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The FNV Non-Cryptographic Hash Algorithm
draft-eastlake-fnv-21

Document Type Active Internet-Draft (individual)
Authors Glenn Fowler , Landon Curt Noll , Kiem-Phong Vo , Donald E. Eastlake 3rd , Tony Hansen
Last updated 2024-01-07
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draft-eastlake-fnv-21
Internet Engineering Task Force                                G. Fowler
Internet-Draft                                                    Google
Intended status: Informational                                   L. Noll
Expires: 10 July 2024                                      Cisco Systems
                                                                   K. Vo
                                                                  Google
                                                             D. Eastlake
                                                  Futurewei Technologies
                                                               T. Hansen
                                                       AT&T Laboratories
                                                          7 January 2024

                The FNV Non-Cryptographic Hash Algorithm
                         draft-eastlake-fnv-21

Abstract

   FNV (Fowler/Noll/Vo) is a fast, non-cryptographic hash algorithm with
   good dispersion.  The purpose of this document is to make information
   on FNV and open source code performing FNV conveniently available to
   the Internet community.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 10 July 2024.

Copyright Notice

   Copyright (c) 2024 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.

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   Please review these documents carefully, as they describe your rights
   and restrictions with respect to this document.  Code Components
   extracted from this document must include Revised BSD License text as
   described in Section 4.e of the Trust Legal Provisions and are
   provided without warranty as described in the Revised BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  FNV Basics  . . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  FNV Primes  . . . . . . . . . . . . . . . . . . . . . . .   4
     2.2.  FNV offset_basis  . . . . . . . . . . . . . . . . . . . .   5
     2.3.  FNV Endianism . . . . . . . . . . . . . . . . . . . . . .   6
   3.  Other Hash Sizes and XOR Folding  . . . . . . . . . . . . . .   6
   4.  Hashing Multiple Values Together  . . . . . . . . . . . . . .   7
   5.  FNV Constants . . . . . . . . . . . . . . . . . . . . . . . .   8
   6.  The Source Code . . . . . . . . . . . . . . . . . . . . . . .  11
     6.1.  FNV-1a C Code . . . . . . . . . . . . . . . . . . . . . .  11
       6.1.1.  FNV32 Code  . . . . . . . . . . . . . . . . . . . . .  17
       6.1.2.  FNV64 Code  . . . . . . . . . . . . . . . . . . . . .  22
       6.1.3.  FNV128 Code . . . . . . . . . . . . . . . . . . . . .  34
       6.1.4.  FNV256 Code . . . . . . . . . . . . . . . . . . . . .  45
       6.1.5.  FNV512 Code . . . . . . . . . . . . . . . . . . . . .  57
       6.1.6.  FNV1024 Code  . . . . . . . . . . . . . . . . . . . .  68
     6.2.  FNV Test Code . . . . . . . . . . . . . . . . . . . . . .  80
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  81
     7.1.  Why is FNV Non-Cryptographic? . . . . . . . . . . . . . .  81
     7.2.  Inducing Collisions . . . . . . . . . . . . . . . . . . .  82
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  82
   9.  Normative References  . . . . . . . . . . . . . . . . . . . .  82
   10. Informative References  . . . . . . . . . . . . . . . . . . .  82
   Appendix A.  Work Comparison with SHA-1 . . . . . . . . . . . . .  84
   Appendix B.  Previous IETF Reference to FNV . . . . . . . . . . .  84
   Appendix C.  A Few Test Vectors . . . . . . . . . . . . . . . . .  85
   Appendix D.  Change History . . . . . . . . . . . . . . . . . . .  86
     D.1.  From -00 to -01 . . . . . . . . . . . . . . . . . . . . .  86
     D.2.  From -01 to -02 . . . . . . . . . . . . . . . . . . . . .  86
     D.3.  From -02 to -03 . . . . . . . . . . . . . . . . . . . . .  86
     D.4.  From -03 to -04 . . . . . . . . . . . . . . . . . . . . .  86
     D.5.  From -04 to -05 . . . . . . . . . . . . . . . . . . . . .  87
     D.6.  From -05 to -06 . . . . . . . . . . . . . . . . . . . . .  87
     D.7.  From -06 to -07 to -08  . . . . . . . . . . . . . . . . .  87
     D.8.  From -08 to -09 . . . . . . . . . . . . . . . . . . . . .  87
     D.9.  From -09 to -10 . . . . . . . . . . . . . . . . . . . . .  87
     D.10. From -10 to -11 . . . . . . . . . . . . . . . . . . . . .  87
     D.11. From -11 to -12 . . . . . . . . . . . . . . . . . . . . .  87
     D.12. From -12 to -13 . . . . . . . . . . . . . . . . . . . . .  88
     D.13. From -13 to -14 to -15 to -16 to -17  . . . . . . . . . .  88

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     D.14. From -17 to -18 . . . . . . . . . . . . . . . . . . . . .  88
     D.15. From -18 to -19 . . . . . . . . . . . . . . . . . . . . .  88
     D.16. From -19 to -20 . . . . . . . . . . . . . . . . . . . . .  88
     D.17. From -20 to -21 . . . . . . . . . . . . . . . . . . . . .  88
   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  88
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  88

1.  Introduction

   The FNV hash algorithm originated from an idea submitted as reviewer
   comments to the [IEEE] POSIX P1003.2 committee in 1991 by Glenn
   Fowler and Phong Vo.  Subsequently, during a ballot round, Landon
   Curt Noll proposed an enhancement to their algorithm.  Some people
   tried this hash and found that it worked rather well.  In an EMail
   message to Landon, they named it the "Fowler/Noll/Vo" or FNV hash.
   [FNV]

   FNV hashes are designed to be fast while maintaining a low collision
   rate.  Their exceptional dispersion makes them particularly well-
   suited for hashing nearly identical strings, including URLs,
   hostnames, filenames, text, and IP addresses.  Their speed allows one
   to quickly hash lots of data while maintaining a reasonably low
   collision rate.  However, they are generally not suitable for
   cryptographic use.  (See Section 7.1.)

   The FNV hash is widely used, for example in [RFC7357], [RFC7873],
   [IEEE8021Qbp], DNS servers, the X (formerly Twitter) service,
   database indexing hashes, major web search / indexing engines,
   netnews history file Message-ID lookup functions, anti-spam filters,
   a spellchecker programmed in Ada 95, flatassembler's open source x86
   assembler - user-defined symbol hashtree, non-cryptographic file
   fingerprints, computing Unique IDs in DASM (DTN (Delay Tolerant
   Networking) Applications for Symbian Mobile-phones), Microsoft's
   hash_map implementation for VC++ 2005, the realpath cache in PHP 5.x
   (php-5.2.3/TSRM/tsrm_virtual_cwd.c), and many other uses.

   A study has recommended FNV in connection with the IPv6 Flow Label
   field [IPv6flow].  Additionally, there was a proposal to use FNV for
   BFD sequence number generation [BFDseq].

   FNV hash algorithms and source code have been released into the
   public domain.  The authors took deliberate steps to disclose the
   algorithm in a public forum soon after it's invention.  More than a
   year passed after this public disclosure and the authors deliberately
   took no steps to patent the FNV algorithm.  Therefore, it is safe to
   say that the FNV authors have no patent claims on the FNV algorithm.

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   If you use an FNV function in an application, you are kindly
   requested to send an EMail about it to: fnv-mail@asthe.com

2.  FNV Basics

   This document focuses on the FNV-1a function whose pseudo-code is as
   follows:

     hash = offset_basis
     for each octet_of_data to be hashed
         hash = hash xor octet_of_data
         hash = hash * FNV_Prime
     return hash

   In the pseudo-code above, hash is a power-of-two number of bits (32,
   64, 128, 256, 512, or 1024) and offset_basis and FNV_Prime depend on
   the size of hash.

   The FNV-1 algorithm is the same, including the values of offset_basis
   and FNV_Prime, except that the order of the two lines with the "xor"
   and multiply operations are reversed.  Operational experience
   indicates better hash dispersion for small amounts of data with FNV-
   1a.  FNV-0 is the same as FNV-1 but with offset_basis set to zero.
   FNV-1a is suggested for general use.

2.1.  FNV Primes

   The theory behind FNV_Prime's is beyond the scope of this document
   but the basic property to look for is how an FNV_Prime would impact
   dispersion.  Now, consider any n-bit FNV hash where n >= 32 and is
   also a power of 2, in particular n = 2**s.  For each such n-bit FNV
   hash, an FNV_Prime p is defined as:

   *  When s is an integer and 4 < s < 11, then FNV_Prime is the
      smallest prime p of the form:

                      256**int((5 + 2**s)/12) + 2**8 + b

   *  where b is an integer such that:

                                 0 < b < 2**8

   *  The number of one-bits in b is 4 or 5

   *  and where

            ( p mod (2**40 - 2**24 - 1) ) > (2**24 + 2**8 + 2**7)

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   Experimentally, FNV_Primes matching the above constraints tend to
   have better dispersion properties.  They improve the polynomial
   feedback characteristic when an FNV_Prime multiplies an intermediate
   hash value.  As such, the hash values produced are more scattered
   throughout the n-bit hash space.

   The case where s < 5 is not considered due to the resulting low hash
   quality.  Such small hashes can, if desired, be derived from a 32 bit
   FNV hash by XOR folding (see Section 3).  The case where s > 10 is
   not considered because of the doubtful utility of such large FNV
   hashes and because the criteria for such large FNV_Primes is more
   complex, due to the sparsity of such large primes, and would
   needlessly clutter the criteria given above.

   Per the above constraints, an FNV_Prime should have only 6 or 7 one-
   bits in it.  Therefore, some compilers may seek to improve the
   performance of a multiplication with an FNV_Prime by replacing the
   multiplication with shifts and adds.  However, note that the
   performance of this substitution is highly hardware-dependent and
   should be done with care.  The selection of FNV_Primes prioritizes
   the quality of the resulting hash function, not compiler optimization
   considerations.

2.2.  FNV offset_basis

   The offset_basis values for the n-bit FNV-1a algorithms are computed
   by applying the n-bit FNV-0 algorithm to the 32 octets representing
   the following character string in ASCII [RFC0020]:

                     chongo <Landon Curt Noll> /\../\

   The \'s in the above string are not C-style escape characters.  In
   C-string notation, these 32 octets are:

                   "chongo <Landon Curt Noll> /\\../\\"

   That string was used because the person testing FNV with non-zero
   offset_basis values was looking at an email message from Landon and
   was copying his standard email signature line; however, they couldn't
   see very well and copied it incorrectly.  In fact, he uses

                     chongo (Landon Curt Noll) /\oo/\

   but, since it doesn't matter, no effort has been made to correct
   this.

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   In the general case, almost any offset_basis will serve so long as it
   is non-zero.  The choice of a non-standard offset_basis may be
   beneficial in defending against some attacks that try to induce hash
   collisions.

2.3.  FNV Endianism

   For persistent storage or interoperability between different hardware
   platforms, an FNV hash shall be represented in the little endian
   format.  That is, the FNV hash will be stored in an array hash[N]
   with N bytes such that its integer value can be retrieved as follows:

     unsigned char   hash[N];
     for ( i = N-1, value = 0; i >= 0; --i )
         value = ( value << 8 ) + hash[i];

   Of course, when FNV hashes are used in a single process or a group of
   processes sharing memory on processors with compatible endian-ness,
   the natural endian-ness of those processors can be used, as long as
   it is used consistantly, regardless of its type, little, big, or some
   other exotic form.

   The code provided in Section 6 has FNV hash functions that return a
   little endian byte vector.  Because they are slightly more efficient,
   code returning FNV hashes of 32-bit or 64-bit size as integers, on
   computers supporting integers of those sides, are also provided.
   Such integers are compatible with the same size byte vectors on
   little endian computers but use of the functions returning integers
   on big endian or other non-little-endian machines will be byte-
   reversed or otherwise incompatible with the byte vectors.

3.  Other Hash Sizes and XOR Folding

   Many hash uses require a hash that is not one of the FNV sizes for
   which constants are provided in Section 5.  If a larger hash size is
   needed, please contact the authors of this document.

   Most hash applications make use of a hash that is a fixed size binary
   field.  Assume that k bits of hash are desired and k is less than
   1024 but not one of the sizes for which constants are provided in
   Section 5.  The recommended technique is to take the smallest FNV
   hash of size S, where S is larger than k, and calculate the desired
   k-bit-hash using xor folding as shown below.  The final bit masking
   operation is logically unnecessary if the size of the variable k-bit-
   hash is exactly k bits.

     temp = FNV_S ( data-to-be-hashed )
     k-bit-hash = ( temp xor temp>>k ) bitwise-and ( 2**k - 1 )

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   Hash functions are a trade-off between speed and strength.  For
   example, a somewhat stronger hash may be obtained for exact FNV sizes
   by calculating an FNV twice as long as the desired output ( S = 2*k )
   and performing such data folding using a k equal to the size of the
   desired output.  However, if a much stronger hash, for example one
   suitable for cryptographic applications, is wanted, algorithms
   designed for that purpose, such as those in [RFC6234], should be
   used.

   If it is desired to obtain a hash result that is a value between 0
   and max, where max+1 is a not a power of two, simply choose an FNV
   hash size S such that 2**S > max.  Then calculate the following:

                            FNV_S mod ( max+1 )

   The resulting remainder will be in the range desired but will suffer
   from a bias against large values with the bias being larger if 2**S
   is only a little bigger than max.  If this bias is acceptable, no
   further processing is needed.  If this bias is unacceptable, it can
   be avoided by retrying for certain high values of hash, as follows,
   before applying the mod operation above:

     X = ( int( ( 2**S - 1 ) / ( max+1 ) ) ) * ( max+1 )
     while ( hash >= X )
         hash = ( hash * FNV_Prime ) + offset_basis

4.  Hashing Multiple Values Together

   It is common for there to be a few different component values, say
   three strings X, Y, and Z, where a hash over all of them is desired.
   The simplest thing to do is to concatenate them and compute the hash
   of that concatenation, as in

                            hash ( X | Y | Z )

   where the vertical bar character ("|") represents string
   concatenation.  Note that, for FNV, the same hash results if X, Y,
   and Z are actually concatenated and the FNV hash applied to the
   resulting string or if FNV is calculated on an initial substring and
   the result used as the offset_basis when calculating the FNV hash of
   the remainder of the string.  This can be done several times.
   Assuming FNVoffset_basis ( v, w ) is FNV of w using v as the
   offset_basis, then in the example above, fnvx = FNV ( X ) could be
   calculated and then fnvxy = FNVoffset_basis ( fnvx, Y ), and finally
   fnvxyz = FNVoffset_basis ( fnvxy, Z).  The resulting fnvxyz would be
   the same as FNV ( X | Y | Z ).

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   Cases are also common where such a hash needs to be repeatedly
   calculated where the component values vary but some vary more
   frequently than others.  For example, assume some sort of computer
   network traffic flow ID, such as the IPv6 flow ID [RFC6437], is to be
   calculated for network packets based on the source and destination
   IPv6 address and the Traffic Class [RFC8200].  If the Flow ID is
   calculated in the originating host, the source IPv6 address would
   likely always be the same or perhaps assume one of a very small
   number of values.  By placing this quasi-constant IPv6 source address
   first in the string being FNV hashed, FNV ( IPv6source ) could be
   calculated and used as the offset_basis for calculating FNV of the
   IPv6 destination address and Traffic Class for each packet.  As a
   result, the per packet hash would be over 17 bytes rather than over
   33 bytes saving computational resources.  The code in this document
   includes functions facilitating the use of a non-standard
   offset_basis.

