zcourts - 3 months ago 22

C++ Question

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.