of "MurmurHashUnaligned2", by Austin Appleby (http://murmurhash.googlepages.com/).
• In the file "gcc/libstdc++-v3/libsupc++/hash_bytes.cc", here (https://github.com/gcc-mirror/gcc/blob/master/libstdc++-v3/libsupc++/hash_bytes.cc), I found the implementations. Here's the one for the "32-bit size_t" return value, for example (pulled 11 Aug 2017):

Code:

// Implementation of Murmur hash for 32-bit size_t.
size_t _Hash_bytes(const void* ptr, size_t len, size_t seed)
{
  const size_t m = 0x5bd1e995;
  size_t hash = seed ^ len;
  const char* buf = static_cast<const char*>(ptr);

  // Mix 4 bytes at a time into the hash.
  while (len >= 4)
  {
    size_t k = unaligned_load(buf);
    k *= m;
    k ^= k >> 24;
    k *= m;
    hash *= m;
    hash ^= k;
    buf += 4;
    len -= 4;
  }

  // Handle the last few bytes of the input array.
  switch (len)
  {
    case 3:
      hash ^= static_cast<unsigned char>(buf[2]) << 16;
      [[gnu::fallthrough]];
    case 2:
      hash ^= static_cast<unsigned char>(buf[1]) << 8;
      [[gnu::fallthrough]];
    case 1:
      hash ^= static_cast<unsigned char>(buf[0]);
      hash *= m;
  };

  // Do a few final mixes of the hash.
  hash ^= hash >> 13;
  hash *= m;
  hash ^= hash >> 15;
  return hash;
}

MurmerHash3 by Austin Appleby is best! It's an improvement over even his gcc C++11 std::unordered_map<> hash used above.

Not only is is the best of all of these, but Austin released MurmerHash3 into the public domain. See my other answer on this here: What is the default hash function used in C++ std::unordered_map?.

See also

1. Other hash table algorithms to try out and test: http://www.cse.yorku.ca/~oz/hash.html. Hash algorithms mentioned there:
   1. djb2
   2. sdbm
   3. lose lose (K&R 1st edition)

Answer 6

djb2 has 317 collisions for this 466k english dictionary while MurmurHash has none for 64 bit hashes, and 21 for 32 bit hashes (around 25 is to be expected for 466k random 32 bit hashes). My recommendation is using MurmurHash if available, it is very fast, because it takes in several bytes at a time. But if you need a simple and short hash function to copy and paste to your project I'd recommend using murmurs one-byte-at-a-time version:

uint32_t inline MurmurOAAT32 ( const char * key)
{
  uint32_t h(3323198485ul);
  for (;*key;++key) {
    h ^= *key;
    h *= 0x5bd1e995;
    h ^= h >> 15;
  }
  return h;
}

uint64_t inline MurmurOAAT64 ( const char * key)
{
  uint64_t h(525201411107845655ull);
  for (;*key;++key) {
    h ^= *key;
    h *= 0x5bd1e9955bd1e995;
    h ^= h >> 47;
  }
  return h;
}

The optimal size of a hash table is - in short - as large as possible while still fitting into memory. Because we don't usually know or want to look up how much memory we have available, and it might even change, the optimal hash table size is roughly 2x the expected number of elements to be stored in the table. Allocating much more than that will make your hash table faster but at rapidly diminishing returns, making your hash table smaller than that will make it exponentially slower. This is because there is a non-linear trade-off between space and time complexity for hash tables, with an optimal load factor of 2-sqrt(2) = 0.58... apparently.

Answer 7

There are a number of existing hashtable implementations for C, from the C standard library hcreate/hdestroy/hsearch, to those in the APR and glib, which also provide prebuilt hash functions. I'd highly recommend using those rather than inventing your own hashtable or hash function; they've been optimized heavily for common use-cases.

If your dataset is static, however, your best solution is probably to use a perfect hash. gperf will generate a perfect hash for you for a given dataset.

Answer 8

I have tried these hash functions and got the following result. I have about 960^3 entries, each 64 bytes long, 64 chars in different order, hash value 32bit. Codes from here.

Hash function    | collision rate | how many minutes to finish
==============================================================
MurmurHash3      |           6.?% |                      4m15s
Jenkins One..    |           6.1% |                      6m54s   
Bob, 1st in link |          6.16% |                      5m34s
SuperFastHash    |            10% |                      4m58s
bernstein        |            20% |       14s only finish 1/20
one_at_a_time    |          6.16% |                       7m5s
crc              |          6.16% |                      7m56s

One strange things is that almost all the hash functions have 6% collision rate for my data.

Answer 9

First, is 40 collisions for 130 words hashed to 0..99 bad? You can't expect perfect hashing if you are not taking steps specifically for it to happen. An ordinary hash function won't have fewer collisions than a random generator most of the time.

A hash function with a good reputation is MurmurHash3.

Finally, regarding the size of the hash table, it really depends what kind of hash table you have in mind, especially, whether buckets are extensible or one-slot. If buckets are extensible, again there is a choice: you choose the average bucket length for the memory/speed constraints that you have.

Answer 10

I want to summarize it all for newbies to C like me. According to Andriy Makukha precision efforts, MurmurHash3 is the best:

unsigned long hash(const char* str){
    unsigned int h = 0x12345678;
    for (; *str; ++str) {
        h ^= *str;
        h *= 0x5bd1e995;
        h ^= h >> 15;
    }
    return h;
}

Answer 11

One thing I've used with good results is the following (I don't know if its mentioned already because I can't remember its name).

You precompute a table T with a random number for each character in your key's alphabet [0,255]. You hash your key 'k0 k1 k2 ... kN' by taking T[k0] xor T[k1] xor ... xor T[kN]. You can easily show that this is as random as your random number generator and its computationally very feasible and if you really run into a very bad instance with lots of collisions you can just repeat the whole thing using a fresh batch of random numbers.