5.  FNV Constants

   The FNV Primes are as follows:

       +==========================================================+
       | Size FNV Prime = Exression                               |
       +==========================================================+
       |                                                = Decimal |
       +==========================================================+
       |                                            = Hexadecimal |
       +==========================================================+
       | 32 bit FNV_Prime = 2**24 + 2**8 + 0x93                   |
       +----------------------------------------------------------+
       |                                             = 16,777,619 |
       +----------------------------------------------------------+
       |                                             = 0x01000193 |
       +----------------------------------------------------------+
       | 64 bit FNV_Prime = 2**40 + 2**8 + 0xB3                   |
       +----------------------------------------------------------+
       |                                      = 1,099,511,628,211 |
       +----------------------------------------------------------+
       |                                    = 0x00000100 000001B3 |
       +----------------------------------------------------------+
       | 128 bit FNV_Prime = 2**88 + 2**8 + 0x3B                  |
       +----------------------------------------------------------+
       |                    = 309,485,009,821,345,068,724,781,371 |
       +----------------------------------------------------------+
       |                  = 0x00000000 01000000 00000000 0000013B |
       +----------------------------------------------------------+
       | 256 bit FNV_Prime = 2**168 + 2**8 + 0x63                 |
       +----------------------------------------------------------+

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       |   = 374,144,419,156,711,147,060,143,317,175,368,453,031, |
       |                                          918,731,002,211 |
       +----------------------------------------------------------+
       |   = 0x0000000000000000 0000010000000000 0000000000000000 |
       |                                         0000000000000163 |
       +----------------------------------------------------------+
       | 512 bit FNV_Prime = 2**344 + 2**8 + 0x57                 |
       +----------------------------------------------------------+
       |    = 35,835,915,874,844,867,368,919,076,489,095,108,449, |
       | 946,327,955,754,392,558,399,825,615,420,669,938,882,575, |
       |                          126,094,039,892,345,713,852,759 |
       +----------------------------------------------------------+
       |   = 0x0000000000000000 0000000000000000 0000000001000000 |
       |       0000000000000000 0000000000000000 0000000000000000 |
       |                        0000000000000000 0000000000000157 |
       +----------------------------------------------------------+
       | 1024 bit FNV_Prime = 2**680 + 2**8 + 0x8D                |
       +----------------------------------------------------------+
       | = 5,016,456,510,113,118,655,434,598,811,035,278,955,030, |
       | 765,345,404,790,744,303,017,523,831,112,055,108,147,451, |
       | 509,157,692,220,295,382,716,162,651,878,526,895,249,385, |
       | 292,291,816,524,375,083,746,691,371,804,094,271,873,160, |
       |      484,737,966,720,260,389,217,684,476,157,468,082,573 |
       +----------------------------------------------------------+
       |   = 0x0000000000000000 0000000000000000 0000000000000000 |
       |       0000000000000000 0000000000000000 0000010000000000 |
       |       0000000000000000 0000000000000000 0000000000000000 |
       |       0000000000000000 0000000000000000 0000000000000000 |
       |       0000000000000000 0000000000000000 0000000000000000 |
       |                                         000000000000018D |
       +----------------------------------------------------------+

                                 Table 1

   The FNV offset_basis values are as follows:

   +===================================================================+
   | Size offset_basis                                                 |
   +===================================================================+
   |                                                         = Decimal |
   +===================================================================+
   |                                                     = Hexadecimal |
   +===================================================================+
   | 32 bit offset_basis                                               |
   +-------------------------------------------------------------------+
   |                                                   = 2,166,136,261 |
   +-------------------------------------------------------------------+
   | = 0x811C9DC5                                                      |

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   +-------------------------------------------------------------------+
   | 64 bit offset_basis                                               |
   +-------------------------------------------------------------------+
   |                                      = 14,695,981,039,346,656,037 |
   +-------------------------------------------------------------------+
   |                                             = 0xCBF29CE4 84222325 |
   +-------------------------------------------------------------------+
   | 128 bit offset_basis                                              |
   +-------------------------------------------------------------------+
   |             = 144,066,263,297,769,815,596,495,629,667,062,367,629 |
   +-------------------------------------------------------------------+
   |                           = 0x6C62272E 07BB0142 62B82175 6295C58D |
   +-------------------------------------------------------------------+
   | 256 bit offset_basis                                              |
   +-------------------------------------------------------------------+
   |            = 100,029,257,958,052,580,907,070,968,620,625,704,837, |
   |               092,796,014,241,193,945,225,284,501,741,471,925,557 |
   +-------------------------------------------------------------------+
   |            = 0xDD268DBCAAC55036 2D98C384C4E576CC C8B1536847B6BBB3 |
   |                                                  1023B4C8CAEE0535 |
   +-------------------------------------------------------------------+
   | 512 bit offset_basis                                              |
   +-------------------------------------------------------------------+
   |          = 9,659,303,129,496,669,498,009,435,400,716,310,466,090, |
   |          418,745,672,637,896,108,374,329,434,462,657,994,582,932, |
   |          197,716,438,449,813,051,892,206,539,805,784,495,328,239, |
   |                           340,083,876,191,928,701,583,869,517,785 |
   +-------------------------------------------------------------------+
   |            = 0xB86DB0B1171F4416 DCA1E50F309990AC AC87D059C9000000 |
   |                0000000000000D21 E948F68A34C192F6 2EA79BC942DBE7CE |
   |                                 182036415F56E34B AC982AAC4AFE9FD9 |
   +-------------------------------------------------------------------+
   | 1024 bit offset_basis                                             |
   +-------------------------------------------------------------------+
   |             = 14,197,795,064,947,621,068,722,070,641,403,218,320, |
   |          880,622,795,441,933,960,878,474,914,617,582,723,252,296, |
   |          732,303,717,722,150,864,096,521,202,355,549,365,628,174, |
   |          669,108,571,814,760,471,015,076,148,029,755,969,804,077, |
   |          320,157,692,458,563,003,215,304,957,150,157,403,644,460, |
   |          363,550,505,412,711,285,966,361,610,267,868,082,893,823, |
   |               963,790,439,336,411,086,884,584,107,735,010,676,915 |
   +-------------------------------------------------------------------+
   |            = 0x0000000000000000 005F7A76758ECC4D 32E56D5A591028B7 |
   |                4B29FC4223FDADA1 6C3BF34EDA3674DA 9A21D90000000000 |
   |                0000000000000000 0000000000000000 0000000000000000 |
   |                0000000000000000 0000000000000000 000000000004C6D7 |
   |                EB6E73802734510A 555F256CC005AE55 6BDE8CC9C6A93B21 |
   |                                                  AFF4B16C71EE90B3 |

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   +-------------------------------------------------------------------+

                                  Table 2

6.  The Source Code

   (((THIS CODE IS BEING WORKED ON)))

   The following sub-sections provide reference C source code and a test
   driver for FNV-1a.

   Alternative source code, including 32 and 64 bit FNV-1 and FNV-1a in
   x86 assembler, is currently available at [FNV].

   Section 6.2 provides the test driver.

6.1.  FNV-1a C Code

   This section provides the direct FNV-1a function for each of the
   lengths for which it is specified in this document.  The functions
   provided are listed below.  The xxx in the function names is "32",
   "64", "128", "256", "512", or "1024" depending on the length of the
   FNV.  The FNV-32 functions return a 32 bit integer.  The FNV-64 bit
   functions return a 64-bit integer or an 8 byte vector depending on
   whether 64-bit integers are or are not supports.  All longer FNV
   functions return a byte vector.  Versions returning an integer may
   NOT compatible between systems of different endian-ness.

   If you want to copy the source code from this document, note that it
   is indented by three spaces in the ".txt" version.  It may be
   simplest to copy from the ".html" version of this documents.

   FNVxxxstring, FNVxxxblock:  These are simple functions for directly
      returning the FNV hash of a zero terminated byte string not
      including the zero and the FNV hash of a counted block of bytes.
      Note that for applications of FNV-32 where 32-bit integers are
      supported and FNV-64 where 64-bit integers are supported and an
      integer data type output is acceptable, the code is sufficiently
      simple that, to maximize performance, use of open coding or macros
      may be more appropriate than calling a subroutine.

   FNVxxxinit, FNVxxxinitBasis:  These functions and the next two sets

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      of functions below provide facilities for incrementally
      calculating FNV hashes.  They all assume a data structure of type
      FNVxxxcontext that holds the current state of the hash.
      FNVxxxinit initializes that context to the standard offset_basis.
      FNVxxxinitBasis takes an offset_basis value as a parameter and may
      be useful for hashing concatenations, as described in Section 4,
      as well as for simply using a non-standard offset_basis.

   FNVxxxblockin, FNVxxxstringin:  These functions hash a sequence of
      bytes into an FNVxxxcontext that was originally initialized by
      FNVxxxinit or FNVxxxinitBasis.  FNVxxxblockin hashes in a counted
      block of bytes.  FNVxxxstringin hashes in a zero terminated byte
      string not incuding the final zero.

   FNVxxxresult:  This function extracts the final FNV hash result from
      an FNVxxxcontext.

   The following code is a private header file used by all the FNV
   functions further below and which states the terms for use and
   redistribution of all of this code.

   <CODE BEGINS> file "fnv-private.h"
   /************************ fnv-private.h ************************/
   /****************** See RFC NNNN for details *******************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    *
    * Redistribution and use in source and binary forms, with or without
    * modification, are permitted provided that the following conditions
    * are met:
    *
    * *  Redistributions of source code must retain the above copyright
    *    notice, this list of conditions and the following disclaimer.
    *
    * *  Redistributions in binary form must reproduce the above
    *    copyright notice, this list of conditions and the following
    *    disclaimer in the documentation and/or other materials provided
    *    with the distribution.
    *
    * *  Neither the name of Internet Society, IETF or IETF Trust, nor
    *    the names of specific contributors, may be used to endorse or
    *    promote products derived from this software without specific
    *    prior written permission.
    *
    * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
    * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
    * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
    * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE

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    * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
    * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
    * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
    * TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
    * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
    * TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
    * THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
    * SUCH DAMAGE.
    */

   #ifndef _FNV_PRIVATE_H_
   #define _FNV_PRIVATE_H_

   /*
    *      Six FNV-1a hashes are defined with these sizes:
    *              FNV32          32 bits, 4 bytes
    *              FNV64          64 bits, 8 bytes
    *              FNV128         128 bits, 16 bytes
    *              FNV256         256 bits, 32 bytes
    *              FNV512         512 bits, 64 bytes
    *              FNV1024        1024 bits, 128 bytes
    */

   /* Private stuff used by this implementation of the FNV
    * (Fowler, Noll, Vo) non-cryptographic hash function FNV-1a.
    * External callers don't need to know any of this.  */

   enum {  /* State value bases for context->Computed */
       FNVinited = 22,
       FNVcomputed = 76,
       FNVemptied = 220,
       FNVclobber = 122 /* known bad value for testing */
   };

   /* Deltas to assure distinct state values for different lengths */
   enum {
      FNV32state = 1,
      FNV64state = 3,
      FNV128state = 5,
      FNV256state = 7,
      FNV512state = 11,
      FNV1024state = 13
   };

   #endif
   <CODE ENDS>

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   The following code is a simple header file to define the return value
   error codes for the FNV routines.

   <CODE BEGINS> file "FNVErrorCodes.h"
   /************************ FNVErrorCodes.h *************************/
   /****************** See RFC NNNN for details. *********************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV_ErrCodes_
   #define _FNV_ErrCodes_
   /*******************************************************************
    *  All FNV functions provided return as integer as follows:
    *       0 -> success
    *      >0 -> error as listed below
    */
   enum {    /* success and errors */
       fnvSuccess = 0,
       fnvNull,          /* Null pointer parameter */
       fnvStateError,    /* called Input after Result or before Init */
       fnvBadParam       /* passed a bad parameter */
   };
   #endif /* _FNV_ErrCodes_ */
   <CODE ENDS>

   The following code is a simple header file to include all the
   specific length FNV header files.

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   <CODE BEGINS> file "FNV.h"
   /***************************** FNV.h ******************************/
   /****************** See RFC NNNN for details. *********************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV_H_
   #define _FNV_H_

   #include "FNV32.h"
   #include "FNV64.h"
   #include "FNV128.h"
   #include "FNV256.h"
   #include "FNV512.h"
   #include "FNV1024.h"

   #endif /* _FNV_H_ */
   <CODE ENDS>

   The following code is a simple header file to control configuration
   related to big integer and big endian support.

   <CODE BEGINS> file "FNVconfig.h"
   /************************** FNVconfig.h ***************************/
   /****************** See RFC NNNN for details. *********************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNVconfig_H_
   #define _FNVconfig_H_

   /*
    *  Description:
    *      This file provides configuration ifdefs for the
    *      FNV-1a non-cryptographic hash algorithms.
    *
    * >>>>>>>> IMPORTANT CONFIGURATION ifdefs: <<<<<<<<<< */

   /*      FNV_64bitIntegers - Define this if your system supports
    *          64-bit arithmetic including 32-bit x 32-bit
    *          multiplication producing a 64-bit product. If
    *          undefined, it will be assumed that 32-bit arithmetic

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    *          is supported including 16-bit x 16-bit multiplication
    *          producing a 32-bit result.
    */
   // #define FNV_64bitIntegers

   /*
    *
    *      FNV_BigEndian - Define this ONLY if your system uses big
    *          endian representation AND your FNV hashes need to
    *          interoperate with little endian systems. If you #define
    *          this symbol when not needed, it will unnecessarily slow
    *          down and increase the code size of the FNV functions.
    */
   // #define FNV_BigEndian

   /*
    *      The following allow the FNV test program to override the
    *      above configuration settings.
    */

   #ifdef FNV_TEST_PROGRAM
   # ifdef TEST_FNV_64bitIntegers
   #  ifndef FNV_64bitIntegers
   #   define FNV_64bitIntegers
   #  endif
   # else
   #  undef FNV_64bitIntegers
   # endif
   # ifndef FNV_64bitIntegers /* causes an error if uint64_t is used */
   #  undef uint64_t
   #  define uint64_t no_64_bit_integers
   # endif
   # ifdef TEST_FNV_BigEndian
   #  ifndef FNV_BigEndian
   #   define FNV_BigEndian
   #  endif
   # else
   #  undef FNV_BigEndian
   # endif
   #endif

   #endif /* _FNVconfig_H_ */
   <CODE ENDS>

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6.1.1.  FNV32 Code

   The header and C source for 32-bit FNV-1a returning a 32-bit integer.

