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The core of the FNV hash

The core of the

FNV-1 hash algorithm is as follows:

hash = offset_basisfor each octet_of_data to be hashed hash = hash * FNV_prime hash = hash xor octet_of_datareturn hash

The offset_basis andFNV_prime can be found in the section below.

FNV-1a alternate algorithm

There is a minor variation of the

FNV hash algorithm known as

FNV-1a:

hash = offset_basisfor each octet_of_data to be hashed hash = hash xor octet_of_data hash = hash * FNV_primereturn hash

The only difference between the FNV-1a hash and the FNV-1 hashis the order of the xor and multiply.The FNV-1a hashuses the same FNV_prime and offset_basisas the FNV-1 hash of the same n-bit size.

Parameters of the FNV-1/FNV-1a hash

The

FNV-1 hash parameters are as follows:

• hash is an n bit unsigned integer,where n is the bit length of hash.
• The multiplication is performed modulo 2ⁿwhere n is the bit length of hash.
• The xor is performed on the low orderoctet (8 bits) of hash.
• The FNV_prime is dependent on n, the size of the hash:

  32 bit

  FNV_prime =2

  ²⁴ + 2

  ⁸ + 0x93 =

  16777619

  64 bit

  FNV_prime = 2

  ⁴⁰ + 2

  ⁸ + 0xb3 =

  1099511628211

  128 bit

  FNV_prime = 2

  ⁸⁸ + 2

  ⁸ + 0x3b =

  309485009821345068724781371

  256 bit

  FNV_prime = 2

  ¹⁶⁸ + 2

  ⁸ + 0x63 =

  374144419156711147060143317175368453031918731002211

  512 bit

  FNV_prime = 2

  ³⁴⁴ + 2

  ⁸ + 0x57 =

  35835915874844867368919076489095108449946327955754392558399825615420669938882575

  126094039892345713852759

  1024 bit

  FNV_prime = 2

  ⁶⁸⁰ + 2

  ⁸ + 0x8d =

  50164565101131186554345988110352789550307653454047907443030175238311120551081474

  51509157692220295382716162651878526895249385292291816524375083746691371804094271

  873160484737966720260389217684476157468082573

  Part of the magic of FNV is the selection of the FNV_primefor a given sized unsigned integer.Some primes do hash better than other primes for a given integer size.

• The offset_basis for FNV-1 is dependent on n, the size of the hash:

  32 bit

  offset_basis =

  2166136261

  64 bit

  offset_basis =

  14695981039346656037

  128 bit

  offset_basis =

  144066263297769815596495629667062367629

  256 bit

  offset_basis =

  100029257958052580907070968620625704837092796014241193945225284501741471925557

  512 bit

  offset_basis =

  96593031294966694980094354007163104660904187456726378961083743294344626579945829

  32197716438449813051892206539805784495328239340083876191928701583869517785

  1024 bit

  offset_basis =

  14197795064947621068722070641403218320880622795441933960878474914617582723252296

  73230371772215086409652120235554936562817466910857181476047101507614802975596980

  40773201576924585630032153049571501574036444603635505054127112859663616102678680

  82893823963790439336411086884584107735010676915

  NOTE: Older versions of this web page incorretly indicated that the 128 bitFNV_prime was 2¹⁶⁸ + 2⁸ + 0x59.This was not correct.While that satisfied all of the significant FNV_prime properties,it was not the smallest 128 bit FNV_prime.The 128 bit offset_basischanged from275519064689413815358837431229664493455to144066263297769815596495629667062367629was changed as a result of the 128 bit FNV_prime correction.(Sorry about that!)