zcourts zcourts - 28 days ago 8
C++ Question

is it possible for MurmurHash3 to produce a 64 bit hash where the upper 32 bits are all 0?

Looking at https://github.com/aappleby/smhasher/blob/master/src/MurmurHash3.cpp I don't think so but I wanted to check.

The situation is this, if I have a key of 1,2,3 or 4 bytes, is it reliable to simply take the numeric value of those bytes instead of hashing to 8 bytes, or will those cause a collision for keys greater than 4 bytes that were hashed with murmur3?

Answer

Such property is a bad property for a hash function. It effectively shrinks function co-domain, increasing collision chance, so it seems very unlikely.

Moreover, this blog post provides an inversion function for MurmurHash:

uint64 murmur_hash_64(const void * key, int len, uint64 seed)
{
    const uint64 m = 0xc6a4a7935bd1e995ULL;
    const int r = 47;

    uint64 h = seed ^ (len * m);

    const uint64 * data = (const uint64 *)key;
    const uint64 * end = data + (len / 8);

    while (data != end)
    {
#ifdef PLATFORM_BIG_ENDIAN
        uint64 k = *data++;
        char *p = (char *)&k;
        char c;
        c = p[0]; p[0] = p[7]; p[7] = c;
        c = p[1]; p[1] = p[6]; p[6] = c;
        c = p[2]; p[2] = p[5]; p[5] = c;
        c = p[3]; p[3] = p[4]; p[4] = c;
#else
        uint64 k = *data++;
#endif

        k *= m;
        k ^= k >> r;
        k *= m;

        h ^= k;
        h *= m;
    }

    const unsigned char * data2 = (const unsigned char*)data;

    switch (len & 7)
    {
    case 7: h ^= uint64(data2[6]) << 48;
    case 6: h ^= uint64(data2[5]) << 40;
    case 5: h ^= uint64(data2[4]) << 32;
    case 4: h ^= uint64(data2[3]) << 24;
    case 3: h ^= uint64(data2[2]) << 16;
    case 2: h ^= uint64(data2[1]) << 8;
    case 1: h ^= uint64(data2[0]);
        h *= m;
    };

    h ^= h >> r;
    h *= m;
    h ^= h >> r;

    return h;
}

uint64 murmur_hash_64_inverse(uint64 h, uint64 seed)
{
    const uint64 m = 0xc6a4a7935bd1e995ULL;
    const uint64 minv = 0x5f7a0ea7e59b19bdULL; // Multiplicative inverse of m under % 2^64
    const int r = 47;

    h ^= h >> r;
    h *= minv;
    h ^= h >> r;
    h *= minv;

    uint64 hforward = seed ^ (((uint64)8) * m);
    uint64 k = h ^ hforward;

    k *= minv;
    k ^= k >> r;
    k *= minv;

#ifdef PLATFORM_BIG_ENDIAN
    char *p = (char *)&k;
    char c;
    c = p[0]; p[0] = p[7]; p[7] = c;
    c = p[1]; p[1] = p[6]; p[6] = c;
    c = p[2]; p[2] = p[5]; p[5] = c;
    c = p[3]; p[3] = p[4]; p[4] = c;
#endif

    return k;
}

You can find as many inputs with hash values <2^32 as you want.

Your question about reliability doesn't make much sense: you always must be ready to handle collisions properly. From my practice, I do not recommend to use plain integers or pointer values as a hash, as they can produce undesired patterns.

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