   <CODE BEGINS> file "FNV32.h"
   /**************************** FNV32.h *****************************/
   /******************* See RFC NNNN for details *********************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
   */

   #ifndef _FNV32_H_
   #define _FNV32_H_

   #include "FNVconfig.h"

   #include <stdint.h>
   /* #define FNV32size (32/8)   not used */

   /* If you do not have the ISO standard stdint.h header file, then you
    * must typedef the following types:
    *
    *    type              meaning
    *  uint32_t         unsigned 32 bit integer
    *  uint8_t          unsigned 8 bit integer (i.e., unsigned char)
    */

   #include "FNVErrorCodes.h"

   /*
    *  This structure holds context information for an FNV32 hash
    */
   typedef struct FNV32context_s {
       int Computed;  /* state */
       uint32_t Hash;
   } FNV32context;

   /*
    *  Function Prototypes
    *    FNV32string: hash a zero terminated string not including
    *                 the terminating zero
    *    FNV32block: hash a specified length byte vector
    *    FNV32init:  initializes an FNV32 context
    *    FNV32initBasis: initializes an FNV32 context with a
    *                    provided basis
    *    FNV32blockin:  hash in a specified length byte vector

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    *    FNV32stringin: hash in a zero terminated string not
    *                   including the zero
    *    FNV32result: returns the hash value
    *
    *    Hash is returned as a 32-bit unsigned integer
    */

   #ifdef __cplusplus
   extern "C" {
   #endif

   /* FNV32 */
   extern int FNV32string ( const char *in,
                            uint32_t * const out );
   extern int FNV32block ( const void *in,
                           long int inlength,
                           uint32_t * const out );
   extern int FNV32init ( FNV32context * const );
   extern int FNV32initBasis ( FNV32context * const,
                               uint32_t basis );
   extern int FNV32blockin ( FNV32context * const,
                             const void *in,
                             long int inlength );
   extern int FNV32stringin ( FNV32context * const,
                              const char *in );
   extern int FNV32result ( FNV32context * const,
                            uint32_t * const out );

   #ifdef __cplusplus
   }
   #endif

   #endif /* _FNV32_H_ */
   <CODE ENDS>

   <CODE BEGINS> file "FNV32.c"
   /*************************** FNV32.c ***************************/
   /***************** See RFC NNNN for details. *******************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified
    * as authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   /* This code implements the FNV (Fowler, Noll, Vo)
    *  non-cryptographic hash function FNV-1a for 32-bit hashes.
    */

   #ifndef _FNV32_C_

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   #define _FNV32_C_

   #include "fnv-private.h"
   #include "FNV32.h"

   /* 32 bit FNV_prime = 2^24 + 2^8 + 0x93 */
   #define FNV32prime 0x01000193
   #define FNV32basis 0x811C9DC5

   #ifdef FNV_BigEndian
   /* Local prototype */
   static void FNV32reverse ( uint32_t *out, uint32_t hash );
   #endif

   /* FNV32 hash a zero terminated string not including the zero
   *****************************************************************/
   int FNV32string ( const char *in, uint32_t * const out )
   {
       uint32_t    temp;
       uint8_t     ch;

       if ( !in || !out )
           return fnvNull; /* Null input pointer */

       temp = FNV32basis;
       while ( (ch = *in++) )
           temp = FNV32prime * ( temp ^ ch );
   #ifdef FNV_BigEndian
       FNV32reverse ( out, temp );
   #else
       *out = temp;
   #endif
       return fnvSuccess;
   }   /* end FNV32string */

   /* FNV32 hash a counted block
    ****************************************************************/
   int FNV32block ( const void *vin,
                    long int length,
                    uint32_t * const out )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t    temp;

       if ( !in || !out )
           return fnvNull; /* Null input pointer */

       if ( length < 0 )

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           return fnvBadParam;
       for ( temp = FNV32basis; length > 0; length-- )
           temp = FNV32prime * ( temp ^ *in++ );
   #ifdef FNV_BigEndian
       FNV32reverse ( out, temp );
   #else
       *out = temp;
   #endif
       return fnvSuccess;
   }   /* end FNV32block */

   #ifdef FNV_BigEndian

   /* Store a Big Endian result back as Little Endian
    ***************************************************************/
   static void FNV32reverse ( uint32_t *out, uint32_t hash )
   {
       uint32_t    temp;

       temp = hash & 0xFF;
       hash >>= 8;
       temp = ( temp << 8 ) + ( hash & 0xFF );
       hash >>= 8;
       temp = ( temp << 8 ) + ( hash & 0xFF );
       hash >>= 8;
       *out = ( temp << 8 ) + ( hash & 0xFF );
   }   /* end FNV32reverse */

   #endif /* FNV_BigEndian */

   /***************************************************************
    *       Set of init, input, and output functions below        *
    *       to incrementally compute FNV32                        *
    ***************************************************************/

   /* initialize context
    ***************************************************************/
   int FNV32init ( FNV32context * const ctx )
   {
       return FNV32initBasis ( ctx, FNV32basis );
   }   /* end FNV32init */

   /* initialize context with a provided basis
    ***************************************************************/
   int FNV32initBasis ( FNV32context * const ctx, uint32_t basis )
   {
       if ( !ctx )

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           return fnvNull;

       ctx->Hash = basis;
       ctx->Computed = FNVinited+FNV32state;
       return fnvSuccess;
   }   /* end FNV32initBasis */

   /* hash in a counted block
    ***************************************************************/
   int FNV32blockin ( FNV32context * const ctx,
                      const void *vin,
                      long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t    temp;

       if ( !ctx || !in )
           return fnvNull;

       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV32state:
               ctx->Computed = FNVcomputed+FNV32state;
           case FNVcomputed+FNV32state:
               break;
           default:
               return fnvStateError;
           }
       for ( temp = ctx->Hash; length > 0; length-- )
           temp = FNV32prime * ( temp ^ *in++ );
       ctx->Hash = temp;
       return fnvSuccess;
   }   /* end FNV32blockin */

   /* hash in a zero terminated string not including the zero
    ***************************************************************/
   int FNV32stringin ( FNV32context * const ctx,
                       const char *in )
   {
       uint32_t    temp;
       uint8_t     ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )

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           {
           case FNVinited+FNV32state:
               ctx->Computed = FNVcomputed+FNV32state;
           case FNVcomputed+FNV32state:
               break;
           default:
               return fnvStateError;
           }
       temp = ctx->Hash;
       while ( (ch = (uint8_t)*in++) )
           temp = FNV32prime * ( temp ^ ch );
       ctx->Hash = temp;
       return fnvSuccess;
   }   /* end FNV32stringin */

   /* return hash
    ***************************************************************/
   int FNV32result ( FNV32context * const ctx,
                     uint32_t * const out )
   {
       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV32state )
           return fnvStateError;
       ctx->Computed = FNVemptied+FNV32state;
   #ifdef FNV_BigEndian
       FNV32reverse ( out, ctx->Hash );
   #else
       *out = ctx->Hash;
   #endif
       ctx->Hash = 0;
       return fnvSuccess;
   }   /* end FNV32result */

   #endif    /* _FNV32_C_ */
   <CODE ENDS>

6.1.2.  FNV64 Code

   The header and C source for 64-bit FNV-1a.  Return a 64-bit integers
   are supported, otherwise return an 8-byte vectir if bytes.

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   <CODE BEGINS> file "FNV64.h"
   /**************************** FNV64.h *****************************/
   /****************** See RFC NNNN for details. *********************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV64_H_
   #define _FNV64_H_

   /*
    *  Description:
    *      This file provides headers for the 64-bit version of the
    *      FNV-1a non-cryptographic hash algorithm.
    */

   #include "FNVconfig.h"

   #include <stdint.h>
   #define FNV64size (64/8)

   /* If you do not have the ISO standard stdint.h header file, then you
    * must typedef the following types:
    *
    *    type             meaning
    *  uint64_t        unsigned 64 bit integer (ifdef FNV_64bitIntegers)
    *  uint32_t        unsigned 32 bit integer
    *  uint16_t        unsigned 16 bit integer
    *  uint8_t         unsigned 8 bit integer (i.e., unsigned char)
    */

   #include "FNVErrorCodes.h"

   /*
    *  This structure holds context information for an FNV64 hash
    */
   #ifdef FNV_64bitIntegers
       /* version if 64 bit integers supported */

   typedef struct FNV64context_s {
           int Computed;  /* state */
           uint64_t Hash;
   } FNV64context;

   #else
       /* version if 64 bit integers NOT supported */

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   typedef struct FNV64context_s {
           int Computed;  /* state */
           uint16_t Hash[FNV64size/2];
   } FNV64context;

   #endif /* FNV_64bitIntegers */

   /*
    *  Function Prototypes
    *    FNV64string: hash a zero terminated string not including
    *                 the terminating zero
    *    FNV64block: FNV64 hash a specified length byte vector
    *    FNV64init: initializes an FNV64 context
    *    FNV64initBasis: initializes an FNV64 context with a
    *                    provided basis
    *    FNV64blockin: hash in a specified length byte vector
    *    FNV64stringin: hash in a zero terminated string not
    *                   incluing the zero
    *    FNV64result: returns the hash value
    *
    *    Hash is returned as a 64-bit integer if supported, otherwise
    *         as a vector of 8-bit unsigned integers
    */

   #ifdef __cplusplus
   extern "C" {
   #endif

   /* FNV64 */
   extern int FNV64init ( FNV64context * const );
   extern int FNV64blockin ( FNV64context * const,
                             const void * in,
                             long int length );
   extern int FNV64stringin ( FNV64context * const,
                              const char * in );

   #ifdef FNV_64bitIntegers
     extern int FNV64string ( const char *in,
                              uint64_t * const out );
     extern int FNV64block ( const void *in,
                             long int length,
                             uint64_t * const out );
     extern int FNV64initBasis ( FNV64context * const,
                               uint64_t basis );
     extern int FNV64result ( FNV64context * const,
                              uint64_t * const out );
   #else
     extern int FNV64string ( const char *in,

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                              uint8_t out[FNV64size] );
     extern int FNV64block ( const void *in,
                             long int length,
                             uint8_t out[FNV64size] );
     extern int FNV64initBasis ( FNV64context * const,
                               const uint8_t basis[FNV64size] );
     extern int FNV64result ( FNV64context * const,
                              uint8_t out[FNV64size] );
   #endif /* FNV_64bitIntegers */

   #ifdef __cplusplus
   }
   #endif

   #endif /* _FNV64_H_ */
   <CODE ENDS>

   <CODE BEGINS> file "FNV64.c"
   /**************************** FNV64.c *****************************/
   /******************* See RFC NNNN for details *********************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   /* This file implements the FNV (Fowler, Noll, Vo) non-cryptographic
    * hash function FNV-1a for 64-bit hashes.
    */

   #ifndef _FNV64_C_
   #define _FNV64_C_

   #include "fnv-private.h"
   #include "FNV64.h"

   /******************************************************************
    *       START VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC        *
    ******************************************************************/
   #ifdef FNV_64bitIntegers

   #ifdef FNV_BigEndian
   /* Local prototype */
   static void FNV64reverse ( uint64_t * out, uint64_t hash );
   #endif /* FNV_BigEndian */

   /* 64 bit FNV_prime = 2^40 + 2^8 + 0xb3 */
   #define FNV64prime 0x00000100000001B3
   #define FNV64basis 0xCBF29CE484222325

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   /* FNV64 hash a null terminated string  (64 bit)
    ******************************************************************/
   int FNV64string ( const char *in, uint64_t * const out )
   {
       uint64_t    temp;
       uint8_t     ch;

       if ( !in || !out )
           return fnvNull; /* Null input pointer */

       temp = FNV64basis;
       while ( (ch = *in++) )
           temp = FNV64prime * ( temp ^ ch );
   #ifdef FNV_BigEndian
       FNV64reverse ( out, temp );
   #else
       *out = temp;
   #endif
       return fnvSuccess;
   }   /* end FNV64string */

   /* FNV64 hash a counted block  (64 bit)
    ******************************************************************/
   int FNV64block ( const void *vin,
                    long int length,
                    uint64_t * const out )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint64_t    temp;

       if ( !in || !out )
           return fnvNull; /* Null input pointer */

       if ( length < 0 )
           return fnvBadParam;
       for ( temp = FNV64basis; length > 0; length-- )
           temp = FNV64prime * ( temp ^ *in++ );
   #ifdef FNV_BigEndian
       FNV64reverse ( out, temp );
   #else
       *out = temp;
   #endif
       return fnvSuccess;
   }   /* end FNV64block */

   #ifdef FNV_BigEndian

   /* Store a Big Endian result back as Little Endian

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    ***************************************************************/
   static void FNV64reverse ( uint64_t *out, uint64_t hash )
   {
       uint64_t    temp;
       int         i;

       temp = hash & 0xFF;
       for ( i = FNV64size - 1; i > 0; i-- )
           {
           hash >>= 8;
           temp = ( temp << 8 ) + ( hash & 0xFF );
           }
       *out = temp;
   }   /* end FNV64reverse */

   #endif /* FNV_BigEndian */

   /******************************************************************
    *        Set of init, input, and output functions below          *
    *        to incrementally compute FNV64                          *
    ******************************************************************/

   /* initialize context  (64 bit)
    ******************************************************************/
   int FNV64init ( FNV64context * const ctx )
   {
       return FNV64initBasis ( ctx, FNV64basis );
   }       /* end FNV64init */

   /* initialize context with a provided basis  (64 bit)
    ******************************************************************/
   int FNV64initBasis ( FNV64context * const ctx, uint64_t basis )
   {
       if ( !ctx )
           return fnvNull;

       ctx->Hash = basis;
       ctx->Computed = FNVinited+FNV64state;
       return fnvSuccess;
   }       /* end FNV64initBasis */

   /* hash in a counted block  (64 bit)
    ******************************************************************/
   int FNV64blockin ( FNV64context * const ctx,
                      const void *vin,
                      long int length )
   {

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       const uint8_t *in = (const uint8_t*)vin;
       uint64_t    temp;

       if ( !ctx || !in )
           return fnvNull;

       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV64state:
               ctx->Computed = FNVcomputed+FNV64state;
           case FNVcomputed+FNV64state:
               break;
           default:
               return fnvStateError;
           }
       for ( temp = ctx->Hash; length > 0; length-- )
           temp = FNV64prime * ( temp ^ *in++ );
       ctx->Hash = temp;
       return fnvSuccess;
   }   /* end FNV64input */

   /* hash in a zero terminated string not including the zero (64 bit)
    ******************************************************************/
   int FNV64stringin ( FNV64context * const ctx,
                       const char *in )
   {
       uint64_t        temp;
       uint8_t         ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV64state:
               ctx->Computed = FNVcomputed+FNV64state;
           case FNVcomputed+FNV64state:
               break;
           default:
                return fnvStateError;
            }
       temp = ctx->Hash;
       while ( (ch = *in++) )
           temp = FNV64prime * ( temp ^ ch );
       ctx->Hash = temp;
       return fnvSuccess;

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   }   /* end FNV64stringin */

   /* return hash  (64 bit)
    ******************************************************************/
   int FNV64result ( FNV64context * const ctx,
                     uint64_t * const out )
   {
       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV64state )
           return fnvStateError;
       ctx->Computed = FNVemptied+FNV64state;
   #ifdef FNV_BigEndian
       FNV64reverse ( out, ctx->Hash );
   #else
       *out = ctx->Hash;
   #endif
       ctx->Hash = 0;
       return fnvSuccess;
   }   /* end FNV64result */

   /****************************************************************
    *       END VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC        *
    ****************************************************************/
   #else    /*  FNV_64bitIntegers */
   /****************************************************************
    *    START VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC    *
    ****************************************************************/

   /* 64 bit FNV_prime = 2^40 + 2^8 + 0xb3 */
   /* #define FNV64prime 0x00000100000001B3 */
   #define FNV64primeX 0x01B3
   #define FNV64shift 8

   /* #define FNV64basis 0xCBF29CE484222325 */
   #define FNV64basis0 0xCBF2
   #define FNV64basis1 0x9CE4
   #define FNV64basis2 0x8422
   #define FNV64basis3 0x2325

   /* FNV64 hash a null terminated string  (32 bit)
    ******************************************************************/
   int FNV64string ( const char *in, uint8_t out[FNV64size] )
   {
       FNV64context     ctx;
       int              err;

