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@lh3
Last active Dec 11, 2022
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Invertible integer hash functions
/*
For any 1<k<=64, let mask=(1<<k)-1. hash_64() is a bijection on [0,1<<k), which means
hash_64(x, mask)==hash_64(y, mask) if and only if x==y. hash_64i() is the inversion of
hash_64(): hash_64i(hash_64(x, mask), mask) == hash_64(hash_64i(x, mask), mask) == x.
*/
// Thomas Wang's integer hash functions. See <https://gist.github.com/lh3/59882d6b96166dfc3d8d> for a snapshot.
uint64_t hash_64(uint64_t key, uint64_t mask)
{
key = (~key + (key << 21)) & mask; // key = (key << 21) - key - 1;
key = key ^ key >> 24;
key = ((key + (key << 3)) + (key << 8)) & mask; // key * 265
key = key ^ key >> 14;
key = ((key + (key << 2)) + (key << 4)) & mask; // key * 21
key = key ^ key >> 28;
key = (key + (key << 31)) & mask;
return key;
}
// The inversion of hash_64(). Modified from <https://naml.us/blog/tag/invertible>
uint64_t hash_64i(uint64_t key, uint64_t mask)
{
uint64_t tmp;
// Invert key = key + (key << 31)
tmp = (key - (key << 31));
key = (key - (tmp << 31)) & mask;
// Invert key = key ^ (key >> 28)
tmp = key ^ key >> 28;
key = key ^ tmp >> 28;
// Invert key *= 21
key = (key * 14933078535860113213ull) & mask;
// Invert key = key ^ (key >> 14)
tmp = key ^ key >> 14;
tmp = key ^ tmp >> 14;
tmp = key ^ tmp >> 14;
key = key ^ tmp >> 14;
// Invert key *= 265
key = (key * 15244667743933553977ull) & mask;
// Invert key = key ^ (key >> 24)
tmp = key ^ key >> 24;
key = key ^ tmp >> 24;
// Invert key = (~key) + (key << 21)
tmp = ~key;
tmp = ~(key - (tmp << 21));
tmp = ~(key - (tmp << 21));
key = ~(key - (tmp << 21)) & mask;
return key;
}
@jgraj
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jgraj commented Mar 26, 2022

@calvin2021y How does this concern me?

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