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Zobrist hashing in C
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Zobrist hashing in C

Zobrist hashing is the simplest form of tabulation-based hashing. It can be shown to be 3-wise independent. The Zobrist approach tested here is used in real systems, e.g., Gigablast Alternatively, one could use a tabulation-based function as a complement to other hash functions: first hash the content down to a few bytes (e.g., 4) and then apply a tabulation-based hash on the result.

Tabulation-based hashing uses a lot of memory and is susceptible to cache faults. E.g., to hash 4-byte strings to 64-bit values, you need 8 KB. Moreover, its speed is limited (in part) by the system's ability to issue random access loads.

In an exhaustive experimental evaluation of hash-table performance, Richter et al. (VLDB, 2016) found that Zobrist hashing produces a low throughput. Consequently, the authors declare it to be "less attractive in practice" than its strong randomness properties would suggest.

This C code expects a GCC-like compiler on an x64 system.

The code demonstrates that it is difficult on a x64 to hash much more than 0.65 bytes per cycle on recent Intel processors, even when repeatedly hashing the same short string. In contrast, it is possible to hash 4 to 10 bytes per cycle using fast hash families. See

C Usage

zobrist_t k;
init_zobrist(& k);// call once

// then you can hash as many strings as you want:
uint64_t hashvalue = zobrist (mystring, mystringsize, &k)

// for null-terminated strings, you can use:
uint64_t hashvalue = zobrist_nt (mystring,  &k)

// strings longer than 256 bytes fail the theoretical bounds



Relevant software libraries


  • Daniel Lemire, The universality of iterated hashing over variable-length strings, Discrete Applied Mathematics 160 (4-5), 2012.
  • Owen Kaser, Daniel Lemire, Strongly universal string hashing is fast, Computer Journal 57(11), 2014.
  • Daniel Lemire, Owen Kaser, Faster 64-bit universal hashing using carry-less multiplications, Journal of Cryptographic Engineering (to appear)
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