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       if ( ( err = FNV64init (&ctx) ) != fnvSuccess )
           return err;
       if ( ( err = FNV64stringin (&ctx, in) ) != fnvSuccess )
           return err;
       return FNV64result (&ctx, out);
   }   /* end FNV64string */

   /* FNV64 hash a counted block  (32 bit)
    ******************************************************************/
   int FNV64block ( const void *in,
                    long int length,
                    uint8_t out[FNV64size] )
   {
       FNV64context     ctx;
       int              err;

       if ( ( err = FNV64init (&ctx) ) != fnvSuccess )
           return err;
       if ( ( err = FNV64blockin (&ctx, in, length) ) != fnvSuccess )
           return err;
       return FNV64result (&ctx, out);
   }   /* end FNV64block */

   /******************************************************************
    *        Set of init, input, and output functions below          *
    *        to incrementally compute FNV64                          *
    ******************************************************************/

   /* initialize context  (32 bit)
    ******************************************************************/
   int FNV64init ( FNV64context * const ctx )
   {
       if ( !ctx )
           return fnvNull;

       ctx->Hash[0] = FNV64basis0;
       ctx->Hash[1] = FNV64basis1;
       ctx->Hash[2] = FNV64basis2;
       ctx->Hash[3] = FNV64basis3;
       ctx->Computed = FNVinited+FNV64state;
       return fnvSuccess;
   }   /* end FNV64init */

   /* initialize context  (32 bit)
    ******************************************************************/
   int FNV64initBasis ( FNV64context * const ctx,
                        const uint8_t basis[FNV64size] )

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   {
       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ctx->Hash[0] = basis[1] + ( basis[0]<<8 );
       ctx->Hash[1] = basis[3] + ( basis[2]<<8 );
       ctx->Hash[2] = basis[5] + ( basis[4]<<8 );
       ctx->Hash[3] = basis[7] + ( basis[6]<<8 );
   #else
       ctx->Hash[0] = basis[0] + ( basis[1]<<8 );
       ctx->Hash[1] = basis[2] + ( basis[3]<<8 );
       ctx->Hash[2] = basis[4] + ( basis[5]<<8 );
       ctx->Hash[3] = basis[6] + ( basis[7]<<8 );
   #endif
       ctx->Computed = FNVinited+FNV64state;
       return fnvSuccess;
   }   /* end FNV64initBasis */

   /* hash in a counted block  (32 bit)
    ******************************************************************/
   int FNV64blockin ( FNV64context * const ctx,
                      const void *vin,
                      long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t   temp[FNV64size/2];
       uint32_t   temp2[2];
       int        i;

       if ( !ctx || !in )
           return fnvNull;

       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV64state:
               ctx->Computed = FNVcomputed+FNV64state;
           case FNVcomputed+FNV64state:
               break;
           default:
               return fnvStateError;
           }
       for ( i=0; i<FNV64size/2; ++i )
            temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {

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           /* temp = FNV64prime * ( temp ^ *in++ ); */
           temp2[1] = temp[3] << FNV64shift;
           temp2[0] = temp[2] << FNV64shift;
           temp[3] = FNV64primeX * ( temp[3] ^ *in++ );
           temp[2] *= FNV64primeX;
           temp[1] = temp[1] * FNV64primeX + temp2[1];
           temp[0] = temp[0] * FNV64primeX + temp2[0];
           temp[2] += temp[3] >> 16;
           temp[3] &= 0xFFFF;
           temp[1] += temp[2] >> 16;
           temp[2] &= 0xFFFF;
           temp[0] += temp[1] >> 16;
           temp[1] &= 0xFFFF;
           }
       for ( i=0; i<FNV64size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV64blockin */

   /* hash in a string  (32 bit)
    ******************************************************************/
   int FNV64stringin ( FNV64context * const ctx,
                       const char *in )
   {
       uint32_t   temp[FNV64size/2];
       uint32_t   temp2[2];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV64state:
               ctx->Computed = FNVcomputed+FNV64state;
           case FNVcomputed+FNV64state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV64size/2; ++i )
            temp[i] = ctx->Hash[i];
       while ( ( ch = (uint8_t)*in++ ) != 0)
           {
           /* temp = FNV64prime * ( temp ^ ch ); */
           temp2[1] = temp[3] << FNV64shift;
           temp2[0] = temp[2] << FNV64shift;

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           temp[3] = FNV64primeX * ( temp[3] ^ *in++ );
           temp[2] *= FNV64primeX;
           temp[1] = temp[1] * FNV64primeX + temp2[1];
           temp[0] = temp[0] * FNV64primeX + temp2[0];
           temp[2] += temp[3] >> 16;
           temp[3] &= 0xFFFF;
           temp[1] += temp[2] >> 16;
           temp[2] &= 0xFFFF;
           temp[0] += temp[1] >> 16;
           temp[1] &= 0xFFFF;
           }
       for ( i=0; i<FNV64size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV64stringin */

   /* return hash  (32 bit)
    ******************************************************************/
   int FNV64result ( FNV64context * const ctx,
                     uint8_t out[FNV64size] )
   {
       int    i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV64state )
           return fnvStateError;
       for ( i=0; i<FNV64size/2; ++i )
           {
   #ifdef FNV_BigEndian
           out[7-2*i] = ctx->Hash[i];
           out[6-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx -> Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV64state;
       return fnvSuccess;
   }   /* end FNV64result */

   #endif    /*  FNV_64bitIntegers */
   /******************************************************************
    *       END VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC     *
    ******************************************************************/

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   #endif    /* _FNV64_C_ */
   <CODE ENDS>

6.1.3.  FNV128 Code

   The header and C source for 128-bit FNV-1a returning a byte vector.

   <CODE BEGINS> file "FNV128.h"
   /*************************** FNV128.h *************************/
   /**************** See RFC NNNN for details. *******************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons identified
    * as authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV128_H_
   #define _FNV128_H_

   /*
    *  Description:
    *      This file provides headers for the 128-bit version of the
    *      FNV-1a non-cryptographic hash algorithm.
    */

   #include "FNVconfig.h"

   #include <stdint.h>
   #define FNV128size (128/8)

   /* If you do not have the ISO standard stdint.h header file, then
    * you must typedef the following types:
    *
    *    type              meaning
    *  uint64_t    unsigned 64 bit integer (ifdef FNV_64bitIntegers)
    *  uint32_t    unsigned 32 bit integer
    *  uint16_t    unsigned 16 bit integer
    *  uint8_t     unsigned 8 bit integer (i.e., unsigned char)
    */

   #include "FNVErrorCodes.h"

   /*
    *  This structure holds context information for an FNV128 hash
    */
   #ifdef FNV_64bitIntegers
       /* version if 64 bit integers supported */
   typedef struct FNV128context_s {

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           int Computed;  /* state */
           uint32_t Hash[FNV128size/4];
   } FNV128context;

   #else
       /* version if 64 bit integers NOT supported */

   typedef struct FNV128context_s {
           int Computed;  /* state */
           uint16_t Hash[FNV128size/2];
   } FNV128context;

   #endif /* FNV_64bitIntegers */

   /*
    *  Function Prototypes
    *    FNV128string: hash a zero terminated string not including
    *                  the terminating zero
    *    FNV128block: FNV128 hash a specified length byte vector
    *    FNV128init: initializes an FNV128 context
    *    FNV128initBasis: initializes an FNV128 context with a
    *                     provided basis
    *    FNV128blockin: hash in a specified length byte vector
    *    FNV128stringin: hash in a zero terminated string not
    *                    including the zero
    *    FNV128result: returns the hash value
    *
    *    Hash is returned as an array of 8-bit unsigned integers
    */

   #ifdef __cplusplus
   extern "C" {
   #endif

   /* FNV128 */
   extern int FNV128string ( const char *in,
                             uint8_t out[FNV128size] );
   extern int FNV128block ( const void *in,
                            long int length,
                            uint8_t out[FNV128size] );
   extern int FNV128init ( FNV128context * const );
   extern int FNV128initBasis ( FNV128context * const,
                                const uint8_t basis[FNV128size] );
   extern int FNV128blockin ( FNV128context * const,
                              const void *in,
                              long int length );
   extern int FNV128stringin ( FNV128context * const,
                               const char *in );

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   extern int FNV128result ( FNV128context * const,
                             uint8_t out[FNV128size] );

   #ifdef __cplusplus
   }
   #endif

   #endif /* _FNV128_H_ */
   <CODE ENDS>

   <CODE BEGINS> file "FNV128.c"
   /***************************** FNV128.c ***************************/
   /******************** See RFC NNNN for details ********************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights
    * See fnv-private.h for terms of use and redistribution.
    */

   /* This file implements the FNV (Fowler, Noll, Vo) non-cryptographic
    * hash function FNV-1a for 128-bit hashes.
    */

   #ifndef _FNV128_C_
   #define _FNV128_C_

   #include "fnv-private.h"
   #include "FNV128.h"

   /* common code for 64 and 32 bit modes */

   /* FNV128 hash a null terminated string  (64/32 bit)
    ******************************************************************/
   int FNV128string ( const char *in, uint8_t out[FNV128size] )
   {
       FNV128context    ctx;
       int              err;

       if ( (err = FNV128init ( &ctx )) != fnvSuccess )
           return err;
       if ( (err = FNV128stringin ( &ctx, in )) != fnvSuccess )
           return err;
       return FNV128result (&ctx, out);
   }   /* end FNV128string */

   /* FNV128 hash a counted block  (64/32 bit)
    ******************************************************************/
   int FNV128block ( const void *in,
                     long int length,

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                     uint8_t out[FNV128size] )
   {
       FNV128context    ctx;
       int              err;

      if ( (err = FNV128init ( &ctx )) != fnvSuccess )
          return err;
      if ( (err = FNV128blockin ( &ctx, in, length )) != fnvSuccess )
          return err;
       return FNV128result ( &ctx, out );
   }   /* end FNV128block */

   /******************************************************************
    *        START VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC       *
    ******************************************************************/
   #ifdef FNV_64bitIntegers

   /* 128 bit FNV_prime = 2^88 + 2^8 + 0x3b */
   /* 0x00000000 01000000 00000000 0000013B */
   #define FNV128primeX 0x013B
   #define FNV128shift 24

   /* 0x6C62272E 07BB0142 62B82175 6295C58D */
   #define FNV128basis0 0x6C62272E
   #define FNV128basis1 0x07BB0142
   #define FNV128basis2 0x62B82175
   #define FNV128basis3 0x6295C58D

   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV128                        *
    ******************************************************************/

   /* initialize context  (64 bit)
    ******************************************************************/
   int FNV128init ( FNV128context * const ctx )
   {
       if ( !ctx )
           return fnvNull;

       ctx->Hash[0] = FNV128basis0;
       ctx->Hash[1] = FNV128basis1;
       ctx->Hash[2] = FNV128basis2;
       ctx->Hash[3] = FNV128basis3;
       ctx->Computed = FNVinited+FNV128state;
       return fnvSuccess;
   }   /* end FNV128init */

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   /* initialize context with a provided basis  (64 bit)
    ******************************************************************/
   int FNV128initBasis ( FNV128context * const ctx,
                         const uint8_t basis[FNV128size] )
   {
       int       i;
       const uint8_t   *ui8p;
       uint32_t  temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV128size/4; ++i )
           {
           temp = (*ui8p++)<<8;
           temp = (temp + *ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #else
       ui8p = basis + ( FNV128size/4 - 1 );
       for ( i=0; i < FNV128size/4; ++i )
           {
               temp = (*ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #endif
       ctx->Computed = FNVinited+FNV128state;
       return fnvSuccess;
   }   /* end FNV128initBasis */

   /* hash in a counted block  (64 bit)
    ******************************************************************/
   int FNV128blockin ( FNV128context * const ctx,
                       const void *vin,
                       long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint64_t    temp[FNV128size/4];
       uint64_t    temp2[2];
       int         i;

       if ( !ctx || !in )
           return fnvNull;

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       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV128state:
               ctx->Computed = FNVcomputed+FNV128state;
           case FNVcomputed+FNV128state:
               break;
           default:
               return fnvStateError;
           }
       for ( i=0; i<FNV128size/4; ++i )
            temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV128prime * ( temp ^ *in++ ); */
           temp2[1] = temp[3] << FNV128shift;
           temp2[0] = temp[2] << FNV128shift;
           temp[3] = FNV128primeX * ( temp[3] ^ *in++ );
           temp[2] *= FNV128primeX;
           temp[1] = temp[1] * FNV128primeX + temp2[1];
           temp[0] = temp[0] * FNV128primeX + temp2[0];
           temp[2] += temp[3] >> 32;
           temp[3] &= 0xFFFFFFFF;
           temp[1] += temp[2] >> 32;
           temp[2] &= 0xFFFFFFFF;
           temp[0] += temp[1] >> 32;
           temp[1] &= 0xFFFFFFFF;
           }
       for ( i=0; i<FNV128size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV128input */

   /* hash in a string  (64 bit)
    ******************************************************************/
   int FNV128stringin ( FNV128context * const ctx, const char *in )
   {
       uint64_t   temp[FNV128size/4];
       uint64_t   temp2[2];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {

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           case FNVinited+FNV128state:
               ctx->Computed = FNVcomputed+FNV128state;
           case FNVcomputed+FNV128state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV128size/4; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV128prime * ( temp ^ ch ); */
           temp2[1] = temp[3] << FNV128shift;
           temp2[0] = temp[2] << FNV128shift;
           temp[3] = FNV128primeX * ( temp[3] ^ *in++ );
           temp[2] *= FNV128primeX;
           temp[1] = temp[1] * FNV128primeX + temp2[1];
           temp[0] = temp[0] * FNV128primeX + temp2[0];
           temp[2] += temp[3] >> 32;
           temp[3] &= 0xFFFFFFFF;
           temp[1] += temp[2] >> 32;
           temp[2] &= 0xFFFFFFFF;
           temp[0] += temp[1] >> 32;
           temp[1] &= 0xFFFFFFFF;
           }
       for ( i=0; i<FNV128size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV128stringin */

   /* return hash  (64 bit)
    ******************************************************************/
   int FNV128result ( FNV128context * const ctx,
                      uint8_t out[FNV128size] )
   {
       int     i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV128state )
           return fnvStateError;
       for ( i=0; i<FNV128size/4; ++i )
           {
   #ifdef FNV_BigEndian
           out[15-4*i] = ctx->Hash[i];
           out[14-4*i] = ctx->Hash[i] >> 8;
           out[13-4*i] = ctx->Hash[i] >> 16;

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           out[12-4*i] = ctx->Hash[i] >> 24;
   #else
           out[4*i] = ctx->Hash[i];
           out[4*i+1] = ctx->Hash[i] >> 8;
           out[4*i+2] = ctx->Hash[i] >> 16;
           out[4*i+3] = ctx->Hash[i] >> 24;
   #endif
           ctx -> Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV128state;
       return fnvSuccess;
   }   /* end FNV128result */

   /*****************************************************************
    *        END VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC        *
    *****************************************************************/
   #else    /*  FNV_64bitIntegers */
   /*****************************************************************
    *     START VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC    *
    *****************************************************************/

   /* 128 bit FNV_prime = 2^88 + 2^8 + 0x3b */
   /* 0x00000000 01000000 00000000 0000013B */
   #define FNV128primeX 0x013B
   #define FNV128shift 8

   /* 0x6C62272E 07BB0142 62B82175 6295C58D */
   uint16_t FNV128basis[FNV128size/2] =
            { 0x6C62, 0x272E, 0x07BB, 0x0142,
              0x62B8, 0x2175, 0x6295, 0xC58D };

   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV128                        *
    ******************************************************************/

   /* initialize context  (32 bit)
    ******************************************************************/
   int FNV128init ( FNV128context *ctx )
   {
       int     i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV128size/2; ++i )
           ctx->Hash[i] = FNV128basis[i];
       ctx->Computed = FNVinited+FNV128state;

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       return fnvSuccess;
   }   /* end FNV128init */

   /* initialize context with a provided basis  (32 bit)
    ******************************************************************/
   int FNV128initBasis ( FNV128context *ctx,
                         const uint8_t basis[FNV128size] )
   {
       int      i;
       const uint8_t  *ui8p;
       uint32_t temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV128size/2; ++i )
           {
           temp = *ui8p++;
           ctx->Hash[i] = ( temp<<8 ) + (*ui8p++);
           }
   #else
       ui8p = basis + (FNV128size/2 - 1);
       for ( i=0; i < FNV128size/2; ++i )
           {
           temp = *ui8p--;
           ctx->Hash[i] = ( temp<<8 ) +  (*ui8p--);
           }
   #endif
       ctx->Computed = FNVinited+FNV128state;
       return fnvSuccess;
   }   /* end FNV128initBasis */

   /* hash in a counted block  (32 bit)
    *****************************************************************/
   int FNV128blockin ( FNV128context *ctx,
                       const void *vin,
                       long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t   temp[FNV128size/2];
       uint32_t   temp2[3];
       int        i;

       if ( !ctx || !in )
           return fnvNull;

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       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV128state:
               ctx->Computed = FNVcomputed+FNV128state;
           case FNVcomputed+FNV128state:
               break;
           default:
               return fnvStateError;
           }
       for ( i=0; i<FNV128size/2; ++i )
            temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV128prime * ( temp ^ *in++ ); */
           temp[7] ^= *in++;
           temp2[2] = temp[7] << FNV128shift;
           temp2[1] = temp[6] << FNV128shift;
           temp2[0] = temp[5] << FNV128shift;
           for ( i=0; i<8; ++i )
               temp[i] *= FNV128primeX;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=7; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
           }
       for ( i=0; i<FNV128size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV128blockin */

   /* hash in a string  (32 bit)
    ******************************************************************/
   int FNV128stringin ( FNV128context *ctx,
                        const char *in )
   {
       uint32_t   temp[FNV128size/2];
       uint32_t   temp2[3];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

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       switch ( ctx->Computed )
           {
           case FNVinited+FNV128state:
               ctx->Computed = FNVcomputed+FNV128state;
           case FNVcomputed+FNV128state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV128size/2; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV128prime * ( temp ^ *in++ ); */
           temp[7] ^= ch;
           temp2[2] = temp[7] << FNV128shift;
           temp2[1] = temp[6] << FNV128shift;
           temp2[0] = temp[5] << FNV128shift;
           for ( i=0; i<8; ++i )
               temp[i] *= FNV128primeX;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=7; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
            }
       for ( i=0; i<FNV128size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV128stringin */

   /* return hash  (32 bit)
    ******************************************************************/
   int FNV128result ( FNV128context *ctx,
                      uint8_t out[FNV128size] )
   {
       int    i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV128state )
           return fnvStateError;
       for ( i=0; i<FNV128size/2; ++i )
           {

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   #ifdef FNV_BigEndian
           out[15-2*i] = ctx->Hash[i];
           out[14-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx -> Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV128state;
       return fnvSuccess;
   }   /* end FNV128result */

   #endif    /*  FNV_64bitIntegers */
   /*******************************************************************
    *        END VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC     *
    *******************************************************************/

   #endif    /* _FNV128_C_ */
   <CODE ENDS>

6.1.4.  FNV256 Code

   The header and C source for 256-bit FNV-1a returning a byte vector.

   <CODE BEGINS> file "FNV256.h"
   /************************** FNV256.h ************************/
   /*************** See RFC NNNN for details. ******************/
   /*
    * Copyright (c) 201, 20236 IETF Trust and the persons
    * identified as authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV256_H_
   #define _FNV256_H_

   /*
    *  Description:
    *      This file provides headers for the 256-bit version of
    *      the FNV-1a non-cryptographic hash algorithm.
    */

   #include "FNVconfig.h"

   #include <stdint.h>
   #define FNV256size (256/8)

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   /* If you do not have the ISO standard stdint.h header file, then
    * you must typedef the following types:
    *
    *    type              meaning
    *  uint64_t    unsigned 64 bit integer (ifdef FNV_64bitIntegers)
    *  uint32_t    unsigned 32 bit integer
    *  uint16_t    unsigned 16 bit integer
    *  uint8_t     unsigned 8 bit integer (i.e., unsigned char)
    */

   #include "FNVErrorCodes.h"

   /*
    *  This structure holds context information for an FNV256 hash
    */
   #ifdef FNV_64bitIntegers
       /* version if 64 bit integers supported */
   typedef struct FNV256context_s {
           int Computed;  /* state */
           uint32_t Hash[FNV256size/4];
   } FNV256context;

   #else
       /* version if 64 bit integers NOT supported */

   typedef struct FNV256context_s {
           int Computed;  /* state */
           uint16_t Hash[FNV256size/2];
   } FNV256context;

   #endif /* FNV_64bitIntegers */

   /*
    *  Function Prototypes
    *    FNV256string: hash a zero terminated string not including
    *                  the zero
    *    FNV256block: FNV256 hash a specified length byte vector
    *    FNV256init: initializes an FNV256 context
    *    FNV256initBasis:  initializes an FNV256 context with a
    *                     provided basis
    *    FNV256blockin: hash in a specified length byte vector
    *    FNV256stringin: hash in a zero terminated string not
    *                    including the zero
    *    FNV256result: returns the hash value
    *
    *    Hash is returned as an array of 8-bit unsigned integers
    */

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   #ifdef __cplusplus
   extern "C" {
   #endif

   /* FNV256 */
   extern int FNV256string ( const char *in,
                             uint8_t out[FNV256size] );
   extern int FNV256block ( const void *in,
                            long int length,
                            uint8_t out[FNV256size] );
   extern int FNV256init ( FNV256context *);
   extern int FNV256initBasis ( FNV256context * const,
                                const uint8_t basis[FNV256size] );
   extern int FNV256blockin ( FNV256context * const,
                              const void *in,
                              long int length );
   extern int FNV256stringin ( FNV256context * const,
                               const char *in );
   extern int FNV256result ( FNV256context * const,
                             uint8_t out[FNV256size] );

   #ifdef __cplusplus
   }
   #endif

   #endif /* _FNV256_H_ */
   <CODE ENDS>

   <CODE BEGINS> file "FNV256.c"
   /***************************** FNV256.c ***************************/
   /******************** See RFC NNNN for details ********************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights
    * See fnv-private.h for terms of use and redistribution.
    */

   /* This file implements the FNV (Fowler, Noll, Vo) non-cryptographic
    * hash function FNV-1a for 256-bit hashes.
    */

   #ifndef _FNV256_C_
   #define _FNV256_C_

   #include "fnv-private.h"
   #include "FNV256.h"

   /* common code for 64 and 32 bit modes */

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   /* FNV256 hash a null terminated string  (64/32 bit)
    ******************************************************************/
   int FNV256string ( const char *in, uint8_t out[FNV256size] )
   {
       FNV256context    ctx;
       int              err;

       if ( (err = FNV256init ( &ctx )) != fnvSuccess )
           return err;
       if ( (err = FNV256stringin ( &ctx, in )) != fnvSuccess )
           return err;
       return FNV256result ( &ctx, out );
   }   /* end FNV256string */

   /* FNV256 hash a counted block  (64/32 bit)
    ******************************************************************/
   int FNV256block ( const void *in,
                     long int length,
                     uint8_t out[FNV256size] )
   {
       FNV256context    ctx;
       int              err;

       if ( (err = FNV256init ( &ctx )) != fnvSuccess )
           return err;
       if ( (err = FNV256blockin ( &ctx, in, length)) != fnvSuccess )
           return err;
       return FNV256result ( &ctx, out );
   }   /* end FNV256block */

   /******************************************************************
    *        START VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC       *
    ******************************************************************/
   #ifdef FNV_64bitIntegers

   /* 256 bit FNV_prime = 2^168 + 2^8 + 0x63 */
   /* 0x0000000000000000 0000010000000000
        0000000000000000 0000000000000163 */
   #define FNV256primeX 0x0163
   #define FNV256shift 8

   /* 0xDD268DBCAAC55036 2D98C384C4E576CC
        C8B1536847B6BBB3 1023B4C8CAEE0535 */
   uint32_t FNV256basis[FNV256size/4] = {
            0xDD268DBC, 0xAAC55036, 0x2D98C384, 0xC4E576CC,
            0xC8B15368, 0x47B6BBB3, 0x1023B4C8, 0xCAEE0535 };

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   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV256                        *
    ******************************************************************/

   /* initialize context  (64 bit)
    ******************************************************************/
   int FNV256init ( FNV256context *ctx )
   {
       int      i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV256size/4; ++i )
           ctx->Hash[i] = FNV256basis[i];
       ctx->Computed = FNVinited+FNV256state;
       return fnvSuccess;
   }   /* end FNV256init */

   /* initialize context with a provided basis  (64 bit)
    ******************************************************************/
   int FNV256initBasis ( FNV256context* const ctx,
                         const uint8_t basis[FNV256size] )
   {
       int      i;
       const uint8_t  *ui8p;
       uint32_t  temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV256size/4; ++i )
           {
               temp = (*ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #else
       ui8p = basis + (FNV256size/4 - 1);
       for ( i=0; i < FNV256size/4; ++i )
           {
               temp = (*ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;

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           ctx->Hash[i] = temp +  *ui8p;
           }
   #endif
       ctx->Computed = FNVinited+FNV256state;
       return fnvSuccess;
   }   /* end FNV256initBasis */

   /* hash in a counted block  (64 bit)
    ******************************************************************/
   int FNV256blockin ( FNV256context *ctx,
                       const void *vin,
                       long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint64_t    temp[FNV256size/4];
       uint64_t    temp2[3];
       int         i;

       if ( !ctx || !in )
           return fnvNull;

       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV256state:
               ctx->Computed = FNVcomputed+FNV256state;
           case FNVcomputed+FNV256state:
               break;
           default:
               return fnvStateError;
           }
       for ( i=0; i<FNV256size/4; ++i )
            temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV256prime * ( temp ^ *in++ ); */
           temp[7] ^= *in++;
           temp2[2] = temp[7] << FNV256shift;
           temp2[1] = temp[6] << FNV256shift;
           temp2[0] = temp[5] << FNV256shift;
           for ( i=0; i<FNV256size/4; ++i )
               temp[i] *= FNV256primeX;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=FNV256size/4-1; i>0; --i )
               {

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               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
          }
       for ( i=0; i<FNV256size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV256input */

   /* hash in a string  (64 bit)
    ******************************************************************/
   int FNV256stringin ( FNV256context *ctx, const char *in )
   {
       uint64_t   temp[FNV256size/4];
       uint64_t   temp2[3];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV256state:
               ctx->Computed = FNVcomputed+FNV256state;
           case FNVcomputed+FNV256state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV256size/4; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV256prime * ( temp ^ ch ); */
           temp[7] ^= ch;
           temp2[2] = temp[7] << FNV256shift;
           temp2[1] = temp[6] << FNV256shift;
           temp2[0] = temp[5] << FNV256shift;
           for ( i=0; i<FNV256size/4; ++i )
               temp[i] *= FNV256primeX;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=FNV256size/4-1; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;

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               }
          }
       for ( i=0; i<FNV256size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV256stringin */

   /* return hash  (64 bit)
    ******************************************************************/
   int FNV256result ( FNV256context *ctx, uint8_t out[FNV256size] )
   {
       int     i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV256state )
           return fnvStateError;
       for ( i=0; i<FNV256size/4; ++i )
           {
   #ifdef FNV_BigEndian
           out[31-4*i] = ctx->Hash[i];
           out[31-4*i] = ctx->Hash[i] >> 8;
           out[31-4*i] = ctx->Hash[i] >> 16;
           out[31-4*i] = ctx->Hash[i] >> 24;
   #else
           out[4*i] = ctx->Hash[i];
           out[4*i+1] = ctx->Hash[i] >> 8;
           out[4*i+2] = ctx->Hash[i] >> 16;
           out[4*i+3] = ctx->Hash[i] >> 24;
   #endif
           ctx -> Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV256state;
       return fnvSuccess;
   }   /* end FNV256result */

   /*****************************************************************
    *        END VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC        *
    *****************************************************************/
   #else    /*  FNV_64bitIntegers */
   /*****************************************************************
    *      START VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC   *
    *****************************************************************/

   /* version for when you only have 32-bit arithmetic
    *****************************************************************/

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   /* 256 bit FNV_prime = 2^168 + 2^8 + 0x63 */
   /* 0x00000000 00000000 00000100 00000000
        00000000 00000000 00000000 00000163 */
   #define FNV256primeX 0x0163
   #define FNV256shift 8

   /* 0xDD268DBCAAC55036 2D98C384C4E576CC
        C8B1536847B6BBB3 1023B4C8CAEE0535 */
   uint16_t FNV256basis[FNV256size/2] = {
            0xDD26, 0x8DBC, 0xAAC5, 0x5036,
            0x2D98, 0xC384, 0xC4E5, 0x76CC,
            0xC8B1, 0x5368, 0x47B6, 0xBBB3,
            0x1023, 0xB4C8, 0xCAEE, 0x0535 };

   /*****************************************************************
    *         Set of init, input, and output functions below        *
    *         to incrementally compute FNV256                       *
    *****************************************************************/

   /* initialize context  (32 bit)
    *****************************************************************/
   int FNV256init ( FNV256context *ctx )
   {
       int     i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV256size/2; ++i )
           ctx->Hash[i] = FNV256basis[i];
       ctx->Computed = FNVinited+FNV256state;
       return fnvSuccess;
   }   /* end FNV256init */

   /* initialize context with a provided basis  (32 bit)
    *****************************************************************/
   int FNV256initBasis ( FNV256context *ctx,
                         const uint8_t basis[FNV256size] )
   {
       int      i;
       const uint8_t  *ui8p;
       uint32_t temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;

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       for ( i=0; i < FNV256size/2; ++i )
           {
           temp = *ui8p++;
           ctx->Hash[i] = ( temp<<8 ) + (*ui8p++);
           }
   #else
       ui8p = basis + FNV256size/2 -1;
       for ( i=0; i < FNV256size/2; ++i )
           {
           temp = *ui8p--;
           ctx->Hash[i] = ( temp<<8 ) +  (*ui8p--);
           }
   #endif
       ctx->Computed = FNVinited+FNV256state;
       return fnvSuccess;
   }   /* end FNV256initBasis */

   /* hash in a counted block  (32 bit)
    *****************************************************************/
   int FNV256blockin ( FNV256context *ctx,
                       const void *vin,
                       long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t   temp[FNV256size/2];
       uint32_t   temp2[6];
       int        i;

       if ( !ctx || !in )
           return fnvNull;

       if ( length < 0 )
           return fnvBadParam;
       switch ( ctx->Computed )
           {
           case FNVinited+FNV256state:
               ctx->Computed = FNVcomputed+FNV256state;
           case FNVcomputed+FNV256state:
               break;
           default:
               return fnvStateError;
           }
       for ( i=0; i<FNV256size/2; ++i )
           temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV256prime * ( temp ^ *in++ ); */
           temp[15] ^= *in++;

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           for ( i=0; i<6; ++i )
               temp2[i] = temp[10+i] << FNV256shift;
           for ( i=0; i<FNV256size/2; ++i )
               temp[i] *= FNV256primeX;
           for ( i=0; i<6; ++i )
               temp[10+i] += temp2[i];
           for ( i=15; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
           }
       for ( i=0; i<FNV256size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV256blockin */

   /* hash in a string  (32 bit)
    *****************************************************************/
   int FNV256stringin ( FNV256context *ctx, const char *in )
   {
       uint32_t   temp[FNV256size/2];
       uint32_t   temp2[6];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV256state:
               ctx->Computed = FNVcomputed+FNV256state;
           case FNVcomputed+FNV256state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV256size/2; ++i )
            temp[i] = ctx->Hash[i];
       while ( ( ch = (uint8_t)*in++ ) != 0)
           {
           /* temp = FNV256prime * ( temp ^ *in++ ); */
           temp[15] ^= ch;
           for ( i=0; i<6; ++i )
               temp2[i] = temp[10+i] << FNV256shift;
           for ( i=0; i<FNV256size/2; ++i )
               temp[i] *= FNV256primeX;

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           for ( i=0; i<6; ++i )
               temp[10+i] += temp2[i];
           for ( i=15; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
            }
       for ( i=0; i<FNV256size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV256stringin */

   /* return hash  (32 bit)
    *****************************************************************/
   int FNV256result ( FNV256context *ctx, uint8_t out[FNV256size] )
   {
       int    i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV256state )
           return fnvStateError;
       for ( i=0; i<FNV256size/2; ++i )
           {
   #ifdef FNV_BigEndian
           out[31-2*i] = ctx->Hash[i];
           out[30-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx->Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV256state;
       return fnvSuccess;
   }   /* end FNV256result */

   #endif    /*  FNV_64bitIntegers */
   /*****************************************************************
    *        END VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC   *
    *****************************************************************/

   #endif    /* _FNV256_C_ */
   <CODE ENDS>

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6.1.5.  FNV512 Code

   The header and C source for 512-bit FNV-1a returning a byte vector.

   <CODE BEGINS> file "FNV512.h"
   /************************** FNV512.h ************************/
   /*************** See RFC NNNN for details. ******************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons
    * identified as authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV512_H_
   #define _FNV512_H_

   /*
    *  Description:
    *      This file provides headers for the 512-bit version of
    *      the FNV-1a non-cryptographic hash algorithm.
    */

   #include "FNVconfig.h"

   #include <stdint.h>
   #define FNV512size (512/8)

   /* If you do not have the ISO standard stdint.h header file, then
    * you must typedef the following types:
    *
    *    type              meaning
    *  uint64_t    unsigned 64 bit integer (ifdef FNV_64bitIntegers)
    *  uint32_t    unsigned 32 bit integer
    *  uint16_t    unsigned 16 bit integer
    *  uint8_t     unsigned 8 bit integer (i.e., unsigned char)
    */

   #include "FNVErrorCodes.h"

   /*
    *  This structure holds context information for an FNV512 hash
    */
   #ifdef FNV_64bitIntegers
       /* version if 64 bit integers supported */
   typedef struct FNV512context_s {
           int Computed;  /* state */
           uint32_t Hash[FNV512size/4];
   } FNV512context;

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   #else
       /* version if 64 bit integers NOT supported */

   typedef struct FNV512context_s {
           int Computed;  /* state */
           uint16_t Hash[FNV512size/2];
   } FNV512context;

   #endif /* FNV_64bitIntegers */

   /*
    *  Function Prototypes
    *    FNV512string: hash a zero terminated string not including
    *                  the terminating zero
    *    FNV512block: FNV512 hash a specified length byte vector
    *    FNV512init: initializes an FNV512 context
    *    FNV512initBasis: initializes an FNV512 context with a
    *                     provided basis
    *    FNV512blockin: hash in a specified length byte vector
    *    FNV512stringin: hash in a zero terminated string not
    *                    including the zero
    *    FNV512result: returns the hash value
    *
    *    Hash is returned as an array of 8-bit unsigned integers
    */

   #ifdef __cplusplus
   extern "C" {
   #endif

   /* FNV512 */
   extern int FNV512string ( const char *in,
                             uint8_t out[FNV512size] );
   extern int FNV512block ( const void *in,
                            long int length,
                            uint8_t out[FNV512size] );
   extern int FNV512init ( FNV512context *);
   extern int FNV512initBasis ( FNV512context * const,
                                const uint8_t basis[FNV512size] );
   extern int FNV512blockin ( FNV512context *,
                              const void *in,
                              long int length );
   extern int FNV512stringin ( FNV512context *,
                               const char *in );
   extern int FNV512result ( FNV512context *,
                             uint8_t out[FNV512size] );

   #ifdef __cplusplus

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   }
   #endif

   #endif /* _FNV512_H_ */
   <CODE ENDS>

   <CODE BEGINS> file "FNV512.c"
   /***************************** FNV512.c ***************************/
   /******************** See RFC NNNN for details ********************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights
    * See fnv-private.h for terms of use and redistribution.
    */

   /* This file implements the FNV (Fowler, Noll, Vo) non-cryptographic
    * hash function FNV-1a for 512-bit hashes.
    */

   #ifndef _FNV512_C_
   #define _FNV512_C_

   #include "fnv-private.h"
   #include "FNV512.h"

   /* common code for 64 and 32 bit modes */

   /* FNV512 hash a null terminated string  (64/32 bit)
    ******************************************************************/
   int FNV512string ( const char *in, uint8_t out[FNV512size] )
   {
       FNV512context    ctx;
       int              err;

       if ( (err = FNV512init ( &ctx )) != fnvSuccess )
           return err;
       if ( (err = FNV512stringin ( &ctx, in )) != fnvSuccess )
           return err;
       return FNV512result ( &ctx, out );
   }   /* end FNV512string */

   /* FNV512 hash a counted block  (64/32 bit)
    ******************************************************************/
   int FNV512block ( const void *in,
                     long int length,
                     uint8_t out[FNV512size] )
   {
       FNV512context    ctx;
       int              err;

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       if ( (err = FNV512init ( &ctx )) != fnvSuccess )
           return err;
       if ( (err = FNV512blockin ( &ctx, in, length)) != fnvSuccess )
           return err;
       return FNV512result ( &ctx, out );
   }   /* end FNV512block */

   /******************************************************************
    *        START VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC       *
    ******************************************************************/
   #ifdef FNV_64bitIntegers

   /*
     512 bit FNV_prime = 2^344 + 2^8 + 0x57 =
      0x0000000000000000 0000000000000000
        0000000001000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000157 */
   #define FNV512primeX 0x0157
   #define FNV512shift 24

   /* 0xB86DB0B1171F4416 DCA1E50F309990AC
        AC87D059C9000000 0000000000000D21
        E948F68A34C192F6 2EA79BC942DBE7CE
        182036415F56E34B AC982AAC4AFE9FD9 */

   uint32_t FNV512basis[FNV512size/4] = {
            0xB86DB0B1, 0x171F4416, 0xDCA1E50F, 0x209990AC,
            0xAC87D059, 0x9C000000, 0x00000000, 0x00000D21,
            0xE948F68A, 0x34C192F6, 0x2EA79BC9, 0x42DBE7CE,
            0x18203641, 0x5F56E34B, 0xAC982AAC, 0x4AFE9FD9 };

   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV512                        *
    ******************************************************************/

   /* initialize context  (64 bit)
    ******************************************************************/
   int FNV512init ( FNV512context *ctx )
   {
       int i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV512size/4; ++i )

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           ctx->Hash[i] = FNV512basis[i];
       ctx->Computed = FNVinited+FNV512state;
       return fnvSuccess;
   }   /* end FNV512init */

   /* initialize context with a provided basis  (64 bit)
    ******************************************************************/
   int FNV512initBasis ( FNV512context* const ctx,
                         const uint8_t basis[FNV512size] )
   {
       int      i;
       const uint8_t  *ui8p;
       uint32_t  temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV512size/4; ++i )
           {
               temp = (*ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #else
       ui8p = basis + (FNV512size/4 - 1);
       for ( i=0; i < FNV512size/4; ++i )
           {
               temp = (*ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #endif
       ctx->Computed = FNVinited+FNV512state;
       return fnvSuccess;
   }   /* end FNV512initBasis */

   /* hash in a counted block  (64 bit)
    ******************************************************************/
   int FNV512blockin ( FNV512context *ctx,
                       const void *vin,
                       long int length )
   {
       int         i;
       const uint8_t *in = (const uint8_t*)vin;

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       uint64_t    temp[FNV512size/4];
       uint64_t    temp2[3];

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV512state:
               ctx->Computed = FNVcomputed+FNV128state;
           case FNVcomputed+FNV512state:
               break;
           default:
               return fnvStateError;
           }
       if ( length < 0 )
           return fnvBadParam;
       for ( i=0; i<FNV512size/4; ++i )
            temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV512prime * ( temp ^ *in++ ); */
           temp[7] ^= *in++;
           temp2[2] = temp[7] << FNV512shift;
           temp2[1] = temp[6] << FNV512shift;
           temp2[0] = temp[5] << FNV512shift;
           for ( i=0; i<FNV512size/4; ++i )
               temp[i] *= FNV512primeX;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=FNV512size/4-1; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
          }
       for ( i=0; i<FNV512size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV512input */

   /* hash in a string  (64 bit)
    ******************************************************************/
   int FNV512stringin ( FNV512context *ctx, const char *in )
   {
       uint64_t   temp[FNV512size/4];
       uint64_t   temp2[2];

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       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV512state:
               ctx->Computed = FNVcomputed+FNV512state;
           case FNVcomputed+FNV512state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV512size/4; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV512prime * ( temp ^ ch ); */
           temp[7] ^= ch;
           temp2[2] = temp[7] << FNV128shift;
           temp2[1] = temp[6] << FNV128shift;
           temp2[0] = temp[5] << FNV128shift;
           for ( i=0; i<FNV512size/4; ++i )
               temp[i] *= FNV512prime;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=FNVsize512/4-1; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
          }
       for ( i=0; i<FNV512size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV512stringin */

   /* return hash  (64 bit)
    ******************************************************************/
   int FNV512result ( FNV512context *ctx, uint8_t out[FNV512size] )
   {
       int i;

       if ( !ctx || !out )
           return fnvNull;

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       if ( ctx->Computed != FNVcomputed+FNV512state )
           return fnvStateError;
       for ( i=0; i<FNV512size/4; ++i )
           {
   #ifdef FNV_BigEndian
           out[15-2*i] = ctx->Hash[i];
           out[14-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx -> Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV512state;
       return fnvSuccess;
   }   /* end FNV512result */

   /******************************************************************
    *        END VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC         *
    ******************************************************************/
   #else    /*  FNV_64bitIntegers */
   /******************************************************************
    *      START VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC    *
    ******************************************************************/

   /* version for when you only have 32-bit arithmetic
    ******************************************************************/

   /*
     512 bit FNV_prime = 2^344 + 2^8 + 0x57 =
      0x0000000000000000 0000000000000000
        0000000001000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000157 */
   #define FNV512primeX 0x0157
   #define FNV512shift 8

   /* 0xB86DB0B1171F4416 DCA1E50F309990AC
        AC87D059C9000000 0000000000000D21
        E948F68A34C192F6 2EA79BC942DBE7CE
        182036415F56E34B AC982AAC4AFE9FD9 */

   uint16_t FNV512basis[FNV512size/2] = {
        0xB86D, 0xB0B1, 0x171F, 0x4416, 0xDCA1, 0xE50F, 0x3099, 0x90AC,
        0xAC87, 0xD059, 0xC900, 0x0000, 0x0000, 0x0000, 0x0000, 0x0D21,
        0xE948, 0xF68A, 0x34C1, 0x92F6, 0x2EA7, 0x9BC9, 0x42DB, 0xE7CE,
        0x1820, 0x3641, 0x5F56, 0xE34B, 0xAC98, 0x2AAC, 0x4AFE, 0x9FD9
        };

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   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV512                        *
    ******************************************************************/

   /* initialize context  (32 bit)
    ******************************************************************/
   int FNV512init ( FNV512context *ctx )
   {
       int     i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV512size/2; ++i )
           ctx->Hash[i] = FNV512basis[i];
       ctx->Computed = FNVinited+FNV512state;
       return fnvSuccess;
   }   /* end FNV512init */

   /* initialize context with a provided basis  (32 bit)
    ******************************************************************/
   int FNV512initBasis ( FNV512context *ctx,
                         const uint8_t basis[FNV512size] )
   {
       int      i;
       const uint8_t  *ui8p;
       uint32_t temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV512size/2; ++i )
           {
           temp = *ui8p++;
           ctx->Hash[i] = ( temp<<8 ) + (*ui8p++);
           }
   #else
       ui8p = basis + ( FNV512size/2 - 1 );
       for ( i=0; i < FNV512size/2; ++i )
           {
           temp = *ui8p--;
           ctx->Hash[i] = ( temp<<8 ) + (*ui8p--);
           }
   #endif
       ctx->Computed = FNVinited+FNV512state;

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       return fnvSuccess;
   }   /* end FNV512initBasis */

   /* hash in a counted block  (32 bit)
    ******************************************************************/
   int FNV512blockin ( FNV512context *ctx,
                       const void *vin,
                       long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t   temp[FNV512size/2];
       uint32_t   temp2[6];
       int        i;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV512state:
               ctx->Computed = FNVcomputed+FNV512state;
           case FNVcomputed+FNV512state:
               break;
           default:
               return fnvStateError;
           }
       if ( length < 0 )
           return fnvBadParam;
       for ( i=0; i<FNV512size/2; ++i )
           temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV512prime * ( temp ^ *in++ ); */
           temp[15] ^= *in++;
           for ( i=0; i<6; ++i )
               temp2[i] = temp[10+i] << FNV512shift;
           for ( i=0; i<FNV512size/2; ++i )
               temp[i] *= FNV512primeX;
           for ( i=0; i<6; ++i )
               temp[10+i] += temp2[i];
           for ( i=15; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
           }
       for ( i=0; i<FNV512size/2; ++i )
           ctx->Hash[i] = temp[i];

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       return fnvSuccess;
   }   /* end FNV512blockin */

   /* hash in a string  (32 bit)
    ******************************************************************/
   int FNV512stringin ( FNV512context *ctx, const char *in )
   {
       uint32_t   temp[FNV512size/2];
       uint32_t   temp2[6];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV512state:
               ctx->Computed = FNVcomputed+FNV512state;
           case FNVcomputed+FNV512state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV512size/2; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV512prime * ( temp ^ *in++ ); */
           temp[15] ^= ch;
           for ( i=0; i<6; ++i )
               temp2[i] = temp[10+i] << FNV512shift;
           for ( i=0; i<FNV512size/2; ++i )
               temp[i] *= FNV512primeX;
           for ( i=0; i<6; ++i )
               temp[10+i] += temp2[i];
           for ( i=15; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
            }
       for ( i=0; i<FNV512size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV512stringin */

   /* return hash  (32 bit)

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    ******************************************************************/
   int FNV512result ( FNV512context *ctx, unsigned char out[16] )
   {
       int    i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV512state )
           return fnvStateError;
       for ( i=0; i<FNV512size/2; ++i )
           {
   #ifdef FNV_BigEndian
           out[31-2*i] = ctx->Hash[i];
           out[30-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx->Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV512state;
       return fnvSuccess;
   }   /* end FNV512result */

   #endif    /*  FNV_64bitIntegers */
   /******************************************************************
    *        END VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC    *
    ******************************************************************/

   #endif    /* _FNV512_C_ */
   <CODE ENDS>

6.1.6.  FNV1024 Code

   The header and C source for 1024-bit FNV-1a returning a byte vector.

   <CODE BEGINS> file "FNV1024.h"
   /************************* FNV1024.h ************************/
   /*************** See RFC NNNN for details. ******************/
   /*
    * Copyright (c) 2016, 2023 IETF Trust and the persons
    *  identified as authors of the code.  All rights reserved.
    * See fnv-private.h for terms of use and redistribution.
    */

   #ifndef _FNV1024_H_
   #define _FNV1024_H_

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   /*
    *  Description:
    *      This file provides headers for the 1024-bit version of
    *      the FNV-1a non-cryptographic hash algorithm.
    */

   #include "FNVconfig.h"

   #include <stdint.h>
   #define FNV1024size (1024/8)

   /* If you do not have the ISO standard stdint.h header file, then
    * you must typedef the following types:
    *
    *    type              meaning
    *  uint64_t    unsigned 64 bit integer (ifdef FNV_64bitIntegers)
    *  uint32_t    unsigned 32 bit integer
    *  uint16_t    unsigned 16 bit integer
    *  uint8_t     unsigned 8 bit integer (i.e., unsigned char)
    */

   #include "FNVErrorCodes.h"

   /*
    *  This structure holds context information for an FNV1024 hash
    */
   #ifdef FNV_64bitIntegers
       /* version if 64 bit integers supported */
   typedef struct FNV1024context_s {
           int Computed;  /* state */
           uint32_t Hash[FNV1024size/4];
   } FNV1024context;

   #else
       /* version if 64 bit integers NOT supported */

   typedef struct FNV1024context_s {
           int Computed;  /* state */
           uint16_t Hash[FNV1024size/2];
   } FNV1024context;

   #endif /* FNV_64bitIntegers */

   /*
    *  Function Prototypes
    *    FNV1024string: hash a zero terminated string not including
    *                   the terminating zero
    *    FNV1024block: FNV1024 hash a specified length byte vector

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    *    FNV1024init: initializes an FNV1024 context
    *    FNV1024initBasis: initializes an FNV1024 context with a
    *                      provided basis
    *    FNV1024blockin: hash in a specified length byte vector
    *    FNV1024stringin: hash in a zero terminated string not
    *                     including the zero
    *    FNV1024result: returns the hash value
    *
    *    Hash is returned as an array of 8-bit unsigned integers
    */

   #ifdef __cplusplus
   extern "C" {
   #endif

   /* FNV1024 */
   extern int FNV1024string ( const char *in,
                              unsigned char out[FNV1024size] );
   extern int FNV1024block ( const void *in,
                             long int length,
                             unsigned char out[FNV1024size] );
   extern int FNV1024init ( FNV1024context *);
   extern int FNV1024initBasis ( FNV1024context * const,
                                 const uint8_t basis[FNV1024size] );
   extern int FNV1024blockin ( FNV1024context *,
                               const void *in,
                               long int length );
   extern int FNV1024stringin ( FNV1024context *,
                               const char *in );
   extern int FNV1024result ( FNV1024context *,
                              unsigned char out[FNV1024size] );

   #ifdef __cplusplus
   }
   #endif

   #endif /* _FNV1024_H_ */
   <CODE ENDS>

   <CODE BEGINS> file "FNV1024.c"
   /***************************** FNV1024.c **************************/
   /******************** See RFC NNNN for details ********************/
   /* Copyright (c) 2016, 2023 IETF Trust and the persons identified as
    * authors of the code.  All rights
    * See fnv-private.h for terms of use and redistribution.
    */

   /* This file implements the FNV (Fowler, Noll, Vo) non-cryptographic

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    * hash function FNV-1a for 1024-bit hashes.
    */

   #ifndef _FNV1024_C_
   #define _FNV1024_C_

   #include "fnv-private.h"
   #include "FNV1024.h"

   /* common code for 64 and 32 bit modes */

   /* FNV1024 hash a null terminated string  (64/32 bit)
    ******************************************************************/
   int FNV1024string ( const char *in, uint8_t out[FNV1024size] )
   {
       FNV1024context    ctx;
       int              err;

       if ( (err = FNV1024init ( &ctx )) != fnvSuccess)
           return err;
       if ( (err = FNV1024stringin ( &ctx, in )) != fnvSuccess)
           return err;
       return FNV1024result ( &ctx, out );
   }   /* end FNV1024string */

   /* FNV1024 hash a counted block  (64/32 bit)
    ******************************************************************/
   int FNV1024block ( const void *in,
                     long int length,
                     uint8_t out[FNV1024size] )
   {
       FNV1024context    ctx;
       int              err;

       if ( (err = FNV1024init ( &ctx )) != fnvSuccess)
           return err;
       if ( (err = FNV1024blockin ( &ctx, in, length)) != fnvSuccess)
           return err;
       return FNV1024result ( &ctx, out );
   }   /* end FNV1024block */

   /******************************************************************
    *        START VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC       *
    ******************************************************************/
   #ifdef FNV_64bitIntegers

   /*

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    1024 bit FNV_prime = 2^680 + 2^8 + 0x8d =
      0x0000000000000000 0000010000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 000000000000018D */
   #define FNV1024primeX 0x018D
   #define FNV1024shift 24

   /* 0x0000000000000000 005F7A76758ECC4D
        32E56D5A591028B7 4B29FC4223FDADA1
        6C3BF34EDA3674DA 9A21D90000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 000000000004C6D7
        EB6E73802734510A 555F256CC005AE55
        6BDE8CC9C6A93B21 AFF4B16C71EE90B3 */

   uint32_t FNV1024basis[FNV1024size/4] = {
     0x00000000, 0x00000000, 0x005F7A76, 0x758ECC4D,
     0x32E56D5A, 0x591028B7, 0x4B29FC42, 0x23FDADA1,
     0x6C3BF34E, 0xDA3674DA, 0x9A21D900, 0x00000000,
     0x00000000, 0x00000000, 0x00000000, 0x00000000,
     0x00000000, 0x00000000, 0x00000000, 0x00000000,
     0x00000000, 0x00000000, 0x00000000, 0x0004C6D7,
     0xEB6E7380, 0x2734510A, 0x555F256C, 0xC005AE55,
     0x6BDE8CC9, 0xC6A93B21, 0xAFF4B16C, 0x71EE90B3
    };

   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV1024                       *
    ******************************************************************/

   /* initialize context  (64 bit)
    ******************************************************************/
   int FNV1024init ( FNV1024context *ctx )
   {
       int i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV1024size/4; ++i )
           ctx->Hash[i] = FNV1024basis[i];
       ctx->Computed = FNVinited+FNV1024state;
       return fnvSuccess;

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   }   /* end FNV1024init */

   /* initialize context with a provided basis  (64 bit)
    ******************************************************************/
   int FNV1024initBasis ( FNV1024context* const ctx,
                          const uint8_t basis[FNV1024size] )
   {
       int            i;
       const uint8_t  *ui8p;
       uint32_t       temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV1024size/4; ++i )
           {
               temp = (*ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
               temp = (temp + *ui8p++)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #else
       ui8p = basis + (FNV1024size/4 - 1);
       for ( i=0; i < FNV1024size/4; ++i )
           {
               temp = (*ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
               temp = (temp + *ui8p--)<<8;
           ctx->Hash[i] = temp +  *ui8p;
           }
   #endif
       ctx->Computed = FNVinited+FNV1024state;
       return fnvSuccess;
   }   /* end FNV1024initBasis */

   /* hash in a counted block  (64 bit)
    ******************************************************************/
   int FNV1024blockin ( FNV1024context *ctx,
                       const void *vin,
                       long int length )
   {
       int         i;
       const uint8_t *in = (const uint8_t*)vin;
       uint64_t    temp[FNV1024size/4];
       uint64_t    temp2[3];

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       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV1024state:
               ctx->Computed = FNVcomputed+FNV128state;
           case FNVcomputed+FNV1024state:
               break;
           default:
               return fnvStateError;
           }
       if ( length < 0 )
           return fnvBadParam;
       for ( i=0; i<FNV1024size/4; ++i )
            temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV1024prime * ( temp ^ *in++ ); */
           temp[7] ^= *in++;
           temp2[2] = temp[7] << FNV1024shift;
           temp2[1] = temp[6] << FNV1024shift;
           temp2[0] = temp[5] << FNV1024shift;
           for ( i=0; i<FNV1024size/4; ++i )
               temp[i] *= FNV1024primeX;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=FNV1024size/4-1; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
          }
       for ( i=0; i<FNV1024size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV1024input */

   /* hash in a string  (64 bit)
    ******************************************************************/
   int FNV1024stringin ( FNV1024context *ctx, const char *in )
   {
       uint64_t   temp[FNV1024size/4];
       uint64_t   temp2[2];
       int        i;
       uint8_t    ch;

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       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV1024state:
               ctx->Computed = FNVcomputed+FNV1024state;
           case FNVcomputed+FNV1024state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV1024size/4; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV1024prime * ( temp ^ ch ); */
           temp[7] ^= ch;
           temp2[2] = temp[7] << FNV128shift;
           temp2[1] = temp[6] << FNV128shift;
           temp2[0] = temp[5] << FNV128shift;
           for ( i=0; i<FNV1024size/4; ++i )
               temp[i] *= FNV1024prime;
           temp[2] += temp2[2];
           temp[1] += temp2[1];
           temp[0] += temp2[0];
           for ( i=FNVsize1024/4-1; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
          }
       for ( i=0; i<FNV1024size/4; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV1024stringin */

   /* return hash  (64 bit)
    ******************************************************************/
   int FNV1024result ( FNV1024context *ctx, uint8_t out[FNV1024size] )
   {
       int i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV1024state )
           return fnvStateError;

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       for ( i=0; i<FNV1024size/4; ++i )
           {
   #ifdef FNV_BigEndian
           out[15-2*i] = ctx->Hash[i];
           out[14-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx -> Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV1024state;
       return fnvSuccess;
   }   /* end FNV1024result */

   /******************************************************************
    *        END VERSION FOR WHEN YOU HAVE 64 BIT ARITHMETIC         *
    ******************************************************************/
   #else    /*  FNV_64bitIntegers */
   /******************************************************************
    *      START VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC    *
    ******************************************************************/

   /* version for when you only have 32-bit arithmetic
    ******************************************************************/

   /*
    1024 bit FNV_prime = 2^680 + 2^8 + 0x8d =
      0x0000000000000000 0000010000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 000000000000018D */
   #define FNV1024primeX 0x018D
   #define FNV1024shift 8

   /* 0x0000000000000000 005F7A76758ECC4D
        32E56D5A591028B7 4B29FC4223FDADA1
        6C3BF34EDA3674DA 9A21D90000000000
        0000000000000000 0000000000000000
        0000000000000000 0000000000000000
        0000000000000000 000000000004C6D7
        EB6E73802734510A 555F256CC005AE55
        6BDE8CC9C6A93B21 AFF4B16C71EE90B3 */

   uint16_t FNV1024basis[FNV1024size/2] = {
     0x0000, 0x0000, 0x0000, 0x0000, 0x005F, 0x7A76, 0x758E, 0xCC4D,

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     0x32E5, 0x6D5A, 0x5910, 0x28B7, 0x4B29, 0xFC42, 0x23FD, 0xADA1,
     0x6C3B, 0xF34E, 0xDA36, 0x74DA, 0x9A21, 0xD900, 0x0000, 0x0000,
     0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
     0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
     0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0004, 0xC6D7,
     0xEB6E, 0x7380, 0x2734, 0x510A, 0x555F, 0x256C, 0xC005, 0xAE55,
     0x6BDE, 0x8CC9, 0xC6A9, 0x3B21, 0xAFF4, 0xB16C, 0x71EE, 0x90B3
   };

   /******************************************************************
    *         Set of init, input, and output functions below         *
    *         to incrementally compute FNV1024                       *
    ******************************************************************/

   /* initialize context  (32 bit)
    ******************************************************************/
   int FNV1024init ( FNV1024context *ctx )
   {
       int     i;

       if ( !ctx )
           return fnvNull;

       for ( i=0; i<FNV1024size/2; ++i )
           ctx->Hash[i] = FNV1024basis[i];
       ctx->Computed = FNVinited+FNV1024state;
       return fnvSuccess;
   }   /* end FNV1024init */

   /* initialize context with a provided basis  (32 bit)
    ******************************************************************/
   int FNV1024initBasis ( FNV1024context *ctx,
                          const uint8_t basis[FNV1024size] )
   {
       int      i;
       const uint8_t  *ui8p;
       uint32_t temp;

       if ( !ctx )
           return fnvNull;

   #ifdef FNV_BigEndian
       ui8p = basis;
       for ( i=0; i < FNV1024size/2; ++i )
           {
           temp = *ui8p++;
           ctx->Hash[i] = ( temp<<8 ) + (*ui8p++);

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           }
   #else
       ui8p = basis + ( FNV1024size/2 - 1 );
       for ( i=0; i < FNV1024size/2; ++i )
           {
           temp = *ui8p--;
           ctx->Hash[i] = ( temp<<8 ) + (*ui8p--);
           }
   #endif
       ctx->Computed = FNVinited+FNV1024state;
       return fnvSuccess;
   }   /* end FNV1024initBasis */

   /* hash in a counted block  (32 bit)
    ******************************************************************/
   int FNV1024blockin ( FNV1024context *ctx,
                       const void *vin,
                       long int length )
   {
       const uint8_t *in = (const uint8_t*)vin;
       uint32_t   temp[FNV1024size/2];
       uint32_t   temp2[6];
       int        i;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV1024state:
               ctx->Computed = FNVcomputed+FNV1024state;
           case FNVcomputed+FNV1024state:
               break;
           default:
               return fnvStateError;
           }
       if ( length < 0 )
           return fnvBadParam;
       for ( i=0; i<FNV1024size/2; ++i )
           temp[i] = ctx->Hash[i];
       for ( ; length > 0; length-- )
           {
           /* temp = FNV1024prime * ( temp ^ *in++ ); */
           temp[15] ^= *in++;
           for ( i=0; i<6; ++i )
               temp2[i] = temp[10+i] << FNV1024shift;
           for ( i=0; i<FNV1024size/2; ++i )
               temp[i] *= FNV1024primeX;

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           for ( i=0; i<6; ++i )
               temp[10+i] += temp2[i];
           for ( i=15; i>0; --i )
               {
               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
           }
       for ( i=0; i<FNV1024size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV1024blockin */

   /* hash in a string  (32 bit)
    ******************************************************************/
   int FNV1024stringin ( FNV1024context *ctx, const char *in )
   {
       uint32_t   temp[FNV1024size/2];
       uint32_t   temp2[6];
       int        i;
       uint8_t    ch;

       if ( !ctx || !in )
           return fnvNull;

       switch ( ctx->Computed )
           {
           case FNVinited+FNV1024state:
               ctx->Computed = FNVcomputed+FNV1024state;
           case FNVcomputed+FNV1024state:
               break;
           default:
                return fnvStateError;
            }
       for ( i=0; i<FNV1024size/2; ++i )
            temp[i] = ctx->Hash[i];
       while ( (ch = (uint8_t)*in++) )
           {
           /* temp = FNV1024prime * ( temp ^ *in++ ); */
           temp[15] ^= ch;
           for ( i=0; i<6; ++i )
               temp2[i] = temp[10+i] << FNV1024shift;
           for ( i=0; i<FNV1024size/2; ++i )
               temp[i] *= FNV1024primeX;
           for ( i=0; i<6; ++i )
               temp[10+i] += temp2[i];
           for ( i=15; i>0; --i )
               {

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               temp[i-1] += temp[i] >> 16;
               temp[i] &= 0xFFFF;
               }
            }
       for ( i=0; i<FNV1024size/2; ++i )
           ctx->Hash[i] = temp[i];
       return fnvSuccess;
   }   /* end FNV1024stringin */

   /* return hash  (32 bit)
    ******************************************************************/
   int FNV1024result ( FNV1024context *ctx, unsigned char out[16] )
   {
       int    i;

       if ( !ctx || !out )
           return fnvNull;

       if ( ctx->Computed != FNVcomputed+FNV1024state )
           return fnvStateError;
       for ( i=0; i<FNV1024size/2; ++i )
           {
   #ifdef FNV_BigEndian
           out[31-2*i] = ctx->Hash[i];
           out[30-2*i] = ctx->Hash[i] >> 8;
   #else
           out[2*i] = ctx->Hash[i];
           out[2*i+1] = ctx->Hash[i] >> 8;
   #endif
           ctx->Hash[i] = 0;
           }
       ctx->Computed = FNVemptied+FNV1024state;
       return fnvSuccess;
   }   /* end FNV1024result */

   #endif    /*  FNV_64bitIntegers */
   /******************************************************************
    *        END VERSION FOR WHEN YOU ONLY HAVE 32-BIT ARITHMETIC    *
    ******************************************************************/

   #endif    /* _FNV1024_C_ */
   <CODE ENDS>

6.2.  FNV Test Code

   Here is a test driver:

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   <CODE BEGINS> file "main.c"
   FNV/main.c
   <CODE ENDS>

7.  Security Considerations

   This document is intended to provide convenient open source access by
   the Internet community to the FNV non-cryptographic hash.  No
   assertion of suitability for cryptographic applications is made for
   the FNV hash algorithms.

7.1.  Why is FNV Non-Cryptographic?

   A full discussion of cryptographic hash requirements and strength is
   beyond the scope of this document.  However, here are three
   characteristics of FNV that would generally be considered to make it
   non-cryptographic:

   1.  Sticky State - A cryptographic hash should not have a state in
       which it can stick for a plausible input pattern.  But, in the
       very unlikely event that the FNV hash variable becomes zero and
       the input is a sequence of zeros, the hash variable will remain
       at zero until there is a non-zero input byte and the final hash
       value will be unaffected by the length of that sequence of zero
       input bytes.  Of course, for the common case of fixed length
       input, this would usually not be significant because the number
       of non-zero bytes would vary inversely with the number of zero
       bytes and for some types of input, runs of zeros do not occur.
       Furthermore, the use of a different offset_basis or the inclusion
       of even a little unpredictable input may be sufficient to stop an
       adversary from inducing a zero hash variable.

   2.  Diffusion - Every output bit of a cryptographic hash should be an
       equally complex function of every input bit.  But it is easy to
       see that the least significant bit of a direct FNV hash is the
       XOR of the least significant bits of every input byte and does
       not depend on any other input bit.  While more complex, the
       second through seventh least significant bits of an FNV hash have
       a similar weakness; only the top bit of the bottom byte of
       output, and higher order bits, depend on all input bits.  If
       these properties are considered a problem, they can be easily
       fixed by XOR folding (see Section 3).

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   3.  Work Factor - Depending on intended use, it is frequently
       desirable that a hash function should be computationally
       expensive for general purpose and graphics processors since these
       may be profusely available through elastic cloud services or
       botnets.  This is to slow down testing of possible inputs if the
       output is known.  But FNV is designed to be inexpensive on a
       general-purpose processor.  (See Appendix A.)

   Nevertheless, none of the above have proven to be a problem in actual
   practice for the many applications of FNV.

7.2.  Inducing Collisions

   While use of a cryptographic hash should be considered when active
   adversaries are a factor, the following attack can be made much more
   difficult with very minor changes in the use of FNV.

   If FNV is being used in a known way for hash tables in a network
   server or the like, for example some part of a web server, an
   adversary could send requests calculated to cause hash table
   collisions and induce substantial processing delays.  As mentioned in
   Section 2.2, use of an offset_basis not knownable by the adversary
   will substantially eliminate this problem.

8.  IANA Considerations

   This document requires no IANA Actions.

9.  Normative References

   [RFC0020]  Cerf, V., "ASCII format for network interchange", STD 80,
              RFC 20, DOI 10.17487/RFC0020, October 1969,
              <https://www.rfc-editor.org/info/rfc20>.

10.  Informative References

   [BFDseq]   Jethanandani, M., Agarwal, S., Mishra, A., Saxena, A., and
              A. DeKok, "Secure BFD Sequence Numbers", 22 March 2022,
              <draft-ietf-bfd-secure-sequence-numbers-09.txt>.

   [FNV]      Fowler-Noll-Vo, "FNV website",
              <http://www.isthe.com/chongo/tech/comp/fnv/index.html>.

   [IEEE]     Institute for Electrical and Electronics Engineers, "IEEE
              website", <http:www.ieee.org>.

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   [IEEE8021Qbp]
              "Media Access Control (MAC) Bridges and Virtual Bridged
              Local Area Networks - Equal Cost Multiple Path (ECMP)",
              IEEE Std 802.1Qbp-2014, 7 April 2014.

   [IPv6flow] Anderson, L., Brownlee, N., and B. Carpenter, "Comparing
              Hash Function Algorithms for the IPv6 Flow Label",
              University of Auckland Department of Computer Science
              Technical Report 2012-002, ISSN 1173-3500, March 2012,
              <https://researchspace.auckland.ac.nz/bitstream/
              handle/2292/13240/flowhashRep.pdf>.

   [RFC3174]  Eastlake 3rd, D. and P. Jones, "US Secure Hash Algorithm 1
              (SHA1)", RFC 3174, DOI 10.17487/RFC3174, September 2001,
              <https://www.rfc-editor.org/info/rfc3174>.

   [RFC6194]  Polk, T., Chen, L., Turner, S., and P. Hoffman, "Security
              Considerations for the SHA-0 and SHA-1 Message-Digest
              Algorithms", RFC 6194, DOI 10.17487/RFC6194, March 2011,
              <https://www.rfc-editor.org/info/rfc6194>.

   [RFC6234]  Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", RFC 6234,
              DOI 10.17487/RFC6234, May 2011,
              <https://www.rfc-editor.org/info/rfc6234>.

   [RFC6437]  Amante, S., Carpenter, B., Jiang, S., and J. Rajahalme,
              "IPv6 Flow Label Specification", RFC 6437,
              DOI 10.17487/RFC6437, November 2011,
              <https://www.rfc-editor.org/info/rfc6437>.

   [RFC7357]  Zhai, H., Hu, F., Perlman, R., Eastlake 3rd, D., and O.
              Stokes, "Transparent Interconnection of Lots of Links
              (TRILL): End Station Address Distribution Information
              (ESADI) Protocol", RFC 7357, DOI 10.17487/RFC7357,
              September 2014, <https://www.rfc-editor.org/info/rfc7357>.

   [RFC7873]  Eastlake 3rd, D. and M. Andrews, "Domain Name System (DNS)
              Cookies", RFC 7873, DOI 10.17487/RFC7873, May 2016,
              <https://www.rfc-editor.org/info/rfc7873>.

   [RFC8200]  Deering, S. and R. Hinden, "Internet Protocol, Version 6
              (IPv6) Specification", STD 86, RFC 8200,
              DOI 10.17487/RFC8200, July 2017,
              <https://www.rfc-editor.org/info/rfc8200>.

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Appendix A.  Work Comparison with SHA-1

   This section provides a simplistic rough comparison of the level of
   effort required per input byte to compute FNV-1a and SHA-1 [RFC3174].

   Ignoring transfer of control and conditional tests and equating all
   logical and arithmetic operations, FNV requires 2 operations per
   byte, an XOR and a multiply.

   SHA-1 is a relatively weak cryptographic hash producing a 160-bit
   hash.  It has been partially broken [RFC6194].  It is actually
   designed to accept a bit vector input although almost all computer
   uses apply it to an integer number of bytes.  It processes blocks of
   512 bits (64 bytes) and we estimate the effort involved in SHA-1
   processing a full block.  Ignoring SHA-1 initial set up, transfer of
   control, and conditional tests, but counting all logical and
   arithmetic operations, including counting indexing as an addition,
   SHA-1 requires 1,744 operations per 64 bytes block or 27.25
   operations per byte.  So by this rough measure, it is a little over
   13 times the effort of FNV for large amounts of data.  However, FNV
   is commonly used for small inputs.  Using the above method, for
   inputs of N bytes, where N is <= 55 so SHA-1 will take one block
   (SHA-1 includes padding and an 8-byte length at the end of the data
   in the last block), the ratio of the effort for SHA-1 to the effort
   for FNV will be 872/N.  For example, with an 8 byte input, SHA-1 will
   take 109 times as much effort as FNV.

   Stronger cryptographic functions than SHA-1 generally have an even
   higher work factor.

Appendix B.  Previous IETF Reference to FNV

   FNV-1a was referenced in draft-ietf-tls-cached-info-08.txt that has
   since expired.  It was later decided that it would be better to use a
   cryptographic hash for that application.

   Below is the Java code for FNV64 from that TLS draft included by the
   kind permission of the author:

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   <CODE BEGINS>
    /*
    * Java code sample, implementing 64 bit FNV-1a
    * By Stefan Santesson
    */

   import java.math.BigInteger;

   public class FNV {

      static public BigInteger getFNV1aToByte(byte[] inp) {

          BigInteger m = new BigInteger("2").pow(64);
          BigInteger fnvPrime = new BigInteger("1099511628211");
          BigInteger fnvOffsetBasis =
                  new BigInteger("14695981039346656037");

          BigInteger digest = fnvOffsetBasis;

          for (byte b : inp) {
              digest = digest.xor(BigInteger.valueOf((int) b & 255));
              digest = digest.multiply(fnvPrime).mod(m);
          }
          return digest;

      }
   }
   <CODE ENDS>

Appendix C.  A Few Test Vectors

   Below are a few test vectors in the form of ASCII strings and their
   FNV32 and FNV64 hashes using the FNV-1a algorithm.

              +==========+============+=====================+
              | String   |   FNV32    |        FNV64        |
              +==========+============+=====================+
              | ""       | 0x811c9dc5 | 0xcbf29ce4 84222325 |
              +----------+------------+---------------------+
              | "a"      | 0xe40c292c | 0xaf63dc4c 8601ec8c |
              +----------+------------+---------------------+
              | "foobar" | 0xbf9cf968 | 0x85944171f 73967e8 |
              +----------+------------+---------------------+

                 Table 3: Strings without null (zero byte)
                                termination

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              +==========+============+=====================+
              | String   |   FNV32    |        FNV64        |
              +==========+============+=====================+
              | ""       | 0x050c5d1f | 0xaf63bd4c 8601b7df |
              +----------+------------+---------------------+
              | "a"      | 0x2b24d044 | 0x089be207 b544f1e4 |
              +----------+------------+---------------------+
              | "foobar" | 0x0c1c9eb8 | 0x34531ca7 168b8f38 |
              +----------+------------+---------------------+

                Table 4: Strings including null (zero byte)
                                termination

Appendix D.  Change History

   RFC Editor Note: Please delete this appendix on publication.

D.1.  From -00 to -01

   1.  Add Security Considerations section on why FNV is non-
       cryptographic.

   2.  Add Appendix A on a work factor comparison with SHA-1.

   3.  Add Appendix B concerning previous IETF draft referenced to FNV.

   4.  Minor editorial changes.

D.2.  From -01 to -02

   1.  Correct FNV_Prime determination criteria and add note as to why s
       < 5 and s > 10 are not considered.

   2.  Add acknowledgements list.

   3.  Add a couple of references.

   4.  Minor editorial changes.

D.3.  From -02 to -03

   Minor editing changes.

D.4.  From -03 to -04

   Minor addition to Section 6, point 3.  Update dates and version
   number.  Minor editing changes.

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D.5.  From -04 to -05

   1.  Add Twitter as a use example and IPv6 flow hash study reference.

   2.  Update dates and version number.

D.6.  From -05 to -06

   1.  Add code subsections.

   2.  Update dates and version number.

D.7.  From -06 to -07 to -08

   1.  Update Author info.

   2.  Minor edits.

D.8.  From -08 to -09

   1.  Change reference for ASCII to [RFC0020].

   2.  Add more details on history of the string used to compute
       offset_basis.

   3.  Re-write "Work Factor" part of Section 6 to be more precise.

   4.  Minor editorial changes.

D.9.  From -09 to -10

   1.  Inclusion of initial partial version of code and some
       documentation about the code, Section 6.

   2.  Insertion of new Section 4 on hashing values.

D.10.  From -10 to -11

   Changes based on code improvements primarily from Tony Hansen who has
   been added as an author.  Changes based on comments from Mukund
   Sivaraman and Roman Donchenko.

D.11.  From -11 to -12

   Keep alive update.

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D.12.  From -12 to -13

   Fixed bug in pseudocode in Section 2.3.

   Change code to eliminate the BigEndian flag and so there are separate
   byte vector output routines for FNV32 and FNV64, equivalent to the
   other routines, and integer output routines for cases where
   Endianness consistency is not required.

D.13.  From -13 to -14 to -15 to -16 to -17

   Keep alive updates.

   Update an author address.  Update reference.  Update author
   affiliation.

D.14.  From -17 to -18

   Add reference to draft-ietf-bfd-secure-sequence-numbers.  Update
   author info.  Minor editorial changes.

D.15.  From -18 to -19

   Add references to the following, each of which uses FNV: RFC 7357,
   RFC 7873, and IEEE Std. 802.1Qbp-2014.

D.16.  From -19 to -20

   Convert to XML v3.  Fix code for loger FNV hashes.

D.17.  From -20 to -21

   Update Twitter to X.  Minor Editorial changes.

Acknowledgements

   The contributions of the following are gratefully acknowledged:

   Roman Donchenko, Frank Ellermann, Tony Finch, Bob Moskowitz, Gayle
   Noble, Stefan Santesson, and Mukund Sivaraman.

Authors' Addresses

   Glenn S. Fowler
   Google
   Email: glenn.s.fowler@gmail.com

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   Landon Curt Noll
   Cisco Systems
   170 West Tasman Drive
   San Jose, California 95134
   United States of America
   Phone: +1-408-424-1102
   Email: fnv-ietf5-mail@asthe.com
   URI:   http://www.isthe.com/chongo/index.html

   Kiem-Phong Vo
   Google
   Email: phongvo@gmail.com

   Donald E. Eastlake 3rd
   Futurewei Technologies
   2386 Panoramic Circle
   Apopka, Florida 32703
   United States of America
   Phone: +1-508-333-2270
   Email: d3e3e3@gmail.com, donald.eastlake@futurewei.com

   Tony Hansen
   AT&T Laboratories
   200 Laurel Avenue South
   Middletown, New Jersey 07748
   United States of America
   Email: tony@att.com

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